Identifier
Mp00159:
Permutations
—Demazure product with inverse⟶
Permutations
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Images
=>
Cc0010;cc-rep-3
[1]=>[1]=>[1]=>[.,.]
[1,2]=>[1,2]=>[1,2]=>[.,[.,.]]
[2,1]=>[2,1]=>[2,1]=>[[.,.],.]
[1,2,3]=>[1,2,3]=>[1,3,2]=>[.,[[.,.],.]]
[1,3,2]=>[1,3,2]=>[1,3,2]=>[.,[[.,.],.]]
[2,1,3]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[2,3,1]=>[3,2,1]=>[3,2,1]=>[[[.,.],.],.]
[3,1,2]=>[3,2,1]=>[3,2,1]=>[[[.,.],.],.]
[3,2,1]=>[3,2,1]=>[3,2,1]=>[[[.,.],.],.]
[1,2,3,4]=>[1,2,3,4]=>[1,4,3,2]=>[.,[[[.,.],.],.]]
[1,2,4,3]=>[1,2,4,3]=>[1,4,3,2]=>[.,[[[.,.],.],.]]
[1,3,2,4]=>[1,3,2,4]=>[1,4,3,2]=>[.,[[[.,.],.],.]]
[1,3,4,2]=>[1,4,3,2]=>[1,4,3,2]=>[.,[[[.,.],.],.]]
[1,4,2,3]=>[1,4,3,2]=>[1,4,3,2]=>[.,[[[.,.],.],.]]
[1,4,3,2]=>[1,4,3,2]=>[1,4,3,2]=>[.,[[[.,.],.],.]]
[2,1,3,4]=>[2,1,3,4]=>[2,1,4,3]=>[[.,.],[[.,.],.]]
[2,1,4,3]=>[2,1,4,3]=>[2,1,4,3]=>[[.,.],[[.,.],.]]
[2,3,1,4]=>[3,2,1,4]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[2,3,4,1]=>[4,2,3,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[2,4,1,3]=>[3,4,1,2]=>[3,4,1,2]=>[[.,[.,.]],[.,.]]
[2,4,3,1]=>[4,3,2,1]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[3,1,2,4]=>[3,2,1,4]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[3,1,4,2]=>[4,2,3,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[3,2,1,4]=>[3,2,1,4]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[3,2,4,1]=>[4,2,3,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[3,4,1,2]=>[4,3,2,1]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[3,4,2,1]=>[4,3,2,1]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[4,1,2,3]=>[4,2,3,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[4,1,3,2]=>[4,2,3,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[4,2,1,3]=>[4,3,2,1]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[4,2,3,1]=>[4,3,2,1]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[4,3,1,2]=>[4,3,2,1]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[4,3,2,1]=>[4,3,2,1]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[1,2,3,4,5]=>[1,2,3,4,5]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,2,3,5,4]=>[1,2,3,5,4]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,2,4,3,5]=>[1,2,4,3,5]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,2,4,5,3]=>[1,2,5,4,3]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,2,5,3,4]=>[1,2,5,4,3]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,2,5,4,3]=>[1,2,5,4,3]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,3,2,4,5]=>[1,3,2,4,5]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,3,2,5,4]=>[1,3,2,5,4]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,3,4,2,5]=>[1,4,3,2,5]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,3,4,5,2]=>[1,5,3,4,2]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,3,5,2,4]=>[1,4,5,2,3]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,3,5,4,2]=>[1,5,4,3,2]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,4,2,3,5]=>[1,4,3,2,5]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,4,2,5,3]=>[1,5,3,4,2]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,4,3,2,5]=>[1,4,3,2,5]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,4,3,5,2]=>[1,5,3,4,2]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,4,5,2,3]=>[1,5,4,3,2]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,4,5,3,2]=>[1,5,4,3,2]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,5,2,3,4]=>[1,5,3,4,2]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,5,2,4,3]=>[1,5,3,4,2]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,5,3,2,4]=>[1,5,4,3,2]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,5,3,4,2]=>[1,5,4,3,2]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,5,4,2,3]=>[1,5,4,3,2]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,5,4,3,2]=>[1,5,4,3,2]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[2,1,3,4,5]=>[2,1,3,4,5]=>[2,1,5,4,3]=>[[.,.],[[[.,.],.],.]]
[2,1,3,5,4]=>[2,1,3,5,4]=>[2,1,5,4,3]=>[[.,.],[[[.,.],.],.]]
[2,1,4,3,5]=>[2,1,4,3,5]=>[2,1,5,4,3]=>[[.,.],[[[.,.],.],.]]
[2,1,4,5,3]=>[2,1,5,4,3]=>[2,1,5,4,3]=>[[.,.],[[[.,.],.],.]]
[2,1,5,3,4]=>[2,1,5,4,3]=>[2,1,5,4,3]=>[[.,.],[[[.,.],.],.]]
[2,1,5,4,3]=>[2,1,5,4,3]=>[2,1,5,4,3]=>[[.,.],[[[.,.],.],.]]
[2,3,1,4,5]=>[3,2,1,4,5]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[2,3,1,5,4]=>[3,2,1,5,4]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[2,3,4,1,5]=>[4,2,3,1,5]=>[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]]
[2,3,4,5,1]=>[5,2,3,4,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[2,3,5,1,4]=>[4,2,5,1,3]=>[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]]
[2,3,5,4,1]=>[5,2,4,3,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[2,4,1,3,5]=>[3,4,1,2,5]=>[3,5,1,4,2]=>[[.,[.,.]],[[.,.],.]]
[2,4,1,5,3]=>[3,5,1,4,2]=>[3,5,1,4,2]=>[[.,[.,.]],[[.,.],.]]
[2,4,3,1,5]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[2,4,3,5,1]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[2,4,5,1,3]=>[4,5,3,1,2]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[2,4,5,3,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[2,5,1,3,4]=>[3,5,1,4,2]=>[3,5,1,4,2]=>[[.,[.,.]],[[.,.],.]]
[2,5,1,4,3]=>[3,5,1,4,2]=>[3,5,1,4,2]=>[[.,[.,.]],[[.,.],.]]
[2,5,3,1,4]=>[4,5,3,1,2]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[2,5,3,4,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[2,5,4,1,3]=>[4,5,3,1,2]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[2,5,4,3,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[3,1,2,4,5]=>[3,2,1,4,5]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[3,1,2,5,4]=>[3,2,1,5,4]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[3,1,4,2,5]=>[4,2,3,1,5]=>[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]]
[3,1,4,5,2]=>[5,2,3,4,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[3,1,5,2,4]=>[4,2,5,1,3]=>[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]]
[3,1,5,4,2]=>[5,2,4,3,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[3,2,1,4,5]=>[3,2,1,4,5]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[3,2,1,5,4]=>[3,2,1,5,4]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[3,2,4,1,5]=>[4,2,3,1,5]=>[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]]
[3,2,4,5,1]=>[5,2,3,4,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[3,2,5,1,4]=>[4,2,5,1,3]=>[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]]
[3,2,5,4,1]=>[5,2,4,3,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[3,4,1,2,5]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[3,4,1,5,2]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[3,4,2,1,5]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[3,4,2,5,1]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[3,4,5,1,2]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[3,4,5,2,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[3,5,1,2,4]=>[4,5,3,1,2]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[3,5,1,4,2]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[3,5,2,1,4]=>[4,5,3,1,2]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[3,5,2,4,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[3,5,4,1,2]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[3,5,4,2,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[4,1,2,3,5]=>[4,2,3,1,5]=>[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]]
[4,1,2,5,3]=>[5,2,3,4,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[4,1,3,2,5]=>[4,2,3,1,5]=>[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]]
[4,1,3,5,2]=>[5,2,3,4,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[4,1,5,2,3]=>[5,2,4,3,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[4,1,5,3,2]=>[5,2,4,3,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[4,2,1,3,5]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[4,2,1,5,3]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[4,2,3,1,5]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[4,2,3,5,1]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[4,2,5,1,3]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[4,2,5,3,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[4,3,1,2,5]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[4,3,1,5,2]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[4,3,2,1,5]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[4,3,2,5,1]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[4,3,5,1,2]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[4,3,5,2,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[4,5,1,2,3]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[4,5,1,3,2]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[4,5,2,1,3]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[4,5,2,3,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[4,5,3,1,2]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[4,5,3,2,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[5,1,2,3,4]=>[5,2,3,4,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[5,1,2,4,3]=>[5,2,3,4,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[5,1,3,2,4]=>[5,2,4,3,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[5,1,3,4,2]=>[5,2,4,3,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[5,1,4,2,3]=>[5,2,4,3,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[5,1,4,3,2]=>[5,2,4,3,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[5,2,1,3,4]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[5,2,1,4,3]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[5,2,3,1,4]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[5,2,3,4,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[5,2,4,1,3]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[5,2,4,3,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[5,3,1,2,4]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[5,3,1,4,2]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[5,3,2,1,4]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[5,3,2,4,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[5,3,4,1,2]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[5,3,4,2,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[5,4,1,2,3]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[5,4,1,3,2]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[5,4,2,1,3]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[5,4,2,3,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[5,4,3,1,2]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[5,4,3,2,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
[1,2,3,6,4,5]=>[1,2,3,6,5,4]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
[1,2,3,6,5,4]=>[1,2,3,6,5,4]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
[1,2,4,6,3,5]=>[1,2,5,6,3,4]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
[1,2,4,6,5,3]=>[1,2,6,5,4,3]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
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[1,4,2,5,3,6]=>[1,5,3,4,2,6]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
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[1,4,3,2,5,6]=>[1,4,3,2,5,6]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
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[1,4,3,5,2,6]=>[1,5,3,4,2,6]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
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[1,4,5,2,3,6]=>[1,5,4,3,2,6]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
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[1,4,5,3,2,6]=>[1,5,4,3,2,6]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
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[1,5,2,3,4,6]=>[1,5,3,4,2,6]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
[1,5,2,3,6,4]=>[1,6,3,4,5,2]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
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[1,5,3,2,4,6]=>[1,5,4,3,2,6]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
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[1,5,4,2,6,3]=>[1,6,4,3,5,2]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
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[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[2,1,6,5,4,3]=>[[.,.],[[[[.,.],.],.],.]]
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[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>[2,1,6,5,4,3]=>[[.,.],[[[[.,.],.],.],.]]
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[2,1,4,6,3,5]=>[2,1,5,6,3,4]=>[2,1,6,5,4,3]=>[[.,.],[[[[.,.],.],.],.]]
[2,1,4,6,5,3]=>[2,1,6,5,4,3]=>[2,1,6,5,4,3]=>[[.,.],[[[[.,.],.],.],.]]
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[2,1,6,5,4,3]=>[2,1,6,5,4,3]=>[2,1,6,5,4,3]=>[[.,.],[[[[.,.],.],.],.]]
[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[2,3,1,6,4,5]=>[3,2,1,6,5,4]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[2,3,1,6,5,4]=>[3,2,1,6,5,4]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[2,3,4,6,1,5]=>[5,2,3,6,1,4]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[2,3,4,6,5,1]=>[6,2,3,5,4,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[2,3,5,1,4,6]=>[4,2,5,1,3,6]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[2,3,5,1,6,4]=>[4,2,6,1,5,3]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[2,3,5,4,1,6]=>[5,2,4,3,1,6]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[2,3,5,4,6,1]=>[6,2,4,3,5,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[2,3,5,6,1,4]=>[5,2,6,4,1,3]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[2,3,5,6,4,1]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[2,3,6,1,4,5]=>[4,2,6,1,5,3]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[2,3,6,1,5,4]=>[4,2,6,1,5,3]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[2,3,6,4,1,5]=>[5,2,6,4,1,3]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[2,3,6,4,5,1]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[2,3,6,5,1,4]=>[5,2,6,4,1,3]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[2,3,6,5,4,1]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[2,4,1,3,5,6]=>[3,4,1,2,5,6]=>[3,6,1,5,4,2]=>[[.,[.,.]],[[[.,.],.],.]]
[2,4,1,3,6,5]=>[3,4,1,2,6,5]=>[3,6,1,5,4,2]=>[[.,[.,.]],[[[.,.],.],.]]
[2,4,1,5,3,6]=>[3,5,1,4,2,6]=>[3,6,1,5,4,2]=>[[.,[.,.]],[[[.,.],.],.]]
[2,4,1,5,6,3]=>[3,6,1,4,5,2]=>[3,6,1,5,4,2]=>[[.,[.,.]],[[[.,.],.],.]]
[2,4,1,6,3,5]=>[3,5,1,6,2,4]=>[3,6,1,5,4,2]=>[[.,[.,.]],[[[.,.],.],.]]
[2,4,1,6,5,3]=>[3,6,1,5,4,2]=>[3,6,1,5,4,2]=>[[.,[.,.]],[[[.,.],.],.]]
[2,4,3,1,5,6]=>[4,3,2,1,5,6]=>[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]]
[2,4,3,1,6,5]=>[4,3,2,1,6,5]=>[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]]
[2,4,3,5,1,6]=>[5,3,2,4,1,6]=>[5,3,2,6,1,4]=>[[[[.,.],.],[.,.]],[.,.]]
[2,4,3,5,6,1]=>[6,3,2,4,5,1]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[2,4,3,6,1,5]=>[5,3,2,6,1,4]=>[5,3,2,6,1,4]=>[[[[.,.],.],[.,.]],[.,.]]
[2,4,3,6,5,1]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[2,4,5,1,3,6]=>[4,5,3,1,2,6]=>[4,6,3,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]]
[2,4,5,1,6,3]=>[4,6,3,1,5,2]=>[4,6,3,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]]
[2,4,5,3,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[2,4,5,3,6,1]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[2,4,5,6,1,3]=>[5,6,3,4,1,2]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[2,4,5,6,3,1]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[2,4,6,1,3,5]=>[4,5,6,1,2,3]=>[4,6,5,1,3,2]=>[[.,[[.,.],.]],[[.,.],.]]
[2,4,6,1,5,3]=>[4,6,5,1,3,2]=>[4,6,5,1,3,2]=>[[.,[[.,.],.]],[[.,.],.]]
[2,4,6,3,1,5]=>[5,4,6,2,1,3]=>[5,4,6,2,1,3]=>[[[[.,.],[.,.]],.],[.,.]]
[2,4,6,3,5,1]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]
[2,4,6,5,1,3]=>[5,6,4,3,1,2]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]
[2,4,6,5,3,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[2,5,1,3,4,6]=>[3,5,1,4,2,6]=>[3,6,1,5,4,2]=>[[.,[.,.]],[[[.,.],.],.]]
[2,5,1,3,6,4]=>[3,6,1,4,5,2]=>[3,6,1,5,4,2]=>[[.,[.,.]],[[[.,.],.],.]]
[2,5,1,4,3,6]=>[3,5,1,4,2,6]=>[3,6,1,5,4,2]=>[[.,[.,.]],[[[.,.],.],.]]
[2,5,1,4,6,3]=>[3,6,1,4,5,2]=>[3,6,1,5,4,2]=>[[.,[.,.]],[[[.,.],.],.]]
[2,5,1,6,3,4]=>[3,6,1,5,4,2]=>[3,6,1,5,4,2]=>[[.,[.,.]],[[[.,.],.],.]]
[2,5,1,6,4,3]=>[3,6,1,5,4,2]=>[3,6,1,5,4,2]=>[[.,[.,.]],[[[.,.],.],.]]
[2,5,3,1,4,6]=>[4,5,3,1,2,6]=>[4,6,3,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]]
[2,5,3,1,6,4]=>[4,6,3,1,5,2]=>[4,6,3,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]]
[2,5,3,4,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[2,5,3,4,6,1]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[2,5,3,6,1,4]=>[5,6,3,4,1,2]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[2,5,3,6,4,1]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[2,5,4,1,3,6]=>[4,5,3,1,2,6]=>[4,6,3,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]]
[2,5,4,1,6,3]=>[4,6,3,1,5,2]=>[4,6,3,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]]
[2,5,4,3,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[2,5,4,3,6,1]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[2,5,4,6,1,3]=>[5,6,3,4,1,2]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[2,5,4,6,3,1]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[2,5,6,1,3,4]=>[4,6,5,1,3,2]=>[4,6,5,1,3,2]=>[[.,[[.,.],.]],[[.,.],.]]
[2,5,6,1,4,3]=>[4,6,5,1,3,2]=>[4,6,5,1,3,2]=>[[.,[[.,.],.]],[[.,.],.]]
[2,5,6,3,1,4]=>[5,6,4,3,1,2]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]
[2,5,6,3,4,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[2,5,6,4,1,3]=>[5,6,4,3,1,2]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]
[2,5,6,4,3,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[2,6,1,3,4,5]=>[3,6,1,4,5,2]=>[3,6,1,5,4,2]=>[[.,[.,.]],[[[.,.],.],.]]
[2,6,1,3,5,4]=>[3,6,1,4,5,2]=>[3,6,1,5,4,2]=>[[.,[.,.]],[[[.,.],.],.]]
[2,6,1,4,3,5]=>[3,6,1,5,4,2]=>[3,6,1,5,4,2]=>[[.,[.,.]],[[[.,.],.],.]]
[2,6,1,4,5,3]=>[3,6,1,5,4,2]=>[3,6,1,5,4,2]=>[[.,[.,.]],[[[.,.],.],.]]
[2,6,1,5,3,4]=>[3,6,1,5,4,2]=>[3,6,1,5,4,2]=>[[.,[.,.]],[[[.,.],.],.]]
[2,6,1,5,4,3]=>[3,6,1,5,4,2]=>[3,6,1,5,4,2]=>[[.,[.,.]],[[[.,.],.],.]]
[2,6,3,1,4,5]=>[4,6,3,1,5,2]=>[4,6,3,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]]
[2,6,3,1,5,4]=>[4,6,3,1,5,2]=>[4,6,3,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]]
[2,6,3,4,1,5]=>[5,6,3,4,1,2]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[2,6,3,4,5,1]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[2,6,3,5,1,4]=>[5,6,3,4,1,2]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[2,6,3,5,4,1]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[2,6,4,1,3,5]=>[4,6,5,1,3,2]=>[4,6,5,1,3,2]=>[[.,[[.,.],.]],[[.,.],.]]
[2,6,4,1,5,3]=>[4,6,5,1,3,2]=>[4,6,5,1,3,2]=>[[.,[[.,.],.]],[[.,.],.]]
[2,6,4,3,1,5]=>[5,6,4,3,1,2]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]
[2,6,4,3,5,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[2,6,4,5,1,3]=>[5,6,4,3,1,2]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]
[2,6,4,5,3,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[2,6,5,1,3,4]=>[4,6,5,1,3,2]=>[4,6,5,1,3,2]=>[[.,[[.,.],.]],[[.,.],.]]
[2,6,5,1,4,3]=>[4,6,5,1,3,2]=>[4,6,5,1,3,2]=>[[.,[[.,.],.]],[[.,.],.]]
[2,6,5,3,1,4]=>[5,6,4,3,1,2]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]
[2,6,5,3,4,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[2,6,5,4,1,3]=>[5,6,4,3,1,2]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]
[2,6,5,4,3,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[3,1,2,4,5,6]=>[3,2,1,4,5,6]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[3,1,2,4,6,5]=>[3,2,1,4,6,5]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[3,1,2,5,4,6]=>[3,2,1,5,4,6]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[3,1,2,5,6,4]=>[3,2,1,6,5,4]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[3,1,2,6,4,5]=>[3,2,1,6,5,4]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[3,1,2,6,5,4]=>[3,2,1,6,5,4]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[3,1,4,2,5,6]=>[4,2,3,1,5,6]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[3,1,4,2,6,5]=>[4,2,3,1,6,5]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[3,1,4,5,2,6]=>[5,2,3,4,1,6]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[3,1,4,5,6,2]=>[6,2,3,4,5,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[3,1,4,6,2,5]=>[5,2,3,6,1,4]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[3,1,4,6,5,2]=>[6,2,3,5,4,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[3,1,5,2,4,6]=>[4,2,5,1,3,6]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[3,1,5,2,6,4]=>[4,2,6,1,5,3]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[3,1,5,4,2,6]=>[5,2,4,3,1,6]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[3,1,5,4,6,2]=>[6,2,4,3,5,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[3,1,5,6,2,4]=>[5,2,6,4,1,3]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[3,1,5,6,4,2]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[3,1,6,2,4,5]=>[4,2,6,1,5,3]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[3,1,6,2,5,4]=>[4,2,6,1,5,3]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[3,1,6,4,2,5]=>[5,2,6,4,1,3]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[3,1,6,4,5,2]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[3,1,6,5,2,4]=>[5,2,6,4,1,3]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[3,1,6,5,4,2]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[3,2,1,4,6,5]=>[3,2,1,4,6,5]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[3,2,1,5,4,6]=>[3,2,1,5,4,6]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[3,2,1,5,6,4]=>[3,2,1,6,5,4]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[3,2,1,6,4,5]=>[3,2,1,6,5,4]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[3,2,1,6,5,4]=>[3,2,1,6,5,4]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[3,2,4,1,5,6]=>[4,2,3,1,5,6]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[3,2,4,1,6,5]=>[4,2,3,1,6,5]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[3,2,4,5,1,6]=>[5,2,3,4,1,6]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[3,2,4,5,6,1]=>[6,2,3,4,5,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[3,2,4,6,1,5]=>[5,2,3,6,1,4]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[3,2,4,6,5,1]=>[6,2,3,5,4,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[3,2,5,1,4,6]=>[4,2,5,1,3,6]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[3,2,5,1,6,4]=>[4,2,6,1,5,3]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[3,2,5,4,1,6]=>[5,2,4,3,1,6]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[3,2,5,4,6,1]=>[6,2,4,3,5,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[3,2,5,6,1,4]=>[5,2,6,4,1,3]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[3,2,5,6,4,1]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[3,2,6,1,4,5]=>[4,2,6,1,5,3]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[3,2,6,1,5,4]=>[4,2,6,1,5,3]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[3,2,6,4,1,5]=>[5,2,6,4,1,3]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[3,2,6,4,5,1]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[3,2,6,5,1,4]=>[5,2,6,4,1,3]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[3,2,6,5,4,1]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[3,4,1,2,5,6]=>[4,3,2,1,5,6]=>[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]]
[3,4,1,2,6,5]=>[4,3,2,1,6,5]=>[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]]
[3,4,1,5,2,6]=>[5,3,2,4,1,6]=>[5,3,2,6,1,4]=>[[[[.,.],.],[.,.]],[.,.]]
[3,4,1,5,6,2]=>[6,3,2,4,5,1]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[3,4,1,6,2,5]=>[5,3,2,6,1,4]=>[5,3,2,6,1,4]=>[[[[.,.],.],[.,.]],[.,.]]
[3,4,1,6,5,2]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[3,4,2,1,5,6]=>[4,3,2,1,5,6]=>[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]]
[3,4,2,1,6,5]=>[4,3,2,1,6,5]=>[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]]
[3,4,2,5,1,6]=>[5,3,2,4,1,6]=>[5,3,2,6,1,4]=>[[[[.,.],.],[.,.]],[.,.]]
[3,4,2,5,6,1]=>[6,3,2,4,5,1]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[3,4,2,6,1,5]=>[5,3,2,6,1,4]=>[5,3,2,6,1,4]=>[[[[.,.],.],[.,.]],[.,.]]
[3,4,2,6,5,1]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[3,4,5,1,2,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[3,4,5,1,6,2]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[3,4,5,2,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[3,4,5,2,6,1]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[3,4,5,6,1,2]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[3,4,5,6,2,1]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[3,4,6,1,2,5]=>[5,4,6,2,1,3]=>[5,4,6,2,1,3]=>[[[[.,.],[.,.]],.],[.,.]]
[3,4,6,1,5,2]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]
[3,4,6,2,1,5]=>[5,4,6,2,1,3]=>[5,4,6,2,1,3]=>[[[[.,.],[.,.]],.],[.,.]]
[3,4,6,2,5,1]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]
[3,4,6,5,1,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[3,4,6,5,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[3,5,1,2,4,6]=>[4,5,3,1,2,6]=>[4,6,3,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]]
[3,5,1,2,6,4]=>[4,6,3,1,5,2]=>[4,6,3,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]]
[3,5,1,4,2,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[3,5,1,4,6,2]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[3,5,1,6,2,4]=>[5,6,3,4,1,2]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[3,5,1,6,4,2]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[3,5,2,1,4,6]=>[4,5,3,1,2,6]=>[4,6,3,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]]
[3,5,2,1,6,4]=>[4,6,3,1,5,2]=>[4,6,3,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]]
[3,5,2,4,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[3,5,2,4,6,1]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[3,5,2,6,1,4]=>[5,6,3,4,1,2]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[3,5,2,6,4,1]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[3,5,4,1,2,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[3,5,4,1,6,2]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[3,5,4,2,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[3,5,4,2,6,1]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[3,5,4,6,1,2]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[3,5,4,6,2,1]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[3,5,6,1,2,4]=>[5,6,4,3,1,2]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]
[3,5,6,1,4,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[3,5,6,2,1,4]=>[5,6,4,3,1,2]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]
[3,5,6,2,4,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[3,5,6,4,1,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[3,5,6,4,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[3,6,1,2,4,5]=>[4,6,3,1,5,2]=>[4,6,3,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]]
[3,6,1,2,5,4]=>[4,6,3,1,5,2]=>[4,6,3,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]]
[3,6,1,4,2,5]=>[5,6,3,4,1,2]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[3,6,1,4,5,2]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[3,6,1,5,2,4]=>[5,6,3,4,1,2]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[3,6,1,5,4,2]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[3,6,2,1,4,5]=>[4,6,3,1,5,2]=>[4,6,3,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]]
[3,6,2,1,5,4]=>[4,6,3,1,5,2]=>[4,6,3,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]]
[3,6,2,4,1,5]=>[5,6,3,4,1,2]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[3,6,2,4,5,1]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[3,6,2,5,1,4]=>[5,6,3,4,1,2]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[3,6,2,5,4,1]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[3,6,4,1,2,5]=>[5,6,4,3,1,2]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]
[3,6,4,1,5,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[3,6,4,2,1,5]=>[5,6,4,3,1,2]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]
[3,6,4,2,5,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[3,6,4,5,1,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[3,6,4,5,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[3,6,5,1,2,4]=>[5,6,4,3,1,2]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]
[3,6,5,1,4,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[3,6,5,2,1,4]=>[5,6,4,3,1,2]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]
[3,6,5,2,4,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[3,6,5,4,1,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[3,6,5,4,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[4,1,2,3,5,6]=>[4,2,3,1,5,6]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[4,1,2,3,6,5]=>[4,2,3,1,6,5]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[4,1,2,5,3,6]=>[5,2,3,4,1,6]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[4,1,2,5,6,3]=>[6,2,3,4,5,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[4,1,2,6,3,5]=>[5,2,3,6,1,4]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[4,1,2,6,5,3]=>[6,2,3,5,4,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[4,1,3,2,5,6]=>[4,2,3,1,5,6]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[4,1,3,2,6,5]=>[4,2,3,1,6,5]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[4,1,3,5,2,6]=>[5,2,3,4,1,6]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[4,1,3,5,6,2]=>[6,2,3,4,5,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[4,1,3,6,2,5]=>[5,2,3,6,1,4]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[4,1,3,6,5,2]=>[6,2,3,5,4,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[4,1,5,2,3,6]=>[5,2,4,3,1,6]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[4,1,5,2,6,3]=>[6,2,4,3,5,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[4,1,5,3,2,6]=>[5,2,4,3,1,6]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[4,1,5,3,6,2]=>[6,2,4,3,5,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[4,1,5,6,2,3]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[4,1,5,6,3,2]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[4,1,6,2,3,5]=>[5,2,6,4,1,3]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[4,1,6,2,5,3]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[4,1,6,3,2,5]=>[5,2,6,4,1,3]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[4,1,6,3,5,2]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[4,1,6,5,2,3]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[4,1,6,5,3,2]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[4,2,1,3,5,6]=>[4,3,2,1,5,6]=>[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]]
[4,2,1,3,6,5]=>[4,3,2,1,6,5]=>[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]]
[4,2,1,5,3,6]=>[5,3,2,4,1,6]=>[5,3,2,6,1,4]=>[[[[.,.],.],[.,.]],[.,.]]
[4,2,1,5,6,3]=>[6,3,2,4,5,1]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[4,2,1,6,3,5]=>[5,3,2,6,1,4]=>[5,3,2,6,1,4]=>[[[[.,.],.],[.,.]],[.,.]]
[4,2,1,6,5,3]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[4,2,3,1,5,6]=>[4,3,2,1,5,6]=>[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]]
[4,2,3,1,6,5]=>[4,3,2,1,6,5]=>[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]]
[4,2,3,5,1,6]=>[5,3,2,4,1,6]=>[5,3,2,6,1,4]=>[[[[.,.],.],[.,.]],[.,.]]
[4,2,3,5,6,1]=>[6,3,2,4,5,1]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[4,2,3,6,1,5]=>[5,3,2,6,1,4]=>[5,3,2,6,1,4]=>[[[[.,.],.],[.,.]],[.,.]]
[4,2,3,6,5,1]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[4,2,5,1,3,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[4,2,5,1,6,3]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[4,2,5,3,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[4,2,5,3,6,1]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[4,2,5,6,1,3]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[4,2,5,6,3,1]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[4,2,6,1,3,5]=>[5,4,6,2,1,3]=>[5,4,6,2,1,3]=>[[[[.,.],[.,.]],.],[.,.]]
[4,2,6,1,5,3]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]
[4,2,6,3,1,5]=>[5,4,6,2,1,3]=>[5,4,6,2,1,3]=>[[[[.,.],[.,.]],.],[.,.]]
[4,2,6,3,5,1]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]
[4,2,6,5,1,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[4,2,6,5,3,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[4,3,1,2,5,6]=>[4,3,2,1,5,6]=>[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]]
[4,3,1,2,6,5]=>[4,3,2,1,6,5]=>[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]]
[4,3,1,5,2,6]=>[5,3,2,4,1,6]=>[5,3,2,6,1,4]=>[[[[.,.],.],[.,.]],[.,.]]
[4,3,1,5,6,2]=>[6,3,2,4,5,1]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[4,3,1,6,2,5]=>[5,3,2,6,1,4]=>[5,3,2,6,1,4]=>[[[[.,.],.],[.,.]],[.,.]]
[4,3,1,6,5,2]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]]
[4,3,2,1,6,5]=>[4,3,2,1,6,5]=>[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]]
[4,3,2,5,1,6]=>[5,3,2,4,1,6]=>[5,3,2,6,1,4]=>[[[[.,.],.],[.,.]],[.,.]]
[4,3,2,5,6,1]=>[6,3,2,4,5,1]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[4,3,2,6,1,5]=>[5,3,2,6,1,4]=>[5,3,2,6,1,4]=>[[[[.,.],.],[.,.]],[.,.]]
[4,3,2,6,5,1]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[4,3,5,1,2,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[4,3,5,1,6,2]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[4,3,5,2,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[4,3,5,2,6,1]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[4,3,5,6,1,2]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[4,3,5,6,2,1]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[4,3,6,1,2,5]=>[5,4,6,2,1,3]=>[5,4,6,2,1,3]=>[[[[.,.],[.,.]],.],[.,.]]
[4,3,6,1,5,2]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]
[4,3,6,2,1,5]=>[5,4,6,2,1,3]=>[5,4,6,2,1,3]=>[[[[.,.],[.,.]],.],[.,.]]
[4,3,6,2,5,1]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]
[4,3,6,5,1,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[4,3,6,5,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[4,5,1,2,3,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[4,5,1,2,6,3]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[4,5,1,3,2,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[4,5,1,3,6,2]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[4,5,1,6,2,3]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[4,5,1,6,3,2]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[4,5,2,1,3,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[4,5,2,1,6,3]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[4,5,2,3,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[4,5,2,3,6,1]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[4,5,2,6,1,3]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[4,5,2,6,3,1]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[4,5,3,1,2,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[4,5,3,1,6,2]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[4,5,3,2,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[4,5,3,2,6,1]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[4,5,3,6,1,2]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[4,5,3,6,2,1]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[4,5,6,1,2,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[4,5,6,1,3,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[4,5,6,2,1,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[4,5,6,2,3,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[4,5,6,3,1,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[4,5,6,3,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[4,6,1,2,3,5]=>[5,6,3,4,1,2]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[4,6,1,2,5,3]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[4,6,1,3,2,5]=>[5,6,3,4,1,2]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[4,6,1,3,5,2]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[4,6,1,5,2,3]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[4,6,1,5,3,2]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[4,6,2,1,3,5]=>[5,6,4,3,1,2]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]
[4,6,2,1,5,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[4,6,2,3,1,5]=>[5,6,4,3,1,2]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]
[4,6,2,3,5,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[4,6,2,5,1,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[4,6,2,5,3,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[4,6,3,1,2,5]=>[5,6,4,3,1,2]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]
[4,6,3,1,5,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[4,6,3,2,1,5]=>[5,6,4,3,1,2]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]
[4,6,3,2,5,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[4,6,3,5,1,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[4,6,3,5,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[4,6,5,1,2,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[4,6,5,1,3,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[4,6,5,2,1,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[4,6,5,2,3,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[4,6,5,3,1,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[4,6,5,3,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,1,2,3,4,6]=>[5,2,3,4,1,6]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[5,1,2,3,6,4]=>[6,2,3,4,5,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[5,1,2,4,3,6]=>[5,2,3,4,1,6]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[5,1,2,4,6,3]=>[6,2,3,4,5,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[5,1,2,6,3,4]=>[6,2,3,5,4,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[5,1,2,6,4,3]=>[6,2,3,5,4,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[5,1,3,2,4,6]=>[5,2,4,3,1,6]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[5,1,3,2,6,4]=>[6,2,4,3,5,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[5,1,3,4,2,6]=>[5,2,4,3,1,6]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[5,1,3,4,6,2]=>[6,2,4,3,5,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[5,1,3,6,2,4]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[5,1,3,6,4,2]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[5,1,4,2,3,6]=>[5,2,4,3,1,6]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[5,1,4,2,6,3]=>[6,2,4,3,5,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[5,1,4,3,2,6]=>[5,2,4,3,1,6]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[5,1,4,3,6,2]=>[6,2,4,3,5,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[5,1,4,6,2,3]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[5,1,4,6,3,2]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[5,1,6,2,3,4]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[5,1,6,2,4,3]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[5,1,6,3,2,4]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[5,1,6,3,4,2]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[5,1,6,4,2,3]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[5,1,6,4,3,2]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[5,2,1,3,4,6]=>[5,3,2,4,1,6]=>[5,3,2,6,1,4]=>[[[[.,.],.],[.,.]],[.,.]]
[5,2,1,3,6,4]=>[6,3,2,4,5,1]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[5,2,1,4,3,6]=>[5,3,2,4,1,6]=>[5,3,2,6,1,4]=>[[[[.,.],.],[.,.]],[.,.]]
[5,2,1,4,6,3]=>[6,3,2,4,5,1]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[5,2,1,6,3,4]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[5,2,1,6,4,3]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[5,2,3,1,4,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[5,2,3,1,6,4]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[5,2,3,4,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[5,2,3,4,6,1]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[5,2,3,6,1,4]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[5,2,3,6,4,1]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[5,2,4,1,3,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[5,2,4,1,6,3]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[5,2,4,3,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[5,2,4,3,6,1]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[5,2,4,6,1,3]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[5,2,4,6,3,1]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[5,2,6,1,3,4]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]
[5,2,6,1,4,3]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]
[5,2,6,3,1,4]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,2,6,3,4,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,2,6,4,1,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,2,6,4,3,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,3,1,2,4,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[5,3,1,2,6,4]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[5,3,1,4,2,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[5,3,1,4,6,2]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[5,3,1,6,2,4]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[5,3,1,6,4,2]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[5,3,2,1,4,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[5,3,2,1,6,4]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[5,3,2,4,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[5,3,2,4,6,1]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[5,3,2,6,1,4]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[5,3,2,6,4,1]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[5,3,4,1,2,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[5,3,4,1,6,2]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[5,3,4,2,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[5,3,4,2,6,1]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[5,3,4,6,1,2]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[5,3,4,6,2,1]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[5,3,6,1,2,4]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,3,6,1,4,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,3,6,2,1,4]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,3,6,2,4,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,3,6,4,1,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,3,6,4,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,4,1,2,3,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[5,4,1,2,6,3]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[5,4,1,3,2,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[5,4,1,3,6,2]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[5,4,1,6,2,3]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[5,4,1,6,3,2]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[5,4,2,1,3,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[5,4,2,1,6,3]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[5,4,2,3,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[5,4,2,3,6,1]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[5,4,2,6,1,3]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[5,4,2,6,3,1]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[5,4,3,1,2,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[5,4,3,1,6,2]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[5,4,3,2,6,1]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[5,4,3,6,1,2]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[5,4,3,6,2,1]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[5,4,6,1,2,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,4,6,1,3,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,4,6,2,1,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,4,6,2,3,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,4,6,3,1,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,4,6,3,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,6,1,2,3,4]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[5,6,1,2,4,3]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[5,6,1,3,2,4]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[5,6,1,3,4,2]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[5,6,1,4,2,3]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[5,6,1,4,3,2]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[5,6,2,1,3,4]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,6,2,1,4,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,6,2,3,1,4]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,6,2,3,4,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,6,2,4,1,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,6,2,4,3,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,6,3,1,2,4]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,6,3,1,4,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,6,3,2,1,4]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,6,3,2,4,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,6,3,4,1,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,6,3,4,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,6,4,1,2,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,6,4,1,3,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,6,4,2,1,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,6,4,2,3,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,6,4,3,1,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[5,6,4,3,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[6,1,2,3,4,5]=>[6,2,3,4,5,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[6,1,2,3,5,4]=>[6,2,3,4,5,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[6,1,2,4,3,5]=>[6,2,3,5,4,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[6,1,2,4,5,3]=>[6,2,3,5,4,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[6,1,2,5,3,4]=>[6,2,3,5,4,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[6,1,2,5,4,3]=>[6,2,3,5,4,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[6,1,3,2,4,5]=>[6,2,4,3,5,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[6,1,3,2,5,4]=>[6,2,4,3,5,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[6,1,3,4,2,5]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[6,1,3,4,5,2]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[6,1,3,5,2,4]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[6,1,3,5,4,2]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[6,1,4,2,3,5]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[6,1,4,2,5,3]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[6,1,4,3,2,5]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[6,1,4,3,5,2]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[6,1,4,5,2,3]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[6,1,4,5,3,2]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[6,1,5,2,3,4]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[6,1,5,2,4,3]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[6,1,5,3,2,4]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[6,1,5,3,4,2]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[6,1,5,4,2,3]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[6,1,5,4,3,2]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[6,2,1,3,4,5]=>[6,3,2,4,5,1]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[6,2,1,3,5,4]=>[6,3,2,4,5,1]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[6,2,1,4,3,5]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[6,2,1,4,5,3]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[6,2,1,5,3,4]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[6,2,1,5,4,3]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[6,2,3,1,4,5]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[6,2,3,1,5,4]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[6,2,3,4,1,5]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[6,2,3,4,5,1]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[6,2,3,5,1,4]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[6,2,3,5,4,1]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[6,2,4,1,3,5]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]
[6,2,4,1,5,3]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]
[6,2,4,3,1,5]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[6,2,4,3,5,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[6,2,4,5,1,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[6,2,4,5,3,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[6,2,5,1,3,4]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]
[6,2,5,1,4,3]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]
[6,2,5,3,1,4]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[6,2,5,3,4,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[6,2,5,4,1,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[6,2,5,4,3,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[6,3,1,2,4,5]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[6,3,1,2,5,4]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[6,3,1,4,2,5]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[6,3,1,4,5,2]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[6,3,1,5,2,4]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[6,3,1,5,4,2]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[6,3,2,1,4,5]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[6,3,2,1,5,4]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[6,3,2,4,1,5]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[6,3,2,4,5,1]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[6,3,2,5,1,4]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[6,3,2,5,4,1]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[6,3,4,1,2,5]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[6,3,4,1,5,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[6,3,4,2,1,5]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[6,3,4,2,5,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[6,3,4,5,1,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[6,3,4,5,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[6,3,5,1,2,4]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[6,3,5,1,4,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[6,3,5,2,1,4]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
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[6,3,5,4,1,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
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[6,4,1,2,3,5]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[6,4,1,2,5,3]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[6,4,1,3,2,5]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[6,4,1,3,5,2]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[6,4,1,5,2,3]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[6,4,1,5,3,2]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[6,4,2,1,3,5]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[6,4,2,1,5,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[6,4,2,3,1,5]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[6,4,2,3,5,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[6,4,2,5,1,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
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[6,4,3,1,2,5]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[6,4,3,1,5,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[6,4,3,2,1,5]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
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[6,4,3,5,1,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[6,4,3,5,2,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[6,4,5,1,2,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[6,4,5,1,3,2]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[6,4,5,2,1,3]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[6,4,5,2,3,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
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[1,5,2,4,3,6,7]=>[1,5,3,4,2,6,7]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
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[1,5,2,4,6,3,7]=>[1,6,3,4,5,2,7]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
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[1,5,2,6,3,4,7]=>[1,6,3,5,4,2,7]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
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[1,5,2,6,4,3,7]=>[1,6,3,5,4,2,7]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
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[1,5,3,2,4,7,6]=>[1,5,4,3,2,7,6]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,5,3,2,6,4,7]=>[1,6,4,3,5,2,7]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
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[1,5,3,4,2,6,7]=>[1,5,4,3,2,6,7]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
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[1,5,3,4,6,2,7]=>[1,6,4,3,5,2,7]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
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[1,5,4,2,6,3,7]=>[1,6,4,3,5,2,7]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
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[1,6,2,5,3,4,7]=>[1,6,3,5,4,2,7]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
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[1,6,3,2,4,7,5]=>[1,7,4,3,5,6,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,6,3,2,5,4,7]=>[1,6,4,3,5,2,7]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
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[1,7,5,4,2,6,3]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,5,4,3,2,6]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,5,4,3,6,2]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,5,4,6,2,3]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,5,4,6,3,2]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,5,6,2,3,4]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,5,6,2,4,3]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,5,6,3,2,4]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,5,6,3,4,2]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,5,6,4,2,3]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,5,6,4,3,2]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,6,2,3,4,5]=>[1,7,6,4,5,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,6,2,3,5,4]=>[1,7,6,4,5,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,6,2,4,3,5]=>[1,7,6,4,5,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,6,2,4,5,3]=>[1,7,6,4,5,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,6,2,5,3,4]=>[1,7,6,4,5,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,6,2,5,4,3]=>[1,7,6,4,5,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,6,3,2,4,5]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,6,3,2,5,4]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,6,3,4,2,5]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,6,3,4,5,2]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,6,3,5,2,4]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,6,3,5,4,2]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,6,4,2,3,5]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,6,4,2,5,3]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,6,4,3,2,5]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,6,4,3,5,2]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,6,4,5,2,3]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,6,4,5,3,2]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,6,5,2,3,4]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,6,5,2,4,3]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,6,5,3,2,4]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,6,5,3,4,2]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,6,5,4,2,3]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,3,4,7,5,6]=>[2,1,3,4,7,6,5]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,3,4,7,6,5]=>[2,1,3,4,7,6,5]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,3,5,7,4,6]=>[2,1,3,6,7,4,5]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,3,5,7,6,4]=>[2,1,3,7,6,5,4]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,3,6,4,5,7]=>[2,1,3,6,5,4,7]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,3,6,4,7,5]=>[2,1,3,7,5,6,4]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,3,6,5,4,7]=>[2,1,3,6,5,4,7]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,3,6,5,7,4]=>[2,1,3,7,5,6,4]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,3,6,7,4,5]=>[2,1,3,7,6,5,4]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,3,6,7,5,4]=>[2,1,3,7,6,5,4]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,3,7,4,5,6]=>[2,1,3,7,5,6,4]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,3,7,4,6,5]=>[2,1,3,7,5,6,4]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,3,7,5,4,6]=>[2,1,3,7,6,5,4]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,3,7,5,6,4]=>[2,1,3,7,6,5,4]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,3,7,6,4,5]=>[2,1,3,7,6,5,4]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,3,7,6,5,4]=>[2,1,3,7,6,5,4]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,4,3,7,5,6]=>[2,1,4,3,7,6,5]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,4,3,7,6,5]=>[2,1,4,3,7,6,5]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,4,5,7,3,6]=>[2,1,6,4,7,3,5]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,4,5,7,6,3]=>[2,1,7,4,6,5,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,4,6,3,5,7]=>[2,1,5,6,3,4,7]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,4,6,3,7,5]=>[2,1,5,7,3,6,4]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,4,6,5,3,7]=>[2,1,6,5,4,3,7]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,4,6,5,7,3]=>[2,1,7,5,4,6,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,4,6,7,3,5]=>[2,1,6,7,5,3,4]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,4,6,7,5,3]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,4,7,3,5,6]=>[2,1,5,7,3,6,4]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,4,7,3,6,5]=>[2,1,5,7,3,6,4]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,4,7,5,3,6]=>[2,1,6,7,5,3,4]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,4,7,5,6,3]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,4,7,6,3,5]=>[2,1,6,7,5,3,4]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,4,7,6,5,3]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,5,3,4,6,7]=>[2,1,5,4,3,6,7]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,5,3,4,7,6]=>[2,1,5,4,3,7,6]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,5,3,6,4,7]=>[2,1,6,4,5,3,7]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,5,3,6,7,4]=>[2,1,7,4,5,6,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,5,3,7,4,6]=>[2,1,6,4,7,3,5]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,5,3,7,6,4]=>[2,1,7,4,6,5,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,5,4,3,6,7]=>[2,1,5,4,3,6,7]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,5,4,3,7,6]=>[2,1,5,4,3,7,6]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,5,4,6,3,7]=>[2,1,6,4,5,3,7]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,5,4,6,7,3]=>[2,1,7,4,5,6,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,5,4,7,3,6]=>[2,1,6,4,7,3,5]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,5,4,7,6,3]=>[2,1,7,4,6,5,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,5,6,3,4,7]=>[2,1,6,5,4,3,7]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,5,6,3,7,4]=>[2,1,7,5,4,6,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,5,6,4,3,7]=>[2,1,6,5,4,3,7]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,5,6,4,7,3]=>[2,1,7,5,4,6,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,5,6,7,3,4]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,5,6,7,4,3]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,5,7,3,4,6]=>[2,1,6,7,5,3,4]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,5,7,3,6,4]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,5,7,4,3,6]=>[2,1,6,7,5,3,4]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,5,7,4,6,3]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,5,7,6,3,4]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,5,7,6,4,3]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,6,3,4,5,7]=>[2,1,6,4,5,3,7]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,6,3,4,7,5]=>[2,1,7,4,5,6,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,6,3,5,4,7]=>[2,1,6,4,5,3,7]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,6,3,5,7,4]=>[2,1,7,4,5,6,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,6,3,7,4,5]=>[2,1,7,4,6,5,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,6,3,7,5,4]=>[2,1,7,4,6,5,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,6,4,3,5,7]=>[2,1,6,5,4,3,7]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,6,4,3,7,5]=>[2,1,7,5,4,6,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,6,4,5,3,7]=>[2,1,6,5,4,3,7]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,6,4,5,7,3]=>[2,1,7,5,4,6,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,6,4,7,3,5]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,6,4,7,5,3]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,6,5,3,4,7]=>[2,1,6,5,4,3,7]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,6,5,3,7,4]=>[2,1,7,5,4,6,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,6,5,4,3,7]=>[2,1,6,5,4,3,7]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,6,5,4,7,3]=>[2,1,7,5,4,6,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,6,5,7,3,4]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,6,5,7,4,3]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,6,7,3,4,5]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,6,7,3,5,4]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,6,7,4,3,5]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,6,7,4,5,3]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,6,7,5,3,4]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,6,7,5,4,3]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,7,3,4,5,6]=>[2,1,7,4,5,6,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,7,3,4,6,5]=>[2,1,7,4,5,6,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,7,3,5,4,6]=>[2,1,7,4,6,5,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,7,3,5,6,4]=>[2,1,7,4,6,5,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,7,3,6,4,5]=>[2,1,7,4,6,5,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,7,3,6,5,4]=>[2,1,7,4,6,5,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,7,4,3,5,6]=>[2,1,7,5,4,6,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,7,4,3,6,5]=>[2,1,7,5,4,6,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,7,4,5,3,6]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,7,4,5,6,3]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,7,4,6,3,5]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,7,4,6,5,3]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,7,5,3,4,6]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,7,5,3,6,4]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,7,5,4,3,6]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,7,5,4,6,3]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,7,5,6,3,4]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,7,5,6,4,3]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,7,6,3,4,5]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,7,6,3,5,4]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,7,6,4,3,5]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,7,6,4,5,3]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,7,6,5,3,4]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[2,3,1,4,7,5,6]=>[3,2,1,4,7,6,5]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[2,3,1,4,7,6,5]=>[3,2,1,4,7,6,5]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[2,3,1,5,7,4,6]=>[3,2,1,6,7,4,5]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[2,3,1,5,7,6,4]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[2,3,1,6,4,5,7]=>[3,2,1,6,5,4,7]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[2,3,1,6,4,7,5]=>[3,2,1,7,5,6,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[2,3,1,6,5,4,7]=>[3,2,1,6,5,4,7]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[2,3,1,6,5,7,4]=>[3,2,1,7,5,6,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[2,3,1,6,7,4,5]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[2,3,1,6,7,5,4]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[2,3,1,7,4,5,6]=>[3,2,1,7,5,6,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[2,3,1,7,4,6,5]=>[3,2,1,7,5,6,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[2,3,1,7,5,4,6]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[2,3,1,7,5,6,4]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[2,3,1,7,6,4,5]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[2,3,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[2,3,4,1,7,5,6]=>[4,2,3,1,7,6,5]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[2,3,4,1,7,6,5]=>[4,2,3,1,7,6,5]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[2,3,4,5,7,1,6]=>[6,2,3,4,7,1,5]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[2,3,4,5,7,6,1]=>[7,2,3,4,6,5,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[2,3,4,6,1,5,7]=>[5,2,3,6,1,4,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[2,3,4,6,1,7,5]=>[5,2,3,7,1,6,4]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[2,3,4,6,5,1,7]=>[6,2,3,5,4,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[2,3,4,6,5,7,1]=>[7,2,3,5,4,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[2,3,4,6,7,1,5]=>[6,2,3,7,5,1,4]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[2,3,4,6,7,5,1]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[2,3,4,7,1,5,6]=>[5,2,3,7,1,6,4]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[2,3,4,7,1,6,5]=>[5,2,3,7,1,6,4]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[2,3,4,7,5,1,6]=>[6,2,3,7,5,1,4]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[2,3,4,7,5,6,1]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[2,3,4,7,6,1,5]=>[6,2,3,7,5,1,4]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[2,3,4,7,6,5,1]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[2,3,5,1,4,6,7]=>[4,2,5,1,3,6,7]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[2,3,5,1,4,7,6]=>[4,2,5,1,3,7,6]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[2,3,5,1,6,4,7]=>[4,2,6,1,5,3,7]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[2,3,5,1,6,7,4]=>[4,2,7,1,5,6,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[2,3,5,1,7,4,6]=>[4,2,6,1,7,3,5]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[2,3,5,1,7,6,4]=>[4,2,7,1,6,5,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[2,3,5,4,1,6,7]=>[5,2,4,3,1,6,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[2,3,5,4,1,7,6]=>[5,2,4,3,1,7,6]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[2,3,5,4,6,1,7]=>[6,2,4,3,5,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[2,3,5,4,6,7,1]=>[7,2,4,3,5,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[2,3,5,4,7,1,6]=>[6,2,4,3,7,1,5]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[2,3,5,4,7,6,1]=>[7,2,4,3,6,5,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[2,3,5,6,1,4,7]=>[5,2,6,4,1,3,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[2,3,5,6,1,7,4]=>[5,2,7,4,1,6,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[2,3,5,6,4,1,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[2,3,5,6,4,7,1]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[2,3,5,6,7,1,4]=>[6,2,7,4,5,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[2,3,5,6,7,4,1]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[2,3,5,7,1,4,6]=>[5,2,6,7,1,3,4]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[2,3,5,7,1,6,4]=>[5,2,7,6,1,4,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[2,3,5,7,4,1,6]=>[6,2,5,7,3,1,4]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[2,3,5,7,4,6,1]=>[7,2,5,6,3,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[2,3,5,7,6,1,4]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[2,3,5,7,6,4,1]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[2,3,6,1,4,5,7]=>[4,2,6,1,5,3,7]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[2,3,6,1,4,7,5]=>[4,2,7,1,5,6,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[2,3,6,1,5,4,7]=>[4,2,6,1,5,3,7]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[2,3,6,1,5,7,4]=>[4,2,7,1,5,6,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[2,3,6,1,7,4,5]=>[4,2,7,1,6,5,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[2,3,6,1,7,5,4]=>[4,2,7,1,6,5,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[2,3,6,4,1,5,7]=>[5,2,6,4,1,3,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[2,3,6,4,1,7,5]=>[5,2,7,4,1,6,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[2,3,6,4,5,1,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[2,3,6,4,5,7,1]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[2,3,6,4,7,1,5]=>[6,2,7,4,5,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[2,3,6,4,7,5,1]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[2,3,6,5,1,4,7]=>[5,2,6,4,1,3,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[2,3,6,5,1,7,4]=>[5,2,7,4,1,6,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[2,3,6,5,4,1,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[2,3,6,5,4,7,1]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[2,3,6,5,7,1,4]=>[6,2,7,4,5,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[2,3,6,5,7,4,1]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[2,3,6,7,1,4,5]=>[5,2,7,6,1,4,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[2,3,6,7,1,5,4]=>[5,2,7,6,1,4,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[2,3,6,7,4,1,5]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[2,3,6,7,4,5,1]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[2,3,6,7,5,1,4]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[2,3,6,7,5,4,1]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[2,3,7,1,4,5,6]=>[4,2,7,1,5,6,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[2,3,7,1,4,6,5]=>[4,2,7,1,5,6,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[2,3,7,1,5,4,6]=>[4,2,7,1,6,5,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[2,3,7,1,5,6,4]=>[4,2,7,1,6,5,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[2,3,7,1,6,4,5]=>[4,2,7,1,6,5,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[2,3,7,1,6,5,4]=>[4,2,7,1,6,5,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[2,3,7,4,1,5,6]=>[5,2,7,4,1,6,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[2,3,7,4,1,6,5]=>[5,2,7,4,1,6,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[2,3,7,4,5,1,6]=>[6,2,7,4,5,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[2,3,7,4,5,6,1]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[2,3,7,4,6,1,5]=>[6,2,7,4,5,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[2,3,7,4,6,5,1]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[2,3,7,5,1,4,6]=>[5,2,7,6,1,4,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[2,3,7,5,1,6,4]=>[5,2,7,6,1,4,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[2,3,7,5,4,1,6]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[2,3,7,5,4,6,1]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[2,3,7,5,6,1,4]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[2,3,7,5,6,4,1]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[2,3,7,6,1,4,5]=>[5,2,7,6,1,4,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[2,3,7,6,1,5,4]=>[5,2,7,6,1,4,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[2,3,7,6,4,1,5]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[2,3,7,6,4,5,1]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[2,3,7,6,5,1,4]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[2,3,7,6,5,4,1]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[2,4,1,3,5,6,7]=>[3,4,1,2,5,6,7]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,4,1,3,5,7,6]=>[3,4,1,2,5,7,6]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,4,1,3,6,5,7]=>[3,4,1,2,6,5,7]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,4,1,3,6,7,5]=>[3,4,1,2,7,6,5]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,4,1,3,7,5,6]=>[3,4,1,2,7,6,5]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,4,1,3,7,6,5]=>[3,4,1,2,7,6,5]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,4,1,5,3,6,7]=>[3,5,1,4,2,6,7]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,4,1,5,3,7,6]=>[3,5,1,4,2,7,6]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,4,1,5,6,3,7]=>[3,6,1,4,5,2,7]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,4,1,5,6,7,3]=>[3,7,1,4,5,6,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,4,1,5,7,3,6]=>[3,6,1,4,7,2,5]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,4,1,5,7,6,3]=>[3,7,1,4,6,5,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,4,1,6,3,5,7]=>[3,5,1,6,2,4,7]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,4,1,6,3,7,5]=>[3,5,1,7,2,6,4]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,4,1,6,5,3,7]=>[3,6,1,5,4,2,7]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,4,1,6,5,7,3]=>[3,7,1,5,4,6,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,4,1,6,7,3,5]=>[3,6,1,7,5,2,4]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,4,1,6,7,5,3]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,4,1,7,3,5,6]=>[3,5,1,7,2,6,4]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,4,1,7,3,6,5]=>[3,5,1,7,2,6,4]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,4,1,7,5,3,6]=>[3,6,1,7,5,2,4]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,4,1,7,5,6,3]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,4,1,7,6,3,5]=>[3,6,1,7,5,2,4]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,4,1,7,6,5,3]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,4,3,1,5,6,7]=>[4,3,2,1,5,6,7]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[2,4,3,1,5,7,6]=>[4,3,2,1,5,7,6]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[2,4,3,1,6,5,7]=>[4,3,2,1,6,5,7]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[2,4,3,1,6,7,5]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[2,4,3,1,7,5,6]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[2,4,3,1,7,6,5]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[2,4,3,5,1,6,7]=>[5,3,2,4,1,6,7]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[2,4,3,5,1,7,6]=>[5,3,2,4,1,7,6]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[2,4,3,5,6,1,7]=>[6,3,2,4,5,1,7]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[2,4,3,5,6,7,1]=>[7,3,2,4,5,6,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[2,4,3,5,7,1,6]=>[6,3,2,4,7,1,5]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[2,4,3,5,7,6,1]=>[7,3,2,4,6,5,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[2,4,3,6,1,5,7]=>[5,3,2,6,1,4,7]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[2,4,3,6,1,7,5]=>[5,3,2,7,1,6,4]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[2,4,3,6,5,1,7]=>[6,3,2,5,4,1,7]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[2,4,3,6,5,7,1]=>[7,3,2,5,4,6,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[2,4,3,6,7,1,5]=>[6,3,2,7,5,1,4]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[2,4,3,6,7,5,1]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[2,4,3,7,1,5,6]=>[5,3,2,7,1,6,4]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[2,4,3,7,1,6,5]=>[5,3,2,7,1,6,4]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[2,4,3,7,5,1,6]=>[6,3,2,7,5,1,4]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[2,4,3,7,5,6,1]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[2,4,3,7,6,1,5]=>[6,3,2,7,5,1,4]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[2,4,3,7,6,5,1]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[2,4,5,1,3,6,7]=>[4,5,3,1,2,6,7]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,4,5,1,3,7,6]=>[4,5,3,1,2,7,6]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,4,5,1,6,3,7]=>[4,6,3,1,5,2,7]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,4,5,1,6,7,3]=>[4,7,3,1,5,6,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,4,5,1,7,3,6]=>[4,6,3,1,7,2,5]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,4,5,1,7,6,3]=>[4,7,3,1,6,5,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,4,5,3,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[2,4,5,3,1,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[2,4,5,3,6,1,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[2,4,5,3,6,7,1]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[2,4,5,3,7,1,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[2,4,5,3,7,6,1]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[2,4,5,6,1,3,7]=>[5,6,3,4,1,2,7]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[2,4,5,6,1,7,3]=>[5,7,3,4,1,6,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[2,4,5,6,3,1,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[2,4,5,6,3,7,1]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[2,4,5,6,7,1,3]=>[6,7,3,4,5,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[2,4,5,6,7,3,1]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[2,4,5,7,1,3,6]=>[5,6,3,7,1,2,4]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[2,4,5,7,1,6,3]=>[5,7,3,6,1,4,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[2,4,5,7,3,1,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[2,4,5,7,3,6,1]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[2,4,5,7,6,1,3]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[2,4,5,7,6,3,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[2,4,6,1,3,5,7]=>[4,5,6,1,2,3,7]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,4,6,1,3,7,5]=>[4,5,7,1,2,6,3]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,4,6,1,5,3,7]=>[4,6,5,1,3,2,7]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,4,6,1,5,7,3]=>[4,7,5,1,3,6,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,4,6,1,7,3,5]=>[4,6,7,1,5,2,3]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,4,6,1,7,5,3]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,4,6,3,1,5,7]=>[5,4,6,2,1,3,7]=>[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[2,4,6,3,1,7,5]=>[5,4,7,2,1,6,3]=>[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[2,4,6,3,5,1,7]=>[6,4,5,2,3,1,7]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[2,4,6,3,5,7,1]=>[7,4,5,2,3,6,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[2,4,6,3,7,1,5]=>[6,4,7,2,5,1,3]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[2,4,6,3,7,5,1]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[2,4,6,5,1,3,7]=>[5,6,4,3,1,2,7]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[2,4,6,5,1,7,3]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[2,4,6,5,3,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[2,4,6,5,3,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[2,4,6,5,7,1,3]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[2,4,6,5,7,3,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[2,4,6,7,1,3,5]=>[5,6,7,4,1,2,3]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,4,6,7,1,5,3]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,4,6,7,3,1,5]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[2,4,6,7,3,5,1]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[2,4,6,7,5,1,3]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,4,6,7,5,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,4,7,1,3,5,6]=>[4,5,7,1,2,6,3]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,4,7,1,3,6,5]=>[4,5,7,1,2,6,3]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,4,7,1,5,3,6]=>[4,6,7,1,5,2,3]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,4,7,1,5,6,3]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,4,7,1,6,3,5]=>[4,6,7,1,5,2,3]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,4,7,1,6,5,3]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,4,7,3,1,5,6]=>[5,4,7,2,1,6,3]=>[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[2,4,7,3,1,6,5]=>[5,4,7,2,1,6,3]=>[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[2,4,7,3,5,1,6]=>[6,4,7,2,5,1,3]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[2,4,7,3,5,6,1]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[2,4,7,3,6,1,5]=>[6,4,7,2,5,1,3]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[2,4,7,3,6,5,1]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[2,4,7,5,1,3,6]=>[5,6,7,4,1,2,3]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,4,7,5,1,6,3]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,4,7,5,3,1,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[2,4,7,5,3,6,1]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[2,4,7,5,6,1,3]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,4,7,5,6,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,4,7,6,1,3,5]=>[5,6,7,4,1,2,3]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,4,7,6,1,5,3]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,4,7,6,3,1,5]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[2,4,7,6,3,5,1]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[2,4,7,6,5,1,3]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,4,7,6,5,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,5,1,3,4,6,7]=>[3,5,1,4,2,6,7]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,5,1,3,4,7,6]=>[3,5,1,4,2,7,6]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,5,1,3,6,4,7]=>[3,6,1,4,5,2,7]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,5,1,3,6,7,4]=>[3,7,1,4,5,6,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,5,1,3,7,4,6]=>[3,6,1,4,7,2,5]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,5,1,3,7,6,4]=>[3,7,1,4,6,5,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,5,1,4,3,6,7]=>[3,5,1,4,2,6,7]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,5,1,4,3,7,6]=>[3,5,1,4,2,7,6]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,5,1,4,6,3,7]=>[3,6,1,4,5,2,7]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,5,1,4,6,7,3]=>[3,7,1,4,5,6,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,5,1,4,7,3,6]=>[3,6,1,4,7,2,5]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,5,1,4,7,6,3]=>[3,7,1,4,6,5,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,5,1,6,3,4,7]=>[3,6,1,5,4,2,7]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,5,1,6,3,7,4]=>[3,7,1,5,4,6,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,5,1,6,4,3,7]=>[3,6,1,5,4,2,7]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,5,1,6,4,7,3]=>[3,7,1,5,4,6,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,5,1,6,7,3,4]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,5,1,6,7,4,3]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,5,1,7,3,4,6]=>[3,6,1,7,5,2,4]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,5,1,7,3,6,4]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,5,1,7,4,3,6]=>[3,6,1,7,5,2,4]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,5,1,7,4,6,3]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,5,1,7,6,3,4]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,5,1,7,6,4,3]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,5,3,1,4,6,7]=>[4,5,3,1,2,6,7]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,5,3,1,4,7,6]=>[4,5,3,1,2,7,6]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,5,3,1,6,4,7]=>[4,6,3,1,5,2,7]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,5,3,1,6,7,4]=>[4,7,3,1,5,6,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,5,3,1,7,4,6]=>[4,6,3,1,7,2,5]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,5,3,1,7,6,4]=>[4,7,3,1,6,5,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,5,3,4,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[2,5,3,4,1,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[2,5,3,4,6,1,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[2,5,3,4,6,7,1]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[2,5,3,4,7,1,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[2,5,3,4,7,6,1]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[2,5,3,6,1,4,7]=>[5,6,3,4,1,2,7]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[2,5,3,6,1,7,4]=>[5,7,3,4,1,6,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[2,5,3,6,4,1,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[2,5,3,6,4,7,1]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[2,5,3,6,7,1,4]=>[6,7,3,4,5,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[2,5,3,6,7,4,1]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[2,5,3,7,1,4,6]=>[5,6,3,7,1,2,4]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[2,5,3,7,1,6,4]=>[5,7,3,6,1,4,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[2,5,3,7,4,1,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[2,5,3,7,4,6,1]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[2,5,3,7,6,1,4]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[2,5,3,7,6,4,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[2,5,4,1,3,6,7]=>[4,5,3,1,2,6,7]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,5,4,1,3,7,6]=>[4,5,3,1,2,7,6]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,5,4,1,6,3,7]=>[4,6,3,1,5,2,7]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,5,4,1,6,7,3]=>[4,7,3,1,5,6,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,5,4,1,7,3,6]=>[4,6,3,1,7,2,5]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,5,4,1,7,6,3]=>[4,7,3,1,6,5,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,5,4,3,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[2,5,4,3,1,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[2,5,4,3,6,1,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[2,5,4,3,6,7,1]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[2,5,4,3,7,1,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[2,5,4,3,7,6,1]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[2,5,4,6,1,3,7]=>[5,6,3,4,1,2,7]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[2,5,4,6,1,7,3]=>[5,7,3,4,1,6,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[2,5,4,6,3,1,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[2,5,4,6,3,7,1]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[2,5,4,6,7,1,3]=>[6,7,3,4,5,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[2,5,4,6,7,3,1]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[2,5,4,7,1,3,6]=>[5,6,3,7,1,2,4]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[2,5,4,7,1,6,3]=>[5,7,3,6,1,4,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[2,5,4,7,3,1,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[2,5,4,7,3,6,1]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[2,5,4,7,6,1,3]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[2,5,4,7,6,3,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[2,5,6,1,3,4,7]=>[4,6,5,1,3,2,7]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,5,6,1,3,7,4]=>[4,7,5,1,3,6,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,5,6,1,4,3,7]=>[4,6,5,1,3,2,7]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,5,6,1,4,7,3]=>[4,7,5,1,3,6,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,5,6,1,7,3,4]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,5,6,1,7,4,3]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,5,6,3,1,4,7]=>[5,6,4,3,1,2,7]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[2,5,6,3,1,7,4]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[2,5,6,3,4,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[2,5,6,3,4,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[2,5,6,3,7,1,4]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[2,5,6,3,7,4,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[2,5,6,4,1,3,7]=>[5,6,4,3,1,2,7]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[2,5,6,4,1,7,3]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[2,5,6,4,3,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[2,5,6,4,3,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[2,5,6,4,7,1,3]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[2,5,6,4,7,3,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[2,5,6,7,1,3,4]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,5,6,7,1,4,3]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,5,6,7,3,1,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,5,6,7,3,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,5,6,7,4,1,3]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,5,6,7,4,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,5,7,1,3,4,6]=>[4,6,7,1,5,2,3]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,5,7,1,3,6,4]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,5,7,1,4,3,6]=>[4,6,7,1,5,2,3]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,5,7,1,4,6,3]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,5,7,1,6,3,4]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,5,7,1,6,4,3]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,5,7,3,1,4,6]=>[5,6,7,4,1,2,3]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,5,7,3,1,6,4]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,5,7,3,4,1,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[2,5,7,3,4,6,1]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[2,5,7,3,6,1,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,5,7,3,6,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,5,7,4,1,3,6]=>[5,6,7,4,1,2,3]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,5,7,4,1,6,3]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,5,7,4,3,1,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[2,5,7,4,3,6,1]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[2,5,7,4,6,1,3]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,5,7,4,6,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,5,7,6,1,3,4]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,5,7,6,1,4,3]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,5,7,6,3,1,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,5,7,6,3,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,5,7,6,4,1,3]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,5,7,6,4,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,6,1,3,4,5,7]=>[3,6,1,4,5,2,7]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,6,1,3,4,7,5]=>[3,7,1,4,5,6,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,6,1,3,5,4,7]=>[3,6,1,4,5,2,7]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,6,1,3,5,7,4]=>[3,7,1,4,5,6,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,6,1,3,7,4,5]=>[3,7,1,4,6,5,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,6,1,3,7,5,4]=>[3,7,1,4,6,5,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,6,1,4,3,5,7]=>[3,6,1,5,4,2,7]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,6,1,4,3,7,5]=>[3,7,1,5,4,6,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,6,1,4,5,3,7]=>[3,6,1,5,4,2,7]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,6,1,4,5,7,3]=>[3,7,1,5,4,6,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,6,1,4,7,3,5]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,6,1,4,7,5,3]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,6,1,5,3,4,7]=>[3,6,1,5,4,2,7]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,6,1,5,3,7,4]=>[3,7,1,5,4,6,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,6,1,5,4,3,7]=>[3,6,1,5,4,2,7]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,6,1,5,4,7,3]=>[3,7,1,5,4,6,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,6,1,5,7,3,4]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,6,1,5,7,4,3]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,6,1,7,3,4,5]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,6,1,7,3,5,4]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,6,1,7,4,3,5]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,6,1,7,4,5,3]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,6,1,7,5,3,4]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,6,1,7,5,4,3]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,6,3,1,4,5,7]=>[4,6,3,1,5,2,7]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,6,3,1,4,7,5]=>[4,7,3,1,5,6,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,6,3,1,5,4,7]=>[4,6,3,1,5,2,7]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,6,3,1,5,7,4]=>[4,7,3,1,5,6,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,6,3,1,7,4,5]=>[4,7,3,1,6,5,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,6,3,1,7,5,4]=>[4,7,3,1,6,5,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,6,3,4,1,5,7]=>[5,6,3,4,1,2,7]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[2,6,3,4,1,7,5]=>[5,7,3,4,1,6,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[2,6,3,4,5,1,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[2,6,3,4,5,7,1]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[2,6,3,4,7,1,5]=>[6,7,3,4,5,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[2,6,3,4,7,5,1]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[2,6,3,5,1,4,7]=>[5,6,3,4,1,2,7]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[2,6,3,5,1,7,4]=>[5,7,3,4,1,6,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[2,6,3,5,4,1,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[2,6,3,5,4,7,1]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[2,6,3,5,7,1,4]=>[6,7,3,4,5,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[2,6,3,5,7,4,1]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[2,6,3,7,1,4,5]=>[5,7,3,6,1,4,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[2,6,3,7,1,5,4]=>[5,7,3,6,1,4,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[2,6,3,7,4,1,5]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[2,6,3,7,4,5,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[2,6,3,7,5,1,4]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[2,6,3,7,5,4,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[2,6,4,1,3,5,7]=>[4,6,5,1,3,2,7]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,6,4,1,3,7,5]=>[4,7,5,1,3,6,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,6,4,1,5,3,7]=>[4,6,5,1,3,2,7]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,6,4,1,5,7,3]=>[4,7,5,1,3,6,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,6,4,1,7,3,5]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,6,4,1,7,5,3]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,6,4,3,1,5,7]=>[5,6,4,3,1,2,7]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[2,6,4,3,1,7,5]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[2,6,4,3,5,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[2,6,4,3,5,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[2,6,4,3,7,1,5]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[2,6,4,3,7,5,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[2,6,4,5,1,3,7]=>[5,6,4,3,1,2,7]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[2,6,4,5,1,7,3]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[2,6,4,5,3,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[2,6,4,5,3,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[2,6,4,5,7,1,3]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[2,6,4,5,7,3,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[2,6,4,7,1,3,5]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,6,4,7,1,5,3]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,6,4,7,3,1,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,6,4,7,3,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,6,4,7,5,1,3]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,6,4,7,5,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,6,5,1,3,4,7]=>[4,6,5,1,3,2,7]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,6,5,1,3,7,4]=>[4,7,5,1,3,6,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,6,5,1,4,3,7]=>[4,6,5,1,3,2,7]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,6,5,1,4,7,3]=>[4,7,5,1,3,6,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,6,5,1,7,3,4]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,6,5,1,7,4,3]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,6,5,3,1,4,7]=>[5,6,4,3,1,2,7]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[2,6,5,3,1,7,4]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[2,6,5,3,4,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[2,6,5,3,4,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[2,6,5,3,7,1,4]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[2,6,5,3,7,4,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[2,6,5,4,1,3,7]=>[5,6,4,3,1,2,7]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[2,6,5,4,1,7,3]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[2,6,5,4,3,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[2,6,5,4,3,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[2,6,5,4,7,1,3]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[2,6,5,4,7,3,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[2,6,5,7,1,3,4]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,6,5,7,1,4,3]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,6,5,7,3,1,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,6,5,7,3,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,6,5,7,4,1,3]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,6,5,7,4,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,6,7,1,3,4,5]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,6,7,1,3,5,4]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,6,7,1,4,3,5]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,6,7,1,4,5,3]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,6,7,1,5,3,4]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,6,7,1,5,4,3]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,6,7,3,1,4,5]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,6,7,3,1,5,4]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,6,7,3,4,1,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,6,7,3,4,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,6,7,3,5,1,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,6,7,3,5,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,6,7,4,1,3,5]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,6,7,4,1,5,3]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,6,7,4,3,1,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,6,7,4,3,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,6,7,4,5,1,3]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,6,7,4,5,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,6,7,5,1,3,4]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,6,7,5,1,4,3]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,6,7,5,3,1,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,6,7,5,3,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,6,7,5,4,1,3]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,6,7,5,4,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,7,1,3,4,5,6]=>[3,7,1,4,5,6,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,7,1,3,4,6,5]=>[3,7,1,4,5,6,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,7,1,3,5,4,6]=>[3,7,1,4,6,5,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,7,1,3,5,6,4]=>[3,7,1,4,6,5,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,7,1,3,6,4,5]=>[3,7,1,4,6,5,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,7,1,3,6,5,4]=>[3,7,1,4,6,5,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,7,1,4,3,5,6]=>[3,7,1,5,4,6,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,7,1,4,3,6,5]=>[3,7,1,5,4,6,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,7,1,4,5,3,6]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,7,1,4,5,6,3]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,7,1,4,6,3,5]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,7,1,4,6,5,3]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,7,1,5,3,4,6]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,7,1,5,3,6,4]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,7,1,5,4,3,6]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,7,1,5,4,6,3]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,7,1,5,6,3,4]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,7,1,5,6,4,3]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,7,1,6,3,4,5]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,7,1,6,3,5,4]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,7,1,6,4,3,5]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,7,1,6,4,5,3]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,7,1,6,5,3,4]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,7,1,6,5,4,3]=>[3,7,1,6,5,4,2]=>[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[2,7,3,1,4,5,6]=>[4,7,3,1,5,6,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,7,3,1,4,6,5]=>[4,7,3,1,5,6,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,7,3,1,5,4,6]=>[4,7,3,1,6,5,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,7,3,1,5,6,4]=>[4,7,3,1,6,5,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,7,3,1,6,4,5]=>[4,7,3,1,6,5,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,7,3,1,6,5,4]=>[4,7,3,1,6,5,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[2,7,3,4,1,5,6]=>[5,7,3,4,1,6,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[2,7,3,4,1,6,5]=>[5,7,3,4,1,6,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[2,7,3,4,5,1,6]=>[6,7,3,4,5,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[2,7,3,4,5,6,1]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[2,7,3,4,6,1,5]=>[6,7,3,4,5,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[2,7,3,4,6,5,1]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[2,7,3,5,1,4,6]=>[5,7,3,6,1,4,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[2,7,3,5,1,6,4]=>[5,7,3,6,1,4,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[2,7,3,5,4,1,6]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[2,7,3,5,4,6,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[2,7,3,5,6,1,4]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[2,7,3,5,6,4,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[2,7,3,6,1,4,5]=>[5,7,3,6,1,4,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[2,7,3,6,1,5,4]=>[5,7,3,6,1,4,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[2,7,3,6,4,1,5]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[2,7,3,6,4,5,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[2,7,3,6,5,1,4]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[2,7,3,6,5,4,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[2,7,4,1,3,5,6]=>[4,7,5,1,3,6,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,7,4,1,3,6,5]=>[4,7,5,1,3,6,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,7,4,1,5,3,6]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,7,4,1,5,6,3]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,7,4,1,6,3,5]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,7,4,1,6,5,3]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,7,4,3,1,5,6]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[2,7,4,3,1,6,5]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[2,7,4,3,5,1,6]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[2,7,4,3,5,6,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[2,7,4,3,6,1,5]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[2,7,4,3,6,5,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[2,7,4,5,1,3,6]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,7,4,5,1,6,3]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,7,4,5,3,1,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,7,4,5,3,6,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,7,4,5,6,1,3]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,7,4,5,6,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,7,4,6,1,3,5]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,7,4,6,1,5,3]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,7,4,6,3,1,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,7,4,6,3,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,7,4,6,5,1,3]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,7,4,6,5,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,7,5,1,3,4,6]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,7,5,1,3,6,4]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,7,5,1,4,3,6]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,7,5,1,4,6,3]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,7,5,1,6,3,4]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,7,5,1,6,4,3]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,7,5,3,1,4,6]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,7,5,3,1,6,4]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,7,5,3,4,1,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,7,5,3,4,6,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,7,5,3,6,1,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,7,5,3,6,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,7,5,4,1,3,6]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,7,5,4,1,6,3]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,7,5,4,3,1,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,7,5,4,3,6,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,7,5,4,6,1,3]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,7,5,4,6,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,7,5,6,1,3,4]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,7,5,6,1,4,3]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,7,5,6,3,1,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,7,5,6,3,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,7,5,6,4,1,3]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,7,5,6,4,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,7,6,1,3,4,5]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,7,6,1,3,5,4]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,7,6,1,4,3,5]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,7,6,1,4,5,3]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,7,6,1,5,3,4]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,7,6,1,5,4,3]=>[4,7,6,1,5,3,2]=>[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[2,7,6,3,1,4,5]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,7,6,3,1,5,4]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,7,6,3,4,1,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,7,6,3,4,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,7,6,3,5,1,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,7,6,3,5,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,7,6,4,1,3,5]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,7,6,4,1,5,3]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,7,6,4,3,1,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,7,6,4,3,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,7,6,4,5,1,3]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,7,6,4,5,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,7,6,5,1,3,4]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,7,6,5,1,4,3]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[2,7,6,5,3,1,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,7,6,5,3,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[2,7,6,5,4,1,3]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[2,7,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,1,2,4,5,6,7]=>[3,2,1,4,5,6,7]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,1,2,4,5,7,6]=>[3,2,1,4,5,7,6]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,1,2,4,6,5,7]=>[3,2,1,4,6,5,7]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,1,2,4,6,7,5]=>[3,2,1,4,7,6,5]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,1,2,4,7,5,6]=>[3,2,1,4,7,6,5]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,1,2,4,7,6,5]=>[3,2,1,4,7,6,5]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,1,2,5,4,6,7]=>[3,2,1,5,4,6,7]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,1,2,5,4,7,6]=>[3,2,1,5,4,7,6]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,1,2,5,6,4,7]=>[3,2,1,6,5,4,7]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,1,2,5,6,7,4]=>[3,2,1,7,5,6,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,1,2,5,7,4,6]=>[3,2,1,6,7,4,5]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,1,2,5,7,6,4]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,1,2,6,4,5,7]=>[3,2,1,6,5,4,7]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,1,2,6,4,7,5]=>[3,2,1,7,5,6,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,1,2,6,5,4,7]=>[3,2,1,6,5,4,7]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,1,2,6,5,7,4]=>[3,2,1,7,5,6,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,1,2,6,7,4,5]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,1,2,6,7,5,4]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,1,2,7,4,5,6]=>[3,2,1,7,5,6,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,1,2,7,4,6,5]=>[3,2,1,7,5,6,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,1,2,7,5,4,6]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,1,2,7,5,6,4]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,1,2,7,6,4,5]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,1,2,7,6,5,4]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,1,4,2,5,6,7]=>[4,2,3,1,5,6,7]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,1,4,2,5,7,6]=>[4,2,3,1,5,7,6]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,1,4,2,6,5,7]=>[4,2,3,1,6,5,7]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,1,4,2,6,7,5]=>[4,2,3,1,7,6,5]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,1,4,2,7,5,6]=>[4,2,3,1,7,6,5]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,1,4,2,7,6,5]=>[4,2,3,1,7,6,5]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,1,4,5,2,6,7]=>[5,2,3,4,1,6,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,1,4,5,2,7,6]=>[5,2,3,4,1,7,6]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,1,4,5,6,2,7]=>[6,2,3,4,5,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,1,4,5,6,7,2]=>[7,2,3,4,5,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,1,4,5,7,2,6]=>[6,2,3,4,7,1,5]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,1,4,5,7,6,2]=>[7,2,3,4,6,5,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,1,4,6,2,5,7]=>[5,2,3,6,1,4,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,1,4,6,2,7,5]=>[5,2,3,7,1,6,4]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,1,4,6,5,2,7]=>[6,2,3,5,4,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,1,4,6,5,7,2]=>[7,2,3,5,4,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,1,4,6,7,2,5]=>[6,2,3,7,5,1,4]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,1,4,6,7,5,2]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,1,4,7,2,5,6]=>[5,2,3,7,1,6,4]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,1,4,7,2,6,5]=>[5,2,3,7,1,6,4]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,1,4,7,5,2,6]=>[6,2,3,7,5,1,4]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,1,4,7,5,6,2]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,1,4,7,6,2,5]=>[6,2,3,7,5,1,4]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,1,4,7,6,5,2]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,1,5,2,4,6,7]=>[4,2,5,1,3,6,7]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,1,5,2,4,7,6]=>[4,2,5,1,3,7,6]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,1,5,2,6,4,7]=>[4,2,6,1,5,3,7]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,1,5,2,6,7,4]=>[4,2,7,1,5,6,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,1,5,2,7,4,6]=>[4,2,6,1,7,3,5]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,1,5,2,7,6,4]=>[4,2,7,1,6,5,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,1,5,4,2,6,7]=>[5,2,4,3,1,6,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,1,5,4,2,7,6]=>[5,2,4,3,1,7,6]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,1,5,4,6,2,7]=>[6,2,4,3,5,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,1,5,4,6,7,2]=>[7,2,4,3,5,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,1,5,4,7,2,6]=>[6,2,4,3,7,1,5]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,1,5,4,7,6,2]=>[7,2,4,3,6,5,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,1,5,6,2,4,7]=>[5,2,6,4,1,3,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,1,5,6,2,7,4]=>[5,2,7,4,1,6,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,1,5,6,4,2,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,1,5,6,4,7,2]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,1,5,6,7,2,4]=>[6,2,7,4,5,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,1,5,6,7,4,2]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,1,5,7,2,4,6]=>[5,2,6,7,1,3,4]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,1,5,7,2,6,4]=>[5,2,7,6,1,4,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,1,5,7,4,2,6]=>[6,2,5,7,3,1,4]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,1,5,7,4,6,2]=>[7,2,5,6,3,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,1,5,7,6,2,4]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,1,5,7,6,4,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,1,6,2,4,5,7]=>[4,2,6,1,5,3,7]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,1,6,2,4,7,5]=>[4,2,7,1,5,6,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,1,6,2,5,4,7]=>[4,2,6,1,5,3,7]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,1,6,2,5,7,4]=>[4,2,7,1,5,6,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,1,6,2,7,4,5]=>[4,2,7,1,6,5,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,1,6,2,7,5,4]=>[4,2,7,1,6,5,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,1,6,4,2,5,7]=>[5,2,6,4,1,3,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,1,6,4,2,7,5]=>[5,2,7,4,1,6,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,1,6,4,5,2,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,1,6,4,5,7,2]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,1,6,4,7,2,5]=>[6,2,7,4,5,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,1,6,4,7,5,2]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,1,6,5,2,4,7]=>[5,2,6,4,1,3,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,1,6,5,2,7,4]=>[5,2,7,4,1,6,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,1,6,5,4,2,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,1,6,5,4,7,2]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,1,6,5,7,2,4]=>[6,2,7,4,5,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,1,6,5,7,4,2]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,1,6,7,2,4,5]=>[5,2,7,6,1,4,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,1,6,7,2,5,4]=>[5,2,7,6,1,4,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,1,6,7,4,2,5]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,1,6,7,4,5,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,1,6,7,5,2,4]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,1,6,7,5,4,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,1,7,2,4,5,6]=>[4,2,7,1,5,6,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,1,7,2,4,6,5]=>[4,2,7,1,5,6,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,1,7,2,5,4,6]=>[4,2,7,1,6,5,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,1,7,2,5,6,4]=>[4,2,7,1,6,5,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,1,7,2,6,4,5]=>[4,2,7,1,6,5,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,1,7,2,6,5,4]=>[4,2,7,1,6,5,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,1,7,4,2,5,6]=>[5,2,7,4,1,6,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,1,7,4,2,6,5]=>[5,2,7,4,1,6,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,1,7,4,5,2,6]=>[6,2,7,4,5,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,1,7,4,5,6,2]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,1,7,4,6,2,5]=>[6,2,7,4,5,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,1,7,4,6,5,2]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,1,7,5,2,4,6]=>[5,2,7,6,1,4,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,1,7,5,2,6,4]=>[5,2,7,6,1,4,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,1,7,5,4,2,6]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,1,7,5,4,6,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,1,7,5,6,2,4]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,1,7,5,6,4,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,1,7,6,2,4,5]=>[5,2,7,6,1,4,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,1,7,6,2,5,4]=>[5,2,7,6,1,4,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,1,7,6,4,2,5]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,1,7,6,4,5,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,1,7,6,5,2,4]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,1,7,6,5,4,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,2,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,2,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,2,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,2,1,4,7,5,6]=>[3,2,1,4,7,6,5]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,2,1,4,7,6,5]=>[3,2,1,4,7,6,5]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,2,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,2,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,2,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,2,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,2,1,5,7,4,6]=>[3,2,1,6,7,4,5]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,2,1,5,7,6,4]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,2,1,6,4,5,7]=>[3,2,1,6,5,4,7]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,2,1,6,4,7,5]=>[3,2,1,7,5,6,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,2,1,6,5,4,7]=>[3,2,1,6,5,4,7]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,2,1,6,5,7,4]=>[3,2,1,7,5,6,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,2,1,6,7,4,5]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,2,1,6,7,5,4]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,2,1,7,4,5,6]=>[3,2,1,7,5,6,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,2,1,7,4,6,5]=>[3,2,1,7,5,6,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,2,1,7,5,4,6]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,2,1,7,5,6,4]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,2,1,7,6,4,5]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[3,2,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,2,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,2,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,2,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,2,4,1,7,5,6]=>[4,2,3,1,7,6,5]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,2,4,1,7,6,5]=>[4,2,3,1,7,6,5]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,2,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,2,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,2,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,2,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,2,4,5,7,1,6]=>[6,2,3,4,7,1,5]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,2,4,5,7,6,1]=>[7,2,3,4,6,5,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,2,4,6,1,5,7]=>[5,2,3,6,1,4,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,2,4,6,1,7,5]=>[5,2,3,7,1,6,4]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,2,4,6,5,1,7]=>[6,2,3,5,4,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,2,4,6,5,7,1]=>[7,2,3,5,4,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,2,4,6,7,1,5]=>[6,2,3,7,5,1,4]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,2,4,6,7,5,1]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,2,4,7,1,5,6]=>[5,2,3,7,1,6,4]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,2,4,7,1,6,5]=>[5,2,3,7,1,6,4]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,2,4,7,5,1,6]=>[6,2,3,7,5,1,4]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,2,4,7,5,6,1]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,2,4,7,6,1,5]=>[6,2,3,7,5,1,4]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,2,4,7,6,5,1]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,2,5,1,4,6,7]=>[4,2,5,1,3,6,7]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,2,5,1,4,7,6]=>[4,2,5,1,3,7,6]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,2,5,1,6,4,7]=>[4,2,6,1,5,3,7]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,2,5,1,6,7,4]=>[4,2,7,1,5,6,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,2,5,1,7,4,6]=>[4,2,6,1,7,3,5]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,2,5,1,7,6,4]=>[4,2,7,1,6,5,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,2,5,4,1,6,7]=>[5,2,4,3,1,6,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,2,5,4,1,7,6]=>[5,2,4,3,1,7,6]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,2,5,4,6,1,7]=>[6,2,4,3,5,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,2,5,4,6,7,1]=>[7,2,4,3,5,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,2,5,4,7,1,6]=>[6,2,4,3,7,1,5]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,2,5,4,7,6,1]=>[7,2,4,3,6,5,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,2,5,6,1,4,7]=>[5,2,6,4,1,3,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,2,5,6,1,7,4]=>[5,2,7,4,1,6,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,2,5,6,4,1,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,2,5,6,4,7,1]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,2,5,6,7,1,4]=>[6,2,7,4,5,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,2,5,6,7,4,1]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,2,5,7,1,4,6]=>[5,2,6,7,1,3,4]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,2,5,7,1,6,4]=>[5,2,7,6,1,4,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,2,5,7,4,1,6]=>[6,2,5,7,3,1,4]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,2,5,7,4,6,1]=>[7,2,5,6,3,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,2,5,7,6,1,4]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,2,5,7,6,4,1]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,2,6,1,4,5,7]=>[4,2,6,1,5,3,7]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,2,6,1,4,7,5]=>[4,2,7,1,5,6,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,2,6,1,5,4,7]=>[4,2,6,1,5,3,7]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,2,6,1,5,7,4]=>[4,2,7,1,5,6,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,2,6,1,7,4,5]=>[4,2,7,1,6,5,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,2,6,1,7,5,4]=>[4,2,7,1,6,5,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,2,6,4,1,5,7]=>[5,2,6,4,1,3,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,2,6,4,1,7,5]=>[5,2,7,4,1,6,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,2,6,4,5,1,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,2,6,4,5,7,1]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,2,6,4,7,1,5]=>[6,2,7,4,5,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,2,6,4,7,5,1]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,2,6,5,1,4,7]=>[5,2,6,4,1,3,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,2,6,5,1,7,4]=>[5,2,7,4,1,6,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,2,6,5,4,1,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,2,6,5,4,7,1]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,2,6,5,7,1,4]=>[6,2,7,4,5,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,2,6,5,7,4,1]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,2,6,7,1,4,5]=>[5,2,7,6,1,4,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,2,6,7,1,5,4]=>[5,2,7,6,1,4,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,2,6,7,4,1,5]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,2,6,7,4,5,1]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,2,6,7,5,1,4]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,2,6,7,5,4,1]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,2,7,1,4,5,6]=>[4,2,7,1,5,6,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,2,7,1,4,6,5]=>[4,2,7,1,5,6,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,2,7,1,5,4,6]=>[4,2,7,1,6,5,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,2,7,1,5,6,4]=>[4,2,7,1,6,5,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,2,7,1,6,4,5]=>[4,2,7,1,6,5,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,2,7,1,6,5,4]=>[4,2,7,1,6,5,3]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[3,2,7,4,1,5,6]=>[5,2,7,4,1,6,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,2,7,4,1,6,5]=>[5,2,7,4,1,6,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,2,7,4,5,1,6]=>[6,2,7,4,5,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,2,7,4,5,6,1]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,2,7,4,6,1,5]=>[6,2,7,4,5,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,2,7,4,6,5,1]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,2,7,5,1,4,6]=>[5,2,7,6,1,4,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,2,7,5,1,6,4]=>[5,2,7,6,1,4,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,2,7,5,4,1,6]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,2,7,5,4,6,1]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,2,7,5,6,1,4]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,2,7,5,6,4,1]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,2,7,6,1,4,5]=>[5,2,7,6,1,4,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,2,7,6,1,5,4]=>[5,2,7,6,1,4,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[3,2,7,6,4,1,5]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,2,7,6,4,5,1]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,2,7,6,5,1,4]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[3,2,7,6,5,4,1]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[3,4,1,2,5,6,7]=>[4,3,2,1,5,6,7]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[3,4,1,2,5,7,6]=>[4,3,2,1,5,7,6]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[3,4,1,2,6,5,7]=>[4,3,2,1,6,5,7]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[3,4,1,2,6,7,5]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[3,4,1,2,7,5,6]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[3,4,1,2,7,6,5]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[3,4,1,5,2,6,7]=>[5,3,2,4,1,6,7]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[3,4,1,5,2,7,6]=>[5,3,2,4,1,7,6]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[3,4,1,5,6,2,7]=>[6,3,2,4,5,1,7]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[3,4,1,5,6,7,2]=>[7,3,2,4,5,6,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[3,4,1,5,7,2,6]=>[6,3,2,4,7,1,5]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[3,4,1,5,7,6,2]=>[7,3,2,4,6,5,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[3,4,1,6,2,5,7]=>[5,3,2,6,1,4,7]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[3,4,1,6,2,7,5]=>[5,3,2,7,1,6,4]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[3,4,1,6,5,2,7]=>[6,3,2,5,4,1,7]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[3,4,1,6,5,7,2]=>[7,3,2,5,4,6,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[3,4,1,6,7,2,5]=>[6,3,2,7,5,1,4]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[3,4,1,6,7,5,2]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[3,4,1,7,2,5,6]=>[5,3,2,7,1,6,4]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[3,4,1,7,2,6,5]=>[5,3,2,7,1,6,4]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[3,4,1,7,5,2,6]=>[6,3,2,7,5,1,4]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[3,4,1,7,5,6,2]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[3,4,1,7,6,2,5]=>[6,3,2,7,5,1,4]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[3,4,1,7,6,5,2]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[3,4,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[3,4,2,1,5,7,6]=>[4,3,2,1,5,7,6]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[3,4,2,1,6,5,7]=>[4,3,2,1,6,5,7]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[3,4,2,1,6,7,5]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[3,4,2,1,7,5,6]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[3,4,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[3,4,2,5,1,6,7]=>[5,3,2,4,1,6,7]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[3,4,2,5,1,7,6]=>[5,3,2,4,1,7,6]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[3,4,2,5,6,1,7]=>[6,3,2,4,5,1,7]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[3,4,2,5,6,7,1]=>[7,3,2,4,5,6,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[3,4,2,5,7,1,6]=>[6,3,2,4,7,1,5]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[3,4,2,5,7,6,1]=>[7,3,2,4,6,5,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[3,4,2,6,1,5,7]=>[5,3,2,6,1,4,7]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[3,4,2,6,1,7,5]=>[5,3,2,7,1,6,4]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[3,4,2,6,5,1,7]=>[6,3,2,5,4,1,7]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[3,4,2,6,5,7,1]=>[7,3,2,5,4,6,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[3,4,2,6,7,1,5]=>[6,3,2,7,5,1,4]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[3,4,2,6,7,5,1]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[3,4,2,7,1,5,6]=>[5,3,2,7,1,6,4]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[3,4,2,7,1,6,5]=>[5,3,2,7,1,6,4]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[3,4,2,7,5,1,6]=>[6,3,2,7,5,1,4]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[3,4,2,7,5,6,1]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[3,4,2,7,6,1,5]=>[6,3,2,7,5,1,4]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[3,4,2,7,6,5,1]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[3,4,5,1,2,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[3,4,5,1,2,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[3,4,5,1,6,2,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[3,4,5,1,6,7,2]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[3,4,5,1,7,2,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[3,4,5,1,7,6,2]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[3,4,5,2,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[3,4,5,2,1,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[3,4,5,2,6,1,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[3,4,5,2,6,7,1]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[3,4,5,2,7,1,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[3,4,5,2,7,6,1]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[3,4,5,6,1,2,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[3,4,5,6,1,7,2]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[3,4,5,6,2,1,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[3,4,5,6,2,7,1]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[3,4,5,6,7,1,2]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,4,5,6,7,2,1]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,4,5,7,1,2,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[3,4,5,7,1,6,2]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[3,4,5,7,2,1,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[3,4,5,7,2,6,1]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[3,4,5,7,6,1,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,4,5,7,6,2,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,4,6,1,2,5,7]=>[5,4,6,2,1,3,7]=>[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[3,4,6,1,2,7,5]=>[5,4,7,2,1,6,3]=>[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[3,4,6,1,5,2,7]=>[6,4,5,2,3,1,7]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[3,4,6,1,5,7,2]=>[7,4,5,2,3,6,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[3,4,6,1,7,2,5]=>[6,4,7,2,5,1,3]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[3,4,6,1,7,5,2]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[3,4,6,2,1,5,7]=>[5,4,6,2,1,3,7]=>[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[3,4,6,2,1,7,5]=>[5,4,7,2,1,6,3]=>[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[3,4,6,2,5,1,7]=>[6,4,5,2,3,1,7]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[3,4,6,2,5,7,1]=>[7,4,5,2,3,6,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[3,4,6,2,7,1,5]=>[6,4,7,2,5,1,3]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[3,4,6,2,7,5,1]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[3,4,6,5,1,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[3,4,6,5,1,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[3,4,6,5,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[3,4,6,5,2,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[3,4,6,5,7,1,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[3,4,6,5,7,2,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[3,4,6,7,1,2,5]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[3,4,6,7,1,5,2]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[3,4,6,7,2,1,5]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[3,4,6,7,2,5,1]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[3,4,6,7,5,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,4,6,7,5,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,4,7,1,2,5,6]=>[5,4,7,2,1,6,3]=>[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[3,4,7,1,2,6,5]=>[5,4,7,2,1,6,3]=>[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[3,4,7,1,5,2,6]=>[6,4,7,2,5,1,3]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[3,4,7,1,5,6,2]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[3,4,7,1,6,2,5]=>[6,4,7,2,5,1,3]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[3,4,7,1,6,5,2]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[3,4,7,2,1,5,6]=>[5,4,7,2,1,6,3]=>[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[3,4,7,2,1,6,5]=>[5,4,7,2,1,6,3]=>[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[3,4,7,2,5,1,6]=>[6,4,7,2,5,1,3]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[3,4,7,2,5,6,1]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[3,4,7,2,6,1,5]=>[6,4,7,2,5,1,3]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[3,4,7,2,6,5,1]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[3,4,7,5,1,2,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[3,4,7,5,1,6,2]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[3,4,7,5,2,1,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[3,4,7,5,2,6,1]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[3,4,7,5,6,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,4,7,5,6,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,4,7,6,1,2,5]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[3,4,7,6,1,5,2]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[3,4,7,6,2,1,5]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[3,4,7,6,2,5,1]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[3,4,7,6,5,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,4,7,6,5,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,5,1,2,4,6,7]=>[4,5,3,1,2,6,7]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,5,1,2,4,7,6]=>[4,5,3,1,2,7,6]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,5,1,2,6,4,7]=>[4,6,3,1,5,2,7]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,5,1,2,6,7,4]=>[4,7,3,1,5,6,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,5,1,2,7,4,6]=>[4,6,3,1,7,2,5]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,5,1,2,7,6,4]=>[4,7,3,1,6,5,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,5,1,4,2,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[3,5,1,4,2,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[3,5,1,4,6,2,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[3,5,1,4,6,7,2]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[3,5,1,4,7,2,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[3,5,1,4,7,6,2]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[3,5,1,6,2,4,7]=>[5,6,3,4,1,2,7]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,5,1,6,2,7,4]=>[5,7,3,4,1,6,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,5,1,6,4,2,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[3,5,1,6,4,7,2]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[3,5,1,6,7,2,4]=>[6,7,3,4,5,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[3,5,1,6,7,4,2]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,5,1,7,2,4,6]=>[5,6,3,7,1,2,4]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,5,1,7,2,6,4]=>[5,7,3,6,1,4,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,5,1,7,4,2,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[3,5,1,7,4,6,2]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[3,5,1,7,6,2,4]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[3,5,1,7,6,4,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,5,2,1,4,6,7]=>[4,5,3,1,2,6,7]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,5,2,1,4,7,6]=>[4,5,3,1,2,7,6]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,5,2,1,6,4,7]=>[4,6,3,1,5,2,7]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,5,2,1,6,7,4]=>[4,7,3,1,5,6,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,5,2,1,7,4,6]=>[4,6,3,1,7,2,5]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,5,2,1,7,6,4]=>[4,7,3,1,6,5,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,5,2,4,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[3,5,2,4,1,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[3,5,2,4,6,1,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[3,5,2,4,6,7,1]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[3,5,2,4,7,1,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[3,5,2,4,7,6,1]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[3,5,2,6,1,4,7]=>[5,6,3,4,1,2,7]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,5,2,6,1,7,4]=>[5,7,3,4,1,6,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,5,2,6,4,1,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[3,5,2,6,4,7,1]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[3,5,2,6,7,1,4]=>[6,7,3,4,5,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[3,5,2,6,7,4,1]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,5,2,7,1,4,6]=>[5,6,3,7,1,2,4]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,5,2,7,1,6,4]=>[5,7,3,6,1,4,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,5,2,7,4,1,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[3,5,2,7,4,6,1]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[3,5,2,7,6,1,4]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[3,5,2,7,6,4,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,5,4,1,2,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[3,5,4,1,2,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[3,5,4,1,6,2,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[3,5,4,1,6,7,2]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[3,5,4,1,7,2,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[3,5,4,1,7,6,2]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[3,5,4,2,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[3,5,4,2,1,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[3,5,4,2,6,1,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[3,5,4,2,6,7,1]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[3,5,4,2,7,1,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[3,5,4,2,7,6,1]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[3,5,4,6,1,2,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[3,5,4,6,1,7,2]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[3,5,4,6,2,1,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[3,5,4,6,2,7,1]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[3,5,4,6,7,1,2]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,5,4,6,7,2,1]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,5,4,7,1,2,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[3,5,4,7,1,6,2]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[3,5,4,7,2,1,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[3,5,4,7,2,6,1]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[3,5,4,7,6,1,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,5,4,7,6,2,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,5,6,1,2,4,7]=>[5,6,4,3,1,2,7]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[3,5,6,1,2,7,4]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[3,5,6,1,4,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[3,5,6,1,4,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[3,5,6,1,7,2,4]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[3,5,6,1,7,4,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[3,5,6,2,1,4,7]=>[5,6,4,3,1,2,7]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[3,5,6,2,1,7,4]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[3,5,6,2,4,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[3,5,6,2,4,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[3,5,6,2,7,1,4]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[3,5,6,2,7,4,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[3,5,6,4,1,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[3,5,6,4,1,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[3,5,6,4,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[3,5,6,4,2,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[3,5,6,4,7,1,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[3,5,6,4,7,2,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[3,5,6,7,1,2,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,5,6,7,1,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,5,6,7,2,1,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,5,6,7,2,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,5,6,7,4,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,5,6,7,4,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,5,7,1,2,4,6]=>[5,6,7,4,1,2,3]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[3,5,7,1,2,6,4]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[3,5,7,1,4,2,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[3,5,7,1,4,6,2]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[3,5,7,1,6,2,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,5,7,1,6,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,5,7,2,1,4,6]=>[5,6,7,4,1,2,3]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[3,5,7,2,1,6,4]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[3,5,7,2,4,1,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[3,5,7,2,4,6,1]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[3,5,7,2,6,1,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,5,7,2,6,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,5,7,4,1,2,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[3,5,7,4,1,6,2]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[3,5,7,4,2,1,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[3,5,7,4,2,6,1]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[3,5,7,4,6,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,5,7,4,6,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,5,7,6,1,2,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,5,7,6,1,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,5,7,6,2,1,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,5,7,6,2,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,5,7,6,4,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,5,7,6,4,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,6,1,2,4,5,7]=>[4,6,3,1,5,2,7]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,6,1,2,4,7,5]=>[4,7,3,1,5,6,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,6,1,2,5,4,7]=>[4,6,3,1,5,2,7]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,6,1,2,5,7,4]=>[4,7,3,1,5,6,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,6,1,2,7,4,5]=>[4,7,3,1,6,5,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,6,1,2,7,5,4]=>[4,7,3,1,6,5,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,6,1,4,2,5,7]=>[5,6,3,4,1,2,7]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,6,1,4,2,7,5]=>[5,7,3,4,1,6,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,6,1,4,5,2,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[3,6,1,4,5,7,2]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[3,6,1,4,7,2,5]=>[6,7,3,4,5,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[3,6,1,4,7,5,2]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,6,1,5,2,4,7]=>[5,6,3,4,1,2,7]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,6,1,5,2,7,4]=>[5,7,3,4,1,6,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,6,1,5,4,2,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[3,6,1,5,4,7,2]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[3,6,1,5,7,2,4]=>[6,7,3,4,5,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[3,6,1,5,7,4,2]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,6,1,7,2,4,5]=>[5,7,3,6,1,4,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,6,1,7,2,5,4]=>[5,7,3,6,1,4,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,6,1,7,4,2,5]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[3,6,1,7,4,5,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,6,1,7,5,2,4]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[3,6,1,7,5,4,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,6,2,1,4,5,7]=>[4,6,3,1,5,2,7]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,6,2,1,4,7,5]=>[4,7,3,1,5,6,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,6,2,1,5,4,7]=>[4,6,3,1,5,2,7]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,6,2,1,5,7,4]=>[4,7,3,1,5,6,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,6,2,1,7,4,5]=>[4,7,3,1,6,5,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,6,2,1,7,5,4]=>[4,7,3,1,6,5,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,6,2,4,1,5,7]=>[5,6,3,4,1,2,7]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,6,2,4,1,7,5]=>[5,7,3,4,1,6,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,6,2,4,5,1,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[3,6,2,4,5,7,1]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[3,6,2,4,7,1,5]=>[6,7,3,4,5,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[3,6,2,4,7,5,1]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,6,2,5,1,4,7]=>[5,6,3,4,1,2,7]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,6,2,5,1,7,4]=>[5,7,3,4,1,6,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,6,2,5,4,1,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[3,6,2,5,4,7,1]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[3,6,2,5,7,1,4]=>[6,7,3,4,5,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[3,6,2,5,7,4,1]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,6,2,7,1,4,5]=>[5,7,3,6,1,4,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,6,2,7,1,5,4]=>[5,7,3,6,1,4,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,6,2,7,4,1,5]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[3,6,2,7,4,5,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,6,2,7,5,1,4]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[3,6,2,7,5,4,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,6,4,1,2,5,7]=>[5,6,4,3,1,2,7]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[3,6,4,1,2,7,5]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[3,6,4,1,5,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[3,6,4,1,5,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[3,6,4,1,7,2,5]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[3,6,4,1,7,5,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[3,6,4,2,1,5,7]=>[5,6,4,3,1,2,7]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[3,6,4,2,1,7,5]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[3,6,4,2,5,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[3,6,4,2,5,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[3,6,4,2,7,1,5]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[3,6,4,2,7,5,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[3,6,4,5,1,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[3,6,4,5,1,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[3,6,4,5,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[3,6,4,5,2,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[3,6,4,5,7,1,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[3,6,4,5,7,2,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[3,6,4,7,1,2,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,6,4,7,1,5,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,6,4,7,2,1,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,6,4,7,2,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,6,4,7,5,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,6,4,7,5,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,6,5,1,2,4,7]=>[5,6,4,3,1,2,7]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[3,6,5,1,2,7,4]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[3,6,5,1,4,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[3,6,5,1,4,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[3,6,5,1,7,2,4]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[3,6,5,1,7,4,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[3,6,5,2,1,4,7]=>[5,6,4,3,1,2,7]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[3,6,5,2,1,7,4]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[3,6,5,2,4,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[3,6,5,2,4,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[3,6,5,2,7,1,4]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[3,6,5,2,7,4,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[3,6,5,4,1,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[3,6,5,4,1,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[3,6,5,4,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[3,6,5,4,2,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[3,6,5,4,7,1,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[3,6,5,4,7,2,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[3,6,5,7,1,2,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,6,5,7,1,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,6,5,7,2,1,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,6,5,7,2,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,6,5,7,4,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,6,5,7,4,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,6,7,1,2,4,5]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[3,6,7,1,2,5,4]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[3,6,7,1,4,2,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,6,7,1,4,5,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,6,7,1,5,2,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,6,7,1,5,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,6,7,2,1,4,5]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[3,6,7,2,1,5,4]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[3,6,7,2,4,1,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,6,7,2,4,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,6,7,2,5,1,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,6,7,2,5,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,6,7,4,1,2,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,6,7,4,1,5,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,6,7,4,2,1,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,6,7,4,2,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,6,7,4,5,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,6,7,4,5,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,6,7,5,1,2,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,6,7,5,1,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,6,7,5,2,1,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,6,7,5,2,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,6,7,5,4,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,6,7,5,4,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,1,2,4,5,6]=>[4,7,3,1,5,6,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,7,1,2,4,6,5]=>[4,7,3,1,5,6,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,7,1,2,5,4,6]=>[4,7,3,1,6,5,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,7,1,2,5,6,4]=>[4,7,3,1,6,5,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,7,1,2,6,4,5]=>[4,7,3,1,6,5,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,7,1,2,6,5,4]=>[4,7,3,1,6,5,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,7,1,4,2,5,6]=>[5,7,3,4,1,6,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,7,1,4,2,6,5]=>[5,7,3,4,1,6,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,7,1,4,5,2,6]=>[6,7,3,4,5,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[3,7,1,4,5,6,2]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,7,1,4,6,2,5]=>[6,7,3,4,5,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[3,7,1,4,6,5,2]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,7,1,5,2,4,6]=>[5,7,3,6,1,4,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,7,1,5,2,6,4]=>[5,7,3,6,1,4,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,7,1,5,4,2,6]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[3,7,1,5,4,6,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,7,1,5,6,2,4]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[3,7,1,5,6,4,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,7,1,6,2,4,5]=>[5,7,3,6,1,4,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,7,1,6,2,5,4]=>[5,7,3,6,1,4,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,7,1,6,4,2,5]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[3,7,1,6,4,5,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,7,1,6,5,2,4]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[3,7,1,6,5,4,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,7,2,1,4,5,6]=>[4,7,3,1,5,6,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,7,2,1,4,6,5]=>[4,7,3,1,5,6,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,7,2,1,5,4,6]=>[4,7,3,1,6,5,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,7,2,1,5,6,4]=>[4,7,3,1,6,5,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,7,2,1,6,4,5]=>[4,7,3,1,6,5,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,7,2,1,6,5,4]=>[4,7,3,1,6,5,2]=>[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[3,7,2,4,1,5,6]=>[5,7,3,4,1,6,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,7,2,4,1,6,5]=>[5,7,3,4,1,6,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,7,2,4,5,1,6]=>[6,7,3,4,5,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[3,7,2,4,5,6,1]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,7,2,4,6,1,5]=>[6,7,3,4,5,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[3,7,2,4,6,5,1]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,7,2,5,1,4,6]=>[5,7,3,6,1,4,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,7,2,5,1,6,4]=>[5,7,3,6,1,4,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,7,2,5,4,1,6]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[3,7,2,5,4,6,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,7,2,5,6,1,4]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[3,7,2,5,6,4,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,7,2,6,1,4,5]=>[5,7,3,6,1,4,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,7,2,6,1,5,4]=>[5,7,3,6,1,4,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[3,7,2,6,4,1,5]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[3,7,2,6,4,5,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,7,2,6,5,1,4]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[3,7,2,6,5,4,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[3,7,4,1,2,5,6]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[3,7,4,1,2,6,5]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[3,7,4,1,5,2,6]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[3,7,4,1,5,6,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[3,7,4,1,6,2,5]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[3,7,4,1,6,5,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[3,7,4,2,1,5,6]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[3,7,4,2,1,6,5]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[3,7,4,2,5,1,6]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[3,7,4,2,5,6,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[3,7,4,2,6,1,5]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[3,7,4,2,6,5,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[3,7,4,5,1,2,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,7,4,5,1,6,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,4,5,2,1,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,7,4,5,2,6,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,4,5,6,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,4,5,6,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,4,6,1,2,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,7,4,6,1,5,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,4,6,2,1,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,7,4,6,2,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,4,6,5,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,4,6,5,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,5,1,2,4,6]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[3,7,5,1,2,6,4]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[3,7,5,1,4,2,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,7,5,1,4,6,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,5,1,6,2,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,7,5,1,6,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,5,2,1,4,6]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[3,7,5,2,1,6,4]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[3,7,5,2,4,1,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,7,5,2,4,6,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,5,2,6,1,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,7,5,2,6,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,5,4,1,2,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,7,5,4,1,6,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,5,4,2,1,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,7,5,4,2,6,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,5,4,6,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,5,4,6,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,5,6,1,2,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,7,5,6,1,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,5,6,2,1,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,7,5,6,2,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,5,6,4,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,5,6,4,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,6,1,2,4,5]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[3,7,6,1,2,5,4]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[3,7,6,1,4,2,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,7,6,1,4,5,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,6,1,5,2,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,7,6,1,5,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,6,2,1,4,5]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[3,7,6,2,1,5,4]=>[5,7,6,4,1,3,2]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[3,7,6,2,4,1,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,7,6,2,4,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,6,2,5,1,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,7,6,2,5,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,6,4,1,2,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,7,6,4,1,5,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,6,4,2,1,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,7,6,4,2,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,6,4,5,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,6,4,5,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,6,5,1,2,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,7,6,5,1,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,6,5,2,1,4]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[3,7,6,5,2,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,6,5,4,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[3,7,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,1,2,3,5,6,7]=>[4,2,3,1,5,6,7]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[4,1,2,3,5,7,6]=>[4,2,3,1,5,7,6]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[4,1,2,3,6,5,7]=>[4,2,3,1,6,5,7]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[4,1,2,3,6,7,5]=>[4,2,3,1,7,6,5]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[4,1,2,3,7,5,6]=>[4,2,3,1,7,6,5]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[4,1,2,3,7,6,5]=>[4,2,3,1,7,6,5]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[4,1,2,5,3,6,7]=>[5,2,3,4,1,6,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[4,1,2,5,3,7,6]=>[5,2,3,4,1,7,6]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[4,1,2,5,6,3,7]=>[6,2,3,4,5,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,2,5,6,7,3]=>[7,2,3,4,5,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,2,5,7,3,6]=>[6,2,3,4,7,1,5]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,2,5,7,6,3]=>[7,2,3,4,6,5,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,2,6,3,5,7]=>[5,2,3,6,1,4,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[4,1,2,6,3,7,5]=>[5,2,3,7,1,6,4]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[4,1,2,6,5,3,7]=>[6,2,3,5,4,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,2,6,5,7,3]=>[7,2,3,5,4,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,2,6,7,3,5]=>[6,2,3,7,5,1,4]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,2,6,7,5,3]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,2,7,3,5,6]=>[5,2,3,7,1,6,4]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[4,1,2,7,3,6,5]=>[5,2,3,7,1,6,4]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[4,1,2,7,5,3,6]=>[6,2,3,7,5,1,4]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,2,7,5,6,3]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,2,7,6,3,5]=>[6,2,3,7,5,1,4]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,2,7,6,5,3]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,3,2,5,6,7]=>[4,2,3,1,5,6,7]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[4,1,3,2,5,7,6]=>[4,2,3,1,5,7,6]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[4,1,3,2,6,5,7]=>[4,2,3,1,6,5,7]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[4,1,3,2,6,7,5]=>[4,2,3,1,7,6,5]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[4,1,3,2,7,5,6]=>[4,2,3,1,7,6,5]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[4,1,3,2,7,6,5]=>[4,2,3,1,7,6,5]=>[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[4,1,3,5,2,6,7]=>[5,2,3,4,1,6,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[4,1,3,5,2,7,6]=>[5,2,3,4,1,7,6]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[4,1,3,5,6,2,7]=>[6,2,3,4,5,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,3,5,6,7,2]=>[7,2,3,4,5,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,3,5,7,2,6]=>[6,2,3,4,7,1,5]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,3,5,7,6,2]=>[7,2,3,4,6,5,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,3,6,2,5,7]=>[5,2,3,6,1,4,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[4,1,3,6,2,7,5]=>[5,2,3,7,1,6,4]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[4,1,3,6,5,2,7]=>[6,2,3,5,4,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,3,6,5,7,2]=>[7,2,3,5,4,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,3,6,7,2,5]=>[6,2,3,7,5,1,4]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,3,6,7,5,2]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,3,7,2,5,6]=>[5,2,3,7,1,6,4]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[4,1,3,7,2,6,5]=>[5,2,3,7,1,6,4]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[4,1,3,7,5,2,6]=>[6,2,3,7,5,1,4]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,3,7,5,6,2]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,3,7,6,2,5]=>[6,2,3,7,5,1,4]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,3,7,6,5,2]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,5,2,3,6,7]=>[5,2,4,3,1,6,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[4,1,5,2,3,7,6]=>[5,2,4,3,1,7,6]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[4,1,5,2,6,3,7]=>[6,2,4,3,5,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,5,2,6,7,3]=>[7,2,4,3,5,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,5,2,7,3,6]=>[6,2,4,3,7,1,5]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,5,2,7,6,3]=>[7,2,4,3,6,5,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,5,3,2,6,7]=>[5,2,4,3,1,6,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[4,1,5,3,2,7,6]=>[5,2,4,3,1,7,6]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[4,1,5,3,6,2,7]=>[6,2,4,3,5,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,5,3,6,7,2]=>[7,2,4,3,5,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,5,3,7,2,6]=>[6,2,4,3,7,1,5]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,5,3,7,6,2]=>[7,2,4,3,6,5,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,5,6,2,3,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,5,6,2,7,3]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,5,6,3,2,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,5,6,3,7,2]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,5,6,7,2,3]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,5,6,7,3,2]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,5,7,2,3,6]=>[6,2,5,7,3,1,4]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,5,7,2,6,3]=>[7,2,5,6,3,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,5,7,3,2,6]=>[6,2,5,7,3,1,4]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,5,7,3,6,2]=>[7,2,5,6,3,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,5,7,6,2,3]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,5,7,6,3,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,6,2,3,5,7]=>[5,2,6,4,1,3,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[4,1,6,2,3,7,5]=>[5,2,7,4,1,6,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[4,1,6,2,5,3,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,6,2,5,7,3]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,6,2,7,3,5]=>[6,2,7,4,5,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,6,2,7,5,3]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,6,3,2,5,7]=>[5,2,6,4,1,3,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[4,1,6,3,2,7,5]=>[5,2,7,4,1,6,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[4,1,6,3,5,2,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,6,3,5,7,2]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,6,3,7,2,5]=>[6,2,7,4,5,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,6,3,7,5,2]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,6,5,2,3,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,6,5,2,7,3]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,6,5,3,2,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,6,5,3,7,2]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,6,5,7,2,3]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,6,5,7,3,2]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,6,7,2,3,5]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,6,7,2,5,3]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,6,7,3,2,5]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,6,7,3,5,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,6,7,5,2,3]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,6,7,5,3,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,7,2,3,5,6]=>[5,2,7,4,1,6,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[4,1,7,2,3,6,5]=>[5,2,7,4,1,6,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[4,1,7,2,5,3,6]=>[6,2,7,4,5,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,7,2,5,6,3]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,7,2,6,3,5]=>[6,2,7,4,5,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,7,2,6,5,3]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,7,3,2,5,6]=>[5,2,7,4,1,6,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[4,1,7,3,2,6,5]=>[5,2,7,4,1,6,3]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[4,1,7,3,5,2,6]=>[6,2,7,4,5,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,7,3,5,6,2]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,7,3,6,2,5]=>[6,2,7,4,5,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,7,3,6,5,2]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,7,5,2,3,6]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,7,5,2,6,3]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,7,5,3,2,6]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,7,5,3,6,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,7,5,6,2,3]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,7,5,6,3,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,7,6,2,3,5]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,7,6,2,5,3]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,7,6,3,2,5]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[4,1,7,6,3,5,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,7,6,5,2,3]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,1,7,6,5,3,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[4,2,1,3,5,6,7]=>[4,3,2,1,5,6,7]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[4,2,1,3,5,7,6]=>[4,3,2,1,5,7,6]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[4,2,1,3,6,5,7]=>[4,3,2,1,6,5,7]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[4,2,1,3,6,7,5]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[4,2,1,3,7,5,6]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[4,2,1,3,7,6,5]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[4,2,1,5,3,6,7]=>[5,3,2,4,1,6,7]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[4,2,1,5,3,7,6]=>[5,3,2,4,1,7,6]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[4,2,1,5,6,3,7]=>[6,3,2,4,5,1,7]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[4,2,1,5,6,7,3]=>[7,3,2,4,5,6,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[4,2,1,5,7,3,6]=>[6,3,2,4,7,1,5]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[4,2,1,5,7,6,3]=>[7,3,2,4,6,5,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[4,2,1,6,3,5,7]=>[5,3,2,6,1,4,7]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[4,2,1,6,3,7,5]=>[5,3,2,7,1,6,4]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[4,2,1,6,5,3,7]=>[6,3,2,5,4,1,7]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[4,2,1,6,5,7,3]=>[7,3,2,5,4,6,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[4,2,1,6,7,3,5]=>[6,3,2,7,5,1,4]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[4,2,1,6,7,5,3]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[4,2,1,7,3,5,6]=>[5,3,2,7,1,6,4]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[4,2,1,7,3,6,5]=>[5,3,2,7,1,6,4]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[4,2,1,7,5,3,6]=>[6,3,2,7,5,1,4]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[4,2,1,7,5,6,3]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[4,2,1,7,6,3,5]=>[6,3,2,7,5,1,4]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[4,2,1,7,6,5,3]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[4,2,3,1,5,6,7]=>[4,3,2,1,5,6,7]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[4,2,3,1,5,7,6]=>[4,3,2,1,5,7,6]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[4,2,3,1,6,5,7]=>[4,3,2,1,6,5,7]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[4,2,3,1,6,7,5]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[4,2,3,1,7,5,6]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[4,2,3,1,7,6,5]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[4,2,3,5,1,6,7]=>[5,3,2,4,1,6,7]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[4,2,3,5,1,7,6]=>[5,3,2,4,1,7,6]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[4,2,3,5,6,1,7]=>[6,3,2,4,5,1,7]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[4,2,3,5,6,7,1]=>[7,3,2,4,5,6,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[4,2,3,5,7,1,6]=>[6,3,2,4,7,1,5]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[4,2,3,5,7,6,1]=>[7,3,2,4,6,5,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[4,2,3,6,1,5,7]=>[5,3,2,6,1,4,7]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[4,2,3,6,1,7,5]=>[5,3,2,7,1,6,4]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[4,2,3,6,5,1,7]=>[6,3,2,5,4,1,7]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[4,2,3,6,5,7,1]=>[7,3,2,5,4,6,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[4,2,3,6,7,1,5]=>[6,3,2,7,5,1,4]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[4,2,3,6,7,5,1]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[4,2,3,7,1,5,6]=>[5,3,2,7,1,6,4]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[4,2,3,7,1,6,5]=>[5,3,2,7,1,6,4]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[4,2,3,7,5,1,6]=>[6,3,2,7,5,1,4]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[4,2,3,7,5,6,1]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[4,2,3,7,6,1,5]=>[6,3,2,7,5,1,4]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[4,2,3,7,6,5,1]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[4,2,5,1,3,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[4,2,5,1,3,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[4,2,5,1,6,3,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[4,2,5,1,6,7,3]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[4,2,5,1,7,3,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[4,2,5,1,7,6,3]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[4,2,5,3,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[4,2,5,3,1,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[4,2,5,3,6,1,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[4,2,5,3,6,7,1]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[4,2,5,3,7,1,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[4,2,5,3,7,6,1]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[4,2,5,6,1,3,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[4,2,5,6,1,7,3]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[4,2,5,6,3,1,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[4,2,5,6,3,7,1]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[4,2,5,6,7,1,3]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,2,5,6,7,3,1]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,2,5,7,1,3,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[4,2,5,7,1,6,3]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[4,2,5,7,3,1,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[4,2,5,7,3,6,1]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[4,2,5,7,6,1,3]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,2,5,7,6,3,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,2,6,1,3,5,7]=>[5,4,6,2,1,3,7]=>[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[4,2,6,1,3,7,5]=>[5,4,7,2,1,6,3]=>[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[4,2,6,1,5,3,7]=>[6,4,5,2,3,1,7]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[4,2,6,1,5,7,3]=>[7,4,5,2,3,6,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[4,2,6,1,7,3,5]=>[6,4,7,2,5,1,3]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[4,2,6,1,7,5,3]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[4,2,6,3,1,5,7]=>[5,4,6,2,1,3,7]=>[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[4,2,6,3,1,7,5]=>[5,4,7,2,1,6,3]=>[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[4,2,6,3,5,1,7]=>[6,4,5,2,3,1,7]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[4,2,6,3,5,7,1]=>[7,4,5,2,3,6,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[4,2,6,3,7,1,5]=>[6,4,7,2,5,1,3]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[4,2,6,3,7,5,1]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[4,2,6,5,1,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[4,2,6,5,1,7,3]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[4,2,6,5,3,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[4,2,6,5,3,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[4,2,6,5,7,1,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,2,6,5,7,3,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,2,6,7,1,3,5]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[4,2,6,7,1,5,3]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[4,2,6,7,3,1,5]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[4,2,6,7,3,5,1]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[4,2,6,7,5,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,2,6,7,5,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,2,7,1,3,5,6]=>[5,4,7,2,1,6,3]=>[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[4,2,7,1,3,6,5]=>[5,4,7,2,1,6,3]=>[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[4,2,7,1,5,3,6]=>[6,4,7,2,5,1,3]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[4,2,7,1,5,6,3]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[4,2,7,1,6,3,5]=>[6,4,7,2,5,1,3]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[4,2,7,1,6,5,3]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[4,2,7,3,1,5,6]=>[5,4,7,2,1,6,3]=>[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[4,2,7,3,1,6,5]=>[5,4,7,2,1,6,3]=>[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[4,2,7,3,5,1,6]=>[6,4,7,2,5,1,3]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[4,2,7,3,5,6,1]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[4,2,7,3,6,1,5]=>[6,4,7,2,5,1,3]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[4,2,7,3,6,5,1]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[4,2,7,5,1,3,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[4,2,7,5,1,6,3]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[4,2,7,5,3,1,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[4,2,7,5,3,6,1]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[4,2,7,5,6,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,2,7,5,6,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,2,7,6,1,3,5]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[4,2,7,6,1,5,3]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[4,2,7,6,3,1,5]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[4,2,7,6,3,5,1]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[4,2,7,6,5,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,2,7,6,5,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,3,1,2,5,6,7]=>[4,3,2,1,5,6,7]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[4,3,1,2,5,7,6]=>[4,3,2,1,5,7,6]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[4,3,1,2,6,5,7]=>[4,3,2,1,6,5,7]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[4,3,1,2,6,7,5]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[4,3,1,2,7,5,6]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[4,3,1,2,7,6,5]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[4,3,1,5,2,6,7]=>[5,3,2,4,1,6,7]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[4,3,1,5,2,7,6]=>[5,3,2,4,1,7,6]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[4,3,1,5,6,2,7]=>[6,3,2,4,5,1,7]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[4,3,1,5,6,7,2]=>[7,3,2,4,5,6,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[4,3,1,5,7,2,6]=>[6,3,2,4,7,1,5]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[4,3,1,5,7,6,2]=>[7,3,2,4,6,5,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[4,3,1,6,2,5,7]=>[5,3,2,6,1,4,7]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[4,3,1,6,2,7,5]=>[5,3,2,7,1,6,4]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[4,3,1,6,5,2,7]=>[6,3,2,5,4,1,7]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[4,3,1,6,5,7,2]=>[7,3,2,5,4,6,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[4,3,1,6,7,2,5]=>[6,3,2,7,5,1,4]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[4,3,1,6,7,5,2]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[4,3,1,7,2,5,6]=>[5,3,2,7,1,6,4]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[4,3,1,7,2,6,5]=>[5,3,2,7,1,6,4]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[4,3,1,7,5,2,6]=>[6,3,2,7,5,1,4]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[4,3,1,7,5,6,2]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[4,3,1,7,6,2,5]=>[6,3,2,7,5,1,4]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[4,3,1,7,6,5,2]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[4,3,2,1,5,7,6]=>[4,3,2,1,5,7,6]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[4,3,2,1,6,5,7]=>[4,3,2,1,6,5,7]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[4,3,2,1,6,7,5]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[4,3,2,1,7,5,6]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[4,3,2,5,1,6,7]=>[5,3,2,4,1,6,7]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[4,3,2,5,1,7,6]=>[5,3,2,4,1,7,6]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[4,3,2,5,6,1,7]=>[6,3,2,4,5,1,7]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[4,3,2,5,6,7,1]=>[7,3,2,4,5,6,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[4,3,2,5,7,1,6]=>[6,3,2,4,7,1,5]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[4,3,2,5,7,6,1]=>[7,3,2,4,6,5,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[4,3,2,6,1,5,7]=>[5,3,2,6,1,4,7]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[4,3,2,6,1,7,5]=>[5,3,2,7,1,6,4]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[4,3,2,6,5,1,7]=>[6,3,2,5,4,1,7]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[4,3,2,6,5,7,1]=>[7,3,2,5,4,6,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[4,3,2,6,7,1,5]=>[6,3,2,7,5,1,4]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[4,3,2,6,7,5,1]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[4,3,2,7,1,5,6]=>[5,3,2,7,1,6,4]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[4,3,2,7,1,6,5]=>[5,3,2,7,1,6,4]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[4,3,2,7,5,1,6]=>[6,3,2,7,5,1,4]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[4,3,2,7,5,6,1]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[4,3,2,7,6,1,5]=>[6,3,2,7,5,1,4]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[4,3,2,7,6,5,1]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[4,3,5,1,2,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[4,3,5,1,2,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[4,3,5,1,6,2,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[4,3,5,1,6,7,2]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[4,3,5,1,7,2,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[4,3,5,1,7,6,2]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[4,3,5,2,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[4,3,5,2,1,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[4,3,5,2,6,1,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[4,3,5,2,6,7,1]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[4,3,5,2,7,1,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[4,3,5,2,7,6,1]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[4,3,5,6,1,2,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[4,3,5,6,1,7,2]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[4,3,5,6,2,1,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[4,3,5,6,2,7,1]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[4,3,5,6,7,1,2]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,3,5,6,7,2,1]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,3,5,7,1,2,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[4,3,5,7,1,6,2]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[4,3,5,7,2,1,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[4,3,5,7,2,6,1]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[4,3,5,7,6,1,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,3,5,7,6,2,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,3,6,1,2,5,7]=>[5,4,6,2,1,3,7]=>[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[4,3,6,1,2,7,5]=>[5,4,7,2,1,6,3]=>[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[4,3,6,1,5,2,7]=>[6,4,5,2,3,1,7]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[4,3,6,1,5,7,2]=>[7,4,5,2,3,6,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[4,3,6,1,7,2,5]=>[6,4,7,2,5,1,3]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[4,3,6,1,7,5,2]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[4,3,6,2,1,5,7]=>[5,4,6,2,1,3,7]=>[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[4,3,6,2,1,7,5]=>[5,4,7,2,1,6,3]=>[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[4,3,6,2,5,1,7]=>[6,4,5,2,3,1,7]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[4,3,6,2,5,7,1]=>[7,4,5,2,3,6,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[4,3,6,2,7,1,5]=>[6,4,7,2,5,1,3]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[4,3,6,2,7,5,1]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[4,3,6,5,1,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[4,3,6,5,1,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[4,3,6,5,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[4,3,6,5,2,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[4,3,6,5,7,1,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,3,6,5,7,2,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,3,6,7,1,2,5]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[4,3,6,7,1,5,2]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[4,3,6,7,2,1,5]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[4,3,6,7,2,5,1]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[4,3,6,7,5,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,3,6,7,5,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,3,7,1,2,5,6]=>[5,4,7,2,1,6,3]=>[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[4,3,7,1,2,6,5]=>[5,4,7,2,1,6,3]=>[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[4,3,7,1,5,2,6]=>[6,4,7,2,5,1,3]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[4,3,7,1,5,6,2]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[4,3,7,1,6,2,5]=>[6,4,7,2,5,1,3]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[4,3,7,1,6,5,2]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[4,3,7,2,1,5,6]=>[5,4,7,2,1,6,3]=>[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[4,3,7,2,1,6,5]=>[5,4,7,2,1,6,3]=>[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[4,3,7,2,5,1,6]=>[6,4,7,2,5,1,3]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[4,3,7,2,5,6,1]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[4,3,7,2,6,1,5]=>[6,4,7,2,5,1,3]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[4,3,7,2,6,5,1]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[4,3,7,5,1,2,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[4,3,7,5,1,6,2]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[4,3,7,5,2,1,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[4,3,7,5,2,6,1]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[4,3,7,5,6,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,3,7,5,6,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,3,7,6,1,2,5]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[4,3,7,6,1,5,2]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[4,3,7,6,2,1,5]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[4,3,7,6,2,5,1]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[4,3,7,6,5,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,3,7,6,5,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,5,1,2,3,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[4,5,1,2,3,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[4,5,1,2,6,3,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[4,5,1,2,6,7,3]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[4,5,1,2,7,3,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[4,5,1,2,7,6,3]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[4,5,1,3,2,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[4,5,1,3,2,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[4,5,1,3,6,2,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[4,5,1,3,6,7,2]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[4,5,1,3,7,2,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[4,5,1,3,7,6,2]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[4,5,1,6,2,3,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[4,5,1,6,2,7,3]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[4,5,1,6,3,2,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[4,5,1,6,3,7,2]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[4,5,1,6,7,2,3]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,5,1,6,7,3,2]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,5,1,7,2,3,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[4,5,1,7,2,6,3]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[4,5,1,7,3,2,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[4,5,1,7,3,6,2]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[4,5,1,7,6,2,3]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,5,1,7,6,3,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,5,2,1,3,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[4,5,2,1,3,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[4,5,2,1,6,3,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[4,5,2,1,6,7,3]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[4,5,2,1,7,3,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[4,5,2,1,7,6,3]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[4,5,2,3,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[4,5,2,3,1,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[4,5,2,3,6,1,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[4,5,2,3,6,7,1]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[4,5,2,3,7,1,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[4,5,2,3,7,6,1]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[4,5,2,6,1,3,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[4,5,2,6,1,7,3]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[4,5,2,6,3,1,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[4,5,2,6,3,7,1]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[4,5,2,6,7,1,3]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,5,2,6,7,3,1]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,5,2,7,1,3,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[4,5,2,7,1,6,3]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[4,5,2,7,3,1,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[4,5,2,7,3,6,1]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[4,5,2,7,6,1,3]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,5,2,7,6,3,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,5,3,1,2,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[4,5,3,1,2,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[4,5,3,1,6,2,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[4,5,3,1,6,7,2]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[4,5,3,1,7,2,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[4,5,3,1,7,6,2]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[4,5,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[4,5,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[4,5,3,2,6,1,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[4,5,3,2,6,7,1]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[4,5,3,2,7,1,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[4,5,3,2,7,6,1]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[4,5,3,6,1,2,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[4,5,3,6,1,7,2]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[4,5,3,6,2,1,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[4,5,3,6,2,7,1]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[4,5,3,6,7,1,2]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,5,3,6,7,2,1]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,5,3,7,1,2,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[4,5,3,7,1,6,2]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[4,5,3,7,2,1,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[4,5,3,7,2,6,1]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[4,5,3,7,6,1,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,5,3,7,6,2,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,5,6,1,2,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[4,5,6,1,2,7,3]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[4,5,6,1,3,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[4,5,6,1,3,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[4,5,6,1,7,2,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,5,6,1,7,3,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,5,6,2,1,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[4,5,6,2,1,7,3]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[4,5,6,2,3,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[4,5,6,2,3,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[4,5,6,2,7,1,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,5,6,2,7,3,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,5,6,3,1,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[4,5,6,3,1,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[4,5,6,3,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[4,5,6,3,2,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[4,5,6,3,7,1,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,5,6,3,7,2,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,5,6,7,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,5,6,7,1,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,5,6,7,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,5,6,7,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,5,6,7,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,5,6,7,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,5,7,1,2,3,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[4,5,7,1,2,6,3]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[4,5,7,1,3,2,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[4,5,7,1,3,6,2]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[4,5,7,1,6,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,5,7,1,6,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,5,7,2,1,3,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[4,5,7,2,1,6,3]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[4,5,7,2,3,1,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[4,5,7,2,3,6,1]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[4,5,7,2,6,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,5,7,2,6,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,5,7,3,1,2,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[4,5,7,3,1,6,2]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[4,5,7,3,2,1,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[4,5,7,3,2,6,1]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[4,5,7,3,6,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,5,7,3,6,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,5,7,6,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,5,7,6,1,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,5,7,6,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,5,7,6,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,5,7,6,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,5,7,6,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,1,2,3,5,7]=>[5,6,3,4,1,2,7]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[4,6,1,2,3,7,5]=>[5,7,3,4,1,6,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[4,6,1,2,5,3,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[4,6,1,2,5,7,3]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[4,6,1,2,7,3,5]=>[6,7,3,4,5,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[4,6,1,2,7,5,3]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,6,1,3,2,5,7]=>[5,6,3,4,1,2,7]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[4,6,1,3,2,7,5]=>[5,7,3,4,1,6,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[4,6,1,3,5,2,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[4,6,1,3,5,7,2]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[4,6,1,3,7,2,5]=>[6,7,3,4,5,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[4,6,1,3,7,5,2]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,6,1,5,2,3,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[4,6,1,5,2,7,3]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[4,6,1,5,3,2,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[4,6,1,5,3,7,2]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[4,6,1,5,7,2,3]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,6,1,5,7,3,2]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,6,1,7,2,3,5]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[4,6,1,7,2,5,3]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,6,1,7,3,2,5]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[4,6,1,7,3,5,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,6,1,7,5,2,3]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,6,1,7,5,3,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,6,2,1,3,5,7]=>[5,6,4,3,1,2,7]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[4,6,2,1,3,7,5]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[4,6,2,1,5,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[4,6,2,1,5,7,3]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[4,6,2,1,7,3,5]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[4,6,2,1,7,5,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,6,2,3,1,5,7]=>[5,6,4,3,1,2,7]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[4,6,2,3,1,7,5]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[4,6,2,3,5,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[4,6,2,3,5,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[4,6,2,3,7,1,5]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[4,6,2,3,7,5,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,6,2,5,1,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[4,6,2,5,1,7,3]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[4,6,2,5,3,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[4,6,2,5,3,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[4,6,2,5,7,1,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,6,2,5,7,3,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,6,2,7,1,3,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,6,2,7,1,5,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,2,7,3,1,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,6,2,7,3,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,2,7,5,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,2,7,5,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,3,1,2,5,7]=>[5,6,4,3,1,2,7]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[4,6,3,1,2,7,5]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[4,6,3,1,5,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[4,6,3,1,5,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[4,6,3,1,7,2,5]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[4,6,3,1,7,5,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,6,3,2,1,5,7]=>[5,6,4,3,1,2,7]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[4,6,3,2,1,7,5]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[4,6,3,2,5,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[4,6,3,2,5,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[4,6,3,2,7,1,5]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[4,6,3,2,7,5,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,6,3,5,1,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[4,6,3,5,1,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[4,6,3,5,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[4,6,3,5,2,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[4,6,3,5,7,1,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,6,3,5,7,2,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,6,3,7,1,2,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,6,3,7,1,5,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,3,7,2,1,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,6,3,7,2,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,3,7,5,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,3,7,5,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,5,1,2,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[4,6,5,1,2,7,3]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[4,6,5,1,3,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[4,6,5,1,3,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[4,6,5,1,7,2,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,6,5,1,7,3,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,6,5,2,1,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[4,6,5,2,1,7,3]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[4,6,5,2,3,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[4,6,5,2,3,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[4,6,5,2,7,1,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,6,5,2,7,3,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,6,5,3,1,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[4,6,5,3,1,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[4,6,5,3,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[4,6,5,3,2,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[4,6,5,3,7,1,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,6,5,3,7,2,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,6,5,7,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,5,7,1,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,5,7,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,5,7,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,5,7,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,5,7,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,7,1,2,3,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,6,7,1,2,5,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,7,1,3,2,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,6,7,1,3,5,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,7,1,5,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,7,1,5,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,7,2,1,3,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,6,7,2,1,5,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,7,2,3,1,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,6,7,2,3,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,7,2,5,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,7,2,5,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,7,3,1,2,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,6,7,3,1,5,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,7,3,2,1,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,6,7,3,2,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,7,3,5,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,7,3,5,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,7,5,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,7,5,1,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,7,5,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,7,5,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,7,5,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,6,7,5,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,1,2,3,5,6]=>[5,7,3,4,1,6,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[4,7,1,2,3,6,5]=>[5,7,3,4,1,6,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[4,7,1,2,5,3,6]=>[6,7,3,4,5,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[4,7,1,2,5,6,3]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,7,1,2,6,3,5]=>[6,7,3,4,5,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[4,7,1,2,6,5,3]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,7,1,3,2,5,6]=>[5,7,3,4,1,6,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[4,7,1,3,2,6,5]=>[5,7,3,4,1,6,2]=>[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[4,7,1,3,5,2,6]=>[6,7,3,4,5,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[4,7,1,3,5,6,2]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,7,1,3,6,2,5]=>[6,7,3,4,5,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[4,7,1,3,6,5,2]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,7,1,5,2,3,6]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[4,7,1,5,2,6,3]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,7,1,5,3,2,6]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[4,7,1,5,3,6,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,7,1,5,6,2,3]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,7,1,5,6,3,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,7,1,6,2,3,5]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[4,7,1,6,2,5,3]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,7,1,6,3,2,5]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[4,7,1,6,3,5,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,7,1,6,5,2,3]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,7,1,6,5,3,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[4,7,2,1,3,5,6]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[4,7,2,1,3,6,5]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[4,7,2,1,5,3,6]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[4,7,2,1,5,6,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,7,2,1,6,3,5]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[4,7,2,1,6,5,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,7,2,3,1,5,6]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[4,7,2,3,1,6,5]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[4,7,2,3,5,1,6]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[4,7,2,3,5,6,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,7,2,3,6,1,5]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[4,7,2,3,6,5,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,7,2,5,1,3,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,7,2,5,1,6,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,2,5,3,1,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,7,2,5,3,6,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,2,5,6,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,2,5,6,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,2,6,1,3,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,7,2,6,1,5,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,2,6,3,1,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,7,2,6,3,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,2,6,5,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,2,6,5,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,3,1,2,5,6]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[4,7,3,1,2,6,5]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[4,7,3,1,5,2,6]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[4,7,3,1,5,6,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,7,3,1,6,2,5]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[4,7,3,1,6,5,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,7,3,2,1,5,6]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[4,7,3,2,1,6,5]=>[5,7,4,3,1,6,2]=>[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[4,7,3,2,5,1,6]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[4,7,3,2,5,6,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,7,3,2,6,1,5]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[4,7,3,2,6,5,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[4,7,3,5,1,2,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,7,3,5,1,6,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,3,5,2,1,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,7,3,5,2,6,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,3,5,6,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,3,5,6,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,3,6,1,2,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,7,3,6,1,5,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,3,6,2,1,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,7,3,6,2,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,3,6,5,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,3,6,5,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,5,1,2,3,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,7,5,1,2,6,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,5,1,3,2,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,7,5,1,3,6,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,5,1,6,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,5,1,6,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,5,2,1,3,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,7,5,2,1,6,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,5,2,3,1,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,7,5,2,3,6,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,5,2,6,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,5,2,6,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,5,3,1,2,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,7,5,3,1,6,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,5,3,2,1,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,7,5,3,2,6,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,5,3,6,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,5,3,6,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,5,6,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,5,6,1,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,5,6,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,5,6,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,5,6,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,5,6,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,6,1,2,3,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,7,6,1,2,5,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,6,1,3,2,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,7,6,1,3,5,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,6,1,5,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,6,1,5,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,6,2,1,3,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,7,6,2,1,5,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,6,2,3,1,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,7,6,2,3,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,6,2,5,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,6,2,5,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,6,3,1,2,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,7,6,3,1,5,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,6,3,2,1,5]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[4,7,6,3,2,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,6,3,5,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,6,3,5,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,6,5,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,6,5,1,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,6,5,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,6,5,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,6,5,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[4,7,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,1,2,3,4,6,7]=>[5,2,3,4,1,6,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[5,1,2,3,4,7,6]=>[5,2,3,4,1,7,6]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[5,1,2,3,6,4,7]=>[6,2,3,4,5,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,2,3,6,7,4]=>[7,2,3,4,5,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,2,3,7,4,6]=>[6,2,3,4,7,1,5]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,2,3,7,6,4]=>[7,2,3,4,6,5,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,2,4,3,6,7]=>[5,2,3,4,1,6,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[5,1,2,4,3,7,6]=>[5,2,3,4,1,7,6]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[5,1,2,4,6,3,7]=>[6,2,3,4,5,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,2,4,6,7,3]=>[7,2,3,4,5,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,2,4,7,3,6]=>[6,2,3,4,7,1,5]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,2,4,7,6,3]=>[7,2,3,4,6,5,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,2,6,3,4,7]=>[6,2,3,5,4,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,2,6,3,7,4]=>[7,2,3,5,4,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,2,6,4,3,7]=>[6,2,3,5,4,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,2,6,4,7,3]=>[7,2,3,5,4,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,2,6,7,3,4]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,2,6,7,4,3]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,2,7,3,4,6]=>[6,2,3,7,5,1,4]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,2,7,3,6,4]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,2,7,4,3,6]=>[6,2,3,7,5,1,4]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,2,7,4,6,3]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,2,7,6,3,4]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,2,7,6,4,3]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,3,2,4,6,7]=>[5,2,4,3,1,6,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[5,1,3,2,4,7,6]=>[5,2,4,3,1,7,6]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[5,1,3,2,6,4,7]=>[6,2,4,3,5,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,3,2,6,7,4]=>[7,2,4,3,5,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,3,2,7,4,6]=>[6,2,4,3,7,1,5]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,3,2,7,6,4]=>[7,2,4,3,6,5,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,3,4,2,6,7]=>[5,2,4,3,1,6,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[5,1,3,4,2,7,6]=>[5,2,4,3,1,7,6]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[5,1,3,4,6,2,7]=>[6,2,4,3,5,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,3,4,6,7,2]=>[7,2,4,3,5,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,3,4,7,2,6]=>[6,2,4,3,7,1,5]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,3,4,7,6,2]=>[7,2,4,3,6,5,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,3,6,2,4,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,3,6,2,7,4]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,3,6,4,2,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,3,6,4,7,2]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,3,6,7,2,4]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,3,6,7,4,2]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,3,7,2,4,6]=>[6,2,5,7,3,1,4]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,3,7,2,6,4]=>[7,2,5,6,3,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,3,7,4,2,6]=>[6,2,5,7,3,1,4]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,3,7,4,6,2]=>[7,2,5,6,3,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,3,7,6,2,4]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,3,7,6,4,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,4,2,3,6,7]=>[5,2,4,3,1,6,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[5,1,4,2,3,7,6]=>[5,2,4,3,1,7,6]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[5,1,4,2,6,3,7]=>[6,2,4,3,5,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,4,2,6,7,3]=>[7,2,4,3,5,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,4,2,7,3,6]=>[6,2,4,3,7,1,5]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,4,2,7,6,3]=>[7,2,4,3,6,5,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,4,3,2,6,7]=>[5,2,4,3,1,6,7]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[5,1,4,3,2,7,6]=>[5,2,4,3,1,7,6]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[5,1,4,3,6,2,7]=>[6,2,4,3,5,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,4,3,6,7,2]=>[7,2,4,3,5,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,4,3,7,2,6]=>[6,2,4,3,7,1,5]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,4,3,7,6,2]=>[7,2,4,3,6,5,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,4,6,2,3,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,4,6,2,7,3]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,4,6,3,2,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,4,6,3,7,2]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,4,6,7,2,3]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,4,6,7,3,2]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,4,7,2,3,6]=>[6,2,5,7,3,1,4]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,4,7,2,6,3]=>[7,2,5,6,3,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,4,7,3,2,6]=>[6,2,5,7,3,1,4]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,4,7,3,6,2]=>[7,2,5,6,3,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,4,7,6,2,3]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,4,7,6,3,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,6,2,3,4,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,6,2,3,7,4]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,6,2,4,3,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,6,2,4,7,3]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,6,2,7,3,4]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,6,2,7,4,3]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,6,3,2,4,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,6,3,2,7,4]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,6,3,4,2,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,6,3,4,7,2]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,6,3,7,2,4]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,6,3,7,4,2]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,6,4,2,3,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,6,4,2,7,3]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,6,4,3,2,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,6,4,3,7,2]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,6,4,7,2,3]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,6,4,7,3,2]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,6,7,2,3,4]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,6,7,2,4,3]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,6,7,3,2,4]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,6,7,3,4,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,6,7,4,2,3]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,6,7,4,3,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,7,2,3,4,6]=>[6,2,7,4,5,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,7,2,3,6,4]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,7,2,4,3,6]=>[6,2,7,4,5,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,7,2,4,6,3]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,7,2,6,3,4]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,7,2,6,4,3]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,7,3,2,4,6]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,7,3,2,6,4]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,7,3,4,2,6]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,7,3,4,6,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,7,3,6,2,4]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,7,3,6,4,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,7,4,2,3,6]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,7,4,2,6,3]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,7,4,3,2,6]=>[6,2,7,5,4,1,3]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[5,1,7,4,3,6,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,7,4,6,2,3]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,7,4,6,3,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,7,6,2,3,4]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,7,6,2,4,3]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,7,6,3,2,4]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,7,6,3,4,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,7,6,4,2,3]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,1,7,6,4,3,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[5,2,1,3,4,6,7]=>[5,3,2,4,1,6,7]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[5,2,1,3,4,7,6]=>[5,3,2,4,1,7,6]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[5,2,1,3,6,4,7]=>[6,3,2,4,5,1,7]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[5,2,1,3,6,7,4]=>[7,3,2,4,5,6,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[5,2,1,3,7,4,6]=>[6,3,2,4,7,1,5]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[5,2,1,3,7,6,4]=>[7,3,2,4,6,5,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[5,2,1,4,3,6,7]=>[5,3,2,4,1,6,7]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[5,2,1,4,3,7,6]=>[5,3,2,4,1,7,6]=>[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[5,2,1,4,6,3,7]=>[6,3,2,4,5,1,7]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[5,2,1,4,6,7,3]=>[7,3,2,4,5,6,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[5,2,1,4,7,3,6]=>[6,3,2,4,7,1,5]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[5,2,1,4,7,6,3]=>[7,3,2,4,6,5,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[5,2,1,6,3,4,7]=>[6,3,2,5,4,1,7]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[5,2,1,6,3,7,4]=>[7,3,2,5,4,6,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[5,2,1,6,4,3,7]=>[6,3,2,5,4,1,7]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[5,2,1,6,4,7,3]=>[7,3,2,5,4,6,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[5,2,1,6,7,3,4]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[5,2,1,6,7,4,3]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[5,2,1,7,3,4,6]=>[6,3,2,7,5,1,4]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[5,2,1,7,3,6,4]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[5,2,1,7,4,3,6]=>[6,3,2,7,5,1,4]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[5,2,1,7,4,6,3]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[5,2,1,7,6,3,4]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[5,2,1,7,6,4,3]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[5,2,3,1,4,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,2,3,1,4,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,2,3,1,6,4,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,2,3,1,6,7,4]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,2,3,1,7,4,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,2,3,1,7,6,4]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,2,3,4,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,2,3,4,1,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,2,3,4,6,1,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,2,3,4,6,7,1]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,2,3,4,7,1,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,2,3,4,7,6,1]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,2,3,6,1,4,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,2,3,6,1,7,4]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,2,3,6,4,1,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,2,3,6,4,7,1]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,2,3,6,7,1,4]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,2,3,6,7,4,1]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,2,3,7,1,4,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,2,3,7,1,6,4]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,2,3,7,4,1,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,2,3,7,4,6,1]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,2,3,7,6,1,4]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,2,3,7,6,4,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,2,4,1,3,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,2,4,1,3,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,2,4,1,6,3,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,2,4,1,6,7,3]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,2,4,1,7,3,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,2,4,1,7,6,3]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,2,4,3,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,2,4,3,1,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,2,4,3,6,1,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,2,4,3,6,7,1]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,2,4,3,7,1,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,2,4,3,7,6,1]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,2,4,6,1,3,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,2,4,6,1,7,3]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,2,4,6,3,1,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,2,4,6,3,7,1]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,2,4,6,7,1,3]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,2,4,6,7,3,1]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,2,4,7,1,3,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,2,4,7,1,6,3]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,2,4,7,3,1,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,2,4,7,3,6,1]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,2,4,7,6,1,3]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,2,4,7,6,3,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,2,6,1,3,4,7]=>[6,4,5,2,3,1,7]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[5,2,6,1,3,7,4]=>[7,4,5,2,3,6,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[5,2,6,1,4,3,7]=>[6,4,5,2,3,1,7]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[5,2,6,1,4,7,3]=>[7,4,5,2,3,6,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[5,2,6,1,7,3,4]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[5,2,6,1,7,4,3]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[5,2,6,3,1,4,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,2,6,3,1,7,4]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,2,6,3,4,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,2,6,3,4,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,2,6,3,7,1,4]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,2,6,3,7,4,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,2,6,4,1,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,2,6,4,1,7,3]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,2,6,4,3,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,2,6,4,3,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,2,6,4,7,1,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,2,6,4,7,3,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,2,6,7,1,3,4]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[5,2,6,7,1,4,3]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[5,2,6,7,3,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,2,6,7,3,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,2,6,7,4,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,2,6,7,4,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,2,7,1,3,4,6]=>[6,4,7,2,5,1,3]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[5,2,7,1,3,6,4]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[5,2,7,1,4,3,6]=>[6,4,7,2,5,1,3]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[5,2,7,1,4,6,3]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[5,2,7,1,6,3,4]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[5,2,7,1,6,4,3]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[5,2,7,3,1,4,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[5,2,7,3,1,6,4]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[5,2,7,3,4,1,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[5,2,7,3,4,6,1]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[5,2,7,3,6,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,2,7,3,6,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,2,7,4,1,3,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[5,2,7,4,1,6,3]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[5,2,7,4,3,1,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[5,2,7,4,3,6,1]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[5,2,7,4,6,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,2,7,4,6,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,2,7,6,1,3,4]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[5,2,7,6,1,4,3]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[5,2,7,6,3,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,2,7,6,3,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,2,7,6,4,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,2,7,6,4,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,3,1,2,4,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,3,1,2,4,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,3,1,2,6,4,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,3,1,2,6,7,4]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,3,1,2,7,4,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,3,1,2,7,6,4]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,3,1,4,2,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,3,1,4,2,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,3,1,4,6,2,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,3,1,4,6,7,2]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,3,1,4,7,2,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,3,1,4,7,6,2]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,3,1,6,2,4,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,3,1,6,2,7,4]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,3,1,6,4,2,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,3,1,6,4,7,2]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,3,1,6,7,2,4]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,3,1,6,7,4,2]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,3,1,7,2,4,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,3,1,7,2,6,4]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,3,1,7,4,2,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,3,1,7,4,6,2]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,3,1,7,6,2,4]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,3,1,7,6,4,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,3,2,1,4,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,3,2,1,4,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,3,2,1,6,4,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,3,2,1,6,7,4]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,3,2,1,7,4,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,3,2,1,7,6,4]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,3,2,4,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,3,2,4,1,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,3,2,4,6,1,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,3,2,4,6,7,1]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,3,2,4,7,1,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,3,2,4,7,6,1]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,3,2,6,1,4,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,3,2,6,1,7,4]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,3,2,6,4,1,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,3,2,6,4,7,1]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,3,2,6,7,1,4]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,3,2,6,7,4,1]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,3,2,7,1,4,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,3,2,7,1,6,4]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,3,2,7,4,1,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,3,2,7,4,6,1]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,3,2,7,6,1,4]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,3,2,7,6,4,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,3,4,1,2,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,3,4,1,2,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,3,4,1,6,2,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,3,4,1,6,7,2]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,3,4,1,7,2,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,3,4,1,7,6,2]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,3,4,2,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,3,4,2,1,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,3,4,2,6,1,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,3,4,2,6,7,1]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,3,4,2,7,1,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,3,4,2,7,6,1]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,3,4,6,1,2,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,3,4,6,1,7,2]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,3,4,6,2,1,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,3,4,6,2,7,1]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,3,4,6,7,1,2]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,3,4,6,7,2,1]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,3,4,7,1,2,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,3,4,7,1,6,2]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,3,4,7,2,1,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,3,4,7,2,6,1]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,3,4,7,6,1,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,3,4,7,6,2,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,3,6,1,2,4,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,3,6,1,2,7,4]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,3,6,1,4,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,3,6,1,4,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,3,6,1,7,2,4]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,3,6,1,7,4,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,3,6,2,1,4,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,3,6,2,1,7,4]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,3,6,2,4,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,3,6,2,4,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,3,6,2,7,1,4]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,3,6,2,7,4,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,3,6,4,1,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,3,6,4,1,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,3,6,4,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,3,6,4,2,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,3,6,4,7,1,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,3,6,4,7,2,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,3,6,7,1,2,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,3,6,7,1,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,3,6,7,2,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,3,6,7,2,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,3,6,7,4,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,3,6,7,4,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,3,7,1,2,4,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[5,3,7,1,2,6,4]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[5,3,7,1,4,2,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[5,3,7,1,4,6,2]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[5,3,7,1,6,2,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,3,7,1,6,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,3,7,2,1,4,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[5,3,7,2,1,6,4]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[5,3,7,2,4,1,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[5,3,7,2,4,6,1]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[5,3,7,2,6,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,3,7,2,6,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,3,7,4,1,2,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[5,3,7,4,1,6,2]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[5,3,7,4,2,1,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[5,3,7,4,2,6,1]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[5,3,7,4,6,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,3,7,4,6,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,3,7,6,1,2,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,3,7,6,1,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,3,7,6,2,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,3,7,6,2,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,3,7,6,4,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,3,7,6,4,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,4,1,2,3,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,4,1,2,3,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,4,1,2,6,3,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,4,1,2,6,7,3]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,4,1,2,7,3,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,4,1,2,7,6,3]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,4,1,3,2,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,4,1,3,2,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,4,1,3,6,2,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,4,1,3,6,7,2]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,4,1,3,7,2,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,4,1,3,7,6,2]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,4,1,6,2,3,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,4,1,6,2,7,3]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,4,1,6,3,2,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,4,1,6,3,7,2]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,4,1,6,7,2,3]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,4,1,6,7,3,2]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,4,1,7,2,3,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,4,1,7,2,6,3]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,4,1,7,3,2,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,4,1,7,3,6,2]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,4,1,7,6,2,3]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,4,1,7,6,3,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,4,2,1,3,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,4,2,1,3,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,4,2,1,6,3,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,4,2,1,6,7,3]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,4,2,1,7,3,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,4,2,1,7,6,3]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,4,2,3,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,4,2,3,1,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,4,2,3,6,1,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,4,2,3,6,7,1]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,4,2,3,7,1,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,4,2,3,7,6,1]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,4,2,6,1,3,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,4,2,6,1,7,3]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,4,2,6,3,1,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,4,2,6,3,7,1]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,4,2,6,7,1,3]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,4,2,6,7,3,1]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,4,2,7,1,3,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,4,2,7,1,6,3]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,4,2,7,3,1,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,4,2,7,3,6,1]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,4,2,7,6,1,3]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,4,2,7,6,3,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,4,3,1,2,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,4,3,1,2,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,4,3,1,6,2,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,4,3,1,6,7,2]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,4,3,1,7,2,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,4,3,1,7,6,2]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[5,4,3,2,6,1,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,4,3,2,6,7,1]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,4,3,2,7,1,6]=>[6,4,3,2,7,1,5]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[5,4,3,2,7,6,1]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[5,4,3,6,1,2,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,4,3,6,1,7,2]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,4,3,6,2,1,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,4,3,6,2,7,1]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,4,3,6,7,1,2]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,4,3,6,7,2,1]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,4,3,7,1,2,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,4,3,7,1,6,2]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,4,3,7,2,1,6]=>[6,5,3,7,2,1,4]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,4,3,7,2,6,1]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,4,3,7,6,1,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,4,3,7,6,2,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,4,6,1,2,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,4,6,1,2,7,3]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,4,6,1,3,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,4,6,1,3,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,4,6,1,7,2,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,4,6,1,7,3,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,4,6,2,1,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,4,6,2,1,7,3]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,4,6,2,3,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,4,6,2,3,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,4,6,2,7,1,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,4,6,2,7,3,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,4,6,3,1,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,4,6,3,1,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,4,6,3,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,4,6,3,2,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,4,6,3,7,1,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,4,6,3,7,2,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,4,6,7,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,4,6,7,1,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,4,6,7,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,4,6,7,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,4,6,7,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,4,6,7,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,4,7,1,2,3,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[5,4,7,1,2,6,3]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[5,4,7,1,3,2,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[5,4,7,1,3,6,2]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[5,4,7,1,6,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,4,7,1,6,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,4,7,2,1,3,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[5,4,7,2,1,6,3]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[5,4,7,2,3,1,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[5,4,7,2,3,6,1]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[5,4,7,2,6,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,4,7,2,6,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,4,7,3,1,2,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[5,4,7,3,1,6,2]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[5,4,7,3,2,1,6]=>[6,5,7,4,2,1,3]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[5,4,7,3,2,6,1]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[5,4,7,3,6,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,4,7,3,6,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,4,7,6,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,4,7,6,1,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,4,7,6,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,4,7,6,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,4,7,6,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,4,7,6,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,1,2,3,4,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,6,1,2,3,7,4]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,6,1,2,4,3,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,6,1,2,4,7,3]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,6,1,2,7,3,4]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,6,1,2,7,4,3]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,6,1,3,2,4,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,6,1,3,2,7,4]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,6,1,3,4,2,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,6,1,3,4,7,2]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,6,1,3,7,2,4]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,6,1,3,7,4,2]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,6,1,4,2,3,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,6,1,4,2,7,3]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,6,1,4,3,2,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[5,6,1,4,3,7,2]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[5,6,1,4,7,2,3]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,6,1,4,7,3,2]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,6,1,7,2,3,4]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,6,1,7,2,4,3]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,6,1,7,3,2,4]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,6,1,7,3,4,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,6,1,7,4,2,3]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,6,1,7,4,3,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,6,2,1,3,4,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,6,2,1,3,7,4]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,6,2,1,4,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,6,2,1,4,7,3]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,6,2,1,7,3,4]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,6,2,1,7,4,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,6,2,3,1,4,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,6,2,3,1,7,4]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,6,2,3,4,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,6,2,3,4,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,6,2,3,7,1,4]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,6,2,3,7,4,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,6,2,4,1,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,6,2,4,1,7,3]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,6,2,4,3,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,6,2,4,3,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,6,2,4,7,1,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,6,2,4,7,3,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,6,2,7,1,3,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,2,7,1,4,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,2,7,3,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,2,7,3,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,2,7,4,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,2,7,4,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,3,1,2,4,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,6,3,1,2,7,4]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,6,3,1,4,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,6,3,1,4,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,6,3,1,7,2,4]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,6,3,1,7,4,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,6,3,2,1,4,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,6,3,2,1,7,4]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,6,3,2,4,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,6,3,2,4,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,6,3,2,7,1,4]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,6,3,2,7,4,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,6,3,4,1,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,6,3,4,1,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,6,3,4,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,6,3,4,2,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,6,3,4,7,1,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,6,3,4,7,2,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,6,3,7,1,2,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,3,7,1,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,3,7,2,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,3,7,2,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,3,7,4,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,3,7,4,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,4,1,2,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,6,4,1,2,7,3]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,6,4,1,3,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,6,4,1,3,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,6,4,1,7,2,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,6,4,1,7,3,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,6,4,2,1,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,6,4,2,1,7,3]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,6,4,2,3,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,6,4,2,3,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,6,4,2,7,1,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,6,4,2,7,3,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,6,4,3,1,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,6,4,3,1,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,6,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[5,6,4,3,2,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[5,6,4,3,7,1,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,6,4,3,7,2,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,6,4,7,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,4,7,1,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,4,7,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,4,7,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,4,7,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,4,7,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,7,1,2,3,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,7,1,2,4,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,7,1,3,2,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,7,1,3,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,7,1,4,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,7,1,4,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,7,2,1,3,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,7,2,1,4,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,7,2,3,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,7,2,3,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,7,2,4,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,7,2,4,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,7,3,1,2,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,7,3,1,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,7,3,2,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,7,3,2,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,7,3,4,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,7,3,4,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,7,4,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,7,4,1,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,7,4,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,7,4,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,7,4,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,6,7,4,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,1,2,3,4,6]=>[6,7,3,4,5,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[5,7,1,2,3,6,4]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,7,1,2,4,3,6]=>[6,7,3,4,5,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[5,7,1,2,4,6,3]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,7,1,2,6,3,4]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,7,1,2,6,4,3]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,7,1,3,2,4,6]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[5,7,1,3,2,6,4]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,7,1,3,4,2,6]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[5,7,1,3,4,6,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,7,1,3,6,2,4]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,7,1,3,6,4,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,7,1,4,2,3,6]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[5,7,1,4,2,6,3]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,7,1,4,3,2,6]=>[6,7,3,5,4,1,2]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[5,7,1,4,3,6,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,7,1,4,6,2,3]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,7,1,4,6,3,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,7,1,6,2,3,4]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,7,1,6,2,4,3]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,7,1,6,3,2,4]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,7,1,6,3,4,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,7,1,6,4,2,3]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,7,1,6,4,3,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[5,7,2,1,3,4,6]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[5,7,2,1,3,6,4]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,7,2,1,4,3,6]=>[6,7,4,3,5,1,2]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[5,7,2,1,4,6,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,7,2,1,6,3,4]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,7,2,1,6,4,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[5,7,2,3,1,4,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[5,7,2,3,1,6,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,2,3,4,1,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[5,7,2,3,4,6,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,2,3,6,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,2,3,6,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,2,4,1,3,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[5,7,2,4,1,6,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,2,4,3,1,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[5,7,2,4,3,6,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,2,4,6,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,2,4,6,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,2,6,1,3,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,2,6,1,4,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,2,6,3,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,2,6,3,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,2,6,4,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,2,6,4,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,3,1,2,4,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[5,7,3,1,2,6,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,3,1,4,2,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[5,7,3,1,4,6,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,3,1,6,2,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,3,1,6,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,3,2,1,4,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[5,7,3,2,1,6,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,3,2,4,1,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[5,7,3,2,4,6,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,3,2,6,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,3,2,6,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,3,4,1,2,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[5,7,3,4,1,6,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,3,4,2,1,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[5,7,3,4,2,6,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,3,4,6,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,3,4,6,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,3,6,1,2,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,3,6,1,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,3,6,2,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,3,6,2,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,3,6,4,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,3,6,4,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,4,1,2,3,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[5,7,4,1,2,6,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,4,1,3,2,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[5,7,4,1,3,6,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,4,1,6,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,4,1,6,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,4,2,1,3,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[5,7,4,2,1,6,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,4,2,3,1,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[5,7,4,2,3,6,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,4,2,6,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,4,2,6,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,4,3,1,2,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[5,7,4,3,1,6,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,4,3,2,1,6]=>[6,7,5,4,3,1,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[5,7,4,3,2,6,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,4,3,6,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,4,3,6,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,4,6,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,4,6,1,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,4,6,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,4,6,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,4,6,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,4,6,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,6,1,2,3,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,6,1,2,4,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,6,1,3,2,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,6,1,3,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,6,1,4,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,6,1,4,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,6,2,1,3,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,6,2,1,4,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,6,2,3,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,6,2,3,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,6,2,4,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,6,2,4,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,6,3,1,2,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,6,3,1,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,6,3,2,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,6,3,2,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,6,3,4,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,6,3,4,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,6,4,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,6,4,1,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,6,4,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,6,4,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,6,4,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[5,7,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,1,2,3,4,5,7]=>[6,2,3,4,5,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[6,1,2,3,4,7,5]=>[7,2,3,4,5,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,2,3,5,4,7]=>[6,2,3,4,5,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[6,1,2,3,5,7,4]=>[7,2,3,4,5,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,2,3,7,4,5]=>[7,2,3,4,6,5,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,2,3,7,5,4]=>[7,2,3,4,6,5,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,2,4,3,5,7]=>[6,2,3,5,4,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[6,1,2,4,3,7,5]=>[7,2,3,5,4,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,2,4,5,3,7]=>[6,2,3,5,4,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[6,1,2,4,5,7,3]=>[7,2,3,5,4,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,2,4,7,3,5]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,2,4,7,5,3]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,2,5,3,4,7]=>[6,2,3,5,4,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[6,1,2,5,3,7,4]=>[7,2,3,5,4,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,2,5,4,3,7]=>[6,2,3,5,4,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[6,1,2,5,4,7,3]=>[7,2,3,5,4,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,2,5,7,3,4]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,2,5,7,4,3]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,2,7,3,4,5]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,2,7,3,5,4]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,2,7,4,3,5]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,2,7,4,5,3]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,2,7,5,3,4]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,2,7,5,4,3]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,3,2,4,5,7]=>[6,2,4,3,5,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[6,1,3,2,4,7,5]=>[7,2,4,3,5,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,3,2,5,4,7]=>[6,2,4,3,5,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[6,1,3,2,5,7,4]=>[7,2,4,3,5,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,3,2,7,4,5]=>[7,2,4,3,6,5,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,3,2,7,5,4]=>[7,2,4,3,6,5,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,3,4,2,5,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[6,1,3,4,2,7,5]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,3,4,5,2,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[6,1,3,4,5,7,2]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,3,4,7,2,5]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,3,4,7,5,2]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,3,5,2,4,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[6,1,3,5,2,7,4]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,3,5,4,2,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[6,1,3,5,4,7,2]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,3,5,7,2,4]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,3,5,7,4,2]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,3,7,2,4,5]=>[7,2,5,6,3,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,3,7,2,5,4]=>[7,2,5,6,3,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,3,7,4,2,5]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,3,7,4,5,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,3,7,5,2,4]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,3,7,5,4,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,4,2,3,5,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[6,1,4,2,3,7,5]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,4,2,5,3,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[6,1,4,2,5,7,3]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,4,2,7,3,5]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,4,2,7,5,3]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,4,3,2,5,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[6,1,4,3,2,7,5]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,4,3,5,2,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[6,1,4,3,5,7,2]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,4,3,7,2,5]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,4,3,7,5,2]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,4,5,2,3,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[6,1,4,5,2,7,3]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,4,5,3,2,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[6,1,4,5,3,7,2]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,4,5,7,2,3]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,4,5,7,3,2]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,4,7,2,3,5]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,4,7,2,5,3]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,4,7,3,2,5]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,4,7,3,5,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,4,7,5,2,3]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,4,7,5,3,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,5,2,3,4,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[6,1,5,2,3,7,4]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,5,2,4,3,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[6,1,5,2,4,7,3]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,5,2,7,3,4]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,5,2,7,4,3]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,5,3,2,4,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[6,1,5,3,2,7,4]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,5,3,4,2,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[6,1,5,3,4,7,2]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,5,3,7,2,4]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,5,3,7,4,2]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,5,4,2,3,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[6,1,5,4,2,7,3]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,5,4,3,2,7]=>[6,2,5,4,3,1,7]=>[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[6,1,5,4,3,7,2]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,5,4,7,2,3]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,5,4,7,3,2]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,5,7,2,3,4]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,5,7,2,4,3]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,5,7,3,2,4]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,5,7,3,4,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,5,7,4,2,3]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,5,7,4,3,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,7,2,3,4,5]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,7,2,3,5,4]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,7,2,4,3,5]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,7,2,4,5,3]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,7,2,5,3,4]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,7,2,5,4,3]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,7,3,2,4,5]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,7,3,2,5,4]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,7,3,4,2,5]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,7,3,4,5,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,7,3,5,2,4]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,7,3,5,4,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,7,4,2,3,5]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,7,4,2,5,3]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,7,4,3,2,5]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,7,4,3,5,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,7,4,5,2,3]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,7,4,5,3,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,7,5,2,3,4]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,7,5,2,4,3]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,7,5,3,2,4]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,7,5,3,4,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,7,5,4,2,3]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,1,7,5,4,3,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[6,2,1,3,4,5,7]=>[6,3,2,4,5,1,7]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[6,2,1,3,4,7,5]=>[7,3,2,4,5,6,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[6,2,1,3,5,4,7]=>[6,3,2,4,5,1,7]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[6,2,1,3,5,7,4]=>[7,3,2,4,5,6,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[6,2,1,3,7,4,5]=>[7,3,2,4,6,5,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[6,2,1,3,7,5,4]=>[7,3,2,4,6,5,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[6,2,1,4,3,5,7]=>[6,3,2,5,4,1,7]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[6,2,1,4,3,7,5]=>[7,3,2,5,4,6,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[6,2,1,4,5,3,7]=>[6,3,2,5,4,1,7]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[6,2,1,4,5,7,3]=>[7,3,2,5,4,6,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[6,2,1,4,7,3,5]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[6,2,1,4,7,5,3]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[6,2,1,5,3,4,7]=>[6,3,2,5,4,1,7]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[6,2,1,5,3,7,4]=>[7,3,2,5,4,6,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[6,2,1,5,4,3,7]=>[6,3,2,5,4,1,7]=>[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[6,2,1,5,4,7,3]=>[7,3,2,5,4,6,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[6,2,1,5,7,3,4]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[6,2,1,5,7,4,3]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[6,2,1,7,3,4,5]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[6,2,1,7,3,5,4]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[6,2,1,7,4,3,5]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[6,2,1,7,4,5,3]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[6,2,1,7,5,3,4]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[6,2,1,7,5,4,3]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[6,2,3,1,4,5,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[6,2,3,1,4,7,5]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[6,2,3,1,5,4,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[6,2,3,1,5,7,4]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[6,2,3,1,7,4,5]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[6,2,3,1,7,5,4]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[6,2,3,4,1,5,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[6,2,3,4,1,7,5]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,2,3,4,5,1,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[6,2,3,4,5,7,1]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,2,3,4,7,1,5]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,2,3,4,7,5,1]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,2,3,5,1,4,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[6,2,3,5,1,7,4]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,2,3,5,4,1,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[6,2,3,5,4,7,1]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,2,3,5,7,1,4]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,2,3,5,7,4,1]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,2,3,7,1,4,5]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,2,3,7,1,5,4]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,2,3,7,4,1,5]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,2,3,7,4,5,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,2,3,7,5,1,4]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,2,3,7,5,4,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,2,4,1,3,5,7]=>[6,4,5,2,3,1,7]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[6,2,4,1,3,7,5]=>[7,4,5,2,3,6,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[6,2,4,1,5,3,7]=>[6,4,5,2,3,1,7]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[6,2,4,1,5,7,3]=>[7,4,5,2,3,6,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[6,2,4,1,7,3,5]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[6,2,4,1,7,5,3]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[6,2,4,3,1,5,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,2,4,3,1,7,5]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,2,4,3,5,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,2,4,3,5,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,2,4,3,7,1,5]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,2,4,3,7,5,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,2,4,5,1,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,2,4,5,1,7,3]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,2,4,5,3,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,2,4,5,3,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,2,4,5,7,1,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,2,4,5,7,3,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,2,4,7,1,3,5]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[6,2,4,7,1,5,3]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[6,2,4,7,3,1,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,2,4,7,3,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,2,4,7,5,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,2,4,7,5,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,2,5,1,3,4,7]=>[6,4,5,2,3,1,7]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[6,2,5,1,3,7,4]=>[7,4,5,2,3,6,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[6,2,5,1,4,3,7]=>[6,4,5,2,3,1,7]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[6,2,5,1,4,7,3]=>[7,4,5,2,3,6,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[6,2,5,1,7,3,4]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[6,2,5,1,7,4,3]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[6,2,5,3,1,4,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,2,5,3,1,7,4]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,2,5,3,4,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,2,5,3,4,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,2,5,3,7,1,4]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,2,5,3,7,4,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,2,5,4,1,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,2,5,4,1,7,3]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,2,5,4,3,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,2,5,4,3,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,2,5,4,7,1,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,2,5,4,7,3,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,2,5,7,1,3,4]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[6,2,5,7,1,4,3]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[6,2,5,7,3,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,2,5,7,3,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,2,5,7,4,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,2,5,7,4,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,2,7,1,3,4,5]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[6,2,7,1,3,5,4]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[6,2,7,1,4,3,5]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[6,2,7,1,4,5,3]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[6,2,7,1,5,3,4]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[6,2,7,1,5,4,3]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[6,2,7,3,1,4,5]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[6,2,7,3,1,5,4]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[6,2,7,3,4,1,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,2,7,3,4,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,2,7,3,5,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,2,7,3,5,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,2,7,4,1,3,5]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[6,2,7,4,1,5,3]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[6,2,7,4,3,1,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,2,7,4,3,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,2,7,4,5,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,2,7,4,5,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,2,7,5,1,3,4]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[6,2,7,5,1,4,3]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[6,2,7,5,3,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,2,7,5,3,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,2,7,5,4,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,2,7,5,4,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,1,2,4,5,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[6,3,1,2,4,7,5]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[6,3,1,2,5,4,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[6,3,1,2,5,7,4]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[6,3,1,2,7,4,5]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[6,3,1,2,7,5,4]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[6,3,1,4,2,5,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[6,3,1,4,2,7,5]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,3,1,4,5,2,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[6,3,1,4,5,7,2]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,3,1,4,7,2,5]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,3,1,4,7,5,2]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,3,1,5,2,4,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[6,3,1,5,2,7,4]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,3,1,5,4,2,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[6,3,1,5,4,7,2]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,3,1,5,7,2,4]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,3,1,5,7,4,2]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,3,1,7,2,4,5]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,3,1,7,2,5,4]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,3,1,7,4,2,5]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,3,1,7,4,5,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,3,1,7,5,2,4]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,3,1,7,5,4,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,3,2,1,4,5,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[6,3,2,1,4,7,5]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[6,3,2,1,5,4,7]=>[6,4,3,2,5,1,7]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[6,3,2,1,5,7,4]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[6,3,2,1,7,4,5]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[6,3,2,1,7,5,4]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[6,3,2,4,1,5,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[6,3,2,4,1,7,5]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,3,2,4,5,1,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[6,3,2,4,5,7,1]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,3,2,4,7,1,5]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,3,2,4,7,5,1]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,3,2,5,1,4,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[6,3,2,5,1,7,4]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,3,2,5,4,1,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[6,3,2,5,4,7,1]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,3,2,5,7,1,4]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,3,2,5,7,4,1]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,3,2,7,1,4,5]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,3,2,7,1,5,4]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,3,2,7,4,1,5]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,3,2,7,4,5,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,3,2,7,5,1,4]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,3,2,7,5,4,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,3,4,1,2,5,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,3,4,1,2,7,5]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,3,4,1,5,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,3,4,1,5,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,3,4,1,7,2,5]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,3,4,1,7,5,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,3,4,2,1,5,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,3,4,2,1,7,5]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,3,4,2,5,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,3,4,2,5,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,3,4,2,7,1,5]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,3,4,2,7,5,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,3,4,5,1,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,3,4,5,1,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,3,4,5,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,3,4,5,2,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,3,4,5,7,1,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,3,4,5,7,2,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,3,4,7,1,2,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,4,7,1,5,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,4,7,2,1,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,4,7,2,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,4,7,5,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,4,7,5,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,5,1,2,4,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,3,5,1,2,7,4]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,3,5,1,4,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,3,5,1,4,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,3,5,1,7,2,4]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,3,5,1,7,4,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,3,5,2,1,4,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,3,5,2,1,7,4]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,3,5,2,4,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,3,5,2,4,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,3,5,2,7,1,4]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,3,5,2,7,4,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,3,5,4,1,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,3,5,4,1,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,3,5,4,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,3,5,4,2,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,3,5,4,7,1,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,3,5,4,7,2,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,3,5,7,1,2,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,5,7,1,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,5,7,2,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,5,7,2,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,5,7,4,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,5,7,4,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,7,1,2,4,5]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[6,3,7,1,2,5,4]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[6,3,7,1,4,2,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,7,1,4,5,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,7,1,5,2,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,7,1,5,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,7,2,1,4,5]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[6,3,7,2,1,5,4]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[6,3,7,2,4,1,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,7,2,4,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,7,2,5,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,7,2,5,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,7,4,1,2,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,7,4,1,5,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,7,4,2,1,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,7,4,2,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,7,4,5,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,7,4,5,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,7,5,1,2,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,7,5,1,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,7,5,2,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,7,5,2,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,7,5,4,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,3,7,5,4,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,1,2,3,5,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[6,4,1,2,3,7,5]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,4,1,2,5,3,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[6,4,1,2,5,7,3]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,4,1,2,7,3,5]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,4,1,2,7,5,3]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,4,1,3,2,5,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[6,4,1,3,2,7,5]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,4,1,3,5,2,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[6,4,1,3,5,7,2]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,4,1,3,7,2,5]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,4,1,3,7,5,2]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,4,1,5,2,3,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[6,4,1,5,2,7,3]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,4,1,5,3,2,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[6,4,1,5,3,7,2]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,4,1,5,7,2,3]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,4,1,5,7,3,2]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,4,1,7,2,3,5]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,4,1,7,2,5,3]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,4,1,7,3,2,5]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,4,1,7,3,5,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,4,1,7,5,2,3]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,4,1,7,5,3,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,4,2,1,3,5,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,4,2,1,3,7,5]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,4,2,1,5,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,4,2,1,5,7,3]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,4,2,1,7,3,5]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,4,2,1,7,5,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,4,2,3,1,5,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,4,2,3,1,7,5]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,4,2,3,5,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,4,2,3,5,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,4,2,3,7,1,5]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,4,2,3,7,5,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,4,2,5,1,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,4,2,5,1,7,3]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,4,2,5,3,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,4,2,5,3,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,4,2,5,7,1,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,4,2,5,7,3,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,4,2,7,1,3,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,2,7,1,5,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,2,7,3,1,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,2,7,3,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,2,7,5,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,2,7,5,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,3,1,2,5,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,4,3,1,2,7,5]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,4,3,1,5,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,4,3,1,5,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,4,3,1,7,2,5]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,4,3,1,7,5,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,4,3,2,1,5,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,4,3,2,1,7,5]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,4,3,2,5,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,4,3,2,5,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,4,3,2,7,1,5]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,4,3,2,7,5,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,4,3,5,1,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,4,3,5,1,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,4,3,5,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,4,3,5,2,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,4,3,5,7,1,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,4,3,5,7,2,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,4,3,7,1,2,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,3,7,1,5,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,3,7,2,1,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,3,7,2,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,3,7,5,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,3,7,5,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,5,1,2,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,4,5,1,2,7,3]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,4,5,1,3,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,4,5,1,3,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,4,5,1,7,2,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,4,5,1,7,3,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,4,5,2,1,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,4,5,2,1,7,3]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,4,5,2,3,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,4,5,2,3,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,4,5,2,7,1,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,4,5,2,7,3,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,4,5,3,1,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,4,5,3,1,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,4,5,3,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,4,5,3,2,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,4,5,3,7,1,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,4,5,3,7,2,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,4,5,7,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,5,7,1,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,5,7,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,5,7,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,5,7,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,5,7,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,7,1,2,3,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,7,1,2,5,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,7,1,3,2,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,7,1,3,5,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,7,1,5,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,7,1,5,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,7,2,1,3,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,7,2,1,5,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,7,2,3,1,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,7,2,3,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,7,2,5,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,7,2,5,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,7,3,1,2,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,7,3,1,5,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,7,3,2,1,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,7,3,2,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,7,3,5,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,7,3,5,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,7,5,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,7,5,1,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,7,5,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,7,5,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,7,5,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,4,7,5,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,1,2,3,4,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[6,5,1,2,3,7,4]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,5,1,2,4,3,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[6,5,1,2,4,7,3]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,5,1,2,7,3,4]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,5,1,2,7,4,3]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,5,1,3,2,4,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[6,5,1,3,2,7,4]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,5,1,3,4,2,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[6,5,1,3,4,7,2]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,5,1,3,7,2,4]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,5,1,3,7,4,2]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,5,1,4,2,3,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[6,5,1,4,2,7,3]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,5,1,4,3,2,7]=>[6,5,3,4,2,1,7]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[6,5,1,4,3,7,2]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[6,5,1,4,7,2,3]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,5,1,4,7,3,2]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,5,1,7,2,3,4]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,5,1,7,2,4,3]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,5,1,7,3,2,4]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,5,1,7,3,4,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,5,1,7,4,2,3]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,5,1,7,4,3,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,5,2,1,3,4,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,5,2,1,3,7,4]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,5,2,1,4,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,5,2,1,4,7,3]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,5,2,1,7,3,4]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,5,2,1,7,4,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,5,2,3,1,4,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,5,2,3,1,7,4]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,5,2,3,4,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,5,2,3,4,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,5,2,3,7,1,4]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,5,2,3,7,4,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,5,2,4,1,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,5,2,4,1,7,3]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,5,2,4,3,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,5,2,4,3,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,5,2,4,7,1,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,5,2,4,7,3,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,5,2,7,1,3,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,2,7,1,4,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,2,7,3,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,2,7,3,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,2,7,4,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,2,7,4,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,3,1,2,4,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,5,3,1,2,7,4]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,5,3,1,4,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,5,3,1,4,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,5,3,1,7,2,4]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,5,3,1,7,4,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,5,3,2,1,4,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,5,3,2,1,7,4]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,5,3,2,4,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,5,3,2,4,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,5,3,2,7,1,4]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,5,3,2,7,4,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,5,3,4,1,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,5,3,4,1,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,5,3,4,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,5,3,4,2,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,5,3,4,7,1,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,5,3,4,7,2,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,5,3,7,1,2,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,3,7,1,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,3,7,2,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,3,7,2,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,3,7,4,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,3,7,4,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,4,1,2,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,5,4,1,2,7,3]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,5,4,1,3,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,5,4,1,3,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,5,4,1,7,2,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,5,4,1,7,3,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,5,4,2,1,3,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,5,4,2,1,7,3]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,5,4,2,3,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,5,4,2,3,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,5,4,2,7,1,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,5,4,2,7,3,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,5,4,3,1,2,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,5,4,3,1,7,2]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[6,5,4,3,2,7,1]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[6,5,4,3,7,1,2]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,5,4,3,7,2,1]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,5,4,7,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,4,7,1,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,4,7,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,4,7,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,4,7,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,4,7,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,7,1,2,3,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,7,1,2,4,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,7,1,3,2,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,7,1,3,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,7,1,4,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,7,1,4,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,7,2,1,3,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,7,2,1,4,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,7,2,3,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,7,2,3,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,7,2,4,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,7,2,4,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,7,3,1,2,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,7,3,1,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,7,3,2,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,7,3,2,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,7,3,4,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,7,3,4,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,7,4,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,7,4,1,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,7,4,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,7,4,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,7,4,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,5,7,4,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,1,2,3,4,5]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,7,1,2,3,5,4]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,7,1,2,4,3,5]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,7,1,2,4,5,3]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,7,1,2,5,3,4]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,7,1,2,5,4,3]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,7,1,3,2,4,5]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,7,1,3,2,5,4]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,7,1,3,4,2,5]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,7,1,3,4,5,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,7,1,3,5,2,4]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,7,1,3,5,4,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,7,1,4,2,3,5]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,7,1,4,2,5,3]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,7,1,4,3,2,5]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,7,1,4,3,5,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,7,1,4,5,2,3]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,7,1,4,5,3,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,7,1,5,2,3,4]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,7,1,5,2,4,3]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,7,1,5,3,2,4]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,7,1,5,3,4,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,7,1,5,4,2,3]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,7,1,5,4,3,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[6,7,2,1,3,4,5]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,7,2,1,3,5,4]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,7,2,1,4,3,5]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,7,2,1,4,5,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,7,2,1,5,3,4]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,7,2,1,5,4,3]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[6,7,2,3,1,4,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,2,3,1,5,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,2,3,4,1,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,2,3,4,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,2,3,5,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,2,3,5,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,2,4,1,3,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,2,4,1,5,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,2,4,3,1,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,2,4,3,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,2,4,5,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,2,4,5,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,2,5,1,3,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,2,5,1,4,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,2,5,3,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,2,5,3,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,2,5,4,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,3,1,2,4,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,3,1,2,5,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,3,1,4,2,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,3,1,4,5,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,3,1,5,2,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,3,1,5,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,3,2,1,4,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,3,2,1,5,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,3,2,4,1,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,3,2,4,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,3,2,5,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,3,2,5,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,3,4,1,2,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,3,4,1,5,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,3,4,2,1,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,3,4,2,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,3,4,5,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,3,4,5,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,3,5,1,2,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,3,5,1,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,3,5,2,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,3,5,2,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,3,5,4,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,4,1,2,3,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,4,1,2,5,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,4,1,3,2,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,4,1,3,5,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,4,1,5,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,4,1,5,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,4,2,1,3,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,4,2,1,5,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,4,2,3,1,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,4,2,3,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,4,2,5,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,4,2,5,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,4,3,1,2,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,4,3,1,5,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,4,3,2,1,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,4,3,2,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,4,3,5,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,4,3,5,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,4,5,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,4,5,1,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,4,5,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,4,5,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,4,5,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,5,1,2,3,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,5,1,2,4,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,5,1,3,2,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,5,1,3,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,5,1,4,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,5,2,1,3,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,5,2,1,4,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,5,2,3,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,5,2,3,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,5,2,4,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,5,3,1,2,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,5,3,1,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,5,3,2,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,5,3,2,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,5,3,4,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,5,4,1,2,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,5,4,2,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[6,7,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[7,1,2,3,4,5,6]=>[7,2,3,4,5,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,2,3,4,6,5]=>[7,2,3,4,5,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,2,3,5,4,6]=>[7,2,3,4,6,5,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,2,3,5,6,4]=>[7,2,3,4,6,5,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,2,3,6,4,5]=>[7,2,3,4,6,5,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,2,3,6,5,4]=>[7,2,3,4,6,5,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,2,4,3,5,6]=>[7,2,3,5,4,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,2,4,3,6,5]=>[7,2,3,5,4,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,2,4,5,3,6]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,2,4,5,6,3]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,2,4,6,3,5]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,2,4,6,5,3]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,2,5,3,4,6]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,2,5,3,6,4]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,2,5,4,3,6]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,2,5,4,6,3]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,2,5,6,3,4]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,2,5,6,4,3]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,2,6,3,4,5]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,2,6,3,5,4]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,2,6,4,3,5]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,2,6,4,5,3]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,2,6,5,3,4]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,2,6,5,4,3]=>[7,2,3,6,5,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,3,2,4,5,6]=>[7,2,4,3,5,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,3,2,4,6,5]=>[7,2,4,3,5,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,3,2,5,4,6]=>[7,2,4,3,6,5,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,3,2,5,6,4]=>[7,2,4,3,6,5,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,3,2,6,4,5]=>[7,2,4,3,6,5,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,3,2,6,5,4]=>[7,2,4,3,6,5,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,3,4,2,5,6]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,3,4,2,6,5]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,3,4,5,2,6]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,3,4,5,6,2]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,3,4,6,2,5]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,3,4,6,5,2]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,3,5,2,4,6]=>[7,2,5,6,3,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,3,5,2,6,4]=>[7,2,5,6,3,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,3,5,4,2,6]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,3,5,4,6,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,3,5,6,2,4]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,3,5,6,4,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,3,6,2,4,5]=>[7,2,5,6,3,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,3,6,2,5,4]=>[7,2,5,6,3,4,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,3,6,4,2,5]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,3,6,4,5,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,3,6,5,2,4]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,3,6,5,4,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,4,2,3,5,6]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,4,2,3,6,5]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,4,2,5,3,6]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,4,2,5,6,3]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,4,2,6,3,5]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,4,2,6,5,3]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,4,3,2,5,6]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,4,3,2,6,5]=>[7,2,5,4,3,6,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,4,3,5,2,6]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,4,3,5,6,2]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,4,3,6,2,5]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,4,3,6,5,2]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,4,5,2,3,6]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,4,5,2,6,3]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,4,5,3,2,6]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,4,5,3,6,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,4,5,6,2,3]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,4,5,6,3,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,4,6,2,3,5]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,4,6,2,5,3]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,4,6,3,2,5]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,4,6,3,5,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,4,6,5,2,3]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,4,6,5,3,2]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,5,2,3,4,6]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,5,2,3,6,4]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,5,2,4,3,6]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,5,2,4,6,3]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,5,2,6,3,4]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,5,2,6,4,3]=>[7,2,6,4,5,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,5,3,2,4,6]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,5,3,2,6,4]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[7,1,5,3,4,2,6]=>[7,2,6,5,4,3,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
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[7,2,1,4,5,3,6]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
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[7,2,1,5,3,4,6]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
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[7,2,1,5,4,3,6]=>[7,3,2,6,5,4,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
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[7,2,3,5,1,4,6]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
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[7,2,3,6,1,4,5]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
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[7,2,4,1,3,5,6]=>[7,4,5,2,3,6,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[7,2,4,1,3,6,5]=>[7,4,5,2,3,6,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[7,2,4,1,5,3,6]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[7,2,4,1,5,6,3]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[7,2,4,1,6,3,5]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[7,2,4,1,6,5,3]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[7,2,4,3,1,5,6]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[7,2,4,3,1,6,5]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
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[7,2,4,5,1,3,6]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[7,2,4,5,1,6,3]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
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[7,2,4,6,1,3,5]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
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[7,2,5,1,4,3,6]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[7,2,5,1,4,6,3]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[7,2,5,1,6,3,4]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[7,2,5,1,6,4,3]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[7,2,5,3,1,4,6]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[7,2,5,3,1,6,4]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
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[7,2,5,4,1,6,3]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
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[7,2,5,4,6,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[7,2,5,4,6,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[7,2,5,6,1,3,4]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[7,2,5,6,1,4,3]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
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[7,2,5,6,4,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[7,2,6,1,3,4,5]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[7,2,6,1,3,5,4]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[7,2,6,1,4,3,5]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[7,2,6,1,4,5,3]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[7,2,6,1,5,3,4]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[7,2,6,1,5,4,3]=>[7,4,6,2,5,3,1]=>[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[7,2,6,3,1,4,5]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[7,2,6,3,1,5,4]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[7,2,6,3,4,1,5]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
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[7,2,6,3,5,1,4]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
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[7,2,6,4,1,3,5]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[7,2,6,4,1,5,3]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
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[7,2,6,4,3,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[7,2,6,4,5,1,3]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
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[7,2,6,5,1,3,4]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[7,2,6,5,1,4,3]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
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[7,3,1,2,4,6,5]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[7,3,1,2,5,4,6]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[7,3,1,2,5,6,4]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[7,3,1,2,6,4,5]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[7,3,1,2,6,5,4]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[7,3,1,4,2,5,6]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[7,3,1,4,2,6,5]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
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[7,3,1,4,5,6,2]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[7,3,1,4,6,2,5]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[7,3,1,4,6,5,2]=>[7,6,3,4,5,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[7,3,1,5,2,4,6]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[7,3,1,5,2,6,4]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[7,3,1,5,4,2,6]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[7,3,1,5,4,6,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[7,3,1,5,6,2,4]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[7,3,1,5,6,4,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[7,3,1,6,2,4,5]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[7,3,1,6,2,5,4]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[7,3,1,6,4,2,5]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[7,3,1,6,4,5,2]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[7,3,1,6,5,2,4]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
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[7,3,2,1,4,5,6]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[7,3,2,1,4,6,5]=>[7,4,3,2,5,6,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[7,3,2,1,5,4,6]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[7,3,2,1,5,6,4]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[7,3,2,1,6,4,5]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[7,3,2,1,6,5,4]=>[7,4,3,2,6,5,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[7,3,2,4,1,5,6]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[7,3,2,4,1,6,5]=>[7,5,3,4,2,6,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
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[7,3,2,5,1,4,6]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[7,3,2,5,1,6,4]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
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[7,3,2,5,4,6,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
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[7,3,2,6,1,4,5]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[7,3,2,6,1,5,4]=>[7,5,3,6,2,4,1]=>[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
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[7,3,2,6,4,5,1]=>[7,6,3,5,4,2,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
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[7,3,4,1,2,5,6]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[7,3,4,1,2,6,5]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[7,3,4,1,5,2,6]=>[7,6,4,3,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
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[7,3,4,2,1,6,5]=>[7,5,4,3,2,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
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[7,3,5,2,1,4,6]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[7,3,5,2,1,6,4]=>[7,5,6,4,2,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
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[7,4,6,3,2,5,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
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[7,6,5,3,1,4,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
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[7,6,5,3,2,4,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
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[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
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[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
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[7,8,6,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
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[7,4,5,6,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
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[7,8,6,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
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[7,8,6,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
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[3,4,5,6,7,2,8,1]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,6,5,4,2,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,7,5,4,2,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
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[7,6,4,5,2,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,7,4,5,2,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,4,6,2,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,4,5,6,2,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
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[5,4,6,7,2,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
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[6,7,5,3,2,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,5,7,3,2,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,6,5,2,3,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,6,2,3,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
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[6,7,4,3,2,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,6,4,2,3,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,6,3,2,4,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,7,3,2,4,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,6,2,3,4,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,7,2,3,4,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,4,3,2,6,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,4,3,5,2,6,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,4,2,3,6,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,4,5,2,3,6,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
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[6,5,3,4,2,7,8,1]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
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[5,4,3,6,2,7,8,1]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,3,5,6,2,7,8,1]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,4,5,6,2,7,8,1]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,5,4,2,3,7,8,1]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
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[4,5,6,2,3,7,8,1]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[6,5,3,2,4,7,8,1]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[6,5,2,3,4,7,8,1]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,6,2,3,4,7,8,1]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[6,2,3,4,5,7,8,1]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,4,3,2,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,5,3,2,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,3,4,2,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,3,5,2,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,4,5,2,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,4,2,3,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,5,2,3,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,3,2,4,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,2,3,4,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,3,2,5,6,7,8,1]=>[8,3,2,4,5,6,7,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,4,2,5,6,7,8,1]=>[8,3,2,4,5,6,7,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,2,3,5,6,7,8,1]=>[8,3,2,4,5,6,7,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,2,4,5,6,7,8,1]=>[8,2,3,4,5,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,4,5,6,7,8,1]=>[8,2,3,4,5,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
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[7,8,5,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,5,7,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,5,8,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
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[8,7,6,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,6,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,7,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
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[8,7,5,4,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,4,5,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,6,4,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
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[7,6,5,4,8,3,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,6,4,8,3,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,7,4,8,3,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,4,5,8,3,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,4,5,8,3,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,4,7,8,3,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,4,7,8,3,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,4,6,7,8,3,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,6,7,8,3,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,6,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,8,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,8,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,5,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,5,7,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,6,7,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,5,8,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,5,8,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,6,8,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,7,8,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,7,8,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,8,4,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,3,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,6,3,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,7,3,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,8,3,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,4,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,4,5,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,4,5,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,3,4,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
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[8,7,3,4,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
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[8,5,4,3,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,3,4,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,3,5,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,4,5,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,5,4,3,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,6,4,3,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,5,7,4,3,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,7,4,3,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,7,4,5,3,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,4,6,3,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,5,4,7,3,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,4,7,3,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,4,5,7,3,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,4,6,7,3,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,5,6,7,3,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,6,5,3,4,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,6,3,4,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,7,3,4,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,6,4,3,5,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,6,3,4,5,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,4,3,6,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,4,5,3,6,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,3,4,6,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,3,4,5,6,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,5,4,3,7,8,1,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,6,4,3,7,8,1,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,4,6,3,7,8,1,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,5,6,3,7,8,1,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,5,3,4,7,8,1,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,6,3,4,7,8,1,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,4,3,5,7,8,1,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,3,4,5,7,8,1,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,4,3,6,7,8,1,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,5,3,6,7,8,1,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,3,4,6,7,8,1,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,3,5,6,7,8,1,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,4,5,6,7,8,1,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,6,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,7,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,8,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,8,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,5,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,5,7,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,5,8,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,5,8,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,6,8,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,7,8,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,7,8,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,4,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,7,4,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,8,4,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,4,5,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,5,4,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,4,5,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,5,6,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,5,4,8,2,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,5,4,8,2,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,6,4,8,2,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,7,4,8,2,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,7,4,8,2,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,4,5,8,2,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,4,6,8,2,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,5,6,8,2,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,4,6,7,8,2,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,6,7,8,2,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,6,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,8,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,8,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,6,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,5,7,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,6,7,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,5,8,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,5,8,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,6,8,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,7,8,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,7,8,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,4,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,7,4,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,8,4,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,5,4,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,4,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,4,5,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,4,5,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,5,4,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,6,4,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,4,5,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,4,6,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,5,6,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,5,4,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,5,4,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,6,4,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,7,4,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,7,4,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,4,5,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,4,5,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,4,6,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,5,6,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,4,7,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,4,7,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,5,7,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,4,6,7,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,6,7,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,6,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,6,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,7,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
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[7,5,4,6,2,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,5,6,2,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,5,4,7,2,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,6,4,7,2,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,4,6,7,2,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,5,6,7,2,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,5,3,2,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,5,7,3,2,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,6,7,3,2,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,5,2,3,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,5,2,3,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,6,2,3,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,5,7,2,3,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,6,7,2,3,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,4,3,2,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,4,3,2,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,3,4,2,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,4,2,3,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,4,2,3,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,3,2,4,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,3,2,4,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,2,3,4,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,2,3,4,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,4,3,2,6,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,5,3,2,6,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,3,4,2,6,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,3,5,2,6,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,4,2,3,6,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,5,2,3,6,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,3,2,4,6,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,2,3,5,6,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,2,3,4,5,6,1,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,5,4,3,2,7,1,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,6,4,3,2,7,1,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,4,6,3,2,7,1,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,6,3,4,2,7,1,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,3,4,5,2,7,1,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,4,3,6,2,7,1,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,5,3,6,2,7,1,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,3,4,6,2,7,1,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,3,5,6,2,7,1,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,4,5,6,2,7,1,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,4,6,2,3,7,1,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,5,3,2,4,7,1,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,4,2,3,5,7,1,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,3,2,4,5,7,1,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,2,3,4,5,7,1,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,2,4,5,6,7,1,8]=>[7,2,3,4,5,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,3,4,5,6,7,1,8]=>[7,2,3,4,5,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,6,5,4,3,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,5,4,3,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,6,4,3,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,4,5,3,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,5,6,3,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,4,6,7,3,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,5,6,7,3,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,5,3,4,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,6,3,4,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,5,7,3,4,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,3,4,5,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,3,4,6,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,5,4,3,7,1,2,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,4,5,3,7,1,2,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[5,6,3,4,7,1,2,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,4,3,5,7,1,2,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,3,4,5,7,1,2,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,3,5,6,7,1,2,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,4,5,6,7,1,2,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,6,5,4,2,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,5,7,4,2,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,4,5,2,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,4,6,2,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,5,6,2,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,4,6,7,2,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,5,6,7,2,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,5,4,1,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,6,4,1,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,6,7,4,1,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,4,5,1,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,4,6,1,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,5,6,1,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,6,4,7,1,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,4,6,7,1,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,5,6,7,1,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,5,3,2,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,5,2,3,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,5,2,3,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,6,2,3,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,5,7,2,3,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,6,7,2,3,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,6,3,1,2,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,6,7,3,1,2,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,5,2,1,3,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,5,2,1,3,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,6,2,1,3,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,6,7,2,1,3,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,5,1,2,3,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,5,1,2,3,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,6,1,2,3,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,5,7,1,2,3,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,6,7,1,2,3,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,4,3,2,1,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,4,3,2,1,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,3,4,2,1,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,3,4,2,1,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,4,2,3,1,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,4,2,3,1,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,3,2,4,1,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,3,2,4,1,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,2,3,4,1,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,2,3,4,1,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,4,3,1,2,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,3,4,1,2,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,4,2,1,3,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,3,2,1,4,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,3,2,1,4,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,2,3,1,4,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,2,3,1,4,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,3,1,2,4,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,1,2,3,4,5,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,7,1,2,3,4,5,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,5,4,3,2,1,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,5,3,2,1,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,3,5,2,1,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,3,4,5,2,1,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,4,2,3,1,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,3,2,4,1,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,2,3,4,1,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,2,3,5,1,6,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,2,3,4,5,1,6,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,5,4,3,1,2,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,3,4,1,2,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,5,2,1,3,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,5,1,2,3,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,3,2,1,4,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,2,3,1,4,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,3,1,2,4,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,1,2,3,4,6,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,4,3,2,1,5,6,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[7,2,3,4,1,5,6,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[7,4,3,1,2,5,6,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[7,3,4,1,2,5,6,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[7,4,1,2,3,5,6,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[7,1,2,3,4,5,6,8]=>[7,2,3,4,5,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,6,4,3,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,4,6,3,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,5,6,3,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,5,3,4,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,6,3,4,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,3,4,5,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,4,3,6,2,1,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,4,5,6,2,1,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,4,6,2,3,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,6,3,2,4,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,5,2,3,4,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,6,2,3,4,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,4,3,2,5,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,2,3,4,5,1,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,4,3,2,6,1,7,8]=>[6,4,3,2,5,1,7,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,5,3,2,6,1,7,8]=>[6,4,3,2,5,1,7,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,3,5,2,6,1,7,8]=>[6,4,3,2,5,1,7,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,4,5,2,6,1,7,8]=>[6,4,3,2,5,1,7,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,3,2,4,6,1,7,8]=>[6,4,3,2,5,1,7,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,2,3,4,6,1,7,8]=>[6,4,3,2,5,1,7,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,2,4,5,6,1,7,8]=>[6,2,3,4,5,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,4,5,6,1,7,8]=>[6,2,3,4,5,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,5,4,3,1,2,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,6,4,3,1,2,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,4,5,3,1,2,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,4,6,3,1,2,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,6,3,4,1,2,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,4,3,5,1,2,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,4,3,6,1,2,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,3,5,6,1,2,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,4,5,6,1,2,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,5,4,2,1,3,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,6,4,2,1,3,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,4,5,2,1,3,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,4,6,2,1,3,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,5,6,2,1,3,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,5,4,1,2,3,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,5,6,1,2,3,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,5,3,2,1,4,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,6,3,2,1,4,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,6,2,1,3,4,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,5,1,2,3,4,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,6,1,2,3,4,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,4,3,2,1,5,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,3,4,2,1,5,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,4,3,1,2,5,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,4,2,1,3,5,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,4,1,2,3,5,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,3,2,1,4,5,7,8]=>[6,4,3,2,5,1,7,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[6,2,3,1,4,5,7,8]=>[6,4,3,2,5,1,7,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[6,3,1,2,4,5,7,8]=>[6,4,3,2,5,1,7,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[6,1,2,3,4,5,7,8]=>[6,2,3,4,5,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,5,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,3,4,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,3,5,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,4,5,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,4,2,3,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,5,2,3,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,3,2,4,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,2,3,4,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,3,2,5,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,4,2,5,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,2,3,5,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,2,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[5,4,3,1,2,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,3,4,1,2,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,3,5,1,2,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,4,5,1,2,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,4,2,1,3,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,5,2,1,3,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,4,1,2,3,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,5,1,2,3,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,3,2,1,4,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,2,3,1,4,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,3,1,2,4,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,2,1,3,4,6,7,8]=>[5,3,2,4,1,6,7,8]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[5,1,2,3,4,6,7,8]=>[5,2,3,4,1,6,7,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,4,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,2,3,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,2,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,3,1,2,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,4,1,2,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,2,1,3,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,1,2,3,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,1,2,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,7,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,8,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,8,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,6,8,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,8,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,8,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,6,8,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,7,8,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,7,8,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,8,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,7,8,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,4,8,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,4,8,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,5,8,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,6,8,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,6,4,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,7,6,5,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,6,7,5,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,4,7,6,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,7,6,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,6,5,7,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,7,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,8,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,8,7,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,6,8,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,8,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,7,8,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,6,8,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,6,5,8,4,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,7,5,8,4,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,5,7,6,8,4,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,5,6,7,8,4,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,3,8,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,7,8,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,6,7,8,5,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,4,8,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,6,7,8,5,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,4,3,8,7,6,2,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,3,7,8,6,2,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,5,3,7,8,6,2,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,5,4,7,8,6,2,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,3,5,7,8,6,2,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,4,5,8,7,6,2,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,4,5,7,8,6,2,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,5,4,3,8,7,2,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,6,4,3,8,7,2,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,5,6,3,8,7,2,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,6,5,4,8,7,2,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,3,6,5,8,7,2,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,4,3,6,8,7,2,1]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,5,3,6,8,7,2,1]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,3,5,6,8,7,2,1]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,4,5,6,8,7,2,1]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,7,6,4,3,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,7,6,5,3,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,4,7,6,3,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,7,6,5,4,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,5,7,6,4,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,5,6,7,4,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,3,7,6,5,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,4,7,6,5,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,4,6,7,5,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,5,3,7,6,8,2,1]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,5,4,7,6,8,2,1]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,3,5,7,6,8,2,1]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,4,5,7,6,8,2,1]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,5,4,7,8,2,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,5,6,4,7,8,2,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,3,6,5,7,8,2,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,4,6,5,7,8,2,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,5,4,6,7,8,2,1]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,8,7,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,8,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,8,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,6,8,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,7,8,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,8,7,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,7,5,8,4,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,6,5,7,8,4,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,5,6,7,8,4,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
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[3,2,6,5,8,7,4,1]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
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[3,2,5,7,6,8,4,1]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,5,6,7,8,4,1]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
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[3,4,2,7,8,6,5,1]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,4,3,8,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,4,3,6,8,7,5,1]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
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[3,2,4,7,8,6,5,1]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,4,8,7,6,5,1]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,4,7,8,6,5,1]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,4,6,8,7,5,1]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
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[3,4,5,2,7,8,6,1]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
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[2,5,4,3,7,8,6,1]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
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[2,4,5,3,7,8,6,1]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,2,5,4,7,8,6,1]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
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[2,3,5,4,7,8,6,1]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
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[3,4,2,5,8,7,6,1]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,4,2,5,7,8,6,1]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,4,3,5,8,7,6,1]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,2,4,5,7,8,6,1]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,4,5,8,7,6,1]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,4,5,7,8,6,1]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,5,4,3,2,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
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[4,5,6,3,2,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
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[3,5,6,4,2,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,3,6,5,2,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,4,3,6,2,8,7,1]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,5,3,6,2,8,7,1]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,5,4,6,2,8,7,1]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,4,5,6,2,8,7,1]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,6,5,4,3,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[2,4,6,5,3,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[2,4,5,6,3,8,7,1]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,2,6,5,4,8,7,1]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,5,6,4,8,7,1]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,3,2,6,5,8,7,1]=>[8,3,2,5,4,7,6,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,4,2,6,5,8,7,1]=>[8,3,2,5,4,7,6,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,4,3,6,5,8,7,1]=>[8,3,2,5,4,7,6,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,2,4,6,5,8,7,1]=>[8,2,3,5,4,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,4,6,5,8,7,1]=>[8,2,3,5,4,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,4,3,2,6,8,7,1]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,5,3,2,6,8,7,1]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,5,4,3,6,8,7,1]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,4,5,3,6,8,7,1]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,2,4,5,6,8,7,1]=>[8,2,3,4,5,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,4,5,6,8,7,1]=>[8,2,3,4,5,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,6,4,3,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,7,6,5,3,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,6,7,5,3,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
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[1,2,4,7,6,5,8,3]=>[1,2,8,6,5,4,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,5,4,7,8,3]=>[1,2,8,5,4,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
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[3,2,1,7,8,6,5,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,6,8,7,5,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,7,6,8,5,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,6,7,8,5,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,5,8,7,6,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,5,7,8,6,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,6,5,8,7,4]=>[3,2,1,8,5,7,6,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,5,6,8,7,4]=>[3,2,1,8,5,7,6,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,7,6,5,8,4]=>[3,2,1,8,6,5,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
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[3,2,1,5,7,6,8,4]=>[3,2,1,8,6,5,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,6,5,7,8,4]=>[3,2,1,8,5,6,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
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[2,3,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,7,8,6,5,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,6,8,7,5,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,7,6,8,5,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,6,7,8,5,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,5,7,8,6,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,6,5,8,7,4]=>[3,2,1,8,5,7,6,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,7,6,5,8,4]=>[3,2,1,8,6,5,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,6,7,5,8,4]=>[3,2,1,8,6,5,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,5,7,6,8,4]=>[3,2,1,8,6,5,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,5,6,7,8,4]=>[3,2,1,8,5,6,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,2,8,7,6,5,4]=>[1,3,2,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,6,8,7,5,4]=>[1,3,2,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,7,6,8,5,4]=>[1,3,2,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,6,7,8,5,4]=>[1,3,2,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,5,8,7,6,4]=>[1,3,2,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,5,7,8,6,4]=>[1,3,2,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,6,5,8,7,4]=>[1,3,2,8,5,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,5,6,8,7,4]=>[1,3,2,8,5,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,7,6,5,8,4]=>[1,3,2,8,6,5,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,6,7,5,8,4]=>[1,3,2,8,6,5,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,5,7,6,8,4]=>[1,3,2,8,6,5,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,3,8,7,6,5,4]=>[2,1,3,8,7,6,5,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,3,7,8,6,5,4]=>[2,1,3,8,7,6,5,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,3,6,8,7,5,4]=>[2,1,3,8,7,6,5,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,3,6,7,8,5,4]=>[2,1,3,8,7,6,5,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,3,6,5,8,7,4]=>[2,1,3,8,5,7,6,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,3,5,7,6,8,4]=>[2,1,3,8,6,5,7,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,3,5,6,7,8,4]=>[2,1,3,8,5,6,7,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,3,8,7,6,5,4]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,7,8,6,5,4]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,6,8,7,5,4]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,7,6,8,5,4]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,6,7,8,5,4]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,5,8,7,6,4]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,5,7,8,6,4]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,6,5,8,7,4]=>[1,2,3,8,5,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,5,6,8,7,4]=>[1,2,3,8,5,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,7,6,5,8,4]=>[1,2,3,8,6,5,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,6,7,5,8,4]=>[1,2,3,8,6,5,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,5,7,6,8,4]=>[1,2,3,8,6,5,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,6,5,7,8,4]=>[1,2,3,8,5,6,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,3,2,1,7,8,6,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,3,2,1,6,8,7,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,3,2,1,7,6,8,5]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,3,2,1,6,7,8,5]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,4,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,4,2,1,7,8,6,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,4,2,1,6,8,7,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,4,2,1,7,6,8,5]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,4,2,1,6,7,8,5]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[2,4,3,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[2,4,3,1,7,8,6,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[2,4,3,1,6,8,7,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[2,4,3,1,7,6,8,5]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[2,4,3,1,6,7,8,5]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,2,4,1,8,7,6,5]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,4,1,7,8,6,5]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,4,1,6,8,7,5]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,4,1,7,6,8,5]=>[4,2,3,1,8,6,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,4,1,8,7,6,5]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,4,1,7,8,6,5]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,4,1,6,8,7,5]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,4,1,7,6,8,5]=>[4,2,3,1,8,6,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,4,3,2,8,7,6,5]=>[1,4,3,2,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,3,2,6,8,7,5]=>[1,4,3,2,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,3,2,7,6,8,5]=>[1,4,3,2,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,3,2,6,7,8,5]=>[1,4,3,2,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,2,8,7,6,5]=>[1,4,3,2,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,2,7,8,6,5]=>[1,4,3,2,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,2,6,8,7,5]=>[1,4,3,2,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,2,7,6,8,5]=>[1,4,3,2,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,2,6,7,8,5]=>[1,4,3,2,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,4,3,8,7,6,5]=>[2,1,4,3,8,7,6,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,4,3,7,8,6,5]=>[2,1,4,3,8,7,6,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,4,3,6,8,7,5]=>[2,1,4,3,8,7,6,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,4,3,7,6,8,5]=>[2,1,4,3,8,6,7,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,4,3,8,7,6,5]=>[1,2,4,3,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,3,7,8,6,5]=>[1,2,4,3,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,3,6,8,7,5]=>[1,2,4,3,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,3,7,6,8,5]=>[1,2,4,3,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,1,4,8,7,6,5]=>[3,2,1,4,8,7,6,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,4,7,8,6,5]=>[3,2,1,4,8,7,6,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,4,6,8,7,5]=>[3,2,1,4,8,7,6,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,4,7,6,8,5]=>[3,2,1,4,8,6,7,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,4,6,7,8,5]=>[3,2,1,4,8,6,7,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,4,8,7,6,5]=>[3,2,1,4,8,7,6,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,4,7,8,6,5]=>[3,2,1,4,8,7,6,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,4,7,6,8,5]=>[3,2,1,4,8,6,7,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,4,6,7,8,5]=>[3,2,1,4,8,6,7,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,2,4,8,7,6,5]=>[1,3,2,4,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,4,6,8,7,5]=>[1,3,2,4,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,4,7,6,8,5]=>[1,3,2,4,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,3,4,8,7,6,5]=>[2,1,3,4,8,7,6,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,3,4,7,8,6,5]=>[2,1,3,4,8,7,6,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,3,4,7,6,8,5]=>[2,1,3,4,8,6,7,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,6,7,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,3,4,8,7,6,5]=>[1,2,3,4,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,4,7,8,6,5]=>[1,2,3,4,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,4,6,8,7,5]=>[1,2,3,4,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,4,7,6,8,5]=>[1,2,3,4,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,4,3,2,1,7,8,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,5,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,5,4,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,5,4,2,1,7,8,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,3,5,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,4,5,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,4,5,2,1,7,8,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[2,5,4,3,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[2,5,4,3,1,7,8,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[2,4,5,3,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[2,4,5,3,1,7,8,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,2,5,4,1,8,7,6]=>[5,2,4,3,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,2,5,4,1,7,8,6]=>[5,2,4,3,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,5,4,1,8,7,6]=>[5,2,4,3,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,3,2,5,1,8,7,6]=>[5,3,2,4,1,8,7,6]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,3,2,5,1,7,8,6]=>[5,3,2,4,1,8,7,6]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,4,2,5,1,8,7,6]=>[5,3,2,4,1,8,7,6]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,4,2,5,1,7,8,6]=>[5,3,2,4,1,8,7,6]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[2,4,3,5,1,8,7,6]=>[5,3,2,4,1,8,7,6]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[2,4,3,5,1,7,8,6]=>[5,3,2,4,1,8,7,6]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,2,4,5,1,8,7,6]=>[5,2,3,4,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,4,5,1,8,7,6]=>[5,2,3,4,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,4,5,1,7,8,6]=>[5,2,3,4,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,5,4,3,2,8,7,6]=>[1,5,4,3,2,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,4,3,2,7,8,6]=>[1,5,4,3,2,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,3,2,8,7,6]=>[1,5,4,3,2,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,3,2,7,8,6]=>[1,5,4,3,2,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,4,2,7,8,6]=>[1,5,4,3,2,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,3,5,2,8,7,6]=>[1,5,3,4,2,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,3,5,2,7,8,6]=>[1,5,3,4,2,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,5,2,8,7,6]=>[1,5,3,4,2,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,5,2,7,8,6]=>[1,5,3,4,2,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,5,4,3,8,7,6]=>[2,1,5,4,3,8,7,6]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,4,5,3,8,7,6]=>[2,1,5,4,3,8,7,6]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,5,4,3,8,7,6]=>[1,2,5,4,3,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,4,3,7,8,6]=>[1,2,5,4,3,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,5,3,8,7,6]=>[1,2,5,4,3,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,5,3,7,8,6]=>[1,2,5,4,3,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,5,4,8,7,6]=>[1,3,2,5,4,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,3,5,4,8,7,6]=>[2,1,3,5,4,8,7,6]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,3,5,4,7,8,6]=>[2,1,3,5,4,8,7,6]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,3,5,4,8,7,6]=>[1,2,3,5,4,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,2,1,5,8,7,6]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,3,2,1,5,7,8,6]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,4,2,1,5,8,7,6]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[2,4,3,1,5,8,7,6]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,2,4,1,5,8,7,6]=>[4,2,3,1,5,8,7,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,4,1,5,7,8,6]=>[4,2,3,1,5,8,7,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,4,1,5,8,7,6]=>[4,2,3,1,5,8,7,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,4,1,5,7,8,6]=>[4,2,3,1,5,8,7,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,4,3,2,5,8,7,6]=>[1,4,3,2,5,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,3,2,5,7,8,6]=>[1,4,3,2,5,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,2,5,8,7,6]=>[1,4,3,2,5,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,2,5,7,8,6]=>[1,4,3,2,5,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,4,3,5,8,7,6]=>[2,1,4,3,5,8,7,6]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,4,3,5,7,8,6]=>[2,1,4,3,5,8,7,6]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,4,3,5,8,7,6]=>[1,2,4,3,5,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,3,5,7,8,6]=>[1,2,4,3,5,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,1,4,5,8,7,6]=>[3,2,1,4,5,8,7,6]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,2,4,5,8,7,6]=>[1,3,2,4,5,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,3,4,5,8,7,6]=>[2,1,3,4,5,8,7,6]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,3,4,5,7,8,6]=>[2,1,3,4,5,8,7,6]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,6,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,6,5,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,4,6,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,5,6,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[3,6,5,4,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[3,5,6,4,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,3,6,5,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[3,4,6,5,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,4,3,6,2,1,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,5,3,6,2,1,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,3,5,6,2,1,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,4,5,6,2,1,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[2,6,5,4,3,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[2,5,6,4,3,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[2,4,6,5,3,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[3,2,6,5,4,1,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,2,5,6,4,1,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,6,5,4,1,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,5,6,4,1,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,3,2,6,5,1,8,7]=>[6,3,2,5,4,1,8,7]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[3,4,2,6,5,1,8,7]=>[6,3,2,5,4,1,8,7]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[2,4,3,6,5,1,8,7]=>[6,3,2,5,4,1,8,7]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[5,4,3,2,6,1,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,5,3,2,6,1,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,5,4,2,6,1,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,3,5,2,6,1,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,4,5,2,6,1,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[2,5,4,3,6,1,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[2,4,5,3,6,1,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,2,5,4,6,1,8,7]=>[6,2,4,3,5,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,4,5,6,1,8,7]=>[6,2,3,4,5,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,6,5,4,3,2,8,7]=>[1,6,5,4,3,2,8,7]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,4,3,2,8,7]=>[1,6,5,4,3,2,8,7]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,4,6,3,2,8,7]=>[1,6,5,4,3,2,8,7]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,6,5,4,2,8,7]=>[1,6,5,4,3,2,8,7]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,6,5,4,3,8,7]=>[2,1,6,5,4,3,8,7]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,5,6,4,3,8,7]=>[2,1,6,5,4,3,8,7]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,4,6,5,3,8,7]=>[2,1,6,5,4,3,8,7]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,5,4,6,3,8,7]=>[2,1,6,4,5,3,8,7]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,2,1,6,5,4,8,7]=>[3,2,1,6,5,4,8,7]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,6,5,4,8,7]=>[3,2,1,6,5,4,8,7]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,2,6,5,4,8,7]=>[1,3,2,6,5,4,8,7]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,5,6,4,8,7]=>[1,3,2,6,5,4,8,7]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,3,6,5,4,8,7]=>[2,1,3,6,5,4,8,7]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,3,5,6,4,8,7]=>[2,1,3,6,5,4,8,7]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,3,6,5,4,8,7]=>[1,2,3,6,5,4,8,7]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,5,6,4,8,7]=>[1,2,3,6,5,4,8,7]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,2,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,4,2,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[2,4,3,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,2,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,5,3,2,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,5,4,2,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,3,5,2,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,4,5,2,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[2,5,4,3,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[2,4,5,3,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,2,5,4,1,6,8,7]=>[5,2,4,3,1,6,8,7]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,5,4,1,6,8,7]=>[5,2,4,3,1,6,8,7]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,4,3,5,1,6,8,7]=>[5,3,2,4,1,6,8,7]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[2,3,4,5,1,6,8,7]=>[5,2,3,4,1,6,8,7]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,1,5,4,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,2,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,4,2,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,1,4,5,6,8,7]=>[3,2,1,4,5,6,8,7]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,4,5,6,8,7]=>[3,2,1,4,5,6,8,7]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,6,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,7,6,5,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,6,7,5,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,4,7,6,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,5,7,6,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,6,5,7,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,5,7,6,4,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,5,6,7,4,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,3,7,6,5,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,4,7,6,5,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,4,3,7,6,2,1,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,5,3,7,6,2,1,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,5,4,7,6,2,1,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,3,5,7,6,2,1,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,6,5,4,7,2,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[3,5,6,4,7,2,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,3,6,5,7,2,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[2,7,6,5,4,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[2,6,7,5,4,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[2,5,7,6,4,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[2,5,6,7,4,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[2,4,6,7,5,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[2,5,4,7,6,3,1,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[2,5,6,4,7,3,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[2,5,4,6,7,3,1,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[2,4,5,6,7,3,1,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,2,7,6,5,4,1,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,2,6,7,5,4,1,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,2,5,7,6,4,1,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,2,6,5,7,4,1,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,2,5,6,7,4,1,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,3,7,6,5,4,1,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,3,6,7,5,4,1,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,3,5,7,6,4,1,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,3,6,5,7,4,1,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,3,5,6,7,4,1,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,2,4,6,7,5,1,8]=>[7,2,3,6,5,4,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,3,4,7,6,5,1,8]=>[7,2,3,6,5,4,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,3,4,6,7,5,1,8]=>[7,2,3,6,5,4,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,4,3,2,7,6,1,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[4,5,3,2,7,6,1,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[3,5,4,2,7,6,1,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[4,3,5,2,7,6,1,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[3,4,5,2,7,6,1,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[3,2,5,4,7,6,1,8]=>[7,2,4,3,6,5,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,3,4,5,7,6,1,8]=>[7,2,3,4,6,5,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,6,5,4,2,7,1,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[3,5,6,4,2,7,1,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[3,4,6,5,2,7,1,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[3,5,4,6,2,7,1,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[2,5,4,6,3,7,1,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[2,4,5,6,3,7,1,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,2,6,5,4,7,1,8]=>[7,2,5,4,3,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,3,5,6,4,7,1,8]=>[7,2,5,4,3,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,3,2,6,5,7,1,8]=>[7,3,2,5,4,6,1,8]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[3,4,2,6,5,7,1,8]=>[7,3,2,5,4,6,1,8]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[2,4,3,6,5,7,1,8]=>[7,3,2,5,4,6,1,8]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[2,3,4,6,5,7,1,8]=>[7,2,3,5,4,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,7,6,5,4,3,2,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,5,4,3,2,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,5,7,4,3,2,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,7,4,3,2,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,6,5,3,2,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,7,5,3,2,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,4,7,6,3,2,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,4,7,3,2,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,5,7,3,2,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,4,6,7,3,2,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,6,7,3,2,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,7,6,5,4,2,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,6,7,5,4,2,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,7,6,4,2,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,6,5,7,4,2,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,6,7,4,2,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,6,7,5,2,8]=>[1,7,3,6,5,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,4,6,3,7,2,8]=>[1,7,5,4,3,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,6,3,7,2,8]=>[1,7,5,4,3,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,6,5,4,7,2,8]=>[1,7,5,4,3,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,6,4,7,2,8]=>[1,7,5,4,3,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,3,6,5,7,2,8]=>[1,7,3,5,4,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,6,5,7,2,8]=>[1,7,3,5,4,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,3,5,6,7,2,8]=>[1,7,3,4,5,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,5,6,7,2,8]=>[1,7,3,4,5,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,7,6,5,4,3,8]=>[2,1,7,6,5,4,3,8]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,6,7,5,4,3,8]=>[2,1,7,6,5,4,3,8]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,5,6,7,4,3,8]=>[2,1,7,6,5,4,3,8]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,4,6,7,5,3,8]=>[2,1,7,6,5,4,3,8]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,7,6,5,4,3,8]=>[1,2,7,6,5,4,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,7,5,4,3,8]=>[1,2,7,6,5,4,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,7,6,4,3,8]=>[1,2,7,6,5,4,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,6,7,4,3,8]=>[1,2,7,6,5,4,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,6,7,5,3,8]=>[1,2,7,6,5,4,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,6,4,7,3,8]=>[1,2,7,5,4,6,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,6,5,7,3,8]=>[1,2,7,5,4,6,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,1,7,6,5,4,8]=>[3,2,1,7,6,5,4,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,6,7,5,4,8]=>[3,2,1,7,6,5,4,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,5,7,6,4,8]=>[3,2,1,7,6,5,4,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,6,5,7,4,8]=>[3,2,1,7,5,6,4,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,5,6,7,4,8]=>[3,2,1,7,5,6,4,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,6,7,5,4,8]=>[3,2,1,7,6,5,4,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,6,5,7,4,8]=>[3,2,1,7,5,6,4,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,5,6,7,4,8]=>[3,2,1,7,5,6,4,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,2,3,7,6,5,4,8]=>[1,2,3,7,6,5,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,6,7,5,4,8]=>[1,2,3,7,6,5,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,5,7,6,4,8]=>[1,2,3,7,6,5,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,6,5,7,4,8]=>[1,2,3,7,5,6,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,5,6,7,4,8]=>[1,2,3,7,5,6,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,2,1,7,6,5,8]=>[4,3,2,1,7,6,5,8]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,3,2,1,6,7,5,8]=>[4,3,2,1,7,6,5,8]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,2,4,1,7,6,5,8]=>[4,2,3,1,7,6,5,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,4,1,6,7,5,8]=>[4,2,3,1,7,6,5,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,4,1,7,6,5,8]=>[4,2,3,1,7,6,5,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,4,1,6,7,5,8]=>[4,2,3,1,7,6,5,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,4,3,2,7,6,5,8]=>[1,4,3,2,7,6,5,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,3,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,1,4,7,6,5,8]=>[3,2,1,4,7,6,5,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,2,3,4,7,6,5,8]=>[1,2,3,4,7,6,5,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,4,6,7,5,8]=>[1,2,3,4,7,6,5,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,5,3,2,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,5,4,2,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,4,5,2,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[2,5,4,3,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[2,4,5,3,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,2,5,4,1,7,6,8]=>[5,2,4,3,1,7,6,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,5,4,1,7,6,8]=>[5,2,4,3,1,7,6,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,4,2,5,1,7,6,8]=>[5,3,2,4,1,7,6,8]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[2,4,3,5,1,7,6,8]=>[5,3,2,4,1,7,6,8]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[2,1,5,4,3,7,6,8]=>[2,1,5,4,3,7,6,8]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,2,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,2,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,2,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,5,4,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,3,6,5,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[2,4,6,5,3,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[2,4,5,6,3,1,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[2,3,6,5,4,1,7,8]=>[6,2,5,4,3,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,5,6,4,1,7,8]=>[6,2,5,4,3,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,3,2,6,5,1,7,8]=>[6,3,2,5,4,1,7,8]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[2,4,3,6,5,1,7,8]=>[6,3,2,5,4,1,7,8]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[2,3,4,6,5,1,7,8]=>[6,2,3,5,4,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,5,4,2,6,1,7,8]=>[6,4,3,2,5,1,7,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,6,5,4,3,2,7,8]=>[1,6,5,4,3,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,4,3,2,7,8]=>[1,6,5,4,3,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,5,3,2,7,8]=>[1,6,5,4,3,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,4,6,3,2,7,8]=>[1,6,5,4,3,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,6,3,2,7,8]=>[1,6,5,4,3,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,6,4,2,7,8]=>[1,6,5,4,3,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,3,6,5,2,7,8]=>[1,6,3,5,4,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,4,3,6,2,7,8]=>[1,6,4,3,5,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,3,6,2,7,8]=>[1,6,4,3,5,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,4,6,2,7,8]=>[1,6,4,3,5,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,3,5,6,2,7,8]=>[1,6,3,4,5,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,5,6,2,7,8]=>[1,6,3,4,5,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,5,4,3,7,8]=>[1,2,6,5,4,3,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,6,4,3,7,8]=>[1,2,6,5,4,3,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,6,5,3,7,8]=>[1,2,6,5,4,3,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,5,6,3,7,8]=>[1,2,6,4,5,3,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,1,6,5,4,7,8]=>[3,2,1,6,5,4,7,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,5,6,4,7,8]=>[3,2,1,6,5,4,7,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,6,5,4,7,8]=>[3,2,1,6,5,4,7,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,5,6,4,7,8]=>[3,2,1,6,5,4,7,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[4,3,2,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[2,4,3,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,2,4,1,6,5,7,8]=>[4,2,3,1,6,5,7,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,4,1,6,5,7,8]=>[4,2,3,1,6,5,7,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,4,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[2,5,4,3,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[2,4,5,3,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,2,5,4,1,6,7,8]=>[5,2,4,3,1,6,7,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,5,4,1,6,7,8]=>[5,2,4,3,1,6,7,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,4,3,5,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,4,3,5,2,6,7,8]=>[1,5,3,4,2,6,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,5,2,6,7,8]=>[1,5,3,4,2,6,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,5,4,3,6,7,8]=>[2,1,5,4,3,6,7,8]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,4,5,3,6,7,8]=>[2,1,5,4,3,6,7,8]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,5,4,3,6,7,8]=>[1,2,5,4,3,6,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,5,3,6,7,8]=>[1,2,5,4,3,6,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,3,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,4,3,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,4,8,6,7,5]=>[1,2,3,4,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,5,8,6,7,4]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,7,5,6,4,8]=>[1,2,3,7,6,5,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,7,5,6,8,4]=>[1,2,3,8,6,5,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,8,5,6,7,4]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,8,5,7,6,4]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,8,6,5,7,4]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,8,6,7,5,4]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,3,8,6,7,5]=>[1,2,4,3,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,5,8,6,7,3]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,7,5,6,8,3]=>[1,2,8,6,5,4,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,8,5,6,7,3]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,8,6,5,7,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,4,8,6,7,3]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,4,5,3,7,8]=>[1,2,6,5,4,3,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,4,5,7,8,3]=>[1,2,8,5,4,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,4,5,8,7,3]=>[1,2,8,5,4,7,6,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,4,5,6,8,3]=>[1,2,8,6,5,4,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,4,5,6,7,3]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,4,6,7,5,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,4,7,6,5,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,5,4,6,3,8]=>[1,2,7,6,5,4,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,5,4,6,8,3]=>[1,2,8,6,5,4,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,5,4,6,7,3]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,5,4,7,6,3]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,5,6,4,7,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,5,6,7,4,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,6,5,4,7,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,6,5,7,4,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,7,5,6,4,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,4,8,6,7,5]=>[1,3,2,4,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,7,5,6,8,4]=>[1,3,2,8,6,5,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,8,5,7,6,4]=>[1,3,2,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,8,6,5,7,4]=>[1,3,2,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
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[2,1,8,4,6,5,7,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,8,4,6,7,5,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,7,5,4,6,8,3]=>[2,1,8,6,5,4,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,8,5,4,6,7,3]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,8,5,4,7,6,3]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,7,5,6,4,8,3]=>[2,1,8,6,5,4,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,8,5,6,4,7,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,8,5,6,7,4,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,8,5,7,6,4,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,8,6,5,4,7,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,8,6,5,7,4,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,3,1,5,8,6,7,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,7,5,6,4,8]=>[3,2,1,7,6,5,4,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,8,5,6,7,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,8,6,7,5,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,4,1,8,6,7,5]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,4,5,8,6,7,1]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,4,7,5,6,1,8]=>[7,2,3,6,5,4,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,3,4,7,5,6,8,1]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,4,8,5,6,7,1]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,4,8,5,7,6,1]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,4,8,6,5,7,1]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,4,8,6,7,5,1]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,5,4,8,6,7,1]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,6,4,5,1,7,8]=>[6,2,5,4,3,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,6,4,5,1,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,6,4,5,7,8,1]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,6,4,5,8,7,1]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,7,4,5,6,8,1]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,8,4,5,6,7,1]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,7,4,6,5,8,1]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,8,4,6,7,5,1]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,7,5,4,6,1,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,3,7,5,4,6,8,1]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,8,5,4,6,7,1]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,7,5,6,4,1,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,3,7,5,6,4,8,1]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,8,5,6,4,7,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,8,5,6,7,4,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,8,5,7,6,4,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,8,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,4,3,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[2,4,3,5,8,6,7,1]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,4,3,8,5,6,7,1]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,4,3,8,5,7,6,1]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,4,3,8,6,5,7,1]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,4,3,8,6,7,5,1]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,5,3,4,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[2,5,3,4,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[2,5,3,4,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,5,3,4,6,8,7,1]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,5,3,4,7,6,8,1]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,5,3,4,8,6,7,1]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,5,3,4,8,7,6,1]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,6,3,4,5,1,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[2,6,3,4,5,7,8,1]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,6,3,4,5,8,7,1]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,7,3,4,5,6,1,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[2,8,3,4,5,6,7,1]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,8,3,4,5,7,6,1]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,6,3,5,4,1,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[2,6,3,5,4,1,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[2,6,3,5,4,7,8,1]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,6,3,5,4,8,7,1]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,7,3,5,4,6,8,1]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,8,3,5,4,7,6,1]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,7,3,5,6,4,8,1]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,8,3,5,6,7,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,8,3,5,7,6,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,7,3,6,5,4,1,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[2,8,3,7,5,6,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,8,3,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,5,4,3,8,6,7,1]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,6,4,3,5,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[2,6,4,3,5,7,8,1]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[2,6,4,3,5,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[2,7,4,3,5,6,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[2,8,4,3,5,6,7,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,8,4,3,5,7,6,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,7,4,3,6,5,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[2,8,4,3,6,5,7,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,8,4,3,6,7,5,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,8,4,3,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,6,4,5,3,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[2,6,4,5,3,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[2,6,4,5,3,7,8,1]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[2,6,4,5,3,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[2,8,4,5,3,6,7,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,7,4,5,6,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[2,7,4,5,6,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,8,4,5,6,3,7,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,4,5,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,7,4,6,5,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[2,7,4,6,5,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,8,4,6,5,3,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,4,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,5,4,3,6,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,8,5,4,3,6,7,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,8,5,4,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,7,5,4,6,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,8,5,4,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,5,4,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,7,6,4,5,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,8,7,4,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,7,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,7,5,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,7,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,2,1,4,8,6,7,5]=>[3,2,1,4,8,7,6,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,5,8,6,7,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,7,5,6,4,8]=>[3,2,1,7,6,5,4,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,7,5,6,8,4]=>[3,2,1,8,6,5,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,8,5,6,7,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,8,5,7,6,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,8,6,5,7,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,8,6,7,5,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,4,1,8,6,7,5]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,4,5,8,6,7,1]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,4,7,5,6,8,1]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,4,8,5,6,7,1]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,4,8,6,7,5,1]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,5,4,8,6,7,1]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,6,4,5,1,7,8]=>[6,2,5,4,3,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,2,6,4,5,1,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,2,6,4,5,7,1,8]=>[7,2,5,4,3,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,2,7,4,5,6,1,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,2,8,4,5,6,7,1]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,7,4,6,5,1,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,2,7,4,6,5,8,1]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,8,4,6,5,7,1]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,7,5,4,6,1,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,2,8,5,4,6,7,1]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,8,5,4,7,6,1]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,7,5,6,4,1,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,2,7,5,6,4,8,1]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,8,5,6,4,7,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,8,5,7,6,4,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,8,6,5,7,4,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,8,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,2,3,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,2,3,1,5,7,8,6]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,2,3,1,5,8,7,6]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,2,3,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,2,3,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,2,3,1,6,7,8,5]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,2,3,1,6,8,7,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,2,3,1,7,6,5,8]=>[4,3,2,1,7,6,5,8]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,2,3,1,7,6,8,5]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,2,3,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,2,3,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,2,3,5,1,6,8,7]=>[5,3,2,4,1,6,8,7]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,2,3,5,1,7,8,6]=>[5,3,2,4,1,8,7,6]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,2,3,5,1,8,7,6]=>[5,3,2,4,1,8,7,6]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,2,3,5,8,7,6,1]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,2,3,6,5,1,7,8]=>[6,3,2,5,4,1,7,8]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[4,2,3,6,5,1,8,7]=>[6,3,2,5,4,1,8,7]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[4,2,3,6,5,8,7,1]=>[8,3,2,5,4,7,6,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,2,3,8,5,6,7,1]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,2,3,8,5,7,6,1]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,2,3,8,6,7,5,1]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,2,3,8,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[5,2,3,4,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,2,3,4,1,7,8,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,2,3,4,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,2,3,4,6,1,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,2,3,4,7,6,1,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[5,2,3,4,8,6,7,1]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,2,3,4,8,7,6,1]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[6,2,3,4,5,1,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,2,3,4,5,8,7,1]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,2,3,4,5,7,6,1]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,3,4,6,5,1,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,2,3,4,7,6,5,1]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,2,3,5,4,1,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,2,3,5,4,1,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,2,3,5,4,7,1,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,2,3,5,4,7,8,1]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,2,3,5,4,6,1,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,2,3,5,4,6,7,1]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,2,3,5,4,7,6,1]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,3,5,6,4,1,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,2,3,5,6,7,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,2,3,5,7,6,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,3,6,5,4,1,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,2,3,6,5,4,7,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,2,3,7,5,6,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,2,3,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,2,4,3,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,2,4,3,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,2,4,3,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,2,4,3,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,2,4,3,6,1,7,8]=>[6,4,3,2,5,1,7,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,2,4,3,6,1,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,2,4,3,7,6,1,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[5,2,4,3,7,6,8,1]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,2,4,3,8,7,6,1]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[6,2,4,3,5,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[7,2,4,3,6,5,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,2,4,3,6,5,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[8,2,4,3,6,5,7,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,2,4,3,6,7,5,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,2,4,3,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,2,4,5,3,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,2,4,5,3,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,2,4,5,3,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[7,2,4,5,3,6,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,2,4,5,3,6,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,2,4,5,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,2,4,5,6,3,7,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,4,5,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,4,5,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,4,6,5,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,2,4,6,5,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,2,4,7,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,4,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
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[6,2,5,4,3,7,1,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,2,5,4,3,7,8,1]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[7,2,5,4,3,6,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,2,5,4,3,6,7,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,2,5,4,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,2,5,4,6,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,2,5,4,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
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[7,2,6,4,5,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,2,6,4,5,3,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,6,4,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,7,4,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
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[7,2,6,5,4,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,2,6,5,4,3,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
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[5,3,2,4,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,3,2,4,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
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[8,3,2,4,7,6,5,1]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
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[6,3,2,5,4,7,1,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,3,2,5,4,7,8,1]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,3,2,5,4,8,7,1]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
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[7,3,2,5,6,4,8,1]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,3,2,5,6,4,7,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,2,5,6,7,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
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[5,3,4,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,3,4,2,6,1,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
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[8,3,4,2,6,5,7,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
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[6,3,4,5,2,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[8,3,4,5,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
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[7,3,4,6,5,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,3,4,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,5,4,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,3,5,4,2,7,1,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,3,5,4,2,7,8,1]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[6,3,5,4,2,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[7,3,5,4,2,6,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,3,5,4,2,6,7,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,3,5,4,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,3,5,4,6,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,3,5,4,6,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,3,5,4,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,5,4,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,6,4,5,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,3,6,4,5,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
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[8,3,6,4,5,7,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,7,4,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,7,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,6,5,4,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,3,6,5,4,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,3,6,5,4,2,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
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[6,4,3,2,5,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[8,4,3,2,5,7,6,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,4,3,2,6,5,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
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[8,4,3,5,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,3,6,5,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,3,6,5,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,4,3,7,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,3,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,3,4,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[8,5,3,4,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,3,4,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,3,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,3,5,4,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,3,5,4,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,6,3,5,4,2,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,3,5,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,3,5,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,3,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,3,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,4,3,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,4,3,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,4,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,4,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,1,3,6,5,8,7]=>[3,4,1,2,6,5,8,7]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,1,4,6,3,5,8,7]=>[2,1,5,6,3,4,8,7]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,1,6,3,5,8,7]=>[3,5,1,6,2,4,8,7]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,6,1,3,5,8,7]=>[4,5,6,1,2,3,8,7]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,1,4,3,6,8,5,7]=>[2,1,4,3,7,8,5,6]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,1,3,6,8,5,7]=>[3,4,1,2,7,8,5,6]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,1,4,6,3,8,5,7]=>[2,1,5,7,3,8,4,6]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,1,6,3,8,5,7]=>[3,5,1,7,2,8,4,6]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,6,1,3,8,5,7]=>[4,5,7,1,2,8,3,6]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,1,4,6,8,3,5,7]=>[2,1,6,7,8,3,4,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,1,6,8,3,5,7]=>[3,6,1,7,8,2,4,5]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,6,1,8,3,5,7]=>[4,6,7,1,8,2,3,5]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,4,6,8,1,3,5,7]=>[5,6,7,8,1,2,3,4]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,4,1,3,6,5,7,8]=>[3,4,1,2,6,5,7,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,1,4,6,3,5,7,8]=>[2,1,5,6,3,4,7,8]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,1,6,3,5,7,8]=>[3,5,1,6,2,4,7,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,6,1,3,5,7,8]=>[4,5,6,1,2,3,7,8]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,4,6,1,3,7,5,8]=>[4,5,7,1,2,6,3,8]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,4,1,6,7,3,5,8]=>[3,6,1,7,5,2,4,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,6,7,1,3,5,8]=>[5,6,7,4,1,2,3,8]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,4,1,3,6,7,8,5]=>[3,4,1,2,8,6,7,5]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,1,4,6,3,7,8,5]=>[2,1,5,8,3,6,7,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,6,1,3,7,8,5]=>[4,5,8,1,2,6,7,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,1,4,6,7,3,8,5]=>[2,1,6,8,5,3,7,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,1,6,7,3,8,5]=>[3,6,1,8,5,2,7,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,6,1,7,3,8,5]=>[4,6,8,1,5,2,7,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,4,6,7,1,3,8,5]=>[5,6,8,4,1,2,7,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,1,4,6,7,8,3,5]=>[2,1,7,8,5,6,3,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,1,6,7,8,3,5]=>[3,7,1,8,5,6,2,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,6,1,7,8,3,5]=>[4,7,8,1,5,6,2,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,4,6,7,1,8,3,5]=>[5,7,8,4,1,6,2,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,4,6,7,8,1,3,5]=>[6,7,8,4,5,1,2,3]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,1,4,3,7,5,8,6]=>[2,1,4,3,8,6,7,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,1,3,7,5,8,6]=>[3,4,1,2,8,6,7,5]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,1,4,7,3,5,8,6]=>[2,1,5,8,3,6,7,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,7,1,3,5,8,6]=>[4,5,8,1,2,6,7,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,1,4,3,7,8,5,6]=>[2,1,4,3,8,7,6,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,1,3,7,8,5,6]=>[3,4,1,2,8,7,6,5]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,1,7,3,8,5,6]=>[3,5,1,8,2,7,6,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,7,1,3,8,5,6]=>[4,5,8,1,2,7,6,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,1,4,7,8,3,5,6]=>[2,1,6,8,7,3,5,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,1,7,8,3,5,6]=>[3,6,1,8,7,2,5,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,7,1,8,3,5,6]=>[4,6,8,1,7,2,5,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,4,7,8,1,3,5,6]=>[5,6,8,7,1,2,4,3]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,4,1,5,3,7,6,8]=>[3,5,1,4,2,7,6,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,5,1,7,3,6,8]=>[4,6,3,1,7,2,5,8]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,4,1,3,5,7,8,6]=>[3,4,1,2,5,8,7,6]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,1,5,3,7,8,6]=>[3,5,1,4,2,8,7,6]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,5,1,3,7,8,6]=>[4,5,3,1,2,8,7,6]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,1,4,5,7,3,8,6]=>[2,1,6,4,8,3,7,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,5,1,7,3,8,6]=>[4,6,3,1,8,2,7,5]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,4,5,7,1,3,8,6]=>[5,6,3,8,1,2,7,4]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,1,4,5,7,8,3,6]=>[2,1,7,4,8,6,3,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,5,1,7,8,3,6]=>[4,7,3,1,8,6,2,5]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,4,5,7,1,8,3,6]=>[5,7,3,8,1,6,2,4]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,4,5,7,8,1,3,6]=>[6,7,3,8,5,1,2,4]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,1,4,3,8,5,6,7]=>[2,1,4,3,8,6,7,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,1,3,8,5,6,7]=>[3,4,1,2,8,6,7,5]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,1,4,8,3,5,6,7]=>[2,1,5,8,3,6,7,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,8,1,3,5,6,7]=>[4,5,8,1,2,6,7,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,1,4,3,5,8,6,7]=>[2,1,4,3,5,8,7,6]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,1,5,3,8,6,7]=>[3,5,1,4,2,8,7,6]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,1,4,5,8,3,6,7]=>[2,1,6,4,8,3,7,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,5,1,8,3,6,7]=>[4,6,3,1,8,2,7,5]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,4,5,8,1,3,6,7]=>[5,6,3,8,1,2,7,4]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,4,1,5,3,6,8,7]=>[3,5,1,4,2,6,8,7]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,1,5,6,3,8,7]=>[3,6,1,4,5,2,8,7]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,5,1,6,3,8,7]=>[4,6,3,1,5,2,8,7]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,4,5,6,1,3,8,7]=>[5,6,3,4,1,2,8,7]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,1,4,5,6,8,3,7]=>[2,1,7,4,5,8,3,6]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,5,6,1,8,3,7]=>[5,7,3,4,1,8,2,6]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,4,5,6,8,1,3,7]=>[6,7,3,4,8,1,2,5]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,4,1,3,5,6,7,8]=>[3,4,1,2,5,6,7,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,1,5,3,6,7,8]=>[3,5,1,4,2,6,7,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,1,5,6,3,7,8]=>[3,6,1,4,5,2,7,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,5,1,6,3,7,8]=>[4,6,3,1,5,2,7,8]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,4,5,6,1,3,7,8]=>[5,6,3,4,1,2,7,8]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,4,1,5,6,7,3,8]=>[3,7,1,4,5,6,2,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,5,1,6,7,3,8]=>[4,7,3,1,5,6,2,8]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,4,5,6,1,7,3,8]=>[5,7,3,4,1,6,2,8]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,4,5,6,7,1,3,8]=>[6,7,3,4,5,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,4,1,5,6,7,8,3]=>[3,8,1,4,5,6,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,5,1,6,7,8,3]=>[4,8,3,1,5,6,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,4,5,6,1,7,8,3]=>[5,8,3,4,1,6,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,4,5,6,7,1,8,3]=>[6,8,3,4,5,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,4,5,6,7,8,1,3]=>[7,8,3,4,5,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,1,5,3,6,4,8,7]=>[2,1,6,4,5,3,8,7]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,5,1,3,6,4,8,7]=>[3,6,1,4,5,2,8,7]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,1,5,6,3,4,8,7]=>[2,1,6,5,4,3,8,7]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,5,1,6,3,4,8,7]=>[3,6,1,5,4,2,8,7]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,5,6,1,3,4,8,7]=>[4,6,5,1,3,2,8,7]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,1,5,3,6,8,4,7]=>[2,1,7,4,5,8,3,6]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,5,1,6,3,8,4,7]=>[3,7,1,5,4,8,2,6]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,5,6,1,3,8,4,7]=>[4,7,5,1,3,8,2,6]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,1,5,6,8,3,4,7]=>[2,1,7,6,8,4,3,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,5,1,6,8,3,4,7]=>[3,7,1,6,8,4,2,5]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,5,6,8,1,3,4,7]=>[5,7,6,8,1,3,2,4]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,5,1,3,6,4,7,8]=>[3,6,1,4,5,2,7,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,5,1,6,3,4,7,8]=>[3,6,1,5,4,2,7,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,5,1,6,3,7,4,8]=>[3,7,1,5,4,6,2,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,1,5,6,7,3,4,8]=>[2,1,7,6,5,4,3,8]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,5,6,1,7,3,4,8]=>[4,7,6,1,5,3,2,8]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,1,5,3,6,7,8,4]=>[2,1,8,4,5,6,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,5,1,3,6,7,8,4]=>[3,8,1,4,5,6,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,1,5,6,3,7,8,4]=>[2,1,8,5,4,6,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,5,1,6,3,7,8,4]=>[3,8,1,5,4,6,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,5,6,1,3,7,8,4]=>[4,8,5,1,3,6,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,1,5,6,7,3,8,4]=>[2,1,8,6,5,4,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,5,1,6,7,3,8,4]=>[3,8,1,6,5,4,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,5,6,7,1,3,8,4]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,1,5,6,7,8,3,4]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,5,1,6,7,8,3,4]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,5,6,1,7,8,3,4]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,5,6,7,1,8,3,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,5,6,7,8,1,3,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,1,5,3,7,4,8,6]=>[2,1,6,4,8,3,7,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,5,7,3,4,8,6]=>[2,1,6,8,5,3,7,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,5,1,7,3,4,8,6]=>[3,6,1,8,5,2,7,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,5,7,1,3,4,8,6]=>[4,6,8,1,5,2,7,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,1,5,3,7,8,4,6]=>[2,1,7,4,8,6,3,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,5,7,3,8,4,6]=>[2,1,7,8,5,6,3,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,5,1,7,3,8,4,6]=>[3,7,1,8,5,6,2,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,5,7,1,3,8,4,6]=>[4,7,8,1,5,6,2,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,1,5,7,8,3,4,6]=>[2,1,7,8,6,5,3,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,5,1,7,8,3,4,6]=>[3,7,1,8,6,5,2,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,5,7,1,8,3,4,6]=>[4,7,8,1,6,5,2,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,5,7,8,1,3,4,6]=>[5,7,8,6,1,4,2,3]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,5,1,3,7,4,6,8]=>[3,6,1,4,7,2,5,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,3,5,1,4,7,6,8]=>[4,2,5,1,3,7,6,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,5,7,1,4,6,8]=>[5,2,6,7,1,3,4,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,5,1,7,4,8,6]=>[4,2,6,1,8,3,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,5,7,1,4,8,6]=>[5,2,6,8,1,3,7,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,1,5,7,8,4,6]=>[3,2,1,7,8,6,4,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,5,7,1,8,4,6]=>[5,2,7,8,1,6,3,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,5,7,8,1,4,6]=>[6,2,7,8,5,1,3,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,1,5,3,8,4,6,7]=>[2,1,6,4,8,3,7,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,5,8,3,4,6,7]=>[2,1,6,8,5,3,7,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,5,1,8,3,4,6,7]=>[3,6,1,8,5,2,7,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,5,8,1,3,4,6,7]=>[4,6,8,1,5,2,7,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,3,5,1,4,8,6,7]=>[4,2,5,1,3,8,7,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,5,1,8,4,6,7]=>[4,2,6,1,8,3,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,5,8,1,4,6,7]=>[5,2,6,8,1,3,7,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,1,5,3,4,6,8,7]=>[2,1,5,4,3,6,8,7]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,3,5,1,6,4,8,7]=>[4,2,6,1,5,3,8,7]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,5,6,1,4,8,7]=>[5,2,6,4,1,3,8,7]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,1,3,5,6,8,4,7]=>[2,1,3,7,5,8,4,6]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,3,1,5,6,8,4,7]=>[3,2,1,7,5,8,4,6]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,5,1,6,8,4,7]=>[4,2,7,1,5,8,3,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,5,6,1,8,4,7]=>[5,2,7,4,1,8,3,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,5,6,8,1,4,7]=>[6,2,7,4,8,1,3,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,1,5,3,4,6,7,8]=>[2,1,5,4,3,6,7,8]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,5,1,3,4,6,7,8]=>[3,5,1,4,2,6,7,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,3,5,1,4,6,7,8]=>[4,2,5,1,3,6,7,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,5,1,6,4,7,8]=>[4,2,6,1,5,3,7,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,5,6,1,4,7,8]=>[5,2,6,4,1,3,7,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,5,6,1,7,4,8]=>[5,2,7,4,1,6,3,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,5,6,7,1,4,8]=>[6,2,7,4,5,1,3,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,5,1,6,7,8,4]=>[4,2,8,1,5,6,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,5,6,1,7,8,4]=>[5,2,8,4,1,6,7,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,5,6,7,1,8,4]=>[6,2,8,4,5,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,5,6,7,8,1,4]=>[7,2,8,4,5,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,1,6,3,7,4,8,5]=>[2,1,8,4,6,5,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,6,7,3,4,8,5]=>[2,1,8,6,5,4,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,6,1,7,3,4,8,5]=>[3,8,1,6,5,4,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,6,7,1,3,4,8,5]=>[4,8,6,1,5,3,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,1,6,3,7,8,4,5]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,6,1,3,7,8,4,5]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,1,6,7,3,8,4,5]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,6,1,7,3,8,4,5]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,6,7,1,3,8,4,5]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,1,6,7,8,3,4,5]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,6,1,7,8,3,4,5]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,6,7,1,8,3,4,5]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,6,7,8,1,3,4,5]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,6,7,1,3,4,5,8]=>[4,7,6,1,5,3,2,8]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,6,1,3,4,7,5,8]=>[3,7,1,4,5,6,2,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,3,1,6,4,7,5,8]=>[3,2,1,7,5,6,4,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,6,1,4,7,5,8]=>[4,2,7,1,5,6,3,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,6,7,1,4,5,8]=>[5,2,7,6,1,4,3,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,1,6,3,4,7,8,5]=>[2,1,8,4,5,6,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,6,1,3,4,7,8,5]=>[3,8,1,4,5,6,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,3,6,1,4,7,8,5]=>[4,2,8,1,5,6,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,1,3,6,7,4,8,5]=>[2,1,3,8,6,5,7,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,3,6,7,8,4,5]=>[2,1,3,8,7,6,5,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,3,1,6,7,8,4,5]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,6,1,7,8,4,5]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,6,7,1,8,4,5]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,6,7,8,1,4,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,1,6,3,8,4,5,7]=>[2,1,7,4,8,6,3,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,6,8,3,4,5,7]=>[2,1,7,8,5,6,3,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,6,1,8,3,4,5,7]=>[3,7,1,8,5,6,2,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,6,8,1,3,4,5,7]=>[4,7,8,1,5,6,2,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,1,6,3,4,8,5,7]=>[2,1,7,4,5,8,3,6]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,3,6,4,8,5,7]=>[2,1,3,7,5,8,4,6]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,3,1,6,4,8,5,7]=>[3,2,1,7,5,8,4,6]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,6,1,4,8,5,7]=>[4,2,7,1,5,8,3,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,1,6,8,4,5,7]=>[3,2,1,7,8,6,4,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,6,1,8,4,5,7]=>[4,2,7,1,8,6,3,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,6,8,1,4,5,7]=>[5,2,7,8,1,6,3,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,1,6,3,4,5,8,7]=>[2,1,6,4,5,3,8,7]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,6,1,3,4,5,8,7]=>[3,6,1,4,5,2,8,7]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,1,3,6,4,5,8,7]=>[2,1,3,6,5,4,8,7]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,3,6,1,4,5,8,7]=>[4,2,6,1,5,3,8,7]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,4,1,6,8,5,7]=>[4,2,3,1,7,8,5,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,4,6,1,8,5,7]=>[5,2,3,7,1,8,4,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,4,6,8,1,5,7]=>[6,2,3,7,8,1,4,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,6,1,3,4,5,7,8]=>[3,6,1,4,5,2,7,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,3,1,6,4,5,7,8]=>[3,2,1,6,5,4,7,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,6,1,4,5,7,8]=>[4,2,6,1,5,3,7,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,4,6,1,5,7,8]=>[5,2,3,6,1,4,7,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,4,6,1,7,5,8]=>[5,2,3,7,1,6,4,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,4,6,7,1,5,8]=>[6,2,3,7,5,1,4,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,4,6,1,7,8,5]=>[5,2,3,8,1,6,7,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,4,6,7,8,1,5]=>[7,2,3,8,5,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,1,7,3,8,4,5,6]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,7,1,3,8,4,5,6]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,1,7,8,3,4,5,6]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,7,1,8,3,4,5,6]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,7,8,1,3,4,5,6]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,1,7,3,4,8,5,6]=>[2,1,8,4,5,7,6,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,3,7,4,8,5,6]=>[2,1,3,8,5,7,6,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,3,1,7,4,8,5,6]=>[3,2,1,8,5,7,6,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,7,1,4,8,5,6]=>[4,2,8,1,5,7,6,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,1,3,7,8,4,5,6]=>[2,1,3,8,7,6,5,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,3,1,7,8,4,5,6]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,7,8,1,4,5,6]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,1,7,3,4,5,8,6]=>[2,1,8,4,5,6,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,7,1,3,4,5,8,6]=>[3,8,1,4,5,6,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,3,1,7,4,5,8,6]=>[3,2,1,8,5,6,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,7,1,4,5,8,6]=>[4,2,8,1,5,6,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,1,3,4,7,5,8,6]=>[2,1,3,4,8,6,7,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,3,4,1,7,5,8,6]=>[4,2,3,1,8,6,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,4,7,1,5,8,6]=>[5,2,3,8,1,6,7,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,1,3,4,7,8,5,6]=>[2,1,3,4,8,7,6,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,3,1,4,7,8,5,6]=>[3,2,1,4,8,7,6,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,4,1,7,8,5,6]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,4,7,1,8,5,6]=>[5,2,3,8,1,7,6,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,4,7,8,1,5,6]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,7,1,3,4,5,6,8]=>[3,7,1,4,5,6,2,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,3,7,1,4,5,6,8]=>[4,2,7,1,5,6,3,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,1,4,7,5,6,8]=>[3,2,1,4,7,6,5,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,4,1,7,5,6,8]=>[4,2,3,1,7,6,5,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,4,7,1,5,6,8]=>[5,2,3,7,1,6,4,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,4,5,7,1,8,6]=>[6,2,3,4,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,4,5,7,8,1,6]=>[7,2,3,4,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,1,8,3,4,5,6,7]=>[2,1,8,4,5,6,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,8,1,3,4,5,6,7]=>[3,8,1,4,5,6,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,1,3,8,4,5,6,7]=>[2,1,3,8,5,6,7,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,3,1,8,4,5,6,7]=>[3,2,1,8,5,6,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,8,1,4,5,6,7]=>[4,2,8,1,5,6,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,1,3,4,8,5,6,7]=>[2,1,3,4,8,6,7,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,3,1,4,8,5,6,7]=>[3,2,1,4,8,6,7,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,4,1,8,5,6,7]=>[4,2,3,1,8,6,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,4,8,1,5,6,7]=>[5,2,3,8,1,6,7,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,1,3,4,5,8,6,7]=>[2,1,3,4,5,8,7,6]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,3,1,4,5,8,6,7]=>[3,2,1,4,5,8,7,6]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,4,1,5,8,6,7]=>[4,2,3,1,5,8,7,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,4,5,1,8,6,7]=>[5,2,3,4,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,4,5,8,1,6,7]=>[6,2,3,4,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,4,5,6,8,1,7]=>[7,2,3,4,5,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,1,4,2,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,4,1,2,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,1,4,6,2,5,8,7]=>[5,2,3,6,1,4,8,7]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,4,1,6,2,5,8,7]=>[5,3,2,6,1,4,8,7]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,4,6,1,2,5,8,7]=>[5,4,6,2,1,3,8,7]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[3,1,4,2,6,8,5,7]=>[4,2,3,1,7,8,5,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,4,1,2,6,8,5,7]=>[4,3,2,1,7,8,5,6]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,1,4,6,2,8,5,7]=>[5,2,3,7,1,8,4,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,4,1,6,2,8,5,7]=>[5,3,2,7,1,8,4,6]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,1,4,6,8,2,5,7]=>[6,2,3,7,8,1,4,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,4,1,6,8,2,5,7]=>[6,3,2,7,8,1,4,5]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[3,4,6,8,1,2,5,7]=>[6,5,7,8,2,1,3,4]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[3,1,4,2,6,5,7,8]=>[4,2,3,1,6,5,7,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,4,1,2,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,1,4,2,6,7,5,8]=>[4,2,3,1,7,6,5,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,4,1,2,6,7,5,8]=>[4,3,2,1,7,6,5,8]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,4,1,6,2,7,5,8]=>[5,3,2,7,1,6,4,8]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,4,1,6,7,2,5,8]=>[6,3,2,7,5,1,4,8]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[3,4,6,7,1,2,5,8]=>[6,5,7,4,2,1,3,8]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[3,1,4,2,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,4,1,2,6,7,8,5]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,1,4,6,2,7,8,5]=>[5,2,3,8,1,6,7,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,4,1,6,2,7,8,5]=>[5,3,2,8,1,6,7,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,1,4,6,7,2,8,5]=>[6,2,3,8,5,1,7,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,4,1,6,7,2,8,5]=>[6,3,2,8,5,1,7,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[3,4,6,1,7,2,8,5]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[3,4,6,7,1,2,8,5]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[3,1,4,6,7,8,2,5]=>[7,2,3,8,5,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,4,1,6,7,8,2,5]=>[7,3,2,8,5,6,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[3,4,6,1,7,8,2,5]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[3,4,6,7,1,8,2,5]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[3,4,6,7,8,1,2,5]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[3,1,4,2,7,5,8,6]=>[4,2,3,1,8,6,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,4,1,2,7,5,8,6]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,1,4,7,2,5,8,6]=>[5,2,3,8,1,6,7,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,4,1,7,2,5,8,6]=>[5,3,2,8,1,6,7,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,1,4,2,7,8,5,6]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,4,1,2,7,8,5,6]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,1,4,7,2,8,5,6]=>[5,2,3,8,1,7,6,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,4,7,1,8,2,5,6]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[3,4,7,8,1,2,5,6]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[3,1,4,2,7,5,6,8]=>[4,2,3,1,7,6,5,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,4,1,2,7,5,6,8]=>[4,3,2,1,7,6,5,8]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,4,1,2,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,4,1,5,2,7,6,8]=>[5,3,2,4,1,7,6,8]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,4,5,1,7,2,6,8]=>[6,4,3,2,7,1,5,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,4,5,7,1,2,6,8]=>[6,5,3,7,2,1,4,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,1,4,2,5,7,8,6]=>[4,2,3,1,5,8,7,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,4,1,2,5,7,8,6]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,1,4,5,2,7,8,6]=>[5,2,3,4,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,4,5,1,2,7,8,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,1,4,5,7,2,8,6]=>[6,2,3,4,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,4,5,7,1,2,8,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,1,4,5,7,8,2,6]=>[7,2,3,4,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,4,1,5,7,8,2,6]=>[7,3,2,4,8,6,1,5]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[3,4,5,1,7,8,2,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[3,4,5,7,1,8,2,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,4,5,7,8,1,2,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,1,4,2,8,5,6,7]=>[4,2,3,1,8,6,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,4,1,2,8,5,6,7]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,1,4,8,2,5,6,7]=>[5,2,3,8,1,6,7,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,4,1,8,2,5,6,7]=>[5,3,2,8,1,6,7,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,1,4,2,5,8,6,7]=>[4,2,3,1,5,8,7,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,4,1,2,5,8,6,7]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,4,1,5,2,8,6,7]=>[5,3,2,4,1,8,7,6]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,4,5,1,2,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,1,4,5,8,2,6,7]=>[6,2,3,4,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,4,5,8,1,2,6,7]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,4,1,2,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,4,5,1,2,6,8,7]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,1,4,5,6,2,8,7]=>[6,2,3,4,5,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,4,5,1,6,2,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,4,5,6,1,2,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,1,4,5,6,8,2,7]=>[7,2,3,4,5,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,4,5,6,1,8,2,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,4,5,6,8,1,2,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,1,4,2,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,1,4,5,2,6,7,8]=>[5,2,3,4,1,6,7,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,4,1,5,2,6,7,8]=>[5,3,2,4,1,6,7,8]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,1,4,5,6,2,7,8]=>[6,2,3,4,5,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,4,5,1,6,2,7,8]=>[6,4,3,2,5,1,7,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,1,4,5,6,7,2,8]=>[7,2,3,4,5,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,4,5,6,1,7,2,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,1,4,5,6,7,8,2]=>[8,2,3,4,5,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,4,1,5,6,7,8,2]=>[8,3,2,4,5,6,7,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,4,5,1,6,7,8,2]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,4,5,6,1,7,8,2]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,4,5,6,7,1,8,2]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,1,5,2,6,4,8,7]=>[4,2,6,1,5,3,8,7]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,5,1,2,6,4,8,7]=>[4,6,3,1,5,2,8,7]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,1,5,6,2,4,8,7]=>[5,2,6,4,1,3,8,7]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,5,1,6,2,4,8,7]=>[5,6,3,4,1,2,8,7]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,5,6,1,2,4,8,7]=>[5,6,4,3,1,2,8,7]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,1,5,2,6,8,4,7]=>[4,2,7,1,5,8,3,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,1,5,6,2,8,4,7]=>[5,2,7,4,1,8,3,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,5,6,1,2,8,4,7]=>[5,7,4,3,1,8,2,6]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,1,5,6,8,2,4,7]=>[6,2,7,4,8,1,3,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,5,1,6,8,2,4,7]=>[6,7,3,4,8,1,2,5]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,5,6,1,8,2,4,7]=>[6,7,4,3,8,1,2,5]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[3,5,6,8,1,2,4,7]=>[6,7,5,8,3,1,2,4]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[3,1,5,6,2,4,7,8]=>[5,2,6,4,1,3,7,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,5,1,6,2,4,7,8]=>[5,6,3,4,1,2,7,8]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,5,6,1,2,4,7,8]=>[5,6,4,3,1,2,7,8]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,5,1,2,6,7,4,8]=>[4,7,3,1,5,6,2,8]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,5,1,6,2,7,4,8]=>[5,7,3,4,1,6,2,8]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,5,1,6,7,2,4,8]=>[6,7,3,4,5,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,5,6,7,1,2,4,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[3,1,5,2,6,7,8,4]=>[4,2,8,1,5,6,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,5,1,2,6,7,8,4]=>[4,8,3,1,5,6,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,1,5,6,2,7,8,4]=>[5,2,8,4,1,6,7,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,5,1,6,2,7,8,4]=>[5,8,3,4,1,6,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,5,6,1,2,7,8,4]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,1,5,6,7,2,8,4]=>[6,2,8,4,5,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,5,1,6,7,2,8,4]=>[6,8,3,4,5,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,5,6,1,7,2,8,4]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[3,5,6,7,1,2,8,4]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[3,1,5,6,7,8,2,4]=>[7,2,8,4,5,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,5,1,6,7,8,2,4]=>[7,8,3,4,5,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,5,6,1,7,8,2,4]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[3,5,6,7,1,8,2,4]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[3,5,6,7,8,1,2,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,1,5,2,7,4,8,6]=>[4,2,6,1,8,3,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,5,1,2,7,4,8,6]=>[4,6,3,1,8,2,7,5]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,1,5,7,2,4,8,6]=>[5,2,6,8,1,3,7,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,5,1,7,2,4,8,6]=>[5,6,3,8,1,2,7,4]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,5,7,1,2,4,8,6]=>[5,6,8,4,1,2,7,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,1,5,2,7,8,4,6]=>[4,2,7,1,8,6,3,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,5,1,2,7,8,4,6]=>[4,7,3,1,8,6,2,5]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,1,5,7,2,8,4,6]=>[5,2,7,8,1,6,3,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,5,1,7,2,8,4,6]=>[5,7,3,8,1,6,2,4]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,5,7,1,2,8,4,6]=>[5,7,8,4,1,6,2,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,1,5,7,8,2,4,6]=>[6,2,7,8,5,1,3,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,5,1,7,8,2,4,6]=>[6,7,3,8,5,1,2,4]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,5,7,8,1,2,4,6]=>[6,7,8,5,4,1,2,3]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[3,1,5,2,7,4,6,8]=>[4,2,6,1,7,3,5,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,5,1,2,7,4,6,8]=>[4,6,3,1,7,2,5,8]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,1,5,7,2,4,6,8]=>[5,2,6,7,1,3,4,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,5,1,7,2,4,6,8]=>[5,6,3,7,1,2,4,8]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,5,7,1,2,4,6,8]=>[5,6,7,4,1,2,3,8]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,1,5,2,4,7,6,8]=>[4,2,5,1,3,7,6,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,1,2,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,5,2,4,7,6,8]=>[1,4,5,2,3,7,6,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,5,7,4,6,8]=>[3,2,1,6,7,4,5,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,5,2,7,4,6,8]=>[1,4,6,2,7,3,5,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,7,2,4,6,8]=>[1,5,6,7,2,3,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,5,2,4,7,8,6]=>[4,2,5,1,3,8,7,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,5,1,2,4,7,8,6]=>[4,5,3,1,2,8,7,6]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,1,2,5,7,4,8,6]=>[3,2,1,6,8,4,7,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,5,2,7,4,8,6]=>[1,4,6,2,8,3,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,7,2,4,8,6]=>[1,5,6,8,2,3,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,5,7,8,4,6]=>[3,2,1,7,8,6,4,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,5,2,7,8,4,6]=>[1,4,7,2,8,6,3,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,7,2,8,4,6]=>[1,5,7,8,2,6,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,7,8,2,4,6]=>[1,6,7,8,5,2,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,5,2,8,4,6,7]=>[4,2,6,1,8,3,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,5,1,2,8,4,6,7]=>[4,6,3,1,8,2,7,5]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,1,5,8,2,4,6,7]=>[5,2,6,8,1,3,7,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,5,1,8,2,4,6,7]=>[5,6,3,8,1,2,7,4]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,1,5,2,4,8,6,7]=>[4,2,5,1,3,8,7,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,5,1,2,4,8,6,7]=>[4,5,3,1,2,8,7,6]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[1,3,2,5,4,8,6,7]=>[1,3,2,5,4,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,5,8,4,6,7]=>[3,2,1,6,8,4,7,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,5,2,8,4,6,7]=>[1,4,6,2,8,3,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,8,2,4,6,7]=>[1,5,6,8,2,3,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,5,2,4,6,8,7]=>[4,2,5,1,3,6,8,7]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,5,1,2,4,6,8,7]=>[4,5,3,1,2,6,8,7]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,1,2,5,6,8,4,7]=>[3,2,1,7,5,8,4,6]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,5,2,6,8,4,7]=>[1,4,7,2,5,8,3,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,6,2,8,4,7]=>[1,5,7,4,2,8,3,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,6,8,2,4,7]=>[1,6,7,4,8,2,3,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,5,2,4,6,7,8]=>[4,2,5,1,3,6,7,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,3,5,2,4,6,7,8]=>[1,4,5,2,3,6,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,5,6,4,7,8]=>[3,2,1,6,5,4,7,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,5,6,2,4,7,8]=>[1,5,6,4,2,3,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,5,6,7,4,8]=>[3,2,1,7,5,6,4,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,5,2,6,7,4,8]=>[1,4,7,2,5,6,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,6,2,7,4,8]=>[1,5,7,4,2,6,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,6,7,2,4,8]=>[1,6,7,4,5,2,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,5,6,7,8,4]=>[3,2,1,8,5,6,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,5,2,6,7,8,4]=>[1,4,8,2,5,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,6,2,7,8,4]=>[1,5,8,4,2,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,6,7,2,8,4]=>[1,6,8,4,5,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,6,7,8,2,4]=>[1,7,8,4,5,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,6,2,7,4,8,5]=>[4,2,8,1,6,5,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,6,1,2,7,4,8,5]=>[4,8,3,1,6,5,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,6,1,7,2,4,8,5]=>[5,8,3,6,1,4,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,6,7,1,2,4,8,5]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,6,1,2,7,8,4,5]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,1,6,7,2,8,4,5]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,6,1,7,2,8,4,5]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,6,7,1,2,8,4,5]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,6,1,7,8,2,4,5]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,6,7,8,1,2,4,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[3,1,6,7,2,4,5,8]=>[5,2,7,6,1,4,3,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,1,6,2,4,7,5,8]=>[4,2,7,1,5,6,3,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,6,1,2,4,7,5,8]=>[4,7,3,1,5,6,2,8]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,1,2,6,4,7,5,8]=>[3,2,1,7,5,6,4,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,6,2,4,7,5,8]=>[1,4,7,2,5,6,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,6,2,4,7,8,5]=>[4,2,8,1,5,6,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,6,1,2,4,7,8,5]=>[4,8,3,1,5,6,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,1,2,6,4,7,8,5]=>[3,2,1,8,5,6,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,6,2,4,7,8,5]=>[1,4,8,2,5,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,6,7,4,8,5]=>[3,2,1,8,6,5,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,2,6,7,4,8,5]=>[1,3,2,8,6,5,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,6,7,8,4,5]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,2,6,7,8,4,5]=>[1,3,2,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,6,2,7,8,4,5]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,6,7,8,2,4,5]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,6,2,8,4,5,7]=>[4,2,7,1,8,6,3,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,6,1,2,8,4,5,7]=>[4,7,3,1,8,6,2,5]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,1,6,8,2,4,5,7]=>[5,2,7,8,1,6,3,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,6,1,8,2,4,5,7]=>[5,7,3,8,1,6,2,4]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,6,8,1,2,4,5,7]=>[5,7,8,4,1,6,2,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,1,6,2,4,8,5,7]=>[4,2,7,1,5,8,3,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,3,2,6,4,8,5,7]=>[1,3,2,7,5,8,4,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,6,2,4,8,5,7]=>[1,4,7,2,5,8,3,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,6,8,4,5,7]=>[3,2,1,7,8,6,4,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,1,6,2,4,5,8,7]=>[4,2,6,1,5,3,8,7]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,6,1,2,4,5,8,7]=>[4,6,3,1,5,2,8,7]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,1,2,6,4,5,8,7]=>[3,2,1,6,5,4,8,7]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,1,2,4,6,8,5,7]=>[3,2,1,4,7,8,5,6]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,2,4,6,8,5,7]=>[1,3,2,4,7,8,5,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,6,8,2,5,7]=>[1,6,3,7,8,2,4,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,6,2,4,5,7,8]=>[4,2,6,1,5,3,7,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,6,1,2,4,5,7,8]=>[4,6,3,1,5,2,7,8]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[1,3,4,6,2,5,7,8]=>[1,5,3,6,2,4,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,4,6,2,7,5,8]=>[1,5,3,7,2,6,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,6,7,2,5,8]=>[1,6,3,7,5,2,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,4,6,7,8,5]=>[3,2,1,4,8,6,7,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,4,6,7,2,8,5]=>[1,6,3,8,5,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,6,7,8,2,5]=>[1,7,3,8,5,6,2,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,7,2,8,4,5,6]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,7,1,2,8,4,5,6]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,1,7,8,2,4,5,6]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,7,1,8,2,4,5,6]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,7,8,1,2,4,5,6]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,7,1,2,4,8,5,6]=>[4,8,3,1,5,7,6,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,1,2,7,4,8,5,6]=>[3,2,1,8,5,7,6,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,2,7,4,8,5,6]=>[1,3,2,8,5,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,7,8,4,5,6]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,7,2,8,4,5,6]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,7,8,2,4,5,6]=>[1,5,8,7,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,7,2,4,5,8,6]=>[4,2,8,1,5,6,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,7,1,2,4,5,8,6]=>[4,8,3,1,5,6,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[1,3,7,2,4,5,8,6]=>[1,4,8,2,5,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,4,7,5,8,6]=>[3,2,1,4,8,6,7,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,2,4,7,5,8,6]=>[1,3,2,4,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,2,7,5,8,6]=>[1,4,3,2,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,7,2,5,8,6]=>[1,5,3,8,2,6,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,4,7,8,5,6]=>[3,2,1,4,8,7,6,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,2,4,7,8,5,6]=>[1,3,2,4,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,2,7,8,5,6]=>[1,4,3,2,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,7,8,2,5,6]=>[1,6,3,8,7,2,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,7,2,4,5,6,8]=>[4,2,7,1,5,6,3,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,7,1,2,4,5,6,8]=>[4,7,3,1,5,6,2,8]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,1,2,7,4,5,6,8]=>[3,2,1,7,5,6,4,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,7,2,4,5,6,8]=>[1,4,7,2,5,6,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,4,7,5,6,8]=>[3,2,1,4,7,6,5,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,4,7,2,5,6,8]=>[1,5,3,7,2,6,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,1,2,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,4,5,7,2,8,6]=>[1,6,3,4,8,2,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,5,7,8,2,6]=>[1,7,3,4,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,8,2,4,5,6,7]=>[4,2,8,1,5,6,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,8,1,2,4,5,6,7]=>[4,8,3,1,5,6,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,1,2,8,4,5,6,7]=>[3,2,1,8,5,6,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,8,2,4,5,6,7]=>[1,4,8,2,5,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,4,8,5,6,7]=>[3,2,1,4,8,6,7,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,2,4,8,5,6,7]=>[1,3,2,4,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,2,8,5,6,7]=>[1,4,3,2,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,8,2,5,6,7]=>[1,5,3,8,2,6,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,4,5,8,6,7]=>[3,2,1,4,5,8,7,6]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,2,5,8,6,7]=>[1,4,3,2,5,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,5,2,8,6,7]=>[1,5,3,4,2,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,5,8,2,6,7]=>[1,6,3,4,8,2,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,4,5,6,8,7]=>[3,2,1,4,5,6,8,7]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,4,5,6,8,2,7]=>[1,7,3,4,5,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,5,2,6,3,8,7]=>[6,2,4,3,5,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,5,1,2,6,3,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,1,5,6,2,3,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,5,1,6,2,3,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,5,6,1,2,3,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,1,5,2,6,8,3,7]=>[7,2,4,3,5,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,5,1,2,6,8,3,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[4,1,5,6,2,8,3,7]=>[7,2,5,4,3,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,5,1,6,2,8,3,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,5,6,1,2,8,3,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,1,5,6,8,2,3,7]=>[7,2,6,4,8,3,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,5,1,6,8,2,3,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,5,6,1,8,2,3,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,5,6,8,1,2,3,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[4,1,5,6,2,3,7,8]=>[6,2,5,4,3,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,5,1,6,2,3,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,5,1,6,2,7,3,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,5,6,1,2,7,3,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,1,5,6,7,2,3,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,5,1,6,7,2,3,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,5,6,1,7,2,3,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,5,1,2,6,7,8,3]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,5,1,6,2,7,8,3]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,5,6,1,2,7,8,3]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,1,5,6,7,2,8,3]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,5,1,6,7,2,8,3]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,5,6,1,7,2,8,3]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,5,6,7,1,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,1,5,6,7,8,2,3]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,5,1,6,7,8,2,3]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,5,6,1,7,8,2,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,5,6,7,1,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,1,5,2,7,3,8,6]=>[6,2,4,3,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,5,1,2,7,3,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,5,1,7,2,3,8,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,5,7,1,2,3,8,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[4,1,5,2,7,8,3,6]=>[7,2,4,3,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,5,1,2,7,8,3,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[4,1,5,7,2,8,3,6]=>[7,2,5,8,3,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,5,1,7,2,8,3,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,5,7,1,2,8,3,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[4,5,1,7,8,2,3,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,5,7,8,1,2,3,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,5,1,2,7,3,6,8]=>[6,4,3,2,7,1,5,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,5,1,7,2,3,6,8]=>[6,5,3,7,2,1,4,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,1,5,2,3,7,6,8]=>[5,2,4,3,1,7,6,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,5,1,2,3,7,6,8]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,1,5,2,3,7,8,6]=>[5,2,4,3,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,1,2,5,3,7,8,6]=>[5,2,3,4,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,4,2,5,3,7,8,6]=>[1,5,3,4,2,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,2,3,7,8,6]=>[1,5,4,3,2,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,5,7,3,8,6]=>[6,2,3,4,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,4,2,5,7,3,8,6]=>[1,6,3,4,8,2,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,7,2,3,8,6]=>[1,6,5,8,3,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,5,7,8,3,6]=>[7,2,3,4,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,4,2,5,7,8,3,6]=>[1,7,3,4,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,2,7,8,3,6]=>[1,7,4,3,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,5,2,8,3,6,7]=>[6,2,4,3,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,5,1,2,8,3,6,7]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,5,1,8,2,3,6,7]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,5,8,1,2,3,6,7]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[4,1,5,2,3,8,6,7]=>[5,2,4,3,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,5,1,2,3,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,1,2,5,3,8,6,7]=>[5,2,3,4,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,4,2,5,3,8,6,7]=>[1,5,3,4,2,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,2,3,8,6,7]=>[1,5,4,3,2,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,5,8,3,6,7]=>[6,2,3,4,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,4,2,5,8,3,6,7]=>[1,6,3,4,8,2,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,8,2,3,6,7]=>[1,6,5,8,3,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,5,1,2,3,6,8,7]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,1,2,5,6,3,8,7]=>[6,2,3,4,5,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,4,5,6,2,3,8,7]=>[1,6,5,4,3,2,8,7]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,5,6,8,3,7]=>[7,2,3,4,5,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,4,2,5,6,8,3,7]=>[1,7,3,4,5,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,6,2,8,3,7]=>[1,7,5,4,3,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,6,8,2,3,7]=>[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,5,2,3,6,7,8]=>[5,2,4,3,1,6,7,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,1,2,5,3,6,7,8]=>[5,2,3,4,1,6,7,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,4,2,5,3,6,7,8]=>[1,5,3,4,2,6,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,5,6,3,7,8]=>[6,2,3,4,5,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,4,5,2,6,3,7,8]=>[1,6,4,3,5,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,6,2,3,7,8]=>[1,6,5,4,3,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,5,6,7,3,8]=>[7,2,3,4,5,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,4,2,5,6,7,3,8]=>[1,7,3,4,5,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,6,2,7,3,8]=>[1,7,5,4,3,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,6,7,2,3,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,5,6,7,8,3]=>[8,2,3,4,5,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,4,2,5,6,7,8,3]=>[1,8,3,4,5,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,2,6,7,8,3]=>[1,8,4,3,5,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,6,2,7,8,3]=>[1,8,5,4,3,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,6,7,2,8,3]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,6,7,8,2,3]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,6,2,7,3,8,5]=>[6,2,8,4,5,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,1,6,7,2,3,8,5]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,6,1,7,2,3,8,5]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,6,7,1,2,3,8,5]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[4,6,1,2,7,8,3,5]=>[7,8,3,4,5,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,1,6,7,2,8,3,5]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,6,1,7,2,8,3,5]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,6,7,1,2,8,3,5]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[4,1,6,7,8,2,3,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,6,1,7,8,2,3,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,6,7,1,8,2,3,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,6,7,8,1,2,3,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,1,6,2,7,3,5,8]=>[6,2,7,4,5,1,3,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,6,1,2,7,3,5,8]=>[6,7,3,4,5,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,6,1,7,2,3,5,8]=>[6,7,3,5,4,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,6,7,1,2,3,5,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[4,1,6,2,3,7,5,8]=>[5,2,7,4,1,6,3,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,6,1,2,3,7,5,8]=>[5,7,3,4,1,6,2,8]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,1,2,6,3,7,5,8]=>[5,2,3,7,1,6,4,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,4,2,6,3,7,5,8]=>[1,5,3,7,2,6,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,6,7,3,5,8]=>[6,2,3,7,5,1,4,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,4,2,6,7,3,5,8]=>[1,6,3,7,5,2,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,2,7,3,5,8]=>[1,6,7,4,5,2,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,6,2,3,7,8,5]=>[5,2,8,4,1,6,7,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,1,2,6,3,7,8,5]=>[5,2,3,8,1,6,7,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,4,6,2,3,7,8,5]=>[1,5,8,4,2,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,6,7,3,8,5]=>[6,2,3,8,5,1,7,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,4,6,2,7,3,8,5]=>[1,6,8,4,5,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,7,2,3,8,5]=>[1,6,8,5,4,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,6,7,8,3,5]=>[1,7,3,8,5,6,2,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,2,7,8,3,5]=>[1,7,8,4,5,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,7,2,8,3,5]=>[1,7,8,5,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,7,8,2,3,5]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,6,2,8,3,5,7]=>[6,2,7,4,8,1,3,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,6,1,2,8,3,5,7]=>[6,7,3,4,8,1,2,5]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,1,6,8,2,3,5,7]=>[6,2,7,8,5,1,3,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,6,1,8,2,3,5,7]=>[6,7,3,8,5,1,2,4]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,6,8,1,2,3,5,7]=>[6,7,8,4,5,1,2,3]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[4,1,6,2,3,8,5,7]=>[5,2,7,4,1,8,3,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,6,1,2,3,8,5,7]=>[5,7,3,4,1,8,2,6]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,1,2,6,3,8,5,7]=>[5,2,3,7,1,8,4,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,4,2,6,3,8,5,7]=>[1,5,3,7,2,8,4,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,2,3,8,5,7]=>[1,5,7,4,2,8,3,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,6,8,3,5,7]=>[1,6,3,7,8,2,4,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,2,8,3,5,7]=>[1,6,7,4,8,2,3,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,8,2,3,5,7]=>[1,6,7,8,5,2,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,6,2,3,5,8,7]=>[5,2,6,4,1,3,8,7]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,6,1,2,3,5,8,7]=>[5,6,3,4,1,2,8,7]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,1,2,6,3,5,8,7]=>[5,2,3,6,1,4,8,7]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,1,2,3,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,2,4,6,3,5,8,7]=>[1,2,5,6,3,4,8,7]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,3,6,8,5,7]=>[4,2,3,1,7,8,5,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,2,4,3,6,8,5,7]=>[1,2,4,3,7,8,5,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,6,3,8,5,7]=>[1,2,5,7,3,8,4,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,6,8,3,5,7]=>[1,2,6,7,8,3,4,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,6,2,3,5,7,8]=>[5,2,6,4,1,3,7,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,6,1,2,3,5,7,8]=>[5,6,3,4,1,2,7,8]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,1,2,6,3,5,7,8]=>[5,2,3,6,1,4,7,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,4,2,6,3,5,7,8]=>[1,5,3,6,2,4,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,2,3,5,7,8]=>[1,5,6,4,2,3,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,3,6,5,7,8]=>[4,2,3,1,6,5,7,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,2,4,6,3,5,7,8]=>[1,2,5,6,3,4,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,3,6,7,5,8]=>[4,2,3,1,7,6,5,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,4,2,3,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,6,3,7,5,8]=>[1,2,5,7,3,6,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,6,7,3,5,8]=>[1,2,6,7,5,3,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,3,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,4,2,3,6,7,8,5]=>[1,4,3,2,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,6,3,7,8,5]=>[1,2,5,8,3,6,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,6,7,3,8,5]=>[1,2,6,8,5,3,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,6,7,8,3,5]=>[1,2,7,8,5,6,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,7,2,8,3,5,6]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,7,1,2,8,3,5,6]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,1,7,8,2,3,5,6]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,7,1,8,2,3,5,6]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,7,8,1,2,3,5,6]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[4,1,7,2,3,8,5,6]=>[5,2,8,4,1,7,6,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,7,1,2,3,8,5,6]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,4,2,7,3,8,5,6]=>[1,5,3,8,2,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,2,3,8,5,6]=>[1,5,8,4,2,7,6,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,7,8,3,5,6]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,4,2,7,8,3,5,6]=>[1,6,3,8,7,2,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,2,8,3,5,6]=>[1,6,8,4,7,2,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,8,2,3,5,6]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,7,2,3,5,8,6]=>[5,2,8,4,1,6,7,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,7,1,2,3,5,8,6]=>[5,8,3,4,1,6,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,1,2,7,3,5,8,6]=>[5,2,3,8,1,6,7,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,4,2,7,3,5,8,6]=>[1,5,3,8,2,6,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,2,3,5,8,6]=>[1,5,8,4,2,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,3,7,5,8,6]=>[4,2,3,1,8,6,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,4,2,3,7,5,8,6]=>[1,4,3,2,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,3,7,5,8,6]=>[1,2,4,3,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,7,3,5,8,6]=>[1,2,5,8,3,6,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,3,7,8,5,6]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,4,2,3,7,8,5,6]=>[1,4,3,2,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,3,7,8,5,6]=>[1,2,4,3,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,7,3,8,5,6]=>[1,2,5,8,3,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,7,8,3,5,6]=>[1,2,6,8,7,3,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,7,2,3,5,6,8]=>[5,2,7,4,1,6,3,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,7,1,2,3,5,6,8]=>[5,7,3,4,1,6,2,8]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,1,2,7,3,5,6,8]=>[5,2,3,7,1,6,4,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,4,2,7,3,5,6,8]=>[1,5,3,7,2,6,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,2,3,5,6,8]=>[1,5,7,4,2,6,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,3,7,5,6,8]=>[4,2,3,1,7,6,5,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,4,2,3,7,5,6,8]=>[1,4,3,2,7,6,5,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,7,3,5,6,8]=>[1,2,5,7,3,6,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,3,5,7,6,8]=>[4,2,3,1,5,7,6,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,2,4,5,7,3,6,8]=>[1,2,6,4,7,3,5,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,3,5,7,8,6]=>[4,2,3,1,5,8,7,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,4,2,3,5,7,8,6]=>[1,4,3,2,5,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,5,7,3,8,6]=>[1,2,6,4,8,3,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,5,7,8,3,6]=>[1,2,7,4,8,6,3,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,8,2,3,5,6,7]=>[5,2,8,4,1,6,7,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,8,1,2,3,5,6,7]=>[5,8,3,4,1,6,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,1,2,8,3,5,6,7]=>[5,2,3,8,1,6,7,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,4,2,8,3,5,6,7]=>[1,5,3,8,2,6,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,8,2,3,5,6,7]=>[1,5,8,4,2,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,3,8,5,6,7]=>[4,2,3,1,8,6,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,4,2,3,8,5,6,7]=>[1,4,3,2,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,3,8,5,6,7]=>[1,2,4,3,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,8,3,5,6,7]=>[1,2,5,8,3,6,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,3,5,8,6,7]=>[4,2,3,1,5,8,7,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,4,2,3,5,8,6,7]=>[1,4,3,2,5,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,3,5,8,6,7]=>[1,2,4,3,5,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,5,3,8,6,7]=>[1,2,5,4,3,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,5,8,3,6,7]=>[1,2,6,4,8,3,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,5,6,8,3,7]=>[1,2,7,4,5,8,3,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,3,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,6,2,7,3,8,4]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,1,2,7,3,8,4]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,1,6,7,2,3,8,4]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,1,7,2,3,8,4]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,6,7,1,2,3,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,1,6,2,7,8,3,4]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,1,2,7,8,3,4]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,1,6,7,2,8,3,4]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,1,7,2,8,3,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,6,7,1,2,8,3,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,1,6,7,8,2,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,1,7,8,2,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,6,7,1,8,2,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,1,6,2,7,3,4,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,6,1,2,7,3,4,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,6,1,7,2,3,4,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,1,6,2,3,7,4,8]=>[7,2,5,4,3,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,2,6,3,7,4,8]=>[7,2,3,5,4,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,5,2,6,3,7,4,8]=>[1,7,3,5,4,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,2,6,7,3,4,8]=>[7,2,3,6,5,4,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,5,2,6,7,3,4,8]=>[1,7,3,6,5,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,2,7,3,4,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,7,2,3,4,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,6,2,3,7,8,4]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,1,2,3,7,8,4]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,1,2,6,3,7,8,4]=>[8,2,3,5,4,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,5,2,6,3,7,8,4]=>[1,8,3,5,4,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,2,3,7,8,4]=>[1,8,5,4,3,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,2,6,7,3,8,4]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,5,6,7,2,3,8,4]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,2,6,7,8,3,4]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,5,2,6,7,8,3,4]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,2,7,8,3,4]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,7,2,8,3,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,7,8,2,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,6,2,8,3,4,7]=>[7,2,6,4,8,3,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,6,1,2,8,3,4,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,6,1,8,2,3,4,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,6,8,1,2,3,4,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[5,1,6,2,3,8,4,7]=>[7,2,5,4,3,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,6,1,2,3,8,4,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,1,2,6,3,8,4,7]=>[7,2,3,5,4,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,5,2,6,3,8,4,7]=>[1,7,3,5,4,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,2,3,8,4,7]=>[1,7,5,4,3,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,2,6,8,3,4,7]=>[7,2,3,6,8,4,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,5,2,6,8,3,4,7]=>[1,7,3,6,8,4,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,2,8,3,4,7]=>[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,6,2,3,4,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,6,1,2,3,4,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,1,2,6,3,4,8,7]=>[6,2,3,5,4,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,5,6,2,3,4,8,7]=>[1,6,5,4,3,2,8,7]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,2,3,6,8,4,7]=>[7,2,3,4,5,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,5,2,3,6,8,4,7]=>[1,7,3,4,5,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,6,3,8,4,7]=>[1,2,7,5,4,8,3,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,6,8,3,4,7]=>[1,2,7,6,8,4,3,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,6,2,3,4,7,8]=>[6,2,5,4,3,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,1,2,6,3,4,7,8]=>[6,2,3,5,4,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,5,2,6,3,4,7,8]=>[1,6,3,5,4,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,2,3,4,7,8]=>[1,6,5,4,3,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,2,3,6,4,7,8]=>[6,2,3,4,5,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,5,2,3,6,4,7,8]=>[1,6,3,4,5,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,3,6,4,7,8]=>[1,2,6,4,5,3,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,6,3,4,7,8]=>[1,2,6,5,4,3,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,2,3,6,7,4,8]=>[7,2,3,4,5,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,5,2,3,6,7,4,8]=>[1,7,3,4,5,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,6,3,7,4,8]=>[1,2,7,5,4,6,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,2,3,6,7,8,4]=>[8,2,3,4,5,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,5,2,3,6,7,8,4]=>[1,8,3,4,5,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,3,6,7,8,4]=>[1,2,8,4,5,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,6,3,7,8,4]=>[1,2,8,5,4,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,6,7,3,8,4]=>[1,2,8,6,5,4,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,6,7,8,3,4]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,7,2,8,3,4,6]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,7,1,2,8,3,4,6]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,1,7,8,2,3,4,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,7,1,8,2,3,4,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,7,8,1,2,3,4,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,1,7,2,3,8,4,6]=>[7,2,8,4,5,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,7,1,2,3,8,4,6]=>[7,8,3,4,5,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,1,2,7,3,8,4,6]=>[7,2,3,8,5,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,5,2,7,3,8,4,6]=>[1,7,3,8,5,6,2,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,2,3,8,4,6]=>[1,7,8,4,5,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,2,8,3,4,6]=>[1,7,8,4,6,5,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,8,2,3,4,6]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,7,2,3,4,8,6]=>[6,2,8,4,5,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,7,1,2,3,4,8,6]=>[6,8,3,4,5,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[5,1,2,7,3,4,8,6]=>[6,2,3,8,5,1,7,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,5,2,7,3,4,8,6]=>[1,6,3,8,5,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,2,3,4,8,6]=>[1,6,8,4,5,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,2,3,7,4,8,6]=>[6,2,3,4,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,5,2,3,7,4,8,6]=>[1,6,3,4,8,2,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,3,7,4,8,6]=>[1,2,6,4,8,3,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,7,3,4,8,6]=>[1,2,6,8,5,3,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,2,3,7,8,4,6]=>[7,2,3,4,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,5,2,3,7,8,4,6]=>[1,7,3,4,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,3,7,8,4,6]=>[1,2,7,4,8,6,3,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,7,3,8,4,6]=>[1,2,7,8,5,6,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,7,8,3,4,6]=>[1,2,7,8,6,5,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,7,2,3,4,6,8]=>[6,2,7,4,5,1,3,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,7,1,2,3,4,6,8]=>[6,7,3,4,5,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[5,1,2,7,3,4,6,8]=>[6,2,3,7,5,1,4,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,5,2,7,3,4,6,8]=>[1,6,3,7,5,2,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,2,3,4,6,8]=>[1,6,7,4,5,2,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,3,7,4,6,8]=>[1,2,6,4,7,3,5,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,7,3,4,6,8]=>[1,2,6,7,5,3,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,5,7,4,6,8]=>[1,2,3,6,7,4,5,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,2,3,4,7,8,6]=>[5,2,3,4,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,5,2,3,4,7,8,6]=>[1,5,3,4,2,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,3,4,7,8,6]=>[1,2,5,4,3,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,5,7,4,8,6]=>[1,2,3,6,8,4,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,5,7,8,4,6]=>[1,2,3,7,8,6,4,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,8,2,3,4,6,7]=>[6,2,8,4,5,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,8,1,2,3,4,6,7]=>[6,8,3,4,5,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[5,1,2,8,3,4,6,7]=>[6,2,3,8,5,1,7,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,5,2,8,3,4,6,7]=>[1,6,3,8,5,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,2,3,4,6,7]=>[1,6,8,4,5,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,2,3,8,4,6,7]=>[6,2,3,4,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,5,2,3,8,4,6,7]=>[1,6,3,4,8,2,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,3,8,4,6,7]=>[1,2,6,4,8,3,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,8,3,4,6,7]=>[1,2,6,8,5,3,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,2,3,4,8,6,7]=>[5,2,3,4,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,5,2,3,4,8,6,7]=>[1,5,3,4,2,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,3,4,8,6,7]=>[1,2,5,4,3,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,5,8,4,6,7]=>[1,2,3,6,8,4,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,2,3,4,6,8,7]=>[5,2,3,4,1,6,8,7]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,2,3,5,6,8,4,7]=>[1,2,3,7,5,8,4,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,3,4,6,7,8]=>[1,5,3,4,2,6,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,3,4,6,7,8]=>[1,2,5,4,3,6,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,7,2,8,3,4,5]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,7,1,2,8,3,4,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,1,7,8,2,3,4,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,7,1,8,2,3,4,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,1,7,2,3,8,4,5]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,7,1,2,3,8,4,5]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,1,2,7,3,8,4,5]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,2,7,3,8,4,5]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,2,3,8,4,5]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,2,7,8,3,4,5]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,2,7,8,3,4,5]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,2,8,3,4,5]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,8,2,3,4,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,7,2,3,4,8,5]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,7,1,2,3,4,8,5]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,1,2,7,3,4,8,5]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,2,7,3,4,8,5]=>[1,8,3,6,5,4,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,2,3,4,8,5]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,7,3,4,8,5]=>[1,2,8,6,5,4,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,2,3,7,8,4,5]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,2,3,7,8,4,5]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,3,7,8,4,5]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,7,3,8,4,5]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,7,8,3,4,5]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,7,2,3,4,5,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,1,2,7,3,4,5,8]=>[7,2,3,6,5,4,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,6,2,7,3,4,5,8]=>[1,7,3,6,5,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,2,3,4,5,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,2,3,7,4,5,8]=>[7,2,3,4,6,5,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,2,6,7,3,4,5,8]=>[1,2,7,6,5,4,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,2,3,4,7,5,8]=>[7,2,3,4,5,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,6,2,3,4,7,5,8]=>[1,7,3,4,5,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,6,4,7,5,8]=>[1,2,3,7,5,6,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,6,7,4,5,8]=>[1,2,3,7,6,5,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,2,3,4,7,8,5]=>[8,2,3,4,5,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,2,3,4,7,8,5]=>[1,8,3,4,5,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,3,4,7,8,5]=>[1,2,8,4,5,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,6,4,7,8,5]=>[1,2,3,8,5,6,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,6,7,4,8,5]=>[1,2,3,8,6,5,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,6,7,8,4,5]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,8,2,3,4,5,7]=>[7,2,8,4,5,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,8,1,2,3,4,5,7]=>[7,8,3,4,5,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[6,1,2,8,3,4,5,7]=>[7,2,3,8,5,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,6,2,8,3,4,5,7]=>[1,7,3,8,5,6,2,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,2,3,4,5,7]=>[1,7,8,4,5,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,2,3,8,4,5,7]=>[7,2,3,4,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,6,2,3,8,4,5,7]=>[1,7,3,4,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,3,8,4,5,7]=>[1,2,7,4,8,6,3,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,8,3,4,5,7]=>[1,2,7,8,5,6,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,2,3,4,8,5,7]=>[7,2,3,4,5,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,6,2,3,4,8,5,7]=>[1,7,3,4,5,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,3,4,8,5,7]=>[1,2,7,4,5,8,3,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,6,4,8,5,7]=>[1,2,3,7,5,8,4,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,6,8,4,5,7]=>[1,2,3,7,8,6,4,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,2,3,4,5,8,7]=>[6,2,3,4,5,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,2,3,6,4,5,8,7]=>[1,2,3,6,5,4,8,7]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,4,6,8,5,7]=>[1,2,3,4,7,8,5,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,2,3,4,5,7,8]=>[1,6,3,4,5,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,3,4,5,7,8]=>[1,2,6,4,5,3,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,8,2,3,4,5,6]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,2,8,3,4,5,6]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,2,8,3,4,5,6]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,2,3,4,5,6]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,2,3,8,4,5,6]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,2,3,8,4,5,6]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,3,8,4,5,6]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,8,3,4,5,6]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,2,3,4,8,5,6]=>[8,2,3,4,5,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,3,7,4,8,5,6]=>[1,2,3,8,5,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,7,8,4,5,6]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,2,3,4,5,8,6]=>[8,2,3,4,5,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,2,3,4,5,8,6]=>[1,8,3,4,5,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,3,4,5,8,6]=>[1,2,8,4,5,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,7,4,5,8,6]=>[1,2,3,8,5,6,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,4,7,5,8,6]=>[1,2,3,4,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,4,7,8,5,6]=>[1,2,3,4,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,3,4,5,6,8]=>[1,7,3,4,5,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,7,4,5,6,8]=>[1,2,3,7,5,6,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,4,7,5,6,8]=>[1,2,3,4,7,6,5,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,3,4,5,6,7]=>[1,8,3,4,5,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,3,4,5,6,7]=>[1,2,8,4,5,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,8,4,5,6,7]=>[1,2,3,8,5,6,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,3,2,6,1,4,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[7,3,2,5,4,8,1,6]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,5,2,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,4,5,2,3,8,1,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,4,5,2,3,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,4,6,2,1,3,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[3,6,1,5,4,2,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,6,5,1,3,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,6,4,3,1,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[7,5,4,3,2,8,1,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,6,4,3,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,4,3,8,2,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,4,3,8,1,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,4,3,1,8,2,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[4,7,5,1,3,8,2,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[3,7,1,5,4,8,2,6]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,1,7,5,4,8,3,6]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,8,1,5,4,7,6,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,8,5,1,3,7,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,8,4,3,1,7,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,8,4,3,7,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,4,3,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,7,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,7,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,6,1,7,3,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,1,6,7,4,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,1,8,6,7,4,5,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,7,6,8,4,3,5]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,7,1,6,8,4,2,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,7,6,1,8,3,2,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,7,6,8,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,7,2,1,8,3,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[6,4,7,2,8,1,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,6,2,8,3,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,6,2,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,2,6,7,4,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,3,2,6,8,4,1,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,3,2,7,8,1,4,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,3,2,7,1,8,4,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,3,2,1,7,8,5,6]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,4,1,2,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[5,3,2,8,1,7,6,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,3,2,8,7,1,5,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,3,2,8,6,5,1,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,7,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,8,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,8,2,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,8,2,1,7,6,3]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,5,8,1,2,7,6,3]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[3,5,1,8,2,7,6,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,1,5,8,3,7,6,4]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,6,8,7,3,5,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,6,1,8,7,2,5,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,6,8,1,7,2,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,8,7,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,8,7,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,6,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,6,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,8,1,6,5,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,7,1,8,6,5,2,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,1,7,8,6,5,3,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,8,1,7,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,8,7,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,7,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[3,4,1,2,6,5,8,7,10,9]=>[4,3,2,1,6,5,8,7,10,9]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[4,3,2,1,6,5,8,7,10,9]=>[4,3,2,1,6,5,8,7,10,9]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[4,5,6,1,2,3,8,7,10,9]=>[6,5,4,3,2,1,8,7,10,9]=>[6,5,4,3,2,1,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[2,1,5,6,3,4,8,7,10,9]=>[2,1,6,5,4,3,8,7,10,9]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,6,5,4,3,8,7,10,9]=>[2,1,6,5,4,3,8,7,10,9]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[6,5,4,3,2,1,8,7,10,9]=>[6,5,4,3,2,1,8,7,10,9]=>[6,5,4,3,2,1,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[8,7,4,3,6,5,2,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[10,7,4,3,6,5,2,9,8,1]=>[10,9,7,6,5,4,3,8,2,1]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[10,9,4,3,6,5,8,7,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,5,6,3,4,10,1,2,7]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[5,6,7,8,1,2,3,4,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[2,1,6,7,8,3,4,5,10,9]=>[2,1,8,7,6,5,4,3,10,9]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[3,4,1,2,7,8,5,6,10,9]=>[4,3,2,1,8,7,6,5,10,9]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[2,1,4,3,7,8,5,6,10,9]=>[2,1,4,3,8,7,6,5,10,9]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,4,3,8,7,6,5,10,9]=>[2,1,4,3,8,7,6,5,10,9]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,3,2,1,8,7,6,5,10,9]=>[4,3,2,1,8,7,6,5,10,9]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[2,1,8,7,6,5,4,3,10,9]=>[2,1,8,7,6,5,4,3,10,9]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[8,7,6,5,4,3,2,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[9,7,6,5,4,3,2,10,1,8]=>[10,9,7,6,5,4,3,8,2,1]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[10,7,6,5,4,3,2,9,8,1]=>[10,9,7,6,5,4,3,8,2,1]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[10,9,6,5,4,3,8,7,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,3,2,9,6,5,8,7,4,1]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[2,1,10,9,6,5,8,7,4,3]=>[2,1,10,9,8,7,6,5,4,3]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[10,9,8,5,4,7,6,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[4,9,10,1,7,8,5,6,2,3]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[10,8,9,6,7,4,5,2,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[2,1,7,8,9,10,3,4,5,6]=>[2,1,10,9,8,7,6,5,4,3]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[6,7,8,9,10,1,2,3,4,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[3,4,1,2,8,9,10,5,6,7]=>[4,3,2,1,10,9,8,7,6,5]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[2,1,4,3,8,9,10,5,6,7]=>[2,1,4,3,10,9,8,7,6,5]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,5,6,3,4,9,10,7,8]=>[2,1,6,5,4,3,10,9,8,7]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,5,6,1,2,3,9,10,7,8]=>[6,5,4,3,2,1,10,9,8,7]=>[6,5,4,3,2,1,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[3,4,1,2,6,5,9,10,7,8]=>[4,3,2,1,6,5,10,9,8,7]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[2,1,4,3,6,5,9,10,7,8]=>[2,1,4,3,6,5,10,9,8,7]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,4,3,6,5,10,9,8,7]=>[2,1,4,3,6,5,10,9,8,7]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,3,2,1,6,5,10,9,8,7]=>[4,3,2,1,6,5,10,9,8,7]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[2,1,6,5,4,3,10,9,8,7]=>[2,1,6,5,4,3,10,9,8,7]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[6,5,4,3,2,1,10,9,8,7]=>[6,5,4,3,2,1,10,9,8,7]=>[6,5,4,3,2,1,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[10,9,4,3,8,7,6,5,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,10,5,9,3,8,1,6,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,5,10,3,8,2,6,1,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[2,1,4,3,10,9,8,7,6,5]=>[2,1,4,3,10,9,8,7,6,5]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,3,2,1,10,9,8,7,6,5]=>[4,3,2,1,10,9,8,7,6,5]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[10,3,2,9,8,7,6,5,4,1]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[2,1,10,9,8,7,6,5,4,3]=>[2,1,10,9,8,7,6,5,4,3]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[3,10,1,9,8,7,6,5,4,2]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[9,10,8,7,6,5,4,3,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[3,2,5,1,4,6,7,8]=>[4,2,5,1,3,6,7,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,2,5,1,3,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,2,4,1,3,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,2,6,1,4,5,7,8]=>[4,2,6,1,5,3,7,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,2,6,1,3,5,7,8]=>[5,4,6,2,1,3,7,8]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[5,3,6,1,2,4,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,3,5,1,2,4,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,2,7,1,3,4,6,8]=>[6,4,7,2,5,1,3,8]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[5,3,7,1,2,4,6,8]=>[6,5,7,4,2,1,3,8]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[5,4,7,1,2,3,6,8]=>[6,5,7,4,2,1,3,8]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[6,2,7,1,3,4,5,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[6,3,7,1,2,4,5,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[6,4,7,1,2,3,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,3,5,1,2,4,6,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[7,3,6,1,2,4,5,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[7,4,6,1,2,3,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,2,8,1,4,5,6,7]=>[4,2,8,1,5,6,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[5,2,8,1,3,4,6,7]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[5,4,8,1,2,3,6,7]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[6,2,8,1,3,4,5,7]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[6,3,8,1,2,4,5,7]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[6,4,8,1,2,3,5,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[6,5,8,1,2,3,4,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[7,2,8,1,3,4,5,6]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,3,8,1,2,4,5,6]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[7,4,8,1,2,3,5,6]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,5,8,1,2,3,4,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,4,1,3,5,6,7]=>[8,4,5,2,3,6,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,3,5,1,2,4,6,7]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,3,6,1,2,4,5,7]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,3,7,1,2,4,5,6]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,4,7,1,2,3,5,6]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,5,7,1,2,3,4,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,2,5,7,1,4,6,8]=>[5,2,6,7,1,3,4,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,2,5,7,1,3,6,8]=>[6,5,3,7,2,1,4,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,3,5,7,1,2,6,8]=>[6,5,3,7,2,1,4,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,2,4,7,1,3,6,8]=>[6,5,3,7,2,1,4,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,3,4,7,1,2,6,8]=>[6,5,3,7,2,1,4,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,2,6,7,1,3,5,8]=>[6,5,7,4,2,1,3,8]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[5,2,6,7,1,3,4,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[5,3,6,7,1,2,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,2,5,7,1,3,4,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[6,3,5,7,1,2,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,2,4,6,1,3,5,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[7,3,4,6,1,2,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,3,5,6,1,2,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,2,5,8,1,4,6,7]=>[5,2,6,8,1,3,7,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,2,5,8,1,3,6,7]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,3,5,8,1,2,6,7]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,2,4,8,1,3,6,7]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,2,6,8,1,4,5,7]=>[5,2,7,8,1,6,3,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,2,6,8,1,3,5,7]=>[6,5,7,8,2,1,3,4]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[4,3,6,8,1,2,5,7]=>[6,5,7,8,2,1,3,4]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[5,2,6,8,1,3,4,7]=>[7,5,6,8,2,3,1,4]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[6,2,4,8,1,3,5,7]=>[7,5,6,8,2,3,1,4]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[6,3,4,8,1,2,5,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[6,2,5,8,1,3,4,7]=>[7,5,6,8,2,3,1,4]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[6,3,5,8,1,2,4,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[6,4,5,8,1,2,3,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[3,2,7,8,1,4,5,6]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,3,7,8,1,2,5,6]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[5,3,7,8,1,2,4,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[5,4,7,8,1,2,3,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[6,2,7,8,1,3,4,5]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[6,3,7,8,1,2,4,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,4,7,8,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,4,8,1,3,5,6]=>[8,5,6,7,2,3,4,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[7,3,4,8,1,2,5,6]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[7,3,5,8,1,2,4,6]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,4,5,8,1,2,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,6,8,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,4,6,1,3,5,7]=>[8,5,6,7,2,3,4,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[8,3,4,6,1,2,5,7]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[8,2,5,6,1,3,4,7]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[8,3,5,6,1,2,4,7]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,2,4,7,1,3,5,6]=>[8,5,6,7,2,3,4,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[8,2,5,7,1,3,4,6]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[8,3,5,7,1,2,4,6]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,2,6,7,1,3,4,5]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[8,4,6,7,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,2,5,1,4,7,8]=>[5,6,3,4,1,2,7,8]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,6,2,5,1,3,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,6,3,5,1,2,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,6,2,4,1,3,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,7,3,5,1,2,6,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[5,7,2,4,1,3,6,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[5,7,3,4,1,2,6,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[4,7,3,6,1,2,5,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[5,7,2,6,1,3,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,7,3,6,1,2,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,2,5,1,3,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,8,2,5,1,3,6,7]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[5,8,2,4,1,3,6,7]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[5,8,3,4,1,2,6,7]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[3,8,2,6,1,4,5,7]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,8,2,6,1,3,5,7]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[5,8,3,6,1,2,4,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,8,4,6,1,2,3,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,8,2,4,1,3,5,7]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[6,8,3,4,1,2,5,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,8,3,5,1,2,4,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,8,4,5,1,2,3,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,8,2,7,1,4,5,6]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,8,2,7,1,3,5,6]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[4,8,3,7,1,2,5,6]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[5,8,2,7,1,3,4,6]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[5,8,3,7,1,2,4,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,8,4,7,1,2,3,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,8,2,7,1,3,4,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,8,3,7,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,7,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,2,4,1,3,5,6]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,8,2,5,1,3,4,6]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,8,3,5,1,2,4,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,4,6,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,2,6,1,5,7,8]=>[5,3,2,6,1,4,7,8]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[5,3,2,6,1,4,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,4,2,6,1,3,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,3,2,5,1,4,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,4,2,5,1,3,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,5,2,4,1,3,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,3,2,7,1,5,6,8]=>[5,3,2,7,1,6,4,8]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[5,3,2,7,1,4,6,8]=>[6,5,3,7,2,1,4,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,4,3,7,1,2,6,8]=>[6,5,3,7,2,1,4,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,3,2,7,1,4,5,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,4,2,7,1,3,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,4,3,7,1,2,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,5,2,7,1,3,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,5,3,7,1,2,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,3,2,5,1,4,6,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[7,4,2,5,1,3,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,3,2,6,1,4,5,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[7,4,2,6,1,3,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,3,6,1,2,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,2,6,1,3,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,3,6,1,2,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,3,5,1,2,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,3,2,8,1,5,6,7]=>[5,3,2,8,1,6,7,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[5,3,2,8,1,4,6,7]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,4,3,8,1,2,6,7]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,3,2,8,1,4,5,7]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,4,2,8,1,3,5,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[6,4,3,8,1,2,5,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[6,5,2,8,1,3,4,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[6,5,3,8,1,2,4,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[6,5,4,8,1,2,3,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[7,3,2,8,1,4,5,6]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,4,2,8,1,3,5,6]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[7,4,3,8,1,2,5,6]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[7,5,3,8,1,2,4,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,4,8,1,2,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,2,8,1,3,4,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,6,4,8,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,2,5,1,4,6,7]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,4,2,5,1,3,6,7]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,3,2,6,1,4,5,7]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,4,2,6,1,3,5,7]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[8,5,3,6,1,2,4,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,2,4,1,3,5,7]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,6,2,5,1,3,4,7]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,3,2,7,1,4,5,6]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,4,2,7,1,3,5,6]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[8,4,3,7,1,2,5,6]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[8,5,2,7,1,3,4,6]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,5,3,7,1,2,4,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,4,7,1,2,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,3,7,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,2,4,1,3,5,6]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,7,2,5,1,3,4,6]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,7,3,5,1,2,4,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,2,6,1,3,4,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,7,3,6,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,4,6,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,2,5,8,1,4,7]=>[6,7,3,4,8,1,2,5]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,6,3,5,8,1,2,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[5,6,2,4,8,1,3,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,7,2,5,8,1,3,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,7,3,5,8,1,2,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,7,2,4,8,1,3,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,7,3,4,8,1,2,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,7,2,6,8,1,4,5]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,7,3,6,8,1,2,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,7,2,6,8,1,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,4,6,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,3,4,8,1,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,3,5,8,1,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,2,5,7,1,4,6]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,8,2,5,7,1,3,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,8,3,5,7,1,2,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,8,2,4,7,1,3,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,8,2,6,7,1,4,5]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,8,3,6,7,1,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,8,2,6,7,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,3,6,7,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,4,6,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,2,5,7,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,3,5,7,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,4,5,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,2,4,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,3,4,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,2,5,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,3,5,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,2,6,8,1,5,7]=>[6,3,2,7,8,1,4,5]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[5,3,2,6,8,1,4,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,4,2,6,8,1,3,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,4,3,6,8,1,2,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,3,2,5,8,1,4,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,4,3,5,8,1,2,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,5,2,4,8,1,3,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,3,2,7,8,1,5,6]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[5,3,2,7,8,1,4,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,4,2,7,8,1,3,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,4,3,7,8,1,2,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,4,2,7,8,1,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,3,7,8,1,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,2,7,8,1,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,2,5,8,1,3,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,3,5,8,1,2,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,3,4,8,1,2,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,2,6,8,1,4,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,5,2,6,8,1,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,3,6,8,1,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,2,4,8,1,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,3,5,8,1,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,2,5,7,1,4,6]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,4,2,5,7,1,3,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,2,4,7,1,3,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,2,6,7,1,4,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,4,2,6,7,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,2,6,7,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,3,6,7,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,2,4,7,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,2,5,7,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,3,5,7,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,2,4,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,3,4,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,2,5,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,3,5,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,7,2,6,1,5,8]=>[6,4,7,2,5,1,3,8]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[5,3,7,2,6,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,4,7,2,6,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,3,7,2,5,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,4,7,2,5,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,4,7,3,5,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,3,6,2,5,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,3,8,2,6,1,5,7]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[5,3,8,2,6,1,4,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[5,4,8,2,6,1,3,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[5,4,8,3,6,1,2,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[6,3,8,2,5,1,4,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[6,4,8,2,5,1,3,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[6,4,8,3,5,1,2,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[6,5,8,2,4,1,3,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[6,5,8,3,4,1,2,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,3,8,2,7,1,5,6]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[5,3,8,2,7,1,4,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[5,4,8,2,7,1,3,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[5,4,8,3,7,1,2,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[6,3,8,2,7,1,4,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,4,8,2,7,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,8,3,7,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,8,2,7,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,8,2,5,1,4,6]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,4,8,3,5,1,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,2,4,1,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,3,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,8,2,6,1,4,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,4,8,2,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,2,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,3,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,4,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,8,2,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,8,3,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,6,2,5,1,4,7]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,4,6,2,5,1,3,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,6,2,4,1,3,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,7,2,5,1,4,6]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,4,7,3,5,1,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,2,4,1,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,7,2,6,1,4,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,4,7,2,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,3,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,2,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,7,2,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,7,2,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,7,3,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,3,2,7,1,6,8]=>[6,4,3,2,7,1,5,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[6,4,3,2,7,1,5,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,5,3,2,7,1,4,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,5,4,2,7,1,3,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,5,3,2,6,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,4,2,6,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,3,2,5,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,4,3,2,8,1,6,7]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[6,5,3,2,8,1,4,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,5,4,2,8,1,3,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,5,4,3,8,1,2,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,5,3,2,8,1,4,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,4,2,8,1,3,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,3,2,8,1,4,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,4,3,8,1,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,5,2,8,1,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,5,3,8,1,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,3,2,6,1,4,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,4,2,6,1,3,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,3,2,5,1,4,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,4,2,5,1,3,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,5,2,4,1,3,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,3,2,7,1,4,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,3,2,7,1,4,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,4,2,7,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,4,3,7,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,5,3,7,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,3,2,5,1,4,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,3,2,6,1,4,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,4,2,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,4,3,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,5,2,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,5,3,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,2,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,2,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,3,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,3,7,2,6,1,5]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[5,8,3,7,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,4,7,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,4,7,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,3,7,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,4,7,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,4,7,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,7,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,7,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,3,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,4,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,4,6,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,6,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,3,8,2,7,1,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,4,3,8,2,7,1,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,5,3,8,2,7,1,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,5,4,8,2,7,1,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,5,4,8,3,7,1,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,4,3,8,2,6,1,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,5,3,8,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,4,8,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,3,8,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,4,8,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,5,8,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,3,7,2,6,1,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,5,3,7,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,4,7,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,4,7,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,3,7,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,4,7,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,4,7,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,5,7,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,3,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,4,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,4,6,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,5,6,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,4,3,2,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[7,6,4,3,2,8,1,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,6,5,4,2,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,4,3,2,7,1,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,6,4,3,2,7,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,5,3,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,5,4,2,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,4,3,2,6,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,5,3,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,5,4,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,3,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,4,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,5,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,2,3,4,7,5,6]=>[8,2,3,4,5,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,3,6,4,5,7]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,3,7,4,5,6]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,2,3,8,7,4,6]=>[7,2,3,4,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,1,2,3,6,7,4,5]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,2,8,3,7,5,6]=>[5,2,3,8,1,7,6,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[8,1,2,5,3,4,6,7]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,2,5,3,4,8,6]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,6,3,4,5,7]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,2,6,3,4,8,5]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,2,5,3,8,4,7]=>[7,2,3,5,4,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,1,2,5,3,7,4,6]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,6,3,7,4,5]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,2,5,3,7,8,4]=>[8,2,3,5,4,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,2,8,6,3,5,7]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,1,2,8,7,3,5,6]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,1,2,7,6,3,8,5]=>[6,2,3,8,5,1,7,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,1,2,5,6,3,4,7]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,5,7,3,4,6]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,7,6,3,4,5]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,2,5,6,3,8,4]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,2,5,8,7,3,6]=>[7,2,3,4,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,1,2,5,6,7,3,4]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,8,2,4,7,5,6]=>[4,2,8,1,5,7,6,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,1,8,2,6,4,5,7]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,1,8,2,7,4,5,6]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,1,7,2,6,4,8,5]=>[4,2,8,1,6,5,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,1,5,2,8,7,4,6]=>[4,2,7,1,8,6,3,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,1,8,2,6,7,4,5]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[8,1,4,2,3,5,6,7]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,4,2,3,5,8,6]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,4,2,3,8,5,7]=>[7,2,5,4,3,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,1,4,2,3,7,5,6]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,4,2,3,7,8,5]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,5,2,3,4,6,7]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,5,2,3,4,8,6]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,2,3,4,5,6]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,5,2,3,8,4,7]=>[7,2,5,4,3,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,1,5,2,3,7,4,6]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,8,2,3,7,4,5]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,5,2,3,7,8,4]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,4,2,8,3,6,7]=>[6,2,4,3,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,1,4,2,7,3,8,6]=>[6,2,4,3,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,1,4,2,6,3,5,7]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,2,7,3,5,6]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,4,2,6,3,8,5]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,5,2,6,3,4,7]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,5,2,7,3,4,6]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,2,6,3,4,5]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,5,2,6,3,8,4]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,4,2,6,8,3,7]=>[7,2,4,3,5,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,4,2,8,7,3,6]=>[7,2,4,3,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,1,4,2,6,7,3,5]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,5,2,6,7,3,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,4,8,2,7,5,6]=>[5,2,3,8,1,7,6,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,1,8,6,2,4,5,7]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,1,6,5,2,8,4,7]=>[5,2,7,4,1,8,3,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,1,8,5,2,7,4,6]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,1,8,6,2,7,4,5]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,1,6,5,2,7,8,4]=>[5,2,8,4,1,6,7,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[8,1,4,5,2,3,6,7]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,4,5,2,3,8,6]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,6,2,3,5,7]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,4,8,2,3,5,6]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,4,6,2,3,8,5]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,6,5,2,3,4,7]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,5,2,3,4,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,6,2,3,4,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,6,5,2,3,8,4]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,4,5,2,8,3,7]=>[7,2,5,4,3,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,1,4,5,2,7,3,6]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,6,2,7,3,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,6,5,2,7,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,4,5,2,7,8,3]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,4,8,6,2,5,7]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,1,4,8,7,2,5,6]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,1,4,7,6,2,8,5]=>[6,2,3,8,5,1,7,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,1,8,5,6,2,4,7]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,1,8,5,7,2,4,6]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,1,8,7,6,2,4,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,1,7,5,6,2,8,4]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,1,4,5,6,2,3,7]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,5,7,2,3,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,7,6,2,3,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,5,6,2,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,4,5,6,2,8,3]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,4,5,8,7,2,6]=>[7,2,3,4,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,1,8,5,6,7,2,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,1,4,5,6,7,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,8,1,3,6,4,5,7]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,8,1,3,7,4,5,6]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,8,1,3,6,7,4,5]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,1,8,3,7,5,6]=>[3,5,1,8,2,7,6,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,8,1,5,3,4,6,7]=>[3,8,1,6,5,4,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,7,1,5,3,4,8,6]=>[3,8,1,6,5,4,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,8,1,6,3,4,5,7]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,7,1,6,3,4,8,5]=>[3,8,1,6,5,4,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,6,1,5,3,8,4,7]=>[3,7,1,5,4,8,2,6]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,8,1,5,3,7,4,6]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,8,1,6,3,7,4,5]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,6,1,5,3,7,8,4]=>[3,8,1,5,4,6,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,1,8,6,3,5,7]=>[3,6,1,8,7,2,5,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,1,8,7,3,5,6]=>[3,6,1,8,7,2,5,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,1,7,6,3,8,5]=>[3,6,1,8,5,2,7,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,8,1,5,6,3,4,7]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,8,1,5,7,3,4,6]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,8,1,7,6,3,4,5]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,7,1,5,6,3,8,4]=>[3,8,1,6,5,4,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,1,8,6,7,3,5]=>[3,7,1,8,6,5,2,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,8,1,5,6,7,3,4]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[7,3,1,2,4,5,8,6]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[6,3,1,2,4,8,5,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[8,3,1,2,4,7,5,6]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[6,3,1,2,4,7,8,5]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,3,1,2,8,4,6,7]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,3,1,2,7,4,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[8,3,1,2,6,4,5,7]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,3,1,2,7,4,5,6]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[7,3,1,2,6,4,8,5]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,3,1,2,6,8,4,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[5,3,1,2,8,7,4,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[8,3,1,2,6,7,4,5]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,3,1,2,6,7,8,4]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[7,4,1,2,3,5,8,6]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,4,1,2,3,8,5,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[8,4,1,2,3,7,5,6]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,4,1,2,3,7,8,5]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,6,1,2,3,4,8,5]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,8,1,2,3,7,4,6]=>[7,8,3,4,5,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[8,6,1,2,3,7,4,5]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,1,2,8,3,6,7]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,4,1,2,7,3,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[8,4,1,2,6,3,5,7]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,4,1,2,7,3,5,6]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,4,1,2,6,3,8,5]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,8,1,2,6,3,4,7]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,8,1,2,7,3,4,6]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[8,7,1,2,6,3,4,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,7,1,2,6,3,8,4]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,4,1,2,6,8,3,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[5,4,1,2,8,7,3,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[8,4,1,2,6,7,3,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,1,2,6,7,3,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,1,2,6,7,8,3]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,3,1,8,2,5,6,7]=>[5,3,2,8,1,6,7,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,3,1,7,2,5,8,6]=>[5,3,2,8,1,6,7,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,3,1,6,2,8,5,7]=>[5,3,2,7,1,8,4,6]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,3,1,8,2,7,5,6]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,3,1,6,2,7,8,5]=>[5,3,2,8,1,6,7,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[8,3,1,5,2,4,6,7]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,3,1,5,2,4,8,6]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,3,1,6,2,4,5,7]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,3,1,8,2,4,5,6]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,3,1,6,2,4,8,5]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,3,1,5,2,8,4,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[8,3,1,5,2,7,4,6]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,3,1,6,2,7,4,5]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,3,1,5,2,7,8,4]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,4,1,5,2,3,6,7]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,4,1,5,2,3,8,6]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,4,1,6,2,3,5,7]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,4,1,8,2,3,5,6]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,4,1,6,2,3,8,5]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,8,1,5,2,3,4,7]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[8,7,1,5,2,3,4,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,1,6,2,3,4,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,1,5,2,3,8,4]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,4,1,5,2,8,3,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[8,4,1,5,2,7,3,6]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,1,6,2,7,3,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,1,5,2,7,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,4,1,5,2,7,8,3]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,3,1,8,6,2,5,7]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[4,3,1,8,7,2,5,6]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[4,3,1,7,6,2,8,5]=>[6,3,2,8,5,1,7,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[8,3,1,5,6,2,4,7]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,3,1,5,7,2,4,6]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,3,1,7,6,2,4,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,3,1,5,6,2,8,4]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,4,1,5,6,2,3,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,1,5,7,2,3,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,1,7,6,2,3,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,1,5,6,2,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,4,1,5,6,2,8,3]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,3,1,5,8,7,2,6]=>[7,3,2,4,8,6,1,5]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[4,3,1,8,6,7,2,5]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[8,3,1,5,6,7,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,1,5,6,7,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,3,1,5,6,7,8,2]=>[8,3,2,4,5,6,7,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,3,8,1,4,7,5,6]=>[4,2,8,1,5,7,6,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,8,1,6,4,5,7]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,8,1,7,4,5,6]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,7,1,6,4,8,5]=>[4,2,8,1,6,5,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,5,1,8,7,4,6]=>[4,2,7,1,8,6,3,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,8,1,6,7,4,5]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,8,4,1,3,5,6,7]=>[4,8,5,1,3,6,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,7,4,1,3,5,8,6]=>[4,8,5,1,3,6,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,6,4,1,3,8,5,7]=>[4,7,5,1,3,8,2,6]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,8,4,1,3,7,5,6]=>[4,8,5,1,3,7,6,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,6,4,1,3,7,8,5]=>[4,8,5,1,3,6,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,8,5,1,3,4,6,7]=>[4,8,6,1,5,3,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,7,5,1,3,4,8,6]=>[4,8,6,1,5,3,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,8,7,1,3,4,5,6]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,6,5,1,3,8,4,7]=>[4,7,5,1,3,8,2,6]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,8,5,1,3,7,4,6]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,6,8,1,3,7,4,5]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,6,5,1,3,7,8,4]=>[4,8,5,1,3,6,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,5,4,1,8,3,6,7]=>[4,6,3,1,8,2,7,5]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,5,4,1,7,3,8,6]=>[4,6,3,1,8,2,7,5]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,8,4,1,6,3,5,7]=>[4,8,6,1,7,3,5,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,8,4,1,7,3,5,6]=>[4,8,6,1,7,3,5,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,7,4,1,6,3,8,5]=>[4,8,6,1,5,3,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,8,5,1,6,3,4,7]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,8,5,1,7,3,4,6]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,7,8,1,6,3,4,5]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,7,5,1,6,3,8,4]=>[4,8,6,1,5,3,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,5,4,1,8,7,3,6]=>[4,7,3,1,8,6,2,5]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,8,4,1,6,7,3,5]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,8,5,1,6,7,3,4]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,5,4,1,6,7,8,3]=>[4,8,3,1,5,6,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[7,3,4,1,2,5,8,6]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[6,3,4,1,2,8,5,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[8,3,4,1,2,7,5,6]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[6,3,4,1,2,7,8,5]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[7,3,5,1,2,4,8,6]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,3,7,1,2,4,8,5]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,3,5,1,2,8,4,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[8,3,5,1,2,7,4,6]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,3,8,1,2,7,4,5]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,3,5,1,2,7,8,4]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[7,5,4,1,2,3,8,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,8,4,1,2,3,5,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,7,4,1,2,3,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,8,5,1,2,3,4,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,7,5,1,2,3,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,5,4,1,2,8,3,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[8,5,4,1,2,7,3,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,8,4,1,2,7,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,5,1,2,7,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,4,1,2,7,8,3]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,3,4,1,8,2,6,7]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,3,4,1,7,2,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[8,3,4,1,6,2,5,7]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[8,3,4,1,7,2,5,6]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,3,4,1,6,2,8,5]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[8,3,5,1,6,2,4,7]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,3,5,1,7,2,4,6]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,3,8,1,6,2,4,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,3,5,1,6,2,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,5,4,1,6,2,3,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,4,1,7,2,3,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,4,1,6,2,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,5,1,6,2,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,4,1,6,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,3,4,1,6,8,2,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[5,3,4,1,8,7,2,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[8,3,4,1,6,7,2,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,3,5,1,6,7,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,4,1,6,7,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,4,1,6,7,8,2]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,3,4,8,1,7,5,6]=>[5,2,3,8,1,7,6,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,8,6,1,4,5,7]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,6,5,1,8,4,7]=>[5,2,7,4,1,8,3,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,8,5,1,7,4,6]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,8,6,1,7,4,5]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,6,5,1,7,8,4]=>[5,2,8,4,1,6,7,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,8,4,5,1,3,6,7]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,7,4,5,1,3,8,6]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,8,4,6,1,3,5,7]=>[5,8,6,7,1,3,4,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,7,4,8,1,3,5,6]=>[5,8,6,7,1,3,4,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,7,4,6,1,3,8,5]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,8,6,5,1,3,4,7]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,7,8,5,1,3,4,6]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,7,8,6,1,3,4,5]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,7,6,5,1,3,8,4]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,6,4,5,1,8,3,7]=>[5,7,4,3,1,8,2,6]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[2,8,4,5,1,7,3,6]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,8,4,6,1,7,3,5]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,8,6,5,1,7,3,4]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,6,4,5,1,7,8,3]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[7,3,4,5,1,2,8,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,3,4,6,1,2,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,3,6,5,1,2,4,7]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,3,8,5,1,2,4,6]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,3,8,6,1,2,4,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,3,6,5,1,2,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,6,4,5,1,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,3,4,5,1,8,2,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[8,3,4,5,1,7,2,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,3,4,6,1,7,2,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,3,6,5,1,7,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,4,5,1,7,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,4,5,1,7,8,2]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[2,3,4,8,6,1,5,7]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,4,8,7,1,5,6]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,4,7,6,1,8,5]=>[6,2,3,8,5,1,7,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,8,5,6,1,4,7]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,8,5,7,1,4,6]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,8,7,6,1,4,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,7,5,6,1,8,4]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,8,4,5,6,1,3,7]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,8,4,5,7,1,3,6]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,8,4,7,6,1,3,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,8,7,5,6,1,3,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,7,4,5,6,1,8,3]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[8,3,4,5,7,1,2,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,4,7,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,7,5,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,4,5,6,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,3,4,5,8,7,1,6]=>[7,2,3,4,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,3,8,5,6,7,1,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,8,4,5,6,7,1,3]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[9,1,2,3,4,5,6,7,8]=>[9,2,3,4,5,6,7,8,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[8,1,2,3,4,5,6,9,7]=>[9,2,3,4,5,6,7,8,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[7,1,2,3,4,5,8,9,6]=>[9,2,3,4,5,6,7,8,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[6,1,2,3,4,7,8,9,5]=>[9,2,3,4,5,6,7,8,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[5,1,2,3,6,7,8,9,4]=>[9,2,3,4,5,6,7,8,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[4,1,2,5,6,7,8,9,3]=>[9,2,3,4,5,6,7,8,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[8,1,7,2,3,4,5,9,6]=>[9,2,7,4,5,6,3,8,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[9,1,6,5,2,3,4,7,8]=>[9,2,7,6,5,4,3,8,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[8,1,4,5,6,2,3,9,7]=>[9,2,7,6,5,4,3,8,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[8,1,9,5,6,2,3,4,7]=>[9,2,8,7,6,5,4,3,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[8,1,9,7,6,2,3,4,5]=>[9,2,8,7,6,5,4,3,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[9,1,4,8,6,7,2,3,5]=>[9,2,8,7,6,5,4,3,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[9,1,8,5,6,7,2,3,4]=>[9,2,8,7,6,5,4,3,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[8,1,4,5,6,7,2,9,3]=>[9,2,7,6,5,4,3,8,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[3,1,4,5,6,7,8,9,2]=>[9,2,3,4,5,6,7,8,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[2,9,1,3,4,5,6,7,8]=>[3,9,1,4,5,6,7,8,2]=>[3,9,1,8,7,6,5,4,2]=>[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]
[2,8,1,3,4,5,6,9,7]=>[3,9,1,4,5,6,7,8,2]=>[3,9,1,8,7,6,5,4,2]=>[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]
[2,7,1,3,4,5,8,9,6]=>[3,9,1,4,5,6,7,8,2]=>[3,9,1,8,7,6,5,4,2]=>[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]
[2,5,1,3,6,7,8,9,4]=>[3,9,1,4,5,6,7,8,2]=>[3,9,1,8,7,6,5,4,2]=>[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]
[2,8,1,9,7,3,4,5,6]=>[3,9,1,8,7,6,5,4,2]=>[3,9,1,8,7,6,5,4,2]=>[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]
[2,9,1,8,6,7,3,4,5]=>[3,9,1,8,7,6,5,4,2]=>[3,9,1,8,7,6,5,4,2]=>[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]
[2,9,1,5,6,7,8,3,4]=>[3,9,1,8,7,6,5,4,2]=>[3,9,1,8,7,6,5,4,2]=>[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]
[2,4,1,5,6,7,8,9,3]=>[3,9,1,4,5,6,7,8,2]=>[3,9,1,8,7,6,5,4,2]=>[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]
[9,6,1,2,3,7,4,5,8]=>[9,8,3,4,5,7,6,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[9,8,1,2,3,7,4,5,6]=>[9,8,3,4,5,7,6,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[9,6,1,2,3,7,8,4,5]=>[9,8,3,4,5,7,6,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[9,8,1,7,6,2,3,4,5]=>[9,8,3,7,6,5,4,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[8,9,1,5,6,7,2,3,4]=>[9,8,3,7,6,5,4,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[9,7,8,1,2,3,4,5,6]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[9,8,5,1,7,2,3,4,6]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[7,8,9,1,6,2,3,4,5]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[9,5,4,1,8,7,2,3,6]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[9,3,5,1,6,7,8,2,4]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[9,5,4,1,6,7,8,2,3]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[9,8,4,5,1,2,3,6,7]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,8,4,6,1,2,3,9,5]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[9,8,6,5,1,2,3,4,7]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,8,9,6,1,2,3,4,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,8,6,5,1,2,3,9,4]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[8,3,6,5,1,7,2,9,4]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[8,6,4,5,1,7,2,9,3]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[8,3,4,7,6,1,2,9,5]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[8,3,7,5,6,1,2,9,4]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[9,7,4,5,6,1,2,3,8]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,9,4,5,6,1,2,3,7]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,9,7,5,6,1,2,3,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,7,4,5,6,1,2,9,3]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[7,3,4,5,6,1,9,2,8]=>[8,6,5,4,3,2,9,1,7]=>[8,6,5,4,3,2,9,1,7]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[9,3,7,5,6,1,8,2,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,3,4,5,6,7,1,2,8]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[9,3,4,5,6,8,1,2,7]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[9,8,4,5,6,7,1,2,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,3,4,5,6,7,8,1,2]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[2,3,4,5,6,7,8,9,1]=>[9,2,3,4,5,6,7,8,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[]=>[]=>[]=>.
[3,5,2,6,1,4,8,7]=>[5,6,3,4,1,2,8,7]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,5,2,6,4,1,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,5,2,7,4,8,1,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,5,2,7,4,8,6,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,5,7,2,3,8,6,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,5,7,2,3,8,1,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[4,5,6,2,3,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,5,6,2,1,3,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[3,5,1,6,4,2,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,5,6,1,3,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,5,6,3,1,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,5,7,3,2,8,1,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[4,5,7,3,2,8,6,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,6,7,3,8,2,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,6,7,3,8,2,1,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,6,7,3,8,1,2,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,5,7,3,1,8,2,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[4,5,7,1,3,8,2,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[3,5,1,7,4,8,2,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[2,1,5,7,4,8,3,6]=>[2,1,7,8,5,6,3,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,5,7,4,8,6,3]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,5,1,7,4,8,6,2]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,5,7,1,3,8,6,2]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,5,7,3,1,8,6,2]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,6,7,3,8,1,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,6,7,3,8,5,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,6,7,3,8,5,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,7,8,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,7,8,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,7,1,8,3,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,1,7,8,4,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,1,6,7,8,4,5,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,6,7,8,4,3,5]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,6,1,7,8,4,2,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,6,7,1,8,3,2,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,6,7,8,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,7,2,1,8,3,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[4,6,7,2,8,1,3,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,6,7,2,8,3,1,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,6,7,2,8,3,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,2,7,8,4,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,2,7,8,4,1,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,6,2,7,8,1,4,5]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,5,2,7,1,8,4,6]=>[5,7,3,8,1,6,2,4]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,4,2,1,7,8,5,6]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,4,1,2,7,8,6,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,5,2,7,1,8,6,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,6,2,7,8,1,5,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,6,2,7,8,5,1,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,6,2,7,8,5,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,6,7,2,8,5,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,6,7,2,8,5,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,6,7,2,8,1,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,7,2,1,8,6,3]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,5,7,1,2,8,6,3]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[3,5,1,7,2,8,6,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,1,5,7,3,8,6,4]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,6,7,8,3,5,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,6,1,7,8,2,5,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,6,7,1,8,2,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,7,8,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,7,8,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,7,8,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,7,8,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,7,8,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,7,1,8,5,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,1,7,8,5,2,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,1,6,7,8,5,3,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,6,1,7,8,5,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,6,7,1,8,5,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,7,8,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,7,8,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,2,1,6,5,8,7,10,9]=>[4,3,2,1,6,5,8,7,10,9]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[2,1,5,6,4,3,8,7,10,9]=>[2,1,6,5,4,3,8,7,10,9]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,5,6,3,2,1,8,7,10,9]=>[6,5,4,3,2,1,8,7,10,9]=>[6,5,4,3,2,1,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[4,6,8,3,9,5,10,7,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[2,1,4,3,7,8,6,5,10,9]=>[2,1,4,3,8,7,6,5,10,9]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[3,4,2,1,7,8,6,5,10,9]=>[4,3,2,1,8,7,6,5,10,9]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[2,1,6,7,8,5,4,3,10,9]=>[2,1,8,7,6,5,4,3,10,9]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[5,6,7,8,4,3,2,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[5,6,8,9,4,3,10,7,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[2,1,6,8,9,5,10,7,4,3]=>[2,1,10,9,8,6,7,5,4,3]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[5,7,8,9,4,10,6,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[6,7,8,9,10,4,5,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,7,8,9,10,1,4,5,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,7,8,9,10,1,4,5,2,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,7,8,9,10,4,5,2,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,7,8,9,10,4,3,2,1,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,7,8,9,10,3,4,5,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,7,8,9,10,3,4,5,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,7,8,9,10,1,3,4,5,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,7,8,9,10,3,4,1,2,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,7,8,9,10,3,4,2,1,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,7,8,9,10,2,3,4,1,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,7,8,9,10,2,3,4,5,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[2,1,4,3,6,5,9,10,8,7]=>[2,1,4,3,6,5,10,9,8,7]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[3,4,2,1,6,5,9,10,8,7]=>[4,3,2,1,6,5,10,9,8,7]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[2,1,5,6,4,3,9,10,8,7]=>[2,1,6,5,4,3,10,9,8,7]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,5,6,3,2,1,9,10,8,7]=>[6,5,4,3,2,1,10,9,8,7]=>[6,5,4,3,2,1,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[4,7,8,3,9,10,6,5,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[2,1,4,3,8,9,10,7,6,5]=>[2,1,4,3,10,9,8,7,6,5]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[3,4,2,1,8,9,10,7,6,5]=>[4,3,2,1,10,9,8,7,6,5]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[3,7,2,8,9,10,6,5,4,1]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[2,1,7,8,9,10,6,5,4,3]=>[2,1,10,9,8,7,6,5,4,3]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[6,7,8,9,10,1,5,4,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,7,8,9,10,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,5,8,7,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,7,4,5,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,6,7,4,5,1,8,3]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,6,7,4,5,2,3,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,4,7,6,2,3,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,4,7,6,1,8,3]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,5,4,7,6,8,1,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,5,3,7,8,6,1,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,3,8,7,6,1,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,4,8,3,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,8,4,5,7,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,4,8,6,7,1,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,3,5,6,8,7,1,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,2,5,6,1,8,7,4]=>[5,2,8,4,1,7,6,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,2,5,6,8,1,7,3]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,2,4,8,6,1,7,3]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,2,8,4,5,1,7,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,8,2,4,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,1,4,5,2,3,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,1,8,4,5,2,3,7]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,4,8,6,2,3,7]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,1,3,2,8,6,5,7]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[5,1,3,8,2,6,4,7]=>[7,2,5,8,3,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,1,8,3,2,5,4,7]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,8,1,3,2,5,4,6]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,2,3,1,5,6,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,2,8,3,1,5,7,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,2,3,8,1,6,7,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,3,8,2,1,7,5,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[7,8,3,2,1,6,5,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,8,4,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,2,8,7,1,6,3]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,5,2,7,8,1,6,3]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,5,3,7,1,6,8,4]=>[5,8,3,6,1,4,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,5,3,7,2,6,4,8]=>[1,7,5,6,3,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,3,2,5,4,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,7,3,1,5,8,4]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,6,7,2,1,8,5,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[7,8,5,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,8,7,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,1,8,7,2,3,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,4,8,1,7,2,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,3,1,2,6,4,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,3,1,8,2,7,4,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,3,1,2,8,7,5,6]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,2,1,3,8,5,7,6]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[5,2,1,8,3,4,7,6]=>[6,3,2,8,5,1,7,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[6,2,8,1,3,4,7,5]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,8,2,1,3,4,6,5]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,3,1,2,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[5,3,1,6,2,4,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,3,1,5,2,4,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[7,3,1,5,2,8,4,6]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,4,5,1,2,7,3,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,4,5,1,2,8,3,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,4,5,1,2,3,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,4,6,1,2,3,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[2,1,6,5,3,4,8,7]=>[2,1,6,5,4,3,8,7]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,6,1,5,2,4,8,7]=>[5,6,3,4,1,2,8,7]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,6,5,1,2,3,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,6,4,1,2,3,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,5,4,1,2,3,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[7,5,4,1,2,8,3,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,6,4,1,7,2,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,4,1,8,2,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,4,1,8,2,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,4,1,2,8,3,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[4,7,5,1,2,8,3,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[3,7,1,5,2,8,4,6]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,1,7,5,3,8,4,6]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,8,5,3,7,4,6]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,8,1,5,2,7,4,6]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,8,5,1,2,7,3,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[5,8,4,1,2,7,3,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[6,8,4,1,7,2,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,4,1,6,2,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,6,7,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,6,1,7,2,3,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,8,1,6,7,2,4,5]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,1,8,6,7,3,4,5]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,7,6,8,3,4,5]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,7,1,6,8,2,4,5]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,7,6,1,8,2,3,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,7,6,8,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,7,1,2,8,3,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[6,4,7,1,8,2,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,6,1,8,2,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,6,1,7,2,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,1,6,7,2,4,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,3,1,6,8,2,4,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,3,1,7,8,2,4,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,3,1,7,2,8,4,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,3,1,2,7,8,5,6]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[2,1,4,3,8,7,5,6]=>[2,1,4,3,8,7,6,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,4,1,2,8,7,5,6]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[6,3,1,8,7,2,4,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,3,1,8,6,2,4,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,4,7,1,6,2,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,8,1,6,2,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,4,8,1,2,7,3,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[4,5,8,1,2,7,3,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[3,5,1,8,2,7,4,6]=>[5,7,3,8,1,6,2,4]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,1,5,8,3,7,4,6]=>[2,1,7,8,5,6,3,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,6,8,7,3,4,5]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,6,1,8,7,2,4,5]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,6,8,1,7,2,3,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,6,8,7,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,6,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,6,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,6,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,8,1,6,2,3,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,7,1,8,6,2,4,5]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,1,7,8,6,3,4,5]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,8,7,6,3,4,5]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,8,1,7,6,2,4,5]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,8,7,1,6,2,3,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,8,7,6,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,7,5,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,7,3,8,5,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,7,3,5,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,4,7,2,5,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,4,2,7,6,1,3,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,4,2,7,6,1,8,3]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,4,3,7,6,8,1,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,3,7,8,6,1,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,4,8,3,5,7,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,3,8,6,7,1,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,3,6,8,7,1,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,2,6,7,1,8,3]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,4,2,6,7,1,3,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,3,2,6,1,7,4,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,3,2,6,1,7,8,4]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,3,2,6,1,8,7,4]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,4,2,6,8,1,7,3]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,4,2,8,6,1,7,3]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,4,8,2,5,1,7,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,8,4,2,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,4,2,5,1,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,2,8,6,1,3,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,3,2,6,1,8,4,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,3,2,1,6,8,5,7]=>[4,3,2,1,7,8,5,6]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,3,2,1,8,6,5,7]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[5,3,2,8,1,6,4,7]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,3,8,2,1,5,4,7]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[7,8,3,2,1,5,4,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,8,3,2,1,5,6,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,3,8,2,1,5,7,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,3,2,8,1,6,7,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,4,2,7,8,1,6,3]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,3,2,7,1,8,6,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,3,2,7,1,6,8,4]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,3,2,7,1,6,4,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,3,7,2,1,5,4,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[6,3,7,2,1,5,8,4]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,3,7,2,1,8,5,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,4,7,2,8,1,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,7,8,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,8,7,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,7,2,1,8,4,5]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,3,7,2,1,4,8,5]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,3,7,2,1,4,5,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[5,3,2,7,1,4,8,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,4,2,8,7,1,3,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,8,4,2,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,3,2,1,6,4,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,3,8,2,1,7,4,5]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,3,2,8,1,7,4,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,3,2,1,8,7,5,6]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,3,2,1,7,5,8,6]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,3,2,1,7,5,6,8]=>[4,3,2,1,7,6,5,8]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,3,2,1,8,5,7,6]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[5,3,2,8,1,4,7,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,3,8,2,1,4,7,5]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[7,8,3,2,1,4,6,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,3,8,2,1,4,5,7]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[4,3,2,1,8,5,6,7]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,3,2,1,5,8,6,7]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[7,8,5,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,4,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,1,4,6,2,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,1,8,4,7,2,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,8,4,7,2,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,3,2,7,5,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,8,3,2,7,5,4]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,8,1,3,2,6,5,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,3,1,2,6,5,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,8,3,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,2,4,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,2,3,1,6,5,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,8,2,1,3,6,5,4]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,8,1,2,3,6,5,4]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,1,8,2,3,7,5,4]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,8,2,3,7,5,4]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,8,3,7,6,4]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,2,8,3,7,6,4]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,2,1,8,3,7,6,4]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,2,8,1,3,7,5,4]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,2,8,3,1,7,5,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,2,8,4,7,1,5,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,3,8,4,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,8,4,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,8,4,7,1,5,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,6,8,3,1,7,5,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,6,8,1,3,7,5,4]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,5,1,8,3,7,6,4]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,2,5,8,3,7,6,4]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,1,3,8,7,6,5]=>[3,4,1,2,8,7,6,5]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,5,3,8,1,7,6,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,5,4,8,7,1,6,3]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,5,4,8,7,6,1,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,3,4,8,7,6,1,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,2,4,8,7,1,6,3]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,2,3,8,1,7,6,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,2,1,3,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,1,2,3,8,7,6,5]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,4,2,3,8,7,6,5]=>[1,4,3,2,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,3,2,8,7,6,5]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,3,1,2,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[6,3,8,1,2,7,5,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,3,1,8,2,7,6,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,1,3,8,2,7,6,4]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,5,3,8,2,7,6,4]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,4,8,7,2,6,3]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,4,8,7,2,6,3]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,4,1,8,7,2,6,3]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,4,8,1,7,2,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,8,7,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,8,7,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,8,7,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,1,8,7,2,6,3]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,1,5,8,7,2,6,3]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,4,5,8,7,2,6,3]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,8,2,7,6,4]=>[1,5,8,7,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,5,8,2,7,6,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,6,8,1,2,7,5,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,6,8,2,1,7,5,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[4,6,8,2,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,8,3,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,3,8,7,6,1,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,5,2,8,7,1,6,3]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,5,2,8,1,7,6,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,1,4,2,8,7,6,5]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,1,2,4,8,7,6,5]=>[3,2,1,4,8,7,6,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,5,8,1,7,6,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,2,5,8,7,1,6,3]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,3,5,8,7,6,1,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,4,5,8,7,6,1,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,4,5,8,7,1,6,3]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,3,5,8,1,7,6,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,1,3,2,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[5,1,3,2,6,4,8,7]=>[6,2,4,3,5,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,1,3,2,5,4,8,7]=>[6,2,4,3,5,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[7,1,3,2,5,4,8,6]=>[8,2,4,3,6,5,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,3,2,5,4,7,6]=>[8,2,4,3,6,5,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,2,5,3,7,6]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,4,2,5,3,8,6]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,4,2,5,3,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,1,4,2,6,3,8,7]=>[6,2,4,3,5,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,1,6,3,5,4,8,7]=>[2,1,6,4,5,3,8,7]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,1,6,2,5,4,8,7]=>[4,2,6,1,5,3,8,7]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,1,6,2,5,3,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,2,5,1,4,3,8,7]=>[6,4,5,2,3,1,8,7]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[5,2,6,1,4,3,8,7]=>[6,4,5,2,3,1,8,7]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[5,2,7,1,4,3,8,6]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[5,2,8,1,4,3,7,6]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[6,2,8,1,4,3,7,5]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,2,7,1,4,3,8,5]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,2,6,1,4,3,8,5]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,2,5,1,4,3,8,6]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,1,7,2,5,3,8,6]=>[6,2,8,4,5,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,1,7,2,5,4,8,6]=>[4,2,8,1,6,5,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,1,7,3,5,4,8,6]=>[2,1,8,4,6,5,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,8,3,5,4,7,6]=>[2,1,8,4,6,5,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,1,8,2,5,4,7,6]=>[4,2,8,1,6,5,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,1,8,2,5,3,7,6]=>[6,2,8,4,5,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,2,5,1,4,3,7,6]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,2,6,1,4,3,7,5]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,1,4,3,8,2,6,5]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,3,7,2,6,5]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,5,3,7,2,6,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,5,3,8,2,6,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,6,1,5,3,7,4]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[5,1,8,2,6,3,7,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,8,2,6,3,7,5]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,1,8,2,6,4,7,5]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,1,8,3,6,4,7,5]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,7,3,6,4,8,5]=>[2,1,8,4,6,5,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[4,1,7,2,6,3,8,5]=>[6,2,8,4,5,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,1,7,2,6,3,8,4]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,6,1,5,3,8,4]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,2,7,1,5,3,8,4]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,2,8,1,5,3,7,4]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,1,5,2,6,3,7,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,5,2,7,3,8,4]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,4,2,7,3,8,5]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,2,6,3,7,5]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,3,2,6,4,7,5]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,3,2,6,4,8,5]=>[8,2,4,3,6,5,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,3,2,7,4,8,5]=>[8,2,4,3,6,5,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,3,2,7,4,8,6]=>[6,2,4,3,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,1,3,2,7,5,8,6]=>[4,2,3,1,8,6,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,1,4,3,8,5,7,6]=>[2,1,4,3,8,6,7,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,1,4,2,8,5,7,6]=>[4,2,3,1,8,6,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,1,3,2,8,5,7,6]=>[4,2,3,1,8,6,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[5,1,3,2,8,4,7,6]=>[6,2,4,3,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,1,3,2,8,4,7,5]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,7,1,3,2,6,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,4,8,1,3,2,6,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,3,8,1,4,2,6,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,3,7,1,4,2,6,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,1,4,2,8,3,7,5]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,4,2,8,3,7,6]=>[6,2,4,3,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,1,5,2,8,3,7,6]=>[6,2,4,3,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,1,5,2,8,4,7,6]=>[4,2,6,1,8,3,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,1,5,3,8,4,7,6]=>[2,1,6,4,8,3,7,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,6,3,8,4,7,5]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,1,6,2,8,4,7,5]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,1,6,2,8,3,7,5]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,1,6,2,8,3,7,4]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,5,2,8,3,7,4]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,7,1,5,2,6,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,3,8,1,5,2,6,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,2,7,3,8,1,5,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,2,8,3,7,1,5,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,3,7,2,6,1,5,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[5,1,8,3,7,2,6,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,8,3,7,2,6,5]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,1,8,4,7,2,6,5]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,1,8,4,7,3,6,5]=>[2,1,8,6,7,4,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,7,4,8,3,6,5]=>[2,1,8,6,7,4,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,1,7,4,8,2,6,5]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,1,7,3,8,2,6,5]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,1,7,3,8,2,6,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,3,8,2,6,1,5,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,2,6,3,7,1,5,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,2,6,3,8,1,5,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[3,4,2,6,8,1,5,7]=>[6,3,2,7,8,1,4,5]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[5,3,6,2,8,1,4,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[5,3,6,2,4,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,7,3,8,2,4,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,7,3,8,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,2,5,8,3,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,2,5,8,3,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,2,6,3,8,1,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,5,2,1,6,8,3,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[5,3,1,6,8,2,4,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,6,2,8,1,3,4,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[3,5,6,1,4,8,2,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,1,5,6,3,8,2,7]=>[7,2,5,4,3,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,5,1,6,3,8,2,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,5,6,3,2,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[7,4,5,3,8,2,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,5,3,8,2,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,4,8,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,4,8,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,4,1,8,3,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,5,3,1,8,2,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,7,1,5,8,3,2,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,3,7,8,1,4,2,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[7,5,8,2,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,5,8,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,1,7,8,3,6,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,4,1,5,8,3,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,4,3,8,1,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,4,8,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,4,8,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,7,3,8,4,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,7,3,1,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,1,7,3,8,4,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,1,6,7,3,8,4,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,7,1,8,3,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,8,3,1,4,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,2,8,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,2,8,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,7,4,8,3,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,6,7,3,2,8,4]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,1,7,3,2,8,4]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,6,7,3,2,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,6,7,3,2,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,2,7,3,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,2,7,3,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,6,2,1,7,3,8,4]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,1,7,4,2,8,3,5]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,7,2,1,8,3,4,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,5,8,2,1,3,4,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,3,1,8,2,4,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,7,1,5,2,8,3,6]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[7,4,2,5,1,8,3,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,7,4,2,1,8,3,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,7,4,2,8,3,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,4,2,8,3,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,7,2,8,4,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,7,2,8,4,1,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,6,7,2,1,8,4,5]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[5,7,3,8,2,1,4,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,4,7,8,2,1,5,6]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[3,7,8,1,4,6,2,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,4,7,8,2,6,1,5]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[5,7,3,8,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,7,2,8,5,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,6,7,8,5,2,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,6,7,8,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,7,8,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,7,8,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,1,5,7,8,2,6,3]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,3,7,8,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,2,8,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,1,7,8,2,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,1,6,2,7,8,4,3]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,2,1,7,8,4,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,6,2,7,1,8,4,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,2,7,8,4,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,7,2,8,4,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,7,2,1,8,4,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,1,7,2,8,4,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,1,6,7,2,8,4,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,7,1,8,2,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,7,1,8,5,2,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,7,8,5,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,8,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,7,8,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,6,7,8,4,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,1,7,8,4,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,6,7,1,8,4,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,1,3,4,2,5,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,2,5,1,6,4,7]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,5,3,6,2,4,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,2,7,4,1,8,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[7,5,3,8,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,4,5,8,3,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,4,5,3,7,1,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[8,2,4,5,6,3,1,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,4,5,6,1,3,7]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,1,2,4,5,6,3,7]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,5,1,3,6,4,7]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,5,6,2,1,4,3,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,3,6,4,1,2,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,1,5,6,3,2,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,4,5,6,3,2,7]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,5,3,7,2,1,8,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[7,4,5,8,3,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,6,7,2,8,5,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,3,6,7,2,8,1,5]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,4,3,6,7,2,8,5]=>[1,6,3,8,5,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,5,3,7,1,8,2,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,1,5,3,7,2,8,6]=>[6,2,4,3,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,3,4,7,1,2,8,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[7,5,8,2,1,4,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,3,8,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,5,8,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,6,7,8,1,5,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,6,4,7,8,3,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,4,7,8,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,6,7,8,4,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,1,5,6,7,8,4,2]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,6,1,7,8,3,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,7,1,4,8,5,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,2,4,1,7,8,5,3]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,6,7,1,4,8,3,5]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,3,6,7,8,1,2,5]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,5,3,6,7,8,2,4]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,6,7,8,2,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,5,6,7,8,2,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,2,7,1,3,8,4,6]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[5,3,1,7,8,2,4,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,5,2,7,8,1,3,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,2,6,7,8,3,1,5]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[4,2,6,7,8,3,5,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[3,6,2,7,4,8,5,1]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,2,7,4,8,1,5]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,2,1,6,4,7,8,5]=>[3,2,1,8,5,6,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,7,4,2,1,5,8,6]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[1,7,3,4,2,5,8,6]=>[1,8,5,4,3,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,7,2,1,3,5,8,6]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[7,8,4,2,1,3,6,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,1,3,4,2,6,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,3,4,2,1,6,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,2,7,1,8,5,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,6,2,7,1,8,5,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[6,7,3,8,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,7,8,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,4,7,8,1,5,3]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[4,6,2,7,8,1,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,5,8,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,1,5,8,6,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,3,8,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,2,1,6,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,7,1,3,8,5,4]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,3,1,7,8,2,5,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,6,1,7,8,5,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,1,2,6,7,8,4,3]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,2,6,7,8,4,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,2,6,7,8,4,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,5,6,7,8,4,1,3]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,5,2,6,7,8,4,3]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,4,7,8,5,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,7,1,3,8,5,4]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[6,7,8,2,1,5,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,3,8,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,7,8,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,2,3,7,6,1,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[6,4,3,7,2,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,4,3,6,5,1,2,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,5,6,3,4,8,7,2]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,2,7,3,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,2,6,7,4,5,1,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,7,2,6,5,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,7,6,2,4,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,7,5,4,8,3,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,5,4,1,3,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,4,2,1,3,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,8,6,2,4,1,3,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,8,2,6,5,1,3,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,2,8,6,5,1,4,7]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,1,2,6,5,8,7,3]=>[8,2,3,5,4,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,6,2,4,8,7,3]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,5,4,2,8,7,3]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,5,4,8,2,6,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,5,4,7,6,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,6,7,4,5,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,6,7,4,5,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,6,8,4,2,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,7,8,2,4,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,7,2,8,4,6,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,2,7,8,5,6,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,1,7,8,5,6,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,8,7,1,5,4,6]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,8,2,7,1,5,3,6]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[5,8,7,2,1,4,3,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,8,7,1,2,4,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,6,1,4,2,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,6,1,4,3,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,7,6,8,4,3,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,8,3,4,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,7,1,3,4,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,8,1,3,2,4,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,8,2,1,3,4,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,7,2,8,1,3,5,6]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[3,2,6,8,4,1,5,7]=>[6,2,7,8,5,1,3,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,6,2,8,3,1,5,7]=>[6,7,5,8,3,1,2,4]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[5,6,8,2,3,1,4,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[6,5,8,3,2,1,4,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[7,5,8,3,1,2,4,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,3,1,4,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,5,7,3,8,4,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,3,7,8,5,6,2]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,4,3,7,1,5,2,6]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,4,3,8,2,1,5,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[4,5,2,3,8,1,6,7]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,2,5,4,8,1,6,7]=>[6,2,4,3,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,5,2,3,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[6,4,3,1,2,8,7,5]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[7,4,3,1,8,2,6,5]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[8,4,3,1,7,6,2,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,5,8,3,7,6,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,5,1,3,7,6,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,1,3,8,2,6,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,5,1,3,2,8,7,4]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,6,1,2,3,8,7,4]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,6,2,1,3,8,7,5]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,2,6,1,4,8,7,5]=>[4,2,8,1,5,7,6,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,7,1,8,4,6,5]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,7,2,1,8,3,6,5]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[5,7,1,2,8,3,6,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,1,8,2,3,5,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,1,8,3,2,5,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,1,7,3,5,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,6,8,7,3,5,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,6,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,1,6,5,3,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,1,6,5,2,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,1,7,2,5,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,1,2,7,6,3,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,8,2,1,7,6,3,5]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[3,2,8,1,7,6,4,5]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,1,2,8,7,6,5,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,8,2,7,6,4,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,8,7,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,6,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,6,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,2,6,5,8,7,4]=>[3,2,1,8,5,7,6,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,1,6,2,4,8,7,5]=>[4,2,8,1,5,7,6,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,1,5,2,4,8,7,6]=>[4,2,5,1,3,8,7,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,5,1,2,3,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,6,1,2,3,8,7,5]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,6,5,3,4,8,7,2]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,5,2,4,8,7,3]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,5,1,2,3,8,7,4]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,4,1,2,3,8,7,5]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,4,1,2,3,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,4,1,2,7,3,6,8]=>[6,4,3,2,7,1,5,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[6,4,1,7,2,3,5,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,4,1,8,2,3,5,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,4,1,2,8,3,6,5]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,5,1,2,8,3,6,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,5,2,8,4,6,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,5,3,8,4,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,3,7,4,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,5,2,7,4,6,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,5,1,2,7,3,6,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,1,2,7,3,6,5]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,4,1,7,2,3,5,6]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,4,1,6,2,3,5,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,6,1,7,2,3,5,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,6,7,2,4,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,6,7,3,4,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,6,8,3,4,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,6,8,2,4,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,1,8,2,3,5,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,7,1,2,8,3,6,5]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,1,7,2,8,4,6,5]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,1,2,7,8,5,6,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,4,3,8,7,5,6,2]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,8,7,5,6,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,2,8,7,5,6,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,1,8,2,7,4,6,5]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,1,8,7,2,4,5,6]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,1,7,6,2,4,5,8]=>[5,2,7,6,1,4,3,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,7,1,6,2,3,5,8]=>[6,7,3,5,4,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,8,1,6,2,3,5,7]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,8,1,7,2,3,5,6]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,8,1,2,7,3,6,5]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[5,8,1,2,7,3,6,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,1,8,2,7,4,6,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,5,8,3,7,4,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,7,3,4,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,8,7,2,4,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,8,1,7,2,3,5,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,7,1,2,3,4,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,7,1,2,3,4,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,8,6,1,2,3,4,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,7,6,1,2,3,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,8,1,6,2,3,5,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,8,6,2,4,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,8,6,3,4,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,7,6,3,4,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,7,6,2,4,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,7,1,6,2,3,5,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,2,5,1,6,4,8,7]=>[4,2,6,1,5,3,8,7]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,5,4,7,1,8,6]=>[6,2,4,3,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,2,5,3,7,6,8,1]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,2,5,3,7,1,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,2,5,3,6,1,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,2,5,1,6,3,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,1,5,4,6,2,8,7]=>[6,2,4,3,5,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,1,5,3,6,2,8,7]=>[6,2,4,3,5,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,3,5,1,6,2,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,3,5,2,7,1,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,3,6,2,7,5,8,1]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,3,6,2,7,1,8,5]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[4,3,6,1,7,2,8,5]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[4,3,5,1,7,2,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,1,5,4,7,2,8,6]=>[6,2,4,3,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,1,5,4,7,3,8,6]=>[2,1,6,4,8,3,7,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,1,5,4,7,6,8,2]=>[8,2,4,3,6,5,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,5,3,7,6,8,2]=>[8,2,4,3,6,5,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,3,5,1,7,6,8,2]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,3,6,1,7,5,8,2]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,3,6,5,7,1,8,2]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,3,6,4,7,2,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,3,6,4,7,1,8,2]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,3,6,1,7,4,8,2]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,1,6,3,7,4,8,2]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,6,3,7,5,8,2]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,6,4,7,5,8,2]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,1,6,4,7,5,8,3]=>[2,1,8,6,5,4,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,6,4,7,3,8,5]=>[2,1,8,6,5,4,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,1,6,4,7,2,8,5]=>[6,2,8,4,5,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,1,6,3,7,2,8,5]=>[6,2,8,4,5,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,1,6,3,7,2,8,4]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,3,6,1,7,2,8,4]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,3,6,2,7,1,8,4]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,3,6,2,7,4,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,2,6,3,7,4,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,2,6,3,7,1,8,4]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,2,6,1,7,3,8,4]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,2,5,1,7,3,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,2,6,1,7,3,8,5]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[4,2,6,3,7,1,8,5]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[4,2,6,3,7,5,8,1]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,2,6,4,7,5,8,1]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,6,4,7,1,8,5]=>[6,2,8,4,5,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,2,6,1,7,4,8,5]=>[4,2,8,1,6,5,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,5,1,7,4,8,6]=>[4,2,6,1,8,3,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,4,1,7,5,8,6]=>[4,2,3,1,8,6,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,1,4,2,7,6,8,5]=>[4,2,3,1,8,6,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,5,1,7,6,8,4]=>[4,2,8,1,6,5,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,6,1,7,5,8,4]=>[4,2,8,1,6,5,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,6,5,7,1,8,4]=>[6,2,8,4,5,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,2,6,5,7,3,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,2,6,5,7,1,8,3]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,2,6,1,7,5,8,3]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,2,5,1,7,6,8,3]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,1,5,2,7,6,8,3]=>[8,2,4,3,6,5,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,5,2,7,6,8,4]=>[4,2,8,1,6,5,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,1,5,3,7,6,8,4]=>[2,1,8,4,6,5,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,6,3,7,5,8,4]=>[2,1,8,4,6,5,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,1,6,2,7,5,8,4]=>[4,2,8,1,6,5,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,1,6,2,7,5,8,3]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,6,2,7,4,8,3]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,2,6,1,7,4,8,3]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[5,2,6,4,7,1,8,3]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,2,6,4,7,3,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,4,6,2,7,3,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,4,6,2,7,1,8,3]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,4,6,1,7,2,8,3]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,1,6,4,7,2,8,3]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,6,5,7,2,8,3]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,6,5,7,2,8,4]=>[6,2,8,4,5,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,1,6,5,7,3,8,4]=>[2,1,8,6,5,4,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,1,6,5,7,4,8,2]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,6,5,7,3,8,2]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,6,4,7,3,8,2]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,4,6,1,7,3,8,2]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,4,6,3,7,1,8,2]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[8,3,5,2,1,6,4,7]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,6,3,5,2,4,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,5,2,4,1,8,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[8,3,7,5,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,4,5,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,4,5,7,3,1,8,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[8,2,4,6,5,3,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,5,4,6,1,3,7]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,6,3,5,1,4,2,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,1,4,5,3,2,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,5,6,4,3,2,7]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,4,3,2,1,8,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[8,5,7,4,3,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,8,3,2,7,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,6,3,2,8,1,5]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,4,6,7,3,2,8,5]=>[1,6,8,5,4,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,7,3,1,8,2,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,7,4,5,3,2,8,6]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,5,1,4,2,8,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[5,7,4,2,1,3,8,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[8,5,7,4,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,7,5,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,1,7,5,3,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,6,3,8,7,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,4,8,6,3,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,4,7,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,5,8,7,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,1,5,8,6,7,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,8,1,6,7,3,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,4,1,8,7,5,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,2,6,1,4,7,5,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,7,6,8,1,4,3,5]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[3,7,1,6,4,8,2,5]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[1,7,3,5,6,8,2,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,6,7,5,8,2,4]=>[1,7,8,5,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,6,5,8,2,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,6,8,5,7,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,3,5,7,6,8,1,4]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,1,6,5,7,8,3,4]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[4,2,7,6,8,3,1,5]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[4,2,6,8,7,3,5,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[3,8,2,4,6,7,5,1]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,7,2,6,4,8,1,5]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,2,6,1,4,7,8,5]=>[4,2,8,1,5,6,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[5,3,7,2,1,8,4,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[4,7,3,2,1,5,8,6]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[8,7,6,1,3,4,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,7,3,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,6,7,2,1,5,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[3,7,8,6,2,1,5,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[8,7,6,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,4,8,1,6,5,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[4,6,8,2,1,7,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,1,5,7,2,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,3,7,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,2,1,3,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,6,7,1,3,5,4]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[8,3,6,1,7,5,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,6,1,8,7,2,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,2,5,6,7,4,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,6,5,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,7,8,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,2,5,7,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,6,8,5,4,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,7,2,5,8,6,4,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,8,2,6,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,8,1,6,5,2,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,7,8,6,1,3,5,4]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[8,7,6,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,1,5,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,6,7,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,5,3,1,2,4,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,6,3,5,1,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[8,5,3,7,2,1,4,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,1,4,5,7,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,2,4,5,1,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,2,4,5,1,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[2,6,1,4,5,3,8,7]=>[3,6,1,5,4,2,8,7]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[6,1,2,4,5,3,8,7]=>[6,2,3,5,4,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,6,3,2,1,4,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,4,3,6,1,2,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,3,1,4,5,2,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,1,6,4,5,2,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,3,7,4,5,1,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,4,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,7,4,1,6,3,5]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[8,1,7,4,2,6,3,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,7,8,4,5,1,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,1,8,7,5,3,4,6]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,6,8,5,7,3,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,6,3,8,1,7,2,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,6,1,4,5,8,3,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,7,6,4,5,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,7,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,8,4,7,6,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,5,8,4,7,6,1,3]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,4,8,3,5,6,7,1]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,1,8,3,5,6,7,2]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,8,4,2,5,6,7,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,4,1,3,5,6,7,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,8,4,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,3,8,4,1,7,2]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[2,1,5,8,4,6,7,3]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,4,8,3,6,7,5]=>[2,1,5,8,3,7,6,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,4,3,8,2,1,7,5]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[7,3,8,4,2,6,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,1,2,5,6,7,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,1,8,2,5,6,7,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,8,1,5,6,7,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,3,8,2,5,6,7,1]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,8,2,3,5,6,7,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,8,2,1,5,6,7,4]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,8,1,3,5,6,7,4]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[8,1,2,3,5,6,7,4]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,8,2,4,3,6,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,3,2,4,1,7,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,1,8,3,4,6,7,5]=>[2,1,8,4,5,7,6,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,7,8,5,4,3,6]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,7,3,8,1,4,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[7,1,8,4,5,3,2,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,7,8,4,5,3,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,7,1,4,3,6,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,7,4,2,6,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,7,8,4,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,3,8,4,2,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[4,8,3,6,2,1,7,5]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[8,6,3,1,4,2,7,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,3,8,2,4,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,3,1,8,5,7,6]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,1,3,2,6,8,7,5]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[7,5,3,6,2,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,6,3,5,1,2,7,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,3,2,6,1,7,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,3,8,6,2,7,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,5,8,4,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,2,4,7,6,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,5,4,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,6,4,5,8,1,3]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[7,1,6,4,5,8,2,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,3,6,1,8,2,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,1,7,6,5,8,3,4]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,8,5,3,6,7,4]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,8,3,5,2,1,7,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,4,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,4,2,5,6,7,3]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,8,4,1,5,6,7,3]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,8,1,2,5,6,7,3]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,4,8,1,5,6,7,2]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,4,2,8,5,6,7,1]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,4,1,8,5,6,7,3]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[4,1,2,8,5,6,7,3]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,2,1,5,6,7,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,5,2,4,8,6,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,3,2,8,1,7,4]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[2,1,5,3,8,6,7,4]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,4,3,5,8,1,7,2]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,3,5,4,8,6,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,4,1,5,6,7,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,3,1,8,5,6,7,2]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,1,4,8,5,6,7,2]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,5,3,7,2,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,3,7,4,5,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,7,2,4,5,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,1,7,4,8,6,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,5,7,4,8,6,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,3,7,1,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,8,7,4,5,2,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,7,5,4,8,6,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,1,4,8,6,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,6,3,1,8,2,7,4]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,6,3,5,8,2,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,6,3,8,1,2,7,5]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[3,7,8,4,1,6,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,2,5,1,6,8,4,7]=>[4,2,7,1,5,8,3,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,6,2,5,4,8,1,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,5,2,4,7,1,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,5,8,2,4,7,6,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,2,5,8,3,7,6,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,2,6,5,3,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,4,2,1,6,8,3,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[6,3,5,1,4,8,2,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,6,1,5,3,8,2,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,1,6,4,3,8,2,7]=>[7,2,5,4,3,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,4,3,2,7,1,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,4,3,8,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,3,6,2,8,7,5,1]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,3,7,6,2,1,8,5]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[6,4,3,1,7,2,8,5]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,5,4,3,1,8,2,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,4,7,5,8,3,2,6]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,3,5,8,4,2,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,5,8,4,1,3,6]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,8,5,7,4,6,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,5,8,7,1,4,6,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,4,5,8,7,3,6,2]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,4,8,7,3,6,2]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,4,3,8,1,7,5,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,3,7,1,8,6,5,2]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,8,3,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,8,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,3,1,8,6,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,8,6,5,3,7,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,6,3,7,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,1,8,7,3,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,7,3,1,4,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,8,7,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,2,8,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,1,6,8,4,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,1,6,3,2,8,4]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,1,7,5,3,2,8,4]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,5,3,2,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,5,3,2,8,7,4,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,2,6,3,8,7,4,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,2,7,6,3,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,5,2,1,7,3,8,4]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,2,7,4,1,8,3,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[4,7,2,6,3,1,8,5]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[2,4,8,6,3,7,5,1]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[3,8,6,2,4,7,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,6,2,4,1,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,6,7,2,1,4,8,5]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[4,3,7,8,2,1,5,6]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[8,3,7,1,4,6,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,2,5,7,1,6,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[8,3,6,2,7,1,5,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,8,3,6,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,3,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,8,2,1,6,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,2,6,8,1,7,5,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[5,4,8,2,7,1,6,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,8,1,5,7,2,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,3,7,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,2,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,2,7,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,8,1,7,5,2,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,1,6,8,2,7,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,5,2,8,1,7,4,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,2,7,1,8,6,4,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[5,8,2,7,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,8,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,2,1,8,5,4,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,1,7,2,8,5,4,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,5,1,8,2,6,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,7,1,8,6,2,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,3,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,4,6,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,1,7,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,8,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,4,2,3,7,6,1,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[6,4,2,7,3,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,2,6,3,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,4,2,6,3,1,5,7]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[3,2,7,6,4,5,1,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,7,2,6,3,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,7,6,2,3,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,6,5,2,3,8,4,7]=>[1,7,5,4,3,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,2,8,3,4,6]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,5,2,3,1,4,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,8,6,2,3,1,4,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,8,2,6,3,1,5,7]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[3,2,8,6,4,1,5,7]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,2,1,6,4,8,5,7]=>[3,2,1,7,5,8,4,6]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[7,1,5,2,8,3,4,6]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,5,2,7,3,4,6]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,6,7,2,3,4,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,6,7,2,3,4,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,6,8,2,3,4,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,1,7,8,4,5,6]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,8,7,1,4,5,6]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[5,8,7,2,1,3,4,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,7,6,8,2,3,4,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,5,8,2,3,1,4,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[8,5,7,2,1,3,4,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,2,8,3,1,5,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[5,4,2,3,8,1,6,7]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,2,5,4,1,8,6,7]=>[5,2,4,3,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,5,2,3,1,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,4,2,3,1,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[6,4,2,1,3,8,5,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[7,4,2,1,8,3,5,6]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[8,4,2,1,7,3,5,6]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,4,2,8,7,3,5,6]=>[1,6,3,8,7,2,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,2,7,3,4,6]=>[1,7,8,4,6,5,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,5,1,2,7,3,4,6]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,1,2,8,3,4,6]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,5,1,2,3,8,4,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,6,2,1,3,8,5,7]=>[5,7,4,3,1,8,2,6]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,2,6,1,4,8,5,7]=>[4,2,7,1,5,8,3,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,7,1,8,4,5,6]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,7,2,1,8,3,5,6]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[7,6,1,8,2,3,4,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,1,7,2,3,4,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,6,8,7,2,3,4,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,6,2,3,4,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,1,6,2,3,4,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,1,7,2,3,4,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,8,2,1,7,3,5,6]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[3,2,8,1,7,4,5,6]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,1,8,7,4,5,6]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[5,1,8,2,7,3,4,6]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,1,8,7,2,3,4,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,6,2,3,4,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,7,6,2,3,4,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,5,1,2,4,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,3,5,6,1,2,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[8,3,7,5,2,1,4,6]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,3,7,5,1,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,5,2,7,1,8,3,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,2,7,4,1,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,1,5,4,3,8,7]=>[3,6,1,5,4,2,8,7]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[6,4,3,5,1,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,3,1,4,6,2,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,1,4,6,5,2,8,7]=>[6,2,3,5,4,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,7,4,6,2,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,1,4,7,2,6,3,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,4,7,8,5,2,1,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[2,1,8,5,7,3,4,6]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,6,3,5,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,2,4,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,4,8,6,5,7,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,4,8,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,4,6,8,2,7,3]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,5,4,6,7,1,8,3]=>[6,8,3,4,5,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,4,6,3,7,5,8,1]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,1,6,3,8,5,7,2]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,7,4,2,8,6,5,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,4,1,3,5,8,6,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,5,8,4,1,7,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,3,7,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,4,8,3,7,6,5]=>[2,1,5,8,3,7,6,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[7,4,3,8,2,1,6,5]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[6,3,7,4,1,8,2,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,3,1,2,5,7,6,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,1,8,2,7,6,5,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,8,1,6,7,5,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,3,7,2,6,8,5,1]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,7,2,3,8,5,6,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,8,2,1,7,5,6,4]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,8,1,3,6,5,7,4]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,7,8,5,4,3,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,7,1,6,3,4,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,6,7,2,4,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,3,8,7,4,2,6,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,3,8,7,2,1,6,5]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[8,3,6,1,4,2,7,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,3,5,8,2,4,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,3,4,1,8,5,7,6]=>[4,2,3,1,8,6,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,1,3,2,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[8,3,5,6,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,6,1,8,7,2,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,6,2,8,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,6,5,4,7,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,1,6,4,5,7,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,8,3,6,1,7,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,8,6,5,7,3,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,7,5,3,6,8,4]=>[2,1,8,6,5,4,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,7,3,5,2,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,1,4,2,5,6,8,3]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,7,4,1,6,5,8,3]=>[4,8,6,1,5,3,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,6,1,2,8,7,3,5]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,4,1,5,8,7,6,3]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[4,1,2,5,8,6,7,3]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,2,1,5,8,7,3]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[8,5,2,4,6,1,7,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,3,2,6,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,1,5,3,6,8,7,4]=>[2,1,8,4,5,7,6,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[7,3,5,4,6,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,3,4,1,5,7,8,2]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,3,1,5,7,6,8,2]=>[8,3,2,4,6,5,7,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,1,4,5,6,8,7,2]=>[8,2,3,4,5,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,5,2,6,3,1,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,5,2,1,4,3,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,5,2,7,4,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,2,7,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,7,5,2,1,6,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,3,7,5,2,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,1,6,5,4,2,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,6,3,2,4,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[3,6,2,4,1,5,8,7]=>[5,6,3,4,1,2,8,7]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,6,1,3,5,4,8,7]=>[3,6,1,4,5,2,8,7]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[6,7,2,3,4,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,7,2,3,4,1,6,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,1,7,3,8,4,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,5,7,3,8,6,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,1,3,5,8,4,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,7,4,1,8,5,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,3,7,4,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,1,6,7,4,8,5,3]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,8,7,4,3,6,5]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,8,3,7,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,4,1,2,6,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[7,8,1,3,5,2,6,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,7,3,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,6,3,1,5,7,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[8,1,6,3,2,5,4,7]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,8,4,1,6,3,7,5]=>[4,8,6,1,7,3,5,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,8,1,2,7,6,3,5]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,8,4,2,5,7,1,6]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[6,8,3,5,2,7,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,5,3,8,7,6,4]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,5,3,2,8,7,1,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,5,2,4,8,1,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,4,2,8,5,7,6,1]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,4,1,8,7,6,5,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[8,4,2,1,7,5,3,6]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,3,1,8,6,7,5,2]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,1,4,8,6,5,7,2]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,6,5,4,8,2,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,7,5,6,8,4,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,1,6,8,2,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,2,5,1,7,4,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,6,2,1,8,7,3,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,6,2,5,8,3,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,5,2,6,3,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,1,2,3,6,8,7,5]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,4,3,1,8,5,6,7]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[7,5,2,8,3,4,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,2,8,4,3,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[4,7,2,8,1,5,3,6]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[8,7,2,1,4,5,6,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,6,8,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,8,5,4,3,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,7,8,4,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,3,8,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,7,8,5,4,6,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,5,8,4,6,3,7]=>[2,1,7,8,5,6,3,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,5,3,8,4,1,2,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[7,5,8,4,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,8,3,5,6,1,7]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,1,8,3,6,5,2,7]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,4,8,1,7,2,5,6]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[8,4,1,3,7,2,6,5]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,1,8,2,4,7,6,5]=>[4,2,8,1,5,7,6,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,8,1,4,6,7,5]=>[4,2,8,1,5,7,6,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,3,8,2,5,1,7,6]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[6,3,8,4,2,5,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,4,3,8,2,5,1,6]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[2,1,4,8,3,5,7,6]=>[2,1,5,8,3,6,7,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,8,2,4,3,5,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,8,2,3,5,1,6,7]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[3,8,2,1,4,6,5,7]=>[4,8,3,1,5,7,6,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,8,1,3,4,5,7,6]=>[3,8,1,4,5,6,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,8,4,1,6,5,3,7]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,8,4,1,6,5,7,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,8,7,6,1,4,3,5]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,8,5,6,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,7,6,1,4,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,5,7,2,4,1,6,8]=>[6,5,7,4,2,1,3,8]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[7,5,8,2,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,5,3,4,7,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,8,5,3,4,1,7,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[2,8,5,3,4,1,6,7]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[2,8,7,6,1,4,5,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,8,5,3,6,1,7,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,8,5,6,7,4,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,8,5,3,4,7,1,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[2,8,5,3,4,6,1,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[2,8,5,3,4,6,7,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,5,7,2,4,6,1,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[6,5,2,7,3,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,5,2,8,3,1,7,4]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[6,5,2,8,3,1,4,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[7,5,8,2,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,8,2,1,3,7,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[3,5,6,2,1,8,7,4]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,5,7,6,1,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,5,7,2,4,1,8,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[3,5,7,2,4,6,8,1]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,5,2,7,3,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,5,2,6,3,1,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,1,2,3,7,6,8,5]=>[4,2,3,1,8,6,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[6,5,2,7,3,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,1,6,7,4,3,8,2]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,2,6,4,8,7,3]=>[8,2,3,5,4,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,2,8,6,4,7,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,6,8,7,3,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,5,2,8,3,7,4,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,1,2,3,8,7,5,6]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,1,2,3,8,6,5,7]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,1,2,3,8,6,7,5]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,1,2,3,7,6,5,8]=>[4,2,3,1,7,6,5,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,1,2,3,8,5,7,6]=>[4,2,3,1,8,6,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[7,1,6,8,4,3,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,2,8,4,5,7,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,8,2,3,1,7,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,5,8,2,4,3,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[6,5,8,2,4,3,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,5,2,8,3,4,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,2,8,3,7,1,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,5,2,7,3,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,1,6,7,4,3,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,6,8,7,3,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,6,8,4,3,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,8,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,1,8,3,6,5,7,2]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,8,3,6,2,7,5]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,1,4,8,6,2,7,5]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[7,1,6,5,8,3,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,6,7,8,3,2,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,1,6,5,7,3,2,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,5,2,6,3,7,1,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,5,2,7,3,8,1,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,5,6,2,4,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[3,5,6,2,4,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[3,7,5,6,8,4,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,5,2,8,1,7,4]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[6,1,2,5,8,4,7,3]=>[8,2,3,6,7,4,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,6,5,8,3,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,5,2,6,3,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,1,2,3,5,8,7,6]=>[4,2,3,1,5,8,7,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,1,2,3,7,8,6,5]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,5,2,7,3,8,6,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,1,6,7,8,3,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,2,6,8,5,7,3]=>[8,2,3,6,7,4,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,2,5,6,8,7,3]=>[8,2,3,4,5,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,5,2,6,3,7,8,1]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,8,5,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,4,2,1,5,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,2,1,6,5,3,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,4,1,2,5,7,3,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[2,4,8,1,5,7,3,6]=>[4,7,8,1,5,6,2,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,3,8,1,7,2,5,6]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[6,3,1,4,7,2,5,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,8,3,4,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,3,5,4,2,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,4,1,2,3,6,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,3,6,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,2,1,5,3,4,6]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,8,2,6,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,2,5,6,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,1,8,7,5,4,3,6]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,3,8,2,6,4,7,5]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,3,7,1,6,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,3,6,2,7,4,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,1,2,5,8,7,4,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,3,1,8,4,2,7,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,4,2,1,5,3,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,4,3,7,5,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,3,8,7,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,7,1,5,3,6,8]=>[4,6,7,1,5,2,3,8]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,3,7,6,4,2,8,5]=>[1,6,8,5,4,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,7,5,6,8,4,3]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,7,2,8,6,4,1,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,8,1,7,6,4,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,5,8,3,6,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,5,6,8,2,4,7,3]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,8,5,3,1,4,7]=>[6,7,8,5,4,1,2,3]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[5,6,7,3,8,4,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,2,8,1,4,7,3,6]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,6,7,5,2,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,5,6,7,2,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,5,7,6,1,8,3,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,5,8,6,2,7,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,5,8,3,2,7,4]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,5,7,1,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,7,5,6,3,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,1,6,3,4,2,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,7,1,4,2,3,8,6]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[5,7,6,4,3,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,3,4,5,8,7,1,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,2,4,1,8,3,7,5]=>[8,4,6,2,7,3,5,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,2,3,5,4,8,1,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,1,3,4,5,8,7,2]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,4,2,7,6,8,3]=>[8,2,4,3,6,5,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,2,4,7,8,3,5]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,2,4,1,6,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,1,4,2,8,5,3,7]=>[7,2,6,4,8,3,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,7,5,8,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,6,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,1,7,2,6,5,3,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,8,2,1,5,6,3,7]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[4,2,7,8,1,6,3,5]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[2,1,8,7,6,5,3,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,1,4,7,8,2,6,5]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,1,7,4,5,6,8,2]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,2,7,1,6,3,8,5]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[4,3,7,5,6,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,8,6,3,5,7,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,1,2,5,3,7,6]=>[6,8,3,4,5,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,8,6,5,2,4,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,8,5,6,1,4,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,7,8,2,1,6,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,2,8,7,1,6,4,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,7,8,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,6,8,5,2,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,7,8,5,1,2,4,6]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[3,7,1,6,4,2,5,8]=>[6,7,3,5,4,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,1,8,6,2,3,5,7]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,7,8,6,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,6,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,7,6,5,3,4,8]=>[2,1,7,6,5,4,3,8]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,8,1,6,4,5,3,7]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,8,7,5,1,4,3,6]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,8,6,7,5,1,3,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,7,8,6,5,4,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,3,1,2,7,4,8,5]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[6,4,2,7,1,3,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,4,2,5,1,3,8,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,3,6,1,8,2,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,3,6,1,7,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,6,2,4,7,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,6,2,4,8,1,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,6,2,7,1,4,8,5]=>[5,8,3,6,1,4,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[5,3,6,7,1,2,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,3,7,4,1,2,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,7,1,5,2,3,8,6]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,7,5,1,2,4,8,6]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[7,6,4,2,3,8,1,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,6,4,2,3,7,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,6,3,8,1,2,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,7,4,2,3,8,1,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[3,7,6,1,4,8,2,5]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[5,7,2,6,1,8,3,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,4,7,5,2,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,4,8,5,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,2,6,3,7,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,6,1,2,7,4,5]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,8,6,2,4,7,1,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,8,4,3,7,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,3,7,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,5,7,1,2,4,6]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,8,5,7,1,3,4,6]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[4,8,6,2,7,1,3,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[7,3,8,5,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,7,5,8,1,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,7,6,4,8,1,3,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,6,5,8,1,3,4,7]=>[5,7,6,8,1,3,2,4]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[3,6,5,8,1,2,4,7]=>[6,7,5,8,3,1,2,4]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[2,5,7,4,8,1,3,6]=>[6,7,8,4,5,1,2,3]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[5,4,6,7,2,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,6,3,7,1,8,2,5]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[3,5,7,1,4,8,2,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[5,3,7,2,4,8,1,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[5,4,7,3,8,1,2,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[7,4,6,3,8,1,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,6,3,7,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,1,6,7,2,3,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,4,1,6,8,2,3,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,1,7,8,2,3,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,5,3,7,1,8,2,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,5,1,2,7,8,3,4]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,3,6,4,7,8,1,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,3,7,4,8,5,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,7,1,5,8,6,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,1,2,8,6,3,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,3,8,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,1,8,6,2,3,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,1,8,5,2,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,1,7,5,2,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,7,2,8,1,6,3,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,4,7,8,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,7,8,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,8,2,7,1,4,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,4,8,7,1,3,5,6]=>[5,6,8,7,1,2,4,3]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[4,3,8,7,1,2,5,6]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[5,3,8,7,1,2,4,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[8,3,7,6,1,2,4,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,4,7,6,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,8,7,1,2,3,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[3,5,8,7,1,2,4,6]=>[6,7,8,5,4,1,2,3]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,5,8,7,1,3,4,6]=>[5,7,8,6,1,4,2,3]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[4,6,8,2,7,1,3,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,7,1,8,6,2,3,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[7,5,8,6,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,4,7,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,1,6,2,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,7,6,1,3,4,5]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[3,8,7,6,1,2,4,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[4,8,7,6,1,2,3,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,6,3,1,4,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[7,5,3,8,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,4,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,1,4,5,8,2,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,1,7,8,5,3,6,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,7,3,8,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,1,4,5,3,2,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,7,8,4,1,6,5,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[7,1,8,4,2,6,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,5,1,4,8,6,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,5,3,1,8,4,7,2]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,4,3,8,1,5,7,2]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[8,6,3,1,2,5,7,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,7,1,4,2,6,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,3,8,4,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,3,4,5,6,7,8,9,10,1]=>[10,2,3,4,5,6,7,8,9,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[2,3,1,6,7,8,9,4,5]=>[3,2,1,9,8,6,7,5,4]=>[3,2,1,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[1,4,5,6,7,8,9,2,3]=>[1,9,8,4,5,6,7,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[3,6,4,5,7,2,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,3,2,7,4,6,8,1]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,5,3,6,2,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,3,2,5,1,8,4,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[8,5,3,6,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,6,3,4,7,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,6,3,4,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,2,7,3,4,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,6,2,7,4,5,8,1]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,2,5,7,3,6,8,1]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,4,7,6,2,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,7,3,5,2,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,7,6,2,4,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,7,6,3,4,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,5,3,1,2,8,4,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[8,6,5,2,3,7,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,2,1,7,3,4,6]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,5,2,1,8,3,4,6]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,6,3,2,8,4,5,7]=>[1,7,4,3,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,3,1,2,8,4,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[5,6,2,3,1,8,4,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,2,6,5,1,8,3,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,4,8,6,2,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,3,5,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,2,3,6,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,2,1,7,3,4,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,8,6,3,7,2,4,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,7,3,4,5,6]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,1,7,3,4,5,6]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,8,6,1,7,2,4,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[4,8,1,5,7,2,3,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,2,8,3,7,1,5,6]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[4,1,7,5,8,2,3,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,7,3,8,2,4,5,6]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,2,7,3,4,5,6]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,2,5,7,1,8,3,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,6,2,7,1,8,4,5]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[6,3,7,1,2,8,4,5]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[7,2,6,1,8,3,4,5]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,2,6,1,7,3,4,5]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,3,1,5,8,2,4,6]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,2,1,5,8,4,6,7]=>[3,2,1,6,8,4,7,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[5,4,1,3,6,8,2,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[4,3,5,1,6,8,2,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[5,4,6,3,8,7,1,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,6,4,5,8,7,1,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,5,3,4,8,7,1,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,3,2,8,7,1,4,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,3,1,8,7,2,4,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,5,3,7,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,8,3,7,2,4,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,3,8,1,7,2,4,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,6,8,2,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,8,2,4,6,1,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,7,3,8,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,7,8,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,2,5,8,7,1,3,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,6,2,8,7,1,4,5]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,7,8,1,6,2,4,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,3,8,7,1,4,5,6]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[7,2,8,6,1,3,4,5]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[2,1,8,7,3,4,5,6]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,2,7,6,1,3,4,5]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,2,8,7,3,4,5,6]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,7,2,4,5,6]=>[1,5,8,7,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,3,6,2,4,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,5,8,7,2,3,6]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,4,8,7,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,3,7,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,6,2,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,6,7,3,2,5,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,6,7,3,2,4,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,5,3,7,2,4,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,5,3,6,2,4,7]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,5,1,3,6,2,4,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,5,8,3,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,8,3,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,1,3,2,6,5,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[8,1,4,3,2,6,5,7]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,3,2,7,5,6]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,3,2,7,6,5]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,5,4,6,7,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,5,3,6,2,7,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,3,2,6,7,5]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,3,2,5,7,6]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,3,2,5,6,7]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,1,3,2,5,6,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[7,4,8,3,2,5,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,3,8,2,5,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[6,4,3,1,2,5,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[7,4,1,3,2,5,8,6]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,4,1,3,2,6,8,5]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,5,1,3,6,2,8,4]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,5,1,4,6,8,2,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,8,3,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,8,3,2,6,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,8,3,2,5,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,3,8,2,5,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[6,4,3,7,2,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,4,3,2,8,6,1,7]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[5,4,3,2,8,7,1,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[6,5,3,8,7,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,4,8,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,4,1,7,8,2,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,5,3,1,7,2,8,4]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,4,3,1,2,7,8,5]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,4,3,2,1,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[6,5,3,1,8,2,7,4]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,5,4,1,8,7,2,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,5,1,4,8,6,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,4,1,3,2,8,6,5]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,4,1,3,2,8,5,6]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,4,3,1,2,8,5,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,4,3,1,2,7,5,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,4,3,8,2,7,5,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,5,3,8,7,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,3,1,7,2,4,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,5,3,1,8,2,4,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,5,1,3,8,2,4,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,1,8,3,2,4,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,1,8,4,5,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,8,1,4,5,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,8,1,3,2,5,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,3,7,8,2,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,3,7,2,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,4,3,7,2,1,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,8,3,2,1,5,6]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,4,8,3,2,1,6,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,5,8,3,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,4,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,4,8,1,7,2,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,5,3,8,1,2,7,4]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[5,4,3,2,8,1,7,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[6,4,3,7,2,1,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,5,3,7,1,2,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,5,4,7,1,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,5,3,7,8,2,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,3,7,2,8,1,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,4,3,2,7,8,1,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[5,4,3,2,6,8,1,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[5,6,2,1,3,4,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,8,2,7,4,1,3,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,3,7,8,2,1,4,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[7,6,1,2,5,8,3,4]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,1,7,8,4,3,5,6]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,3,7,4,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,1,2,5,4,6,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,6,8,3,1,4,7,5]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[6,1,8,3,2,4,5,7]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,4,1,3,7,6,2,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,7,4,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,1,6,8,3,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,5,2,1,8,7,4,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,7,2,8,1,3,6,5]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[7,3,8,6,1,2,5,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[3,4,7,1,8,2,6,5]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[1,8,2,4,3,5,6,7]=>[1,8,3,5,4,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,4,3,5,6,8]=>[1,7,3,5,4,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,2,4,3,5,7,8]=>[1,6,3,5,4,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,4,3,6,7,8]=>[1,5,3,4,2,6,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,2,5,3,4,7,8]=>[1,6,3,5,4,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,5,3,4,6,8]=>[1,7,3,6,5,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,5,3,4,6,7]=>[1,8,3,6,5,4,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,6,3,4,5,7]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,6,3,4,5,8]=>[1,7,3,6,5,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,7,3,5,4,6]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,8,3,5,4,6]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,2,8,3,5,4,7]=>[1,7,3,8,5,6,2,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,8,3,6,4,7]=>[1,7,3,8,5,6,2,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,8,3,6,5,7]=>[1,5,3,8,2,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,8,4,6,5,7]=>[1,3,2,8,5,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,8,4,6,5,7]=>[1,2,3,8,5,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,7,4,6,5,8]=>[1,2,3,7,5,6,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,7,3,6,5,8]=>[1,5,3,7,2,6,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,7,3,6,4,8]=>[1,7,3,6,5,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,2,7,3,5,4,8]=>[1,7,3,6,5,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,6,3,5,4,8]=>[1,7,3,6,5,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,6,3,5,4,7]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,5,3,6,4,7]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,5,3,6,4,8]=>[1,7,3,6,5,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,2,5,3,7,4,8]=>[1,7,3,5,4,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,2,4,3,7,5,8]=>[1,7,3,5,4,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,4,3,6,5,8]=>[1,7,3,5,4,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,4,3,6,5,7]=>[1,8,3,5,4,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,3,4,6,5,8]=>[1,7,3,4,5,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,4,3,7,5,6]=>[1,8,3,5,4,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,4,3,8,5,6]=>[1,8,3,5,4,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,2,4,3,8,5,7]=>[1,7,3,5,4,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,4,3,8,6,7]=>[1,5,3,4,2,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,2,5,3,8,4,7]=>[1,7,3,5,4,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,5,3,8,4,6]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,5,3,7,4,6]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,6,3,7,4,5]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,6,3,8,4,5]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,8,4,7,5,6]=>[1,2,3,8,5,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,8,4,7,5,6]=>[1,3,2,8,5,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,8,3,7,5,6]=>[1,5,3,8,2,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,8,3,7,4,6]=>[1,7,3,8,5,6,2,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,2,8,3,7,4,5]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,8,3,6,4,5]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,7,3,6,4,5]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,3,7,2,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,6,3,7,5,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,6,3,8,5,1,7,2]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[4,6,3,8,5,1,2,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[5,6,8,3,4,1,2,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[5,6,8,3,4,1,7,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,6,2,7,5,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,6,7,2,4,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,6,8,4,3,1,7,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,6,8,4,3,1,2,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[5,7,8,4,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,4,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,8,4,2,1,7,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,6,8,2,4,1,7,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,6,2,8,5,1,7,3]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[3,2,6,8,5,1,7,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,2,6,8,5,1,4,7]=>[6,2,7,8,5,1,3,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,6,2,8,5,1,3,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[5,6,8,2,4,1,3,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[5,6,8,4,2,1,3,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[5,7,8,4,1,3,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,7,8,4,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,4,1,2,3,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,7,8,1,5,2,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,8,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,8,1,5,3,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,8,1,3,5,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,8,2,1,6,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,2,8,1,6,3,5]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[3,2,7,8,1,6,4,5]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,2,7,8,1,6,5,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,7,2,8,1,6,5,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,7,8,2,1,6,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,8,1,3,5,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,8,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,8,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,8,1,5,4,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,8,1,4,5,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,8,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,8,1,4,3,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,8,1,3,4,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,8,2,1,4,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,2,8,1,5,6,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[3,2,7,8,1,5,6,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,2,6,8,4,1,7,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,6,2,8,3,1,7,5]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[5,6,8,3,2,1,7,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,7,8,3,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,3,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,3,8,1,6,2,5]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[4,7,3,8,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,7,3,8,1,5,6,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,6,3,8,2,1,7,5]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[4,5,3,2,8,1,7,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,5,2,3,8,1,7,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,2,5,4,8,1,7,6]=>[6,2,4,3,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,5,3,2,8,1,6,7]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,6,3,8,2,1,5,7]=>[6,7,5,8,3,1,2,4]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[4,7,3,8,1,5,2,6]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[4,7,3,8,1,2,6,5]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[4,7,3,8,1,2,5,6]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[5,7,8,3,1,2,4,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,7,8,3,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,3,1,4,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,6,8,3,2,1,4,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[3,2,7,8,1,5,4,6]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[5,7,8,2,1,4,3,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,7,8,1,3,4,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,8,1,4,3,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,8,1,4,2,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,8,1,4,2,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,8,1,2,5,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,8,1,2,5,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,8,1,2,4,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,8,1,3,2,5,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,8,2,1,3,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,2,7,8,1,4,6,5]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[6,7,8,1,3,2,4,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,8,1,2,4,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,8,1,2,3,5,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,8,5,1,6,4,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[7,2,8,5,4,1,6,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,8,5,4,3,1,7,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[2,8,4,5,6,1,7,3]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,8,6,5,7,3,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,8,4,5,3,7,1,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[2,8,4,3,5,6,1,7]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[7,2,8,4,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,3,7,5,2,4,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,2,3,8,5,1,7,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,3,2,8,5,1,4,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,4,8,2,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,8,5,2,1,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,8,5,1,3,7,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,3,7,5,2,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,3,7,5,1,2,8,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[4,3,7,1,5,6,8,2]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,6,1,7,5,2,8,4]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,4,1,2,7,6,8,5]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,4,2,1,7,5,8,6]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,6,5,7,1,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,5,2,7,4,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,5,2,6,4,8,7,1]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,3,1,8,6,4,7,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,6,1,8,7,2,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,3,5,8,2,7,4,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,5,8,4,2,3,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,2,5,8,3,7,1,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,6,5,7,3,4,2,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,7,4,6,3,8]=>[1,7,3,6,5,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,2,1,8,7,6,3,4]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,1,3,8,4,6,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,4,8,6,1,7,5]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,7,3,5,8,6,1,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[1,5,4,6,2,7,3,8]=>[1,7,5,4,3,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,2,4,7,1,8,3,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,3,6,4,1,8,7,2]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,3,6,1,4,8,2,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[7,3,5,6,8,4,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,5,1,8,2,7,4]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[2,6,1,5,8,4,7,3]=>[3,8,1,6,7,4,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,7,6,5,8,3,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,1,6,3,8,4,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,2,4,1,7,8,5,6]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,1,4,2,7,8,6,5]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[5,1,4,7,2,8,6,3]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,6,4,7,8,2,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,1,4,6,8,5,7,2]=>[8,2,3,6,7,4,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,3,4,5,7,1,8,2]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[2,5,4,6,1,7,8,3]=>[5,8,3,4,1,6,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[7,2,1,4,3,6,5,8]=>[7,3,2,5,4,6,1,8]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[7,3,4,1,2,6,5,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[7,4,3,2,1,6,5,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[7,6,3,2,5,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,3,2,5,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,8,3,2,5,4,7,6]=>[1,8,4,3,6,5,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,4,5,2,3,7,6]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,3,5,1,6,2,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,3,6,1,5,4,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,6,5,1,3,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,8,5,4,3,2,7,6]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,6,4,3,7,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,5,7,4,3,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,4,7,5,1,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,3,7,1,5,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,2,1,8,5,4,7,6]=>[3,2,1,8,6,5,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,8,1,5,4,7,6]=>[4,2,8,1,6,5,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,4,8,5,1,3,7,6]=>[5,6,8,4,1,2,7,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,5,8,4,3,1,7,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[2,6,8,4,3,7,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,7,8,4,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,7,4,3,6,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,7,5,6,3,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,8,5,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,8,5,7,3,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,5,8,6,7,1,3,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,4,8,6,1,7,3,5]=>[5,7,8,6,1,4,2,3]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[3,2,1,8,6,7,4,5]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[5,2,1,7,6,8,4,3]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[5,3,7,1,6,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,4,7,6,1,8,3,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,5,7,6,8,1,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,6,7,5,8,3,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,8,6,5,7,3,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,6,7,2,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,7,5,6,8,2,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,6,5,7,8,2,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,4,6,7,1,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,3,6,1,7,8,2,4]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,2,1,6,7,8,3,4]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,3,5,1,7,2,8,4]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,4,5,7,1,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,5,4,7,2,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,6,4,7,2,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,8,4,6,2,7,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,3,2,6,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,3,2,7,8,1,4]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,5,3,2,7,1,8,4]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,4,3,2,1,7,8,5]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,2,1,4,3,8,7,6]=>[5,3,2,4,1,8,7,6]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[5,3,4,1,2,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,6,3,2,8,7,1,5]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[4,7,3,2,8,6,5,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,8,4,7,2,6,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,4,8,2,6,5,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[3,6,4,8,2,7,1,5]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[3,5,4,8,2,1,7,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,4,5,8,1,2,7,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,3,5,1,8,2,7,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,2,1,6,8,7,3,5]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[4,3,6,1,8,7,2,5]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[3,4,6,8,1,7,2,5]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[3,5,6,8,7,1,2,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,6,5,8,7,2,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,7,5,8,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,5,7,6,2,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,6,7,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,7,8,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,7,8,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,7,8,1,6,5,2]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[4,2,1,7,8,6,5,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,3,8,1,7,6,5,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,4,8,7,1,6,5,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,5,8,7,6,1,4,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,6,8,7,5,4,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,6,5,8,7,12,11,10,9]=>[2,1,4,3,6,5,8,7,12,11,10,9]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,6,5,10,9,8,7,12,11]=>[2,1,4,3,6,5,10,9,8,7,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,6,5,12,11,10,9,8,7]=>[2,1,4,3,6,5,12,11,10,9,8,7]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,8,7,6,5,10,9,12,11]=>[2,1,4,3,8,7,6,5,10,9,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,8,7,6,5,12,11,10,9]=>[2,1,4,3,8,7,6,5,12,11,10,9]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,10,9,8,7,6,5,12,11]=>[2,1,4,3,10,9,8,7,6,5,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,12,11,8,7,10,9,6,5]=>[2,1,4,3,12,11,10,9,8,7,6,5]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,12,11,10,9,8,7,6,5]=>[2,1,4,3,12,11,10,9,8,7,6,5]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,6,5,4,3,8,7,10,9,12,11]=>[2,1,6,5,4,3,8,7,10,9,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,6,5,4,3,8,7,12,11,10,9]=>[2,1,6,5,4,3,8,7,12,11,10,9]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,6,5,4,3,10,9,8,7,12,11]=>[2,1,6,5,4,3,10,9,8,7,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,6,5,4,3,12,11,10,9,8,7]=>[2,1,6,5,4,3,12,11,10,9,8,7]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,8,7,6,5,4,3,10,9,12,11]=>[2,1,8,7,6,5,4,3,10,9,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,8,7,6,5,4,3,12,11,10,9]=>[2,1,8,7,6,5,4,3,12,11,10,9]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,10,9,6,5,8,7,4,3,12,11]=>[2,1,10,9,8,7,6,5,4,3,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,12,11,6,5,8,7,10,9,4,3]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,12,11,6,5,10,9,8,7,4,3]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,10,9,8,7,6,5,4,3,12,11]=>[2,1,10,9,8,7,6,5,4,3,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,12,11,8,7,6,5,10,9,4,3]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,12,11,10,7,6,9,8,5,4,3]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,12,11,10,9,8,7,6,5,4,3]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[4,3,2,1,6,5,8,7,10,9,12,11]=>[4,3,2,1,6,5,8,7,10,9,12,11]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,3,2,1,6,5,8,7,12,11,10,9]=>[4,3,2,1,6,5,8,7,12,11,10,9]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,3,2,1,6,5,10,9,8,7,12,11]=>[4,3,2,1,6,5,10,9,8,7,12,11]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,3,2,1,6,5,12,11,10,9,8,7]=>[4,3,2,1,6,5,12,11,10,9,8,7]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,3,2,1,8,7,6,5,10,9,12,11]=>[4,3,2,1,8,7,6,5,10,9,12,11]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,3,2,1,8,7,6,5,12,11,10,9]=>[4,3,2,1,8,7,6,5,12,11,10,9]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,3,2,1,10,9,8,7,6,5,12,11]=>[4,3,2,1,10,9,8,7,6,5,12,11]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,3,2,1,12,11,8,7,10,9,6,5]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,3,2,1,12,11,10,9,8,7,6,5]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[6,5,4,3,2,1,8,7,10,9,12,11]=>[6,5,4,3,2,1,8,7,10,9,12,11]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[6,5,4,3,2,1,8,7,12,11,10,9]=>[6,5,4,3,2,1,8,7,12,11,10,9]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[6,5,4,3,2,1,10,9,8,7,12,11]=>[6,5,4,3,2,1,10,9,8,7,12,11]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[6,5,4,3,2,1,12,11,10,9,8,7]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[8,7,4,3,6,5,2,1,10,9,12,11]=>[8,7,6,5,4,3,2,1,10,9,12,11]=>[8,7,6,5,4,3,2,1,12,11,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[[[.,.],.],.],.]]
[8,7,4,3,6,5,2,1,12,11,10,9]=>[8,7,6,5,4,3,2,1,12,11,10,9]=>[8,7,6,5,4,3,2,1,12,11,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[[[.,.],.],.],.]]
[10,9,4,3,6,5,8,7,2,1,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[[.,.],.]]
[12,11,4,3,6,5,8,7,10,9,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[12,11,4,3,6,5,10,9,8,7,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[10,9,4,3,8,7,6,5,2,1,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[[.,.],.]]
[12,11,4,3,8,7,6,5,10,9,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,4,3,10,7,6,9,8,5,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,4,3,10,9,8,7,6,5,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,7,6,5,4,3,2,1,10,9,12,11]=>[8,7,6,5,4,3,2,1,10,9,12,11]=>[8,7,6,5,4,3,2,1,12,11,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[[[.,.],.],.],.]]
[8,7,6,5,4,3,2,1,12,11,10,9]=>[8,7,6,5,4,3,2,1,12,11,10,9]=>[8,7,6,5,4,3,2,1,12,11,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[[[.,.],.],.],.]]
[10,9,6,5,4,3,8,7,2,1,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[[.,.],.]]
[12,11,6,5,4,3,8,7,10,9,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[10,9,8,5,4,7,6,3,2,1,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[[.,.],.]]
[12,11,8,5,4,7,6,3,10,9,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,5,4,7,6,9,8,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,5,4,9,8,7,6,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,6,5,4,3,2,1,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[[.,.],.]]
[12,11,8,7,6,5,4,3,10,9,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,7,6,5,4,9,8,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,4,6,1,8,3,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,5,1,7,4,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,4,1,7,5,6,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,8,3,1,7,5,6,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,6,2,1,7,5,8,3]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,4,6,2,7,5,8,3]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,2,6,8,4,3]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,5,2,1,6,8,4,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,8,4,3,1,7,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,8,4,1,7,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,7,5,1,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,6,1,8,3,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,4,6,5,7,1,8,2]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,7,5,6,1,8,3,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,7,5,1,8,4,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,4,1,7,5,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,5,3,1,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,4,2,1,6,7,5,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,8,4,2,6,7,5,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,3,2,7,6,8,4]=>[1,8,4,3,6,5,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,3,2,1,7,6,8,4]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,5,3,1,7,6,8,4]=>[4,8,3,1,6,5,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,8,4,1,6,7,5,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,7,5,1,6,8,4,3]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,4,6,1,7,5,8,3]=>[4,8,6,1,5,3,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,7,1,6,5,8,2,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,8,2,6,5,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,1,2,7,5,8,3]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,5,1,2,6,8,4,3]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,1,2,6,7,5,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,3,1,2,7,6,8,4]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,3,1,2,7,6,8,5]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,5,1,2,7,6,8,4]=>[4,8,3,1,6,5,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[6,7,1,5,8,2,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,7,6,1,5,8,3,4]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,3,5,1,7,6,8,4]=>[4,2,8,1,6,5,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[7,6,1,5,8,3,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,7,1,5,8,2,4]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[7,1,6,5,8,2,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,5,1,6,8,4,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,1,6,7,5,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,2,3,1,7,6,8,4]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,5,2,1,7,6,8,4]=>[4,8,3,1,6,5,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[1,7,6,2,5,8,3,4]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,2,1,5,8,3,4]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,3,1,5,7,6,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,2,4,1,7,5,8,3]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,2,5,1,7,4,8,3]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,1,6,4,8,2,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,6,4,7,1,5,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,1,5,2,7,4,8,3]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,2,5,8,3,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,5,7,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,3,5,7,6,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,2,1,3,7,6,8,4]=>[8,3,2,4,6,5,7,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,5,2,6,8,4,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,2,6,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,4,2,7,5,8,3]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,6,5,7,1,4,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[3,6,8,2,5,7,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[8,3,2,5,7,6,1,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,1,3,2,7,6,8,4]=>[8,2,4,3,6,5,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,3,2,7,6,8,5]=>[4,2,3,1,8,6,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,2,1,3,7,6,8,5]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,4,2,3,7,6,8,5]=>[1,4,3,2,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,1,3,7,6,8,5]=>[3,4,1,2,8,6,7,5]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,8,3,5,7,6,1,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[6,8,2,3,5,7,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,1,3,5,8,2,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,5,7,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,1,2,4,7,6,8,5]=>[3,2,1,4,8,6,7,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[10,8,9,5,6,7,1,2,3,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,8,9,4,5,6,1,2,3,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,7,8,5,6,9,1,2,3,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,7,8,4,5,9,1,2,3,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,6,7,4,5,8,1,2,3,9]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[10,7,8,3,4,9,1,2,5,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,6,7,3,4,8,1,2,5,9]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[9,8,10,5,6,7,1,2,3,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,8,10,4,5,6,1,2,3,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,10,5,6,8,1,2,3,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,10,4,5,8,1,2,3,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,6,10,4,5,7,1,2,3,8]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,10,3,4,8,1,2,5,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,6,10,3,4,7,1,2,5,8]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,7,9,5,6,10,1,2,3,4]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,7,9,4,5,10,1,2,3,6]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,6,9,4,5,10,1,2,3,7]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,7,9,3,4,10,1,2,5,6]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,6,9,3,4,10,1,2,5,7]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[9,6,10,5,7,8,1,2,3,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,6,10,4,7,8,1,2,3,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,5,10,4,6,7,1,2,3,8]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,6,10,3,7,8,1,2,4,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,5,10,3,6,7,1,2,4,8]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,6,9,5,7,10,1,2,3,4]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,6,9,4,7,10,1,2,3,5]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,5,9,4,6,10,1,2,3,7]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,6,9,3,7,10,1,2,4,5]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,5,9,3,6,10,1,2,4,7]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[9,6,10,2,7,8,1,3,4,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,5,10,2,6,7,1,3,4,8]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,6,9,2,7,10,1,3,4,5]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,5,9,2,6,10,1,3,4,7]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,1,2,4,3,6,5,7]=>[8,2,3,5,4,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,3,5,6,2,7,4]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,3,4,2,6,7,5]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,7,8,3,4,5,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,6,3,8,4,5,7,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,3,2,1,4,5,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[7,3,1,4,2,6,8,5]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,4,1,5,6,8,2,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,7,8,5,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,8,5,6,2,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,7,8,4,2,6,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,7,8,2,4,5,1,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,6,2,8,4,5,1,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[2,3,6,7,4,5,8,1]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,5,2,4,8,6,1,7]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[3,5,4,2,8,7,1,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[4,6,5,8,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,5,1,7,8,2,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,4,1,2,3,8,5,6]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,2,4,1,3,7,5,8]=>[7,4,5,2,3,6,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[2,6,4,8,3,7,5,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[2,6,5,8,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,5,1,7,3,4,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[6,5,2,1,8,3,4,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[2,5,6,7,8,3,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,4,6,7,3,8,5,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,2,6,7,3,1,5,8]=>[6,5,7,4,2,1,3,8]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[4,7,8,2,3,1,5,6]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[4,7,8,3,2,1,6,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[5,6,4,8,1,7,2,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,6,3,8,1,2,7,4]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[4,2,5,3,7,1,6,8]=>[6,4,3,2,7,1,5,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,3,6,7,2,1,8,5]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[3,4,6,7,2,8,1,5]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[3,4,5,2,7,8,1,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[5,2,7,8,6,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,2,7,8,6,4,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,7,1,8,6,5,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,7,1,2,8,6,5,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,6,8,1,2,7,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,7,1,5,3,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,7,3,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,1,6,3,5,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,1,3,6,5,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,3,6,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,2,8,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,3,4,8,6,5,2]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,2,7,1,8,6,5,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,8,2,3,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,7,1,6,2,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,7,1,2,6,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,2,7,1,3,5,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,8,7,2,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,4,8,7,1,5,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,6,8,3,7,4,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,3,4,7,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,2,4,8,1,7,5,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[6,8,7,2,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,2,1,7,3,5,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,5,7,2,1,6,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,1,2,3,6,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,6,2,1,4,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,2,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,4,2,7,1,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,8,7,5,3,4,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,7,3,5,4,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,5,4,7,1,6,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,5,2,7,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,2,4,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,1,2,4,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,6,1,4,2,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,6,4,1,3,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,4,7,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,7,5,4,3,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,4,3,7,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,7,3,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,1,7,3,2,5,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,7,3,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,1,3,2,6,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,7,3,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,4,7,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,4,1,7,2,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,4,7,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,2,6,5,7,4,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,5,6,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,5,7,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,5,7,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,5,1,7,2,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,3,1,7,2,6,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,3,7,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,1,3,7,2,5,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,6,2,8,1,7,5,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,6,4,8,3,7,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,7,4,5,3,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,8,5,7,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,3,7,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,3,1,4,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,1,3,2,4,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,3,2,7,1,6,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,5,2,7,1,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,8,7,4,3,5,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,7,3,4,5,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,4,5,7,1,6,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,5,2,3,7,1,6,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,1,5,4,2,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[8,3,1,5,2,7,6,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,5,4,2,1,7,3,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,4,2,1,7,6,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,5,4,2,1,3,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,5,4,2,3,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,3,2,5,1,4,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,5,4,3,1,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,5,4,1,3,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[8,5,4,1,2,7,6,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,7,4,1,6,3,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,4,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,4,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,4,1,3,7,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,4,3,1,7,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,3,2,5,1,7,6,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,1,8,5,3,7,6,4]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,3,2,5,1,7,4,6]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,5,4,3,1,7,2,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,4,1,3,7,2,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,7,4,1,6,5,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,4,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,6,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,4,3,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,2,7,6,4,1,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,1,8,7,6,4,3,5]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,8,7,6,4,5,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,3,2,7,6,4,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,4,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,4,2,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,7,4,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,4,2,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,4,2,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,1,7,6,4,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,1,7,6,4,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,1,7,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,1,5,4,7,6,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,1,5,4,7,2,6]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,1,7,6,5,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,1,7,6,2,5,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,7,4,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,4,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,4,2,3,7,1,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,3,2,5,4,7,1,6]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,1,8,5,4,7,3,6]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,3,2,7,6,5,1,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,4,3,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,5,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,4,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,2,7,6,1,5,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,1,8,7,6,3,5,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,3,2,7,6,1,4,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,7,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,5,1,8,4,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,4,1,8,5,6,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,5,6,2,1,8,7,3]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[1,6,5,2,7,4,3,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,3,1,8,6,5,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,6,5,1,8,4,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,4,1,8,5,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,2,1,8,7,5,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,6,4,2,7,5,3,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,3,2,1,8,7,6,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,5,3,1,7,8,6,4]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,6,4,1,7,8,5,3]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,6,5,1,7,8,4,3]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,5,7,1,6,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,5,1,2,8,4,3,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,4,1,2,8,5,3,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,3,1,2,8,6,4,7]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[4,3,1,2,8,6,5,7]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[6,1,2,5,8,3,4,7]=>[7,2,3,6,8,4,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,1,3,4,8,2,5,6]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,5,6,8,2,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,6,1,5,7,8,3,4]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[7,4,1,6,8,5,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,2,3,1,8,6,7,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,5,2,1,6,8,7,4]=>[4,8,3,1,5,7,6,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[1,6,2,5,7,3,4,8]=>[1,7,3,6,5,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,2,1,5,8,7,3,4]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,3,1,5,8,6,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,2,4,1,8,5,7,3]=>[8,4,6,2,7,3,5,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,2,5,1,8,4,7,3]=>[8,4,6,2,7,3,5,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,3,1,4,8,6,2,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,2,1,4,8,7,3,5]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,6,2,4,7,3,5,8]=>[1,7,3,6,5,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,2,1,3,8,7,4,6]=>[7,3,2,4,8,6,1,5]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[7,4,1,3,8,5,2,6]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,1,3,8,4,2,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,7,1,4,8,2,5]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[7,6,1,4,8,3,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,2,1,3,8,7,5,6]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[2,6,1,4,7,8,3,5]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[7,1,4,6,8,2,3,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,3,5,8,2,4,6]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,2,4,8,3,5,7]=>[7,2,3,6,8,4,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,2,3,1,6,4,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[7,4,5,2,3,1,8,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,6,7,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,5,2,4,1,8,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,3,5,2,4,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,2,4,1,6,3,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,1,6,3,5,2,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,3,4,1,5,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,2,6,3,4,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,2,7,3,4,1,8,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[5,2,8,6,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,8,5,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,7,3,4,1,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,3,4,1,5,2,8,6]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,1,7,3,5,2,8,6]=>[6,2,8,4,5,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,1,7,4,5,2,8,6]=>[6,2,8,4,5,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,1,7,4,5,3,8,6]=>[2,1,8,6,5,4,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,1,8,6,7,4,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,8,6,7,3,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,7,3,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,3,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,6,2,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,3,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,8,4,7,3,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,8,5,7,3,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,8,5,7,4,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,1,8,5,7,4,6,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,7,4,6,3,8,5]=>[2,1,8,6,5,4,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,1,7,4,6,2,8,5]=>[6,2,8,4,5,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,1,7,3,6,2,8,5]=>[6,2,8,4,5,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,1,7,3,6,2,8,4]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,2,7,3,5,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,2,8,4,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,6,2,5,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,2,5,1,7,3,8,4]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[5,2,4,1,7,3,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[6,2,4,1,7,3,8,5]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,5,7,3,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,4,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,6,2,3,1,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,2,3,1,7,4,8,5]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,2,3,1,7,4,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,2,3,1,7,5,8,6]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,1,4,2,8,6,7,5]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[6,2,3,1,8,5,7,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,5,6,2,3,1,7,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,8,5,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,8,5,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,6,2,4,1,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,4,1,8,6,7,3]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,1,5,2,8,6,7,3]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,5,2,8,6,7,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,1,6,3,8,5,7,4]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,1,6,2,8,5,7,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,1,6,2,8,5,7,3]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,6,2,8,4,7,3]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,6,2,5,1,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,8,4,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,7,3,8,4,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,5,1,6,2,7,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,1,8,4,6,2,7,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,8,5,6,2,7,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,8,5,6,2,7,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,1,8,5,6,3,7,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,7,4,8,5,6,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,1,7,4,8,5,6,2]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,7,3,8,5,6,2]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,3,8,4,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,5,1,7,3,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,6,2,8,4,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,5,6,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,1,3,6,2,5,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,3,8,4,7,2,5,6]=>[1,6,8,4,7,2,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,1,4,7,2,5,8]=>[6,7,3,4,5,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,6,1,2,5,7,3,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,4,8,2,5,7,3,6]=>[1,7,8,4,5,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,2,4,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,1,5,4,6,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,2,1,6,3,4,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,8,3,5,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,1,4,2,3,6,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,5,1,4,2,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,4,5,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,5,8,4,3,2,7,6]=>[1,6,8,5,4,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,6,1,4,3,2,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[2,6,4,8,3,7,1,5]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,4,6,8,3,7,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,8,5,3,1,6,7]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[2,5,8,1,4,7,6,3]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,5,8,4,7,6,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,6,2,4,7,3,8,5]=>[1,8,3,6,5,4,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,6,2,1,4,7,8,3]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,6,2,5,3,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,7,5,1,3,6,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,3,6,2,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,7,3,6,1,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,3,6,7,2,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,1,7,5,2,4,8,3]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,3,1,2,4,5,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,4,7,2,5,3,8,6]=>[1,6,8,4,5,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,7,8,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,1,8,4,2,5,7]=>[6,7,3,8,5,1,2,4]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[1,6,7,5,8,2,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,6,7,8,1,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,5,7,8,2,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,2,7,6,1,4,3,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[2,5,7,6,8,1,3,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,7,5,6,8,4,1,3]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,1,6,8,4,5,3,7]=>[2,1,7,8,6,5,3,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,7,1,8,5,3,4,6]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,7,6,8,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,8,5,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,2,8,1,6,3,7,5]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[3,1,8,5,4,6,7,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,8,4,5,6,1,7]=>[7,2,8,4,5,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,4,2,8,6,1,7,5]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[3,4,7,1,5,2,6,8]=>[6,4,7,2,5,1,3,8]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[4,3,7,8,1,2,6,5]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[1,7,3,8,5,2,6,4]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,8,3,6,2,5,7]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,7,8,6,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,6,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,5,8,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,4,3,8,2,5,7]=>[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,3,4,8,2,6,5]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,6,5,4,1,2,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[2,4,5,1,7,8,6,3]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,6,3,4,5,8,1,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[2,6,4,1,8,3,7,5]=>[4,8,6,1,7,3,5,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[7,3,6,4,8,5,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,1,4,8,3,5,6]=>[8,3,2,6,7,4,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,1,6,5,3,8,4,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,5,6,3,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,5,2,7,1,8,4,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,2,7,3,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,6,7,4,2,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,6,4,1,8,3,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,7,1,5,2,8,3,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,7,5,2,4,8,3,6]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,5,2,8,3,4,7]=>[7,2,6,4,8,3,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,7,5,3,8,4,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,6,5,4,2,3,8,7]=>[1,6,5,4,3,2,8,7]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,5,3,4,2,8,6]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,1,5,3,2,8,4]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,5,6,4,1,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,7,5,4,3,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,2,4,3,1,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,6,1,2,5,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,1,4,2,5,3,6,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,8,1,4,2,5,7,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,6,4,2,5,7,3,8]=>[1,7,5,4,3,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,3,7,5,4,2,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,1,3,7,5,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,3,5,6,4,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,3,1,6,4,5,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,4,2,6,5,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,6,3,1,5,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,2,4,1,5,3,6,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[7,2,3,5,4,1,6,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,8,1,2,3,4,7,5]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,5,7,2,3,8,6,4]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,8,2,3,6,7,4]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,8,2,3,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,2,8,1,3,7,4,5]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,8,2,3,5,4,7,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,2,4,1,5,7,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,8,3,1,2,4,7,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,6,3,5,7,1,4,8]=>[6,7,3,4,5,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,5,1,7,8,3,6,4]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,5,3,6,8,4,7,1]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,1,4,7,8,5,6,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,7,6,8,5,1,3]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,5,3,7,6,1,8,4]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,5,7,8,1,4,6,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[3,5,7,4,1,6,2,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[5,3,4,1,8,6,7,2]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,2,8,4,6,1,7,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[5,2,1,8,6,3,7,4]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,2,8,6,5,3,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,2,8,5,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,4,2,7,5,8,6,3]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,8,6,7,5,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,3,8,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,4,7,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,4,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,8,3,1,7,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,2,8,7,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,8,7,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,3,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,3,8,6,7,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,5,3,7,8,6,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,6,4,2,8,3]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,7,4,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,8,1,2,7,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,5,1,2,3,7,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,5,2,4,3,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,3,1,2,7,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,1,2,7,6,3,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[4,5,1,2,6,8,7,3]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,5,6,1,8,4,7,2]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[3,5,7,1,2,8,6,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,6,2,7,5,1,4,8]=>[6,7,3,5,4,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,2,6,1,7,3,5,8]=>[6,4,7,2,5,1,3,8]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[4,5,3,1,7,6,2,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[4,2,5,7,1,6,3,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,5,2,7,8,1,6,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,1,4,7,5,6,2,8]=>[7,2,3,6,5,4,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,4,6,5,8,7,1,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,1,4,5,8,6,7,2]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,4,6,8,5,2,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[3,5,6,2,8,4,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,2,5,6,1,8,7,3]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,5,3,1,6,8,7,2]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,1,7,5,8,6,4,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,7,5,3,8,6,4]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,7,3,8,6,5]=>[5,2,3,8,1,7,6,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[6,4,1,7,5,2,3,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,1,3,7,5,2,4,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,1,2,6,8,5,4,7]=>[3,2,1,7,8,6,4,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,7,1,2,5,4,8,6]=>[4,8,3,1,6,5,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,4,1,7,8,6,5,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,4,7,5,1,8,6,2]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[2,7,4,1,5,8,6,3]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,3,7,1,5,8,6,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[5,2,8,1,3,7,4,6]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[2,1,6,8,3,4,7,5]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,6,8,3,1,5,7,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,8,6,4,1,5,7,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[3,6,4,8,5,1,7,2]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[6,3,7,4,5,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,6,3,7,5,8,1,4]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,2,1,7,8,3,4,6]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[4,7,2,3,6,8,1,5]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[5,2,7,3,6,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,4,6,2,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,3,4,6,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,3,8,4,6,1,7,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,5,2,4,1,6,7,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,2,3,5,1,6,7,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,2,8,3,6,7,1,5]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[2,4,8,1,7,3,5,6]=>[4,6,8,1,7,2,5,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[8,4,1,3,6,2,5,7]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,8,3,1,7,2,5,6]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[5,2,8,4,7,1,6,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[5,8,4,7,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,8,3,1,7,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,8,2,7,1,5,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,3,1,8,2,4,7,5]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,3,8,1,2,6,4,7]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[5,7,4,1,6,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,5,4,1,2,6,3,7]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,1,8,4,2,7,3,6]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,6,2,8,5,3,7,4]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,5,3,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,5,1,2,6,3,7]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,3,7,1,2,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,6,3,7,2,8,4,5]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,2,7,8,5,1,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,5,7,8,3,1,6,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,7,2,5,8,1,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,3,4,6,2,5,7]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,8,2,4,6,7,1,5]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,5,6,8,2,7,1,4]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[2,4,5,6,8,1,7,3]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,8,3,5,6,1,7,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,2,3,7,8,1,4]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,8,7,3,4,1,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,8,7,3,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,4,7,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,4,7,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,8,7,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,8,7,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,8,7,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,8,7,6,1,2,5]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,8,3,7,5,1,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,3,4,6,5,1,2,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,4,7,5,1,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,4,8,7,6,1,2,5]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[3,5,8,7,6,1,2,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,5,8,7,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,8,7,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,8,7,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,8,2,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,5,8,1,7,6,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,5,8,1,7,6,4,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,5,8,7,1,6,3,4]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,4,8,7,1,6,3,5]=>[5,7,8,6,1,4,2,3]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,8,4,7,1,5,3,6]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[8,2,4,6,1,5,3,7]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[8,1,4,6,2,5,3,7]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,4,7,2,5,3,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,8,7,2,6,3,5]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,7,2,6,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,2,7,6,4,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,8,3,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,4,2,8,7,6,5,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,2,7,6,4,5]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,3,2,6,5,4,7]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,3,1,6,5,4,7]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,8,3,1,7,5,4,6]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,3,8,1,7,6,4,5]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,4,1,8,7,6,5,2]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,3,1,8,7,6,5,2]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,2,1,8,7,6,5,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,8,2,1,7,5,4,6]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[8,3,2,1,6,5,4,7]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,4,2,6,1,5,3,7]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,2,8,7,1,6,3,5]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[5,2,8,7,1,6,3,4]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[5,2,8,1,7,6,4,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[5,3,8,1,7,6,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,8,2,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,3,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,3,1,7,5,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,2,1,7,5,4,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,8,2,7,1,5,3,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,8,7,2,1,4,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,6,1,2,4,3,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,7,1,2,4,3,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,8,1,2,7,5,4,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,2,3,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,2,8,3,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,1,8,3,7,6,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,8,7,2,6,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,8,7,2,6,3,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,8,1,7,2,5,3,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[8,4,1,6,2,5,3,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,1,2,6,5,4,7]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,8,1,2,7,5,4,6]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,1,8,2,7,6,4,5]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,1,2,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[4,1,3,8,7,6,5,2]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,4,8,7,6,5,2]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,1,8,3,7,6,4,5]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,8,1,3,7,5,4,6]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[8,2,1,3,6,5,4,7]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,1,2,3,6,5,4,7]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,2,3,7,5,4,6]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,3,7,6,4,5]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,3,6,8,2,5,7]=>[1,6,3,7,8,2,4,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,6,2,5,8,4,7]=>[4,2,7,1,5,8,3,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,5,1,8,2,4,7,6]=>[5,6,3,8,1,2,7,4]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,4,2,6,5,8,3,7]=>[1,7,3,5,4,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,6,5,8,2,4,7]=>[6,2,7,4,8,1,3,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,6,4,2,5,8,3,7]=>[1,7,5,4,3,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,6,4,8,3,7]=>[1,7,3,5,4,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,5,4,8,3,7]=>[1,2,7,5,4,8,3,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,4,7,3,8,6]=>[1,2,6,4,8,3,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,6,3,8,7,5]=>[5,2,3,8,1,7,6,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[7,1,5,4,2,8,3,6]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,4,7,5,2,8,3,6]=>[1,7,8,5,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,3,5,2,8,4,6]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,5,1,8,3,4,6]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[1,4,5,2,8,7,3,6]=>[1,7,4,3,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,8,3,7,6,5]=>[1,5,3,8,2,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,3,8,7,6,4]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,6,5,3,7,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,8,6,3,7,4]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,4,2,8,7,3,5]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,2,1,8,7,3,4,5]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,6,2,1,8,3,4,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,3,1,6,2,8,4,5]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,7,6,4,2,8,3,5]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,2,6,3,8,4]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,2,7,5,3,8,4]=>[1,8,3,6,5,4,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,6,5,3,8,4]=>[1,2,8,6,5,4,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,5,3,8,7,4]=>[1,2,8,5,4,7,6,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,6,3,8,7,4]=>[1,8,3,5,4,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,7,6,3,8,4]=>[1,8,3,6,5,4,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,5,2,7,3,8,4]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,4,2,8,3,6]=>[1,7,8,5,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,8,6,3,7,5]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,1,8,6,2,4,7,5]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,3,7,1,8,2,5,6]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[8,3,1,6,2,4,7,5]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,1,8,3,2,4,6,5]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,7,3,2,4,6,5]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,8,7,3,6,5]=>[1,6,3,8,7,2,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,5,4,2,7,3,6]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,4,8,5,2,7,3,6]=>[1,7,8,5,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,5,3,1,7,2,4,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,2,1,7,3,4,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,8,6,4,2,7,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,2,6,3,7,4]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,7,3,8,6,4]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,5,3,7,6,4]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,3,8,7,5,4]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,6,3,8,5,4]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,2,7,3,8,5,4]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,8,5,3,6,4]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,2,8,6,3,5]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,8,3,2,6,4,5]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,1,8,6,3,4,5]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,8,7,3,2,6,4,5]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,7,5,3,6,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,6,3,7,5,4]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,3,8,6,5,4]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,7,3,6,5,8,2]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,8,7,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,6,3,4,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,8,6,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,1,6,2,4,3,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,4,1,5,2,7,3,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[8,1,4,5,3,7,6,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,4,5,3,8,7,2]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,4,5,3,7,8,2]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,7,8,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,4,8,3,5,7,2]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,6,3,4,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,4,5,3,8,6,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,4,5,3,6,8,2]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,5,3,6,7,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,1,5,2,6,3,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,3,5,7,2,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,3,5,8,2,1,7,4]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[6,3,5,7,2,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,4,5,7,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,5,8,3,7,2,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,8,7,6,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,8,6,3,1,7,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,4,1,8,2,3,7,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,8,1,6,2,4,3,7]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[8,4,1,5,2,6,3,7]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,3,5,8,2,1,4,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[2,3,4,1,8,6,5,7]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[8,3,5,6,2,1,4,7]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,3,8,6,1,5,7,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,8,6,7,1,3,5,4]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[8,3,5,7,2,1,6,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,3,8,5,6,1,7,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[7,4,5,6,3,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,4,5,6,3,1,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,5,6,2,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,3,5,8,2,1,6,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,3,5,6,2,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[2,7,6,8,1,3,5,4]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,7,6,5,8,3,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[8,7,5,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,4,1,8,5,7,3]=>[4,8,6,1,7,3,5,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,6,1,3,8,5,7,4]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,7,6,8,4,3,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,7,6,1,8,3,4,5]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,7,6,1,4,3,5,8]=>[4,7,6,1,5,3,2,8]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[7,3,5,1,2,8,4,6]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,4,1,5,2,3,7,6]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,8,1,6,3,4,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,4,1,8,3,2,7,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,3,8,6,4,1,7,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,8,6,7,4,3,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,3,5,7,2,4,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,3,4,1,8,7,5,6]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,8,6,1,7,3,4,5]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,3,8,1,6,4,7,5]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,8,1,4,5,7,6]=>[4,2,8,1,5,6,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,8,6,1,4,3,5,7]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>[2,1,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>[1,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[9,1,2,3,4,5,6,7,10,8]=>[10,2,3,4,5,6,7,8,9,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[1,8,2,3,4,5,6,9,7]=>[1,9,3,4,5,6,7,8,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,9,3,4,5,6,7,8]=>[2,1,9,4,5,6,7,8,3]=>[2,1,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,1,3,4,5,6,7,9]=>[3,8,1,4,5,6,7,2,9]=>[3,9,1,8,7,6,5,4,2]=>[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]
[2,10,1,3,4,5,6,7,8,9]=>[3,10,1,4,5,6,7,8,9,2]=>[3,10,1,9,8,7,6,5,4,2]=>[[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[8,4,3,6,5,1,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,6,3,4,1,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,5,4,3,1,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,6,5,4,2,3,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,6,5,2,7,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,5,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,4,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,4,2,1,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,2,4,1,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,2,6,5,1,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,2,8,6,5,1,7,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,2,1,7,6,4,5,8]=>[3,2,1,7,6,5,4,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[4,1,3,7,6,2,5,8]=>[6,2,3,7,5,1,4,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,1,7,3,6,2,4,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,1,7,5,3,2,4,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,1,6,5,2,4,3,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,1,6,5,2,3,7,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,7,6,3,4,5,8]=>[1,2,7,6,5,4,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,3,7,4,5,6]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,7,2,6,3,5,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,2,6,4,3,5]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,8,2,4,7,3,5]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,8,3,2,7,4,6]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,1,3,8,2,7,5,6]=>[5,2,3,8,1,7,6,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,2,1,8,4,7,5,6]=>[3,2,1,8,5,7,6,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,8,7,1,6,5,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,8,2,7,1,6,5,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,8,7,2,1,6,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,7,1,3,5,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,6,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,8,7,2,6,5,3,4]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,2,5,6,3,4]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,7,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,8,1,4,3,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,8,3,2,1,7,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,5,8,3,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,8,4,2,7,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,4,3,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,4,3,8,1,5,6,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,4,3,1,5,2,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[7,4,3,1,2,6,5,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[8,4,3,1,2,5,7,6]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[8,5,1,4,2,3,7,6]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,5,1,4,2,6,3,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,5,1,4,3,2,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,6,1,3,4,2,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,6,2,1,5,3,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[3,2,6,1,5,4,7,8]=>[4,2,6,1,5,3,7,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,7,1,4,6,5,8]=>[4,2,7,1,5,6,3,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[5,7,1,3,2,6,4,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,7,1,2,4,5,3,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,6,1,2,5,4,3,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,6,1,2,5,3,7,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,1,2,3,6,5,4]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,1,2,3,5,6,4]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,1,2,4,3,7,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,1,3,2,4,7,6]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,8,2,1,3,5,7,6]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,2,8,1,4,5,7,6]=>[4,2,8,1,5,6,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,1,3,2,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[5,1,2,4,3,6,7,8]=>[5,2,3,4,1,6,7,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[6,1,2,3,5,4,7,8]=>[6,2,3,4,5,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[7,1,2,3,4,6,5,8]=>[7,2,3,4,5,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,1,2,3,4,5,7,6]=>[8,2,3,4,5,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,7,3,8,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,4,5,1,8,3,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,4,7,6,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,7,8,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,4,5,7,1,2,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,4,8,6,7,1,2,5]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,5,6,7,1,8,3,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,5,6,2,7,4,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[3,5,6,1,7,8,4,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,5,6,1,8,7,4,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,5,6,8,1,7,3,4]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[8,2,4,5,1,6,3,7]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,4,8,6,2,3,7,5]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,8,2,3,7,4]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,6,3,4,7,8,1]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[1,4,2,6,8,5,7,3]=>[1,8,3,6,7,4,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,3,2,5,4,6,7]=>[8,2,4,3,6,5,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,3,1,5,6,4,7]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,8,3,1,5,7,4,6]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,4,1,6,8,7,5,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,4,1,6,7,8,5,2]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,3,1,7,6,8,5,2]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[5,2,7,8,1,6,3,4]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[5,3,7,2,6,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,7,3,1,5,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,7,2,1,8,5,4,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,7,2,8,1,5,3,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,7,8,2,1,4,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,1,2,8,4,5,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,1,3,4,8,5,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,2,7,3,4,6,8,1]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,1,7,3,4,8,6,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,7,8,2,3,6,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,8,7,2,3,6,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,8,1,2,7,4,5,6]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[4,1,3,7,5,8,6,2]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,4,5,7,8,6,2]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,1,8,3,4,7,6,5]=>[2,1,8,4,5,7,6,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,8,2,3,4,5,7,6]=>[1,8,3,4,5,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,2,1,6,5,8,7,3]=>[8,3,2,5,4,7,6,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[5,2,6,1,4,8,7,3]=>[8,4,5,2,3,7,6,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[5,2,6,4,1,8,7,3]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,2,7,4,8,1,6,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[5,2,7,4,8,6,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,2,3,8,6,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,2,3,8,1,6,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,2,3,1,8,7,4]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,6,2,1,3,8,7,4]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,1,6,4,2,8,7,3]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,1,3,2,8,7,4]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,6,3,1,2,8,7,4]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,6,3,2,1,8,7,4]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,7,3,2,8,1,6,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,3,2,8,6,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,3,8,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,3,8,1,2,5,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,3,1,8,2,6,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,1,3,8,2,6,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,1,7,4,8,2,6,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,5,7,4,8,3,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,4,8,6,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,7,4,8,6,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,1,3,8,6,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,7,3,1,8,6,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,3,8,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,3,8,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,8,3,1,4,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,1,8,3,5,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,1,7,8,4,5,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,7,8,4,5,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,8,4,3,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,7,8,4,2,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,7,1,8,3,2,5,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,7,2,1,8,3,6,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,7,2,8,1,3,5,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,7,2,8,3,1,5,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,2,8,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,7,8,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,7,8,4,1,5,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,2,7,8,1,4,5,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[5,2,7,1,8,4,6,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,2,1,7,8,5,6,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,1,2,7,8,6,5,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,2,7,8,1,5,4,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[6,2,7,8,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,2,7,8,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,2,8,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,2,1,8,6,3,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,7,1,2,8,6,3,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,1,7,2,8,6,4,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,5,7,3,8,6,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,8,3,5,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,7,8,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,7,1,8,2,5,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,8,2,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,8,2,4,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,1,8,5,2,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,1,7,8,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,7,8,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,7,8,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,7,1,8,5,3,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,8,4,1,3,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,8,5,2,7,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,2,8,4,7,3,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,3,4,5,8,7,2,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,8,4,7,5,2,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,8,1,4,7,2,3,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,6,1,4,8,7,3,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,4,8,5,7,1,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,1,4,8,6,3,7,2]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,4,7,1,8,6,5,2]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,3,8,4,2,7,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,8,7,1,4,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,3,7,1,6,8,2,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,3,8,5,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,1,7,6,2,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,6,1,2,7,8,5,3]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,4,2,8,7,5,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,3,7,5,2,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,5,2,7,4,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,1,4,8,3,2,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[7,8,3,5,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,1,4,6,7,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,5,8,4,3,7,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,7,4,2,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,7,1,6,2,4,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,6,7,1,4,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,8,7,4,1,2,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,3,8,7,1,5,6,2]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[8,3,6,1,2,5,7,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,6,1,8,7,3,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,2,7,3,6,8,1]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,5,3,6,4,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,4,1,5,3,8,2,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[8,5,2,6,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,6,3,4,7,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,6,3,5,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,2,7,4,3,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,7,3,6,4,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,7,6,4,5,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,7,6,5,3,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,5,4,3,1,8,2,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[8,6,5,4,2,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,4,1,7,2,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,4,1,8,3,2,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,6,5,2,8,3,4,7]=>[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,4,2,1,8,3,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,6,5,3,4,8,2,7]=>[1,7,5,4,3,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,6,3,1,8,2,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,5,8,4,2,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,2,6,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,6,2,5,7,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,5,3,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,3,1,7,2,5,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,8,6,3,7,5,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,5,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,1,6,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,1,6,3,2,5,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,8,1,7,3,5,6,4]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,8,6,1,7,4,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,1,3,7,2,6,5]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,2,8,5,7,3,6,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[5,1,7,6,8,3,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,7,1,5,8,4,2,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[6,7,3,1,8,4,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,7,3,8,4,5,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,8,5,3,4,6]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,1,8,4,3,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,1,7,4,2,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,2,7,3,4,6,5]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,2,8,3,5,4,6]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,6,1,8,4,3,5]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,2,6,1,7,3,5,4]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,3,1,4,7,5,6,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,3,1,5,8,4,2,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,2,7,1,8,3,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,4,3,1,6,8,2,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[4,7,5,6,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,4,8,2,7,3,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,5,2,8,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,1,8,7,4,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,4,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,8,3,7,6,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,4,8,1,7,2,6,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,5,8,3,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,8,2,4,7,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,3,8,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,6,8,2,7,3,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,2,6,8,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,2,8,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,8,1,7,2,5,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,3,8,7,4,5,6,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,8,6,4,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,8,7,5,6,3,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,2,7,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,7,6,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,6,5,3,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,8,7,6,3,4,5]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,7,4,6,2,5]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,3,7,6,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,6,8,7,4,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,8,4,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,7,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,6,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,7,6,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,7,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,6,7,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,6,7,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,6,7,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,6,7,4,5,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,8,6,7,4,5,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,7,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,8,5,7,4,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,5,7,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,3,6,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,3,7,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,3,7,4,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,4,8,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,3,8,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,2,8,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,1,8,5,6,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,7,1,8,5,6,2,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,7,2,8,5,6,1,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,7,3,8,5,6,1,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,7,4,8,5,6,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,8,2,7,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,2,7,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,2,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,1,6,4,5,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,1,7,4,5,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,1,7,4,6,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,7,4,8,5,6,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,8,5,6,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,5,6,1,7,3,4]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,8,5,6,2,7,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,8,4,6,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,8,1,7,3,6,2,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,8,1,7,3,6,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,1,7,3,5,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,2,6,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,2,7,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,2,7,3,6,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,2,7,3,6,1,5]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[2,7,3,8,4,6,1,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,7,2,8,4,6,1,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,7,1,8,4,6,2,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[1,8,4,7,3,6,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,4,7,3,6,1,5]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[3,8,4,7,2,6,1,5]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[4,8,5,7,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,5,7,2,6,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,8,5,7,3,6,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,8,5,7,3,6,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,6,7,3,5,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,6,7,3,5,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,8,6,7,2,5,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,8,6,7,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,7,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,7,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,7,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,6,7,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,6,7,1,5,2,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,5,2,8,6,7,3,4]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,1,8,6,7,3,4]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,6,1,8,5,7,3,4]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,6,2,8,5,7,3,4]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,8,5,7,1,6,2,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,8,4,7,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,4,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,3,6,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,3,7,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,3,7,1,6,2,5]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[3,8,4,7,1,6,2,5]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,6,2,8,4,7,3,5]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,1,8,4,7,3,5]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,7,2,6,1,8,4,5]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,7,1,6,2,8,4,5]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,8,1,6,2,7,3,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,8,1,6,2,7,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,1,5,2,6,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,2,5,1,6,3,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,8,2,5,1,7,3,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,8,2,6,1,7,3,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,8,2,6,1,7,3,5]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,7,3,6,2,8,4,5]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,3,6,1,8,4,5]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,9,8,7]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,5,7,8,9,6]=>[1,2,3,4,5,9,7,8,6]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,6,7,8,9,5]=>[1,2,3,4,9,6,7,8,5]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,5,6,7,8,9,4]=>[1,2,3,9,5,6,7,8,4]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,4,5,6,7,8,9,3]=>[1,2,9,4,5,6,7,8,3]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,3,4,5,6,7,8,9,2]=>[1,9,3,4,5,6,7,8,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,4,5,6,9,8,7]=>[1,2,3,4,5,6,9,8,7]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,5,6,7,9,10,8]=>[1,2,3,4,5,6,7,10,9,8]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,4,5,8,7,9,6]=>[1,2,3,4,5,9,7,8,6]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,5,6,8,9,10,7]=>[1,2,3,4,5,6,10,8,9,7]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,4,7,6,8,9,5]=>[1,2,3,4,9,6,7,8,5]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,5,7,8,9,10,6]=>[1,2,3,4,5,10,7,8,9,6]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,6,5,7,8,9,4]=>[1,2,3,9,5,6,7,8,4]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,6,7,8,9,10,5]=>[1,2,3,4,10,6,7,8,9,5]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,5,4,6,7,8,9,3]=>[1,2,9,4,5,6,7,8,3]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,5,6,7,8,9,10,4]=>[1,2,3,10,5,6,7,8,9,4]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,4,3,5,6,7,8,9,2]=>[1,9,3,4,5,6,7,8,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,4,5,6,7,8,9,10,3]=>[1,2,10,4,5,6,7,8,9,3]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[3,2,4,5,6,7,8,9,1]=>[9,2,3,4,5,6,7,8,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[1,3,4,5,6,7,8,9,10,2]=>[1,10,3,4,5,6,7,8,9,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[6,7,4,8,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,4,5,2,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,4,6,2,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,7,4,6,3,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,4,8,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,4,5,3,7,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,4,6,3,7,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,4,8,3,7,1,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,6,3,7,2,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,6,3,7,2,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,3,8,2,7,1,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,6,4,8,2,7,1,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,8,4,6,2,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,4,5,2,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,4,5,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,4,5,2,3,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,8,4,6,2,3,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,6,4,8,2,3,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[5,6,3,8,2,4,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[5,6,3,4,2,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,6,3,5,2,7,1,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,6,3,5,2,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,6,3,8,2,5,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[4,8,3,6,2,5,1,7]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[5,8,3,6,2,4,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,8,3,5,2,4,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[7,8,3,5,2,4,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,3,5,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,3,6,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,3,6,2,7,1,5]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[4,6,3,8,2,7,1,5]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[4,6,3,7,2,8,1,5]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[4,7,3,6,2,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,7,3,6,2,8,1,5]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[4,7,3,8,2,6,1,5]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[5,7,4,8,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,3,6,2,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,3,6,2,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,3,5,2,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,3,5,2,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,7,4,8,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,5,8,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,7,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,4,8,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,3,8,2,4,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,3,4,2,8,1,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,3,4,2,6,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,7,3,4,2,8,1,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[5,7,4,8,2,3,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,8,4,7,2,3,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,8,4,7,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,4,6,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,3,6,2,4,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,3,7,2,4,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,3,7,2,4,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,8,3,7,2,5,1,6]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[4,7,3,8,2,5,1,6]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[4,7,3,5,2,8,1,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[4,7,3,5,2,6,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,5,3,7,2,6,1,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,5,3,7,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,5,3,8,2,7,1,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,8,3,5,2,7,1,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[5,8,3,4,2,7,1,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[6,8,3,4,2,7,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,3,4,2,6,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,3,4,2,5,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,8,3,4,2,6,1,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[4,8,3,5,2,6,1,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[4,5,3,8,2,6,1,7]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,5,3,6,2,8,1,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,7,5,2,1,8,3,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[4,8,5,2,1,7,6,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,6,5,2,1,3,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,6,4,2,3,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,4,5,3,1,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,4,6,1,3,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,6,8,1,7,3,2,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,7,8,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,8,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,4,8,1,3,7,6,2]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,4,5,3,1,7,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,4,7,1,3,8,2,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[6,4,8,1,7,5,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,8,7,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,6,3,7,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,2,8,7,4,1,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,1,6,8,7,4,3,5]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,7,8,6,4,5,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[7,3,2,8,6,4,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,8,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,6,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,6,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,7,5,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,4,2,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,8,4,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,2,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,6,2,7,3,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,6,1,8,7,4,2,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,7,1,8,6,4,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,1,6,7,5,2,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,7,1,6,8,2,5,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,7,6,2,8,1,3,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,7,4,2,8,1,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,4,2,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,8,6,7,5,3,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,3,2,6,7,5,1,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,4,3,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,7,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,5,8,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,5,8,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,5,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,4,3,8,1,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,2,6,8,1,5,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,1,7,6,8,3,5,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[7,5,6,8,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,7,8,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,3,7,4,6,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,2,8,7,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,2,5,4,7,3,8]=>[1,7,3,5,4,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,2,7,5,4,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,1,3,5,4,7,6,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,5,4,3,8,7,2]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,8,3,4,5,7,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,5,3,4,8,6,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,4,3,5,6,8,2]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,3,4,5,6,7,2]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,2,4,5,6,3,8]=>[1,7,3,6,5,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,2,7,5,1,8,4]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,4,7,2,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,8,2,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,2,1,4,3,7,6]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,5,2,8,4,1,3,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[5,6,2,1,4,8,3,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[3,6,1,8,5,2,4,7]=>[6,7,3,8,5,1,2,4]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[1,2,6,3,5,4,7,8]=>[1,2,6,4,5,3,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,4,1,2,8,6,5,7]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,3,1,2,6,8,5,7]=>[4,3,2,1,7,8,5,6]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[5,8,1,6,3,2,4,7]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[6,3,8,5,2,1,4,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[8,3,1,5,2,4,7,6]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,8,2,6,1,5,7,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,8,6,7,2,1,5,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[8,5,6,4,2,1,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,5,8,3,1,6,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,7,5,6,3,2,4,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,2,3,8,5,7,4]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,1,3,8,6,4,5]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[5,2,7,3,1,8,4,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[5,8,2,4,1,3,7,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[8,7,2,6,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,1,6,3,2,7,5]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,1,8,6,4,2,7,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,1,6,7,4,3,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,5,8,7,2,4,1,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,2,1,3,7,8,5,6]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[2,4,1,3,8,7,5,6]=>[3,4,1,2,8,7,6,5]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,5,8,3,1,7,4,6]=>[5,7,8,4,1,6,2,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[8,6,1,3,7,2,4,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,8,1,3,6,4,7,5]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[6,8,2,3,4,1,5,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,1,8,3,2,4,6,7]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,9,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,7,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,7,6,9,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,7,6,5,9,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,7,6,5,4,9,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[8,7,6,5,4,3,9,2,1]=>[9,8,6,5,4,3,7,2,1]=>[9,8,6,5,4,3,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[8,7,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[9,10,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,6,7,9,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,7,5,6,9,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,6,10,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,7,6,4,5,9,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[9,8,7,6,5,10,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,7,6,5,3,4,9,2,1]=>[9,8,6,5,4,3,7,2,1]=>[9,8,6,5,4,3,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[9,8,7,6,5,4,10,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[8,7,6,5,4,2,3,9,1]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[9,8,7,6,5,4,3,10,2,1]=>[10,9,7,6,5,4,3,8,2,1]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[8,7,6,5,4,3,1,2,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[9,8,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,6,2,4,8,5,3,7]=>[1,7,3,6,8,4,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,2,4,7,5,3,8]=>[1,7,3,6,5,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,8,5,2,4,6]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,2,5,7,8,6,1,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,3,1,8,5,6,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,2,5,1,7,3,4,6]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,2,1,8,3,4,7,5]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,2,8,3,5,1,7,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,2,4,8,5,7,1,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,3,6,4,7,5,8,2]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,2,4,7,5,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,2,1,3,7,8,4,5]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,8,2,1,4,3,5,6]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,6,4,2,3,1,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,7,2,3,1,6,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,4,2,6,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,7,5,3,4,6,8,2]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,5,4,6,7,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,2,6,3,1,8,7,4]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[8,2,6,4,3,1,7,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,2,7,4,1,3,5,6]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,2,8,4,3,5,6,7]=>[1,2,8,5,4,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,2,3,5,6,8]=>[1,7,5,4,3,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,4,1,3,2,5,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,8,7,4,3,2,5,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,3,8,2,4,7,5]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,3,8,1,2,7,4,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[5,1,8,3,2,6,4,7]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,7,3,1,2,6,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,7,5,4,2,6,3,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,2,4,6,3,7]=>[1,7,8,4,5,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,4,2,7,3,6]=>[1,7,8,5,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,2,8,3,7,5]=>[1,6,8,4,7,2,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,3,1,6,7,2,4,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,3,6,1,2,8,4,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,7,4,5,3,8,6,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,4,1,2,5,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,3,1,4,2,7,5,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,8,3,2,4,5,6,7]=>[1,8,4,3,5,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,3,2,4,1,7,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,3,2,6,7,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,2,6,8,1,7,3]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,2,5,6,7,8,1,3]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,2,3,6,7,1,8,4]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,2,3,4,1,7,8,5]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,2,3,1,4,5,8,6]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,6,1,4,3,2,5,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,1,6,5,2,4,7]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,7,5,1,8,2,4,6]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[4,1,5,2,8,7,3,6]=>[7,2,4,3,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,1,2,4,6,5,3,7]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,5,4,6,3,7]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,6,5,1,3,4,7]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[8,3,1,6,2,5,4,7]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,1,2,6,4,5,3,7]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,5,6,4,3,7]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,6,5,4,3,7]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,5,4,2,8,3,6]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,4,8,2,7,3,6]=>[7,2,5,8,3,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,4,6,8,2,7,3,5]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,6,2,8,3,5]=>[1,7,8,5,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,4,7,2,8,3,6]=>[7,2,5,8,3,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,7,4,5,2,8,3,6]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,5,1,2,8,4,6]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[5,7,2,8,1,3,4,6]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[5,2,8,7,1,3,4,6]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[4,1,5,8,2,7,3,6]=>[7,2,5,8,3,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,4,6,2,8,7,3,5]=>[1,7,8,4,6,5,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,6,4,8,7,5]=>[3,2,1,8,5,7,6,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,1,7,6,3,4,8,5]=>[2,1,8,6,5,4,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,1,2,7,4,6,8,5]=>[3,2,1,8,5,6,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,4,7,2,6,8,3,5]=>[1,7,8,4,5,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,6,8,5,7,4]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,4,2,7,8,3,6]=>[7,2,4,3,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,4,2,7,6,8,3,5]=>[1,7,3,8,5,6,2,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,8,4,6,7,5]=>[3,2,1,8,5,7,6,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,1,2,7,6,4,8,5]=>[3,2,1,8,6,5,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[5,3,7,1,8,2,4,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,7,4,3,2,5,8,6]=>[1,8,5,4,3,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,8,7,2,1,3,5,6]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[1,8,7,3,4,2,5,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,7,8,2,6,4,5]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,4,2,7,8,3,6,5]=>[1,6,3,8,7,2,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,2,8,1,3,4,7,6]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[2,1,8,6,3,4,7,5]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,4,2,6,8,3,7,5]=>[1,6,3,8,7,2,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,7,8,5,6,4]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,7,5,8,6,4]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,7,3,8,6,5]=>[1,5,3,8,2,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,7,2,8,6,4,5]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,1,7,8,3,4,6,5]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,3,8,7,5,6,4]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[10,1,2,3,4,5,6,7,8,9]=>[10,2,3,4,5,6,7,8,9,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[8,1,2,3,4,5,6,9,10,7]=>[10,2,3,4,5,6,7,8,9,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[4,7,8,5,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,4,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,8,4,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,3,7,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,3,8,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,8,3,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,3,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,8,4,3,5,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,8,4,2,5,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,7,8,3,2,1,5,6]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[5,7,8,3,2,1,4,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[7,6,3,8,2,1,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,3,7,2,1,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,3,8,2,1,4,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[3,6,4,8,2,5,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[2,6,4,8,3,5,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[2,6,4,7,3,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,6,4,7,2,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,6,3,7,2,1,5,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[5,6,3,7,2,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,4,3,2,1,6,5,7]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[6,4,3,2,1,7,5,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,5,3,2,7,1,6,8]=>[6,4,3,2,7,1,5,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,5,4,2,8,6,1,7]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[6,4,3,2,1,8,5,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[7,4,3,2,1,8,5,6]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[8,4,3,2,1,7,5,6]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[8,4,3,2,1,7,6,5]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[7,4,3,2,1,8,6,5]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[6,4,3,2,1,8,7,5]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,6,3,8,2,1,7,4]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[7,5,3,2,8,1,6,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,4,2,7,6,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,4,2,8,6,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,4,2,8,7,1,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,6,5,8,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,5,7,8,3,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,4,2,7,8,1,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,5,4,2,6,7,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,3,2,6,1,7,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,3,2,6,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,6,3,7,2,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,6,3,7,2,1,8,5]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[3,6,4,7,2,8,1,5]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[2,6,4,7,3,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,5,4,2,7,8,1,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[4,5,3,2,7,1,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[7,4,3,2,1,6,8,5]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[8,4,3,2,1,6,7,5]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[8,4,3,2,1,5,7,6]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[7,4,3,2,1,5,8,6]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[6,4,3,2,1,5,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[3,5,4,2,6,8,1,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[5,6,3,4,1,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[8,5,3,7,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,4,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,4,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,7,8,5,6,3,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,8,3,7,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,3,8,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,2,6,4,8,5,1,7]=>[7,2,6,4,8,3,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,2,5,8,4,6,1,7]=>[7,2,5,8,3,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,5,2,4,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,5,2,3,7,1,6,8]=>[6,4,3,2,7,1,5,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,2,5,3,8,1,6,7]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,2,5,8,3,1,6,7]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,1,5,4,2,8,6,7]=>[5,2,4,3,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,1,5,3,8,2,6,7]=>[6,2,4,3,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,3,8,5,2,1,6,7]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[4,7,3,5,2,1,6,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[4,3,2,7,5,1,6,8]=>[6,3,2,7,5,1,4,8]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[4,6,3,2,5,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,6,7,1,3,2,5,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[4,5,1,7,3,2,6,8]=>[6,5,3,7,2,1,4,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,5,1,3,7,2,6,8]=>[6,4,3,2,7,1,5,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,5,1,4,2,7,6,8]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[2,5,1,4,3,7,8,6]=>[3,5,1,4,2,8,7,6]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[5,2,1,4,3,7,8,6]=>[5,3,2,4,1,8,7,6]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[5,3,1,4,2,7,6,8]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,3,1,7,5,2,6,8]=>[6,3,2,7,5,1,4,8]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[4,6,3,1,5,2,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,3,6,4,1,2,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,3,6,1,7,2,5,8]=>[6,4,7,2,5,1,3,8]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[6,3,4,1,2,7,5,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,2,4,1,3,7,8,5]=>[8,4,5,2,3,6,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[5,3,6,2,1,4,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,6,2,7,1,3,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,5,2,7,3,1,6,8]=>[6,5,3,7,2,1,4,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,6,7,2,3,1,5,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[3,2,6,1,4,7,5,8]=>[4,2,7,1,5,6,3,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,6,2,1,4,7,5,8]=>[4,7,3,1,5,6,2,8]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,6,7,2,4,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,5,2,7,4,6,1,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,7,2,4,8,5,1,6]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[7,3,1,4,6,8,2,5]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,2,6,1,5,7,4,8]=>[4,2,7,1,5,6,3,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,6,2,1,5,7,4,8]=>[4,7,3,1,5,6,2,8]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[6,4,2,1,5,3,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,2,1,7,5,3,6,8]=>[6,3,2,7,5,1,4,8]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[7,4,1,5,6,2,3,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,3,1,5,2,6,4,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,2,5,1,3,7,8,4]=>[8,4,5,2,3,6,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,3,5,1,2,7,4,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,4,5,1,7,2,3,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[5,2,6,4,1,3,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,6,5,1,7,2,3,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,5,2,1,4,7,8,3]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[6,5,3,1,4,7,2,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[2,3,1,8,5,4,7,6]=>[3,2,1,8,6,5,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,4,1,5,3,8,7,6]=>[3,5,1,4,2,8,7,6]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,4,5,1,2,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,4,5,1,8,2,7,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,8,4,5,3,2,7,6]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,8,5,3,1,7,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[3,4,5,8,2,1,7,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,4,5,2,8,1,7,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,5,6,2,7,1,8,4]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[3,5,6,2,7,8,1,4]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[3,4,6,2,8,7,1,5]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[3,4,6,8,2,7,1,5]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[2,4,8,6,3,7,1,5]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[1,8,4,6,3,7,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,4,6,3,7,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,4,6,8,2,7,5,1]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[3,4,6,2,8,7,5,1]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,5,6,2,7,8,4,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,5,6,2,7,4,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,5,6,7,2,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,5,6,8,7,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,8,6,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,5,6,7,3,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,6,7,3,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,8,6,7,3,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,5,6,8,7,2,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,5,6,7,2,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,4,6,1,8,7,2,5]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[2,4,1,6,8,7,3,5]=>[3,7,1,8,6,5,2,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,3,1,8,6,7,4,5]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,5,1,6,7,8,4,3]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,5,1,6,7,4,8,3]=>[3,8,1,6,5,4,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,5,6,1,7,4,2,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[3,5,6,1,7,4,8,2]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[3,4,6,1,8,7,5,2]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,4,6,8,1,7,5,2]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[2,4,8,6,1,7,5,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,8,4,6,2,7,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,6,7,2,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,8,6,7,1,4,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[3,5,6,8,7,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,6,7,8,1,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,6,7,1,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,5,6,7,1,3,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,5,6,7,3,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,5,6,8,7,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,8,6,7,4,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,8,5,6,7,4,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,6,7,4,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,8,6,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,5,3,7,1,6,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,2,4,3,7,1,6,5]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,8,2,4,3,7,1,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[4,2,5,6,1,8,3,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,2,5,6,1,7,3,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,1,5,7,3,2,4,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,1,5,8,3,2,4,7]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,8,2,4,7,1,5,6]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,6,8,2,4,7,1,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,3,5,6,7,1,8,2]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,7,1,5,6,8,2,4]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,7,1,5,8,2,4,6]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[8,3,2,4,6,1,5,7]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,3,2,4,6,1,5,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,2,5,1,7,4,6,8]=>[4,2,6,1,7,3,5,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,5,1,8,4,6,7]=>[4,2,6,1,8,3,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,5,1,7,8,4,6]=>[4,2,7,1,8,6,3,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[7,8,3,2,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,1,5,7,8,3,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,2,5,6,1,7,8,3]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,7,6,1,8,3,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,6,1,7,3,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,1,5,8,7,3,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,7,3,2,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,2,5,1,8,7,4,6]=>[4,2,7,1,8,6,3,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,5,1,6,4,7,8]=>[4,2,6,1,5,3,7,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,4,1,8,7,5,6]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,5,1,6,8,7,4]=>[4,2,8,1,5,7,6,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,8,6,5,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,6,5,1,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,5,1,7,8,4,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,2,5,1,6,7,8,4]=>[4,2,8,1,5,6,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,4,1,8,5,6,7]=>[4,2,3,1,8,6,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,4,1,7,5,6,8]=>[4,2,3,1,7,6,5,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,4,1,6,8,5,7]=>[4,2,3,1,7,8,5,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,4,1,8,5,7,6]=>[4,2,3,1,8,6,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[8,3,2,4,7,6,1,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,2,5,1,8,4,7,6]=>[4,2,6,1,8,3,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,5,1,6,7,4,8]=>[4,2,7,1,5,6,3,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[6,5,1,7,4,2,3,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,5,1,8,4,2,3,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,4,2,3,7,5,1,6]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,2,6,1,8,3,7,5]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[5,2,6,1,8,3,7,4]=>[8,4,6,2,7,3,5,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,4,6,1,7,3,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,2,6,1,8,4,7,3]=>[8,4,6,2,7,3,5,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,4,2,3,8,5,1,6]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,5,1,6,4,2,3,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,1,6,4,2,3,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,2,5,1,8,6,4,7]=>[4,2,7,1,8,6,3,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[7,3,2,4,8,6,1,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,1,5,7,3,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,2,6,1,8,5,7,3]=>[8,4,6,2,7,3,5,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,5,6,1,7,3,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,8,5,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,1,6,7,4,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,2,5,1,8,6,7,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,4,1,8,6,5,7]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,4,1,5,8,6,7]=>[4,2,3,1,5,8,7,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,5,1,7,8,6,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[7,8,5,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,5,1,7,6,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,7,5,1,8,6,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,5,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,2,5,1,8,7,6,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[6,5,7,3,1,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,6,3,7,1,8,5,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,6,3,7,5,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,2,6,1,7,5,3,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[2,5,7,4,1,6,8,3]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[5,4,7,3,6,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,4,7,8,3,1,6,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,3,7,5,1,8,6,2]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,4,3,8,5,1,7,2]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[5,8,4,3,6,1,7,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,4,8,3,6,1,7,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[5,4,3,6,7,1,8,2]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,5,4,6,1,7,3,8]=>[5,7,3,4,1,6,2,8]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,2,5,8,1,6,7,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,5,4,6,8,1,7,3]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[5,2,8,4,1,6,7,3]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,6,2,1,8,5,7,3]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[2,4,1,7,5,8,6,3]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,1,7,5,3,8,6]=>[3,6,1,8,5,2,7,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,6,4,1,8,5,3,7]=>[4,7,6,1,8,3,2,5]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[5,4,8,2,1,6,3,7]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[2,5,8,4,1,6,3,7]=>[5,7,8,4,1,6,2,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,2,5,6,1,8,4,7]=>[5,2,7,4,1,8,3,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,8,3,2,6,1,5,7]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[3,5,2,8,1,6,4,7]=>[5,7,3,8,1,6,2,4]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,2,1,6,8,5,4,7]=>[3,2,1,7,8,6,4,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,7,1,5,4,8,6]=>[4,2,8,1,6,5,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,7,1,5,8,6,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,8,2,5,1,6,7,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,8,3,2,6,7,1,5]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[4,3,8,2,6,7,1,5]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,3,2,6,7,8,1,5]=>[7,3,2,8,5,6,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[4,3,2,6,7,1,5,8]=>[6,3,2,7,5,1,4,8]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[4,3,7,2,6,8,1,5]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,3,7,8,2,6,1,5]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[2,5,7,4,8,1,6,3]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[3,2,5,7,8,1,6,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,2,5,7,1,6,4,8]=>[5,2,7,6,1,4,3,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[6,3,2,7,1,5,4,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,3,2,7,1,5,8,4]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,3,2,7,8,1,5,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,2,6,1,7,8,5,3]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,5,2,1,7,8,4,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,1,7,5,3,8,6,4]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,2,1,8,5,3,7,4]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,3,2,7,1,4,8,5]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,3,2,1,4,7,8,5]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,5,2,1,7,4,6,8]=>[4,6,3,1,7,2,5,8]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,5,2,1,7,8,4,6]=>[4,7,3,1,8,6,2,5]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[5,8,4,2,1,7,3,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[4,6,2,1,8,3,7,5]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[2,4,1,7,3,8,6,5]=>[3,5,1,8,2,7,6,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,2,7,1,4,8,6,5]=>[4,2,8,1,5,7,6,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,5,8,2,1,7,4,6]=>[5,7,8,4,1,6,2,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[4,8,3,7,2,1,5,6]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[4,3,7,2,8,1,5,6]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[4,8,3,2,7,1,5,6]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[3,5,2,8,1,7,4,6]=>[5,7,3,8,1,6,2,4]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[6,3,2,8,1,4,7,5]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,2,1,4,7,5,8,6]=>[3,2,1,4,8,6,7,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[5,3,2,1,8,4,6,7]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,8,3,2,1,5,6,7]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[8,7,6,4,5,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,9,8,7,5,6,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[9,8,7,5,6,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[8,7,5,4,6,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[8,7,4,6,5,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,9,8,6,5,7,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,9,8,5,7,6,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,10,9,8,6,7,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,11,10,9,8,7,6,5,4,3,2]=>[1,11,10,9,8,7,6,5,4,3,2]=>[1,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[6,2,3,1,5,4,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[8,4,5,2,3,1,7,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,6,7,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,5,3,4,1,7,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,2,5,3,4,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,1,5,2,4,3,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,4,5,1,3,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,1,5,3,4,2,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,3,5,1,4,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[8,3,5,2,4,1,7,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,3,7,5,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,7,2,4,1,6,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,3,5,1,4,2,7,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,1,5,3,4,2,7,6]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,5,1,3,2,7,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,1,8,4,5,3,7,6]=>[2,1,8,6,5,4,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,6,7,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,7,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,7,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,7,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,3,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,7,4,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,7,4,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,7,1,6,4,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,7,3,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,5,6,3,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,7,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,8,4,7,5,6,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,1,7,3,4,2,6,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,3,6,2,5,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,7,1,6,2,5,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,3,7,2,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,7,3,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,7,3,6,1,5,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,2,7,1,6,3,5,4]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,1,7,2,4,3,6,5]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,3,2,7,4,6,5]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,1,8,3,7,4,6,5]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,1,5,2,4,3,7,6]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,7,1,4,3,6,5]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,2,7,3,4,1,6,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,2,7,5,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,5,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,2,3,1,6,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,2,3,1,7,4,6,5]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,2,3,1,5,4,7,6]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,2,3,1,8,5,7,6]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,1,3,2,8,6,7,5]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[8,6,7,2,3,1,5,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,3,1,7,5,6,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,5,7,2,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,2,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,7,5,6,1,4,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,6,7,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,7,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,7,1,3,2,5,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,1,8,6,7,3,5,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,8,3,7,5,6,4]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,1,3,2,7,5,6,4]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,5,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,2,6,4,5,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,7,1,6,4,5,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,2,7,4,6,1,5,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,2,7,4,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,2,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,7,4,6,2,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,5,7,1,6,2,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,1,8,5,7,3,6,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,5,7,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,1,6,3,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,7,4,6,3,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,7,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,7,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,8,3,6,1,7,5]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[6,5,8,1,3,2,7,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,5,8,6,3,2,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,5,8,7,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,5,8,7,3,6,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,8,4,6,5,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,7,2,8,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,2,8,4,5,7,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,6,1,8,4,5,7,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,8,4,6,1,5,7,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[6,3,1,8,4,5,7,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,1,6,8,4,5,7,2]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,6,8,4,5,7,1]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,3,7,8,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,3,7,8,4,6,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,8,2,4,6,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,7,8,2,4,6,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,6,7,8,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,1,8,4,2,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,6,8,7,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,3,7,1,6,5,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[5,2,8,7,3,6,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,1,8,4,6,5,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,2,7,8,4,6,5,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,2,7,8,1,4,6,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,2,7,8,5,4,6,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,2,1,3,8,5,6,7]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[7,2,5,8,3,4,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,8,5,4,3,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[2,8,3,5,4,1,6,7]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,8,4,5,3,1,6,7]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[6,4,8,5,2,3,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[7,3,5,8,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,1,2,8,5,6,7]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,4,2,1,8,5,6,7]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[2,7,6,8,4,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,1,8,3,4,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,7,5,8,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,5,8,3,4,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,5,4,3,2,7]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,8,5,1,3,2,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[5,6,8,1,4,3,2,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[7,5,8,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,8,3,6,5,1,7]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[2,8,4,1,5,6,3,7]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,1,8,3,5,6,2,7]=>[7,2,8,4,5,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,6,8,4,1,3,2,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,6,8,1,5,3,2,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,6,8,4,5,3,2,7]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,8,5,4,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,1,8,5,4,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,7,3,8,4,6,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,3,8,4,6,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,8,4,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,7,4,1,6,5,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,8,5,4,3,1,6,7]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[6,5,8,4,2,3,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,1,3,2,8,5,6,7]=>[4,2,3,1,8,6,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,4,3,2,8,5,6,7]=>[1,4,3,2,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,3,2,8,5,4,6,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,4,8,2,5,3,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[2,8,4,3,5,1,6,7]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[2,8,3,4,5,1,6,7]=>[6,8,3,4,5,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[6,2,8,4,5,3,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[7,2,3,8,5,4,6,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,2,3,1,8,5,6,7]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,2,1,4,8,5,6,7]=>[3,2,1,4,8,6,7,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[5,1,3,2,4,8,6,7]=>[5,2,4,3,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,8,1,5,3,4,7,6]=>[3,8,1,6,5,4,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,2,8,4,5,3,7,6]=>[1,2,8,6,5,4,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,8,5,3,6,7]=>[1,6,3,8,5,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,4,2,5,3,6,7]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,5,3,2,4,6,7]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,8,1,5,2,4,6,7]=>[5,8,3,6,1,4,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,5,1,4,8,2,6,7]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,5,2,8,4,3,6,7]=>[1,6,3,8,5,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,5,4,3,6,7]=>[1,2,8,6,5,4,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,4,3,8,6,7]=>[1,2,5,4,3,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,8,5,3,7,6]=>[1,2,6,8,5,3,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,4,8,5,3,6]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,2,7,4,8,3,6]=>[7,2,3,8,5,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,3,5,1,4,7,2,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,8,1,5,4,7,3,6]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,2,8,5,7,4,3,6]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,8,7,5,3,6]=>[1,2,7,8,6,5,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,1,4,3,7,6,5]=>[3,8,1,5,4,7,6,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[6,1,2,8,7,4,3,5]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,1,2,8,7,3,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,4,8,1,7,2,5]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[7,6,1,4,2,8,3,5]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,6,2,8,4,3,5]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,7,2,8,4,3,5]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,7,1,4,2,8,3,5]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,3,7,1,4,8,2,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,7,8,1,5,2,4,6]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[7,1,2,8,5,3,4,6]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,2,8,4,5,3,6]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,2,8,4,3,7,5]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,1,2,8,3,7,5]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,6,1,3,2,4,8,5]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,7,1,3,2,4,8,5]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,2,7,3,5,8,4,6]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,5,8,3,4,6]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,1,3,7,2,4,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[1,2,5,8,7,3,4,6]=>[1,2,7,8,6,5,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,8,3,7,4,6]=>[1,2,7,8,5,6,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,1,7,3,5,4,6]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[8,6,1,3,2,4,7,5]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,2,8,1,7,3,6,5]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[2,8,1,7,4,3,6,5]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[7,1,2,8,4,3,6,5]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,8,4,7,5,3,6]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,7,4,5,3,6]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,1,7,5,3,4,6]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[8,3,7,1,5,2,4,6]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[3,8,6,1,4,7,2,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[8,6,1,4,2,7,3,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,6,2,7,4,3,5]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,2,8,6,4,3,5]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,1,2,8,6,3,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,7,4,8,1,6,2,5]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[3,4,8,7,1,6,2,5]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[4,2,8,1,7,6,3,5]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[2,8,1,7,6,4,3,5]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[7,8,3,4,1,5,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,3,4,1,6,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,3,4,1,7,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,3,4,1,8,2,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,3,4,1,8,2,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[5,8,3,4,1,7,2,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[5,8,3,4,1,6,2,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[6,8,3,4,1,5,2,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,7,3,4,1,5,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,7,3,4,1,6,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,6,2,8,3,4,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[5,6,2,7,3,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,6,2,8,3,5,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[4,7,3,5,1,6,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,8,3,5,1,6,2,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[4,8,3,5,1,7,2,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[4,7,3,5,1,8,2,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[5,6,2,3,1,7,4,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,6,2,4,1,8,3,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,6,2,4,1,7,3,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,6,2,5,1,7,3,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,6,2,5,1,8,3,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,5,1,8,3,7,2,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,5,1,7,3,8,2,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,6,2,7,3,8,1,5]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[5,6,2,7,3,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,2,7,4,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,3,8,4,7,1,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,6,2,8,4,7,1,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,6,2,8,3,7,1,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,6,2,8,3,7,1,5]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[4,5,1,7,3,6,2,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,5,1,8,3,6,2,7]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[10,2,1,3,4,5,6,7,8,9]=>[10,3,2,4,5,6,7,8,9,1]=>[10,3,2,9,8,7,6,5,4,1]=>[[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.]
[3,2,4,5,6,7,8,9,10,1]=>[10,2,3,4,5,6,7,8,9,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[6,5,3,2,1,4,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,6,3,5,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[8,7,3,5,2,4,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,2,4,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,2,4,5,3,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,1,4,5,2,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[8,3,7,4,5,2,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,8,4,5,7,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,4,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,7,4,3,6,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,1,7,4,3,6,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,7,3,5,1,4,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,6,8,5,7,4,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,8,3,5,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,8,4,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,5,8,4,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,3,8,1,5,6,7,2]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,8,1,3,5,6,7,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,7,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,3,6,1,4,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,3,6,1,2,7,5]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[3,8,7,4,1,6,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,8,1,2,5,6,7,4]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[8,7,1,4,2,6,3,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,3,1,2,4,7,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,1,7,4,5,2,3,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,8,7,4,5,1,3,6]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[8,7,2,4,1,6,3,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,8,3,6,2,4,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,3,2,1,4,7,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,7,3,5,2,1,4,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,3,6,2,1,7,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,4,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,8,4,5,7,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,1,8,4,5,7,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,8,3,5,1,7,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,5,8,3,6,7,4]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,8,3,6,1,2,7,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,1,8,2,5,6,7,3]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,4,8,1,5,6,7,3]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,8,2,1,5,6,7,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,4,8,2,5,6,7,1]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[5,8,1,4,7,6,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,3,1,6,2,7,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,3,8,6,1,7,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,4,1,8,5,6,7,2]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[5,7,8,9,10,1,2,3,4,6]=>[9,10,8,7,6,5,4,3,1,2]=>[9,10,8,7,6,5,4,3,1,2]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[7,8,9,10,11,12,1,2,3,4,5,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[4,5,7,6,2,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,5,7,2,6,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,5,7,3,6,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,5,7,3,6,8,4,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,4,3,7,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,2,3,5,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,2,7,3,6,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,3,4,7,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,4,7,1,6,5,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[3,1,4,7,6,8,5,2]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,3,7,6,8,5,2]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,7,3,6,8,4,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,7,1,3,5,8,4,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,7,3,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,3,7,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,4,7,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,4,7,1,6,5,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[8,1,4,7,2,6,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,3,2,7,6,5,4]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,8,3,1,7,6,5,4]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,8,2,1,7,6,5,4]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[6,7,1,2,8,5,4,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,2,3,1,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,3,2,1,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,4,1,7,6,8,5,2]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,4,2,7,8,6,5,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,4,2,7,1,6,5,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,5,7,2,1,6,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,5,7,2,8,6,4,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,7,1,8,6,4,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,5,7,1,6,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,7,4,5,8,1,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,4,7,6,8,1,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,5,7,8,1,6,4,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,5,7,8,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,5,7,1,2,6,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,1,7,2,6,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,4,8,7,2,6,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,4,8,7,6,1,5,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,3,8,7,6,1,5,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,3,7,8,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,2,8,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,2,7,8,1,6,4,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[4,2,8,7,1,6,5,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[3,2,8,1,7,6,5,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,3,8,2,7,6,5,4]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,3,1,2,7,6,5,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,2,1,3,7,6,5,4]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,2,8,3,7,6,5,4]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,8,3,7,6,5,4]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[4,1,8,7,2,6,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,7,8,2,6,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,7,1,8,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,7,1,2,6,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,1,7,2,6,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,1,2,7,6,5,4]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,8,1,3,7,6,5,4]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,8,2,3,7,6,5,4]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,2,3,7,6,5,4]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,4,5,6,7,8,9,10,2]=>[10,2,3,4,5,6,7,8,9,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[6,7,1,8,4,5,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,7,1,5,8,2,6,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,7,1,5,8,3,6,4]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,6,5,1,8,3,7,4]=>[4,8,6,1,7,3,5,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,6,5,1,8,2,7,4]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[4,6,5,1,8,7,2,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,6,4,1,8,7,2,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,1,4,5,7,6,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,5,1,8,7,2,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,4,6,1,8,7,2,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,5,6,1,8,7,2,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,5,6,1,8,2,7,4]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[2,5,6,1,8,3,7,4]=>[4,8,6,1,7,3,5,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,4,6,1,3,8,7,5]=>[4,5,8,1,2,7,6,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,4,6,1,2,8,7,5]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[4,3,6,1,2,8,7,5]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[5,3,6,1,8,2,7,4]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,3,1,5,8,2,6,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,1,3,5,7,2,6,4]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,5,7,3,6,4]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,1,5,8,3,6,4]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,2,5,1,8,3,7,4]=>[8,4,6,2,7,3,5,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,2,6,1,3,8,7,5]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[2,3,6,1,4,8,7,5]=>[4,2,8,1,5,7,6,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,2,5,3,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[6,2,4,1,3,8,7,5]=>[8,4,5,2,3,7,6,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,2,1,4,3,8,6,5]=>[8,3,2,5,4,7,6,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,1,2,4,3,7,6,5]=>[8,2,3,5,4,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,3,4,2,7,6,5]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,3,1,4,2,8,6,5]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,3,4,1,2,8,7,5]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,6,3,1,2,8,7,5]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,6,4,1,2,8,7,5]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[2,6,4,1,3,8,7,5]=>[4,8,5,1,3,7,6,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,7,1,4,3,8,6,5]=>[3,8,1,5,4,7,6,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,7,1,4,2,8,6,5]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,7,1,3,2,8,6,5]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[8,1,6,7,2,3,5,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,7,1,2,3,8,6,5]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,7,1,2,4,8,6,5]=>[4,8,3,1,5,7,6,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,6,3,1,4,8,7,5]=>[4,8,3,1,5,7,6,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,6,2,1,4,8,7,5]=>[4,8,3,1,5,7,6,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[5,6,2,1,8,3,7,4]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,5,2,1,8,3,7,4]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[8,1,5,2,7,3,6,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,2,3,7,6,5]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,1,2,3,8,6,5]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,4,2,1,3,8,7,5]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,4,2,3,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,5,2,4,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[6,3,2,1,4,8,7,5]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[7,3,1,2,4,8,6,5]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,1,2,3,4,7,6,5]=>[8,2,3,4,5,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,2,3,1,4,8,7,5]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,4,3,6,1,5,8,7]=>[5,3,2,6,1,4,8,7]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[2,4,3,6,5,8,1,7]=>[7,3,2,5,4,8,1,6]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[2,4,6,3,5,8,7,1]=>[8,4,5,2,3,7,6,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,4,6,3,5,8,1,7]=>[7,4,5,2,3,8,1,6]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[2,4,6,3,5,1,8,7]=>[6,4,5,2,3,1,8,7]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[2,4,6,3,1,5,8,7]=>[5,4,6,2,1,3,8,7]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[2,4,1,6,5,3,8,7]=>[3,6,1,5,4,2,8,7]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,6,1,5,3,8,7]=>[4,6,5,1,3,2,8,7]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,2,6,5,3,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,2,6,5,1,3,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,2,6,5,1,8,7,3]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,2,6,5,8,1,7,3]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,2,6,5,8,1,3,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,2,6,5,8,3,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[2,4,6,1,5,8,3,7]=>[4,7,5,1,3,8,2,6]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,4,1,6,5,8,3,7]=>[3,7,1,5,4,8,2,6]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,1,4,6,5,8,3,7]=>[2,1,7,5,4,8,3,6]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,1,6,5,8,7,3]=>[3,8,1,5,4,7,6,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,6,1,5,8,7,3]=>[4,8,5,1,3,7,6,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,2,6,5,3,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,2,6,5,8,3,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[2,6,4,3,8,7,1,5]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[2,6,4,3,8,7,5,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,2,6,8,5,3,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[2,4,6,8,1,5,7,3]=>[5,8,6,7,1,3,4,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,4,6,1,8,5,7,3]=>[4,8,6,1,7,3,5,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,4,1,6,8,5,7,3]=>[3,8,1,6,7,4,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,1,4,6,8,5,7,3]=>[2,1,8,6,7,4,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,4,6,8,5,3,7]=>[2,1,7,6,8,4,3,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,1,6,8,5,3,7]=>[3,7,1,6,8,4,2,5]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,6,1,8,5,3,7]=>[4,7,6,1,8,3,2,5]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,4,6,8,1,5,3,7]=>[5,7,6,8,1,3,2,4]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[4,2,6,8,5,3,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[4,2,6,8,5,1,3,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[4,2,6,8,5,1,7,3]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[2,4,6,8,3,5,7,1]=>[8,5,6,7,2,3,4,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[2,4,6,8,3,5,1,7]=>[7,5,6,8,2,3,1,4]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[2,4,6,8,3,1,5,7]=>[6,5,7,8,2,1,3,4]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[2,4,6,3,1,8,5,7]=>[5,4,7,2,1,8,3,6]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[2,4,6,3,8,1,5,7]=>[6,4,7,2,8,1,3,5]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[2,4,6,3,8,5,1,7]=>[7,4,6,2,8,3,1,5]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[2,4,6,3,8,5,7,1]=>[8,4,6,2,7,3,5,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,4,3,6,8,5,7,1]=>[8,3,2,6,7,4,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,4,3,6,8,5,1,7]=>[7,3,2,6,8,4,1,5]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[2,4,3,6,8,1,5,7]=>[6,3,2,7,8,1,4,5]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[2,4,3,6,1,8,5,7]=>[5,3,2,7,1,8,4,6]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[2,4,3,1,6,8,5,7]=>[4,3,2,1,7,8,5,6]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[2,4,1,3,6,8,7,5]=>[3,4,1,2,8,7,6,5]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,3,6,1,8,7,5]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[2,4,3,6,8,1,7,5]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[4,6,5,2,8,7,3,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,6,5,2,8,7,1,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,6,2,5,8,7,1,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,6,2,5,8,7,3,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,4,6,3,8,1,7,5]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[2,4,6,3,1,8,7,5]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[2,4,1,6,3,8,7,5]=>[3,5,1,8,2,7,6,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,1,4,6,3,8,7,5]=>[2,1,5,8,3,7,6,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,4,6,8,3,7,5]=>[2,1,6,8,7,3,5,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,1,6,8,3,7,5]=>[3,6,1,8,7,2,5,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,6,1,8,3,7,5]=>[4,6,8,1,7,2,5,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,4,6,8,1,3,7,5]=>[5,6,8,7,1,2,4,3]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,4,6,8,3,1,7,5]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[4,6,2,8,5,7,3,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,6,2,8,5,7,1,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,2,4,8,7,1,3,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,4,2,8,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,4,8,1,7,5,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,6,4,1,8,7,5,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,6,1,4,8,7,5,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,1,6,4,8,7,5,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,6,4,8,7,3,5]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,6,1,4,8,7,3,5]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,6,4,1,8,7,3,5]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,6,4,8,1,7,3,5]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[6,4,2,8,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,4,8,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,4,8,7,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,4,7,3,8,2,5]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,7,4,5,8,2,6]=>[1,7,8,4,5,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,2,4,7,3,6,8,1]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,7,6,3,4,8,2,5]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,6,3,7,2,4,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,6,3,8,2,4,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,7,3,4,8,2,5]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,1,7,4,5,8,3,6]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,1,4,7,3,8,2,6]=>[7,2,5,8,3,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,3,1,7,5,8,2,6]=>[7,3,2,8,5,6,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[2,8,6,3,7,1,4,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[6,8,1,3,7,2,4,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,2,1,7,3,4,6]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[5,7,2,1,8,3,4,6]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[6,7,1,3,8,2,4,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,1,2,4,8,3,6,7]=>[6,2,3,4,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,3,6,1,5,8,2,7]=>[7,4,5,2,3,8,1,6]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[2,6,1,4,5,8,3,7]=>[3,7,1,5,4,8,2,6]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[6,5,1,3,4,8,2,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,6,2,4,8,3,5,7]=>[1,7,3,6,8,4,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,5,1,3,7,2,4,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,4,2,1,5,8,3,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[2,5,3,4,1,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,3,5,2,1,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[2,6,4,8,7,1,3,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[1,6,4,8,7,2,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,8,3,6,1,4,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[4,3,2,8,7,1,5,6]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[5,2,4,8,7,1,3,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,2,8,3,7,1,4,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[5,1,4,8,7,2,3,6]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,8,2,5,1,3,7,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[4,7,2,5,1,3,8,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[3,7,2,1,5,4,8,6]=>[4,8,3,1,6,5,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,8,2,1,5,4,7,6]=>[4,8,3,1,6,5,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[8,3,2,1,5,4,6,7]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,3,2,1,6,4,5,7]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,4,2,5,1,6,3,7]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,3,2,1,5,6,4,7]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,3,2,1,4,6,5,7]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,8,2,1,4,5,7,6]=>[4,8,3,1,5,6,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,7,2,1,4,5,8,6]=>[4,8,3,1,5,6,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,2,7,1,4,6,8,5]=>[4,2,8,1,5,6,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,8,1,4,6,7,5]=>[4,2,8,1,5,7,6,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,8,1,4,7,6,5]=>[4,2,8,1,5,7,6,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,8,2,1,4,7,5,6]=>[4,8,3,1,5,7,6,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,8,2,1,5,7,4,6]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[4,8,2,5,1,7,3,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[4,7,2,5,1,8,3,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[3,7,2,1,5,8,4,6]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,7,2,1,4,8,5,6]=>[4,8,3,1,5,7,6,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,2,1,7,5,8,6,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,7,1,6,8,4,5]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,2,7,6,1,8,3,5]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[4,3,7,6,8,1,2,5]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[4,3,8,6,7,1,2,5]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,2,8,6,1,7,3,5]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[3,2,8,1,6,7,4,5]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,1,8,7,5,6,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,8,2,1,7,4,5,6]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,2,8,1,7,4,6,5]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,8,1,6,4,7,5]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,7,1,6,4,8,5]=>[4,2,8,1,6,5,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,2,7,6,1,3,8,5]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[4,2,8,6,1,3,7,5]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[4,2,8,7,1,3,6,5]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[5,7,8,3,4,1,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,2,7,8,1,3,6,5]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[4,2,6,8,1,3,7,5]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[4,2,6,7,1,3,8,5]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[3,2,6,1,8,4,7,5]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,7,2,1,8,4,5,6]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,7,2,1,8,5,4,6]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[4,7,3,8,5,1,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,3,7,8,6,1,2,5]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[3,2,7,1,8,6,4,5]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,1,6,8,5,7,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,6,1,8,7,4,5]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,2,6,8,1,7,3,5]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[4,3,6,8,7,1,2,5]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,2,6,7,1,8,3,5]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[3,2,6,1,7,8,4,5]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,4,6,8,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,6,4,8,7,1,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,4,6,2,7,8,5,3]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,8,5,4,2,6,7]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,2,7,5,4,8,6,3]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,7,5,4,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,3,8,5,4,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,5,4,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,6,7,8,5,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,6,3,8,7,1,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,6,8,5,4,7,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,3,5,4,7,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,3,5,4,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,6,2,5,4,8,7,3]=>[1,8,3,5,4,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,2,5,8,3,6,4]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,2,5,7,3,6,4]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,2,1,5,4,8,7,3]=>[8,3,2,5,4,7,6,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,1,6,2,8,7,5,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,8,1,2,4,6,5,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,3,1,4,2,6,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,3,6,1,8,2,7,5]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[2,3,8,5,4,1,6,7]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,8,1,5,2,3,7,6]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[7,5,1,6,4,3,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,8,1,6,4,3,2,7]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[6,1,5,7,4,3,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,5,8,6,4,3,2,7]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,4,6,1,5,8,2,7]=>[7,4,5,2,3,8,1,6]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[7,8,4,1,5,3,2,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,5,1,6,3,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,6,1,5,7,3,8,4]=>[3,8,1,6,5,4,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,6,8,7,4,3,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,1,7,4,3,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,6,1,7,4,3,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,1,7,6,4,3,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,1,7,8,4,3,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,6,4,3,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,7,6,4,3,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,7,5,6,3,8,4]=>[2,1,8,6,5,4,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,1,6,7,5,8,2,4]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,8,1,6,5,3,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,2,1,4,5,6,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,8,1,5,4,6,7,3]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,2,8,5,6,3,7,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,2,5,7,3,8,4]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,3,6,1,5,7,2,8]=>[7,4,5,2,3,6,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[5,1,6,3,7,8,2,4]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,3,6,8,5,7,2,4]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,6,3,7,1,8,5]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[1,3,6,4,8,7,2,5]=>[1,7,8,4,6,5,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,6,7,3,8,2,5]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,4,6,1,3,7,2,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,4,1,5,2,3,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,1,7,5,2,3,8,6]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,2,4,5,8,3,7,6]=>[1,2,6,4,8,3,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,3,5,4,1,8,6]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,8,3,5,4,1,7,6]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,2,6,3,8,1,7,5]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[7,8,2,3,4,1,6,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,1,4,6,3,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,1,6,4,7,8,2,5]=>[7,2,8,4,5,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,8,5,7,4,3,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,5,8,4,3,2,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,8,7,4,3,2,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,5,1,8,4,3,2,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,5,7,1,4,3,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,8,1,4,3,2,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,7,1,4,3,2,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,5,7,8,4,3,2,6]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,7,5,1,3,8,6]=>[5,6,8,4,1,2,7,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[7,8,4,6,1,3,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,4,1,3,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,6,4,1,8,2,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[2,6,4,5,1,3,8,7]=>[5,6,4,3,1,2,8,7]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[6,8,5,1,4,3,2,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[7,6,5,1,4,3,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,9,8,7]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,5,8,6,9,7]=>[1,2,3,4,5,9,7,8,6]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,7,5,8,9,6]=>[1,2,3,4,9,6,7,8,5]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,6,4,7,8,9,5]=>[1,2,3,9,5,6,7,8,4]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,5,3,6,7,8,9,4]=>[1,2,9,4,5,6,7,8,3]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,4,2,5,6,7,8,9,3]=>[1,9,3,4,5,6,7,8,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[7,8,9,1,2,3,4,5,6]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[9,8,7,1,2,3,4,5,6]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[6,7,8,9,1,2,3,4,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,6,7,8,1,2,3,4,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,9,6,7,1,2,3,4,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,6,7,1,2,3,4,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,6,1,2,3,4,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,5,6,7,8,1,2,3,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,9,5,6,7,1,2,3,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,5,6,7,1,2,3,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,7,8,5,6,1,2,3,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,5,6,1,2,3,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,6,5,1,2,3,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,8,9,4,5,6,1,2,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,7,8,4,5,6,1,2,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,4,5,6,1,2,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,9,6,7,4,5,1,2,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,6,7,4,5,1,2,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,6,4,5,1,2,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,6,5,4,1,2,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,7,8,5,6,3,4,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,5,6,3,4,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,6,5,3,4,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,8,9,10,1,2,3,4,5,6]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[10,7,8,9,1,2,3,4,5,6]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[9,10,7,8,1,2,3,4,5,6]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[10,9,7,8,1,2,3,4,5,6]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[10,9,8,7,1,2,3,4,5,6]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[10,6,7,8,9,1,2,3,4,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,6,7,8,1,2,3,4,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,6,7,8,1,2,3,4,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,8,9,6,7,1,2,3,4,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,6,7,1,2,3,4,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,6,1,2,3,4,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,5,6,7,8,1,2,3,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,5,6,7,8,1,2,3,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,5,6,7,1,2,3,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,5,6,7,1,2,3,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,7,8,5,6,1,2,3,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,7,8,5,6,1,2,3,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,5,6,1,2,3,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,6,5,1,2,3,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,7,8,9,4,5,6,1,2,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,7,8,4,5,6,1,2,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,7,8,4,5,6,1,2,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,4,5,6,1,2,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,8,9,6,7,4,5,1,2,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,6,7,4,5,1,2,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,6,4,5,1,2,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,6,5,4,1,2,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,7,8,5,6,3,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,7,8,5,6,3,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,5,6,3,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,6,5,3,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,6,5,4,3,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[3,4,6,2,7,1,5,8]=>[6,4,7,2,5,1,3,8]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[3,6,2,5,4,1,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,3,6,2,8,1,5,7]=>[6,4,7,2,8,1,3,5]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[6,1,2,5,4,7,8,3]=>[8,2,3,5,4,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,2,4,5,1,3,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,2,8,5,1,3,7,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[4,3,6,8,1,7,2,5]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[5,3,6,4,1,7,2,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,2,1,5,8,3,7,4]=>[8,3,2,6,7,4,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,6,7,4,8,3,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,3,7,5,8,2]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,7,2,5,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,4,6,1,7,5,3,8]=>[4,7,6,1,5,3,2,8]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[7,5,4,6,2,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,7,5,4,3,8,6,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,3,5,8,7,2]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,4,3,6,7,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,6,2,7,8,1,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,5,4,1,6,7,3,8]=>[4,7,3,1,5,6,2,8]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[5,6,3,2,7,1,4,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[5,6,3,2,7,1,8,4]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[8,5,6,3,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,6,2,8,1,7,3]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[2,4,1,7,8,5,3,6]=>[3,7,1,8,6,5,2,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,5,4,1,6,3,8,7]=>[4,6,3,1,5,2,8,7]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[5,6,3,2,1,8,4,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[3,5,2,1,6,4,7,8]=>[4,6,3,1,5,2,7,8]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[6,8,4,3,2,1,5,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,3,8,2,1,6,4,7]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[3,7,5,8,2,1,4,6]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[7,3,2,8,5,1,6,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,4,6,3,2,1,7,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,6,4,3,2,1,7,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,4,3,2,1,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,8,4,3,2,1,6,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,7,2,1,8,6,3]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[7,5,8,3,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,3,2,1,6,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,7,3,2,1,6,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,3,7,2,5,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,7,8,3,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,5,7,8,4,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,1,5,7,8,6,3,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,6,7,2,8,1,4,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[6,3,7,2,8,1,4,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,3,5,2,1,8,4,6]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[2,5,4,1,3,7,8,6]=>[4,5,3,1,2,8,7,6]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,5,8,4,1,3,7,6]=>[5,6,8,4,1,2,7,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,4,1,7,8,3,6,5]=>[3,6,1,8,7,2,5,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,7,2,8,6,1,4,5]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,6,8,2,1,7,4,5]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[5,3,8,2,1,4,7,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[4,8,7,3,2,1,5,6]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[8,4,7,3,2,1,5,6]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,3,5,2,1,4,7,6]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[7,3,2,8,6,1,4,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,5,2,1,4,6,8,7]=>[4,5,3,1,2,6,8,7]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[7,8,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,8,9,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[8,9,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[7,6,8,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[6,8,7,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,8,7,9,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,7,9,8,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,9,10,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[7,8,3,5,4,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,3,7,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,1,6,3,2,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,4,1,6,2,3,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,7,1,6,2,8,3,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,7,1,6,2,8,4,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,7,6,5,1,8,3,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,7,6,5,1,8,4,3]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,3,6,5,1,4,8,7]=>[5,2,6,4,1,3,8,7]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,6,4,1,5,8,7]=>[5,2,6,4,1,3,8,7]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,6,1,5,4,8,7]=>[4,2,6,1,5,3,8,7]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,7,6,1,4,8,5,3]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,7,6,1,4,8,3,5]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[7,3,5,1,8,4,2,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,5,1,8,6,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,7,6,1,5,8,4,3]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,7,6,4,1,8,5,3]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,1,7,6,3,8,5,4]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,7,6,3,8,4,5]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,7,3,6,2,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,7,6,4,1,8,3,5]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[7,3,5,1,8,6,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,5,1,8,2,4,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[2,3,4,8,5,7,1,6]=>[7,2,3,8,5,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,3,5,4,8,1,2,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,3,5,8,7,2,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,1,4,5,8,7,3,6]=>[2,1,7,4,8,6,3,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,4,3,5,8,7,1,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,3,5,4,8,1,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,3,4,8,7,5,6,1]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,7,6,5,4,8,1,3]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[7,3,5,6,8,4,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,5,6,8,1,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,5,6,8,1,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,1,5,8,7,2,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,4,1,5,8,7,3,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,4,1,5,8,3,7,2]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,7,1,6,3,8,2,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,4,1,5,8,3,2,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,4,1,5,8,2,3,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,4,1,5,8,2,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,3,5,7,8,2,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,5,7,8,2,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,7,6,4,5,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,3,6,1,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,1,4,5,8,6,3,7]=>[2,1,7,4,8,6,3,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[7,3,5,4,8,6,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,3,4,8,5,6,1,7]=>[7,2,3,8,5,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,3,4,8,7,1,6,5]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,4,8,1,7,6,5]=>[5,2,3,8,1,7,6,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,4,8,1,6,7,5]=>[5,2,3,8,1,7,6,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,4,8,5,1,7,6]=>[6,2,3,8,5,1,7,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,3,5,4,8,2,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,4,3,5,8,2,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,1,4,5,8,3,7,6]=>[2,1,6,4,8,3,7,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[7,4,3,5,8,2,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,5,4,8,2,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[2,3,4,8,5,1,6,7]=>[6,2,3,8,5,1,7,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,4,8,1,6,5,7]=>[5,2,3,8,1,7,6,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,4,8,1,5,7,6]=>[5,2,3,8,1,6,7,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[7,8,2,6,1,5,3,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,8,1,6,2,5,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,8,6,7,2,5,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,7,2,6,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,1,7,2,6,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,2,7,1,6,3,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[2,8,6,7,1,5,3,4]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,8,5,7,1,6,3,4]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,8,1,7,5,6,3,4]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,8,2,7,5,6,3,4]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,7,4,6,3,5]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,1,7,4,6,3,5]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,8,4,7,1,6,3,5]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[4,8,2,7,1,6,3,5]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[4,8,1,7,2,6,3,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[1,8,4,7,2,6,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,8,1,7,5,6,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,8,4,7,5,6,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,3,7,5,6,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,8,1,7,5,6,2,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,8,1,7,4,6,2,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[1,8,3,7,4,6,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,3,7,2,6,4,5]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,8,1,7,2,6,4,5]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,8,2,7,1,6,4,5]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,8,2,7,4,6,1,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,8,2,7,5,6,1,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,8,2,7,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,3,7,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,4,7,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,4,7,5,6,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,8,3,7,5,6,1,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,8,3,7,4,6,1,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,8,3,7,1,6,4,5]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,8,1,7,3,6,4,5]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[7,5,2,8,6,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,1,8,6,2,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,4,8,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,8,4,5,2,6,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,8,1,7,4,2,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,6,7,4,2,8,5,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,3,8,5,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,8,3,5,6,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,3,8,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,2,8,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,1,8,4,2,5,6]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,2,8,4,1,5,3,6]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[7,2,8,3,5,1,6,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,2,8,3,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,5,7,8,2,6,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,2,3,8,5,7,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,2,4,8,5,3,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[6,3,1,4,8,5,2,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[2,6,3,7,8,5,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,6,3,7,8,4,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,4,7,3,5,6,8,1]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,4,7,3,6,8,5,1]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,5,3,7,8,1,6,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,1,5,4,7,8,2,6]=>[7,2,4,3,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,3,1,4,8,2,6,7]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,2,4,8,6,1,3,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,2,3,8,4,6,7,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,8,2,3,6,1,7,5]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[4,8,2,3,5,7,1,6]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[1,4,7,8,3,6,2,5]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,8,1,3,6,7,2,5]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,3,8,2,4,7,1,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[5,4,3,8,1,2,7,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,4,2,8,1,3,7,5]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[6,3,8,2,5,1,7,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,3,8,1,4,7,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,1,3,6,2,7,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,5,7,4,2,6,8,3]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,1,4,2,6,3,7]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,8,4,1,2,7,6,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,5,1,2,8,7,3,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,5,3,1,4,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,3,1,6,4,2,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,2,6,4,1,7,3,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,6,1,7,5,2,8,3]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,5,1,7,2,6,3,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,5,6,1,2,8,7,4]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,5,7,1,8,6,2,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,6,2,7,5,1,8,4]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,2,5,7,1,8,6,3]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,4,7,2,8,6,1,5]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[3,4,5,8,2,7,1,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,4,6,2,8,1,5,7]=>[6,4,7,2,8,1,3,5]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[3,5,2,6,8,1,7,4]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,2,5,6,1,3,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,3,1,2,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[5,3,6,8,4,7,2,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[3,7,2,5,4,8,6,1]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,2,5,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,7,2,5,8,3,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,2,6,8,4,3,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[3,1,6,5,4,8,2,7]=>[7,2,5,4,3,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,1,6,5,8,3,2,7]=>[7,2,6,4,8,3,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,6,8,4,3,2,7]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,5,4,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,1,8,4,3,2,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,7,1,5,4,3,8,6]=>[3,8,1,6,5,4,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[8,4,1,5,7,3,2,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,6,7,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,6,1,7,3,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,6,1,4,7,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,7,6,1,4,3,8,5]=>[4,8,6,1,5,3,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[6,7,8,5,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,6,8,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,2,8,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,8,2,4,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,6,2,8,3,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,6,2,4,7,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,7,6,2,4,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,3,8,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,3,5,8,6,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,2,1,4,3,6,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,7,3,1,4,6,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,6,3,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,3,5,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,2,5,1,3,6,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,2,6,5,1,3,7,4]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[8,4,6,5,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,6,8,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,6,5,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,7,6,5,1,8,2,4]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,9,2,3,4,5,6,7,8]=>[1,9,3,4,5,6,7,8,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,8,9,2,3,4,5,6,7]=>[1,9,8,4,5,6,7,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,10,2,3,4,5,6,7,8,9]=>[1,10,3,4,5,6,7,8,9,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,9,10,2,3,4,5,6,7,8]=>[1,10,9,4,5,6,7,8,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[3,6,4,8,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,4,3,8,7,1,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,6,2,4,7,8,5,3]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,2,4,8,1,5,7]=>[6,7,3,4,8,1,2,5]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,4,7,2,8,1,6,5]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[1,4,7,2,5,8,6,3]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,3,8,4,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,6,4,8,7,1,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,6,8,5,3,7,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,3,4,7,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,5,4,2,8,7,3]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,2,7,3,6,4]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,2,7,5,1,8,6,3]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[7,8,1,4,2,6,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,3,6,4,8,2,5,7]=>[1,6,7,4,8,2,3,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,5,1,3,4,2,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,8,5,3,1,7,2,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[7,4,5,3,2,8,1,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,8,3,6,1,4,2,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,5,8,6,4,1,3,7]=>[6,7,8,5,4,1,2,3]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[1,4,6,2,5,8,3,7]=>[1,7,5,4,3,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,2,5,8,1,7,4]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[1,6,8,7,4,2,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,7,8,2,4,3,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,6,3,4,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,8,3,6,5,7,4]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,3,2,7,5,8,4]=>[8,2,4,3,6,5,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,3,8,5,7,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,4,1,7,5,8,3]=>[4,8,6,1,5,3,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[7,6,5,8,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,7,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,4,3,7,2,8,5]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,3,4,8,7,1,5]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[7,1,3,4,5,2,8,6]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,3,5,4,2,7,6]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,6,3,8,2,7,5]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[7,8,2,4,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,2,6,4,7,8,1,5]=>[7,2,8,4,5,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,8,5,7,4,3,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[7,2,5,8,3,4,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,8,7,1,2,6,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,5,3,8,2,1,7,4]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[7,5,8,4,1,2,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,4,1,3,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,5,7,8,4,1,2,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,4,7,5,3,8,2,6]=>[1,7,8,5,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,6,7,3,1,8,5]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[7,8,4,6,3,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,4,5,3,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[3,6,5,8,4,2,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[5,6,8,4,2,3,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[6,8,5,4,3,1,2,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,1,4,2,8,5,7,3]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,8,6,5,3,2,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,5,1,2,4,7,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,5,8,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,5,8,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,5,7,6,2,4]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,8,5,7,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,1,5,6,2,7,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,8,5,2,1,4,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,2,5,6,1,7,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,8,1,5,6,3,7,4]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[8,1,2,5,6,3,7,4]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,2,5,7,6,3,4]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,8,6,2,7,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,5,8,6,1,7,3,4]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[8,6,1,5,7,2,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,6,5,7,1,2,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[7,6,5,8,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,7,6,8,4,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,3,7,8,6,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,5,8,1,6,4,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[3,2,8,5,7,6,1,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,2,1,5,7,6,3,4]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[5,2,8,6,1,7,3,4]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,2,8,6,5,7,3,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,2,1,3,6,7,8,5]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[8,2,5,6,3,7,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,6,5,4,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,1,3,5,4,7,8,2]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,5,3,4,7,8,2]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,5,6,2,4,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,5,2,6,3,7,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,1,2,6,7,8,5]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[8,1,6,5,7,3,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,5,8,6,2,7,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,8,1,6,3,7,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,8,5,6,3,7,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,6,5,4,2,8,3]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,6,1,4,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,1,4,2,6,5,8,3]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,7,3,5,6,8,2]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,7,4,1,5,6,8,3]=>[4,8,6,1,5,3,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[5,7,6,4,1,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,7,6,1,5,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,7,6,4,5,2,8,3]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,3,6,5,7,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,8,1,6,5,7,2,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[8,1,3,5,7,6,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,8,5,4,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,5,4,3,7,8,2]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,5,6,4,2,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,3,2,6,5,7,1,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,4,6,2,5,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,1,4,3,5,7,8,2]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,3,4,5,7,8,2]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,6,4,5,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,2,3,6,5,7,1,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,7,3,6,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,4,7,8,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,7,2,5,1,6,8]=>[6,4,7,2,5,1,3,8]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[1,4,7,2,5,8,3,6]=>[1,7,8,4,5,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,2,4,7,1,5,8]=>[6,7,3,4,5,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[6,8,3,4,5,7,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,6,7,5,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,3,7,5,8,4,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,8,6,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,2,7,6,5,8,3,4]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,8,2,6,1,5,3,7]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[2,3,8,6,4,1,5,7]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,3,6,2,5,1,8,7]=>[6,4,5,2,3,1,8,7]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[7,8,3,2,5,1,4,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,1,2,5,6,3,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,1,6,2,5,7,3,8]=>[7,2,5,4,3,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,1,2,5,8,7,3,4]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,1,8,6,4,7,3,5]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[7,1,3,6,8,4,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,3,6,7,4,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,5,8,3,6,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,8,7,2,3,6,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,5,7,4,2,8,3]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,6,4,7,2,5,8]=>[6,2,7,4,5,1,3,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,4,7,5,1,8,3,6]=>[5,7,8,4,1,6,2,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[6,5,7,1,4,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,6,8,1,3,2,4,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[6,8,5,1,3,4,2,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,8,3,4,5,1,7,6]=>[6,8,3,4,5,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[6,2,4,3,1,5,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,2,8,3,1,7,5,6]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[1,3,7,4,8,2,5,6]=>[1,6,8,4,7,2,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,3,7,4,1,6,2,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[2,4,7,3,6,1,8,5]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[5,8,7,6,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,6,8,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,7,1,6,5,3,8]=>[4,7,6,1,5,3,2,8]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,2,7,8,5,4,3,6]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,1,2,8,4,5,7]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[4,2,1,3,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[2,8,1,4,5,6,3,7]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[4,2,6,1,8,5,3,7]=>[7,4,6,2,8,3,1,5]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[7,8,2,1,4,5,3,6]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,8,4,1,5,3,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,4,6,1,5,8,7,2]=>[8,4,5,2,3,7,6,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,5,1,6,4,3,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,8,1,6,3,4,7,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,5,1,8,2,7,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,1,7,5,2,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,1,8,5,3,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,6,1,7,4,8,2,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,1,5,7,4,2,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[2,5,6,1,7,4,8,3]=>[4,8,6,1,5,3,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,1,7,5,6,4,8,2]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,7,6,4,8,3,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,7,8,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,6,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,6,5,7,3,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,6,4,7,5,8,2,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,5,3,6,2,7,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,3,7,4,6,8,2,5]=>[1,7,8,4,5,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,7,5,6,3,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,7,6,5,4,8,2,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,6,5,7,2,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,7,6,8,3,4,5]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,7,5,3,8,2,4]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,1,7,5,6,8,3,4]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,4,1,7,6,8,2,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,8,5,6,2,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,6,4,2,7,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,2,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,6,3,7,4,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,1,6,2,4,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,1,4,7,2,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,4,1,7,2,6,5]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[5,4,7,1,8,3,2,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[3,7,4,1,8,5,2,6]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[6,7,1,4,8,3,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,7,1,8,4,5,3,6]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[6,5,1,4,3,8,2,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,6,2,5,8,3,4,7]=>[1,7,3,6,8,4,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,5,1,3,7,2,6,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,2,1,7,3,6,5]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,4,2,1,8,5,3,6]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,4,3,1,5,8,2,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[3,7,6,8,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,6,8,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,6,8,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,8,6,7,5,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,8,6,7,3,5,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,3,8,5,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,8,5,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,5,8,4,7,2,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,4,3,8,6,7,2,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,2,8,7,3,6,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,2,5,8,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,2,8,5,7,4,6,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,3,8,7,5,6,2,4]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,8,7,4,6,3,5]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,1,8,5,7,6,2,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,1,5,8,7,4,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,4,1,8,7,6,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,6,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,2,1,6,3,5,8,7]=>[5,3,2,6,1,4,8,7]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[6,2,1,4,3,5,8,7]=>[6,3,2,5,4,1,8,7]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[6,2,1,4,3,8,5,7]=>[7,3,2,5,4,8,1,6]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[8,2,1,4,3,6,5,7]=>[8,3,2,5,4,7,6,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,2,4,1,3,6,5,7]=>[8,4,5,2,3,7,6,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,2,4,1,3,8,5,7]=>[7,4,5,2,3,8,1,6]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[6,2,4,1,3,5,8,7]=>[6,4,5,2,3,1,8,7]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[4,2,6,1,3,5,8,7]=>[5,4,6,2,1,3,8,7]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[2,1,6,4,3,5,8,7]=>[2,1,6,5,4,3,8,7]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,6,1,4,3,5,8,7]=>[3,6,1,5,4,2,8,7]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,6,4,1,3,5,8,7]=>[4,6,5,1,3,2,8,7]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,6,2,1,3,5,8,7]=>[5,6,4,3,1,2,8,7]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[6,4,2,1,3,5,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[8,4,2,1,3,6,5,7]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[8,4,2,1,6,3,5,7]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,4,2,1,8,3,5,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,6,2,1,8,3,5,7]=>[6,7,4,3,8,1,2,5]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[2,6,1,4,3,8,5,7]=>[3,7,1,5,4,8,2,6]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,1,6,4,3,8,5,7]=>[2,1,7,5,4,8,3,6]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,8,4,3,6,5,7]=>[2,1,8,5,4,7,6,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,8,1,4,3,6,5,7]=>[3,8,1,5,4,7,6,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,8,4,1,3,6,5,7]=>[4,8,5,1,3,7,6,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,8,2,1,3,6,5,7]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[4,8,2,1,6,3,5,7]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[6,8,2,1,4,3,5,7]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[8,6,2,1,4,3,5,7]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,8,1,4,6,3,5,7]=>[3,8,1,6,7,4,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,1,8,4,6,3,5,7]=>[2,1,8,6,7,4,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,6,4,8,3,5,7]=>[2,1,7,6,8,4,3,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,6,1,4,8,3,5,7]=>[3,7,1,6,8,4,2,5]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,6,4,1,8,3,5,7]=>[4,7,6,1,8,3,2,5]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,6,4,8,1,3,5,7]=>[5,7,6,8,1,3,2,4]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[4,6,2,8,1,3,5,7]=>[6,7,5,8,3,1,2,4]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[4,2,6,1,3,8,5,7]=>[5,4,7,2,1,8,3,6]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[4,2,6,1,8,3,5,7]=>[6,4,7,2,8,1,3,5]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[6,2,4,1,8,3,5,7]=>[7,4,6,2,8,3,1,5]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[8,2,4,1,6,3,5,7]=>[8,4,6,2,7,3,5,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,2,1,4,6,3,5,7]=>[8,3,2,6,7,4,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,2,1,4,8,3,5,7]=>[7,3,2,6,8,4,1,5]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[4,2,1,6,8,3,5,7]=>[6,3,2,7,8,1,4,5]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[4,2,1,6,3,8,5,7]=>[5,3,2,7,1,8,4,6]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,2,1,3,6,8,5,7]=>[4,3,2,1,7,8,5,6]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[2,1,4,3,8,6,5,7]=>[2,1,4,3,8,7,6,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,1,3,8,6,5,7]=>[3,4,1,2,8,7,6,5]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[4,2,1,3,8,6,5,7]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,2,1,8,3,6,5,7]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,2,1,8,6,3,5,7]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[6,2,1,8,4,3,5,7]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[8,2,1,6,4,3,5,7]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,2,6,1,4,3,5,7]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,2,8,1,4,3,5,7]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,2,8,1,6,3,5,7]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[4,2,8,1,3,6,5,7]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[2,4,8,1,3,6,5,7]=>[4,5,8,1,2,7,6,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,4,1,8,3,6,5,7]=>[3,5,1,8,2,7,6,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,1,4,8,3,6,5,7]=>[2,1,5,8,3,7,6,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,4,8,6,3,5,7]=>[2,1,6,8,7,3,5,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,8,1,6,3,5,7]=>[4,6,8,1,7,2,5,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,4,8,6,1,3,5,7]=>[5,6,8,7,1,2,4,3]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[4,2,8,6,1,3,5,7]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[6,2,8,4,1,3,5,7]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[8,2,6,4,1,3,5,7]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[8,4,6,2,1,3,5,7]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,4,8,2,1,3,5,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,6,8,2,1,3,5,7]=>[6,7,8,5,4,1,2,3]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,6,8,4,1,3,5,7]=>[5,7,8,6,1,4,2,3]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,6,8,1,4,3,5,7]=>[4,7,8,1,6,5,2,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,6,1,8,4,3,5,7]=>[3,7,1,8,6,5,2,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,1,6,8,4,3,5,7]=>[2,1,7,8,6,5,3,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,8,6,4,3,5,7]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,8,1,6,4,3,5,7]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,8,6,4,1,3,5,7]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[4,8,6,2,1,3,5,7]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[6,8,4,2,1,3,5,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,2,6,1,5,4,8,7]=>[4,2,6,1,5,3,8,7]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[5,2,4,3,8,1,7,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[6,2,4,1,5,3,8,7]=>[6,4,5,2,3,1,8,7]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[4,3,6,1,5,2,8,7]=>[6,4,5,2,3,1,8,7]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[4,3,5,2,8,1,7,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,3,7,2,6,5,8,1]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,3,8,2,6,1,7,5]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[4,3,8,1,7,2,6,5]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[4,3,8,1,5,2,7,6]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[5,1,8,3,4,2,7,6]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,4,8,1,3,2,7,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[2,1,5,4,8,3,7,6]=>[2,1,6,4,8,3,7,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,1,7,6,8,3,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,3,7,6,8,1,5,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,3,7,1,8,5,6,2]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,3,6,5,8,1,7,2]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,3,5,4,7,2,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,3,5,4,8,1,7,2]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,1,6,3,8,4,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,6,5,8,1,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,1,8,4,6,3,7,5]=>[2,1,8,6,7,4,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,4,6,1,3,2,7,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,1,6,3,4,2,7,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,6,3,7,2,5,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,5,1,7,2,6,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,3,5,2,6,1,7,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,3,5,2,6,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,2,6,3,5,1,7,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,2,7,1,5,3,6,4]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,2,4,1,5,3,7,6]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,2,4,1,7,3,6,5]=>[8,4,6,2,7,3,5,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,2,4,3,6,1,7,5]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[3,2,8,4,6,1,7,5]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,2,8,1,5,4,7,6]=>[4,2,8,1,6,5,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,7,6,8,1,5,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,2,7,1,8,5,6,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,6,5,8,1,7,4]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,5,7,2,4,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,5,8,2,4,1,7,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,2,4,1,8,5,6,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,6,8,2,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,8,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,1,7,3,8,5,6,4]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[7,1,3,2,8,5,6,4]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,5,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,2,6,4,5,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,8,1,5,4,6,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,2,7,4,5,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,4,7,2,6,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,4,8,2,6,1,7,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,5,8,1,7,2,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,1,6,5,8,3,7,4]=>[2,1,8,6,7,4,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,5,7,4,8,1,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,7,1,8,3,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,1,7,4,8,3,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,4,7,1,8,3,6,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[5,4,6,3,8,1,7,2]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[2,1,4,3,6,5,8,7,11,12,10,9]=>[2,1,4,3,6,5,8,7,12,11,10,9]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,6,5,9,10,8,7,12,11]=>[2,1,4,3,6,5,10,9,8,7,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,6,5,10,11,12,9,8,7]=>[2,1,4,3,6,5,12,11,10,9,8,7]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,7,8,6,5,10,9,12,11]=>[2,1,4,3,8,7,6,5,10,9,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,7,8,6,5,11,12,10,9]=>[2,1,4,3,8,7,6,5,12,11,10,9]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,8,9,10,7,6,5,12,11]=>[2,1,4,3,10,9,8,7,6,5,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,9,10,11,12,8,7,6,5]=>[2,1,4,3,12,11,10,9,8,7,6,5]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,5,6,4,3,8,7,10,9,12,11]=>[2,1,6,5,4,3,8,7,10,9,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,5,6,4,3,8,7,11,12,10,9]=>[2,1,6,5,4,3,8,7,12,11,10,9]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,5,6,4,3,9,10,8,7,12,11]=>[2,1,6,5,4,3,10,9,8,7,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,5,6,4,3,10,11,12,9,8,7]=>[2,1,6,5,4,3,12,11,10,9,8,7]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,6,7,8,5,4,3,10,9,12,11]=>[2,1,8,7,6,5,4,3,10,9,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,6,7,8,5,4,3,11,12,10,9]=>[2,1,8,7,6,5,4,3,12,11,10,9]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,7,8,9,10,6,5,4,3,12,11]=>[2,1,10,9,8,7,6,5,4,3,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,8,9,10,11,12,7,6,5,4,3]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[3,4,2,1,6,5,8,7,10,9,12,11]=>[4,3,2,1,6,5,8,7,10,9,12,11]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[3,4,2,1,6,5,8,7,11,12,10,9]=>[4,3,2,1,6,5,8,7,12,11,10,9]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[3,4,2,1,6,5,9,10,8,7,12,11]=>[4,3,2,1,6,5,10,9,8,7,12,11]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[3,4,2,1,6,5,10,11,12,9,8,7]=>[4,3,2,1,6,5,12,11,10,9,8,7]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[3,4,2,1,7,8,6,5,10,9,12,11]=>[4,3,2,1,8,7,6,5,10,9,12,11]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[3,4,2,1,7,8,6,5,11,12,10,9]=>[4,3,2,1,8,7,6,5,12,11,10,9]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[3,4,2,1,8,9,10,7,6,5,12,11]=>[4,3,2,1,10,9,8,7,6,5,12,11]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[3,4,2,1,9,10,11,12,8,7,6,5]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,5,6,3,2,1,8,7,10,9,12,11]=>[6,5,4,3,2,1,8,7,10,9,12,11]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[4,5,6,3,2,1,8,7,11,12,10,9]=>[6,5,4,3,2,1,8,7,12,11,10,9]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[4,5,6,3,2,1,9,10,8,7,12,11]=>[6,5,4,3,2,1,10,9,8,7,12,11]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[4,5,6,3,2,1,10,11,12,9,8,7]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[5,6,7,8,4,3,2,1,10,9,12,11]=>[8,7,6,5,4,3,2,1,10,9,12,11]=>[8,7,6,5,4,3,2,1,12,11,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[[[.,.],.],.],.]]
[5,6,7,8,4,3,2,1,11,12,10,9]=>[8,7,6,5,4,3,2,1,12,11,10,9]=>[8,7,6,5,4,3,2,1,12,11,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[[[.,.],.],.],.]]
[6,7,8,9,10,5,4,3,2,1,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[[.,.],.]]
[7,8,9,10,11,12,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[2,8,3,1,5,4,6,7]=>[4,8,3,1,6,5,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,5,3,4,7,1,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[2,4,8,3,5,7,6,1]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,2,5,3,1,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,2,1,8,5,3,6,7]=>[6,3,2,8,5,1,7,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[5,4,1,3,8,2,6,7]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,5,8,4,3,2,6,7]=>[1,6,8,5,4,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,4,3,2,6,7]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,3,8,5,2,6]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,3,8,4,2,6]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,4,7,8,3,2,6]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,8,1,5,7,3,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,5,3,7,4,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,8,4,7,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,8,5,3,7,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,1,7,4,3,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,4,8,1,7,3,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,8,7,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,4,1,3,8,2,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,7,5,6,3,2,8,4]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,2,1,7,8,5,3,6]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[2,7,4,6,3,1,8,5]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[2,6,8,4,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,4,8,3,7,5,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,2,6,3,4,1,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,6,7,3,1,4,8,5]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,7,1,8,3,5,4,6]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,1,7,3,5,8,4,6]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,7,1,3,6,2,4,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,2,1,7,3,5,6,4]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,8,2,6,3,1,5,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,2,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,2,8,7,4,5,6,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,3,7,1,5,6,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,1,2,7,5,3,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,6,2,7,4,5,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,5,2,6,7,4,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,2,1,8,6,7,4,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,8,5,7,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,8,5,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,1,6,4,2,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,6,1,5,3,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,8,6,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,1,6,4,5,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,7,5,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,6,7,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,5,2,1,4,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,3,5,7,2,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,2,7,4,3,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,3,6,1,2,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,5,1,4,6,2,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[8,3,4,5,7,2,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,4,6,3,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,8,4,6,3,7,1,5]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[8,1,4,7,3,6,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,4,7,5,1,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,1,4,7,3,2,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,3,7,1,4,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,8,5,7,4,3,6]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,5,3,7,1,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,5,1,4,7,8,3,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,3,4,7,5,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,1,4,6,8,3,7,2]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,7,1,3,5,8,6,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,8,3,7,1,2,6,5]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[3,8,6,4,1,7,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,8,1,2,5,7,6,4]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,8,7,5,4,1,3,6]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[8,7,2,6,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,6,7,4,2,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,7,6,8,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,7,8,2,4,6,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,3,6,2,1,4,7,5]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,3,7,6,2,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,3,6,2,8,7,1,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,7,8,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,7,5,4,8,1,3]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[6,1,7,4,5,8,2,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,7,3,5,1,8,2,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,1,6,7,5,8,3,4]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,5,7,3,6,8,4]=>[2,1,8,6,5,4,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,7,3,6,1,2,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,1,7,2,5,6,8,3]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,4,7,1,6,5,8,3]=>[4,8,6,1,5,3,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,6,2,1,8,7,5,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,4,6,2,7,8,5,1]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,6,1,2,5,8,7,3]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,6,1,4,8,2,7,3]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,6,3,1,8,7,2,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,5,6,4,7,1,8,2]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[3,4,6,1,5,7,8,2]=>[8,4,5,2,3,6,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,4,1,5,7,6,8,2]=>[8,3,2,4,6,5,7,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,8,2,7,1,6,5,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,8,2,7,6,1,5,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,8,2,7,6,5,1,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,8,2,7,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,8,7,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,2,1,6,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,3,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,3,2,1,6,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[4,8,7,3,2,6,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,8,7,3,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,3,6,2,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,8,7,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,3,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,6,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,6,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,4,2,1,6,5,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[7,3,5,2,6,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,3,5,2,6,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,3,5,2,7,4,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,3,5,1,6,4,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,5,6,1,3,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,4,5,7,3,2,8,6]=>[1,6,5,8,3,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,7,3,8,2,5]=>[1,7,8,5,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,4,5,7,3,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,4,5,7,1,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,3,5,1,7,4,8,2]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[3,2,1,5,7,4,8,6]=>[3,2,1,6,8,4,7,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,4,6,7,3,8,1,5]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,4,6,7,3,8,5,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,7,8,3,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,6,7,8,3,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,2,1,6,7,8,4,5]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[5,2,1,6,7,8,4,3]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[5,3,6,1,7,8,4,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,4,6,7,1,8,3,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,5,6,7,8,3,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,4,5,7,2,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,4,6,7,2,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,3,6,2,7,8,4,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,3,6,2,7,8,1,4]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,3,5,2,7,1,8,4]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,3,4,2,1,7,8,5]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,3,4,1,2,7,8,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,3,6,2,7,8,1,5]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,3,6,2,7,8,5,1]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[1,3,6,2,7,8,5,4]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,7,2,8,5,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,4,6,7,2,8,5,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[3,4,5,7,2,1,8,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,2,1,6,7,8,3,5]=>[7,3,2,8,5,6,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[4,3,6,1,7,8,2,5]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,5,6,7,8,2,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,7,8,4,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,4,6,7,1,8,5,2]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,3,6,1,7,8,5,2]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,2,1,6,7,8,5,3]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,3,6,1,7,8,5,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,4,6,7,1,8,5,3]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,5,6,7,8,1,4,3]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,1,3,6,5,8,7,9]=>[3,4,1,2,6,5,8,7,9]=>[3,9,1,8,7,6,5,4,2]=>[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]
[2,4,1,6,3,5,8,7,9]=>[3,5,1,6,2,4,8,7,9]=>[3,9,1,8,7,6,5,4,2]=>[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]
[2,3,1,5,4,7,6,9,8]=>[3,2,1,5,4,7,6,9,8]=>[3,2,1,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,4,1,3,6,5,8,7,10,9]=>[3,4,1,2,6,5,8,7,10,9]=>[3,10,1,9,8,7,6,5,4,2]=>[[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,1,6,3,5,8,7,10,9]=>[3,5,1,6,2,4,8,7,10,9]=>[3,10,1,9,8,7,6,5,4,2]=>[[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,1,6,3,8,5,7,10,9]=>[3,5,1,7,2,8,4,6,10,9]=>[3,10,1,9,8,7,6,5,4,2]=>[[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,1,6,3,8,5,10,7,9]=>[3,5,1,7,2,9,4,10,6,8]=>[3,10,1,9,8,7,6,5,4,2]=>[[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]]
[2,3,1,5,4,7,6,9,8,10]=>[3,2,1,5,4,7,6,9,8,10]=>[3,2,1,10,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,4,3,6,2,5,7,8]=>[1,5,3,6,2,4,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,3,7,2,5,6,8]=>[1,5,3,7,2,6,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,3,7,6,8,2,5]=>[1,7,3,8,5,6,2,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,3,7,5,8,2,6]=>[1,7,3,8,5,6,2,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,3,7,2,6,5,8]=>[1,5,3,7,2,6,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,6,5,8,4,7]=>[1,3,2,7,5,8,4,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,6,5,8,4,7]=>[1,2,3,7,5,8,4,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,2,4,5,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,8,4,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,1,4,5,3,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,7,4,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,3,6,1,5,7,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,8,3,1,6,4,7,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,1,4,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,1,8,6,2,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,4,1,8,2,6,3,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,8,4,2,6,3,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,3,8,5,2,4,7]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,1,8,3,6,2,5,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,3,1,8,4,2,6,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,2,8,4,1,6,5,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[7,2,8,3,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,8,3,6,1,5,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,1,8,2,3,6,5,4]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,2,8,3,5,4,7]=>[7,2,3,8,5,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,5,2,3,8,4,7,6]=>[1,6,3,4,8,2,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,2,3,8,4,7,6]=>[6,2,3,4,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,2,3,8,1,4,7,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,2,8,1,3,5,4,7]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[6,2,4,1,8,7,3,5]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,3,1,4,2,8,5,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,1,6,4,2,8,5,7]=>[5,2,7,4,1,8,3,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,6,3,8,7,1,5,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,6,3,8,5,1,4,7]=>[6,7,3,8,5,1,2,4]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,5,1,8,3,4,7,6]=>[3,6,1,8,5,2,7,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,2,5,3,8,4,7,6]=>[1,2,6,4,8,3,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,8,3,7,6,5]=>[1,2,5,8,3,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,8,1,3,7,6,5]=>[4,5,8,1,2,7,6,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,4,8,3,7,1,6,5]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[2,4,8,3,7,6,1,5]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[2,5,3,8,1,7,4,6]=>[5,7,3,8,1,6,2,4]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,5,4,1,3,8,7,6]=>[4,5,3,1,2,8,7,6]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,1,5,4,8,2,7,6]=>[6,2,4,3,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,3,1,4,8,2,7,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,2,3,8,4,7,1,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,8,2,3,7,6,1,5]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[4,8,2,3,7,1,6,5]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[4,8,1,2,3,7,6,5]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,4,8,2,3,7,6,5]=>[1,5,8,4,2,7,6,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,8,3,7,2,6,5]=>[1,6,8,4,7,2,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,8,1,5,2,4,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[5,3,8,1,2,4,7,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[1,5,3,8,2,4,7,6]=>[1,6,5,8,3,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,4,8,2,7,6,3]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,4,8,2,7,6,3]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,4,8,1,2,7,6,3]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,5,1,2,8,7,4,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,3,1,6,4,2,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,1,6,2,8,7,4,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,5,8,2,7,6,3]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,2,5,8,7,6,3]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,4,2,5,8,7,6,3]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,2,8,7,4,6]=>[1,4,7,2,8,6,3,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,1,2,8,7,4,6]=>[4,7,3,1,8,6,2,5]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,6,2,8,7,5,1,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,2,6,1,8,7,3,5]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[3,5,2,8,7,1,4,6]=>[6,7,3,8,5,1,2,4]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,4,8,7,2,6,1,5]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[3,4,8,7,1,2,6,5]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[3,4,8,1,7,2,6,5]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[1,3,4,8,7,2,6,5]=>[1,6,3,8,7,2,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,8,2,7,6,5]=>[1,5,3,8,2,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,4,8,1,2,7,6,5]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[3,4,8,2,7,1,6,5]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[3,4,8,2,7,6,1,5]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,2,5,8,1,7,6,3]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,3,1,2,5,8,7,6]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,1,4,2,5,8,7,6]=>[4,2,3,1,5,8,7,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,5,1,8,7,6,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[7,8,2,1,5,3,6,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,4,1,2,7,3,5,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[2,3,7,5,4,1,8,6]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,3,1,5,4,2,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[7,8,1,5,4,2,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,3,5,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,2,5,4,1,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,2,5,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,1,5,4,7,3,8]=>[7,3,2,5,4,6,1,8]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[5,3,6,1,4,7,8,2]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,3,6,2,4,7,1,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,4,2,1,7,3,8,5]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,3,7,5,8,6,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,2,7,1,8,3,6,5]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[3,2,6,7,4,8,1,5]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,1,6,7,4,8,5,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,6,5,3,8,4,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,6,5,3,8,1,4]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,7,6,5,2,4,8,3]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,6,5,3,1,4,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[2,7,1,4,8,3,5,6]=>[3,8,1,6,7,4,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,7,6,4,8,5,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,6,3,8,4,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,1,6,2,4,8,3,7]=>[7,2,5,4,3,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,7,6,5,2,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,7,6,5,2,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,7,6,5,1,8,3,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,7,6,5,2,8,3,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,6,5,3,2,8,4]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,7,6,5,1,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,7,6,5,3,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,1,3,5,4,8,7,2]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,2,6,3,4,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,1,6,2,4,7,8,3]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,2,4,8,3,6,5]=>[1,8,3,6,7,4,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,4,2,8,3,5,7]=>[7,2,6,4,8,3,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,1,8,2,6,3,5,7]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,7,1,6,2,3,8,5]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[1,7,2,6,8,3,5,4]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,7,4,8,5,3]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,6,7,4,2,8,5]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,2,8,5,4,6,1,7]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,7,6,3,5,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,7,1,2,5,3,8,6]=>[6,8,3,4,5,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,7,6,5,2,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,7,6,5,1,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,7,6,5,2,1,8,4]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,7,6,5,8,2,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,6,5,8,1,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,7,6,5,1,2,4,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[3,1,6,8,4,2,5,7]=>[6,2,7,8,5,1,3,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,7,6,8,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,6,5,8,1,3,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,7,6,5,8,4,1,3]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,3,2,1,7,4,8,5]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,2,1,7,3,5,8,6]=>[5,3,2,8,1,6,7,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[7,3,1,5,4,2,8,6]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,4,1,5,2,7,6,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,2,5,1,3,7,6,4]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,3,7,4,2,1,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,7,2,5,3,1,8,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[2,7,5,4,1,3,8,6]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[7,5,4,3,2,1,8,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,5,3,2,1,7,6,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,5,2,1,8,4,3,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,6,3,2,8,1,5,7]=>[6,7,4,3,8,1,2,5]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[5,7,4,3,2,8,1,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,7,6,2,4,8,3,5]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,3,6,4,8,1,5]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[6,2,7,5,3,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,1,8,5,3,6,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,8,1,6,2,7,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,8,6,2,3,7,5,4]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,6,3,2,7,5,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,3,2,7,1,6,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,2,6,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,8,5,7,4,3,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,7,2,4,6,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,8,6,1,7,2,5,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[5,8,4,6,7,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,8,5,6,1,4,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,3,7,5,8,2,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,7,2,6,8,4,1,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,6,5,8,1,4,2,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[2,6,5,8,4,1,3,7]=>[6,7,5,8,3,1,2,4]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[6,5,4,8,3,2,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[8,4,3,7,2,1,6,5]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[8,2,4,7,1,3,6,5]=>[8,5,6,7,2,3,4,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[6,2,5,8,1,4,3,7]=>[7,5,6,8,2,3,1,4]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[4,3,6,8,2,1,5,7]=>[6,5,7,8,2,1,3,4]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[6,3,5,1,8,4,2,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[8,4,1,5,7,3,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,4,2,5,8,3,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[5,4,1,6,8,2,3,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,5,2,1,7,8,3,4]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,3,7,4,8,5,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,7,2,5,8,6,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,1,8,4,7,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,4,2,8,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,3,8,7,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,3,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,8,1,7,6,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,2,8,1,7,3,6,4]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,4,8,2,1,7,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,8,1,4,7,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,3,8,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,7,8,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,7,8,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,8,7,1,3,6,4]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[5,3,8,7,2,1,6,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,3,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,7,6,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,3,8,7,6,2,1,5]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[2,4,8,7,6,1,3,5]=>[6,7,8,5,4,1,2,3]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[3,5,8,7,2,6,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,7,3,8,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,7,6,5,4,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,4,1,2,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>[3,2,1,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[4,5,6,1,2,3,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]
[4,2,5,1,3,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[5,6,7,8,1,2,3,4,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[5,6,3,4,1,2,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]
[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[6,4,7,2,5,1,3,8,9]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]
[7,4,8,2,5,9,1,3,6]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[7,8,5,6,3,4,1,2,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[7,5,3,8,2,6,1,4,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[8,6,9,4,7,2,5,1,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,6,4,3,9,2,7,1,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,6,5,4,3,2,9,1,7]=>[9,8,6,5,4,3,7,2,1]=>[9,8,6,5,4,3,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[3,4,1,2,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,10,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[4,5,6,1,2,3,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[4,2,5,1,3,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,10,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[5,6,7,8,1,2,3,4,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[5,6,3,4,1,2,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,10,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[6,4,7,2,5,1,3,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,10,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[7,8,3,4,9,10,1,2,5,6]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,8,9,4,5,6,1,2,3,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[7,8,5,6,3,4,1,2,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[7,5,3,8,2,6,1,4,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,10,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[8,5,9,10,2,6,7,1,3,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,5,3,9,2,6,10,1,4,7]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[8,6,9,4,7,2,5,1,3,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[8,6,4,3,9,2,7,1,5,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[9,7,5,4,3,10,2,8,1,6]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[3,6,5,1,2,4,8,7]=>[5,6,4,3,1,2,8,7]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,7,5,8,2,4,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,8,5,7,2,4,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,1,7,8,4,3,2,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,2,6,4,3,8,7]=>[6,2,3,5,4,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,1,2,5,4,3,8,7]=>[6,2,3,5,4,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,1,2,4,6,3,8,7]=>[6,2,3,4,5,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,1,2,6,5,3,8,7]=>[6,2,3,5,4,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,1,5,7,8,3,2,6]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,1,5,8,7,3,2,6]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,7,1,8,3,6,2,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,1,7,8,5,2,3,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,7,4,8,2,3,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,5,3,8,1,4,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,5,8,7,3,4,6]=>[2,1,7,8,6,5,3,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,1,8,4,7,2,3,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,1,8,7,5,2,3,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,7,1,6,3,2,8,5]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[7,1,2,3,8,6,5,4]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,2,3,5,8,6,4]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,8,1,4,3,7,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,3,2,4,1,6,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,1,7,3,4,8,6,5]=>[2,1,8,4,5,7,6,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[7,8,3,2,4,1,6,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,1,4,3,8,2,5]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,2,3,5,7,6,4]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,3,6,7,5,4]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,2,3,6,8,5,4]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,2,3,8,5,6,4]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,3,7,5,6,4]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,3,6,5,7,4]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,5,4,3,2,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,8,2,6,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,2,7,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,2,8,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,1,4,2,6,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[3,7,8,1,4,2,6,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[3,6,8,1,4,2,7,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[3,5,7,8,2,4,1,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[3,6,7,1,4,2,8,5]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[7,6,2,8,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,2,7,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,7,5,4,3,2,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,4,5,3,2,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,8,3,7,1,4,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,1,7,3,4,6,8,5]=>[2,1,8,4,5,6,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,7,3,2,4,1,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,7,2,4,3,6,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,2,3,8,7,4,5]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,2,3,7,8,6,4]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,2,3,8,7,6,4]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,2,3,8,6,7,4]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,2,3,5,8,7,4]=>[8,2,3,4,5,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,2,4,3,1,7,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,3,2,4,8,1,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,1,6,3,4,8,7,5]=>[2,1,8,4,5,7,6,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,6,3,2,4,7,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,2,4,3,1,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,1,2,3,5,7,8,4]=>[8,2,3,4,5,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,2,3,6,8,7,4]=>[8,2,3,4,5,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,8,1,2,6,3,5,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,4,8,2,7,3,5,6]=>[1,6,8,4,7,2,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,5,4,7,3,6]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,5,4,2,7,6]=>[1,6,8,5,4,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,3,6,8,4,7,1,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,3,6,8,4,7,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,8,1,7,3,6,5]=>[4,6,8,1,7,2,5,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,4,8,5,7,6,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,2,6,8,4,5,7,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,5,1,2,4,3,6,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,4,6,1,5,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,1,4,2,6,3,5,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,8,1,4,7,2,3,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,6,4,2,8,3,5,7]=>[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,1,7,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,3,6,5,4,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,3,1,6,5,4,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,2,3,6,5,1,4,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,1,2,3,6,5,4,8]=>[7,2,3,4,6,5,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,8,1,2,7,3,5,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,6,2,3,8,5,4,7]=>[1,7,3,4,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,2,7,6,3,4]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,8,2,7,6,3,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,8,2,7,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,8,1,7,3,5,4]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,8,2,1,7,4,3,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,6,4,1,2,8,5,7]=>[5,7,4,3,1,8,2,6]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[2,1,6,3,8,5,4,7]=>[2,1,7,4,8,6,3,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,5,1,8,7,6,3,4]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,5,3,8,7,4,6,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,2,5,3,8,7,4,6]=>[1,2,7,4,8,6,3,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,8,7,6,5,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,5,3,8,7,1,6,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,5,8,4,1,7,6,3]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,5,8,7,1,4,2,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[5,3,8,4,1,7,6,2]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,2,8,7,6,3,5,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,2,8,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,1,8,7,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,3,8,7,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,1,8,7,2,5,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,8,3,7,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,3,8,7,6,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,5,3,8,7,6,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,4,7,2,6,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,8,4,7,2,6,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,8,7,4,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,1,2,4,7,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,3,1,2,4,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,6,2,4,3,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,6,1,2,4,3,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,5,8,1,7,2,3,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[4,5,8,1,7,2,6,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[3,5,1,8,7,4,6,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,5,1,8,7,2,6,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,3,6,1,2,8,5,7]=>[5,4,7,2,1,8,3,6]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[4,5,8,3,1,7,2,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[4,5,2,8,7,1,3,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,2,5,8,7,1,6,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,4,8,7,6,2,1,5]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[3,4,8,7,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,8,7,6,2,5,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[3,2,5,8,7,4,6,1]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,5,8,3,1,7,6,2]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[2,1,3,5,8,7,4,6]=>[2,1,3,7,8,6,4,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,7,5,8,6,4,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,4,8,2,6,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,8,1,3,7,5,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,7,8,1,2,6,5,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[1,3,7,8,2,6,5,4]=>[1,5,8,7,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,3,7,8,1,6,5,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,7,8,1,3,6,5,4]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[8,1,2,6,7,3,5,4]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,6,7,5,3,4]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,5,7,1,3,6,4]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[2,8,1,6,7,3,5,4]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,6,8,3,7,1,5,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,8,6,4,7,1,5,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[6,8,3,4,1,7,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,3,7,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,8,3,7,5,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,8,1,6,7,5,3,4]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[8,2,5,7,1,6,3,4]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[8,4,7,2,3,6,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,4,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,5,7,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,2,4,7,1,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,3,5,7,1,6,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,2,4,7,3,6,1,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,2,7,1,4,6,3,5]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,7,1,2,4,6,3,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,1,4,6,2,3,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,7,1,3,6,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,6,8,3,7,2,5,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,3,5,7,1,2,6,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,8,7,1,3,6,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,4,7,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,4,7,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,1,4,7,2,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,4,6,8,2,7,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,5,8,2,7,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,5,6,3,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,2,8,1,7,4,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,8,4,5,7,2,6,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,7,3,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,5,7,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,8,3,7,5,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,8,2,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,4,2,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,4,7,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,5,7,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,2,5,7,1,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,4,7,2,6,1,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,7,1,3,4,6,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,7,2,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,4,5,7,1,6,3]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[8,7,3,4,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,4,5,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,2,3,6,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,2,3,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,2,3,6,1,4,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,3,2,8,5,4,7,6]=>[1,3,2,8,6,5,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,2,8,5,3,7,1,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[5,2,1,8,4,3,7,6]=>[6,3,2,8,5,1,7,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[6,2,8,4,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,8,4,3,1,6,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,3,4,8,2,1,6,5]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[6,3,4,8,2,7,5,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,3,4,1,8,2,7,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[8,1,4,5,2,3,7,6]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,5,4,3,2,7,6]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,5,4,2,8,1,7,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,5,3,2,8,7,1,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[6,4,3,2,8,7,5,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,5,3,2,1,7,8,4]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,6,3,2,7,8,4,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,1,6,3,2,7,8,5]=>[5,2,8,4,1,6,7,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,6,4,2,7,8,1,5]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[8,1,6,4,3,7,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,4,3,6,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,7,3,2,6,5,8]=>[5,2,7,4,1,6,3,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[5,7,3,2,6,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,7,3,2,5,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,3,2,1,5,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,7,5,6,2,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,6,5,7,1,3,8,4]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[4,6,5,7,2,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,4,7,2,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,5,4,1,7,2,8,3]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,5,4,6,2,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,4,5,7,1,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,4,6,1,7,8,2,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,1,5,6,7,2,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,1,4,6,8,7,3,5]=>[2,1,7,8,6,5,3,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,4,6,8,7,1,2,5]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,3,1,6,8,7,2,5]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[5,3,6,8,7,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,5,1,8,7,2,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,3,5,8,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,8,5,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,8,5,1,7,3,4]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[4,2,1,8,6,7,3,5]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[1,3,2,8,6,7,4,5]=>[1,3,2,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,3,8,6,7,1,4,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,1,3,2,6,7,4,5]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,8,7,1,6,5,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,2,8,7,6,1,5,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,2,8,7,6,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,1,8,6,5,4,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,3,6,1,8,5,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,7,8,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,7,8,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,1,7,8,6,5,2]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,4,7,8,6,1,5,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,1,5,7,6,2,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,5,7,6,8,1,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,7,6,8,3,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,4,1,7,6,8,3,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,4,7,5,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,6,5,1,8,3,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,6,4,3,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,5,1,7,4,3,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,6,7,5,3,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,6,7,5,1,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,1,6,7,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,6,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,7,6,1,5,4,3,8]=>[4,7,6,1,5,3,2,8]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,7,6,5,1,4,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,7,6,5,3,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,6,4,3,1,5,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,4,1,5,2,7,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,5,1,3,2,7,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,3,1,7,2,4,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,3,1,5,2,4,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,1,7,2,4,6,8]=>[6,5,3,7,2,1,4,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[8,7,1,2,4,5,3,6]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,1,2,4,7,3,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,1,2,6,7,3,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,1,6,4,2,7,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,1,3,6,4,7,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,1,5,3,4,7,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,1,5,2,4,7,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,1,2,5,7,3,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,1,2,7,4,3,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,1,2,5,4,3,6]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,1,4,2,3,8,6,7]=>[5,2,4,3,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[7,1,5,8,2,6,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,8,1,2,4,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,8,1,3,4,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,1,7,3,4,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,5,7,2,4,6,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,1,2,7,6,3,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,4,2,3,8,7,5,6]=>[1,4,3,2,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,7,6,3,5,8]=>[1,6,3,7,5,2,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,2,8,7,5,3,4]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,2,4,8,7,5,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,8,4,6,7,5,2]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,7,6,4,8,5,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,2,4,6,8,5,3]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,2,6,8,5,3,4]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,2,7,8,5,3,4]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,2,7,4,8,5,3]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,6,4,7,8,5,2]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,1,3,8,4,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,7,1,8,4,2,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,5,3,2,8,6,4]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,4,5,2,8,6,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,7,3,1,5,8,6,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,8,7,3,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,7,4,5,2,6,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,5,3,2,6,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,7,1,2,6,4,5]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[3,1,2,8,4,7,5,6]=>[3,2,1,8,5,7,6,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,1,2,8,6,4,5,7]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,4,2,3,8,6,5,7]=>[1,4,3,2,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,3,8,5,7,6]=>[1,4,3,2,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,1,7,2,4,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,1,3,4,7,6,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,1,8,6,4,7,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,6,7,4,5,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,2,8,7,3,5,4]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,3,5,8,4,7,6]=>[1,2,3,6,8,4,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,5,8,6,4,7]=>[1,2,3,7,8,6,4,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,2,8,3,6,5,4]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,2,8,6,4,5,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,7,8,4,6,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,8,7,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,7,4,6,5,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,7,3,6,5,4]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,3,5,8,7,4,6]=>[1,2,3,7,8,6,4,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,6,8,5,4,7]=>[1,2,3,7,8,6,4,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,5,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,3,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,6,3,1,4,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,8,3,1,4,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,3,1,4,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,3,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,3,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,3,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,3,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,3,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,3,8,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,3,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,3,4,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,6,3,4,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,6,3,1,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,6,3,1,2,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,3,6,1,2,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,3,4,1,2,8,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,3,1,4,2,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,3,1,4,2,8,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,3,1,6,2,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,3,1,6,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,3,6,1,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,3,6,4,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,3,6,4,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,3,8,4,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,3,8,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,3,1,8,4,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,3,1,8,2,6,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,3,1,8,2,4,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,3,1,6,2,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,3,1,6,4,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,3,1,8,4,2,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,3,1,8,6,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,3,8,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,3,8,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,3,8,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,3,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,3,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,3,6,1,4,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,3,6,4,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,3,8,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,6,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,6,8,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,6,3,8,1,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,3,4,1,6,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,3,4,1,8,2,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,6,3,1,8,2,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,6,3,1,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,6,3,8,1,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,6,3,8,4,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,3,6,8,4,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,3,6,8,1,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,3,6,1,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,3,1,6,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,3,1,6,8,2,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,3,1,4,8,2,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,3,1,4,6,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,3,1,2,6,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,3,1,2,8,4,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,3,1,2,8,6,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,3,1,4,8,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,3,4,1,8,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,3,4,8,1,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,3,4,8,6,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,3,4,6,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,3,4,1,6,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,3,1,4,6,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,3,1,2,6,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,3,1,2,4,8,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,6,2,5,4,1,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,5,2,8,4,7,6,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,4,7,3,2,8,6,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,4,8,3,2,7,6,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,4,5,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,3,2,6,4,1,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,5,8,3,2,7,6,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,7,6,3,8,5,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,6,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,5,3,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,8,4,3,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,3,2,8,4,7,6,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,1,5,8,4,7,6,3]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,3,2,7,4,8,6,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,7,4,3,2,8,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,7,5,3,2,8,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,7,8,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,8,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,4,3,8,5,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,2,6,8,5,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,1,8,6,7,5,4,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,3,2,6,7,5,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,4,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,6,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,5,3,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,4,7,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,6,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,6,3,8,5,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,7,2,6,8,5,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,2,6,7,5,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,2,5,4,7,6,1]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,7,2,8,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,2,8,7,5,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,4,7,3,8,5,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,8,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,8,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,5,3,2,8,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,4,3,2,8,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,3,2,5,4,8,6,1]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,1,7,5,4,8,6,3]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[7,3,2,8,6,5,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,4,3,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,7,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,4,3,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,2,8,7,5,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,3,2,7,8,5,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,4,3,8,5,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>[3,2,1,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[2,3,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,10,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,3,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[4,6,8,3,5,7,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,1,2,4,5,7,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,5,8,2,4,7,1,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[8,3,5,2,4,1,6,7]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,2,5,7,3,6,1,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,5,2,8,3,1,6,7]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,2,5,8,3,7,1,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[2,1,6,8,4,7,3,5]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,5,8,3,6,7,4]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,3,6,8,4,7,1,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,6,5,8,2,4,7,3]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,6,8,5,7,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,4,3,8,2,6,7,5]=>[1,5,3,8,2,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,8,3,2,1,6,7]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[5,4,3,7,2,6,1,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,3,6,2,7,5,1,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,6,3,2,1,8,5,7]=>[5,7,4,3,1,8,2,6]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[4,1,7,3,2,5,8,6]=>[5,2,8,4,1,6,7,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,3,1,7,8,2,6,5]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[3,5,1,2,7,8,6,4]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[7,5,1,4,8,2,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,7,3,8,6,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,4,7,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,1,4,2,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,5,1,2,7,6,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,8,3,1,7,2,6,5]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[1,8,4,3,5,2,7,6]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,3,1,5,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,7,3,6,5,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,3,7,6,4,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,6,3,4,2,8,7,5]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,3,6,2,7,5,4]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,7,4,2,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,4,8,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,4,3,8,5,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,7,6,2,8,4,5,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,3,2,6,8,5,4]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,3,2,1,8,5,4,7]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[6,5,3,2,7,4,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[5,2,6,3,7,4,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[2,8,5,3,1,6,4,7]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,1,7,3,8,5,4,6]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,6,2,3,7,8,5,4]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,2,8,4,5,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,1,8,2,4,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,1,2,7,8,3,6,4]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,4,1,7,8,6,3,5]=>[3,7,1,8,6,5,2,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[4,2,1,7,3,8,5,6]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[6,2,8,4,3,1,5,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[7,3,2,1,8,4,5,6]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[7,8,3,2,5,6,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,1,8,2,4,5,6,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,7,6,1,2,4,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,7,6,2,1,4,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[3,2,8,7,5,1,4,6]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,3,6,5,2,1,4,7]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,6,3,5,2,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,6,2,5,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,2,4,1,6,5,3,7]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,2,8,1,7,5,3,6]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[8,2,4,1,7,6,3,5]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,7,1,5,6,2,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,7,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,3,7,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,6,7,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,6,4,3,7,5]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,8,1,7,5,4,3,6]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,5,1,8,6,4,3,7]=>[3,7,1,8,6,5,2,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[5,7,2,6,4,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,2,7,5,4,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[2,1,8,6,5,4,3,7]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,7,5,4,3,8,6]=>[1,2,8,6,5,4,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,4,3,8,6,5]=>[1,8,3,5,4,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,8,3,6,5,4]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,6,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,3,8,6,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,7,6,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,7,3,2,6,5,4]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,4,3,2,8,7,6]=>[5,2,4,3,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[8,6,5,3,2,1,7,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,3,2,1,7,4,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,6,5,4,1,7,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,5,1,7,3,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,1,7,4,3,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,6,3,2,7,5,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,4,3,7,2,5,8,6]=>[1,5,3,8,2,6,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,8,3,1,6,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,5,8,3,2,6,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,4,1,8,2,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,4,3,1,8,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,8,7,2,5,4,6,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,3,7,2,6,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,1,8,7,5,2,6]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[1,4,8,6,3,5,2,7]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,6,3,5,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,3,5,6,8,4,2,7]=>[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,4,8,7,1,2,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,6,3,8,7,2,5,4]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,2,4,8,7,5,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,4,1,6,7,5,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,6,4,8,5,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,3,6,8,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,3,7,2,6,8,4,5]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,5,2,8,1,4,7]=>[6,7,4,3,8,1,2,5]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[3,6,5,7,2,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,2,6,3,8,1,5,7]=>[6,4,7,2,8,1,3,5]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[4,2,6,7,3,5,1,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[3,6,2,4,7,5,1,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,6,2,4,1,8,5,7]=>[5,7,3,4,1,8,2,6]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[7,3,8,2,1,6,4,5]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[7,3,5,2,1,8,6,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,7,6,4,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,4,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,2,1,4,6,5]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,8,2,7,1,5,4,6]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,6,8,2,1,5,4,7]=>[5,7,8,4,1,6,2,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,4,8,1,6,5,3,7]=>[4,7,8,1,6,5,2,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,2,8,1,5,7,3,6]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[8,5,7,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,1,7,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,1,7,5,4,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,6,2,8,7,3,5,4]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,4,6,7,3,5]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,5,4,7,1,3,6]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,1,5,8,6,4,3,7]=>[2,1,7,8,6,5,3,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[7,2,5,6,4,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,2,5,7,8,4,3,6]=>[1,2,7,8,6,5,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,4,8,6,3,5]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,8,3,6,5,4]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,8,6,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,7,6,3,5,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,7,4,6,3,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,5,8,3,4,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,6,4,2,3,5,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,6,2,4,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,2,4,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,1,4,5,8,3,6]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[7,1,6,4,5,2,3,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,1,4,5,6,8,2,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,4,6,5,8,3,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,2,3,8,5,4,6]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,5,4,3,8,2,6]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,3,4,2,6,8,5]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,5,4,6,2,8,3]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,5,6,4,3,8,2]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,6,5,4,3,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,6,2,5,4,3,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,1,7,4,3,6,8]=>[3,6,1,7,5,2,4,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,5,1,4,7,8,6,3]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,5,1,4,8,6,2,7]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[3,6,2,4,7,8,1,5]=>[7,8,3,4,5,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,6,2,4,8,7,1,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,3,8,2,4,7,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,8,7,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,7,8,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,4,2,8,5,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[3,4,7,2,5,8,1,6]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,6,8,1,3,5,2,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[4,3,8,1,2,7,5,6]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[2,8,3,1,5,6,4,7]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,8,7,1,5,4,2,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,3,1,7,6,8,2,5]=>[7,3,2,8,5,6,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[3,7,4,1,6,2,8,5]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[8,4,7,2,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,8,1,2,3,6,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,8,6,1,5,3,7,4]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[7,6,5,1,3,8,2,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,6,5,1,3,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,2,6,4,1,3,8,5]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,7,5,2,1,3,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,4,5,3,7,2,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,7,5,2,8,1,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,6,4,3,1,5,7,8]=>[5,6,4,3,1,2,7,8]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[7,3,8,4,1,5,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,3,4,1,6,5,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,2,8,3,6,1,5,7]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[6,8,5,7,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,5,2,7,1,3,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,3,5,2,1,7,4,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,8,5,3,1,4,2,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,6,5,4,2,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,6,4,7,2,5,3,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,2,4,3,7,5]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,2,4,3,7,8,5]=>[1,8,3,5,4,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,2,4,7,3,8]=>[1,7,5,4,3,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,2,4,7,8,3]=>[1,8,5,4,3,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,2,4,7,3,6]=>[1,7,8,4,5,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,2,4,8,3,6]=>[1,7,8,4,5,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,5,7,2,4,3,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,2,4,3,8,5]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,7,2,4,8,3]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,2,4,6,7,3]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,2,4,6,8,3]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,8,3,2,4,6]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,3,2,4,6,7]=>[1,6,8,5,4,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,2,4,8,3,7]=>[1,7,5,4,3,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,6,2,8,3,4,5]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,4,2,8,6,5]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,2,4,3,8,7,5]=>[1,8,3,5,4,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,2,4,8,7,3]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,7,3,2,4,6]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,3,5,8,7,6]=>[1,4,3,2,5,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,3,4,8,7,6]=>[1,5,3,4,2,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,5,2,3,8,7,4]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,2,8,6,5,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,6,5,2,8,4,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,5,2,3,8,4]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,2,8,4,3,6]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,6,2,8,3,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,6,2,4,8,3]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,3,2,4,7,6]=>[1,6,8,5,4,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,5,2,3,7,4,8]=>[1,7,5,4,3,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,5,2,3,7,8,4]=>[1,8,5,4,3,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,4,2,3,7,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,6,2,8,3,5]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,5,2,8,4,6]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,5,2,3,7,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,4,2,3,7,8,5]=>[1,8,5,4,3,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,4,2,3,7,5,8]=>[1,7,5,4,3,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,6,2,4,7,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,3,2,4,8,6]=>[1,6,8,5,4,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,4,2,8,5,6]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,2,8,5,3,6]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,4,2,3,8,5]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,4,2,3,8,5,7]=>[1,7,5,4,3,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,6,4,2,8,5,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,2,8,6,4,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,4,2,3,8,7,5]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,3,5,6,1,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,7,5,6,1,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,2,4,1,6,7,5,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,6,1,4,2,7,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,1,4,2,8,5,7]=>[5,7,3,4,1,8,2,6]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,6,7,4,3,5,8,2]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,7,1,4,3,5,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,6,1,4,3,5,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,5,4,1,6,7,8,2]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,7,1,6,3,5,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,1,4,7,6,5,8,2]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,7,4,3,5,8,2]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,6,4,3,5,8,2]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,6,4,3,5,8,2]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,6,4,2,7,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,1,3,7,2,5,6]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,7,1,3,8,2,5,6]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[7,4,1,3,8,2,5,6]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,3,6,4,2,8,5,7]=>[1,5,7,4,2,8,3,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,7,3,1,2,8,5,6]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[4,7,8,1,2,6,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,1,4,2,7,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,8,6,4,2,7,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,8,1,3,7,2,5,6]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[8,7,1,3,6,2,5,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,5,7,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,3,4,7,6,1,5]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,7,8,4,6,2,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,7,4,6,8,2,1,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,4,3,7,8,6,1,5]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[1,4,7,3,8,2,5,6]=>[1,6,8,4,7,2,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,6,8,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,3,4,8,6,1,7]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[3,7,5,4,8,2,1,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[7,1,3,4,2,8,5,6]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,4,3,8,2,5,7]=>[7,2,6,4,8,3,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,1,7,3,8,2,5,6]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,1,4,3,7,2,5,6]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,3,4,7,6,1,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,2,3,7,8,6,1,5]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[5,2,3,4,8,6,1,7]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[2,7,5,6,3,8,1,4]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[5,7,2,6,3,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,2,6,8,4,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,5,6,8,4,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,2,3,8,5,6,1,7]=>[7,3,2,8,5,6,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[5,2,3,8,7,6,1,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,2,3,7,5,6,1,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,1,8,3,7,2,5,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,8,4,2,6,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,7,1,8,2,5,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,7,4,8,5,2,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,4,3,8,5,6,1,7]=>[7,3,2,8,5,6,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[1,4,8,3,6,2,5,7]=>[1,6,8,4,7,2,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,5,8,6,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,8,7,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,6,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,3,8,7,6,1,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,7,5,8,6,2,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,7,8,6,5,2,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,8,7,3,6,2,5,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,7,5,3,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,6,8,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,6,8,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,5,4,7,6,8,2,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,6,5,8,2,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,4,6,5,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,5,4,8,6,7,1,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,4,6,5,7,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,4,7,5,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,6,2,7,5,8,3,4]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,4,8,5,7,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,4,6,5,7,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,4,8,6,7,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,1,5,4,6,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,1,5,2,4,3,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,8,2,6,5,7,3,4]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,8,5,6,3,4]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,6,5,8,3,4]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,7,6,8,3,4]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,6,8,2,5,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,6,8,4,5,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,6,8,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,6,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,7,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,3,2,7,6,8,4,5]=>[1,3,2,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,6,8,2,4,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,1,3,2,6,4,5]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,1,6,2,4,3,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,8,6,7,2,4,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,1,4,2,6,3,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,1,4,2,5,3,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,2,1,4,3,6,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,8,1,2,4,3,5,6]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,3,6,5,8,7,1,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,4,6,5,7,8,1,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,4,1,5,6,7,8,9,10,2]=>[10,3,2,4,5,6,7,8,9,1]=>[10,3,2,9,8,7,6,5,4,1]=>[[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.]
[3,4,5,1,2,7,8,9,6]=>[5,4,3,2,1,9,7,8,6]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[1,6,2,3,8,7,4,5]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,3,2,8,6,5]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,6,2,5,8,3]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,5,3,7,4,8]=>[1,2,7,5,4,6,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,5,3,7,8,4]=>[1,2,8,5,4,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,7,4,2,6,8,5]=>[1,5,8,4,2,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,4,3,7,8,5]=>[1,2,8,5,4,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,4,3,7,5,8]=>[1,2,7,5,4,6,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,3,2,5,8,6]=>[1,5,8,4,2,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,3,2,5,8,6,7]=>[1,4,3,2,5,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,3,2,4,8,6,7]=>[1,5,4,3,2,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,3,2,8,6,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,3,2,4,8,7,6]=>[1,5,4,3,2,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,5,4,3,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,8,5,4,3,2,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,7,6,5,4,3,1,9,2]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[7,9,6,5,4,3,2,1,8]=>[8,9,7,6,5,4,3,1,2]=>[8,9,7,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[9,8,7,6,5,4,3,1,10,2]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[7,1,5,4,3,8,6,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,6,5,4,8,1,7,2]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,8,1,4,3,2,7,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,8,5,4,3,7,1,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[8,10,7,6,5,4,3,2,1,9]=>[9,10,8,7,6,5,4,3,1,2]=>[9,10,8,7,6,5,4,3,1,2]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[7,6,1,4,3,8,5,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,6,5,8,3,1,7,2]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[6,8,5,1,3,2,7,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,8,2,4,3,7,6,5]=>[1,8,3,5,4,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,9,1,5,4,3,2,8,6]=>[9,8,3,7,6,5,4,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[3,8,5,4,7,2,1,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[8,7,1,5,4,3,9,6,2]=>[9,8,3,6,5,4,7,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[7,6,5,1,3,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,6,3,4,8,7,5,2]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,8,3,7,6,2]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,5,4,1,2,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,5,2,3,7,6,4]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,9,6,1,4,3,2,8,5]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[6,8,2,4,3,7,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,10,1,6,5,4,3,2,9,7]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[7,5,8,4,3,2,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,5,7,3,2,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,1,7,6,8,4,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,8,5,2,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,8,6,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,7,5,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,6,8,2,1,7,3]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[6,4,5,8,1,2,7,3]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[7,4,6,5,2,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,4,6,5,2,1,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,5,1,8,4,3,6]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[5,1,8,7,4,2,3,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,8,6,7,4,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,5,2,4,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,2,3,6,4,1,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,1,4,5,3,2,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,8,7,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,1,2,4,3,8,6]=>[6,8,3,4,5,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,3,7,6,8,2,5,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[5,3,6,8,1,7,2,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[3,2,6,8,5,7,1,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,3,7,2,4,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,4,8,6,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,8,2,5,4,3,6]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,5,3,7,4,1,8,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,6,4,7,5,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,4,7,6,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,1,2,5,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,2,8,7,3,5,6,1]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[8,1,7,4,2,5,6,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,3,8,2,5,6,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,4,1,5,8,2,7,3]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,5,8,7,3,6,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,1,5,8,7,4,6,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,3,5,6,7,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,3,2,8,5,6,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,2,7,1,8,5,6,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,1,7,2,8,5,6,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,4,8,7,3,5,6,1]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[4,7,8,3,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,7,2,8,5,6,1]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,7,1,4,8,5,6,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,3,4,8,5,6,1]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,1,8,5,2,7,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,1,7,4,5,8,6,3]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,8,3,6,7,5,4]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,2,1,6,4,7,5,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,8,2,6,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,3,5,8,7,1,4]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[7,6,2,1,5,8,4,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,5,2,7,6,1,8,3]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,1,6,8,4,7,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,6,8,7,5,2,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[7,4,8,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,6,4,7,3,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,4,1,2,3,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,6,4,8,5,3,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[7,3,5,8,4,2,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,1,5,2,3,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,7,5,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,4,8,7,3,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,8,4,3,5,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,8,1,3,5,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,3,4,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,2,7,3,5,6,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[3,1,8,7,2,5,6,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,8,1,7,2,5,6,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[8,2,3,7,1,5,6,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,4,8,7,1,3,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,4,6,7,3,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,3,8,2,7,6,1,5]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[6,8,4,2,1,3,7,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,2,4,3,5,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,3,7,1,5,6,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[8,1,2,7,3,5,6,4]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,1,3,2,8,5,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,3,8,6,2,1,4,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,6,5,2,8,3,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,3,7,5,1,8,2,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[6,8,5,2,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,5,4,3,8,1,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,6,8,1,4,5,2,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[6,8,1,2,4,5,3,7]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[8,1,6,2,4,5,3,7]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,8,6,1,2,5,4,7]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[5,8,1,6,2,3,4,7]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,1,6,5,8,2,3,7]=>[7,2,6,4,8,3,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,3,8,6,2,5,1,7]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[8,3,6,1,4,5,2,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,3,6,8,4,5,1,7]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,7,5,4,3,8,1,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[6,3,8,7,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,4,3,7,6,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,4,3,1,6,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,4,3,8,6,2,5]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,5,3,4,8,2,6]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,8,6,1,7,4,5,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,8,6,5,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,6,8,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,8,7,4,3,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,5,4,3,1,6,7,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,5,8,6,3,4,7,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,8,6,3,4,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,1,3,8,5,6,7,2]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,5,8,4,3,1,7,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,6,5,2,8,1,7,3]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,2,8,1,3,6,4,5]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[1,8,5,2,3,6,7,4]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,3,1,5,6,7,4]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[4,8,3,2,5,6,7,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,2,3,1,5,6,7,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,1,8,3,5,6,7,4]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,4,8,2,3,6,7,5]=>[1,5,8,4,2,7,6,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,7,8,6,4,5]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[7,5,1,8,2,4,3,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,5,8,1,2,4,7,6]=>[5,6,8,4,1,2,7,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[4,5,8,1,2,3,7,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[4,2,7,1,8,6,3,5]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[3,8,4,1,2,6,7,5]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[5,4,8,2,3,6,7,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,8,3,6,7,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,3,1,6,8,4,7,5]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,4,3,7,1,8,5,6]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,4,7,3,2,8,5,6]=>[1,5,8,4,2,7,6,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,1,4,3,8,5,6]=>[3,8,1,5,4,7,6,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,1,8,6,3,7,5]=>[3,6,1,8,7,2,5,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[8,4,1,3,6,2,7,5]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,8,5,1,7,2,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,6,5,8,2,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,3,5,8,2,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,8,7,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,2,8,6,1,7,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[8,2,5,6,1,4,7,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[8,6,5,4,1,2,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,1,8,3,7,5,4]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[4,7,1,6,2,8,5,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,1,5,3,8,7,2,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,8,6,3,7,1,5,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[7,6,1,5,8,2,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,8,5,1,2,7,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[6,5,2,4,8,1,7,3]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,1,4,8,2,6,7,3]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,8,2,5,1,6,7,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,4,8,5,2,6,7,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,2,1,8,5,6,7,3]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,5,4,8,2,6,7,3]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,1,5,8,6,3,4]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,8,4,5,1,6,7,3]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[5,4,8,3,7,6,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,1,5,8,6,2,7,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,3,4,8,5,1,7,2]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[5,3,4,8,1,6,7,2]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,6,1,2,8,3,5,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,8,4,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,4,8,7,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,4,8,1,2,7,3]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[7,5,1,6,2,3,8,4]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,5,1,6,8,2,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,5,4,1,8,2,7,3]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,5,4,7,1,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,5,4,7,8,1,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,3,7,1,4,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,5,3,1,8,4,2,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,5,1,4,8,3,2,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,6,4,7,3,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,5,1,4,8,3,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,5,3,7,1,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,4,3,1,5,8,7,2]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[7,4,1,5,3,8,6,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,5,4,3,7,6,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,5,4,3,7,2,6]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,1,5,3,8,2,6]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,4,1,5,3,2,6,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,1,5,4,3,2,6,7]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,6,4,2,5,3,7]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,5,3,1,2,7,4,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,5,3,8,1,4,2,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[7,6,8,1,4,3,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,7,2,5,4,3,6]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,2,5,4,6,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,1,2,5,4,8,3]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,5,3,8,1,4,7,2]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[6,5,3,1,2,7,8,4]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[7,5,1,4,2,6,8,3]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,1,6,4,2,5,7,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,1,5,3,2,8,6]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,4,3,1,5,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,4,3,1,5,7,2,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[7,4,1,5,3,6,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,1,5,4,3,6,2,7]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,5,4,3,6,7,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,1,5,3,6,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,4,3,1,5,7,8,2]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[6,7,3,8,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,4,5,1,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,7,5,6,2,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,7,5,6,1,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,7,5,6,3,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,7,5,8,4,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,3,8,6,7,1,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,8,3,6,5,7,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,4,7,1,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,1,7,3,8,2,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,6,1,8,2,7,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,6,1,8,4,7,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,8,1,6,5,7,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,5,1,8,6,7,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,4,5,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,2,3,1,6,5,7]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[5,6,2,8,1,4,3,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[5,6,3,4,1,8,2,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[3,6,4,5,2,7,1,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[3,6,4,5,1,8,2,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[2,6,4,8,1,5,3,7]=>[5,7,6,8,1,3,2,4]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,8,3,6,1,5,4,7]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,8,3,4,1,6,5,7]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[7,8,2,5,3,4,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,1,5,3,6,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,5,3,8,6,7,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,3,6,2,7,4,5]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,4,8,2,7,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,4,7,3,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[2,7,3,6,4,5,1,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,7,3,6,4,8,2,5]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,8,4,6,3,5]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,8,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,8,2,6,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,6,3,8,2,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,5,6,3,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,2,5,3,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,1,5,3,8,2,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,5,8,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,7,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,2,3,1,8,4,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,7,2,8,1,4,3,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[3,4,1,7,5,8,2,6]=>[7,3,2,8,5,6,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[2,7,5,8,1,4,3,6]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,3,1,7,5,8,4,6]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,8,4,7,5,6]=>[3,2,1,8,5,7,6,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[7,8,2,3,1,6,4,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,8,2,6,1,4,3,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[2,8,6,7,1,4,3,5]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,8,1,4,3,7,5,6]=>[3,8,1,5,4,7,6,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,7,2,5,4,6,1,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,5,2,7,3,6,1,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,5,1,8,2,7,3,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,4,1,8,2,7,5,6]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,4,1,8,6,7,2,5]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[3,4,2,5,1,8,6,7]=>[5,3,2,4,1,8,7,6]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,4,2,8,1,6,5,7]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,8,2,5,1,6,4,7]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,5,2,8,1,6,3,7]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,5,3,6,1,8,2,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[7,1,5,8,4,6,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,7,1,4,2,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,3,7,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,1,7,3,2,5,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,1,8,3,5,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,1,3,8,5,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,8,2,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,2,8,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,2,3,8,5,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,1,5,2,6,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,1,5,2,3,6,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,2,3,1,7,6,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,6,2,3,7,1,5,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,2,7,3,1,5,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,7,2,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,7,3,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,2,5,1,6,3,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,7,2,1,4,6,3,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,4,2,1,7,6,3,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,5,2,7,1,6,3,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,5,7,2,1,4,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,3,1,4,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,8,7,3,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,2,1,4,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,2,7,1,3,6,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,4,2,1,3,7,6,5]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[8,7,4,1,2,3,6,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,4,1,2,6,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,3,1,7,2,6,5]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[8,4,3,1,2,7,6,5]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[8,6,1,3,7,2,5,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,1,3,2,7,6,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,7,4,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,4,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,5,4,2,7,6,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,6,4,7,2,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,5,8,4,2,7,3]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,8,3,6,4,1,2,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,2,8,6,4,1,3,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[8,4,7,5,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,5,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,5,1,2,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,3,5,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,2,6,5,1,4,7]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,8,6,3,5,1,2,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,8,7,3,1,5,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,4,7,2,1,5,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,2,7,1,5,4,6]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,3,2,1,7,6,4,5]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,7,3,1,4,2,6,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,3,1,6,2,4,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,3,1,2,6,4,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,7,3,1,2,4,6,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,3,2,1,4,7,6,5]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,3,2,1,7,4,6,5]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,3,2,7,1,5,6,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,4,7,2,1,5,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,4,1,2,5,6]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[8,7,2,1,6,3,4,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,7,2,1,3,6,4,5]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,7,2,1,3,4,6,5]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,6,5,4,1,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[3,8,5,6,7,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,5,8,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,7,8,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,5,7,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,3,2,1,5,8,7]=>[5,6,4,3,1,2,8,7]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[6,2,1,5,3,4,8,7]=>[6,3,2,5,4,1,8,7]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[5,8,1,3,7,6,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,7,2,3,6,1,8,5]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[3,7,4,2,8,1,5,6]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[4,2,6,8,5,7,3,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,4,2,7,3,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,1,6,7,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,1,5,8,7,6,3,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,4,7,6,3,8,5]=>[2,1,6,8,5,3,7,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,4,7,8,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,1,3,7,6,2,8,5]=>[6,2,3,8,5,1,7,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,5,1,6,3,2,7,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,3,7,1,5,2,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,2,6,8,4,7,5,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,6,1,3,2,5,7]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,2,8,6,7,3,1,5]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[7,4,3,8,2,1,5,6]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[4,7,5,8,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,3,2,7,8,1,5]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,2,5,1,6,7,8,3]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,4,8,5,7,1,3,6]=>[6,7,8,4,5,1,2,3]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[3,7,1,4,6,8,5,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,2,5,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,3,8,7,5,6,1]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,6,7,3,5,1,8,4]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[7,6,8,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,1,6,3,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,7,2,8,4,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,4,8,6,5,2,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[2,7,6,1,4,5,8,3]=>[4,8,6,1,5,3,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[6,5,8,2,1,7,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,3,5,1,6,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,1,6,3,5,8,7,2]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,2,5,8,4,3,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[8,6,7,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,1,6,5,8,4,7,3]=>[2,1,8,6,7,4,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,6,8,5,4,3,7]=>[2,1,7,8,6,5,3,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[4,1,8,5,6,2,3,7]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,6,4,8,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,8,4,3,5,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,8,2,7,6,1,3,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,1,8,2,7,5,4,6]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,8,1,2,6,7,4,5]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[5,8,4,3,2,7,1,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[7,4,8,6,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,4,7,2,1,3,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,1,8,4,3,7,5,6]=>[2,1,8,5,4,7,6,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,3,8,2,4,5,7,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[5,8,4,2,3,6,1,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[5,8,2,4,3,1,6,7]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[2,8,3,1,6,4,5,7]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[1,4,8,2,6,3,5,7]=>[1,6,8,4,7,2,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,8,4,5,7,6]=>[1,2,3,8,5,6,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,3,4,5,7,6]=>[1,2,8,4,5,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,2,6,4,5,7]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,2,3,6,4,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,2,4,5,7,6]=>[1,4,8,2,5,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,8,4,6,7,5]=>[1,2,3,8,5,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,2,3,6,4,5]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,8,2,3,5,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,2,5,3,6,4]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,2,4,5,3,6]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,3,6,4,5,7]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,3,6,4,5,7]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,8,3,6,4,5]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,7,8,3,6,4]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,8,4,6,7,5]=>[1,3,2,8,5,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,2,4,3,6,5]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,3,1,5,2,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,3,1,5,2,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,8,3,1,5,2,7,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,4,5,1,2,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,4,5,1,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,3,6,1,5,2,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,6,5,1,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,5,4,1,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,8,6,4,1,7,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,6,4,1,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,7,4,1,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,5,7,4,1,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,4,7,5,1,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,3,8,1,5,2,7,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,4,8,5,1,2,7,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,5,8,4,1,2,7,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,6,8,4,1,7,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,8,5,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,8,6,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,8,6,1,7,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,8,1,6,7,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,2,1,8,6,7,3,4]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[5,2,1,7,6,8,3,4]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[5,4,7,6,1,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,5,7,6,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,6,7,5,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,6,5,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,5,6,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,5,6,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,6,5,7,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,4,6,1,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,8,4,6,1,7,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,3,1,6,7,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,3,1,6,8,2,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,3,1,7,8,2,4]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,2,1,4,3,8,7,5]=>[8,3,2,5,4,7,6,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[5,8,3,1,7,6,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,4,8,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,1,6,8,7,3,4]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[5,4,6,8,1,7,2,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,5,6,8,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,5,8,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,5,7,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,6,7,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,6,8,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,7,8,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,7,8,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,7,8,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,7,1,8,6,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,2,1,7,8,6,3,4]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[5,3,8,1,7,6,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,4,8,7,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,8,7,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,8,6,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,6,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,4,7,3,6,1,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[2,4,6,3,7,5,1,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,2,7,3,6,5,1,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,2,6,3,1,5,8,7]=>[5,4,6,2,1,3,8,7]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[2,5,3,1,6,4,8,7]=>[4,6,3,1,5,2,8,7]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,5,3,7,6,4,1,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[2,6,5,3,7,4,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,2,7,6,3,5,1,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[2,7,5,3,6,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[2,6,3,7,5,4,1,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,7,5,2,3,8,4,6]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,3,7,5,4,8,6]=>[2,1,3,8,6,5,7,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,3,1,8,6,5,4,7]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,5,3,1,8,6,4,7]=>[4,7,3,1,8,6,2,5]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[4,2,8,3,1,6,5,7]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[8,3,2,6,4,1,5,7]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,6,8,2,1,4,5,7]=>[5,7,8,4,1,6,2,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[1,5,2,8,3,4,7,6]=>[1,6,3,8,5,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,3,8,7,4,5]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,3,6,4,7,5]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,6,3,4,8,5]=>[1,2,8,6,5,4,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,3,8,7,5,4,6]=>[2,1,3,8,7,6,5,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,3,8,6,4,7,5]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,7,4,8,6,5]=>[1,2,3,8,5,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,6,3,8,4,5]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,6,4,8,7,5]=>[1,2,3,8,5,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,7,6,4,8,5]=>[1,2,3,8,6,5,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,3,1,8,5,4,7]=>[4,7,3,1,8,6,2,5]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,1,3,8,5,4,7,6]=>[2,1,3,8,6,5,7,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[7,1,8,4,2,3,5,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,1,8,4,3,5,7,6]=>[2,1,8,5,4,6,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[4,2,6,3,1,8,5,7]=>[5,4,7,2,1,8,3,6]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[5,4,2,8,3,1,6,7]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,5,8,2,4,1,6,7]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[2,5,4,8,3,1,6,7]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,2,1,8,3,5,7,6]=>[5,3,2,8,1,6,7,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,8,7,4,2,3,5,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,6,3,7,4,5]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,3,8,6,4,5]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,8,4,7,6,5]=>[1,2,3,8,5,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,3,8,4,7,5]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,3,8,7,4,6]=>[1,7,3,4,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,2,1,8,3,7,5,6]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[8,3,2,1,7,4,5,6]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,2,8,6,3,4,7,5]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,3,8,4,6,5]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,8,7,4,6,5]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,8,7,6,4,5]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,3,8,1,6,4,7]=>[5,7,3,8,1,6,2,4]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,8,5,7,1,2,6,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[3,8,5,7,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,8,6,2,5,7,1]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[3,4,8,6,1,2,5,7]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[2,5,7,1,4,8,6,3]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,4,8,1,5,7,6,3]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,4,3,8,1,6,5,7]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[2,8,1,7,5,6,4,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,3,8,1,6,5,7,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,4,8,1,3,5,7,6]=>[4,5,8,1,2,6,7,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,5,7,6,1,2,4,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[3,5,7,6,2,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,8,6,7,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,6,7,1,2,3,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,8,6,7,1,3,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,8,6,1,5,7,2]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[3,8,5,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,2,8,5,6,1,7,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,8,5,7,2,1,6,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[3,4,8,6,2,1,5,7]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[3,5,7,6,2,1,4,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[4,8,6,7,2,1,3,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,8,6,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,7,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,7,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,7,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,6,7,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,1,7,5,2,8,6]=>[6,3,2,8,5,1,7,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[4,3,2,8,5,1,7,6]=>[6,3,2,8,5,1,7,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[4,3,8,5,1,6,7,2]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,8,6,7,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,7,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,7,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,7,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,2,3,8,5,1,6,7]=>[6,3,2,8,5,1,7,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[4,2,8,5,1,7,6,3]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[3,4,2,8,5,6,1,7]=>[7,3,2,8,5,6,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[3,2,4,8,6,1,5,7]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,8,6,7,1,3,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,8,6,7,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,6,7,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,8,5,2,6,7,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,3,8,5,1,2,6,7]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[4,2,6,7,5,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,8,5,7,1,4,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,8,4,7,1,5,2,6]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[3,5,2,8,4,6,1,7]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,5,1,7,4,6,2,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,8,4,7,2,5,1,6]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[4,1,3,8,5,2,6,7]=>[6,2,3,8,5,1,7,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,1,2,6,7,5,3,8]=>[7,2,3,6,5,4,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,2,6,7,5,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,8,6,7,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,6,7,3,1,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,1,7,5,2,8,6,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,6,7,5,2,3,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,8,6,7,2,3,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,8,6,7,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,7,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,7,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,6,7,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,1,6,7,5,3,8,2]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,7,5,3,2,8,6]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,2,8,5,3,1,7,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[4,8,6,7,3,2,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,8,6,7,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,7,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,5,8,1,4,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,6,1,4,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,1,8,3,6,7,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,4,7,8,5,6,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,4,7,1,5,8,6,2]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,6,1,4,7,8,5,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,6,8,4,7,5,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,1,3,5,7,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,1,4,3,8,2,5]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,1,6,5,4,2,7]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,1,3,7,5,8,2,6]=>[7,2,3,8,5,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,1,7,3,8,4,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,6,3,5,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,7,6,5,8,4,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,7,6,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,2,6,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,1,6,7,5,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,4,1,6,8,2,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,3,8,6,2,7,5,4]=>[1,5,8,7,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,3,2,7,8,4,5]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,6,2,5,3,4,7]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,7,2,6,8,1,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,3,6,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,4,1,6,8,3,5]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,7,2,4,5,1,6,8]=>[6,7,3,4,5,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[1,8,6,4,5,2,3,7]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,4,6,5,1,3,7]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[3,4,1,7,5,2,6,8]=>[6,3,2,7,5,1,4,8]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[7,5,8,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,8,7,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,4,3,6,8,1,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[3,8,5,4,6,2,1,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,8,2,1,3,7,5,6]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[6,4,1,2,7,5,8,3]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,1,8,3,6,7,5,2]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,7,4,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,7,8,5,1,6,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,4,8,2,7,6,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,7,6,3,4,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,8,2,6,3,4,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,1,7,5,8,6,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,7,8,4,3,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,7,5,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,8,1,4,7,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,4,5,6,1,2,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,4,3,5,7,8,2,6]=>[1,7,3,4,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,5,8,7,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,7,2,4,8,1,5]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,5,2,7,4,3,8,6]=>[1,6,3,8,5,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,5,6,4,3,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,8,6,5,4,3,2,7]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,5,2,8,4,7,3]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,6,1,8,5,7,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,7,1,2,8,5,6,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,4,7,2,8,5,6,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,5,8,6,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,3,5,8,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,8,1,5,7,2,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,4,6,5,8,1,7,2]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,8,1,5,7,2,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,2,5,8,6,3,4]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,2,5,8,6,3,4]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,6,8,2,3,5,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,8,1,2,3,5,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,7,1,5,8,6,3,4]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,7,1,8,5,6,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,7,5,8,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,2,1,8,5,6,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,6,8,2,1,3,5,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,2,7,6,8,3,5,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,6,8,2,1,5,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[7,4,2,1,6,8,5,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,7,4,1,8,5,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,4,3,1,8,5,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,7,4,1,6,8,5,3]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,3,7,6,8,1,5,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[7,4,2,6,8,5,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,2,5,8,6,1,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,1,7,6,8,2,5,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,7,6,8,1,2,5,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[1,3,7,6,8,2,5,4]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,2,6,8,5,3]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,1,2,6,8,5,3]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,4,2,8,5,6,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,2,5,4,6,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,3,8,4,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,8,1,6,4,5,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,1,6,8,5,4,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,2,6,8,5,4,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,2,6,8,5,4,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,6,8,3,2,5,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,8,3,1,2,5,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,5,8,6,3,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,5,8,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,7,1,8,5,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,6,8,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,8,2,3,1,5,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,6,8,3,1,5,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,7,1,6,8,5,4,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[6,7,3,1,8,5,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,1,8,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,1,6,8,5,4,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,6,8,3,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,8,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,5,8,7,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,4,8,1,2,7,3]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[8,1,5,6,7,2,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,5,1,8,2,7,3]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,4,6,7,1,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,3,6,7,2,1,5,8]=>[6,5,7,4,2,1,3,8]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[5,3,6,7,1,4,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,1,4,6,7,3,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,3,6,7,4,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,1,6,8,4,5,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[5,2,6,7,1,4,8,3]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,2,6,7,3,1,8,5]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[6,2,4,1,5,8,7,3]=>[8,4,5,2,3,7,6,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,2,1,5,4,8,6,3]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,1,4,5,3,7,2,6]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,3,1,5,4,8,2,6]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,3,4,1,5,8,2,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,3,4,2,1,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,3,5,2,7,1,6,8]=>[6,4,3,2,7,1,5,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,6,3,8,1,4,2,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[8,1,7,2,4,5,6,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,1,2,4,5,8,3]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,7,8,2,3,1,6,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[5,6,2,8,1,4,7,3]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[6,5,2,1,3,7,8,4]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[7,5,1,3,2,6,8,4]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,1,6,3,2,5,7,4]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,1,3,5,2,8,6]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,4,2,3,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[7,3,1,4,5,6,2,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,1,4,3,5,6,2,7]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,2,3,1,5,7,8,4]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[7,8,4,2,1,6,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,4,2,1,5,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,3,4,8,7,1,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,2,3,4,7,8,1,5]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,3,4,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,3,6,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,3,5,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,3,8,7,5,1,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,2,3,7,8,5,1,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,2,6,3,8,1,7,4]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,3,2,5,8,7,1,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,3,2,8,4,7,1,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,4,3,8,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,3,7,8,5,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,2,4,1,7,3,5,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[6,3,2,7,4,8,1,5]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,3,2,5,7,8,1,4]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,7,2,3,6,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,8,2,3,6,1,7,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,7,5,8,3,2,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,5,6,8,3,2,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[4,6,8,5,3,2,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[5,6,1,4,2,3,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,6,8,4,3,7,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,1,4,2,3,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,2,8,3,4,1,7,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[4,5,8,6,3,2,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,6,5,8,3,2,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[4,7,5,6,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,2,3,4,5,8,1,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,1,4,3,6,2,8,7]=>[6,2,4,3,5,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,1,4,3,7,2,8,6]=>[6,2,4,3,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,1,4,3,8,2,7,6]=>[6,2,4,3,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,6,2,4,1,7,8,3]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,6,2,4,1,8,7,3]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,7,2,4,1,8,6,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,1,4,2,8,7,5,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,4,2,7,8,5,3]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,8,2,4,1,7,6,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,2,7,4,1,6,8,3]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,4,1,3,7,2,6,8]=>[6,4,3,2,7,1,5,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,8,6,4,3,7,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,1,4,2,3,7,6]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[5,1,6,3,4,2,7,8]=>[6,2,5,4,3,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,8,6,5,3,2,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,8,5,6,3,2,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,4,7,8,3,2,1,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[5,4,8,7,3,2,1,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,6,8,7,3,2,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,6,7,8,3,2,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,7,6,8,3,2,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,7,8,5,3,2,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,7,1,3,4,2,6,8]=>[6,7,3,5,4,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[5,1,8,4,2,3,6,7]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,8,1,3,4,2,6,7]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,8,7,5,3,2,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,7,8,6,3,2,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,8,7,6,3,2,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,8,2,6,3,7,5,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,8,2,3,6,7,5,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,8,3,1,6,7,5,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,3,8,1,6,2,5,7]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[1,4,8,7,3,5,2,6]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,8,7,2,5,1,6]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[5,8,4,3,7,1,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,1,4,7,2,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,1,7,4,2,3,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[6,8,1,2,4,3,5,7]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,8,7,1,3,4,2,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,8,7,6,3,1,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,8,4,7,3,1,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,3,8,2,7,5,6,1]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[1,4,8,3,7,5,6,2]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,3,8,2,6,5,7]=>[1,5,3,8,2,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,2,8,1,6,5,7]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,1,3,8,2,6,5,7]=>[5,2,3,8,1,7,6,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,1,8,3,7,5,6,2]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,8,7,3,5,2,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,7,8,1,5,4,2,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[7,3,8,1,5,4,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,4,8,1,6,2,5,7]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[3,4,8,7,2,5,1,6]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[3,4,8,2,7,5,6,1]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[1,2,4,8,3,6,5,7]=>[1,2,5,8,3,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,3,8,6,5,7]=>[1,2,4,3,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,4,2,1,8,6,5,7]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,4,1,8,2,6,5,7]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,6,7,8,4,1,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,1,7,8,5,3,2,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,1,2,8,3,6,5,7]=>[5,2,3,8,1,7,6,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,4,3,2,8,6,5,7]=>[1,4,3,2,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,2,3,1,8,6,5,7]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,7,6,8,4,2,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,7,1,8,5,2,3,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,6,8,7,4,3,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,7,8,6,2,4,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,7,8,2,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,2,3,8,1,6,5,7]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,3,1,8,2,6,5,7]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,4,7,8,5,3,2,6]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,7,8,5,2,1,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[3,7,2,8,4,6,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,2,8,6,3,1,5,7]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[2,6,8,4,7,3,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,4,8,6,3,1,5,7]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[7,3,6,8,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,2,8,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,3,8,4,6,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,8,2,6,5,7]=>[1,5,3,8,2,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,4,8,1,6,5,7]=>[5,2,3,8,1,7,6,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[7,3,8,6,2,4,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,8,2,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,4,8,3,6,1,5,7]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[6,2,8,7,4,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,1,8,5,2,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,3,2,8,4,6,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,4,3,1,8,6,5,7]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,3,4,2,8,6,5,7]=>[1,4,3,2,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,4,8,6,5,7]=>[1,3,2,4,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,1,4,8,6,5,7]=>[3,2,1,4,8,7,6,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,1,2,4,8,6,5,7]=>[3,2,1,4,8,7,6,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,1,4,2,8,6,5,7]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,1,4,8,2,6,5,7]=>[5,2,3,8,1,7,6,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[7,3,4,8,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,4,8,5,1,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,7,2,8,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,3,1,4,8,6,5,7]=>[3,2,1,4,8,7,6,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,1,3,4,8,6,5,7]=>[2,1,3,4,8,7,6,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,3,4,8,6,5,7]=>[1,2,3,4,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,8,3,6,2,1,5,7]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[3,5,8,2,6,1,4,7]=>[6,7,8,4,5,1,2,3]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[3,6,5,8,2,4,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[5,3,8,7,2,4,6,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,8,4,5,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,4,5,7,3,8,1,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,2,4,5,8,3,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,8,1,2,5,6,3,7]=>[7,8,3,4,5,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[8,1,3,5,2,6,4,7]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,2,1,6,3,8,4,7]=>[7,3,2,5,4,8,1,6]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[6,2,5,1,8,4,3,7]=>[7,4,6,2,8,3,1,5]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[3,6,1,5,8,4,2,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,1,4,5,8,3,2,7]=>[7,2,6,4,8,3,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,6,4,8,1,3,2,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[6,5,4,3,8,2,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[5,4,3,7,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,8,4,3,7,2,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,6,8,3,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,6,3,2,8,1,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,4,3,6,2,7,8,5]=>[1,5,3,8,2,6,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,7,8,5,3,1,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,7,3,4,1,2,8,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[8,5,4,7,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,4,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,8,1,6,7,5,2]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,7,8,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,8,6,7,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,3,8,6,4,7,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,2,7,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,2,1,4,3,8,5]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,6,1,3,4,2,8,5]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,5,7,3,2,6,8,4]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,3,2,5,8,4]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,6,8,5,7,4,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,8,2,3,6,7,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,2,3,1,6,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,6,4,7,2,3,8,5]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,7,5,2,8,4,6]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,5,7,4,1,8,3,6]=>[5,7,8,4,1,6,2,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[4,2,6,1,7,8,3,5]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,2,7,6,3,8,1,5]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[6,4,8,7,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,2,6,8,7,4,5,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,7,4,1,6,8,5]=>[5,2,8,4,1,6,7,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[6,3,2,1,7,8,4,5]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,7,1,8,4,2,5,6]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,2,1,3,7,5,8,6]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[8,1,3,7,4,2,6,5]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,3,7,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,5,2,7,6,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,2,8,7,1,5,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[7,3,2,8,1,6,5,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,8,7,2,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,2,7,8,6,1,5,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,8,2,4,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,1,8,7,3,6,4]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,2,1,6,3,7,5,4]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,8,3,1,7,5,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,1,6,7,2,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,2,8,1,5,7,4,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[5,7,8,2,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,2,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,7,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,6,8,1,5,4,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,2,7,8,5,6,4,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,8,1,6,2,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,7,1,8,2,6,5,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,1,7,3,8,6,5,4]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,2,1,7,6,5,4,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,1,4,7,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,7,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,6,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,4,3,2,1,6,7]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[6,4,7,3,2,1,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,4,7,3,2,1,6,8]=>[6,5,7,4,2,1,3,8]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[6,5,3,7,2,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,8,3,6,2,1,4,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,3,7,8,2,1,4,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,3,7,6,2,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,8,7,6,2,1,4,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[5,8,4,2,6,1,3,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,8,7,2,5,1,3,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,8,3,2,6,1,4,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,8,3,2,5,1,7,6]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[4,3,7,2,5,1,8,6]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[3,8,7,2,5,1,4,6]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[6,4,2,7,5,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,3,2,7,5,1,4,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,3,2,6,7,1,4,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,8,2,6,5,1,4,7]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[6,2,7,8,5,1,3,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,2,7,6,8,1,3,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,2,7,6,5,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[2,8,7,6,5,1,3,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[6,5,4,3,1,7,8,2]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[6,4,7,3,1,5,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,4,7,3,1,8,6,2]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,4,3,7,1,5,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,4,3,6,1,8,7,2]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,3,7,8,1,4,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,7,6,1,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,3,7,6,1,5,8,2]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[3,8,7,6,1,4,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,4,2,1,7,3,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,4,7,2,1,5,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,8,7,2,1,5,3,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,8,3,2,1,4,7,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[4,8,3,2,1,5,7,6]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[5,3,7,2,1,4,8,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[3,8,7,2,1,4,5,6]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[6,5,2,7,1,4,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,8,2,6,1,4,3,7]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[6,4,2,7,1,5,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,4,2,6,1,8,3,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,3,2,6,1,5,8,7]=>[5,3,2,6,1,4,8,7]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[6,2,7,8,1,4,3,5]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[4,2,7,6,1,5,3,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[3,2,7,6,1,4,5,8]=>[5,2,7,6,1,4,3,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[6,5,4,1,8,7,3,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,8,4,1,6,7,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,7,1,5,8,3,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,4,7,1,6,8,3,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,8,7,1,5,6,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,4,3,1,6,8,7,2]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,8,3,1,5,6,7,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,8,7,1,5,4,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,2,1,6,4,3,7]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[6,3,2,1,5,4,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,3,2,1,6,4,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,8,2,1,5,4,6,7]=>[4,8,3,1,6,5,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[6,2,7,1,5,4,3,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[5,2,7,1,6,4,3,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,2,7,1,5,6,3,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[2,8,7,1,5,4,3,6]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[6,5,1,7,8,4,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,1,6,7,4,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,4,1,7,5,8,3,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,1,6,7,8,3,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,8,1,6,5,7,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,3,1,7,5,4,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,3,1,6,7,4,8,2]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,8,1,6,5,4,7,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,2,1,6,5,7,3,8]=>[7,3,2,5,4,6,1,8]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[2,8,1,6,5,4,3,7]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[6,1,7,8,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,7,6,5,8,3,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,7,6,5,4,8,2]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,5,8,1,2,6,3,7]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,4,5,7,2,6,3,8]=>[1,7,5,6,3,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,5,6,2,4,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,3,5,7,2,4,6]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,6,8,1,7,2,4,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[3,4,5,6,8,1,7,2]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,5,8,2,6,7,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,3,5,6,7,1,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,7,8,1,3,5,4,6]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,7,8,3,5,6,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,4,5,7,8,1,6,3]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,5,8,1,7,6,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,8,7,2,1,6,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,7,3,5,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,2,1,3,5,4,6]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,6,8,7,2,1,5,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[8,6,4,1,7,5,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,4,3,1,8,5,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,3,6,7,8,1,5,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,6,8,1,2,5,4,7]=>[5,7,8,4,1,6,2,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[7,4,1,8,5,2,3,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,4,2,8,3,6,5]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,2,5,3,6,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,5,4,2,3,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,2,6,5,4,3,8]=>[1,7,3,6,5,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,6,3,2,5,4,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,3,1,2,5,4,7]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,1,7,6,3,2,4,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,5,7,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,8,1,7,5,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,6,7,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,8,6,3,1,5,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,7,8,1,6,5,4,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[7,3,1,8,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,2,1,6,5,4,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,7,6,3,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,8,6,3,7,4,5]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,6,1,5,2,7,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,1,7,4,2,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,1,7,5,4,3,8,6]=>[2,1,8,6,5,4,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,8,4,5,3,6,7]=>[2,1,8,6,5,4,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,7,8,3,6,5,4]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,8,5,7,6,3,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,4,8,5,7,3,6]=>[2,1,7,8,5,6,3,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,5,4,6,8,3,7]=>[2,1,7,4,5,8,3,6]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,5,3,1,6,2,4,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,1,4,6,8,3,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,4,1,5,2,3,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[8,3,7,5,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,7,4,6,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,8,3,7,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,4,8,6,3,1,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,2,6,3,8,5,1,7]=>[7,4,6,2,8,3,1,5]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,6,3,2,7,8,1,5]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[3,8,2,4,7,5,1,6]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,6,8,7,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,2,7,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,2,1,7,6,4,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,3,8,1,5,7,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,2,4,1,7,5,6]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,4,2,3,1,8,6,5]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[7,2,4,3,1,5,8,6]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[7,8,3,1,5,4,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,8,1,4,6,5,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,2,3,1,4,5,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,6,1,4,3,2,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,7,1,8,3,6,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,1,4,5,3,2,7]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[6,7,1,5,4,3,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,7,5,1,3,4,2,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,7,1,3,8,2,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,2,6,1,4,7,3,5]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[5,8,1,6,3,7,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,5,6,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,4,8,2,1,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,6,5,4,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,3,6,4,5,1,2,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,5,8,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,5,4,1,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[2,6,3,5,1,4,8,7]=>[5,6,3,4,1,2,8,7]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,7,8,5,1,6,4,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[8,7,3,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,3,4,6,1,5,7]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,7,4,3,6,1,8,5]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[3,4,7,2,8,1,5,6]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[3,2,8,4,7,1,6,5]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,2,4,7,5,1,6,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[3,8,4,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[3,2,4,6,1,5,8,7]=>[5,2,3,6,1,4,8,7]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[8,3,4,5,7,6,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,4,6,5,7,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,3,8,4,6,7,1,5]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,4,3,5,8,7,1,6]=>[7,3,2,4,8,6,1,5]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[3,2,4,5,6,8,1,7]=>[7,2,3,4,5,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,6,8,1,4,2,7,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,5,7,8,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,7,8,6,2,4]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,7,8,6,1,2,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,5,1,6,8,2,7,4]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,1,5,6,8,2,7,4]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,5,6,8,1,7,4]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,6,4,8,2,1,7,3]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[5,1,6,3,8,4,7,2]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,5,1,6,8,3,7,4]=>[3,8,1,6,7,4,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[5,1,2,6,8,3,7,4]=>[8,2,3,6,7,4,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,1,8,6,2,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,5,2,7,8,6,3,4]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,5,2,8,3,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,7,5,2,8,3,4]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,6,7,5,1,8,3,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[5,7,2,8,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,7,8,6,2,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,1,7,8,6,3,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,3,7,8,6,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,2,7,8,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,2,5,7,8,6,1,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,2,7,5,1,8,3,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,2,6,7,5,8,3,4]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,2,7,5,4,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,7,5,2,4,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,7,2,5,3,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,7,4,5,2,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,1,7,8,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,5,7,8,6,3,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,1,7,8,6,3,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,3,7,5,1,8,2,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,6,7,5,3,8,2,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,5,4,2,8,3]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,7,5,1,4,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,7,8,6,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,1,7,2,6,5,8,3]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,4,7,1,5,6,8,3]=>[4,8,6,1,5,3,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[6,7,4,1,5,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,6,7,4,5,2,8,3]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,3,7,5,8,2,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,1,7,5,8,2,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,5,3,7,8,6,1,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[6,7,5,4,2,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,3,2,7,5,8,1,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,4,2,5,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,2,7,4,5,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,2,3,7,5,8,1,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,5,1,6,3,2,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[7,5,1,6,3,8,2,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,1,6,3,8,4,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,7,6,1,3,8,4,5]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,7,6,1,3,8,5,4]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[7,3,5,1,8,2,6,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,3,5,1,8,2,4,6]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[3,7,5,1,8,6,2,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,6,7,1,5,8,3,4]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,6,7,4,1,8,3,5]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,1,6,7,3,8,5,4]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,6,7,4,1,8,5,3]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,6,7,1,5,8,4,3]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,6,5,1,8,4,7,2]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[3,6,5,1,8,4,2,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[3,7,5,4,8,1,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,7,5,4,8,1,2,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,6,1,5,8,7,3,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,6,1,5,8,7,2,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,6,1,5,8,2,7,3]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,5,1,6,2,8,3,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,1,6,2,8,4,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,6,1,5,8,2,3,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,7,1,5,8,3,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,3,4,7,8,1,6,5]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,8,5,4,3,2,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[10,11,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[7,9,6,5,4,3,2,8,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,9,6,5,4,3,2,1,7]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,8,5,4,3,7,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,4,3,2,1,7,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[6,5,4,3,1,8,7,2]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[8,7,6,5,4,3,9,1,2]=>[9,8,6,5,4,3,7,2,1]=>[9,8,6,5,4,3,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[8,7,5,4,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[9,7,6,5,4,3,1,8,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[11,10,9,8,7,6,5,4,3,1,2]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[8,3,4,6,2,1,5,7]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[3,5,6,2,1,8,4,7]=>[5,7,4,3,1,8,2,6]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,5,2,6,8,4,1,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,5,3,2,8,4,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,3,2,8,4,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,4,5,7,3,8,6,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,2,5,6,8,3,1,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,2,8,1,5,6,3,7]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[2,5,6,1,8,4,3,7]=>[4,7,6,1,8,3,2,5]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[5,3,6,8,1,4,2,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[4,5,6,8,1,3,2,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,4,5,6,8,3,2,7]=>[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,5,6,3,8,2,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,5,3,7,2,8,6,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,4,7,3,2,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,1,4,7,3,2,8,5]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,8,4,5,3,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,7,3,8,4,2,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,5,1,7,4,3,8,6]=>[3,6,1,8,5,2,7,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,5,7,4,1,8,6,3]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[5,3,7,1,4,8,6,2]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,4,3,1,7,8,5,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,4,1,7,3,8,5,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,6,3,7,8,4,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,1,6,3,7,8,4,2]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,1,3,7,8,4,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,6,1,7,8,3,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,6,3,7,4,8,5,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,7,2,4,1,8,5,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,7,2,1,4,3,8,5]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,4,7,3,1,2,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,6,3,1,2,7,8,4]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,6,1,3,2,7,8,4]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,6,3,2,1,7,8,4]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[2,5,6,3,7,8,4,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,5,6,3,1,7,8,4]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[2,6,4,7,3,1,8,5]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[6,3,7,2,8,4,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,7,2,8,4,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,2,7,1,8,4,5]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,5,3,2,1,8,4,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,3,8,4,2,1,5,6]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,7,2,1,3,8,6,5]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[1,3,7,8,6,4,2,5]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,3,8,4,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,3,8,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,7,8,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,2,7,8,5,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,6,2,1,7,8,5,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,4,5,8,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,1,7,3,8,6,4]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[6,7,2,1,3,8,5,4]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,1,6,7,8,2,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,3,7,1,8,5,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,2,1,7,3,8,5,4]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,2,7,1,8,5,4,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,3,1,7,8,5,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,1,3,6,8,2,5,7]=>[6,2,3,7,8,1,4,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,2,3,6,8,1,5,7]=>[6,3,2,7,8,1,4,5]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[5,3,2,1,8,4,7,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,6,5,8,2,1,7,4]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[4,5,2,1,3,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,2,6,4,5,8,1,7]=>[7,2,5,4,3,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,4,6,5,8,1,3,7]=>[6,7,4,3,8,1,2,5]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[1,6,2,4,5,8,3,7]=>[1,7,3,5,4,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,3,2,1,6,8,4,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[6,2,4,5,8,1,3,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,3,4,6,5,8,2,7]=>[1,7,3,5,4,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,3,4,5,8,2,7]=>[1,7,5,4,3,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,4,1,8,5,2,7,6]=>[6,3,2,8,5,1,7,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[2,8,4,1,7,6,3,5]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[8,1,4,2,7,3,6,5]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,5,3,2,8,7,4,6]=>[1,7,4,3,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,1,7,5,3,4,6]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,7,6,4,5,8,3,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,7,4,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,4,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,2,5,8,6,7,1]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,1,3,5,6,8,7,2]=>[8,2,3,4,5,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,4,8,6,7,1,3,5]=>[6,7,8,5,4,1,2,3]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[4,3,6,2,8,1,7,5]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[3,7,4,8,2,1,6,5]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[2,3,5,8,6,7,1,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,2,5,6,8,7,1,4]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,1,8,5,6,7,3,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,8,3,5,6,7,4]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,2,3,7,1,8,6,5]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,2,6,4,8,1,7,5]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,2,1,6,7,3,4,5]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,7,8,5,4,1,3,6]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[1,7,5,3,8,4,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,7,5,3,1,2,8,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[7,2,4,8,5,3,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,3,1,2,7,6,5]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,5,2,7,4,1,8,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[8,4,2,3,7,1,5,6]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[2,8,4,7,1,3,5,6]=>[5,8,6,7,1,3,4,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[8,2,4,6,7,1,3,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,8,2,3,6,7,1,5]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[3,5,2,7,6,1,8,4]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[5,8,3,2,1,6,7,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,8,7,3,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,2,7,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,4,2,8,7,6,3]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,7,6,5,8,2,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,7,1,6,2,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,2,6,8,7,1,3,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,3,2,1,8,5,7,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,7,5,4,1,8,6,3]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[4,2,5,6,8,7,1,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,8,4,2,5,6,7,3]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,8,4,1,5,6,7,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,2,8,5,6,7,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,2,4,7,1,8,6,3]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,3,4,7,1,8,6,2]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,6,4,1,3,2,5,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,3,6,5,2,4,7]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,3,6,5,2,7]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,6,5,2,1,8,7,4]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[8,3,2,4,6,5,1,7]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,2,1,6,5,3,7]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,4,1,2,6,5,3,7]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,4,2,1,5,3,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,6,4,1,5,2,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,6,3,4,5,1,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,3,4,8,5,7,2,6]=>[1,7,3,8,5,6,2,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,4,7,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,3,4,7,5,8,2,6]=>[1,7,3,8,5,6,2,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,5,1,3,8,7,4]=>[4,8,5,1,3,7,6,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,7,1,6,5,8,3,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,8,7,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,5,1,4,7,6,3]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,3,1,5,8,6,7,2]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,1,3,5,8,6,7,2]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,5,3,8,4,7,1,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,4,2,1,6,8,7,3]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[6,8,4,3,2,7,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,7,8,2,1,6,5]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[5,1,3,2,8,6,7,4]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,3,1,2,8,6,7,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,2,3,1,6,8,7,4]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,3,2,1,8,6,7,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,4,7,3,8,1,6,5]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[6,3,8,2,7,4,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,1,3,6,4,7,5]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,5,1,7,8,4,2,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[2,7,4,5,8,3,1,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,4,8,7,2,1,6,5]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[5,4,7,8,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,3,8,7,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,8,7,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,7,2,4,8,1,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[8,4,7,2,3,1,5,6]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,4,7,1,3,2,5,6]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,4,7,2,1,3,5,6]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,6,4,2,1,3,7,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,4,1,3,2,7,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,4,2,3,1,7,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,7,2,6,1,8,4]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[6,1,3,8,5,7,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,8,3,2,6,7,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,5,3,6,2,7,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,1,5,4,7,6,3]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,5,8,7,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,7,6,4,5,8,3]=>[2,1,8,6,5,4,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,7,2,4,6,5,8,3]=>[1,8,3,6,5,4,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,1,7,6,8,2,4]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,8,2,6,1,3,7,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,3,5,8,7,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,7,8,4,1,6,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[4,2,8,1,5,6,7,3]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,4,5,1,6,8,7,2]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,2,8,5,1,6,7,3]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,1,8,5,2,6,7,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,7,1,8,5,4,6,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[5,8,6,2,1,3,7,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,4,1,5,6,7,3]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,6,3,5,8,1,7,2]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,7,8,3,5,4,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,4,5,1,8,6,7,2]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,8,1,4,5,6,7,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,4,5,6,8,2,1,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,4,5,7,1,8,6,2]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,4,5,7,8,2,6,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,4,6,2,8,5,1,7]=>[7,4,6,2,8,3,1,5]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[3,4,6,8,1,5,2,7]=>[7,5,6,8,2,3,1,4]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[3,4,7,2,1,8,6,5]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[3,4,7,8,1,5,6,2]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[3,5,2,6,7,8,1,4]=>[7,8,3,4,5,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,5,2,7,8,4,6,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,5,2,8,4,1,6,7]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,5,6,2,8,4,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[3,5,6,8,4,1,2,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[3,5,7,2,4,8,6,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[3,5,7,2,8,4,6,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[3,5,7,8,4,1,6,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[3,6,2,1,7,8,5,4]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,6,2,1,8,5,4,7]=>[4,7,3,1,8,6,2,5]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,6,7,2,4,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,6,7,2,8,5,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,7,8,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,8,2,4,5,1,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[3,7,2,1,4,8,6,5]=>[4,8,3,1,5,7,6,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,7,2,1,8,5,6,4]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,7,2,8,4,5,6,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,7,8,2,4,5,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,2,1,4,5,6,7]=>[4,8,3,1,5,6,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[4,1,5,6,7,8,3,2]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,5,7,3,8,6,2]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,6,3,7,8,5,2]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,6,3,8,5,2,7]=>[7,2,6,4,8,3,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,1,6,7,3,8,5,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,6,7,8,5,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,6,8,3,5,2,7]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,1,7,3,2,8,6,5]=>[5,2,8,4,1,7,6,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,1,7,8,3,5,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,8,3,2,5,6,7]=>[5,2,8,4,1,6,7,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,5,2,6,7,8,3,1]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,5,2,6,8,1,3,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,5,6,3,8,1,2,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,5,6,8,3,1,2,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[4,5,7,3,8,1,6,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,5,8,3,2,1,6,7]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[4,6,2,3,7,8,5,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,6,2,3,8,5,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,6,2,7,3,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,6,2,7,8,5,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,6,7,3,2,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,6,8,3,2,5,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,7,2,3,1,8,6,5]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[4,7,2,8,3,5,6,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,7,8,3,2,5,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,2,3,1,5,6,7]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[5,1,2,6,8,4,3,7]=>[7,2,3,6,8,4,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,2,7,4,8,6,3]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,2,7,8,4,6,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,2,8,4,3,6,7]=>[6,2,3,8,5,1,7,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,1,6,3,8,4,2,7]=>[7,2,6,4,8,3,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,6,7,4,8,2,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,6,7,8,4,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,8,3,4,2,6,7]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,6,2,3,8,4,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[5,6,2,7,8,4,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,8,3,4,2,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[5,7,2,3,4,8,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,2,3,8,4,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,8,3,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,2,3,4,1,6,7]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[6,1,2,3,7,8,5,4]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,2,3,8,5,4,7]=>[7,2,3,4,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,1,2,7,8,5,4,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,7,3,4,8,5,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,7,3,8,5,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,7,8,4,5,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,8,3,4,5,2,7]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,7,2,3,8,5,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,2,8,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,2,3,4,5,1,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[7,1,2,3,4,8,6,5]=>[8,2,3,4,5,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,2,8,4,5,6,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,3,4,5,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,1,8,2,3,7,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,8,1,2,4,3,7,6]=>[6,8,3,4,5,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,5,8,6,1,2,4,7]=>[6,7,8,5,4,1,2,3]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[3,1,6,8,2,4,7,5]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,6,2,8,1,5,7,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,6,1,3,8,4,7,5]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,7,5,2,3,4,6,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,5,1,3,8,4,6]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[8,2,5,7,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,1,3,7,6,4,5]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,2,5,1,3,7,4,6]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,2,7,5,3,1,6,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,2,6,5,4,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,5,2,4,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,8,2,5,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,8,6,3,2,4,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,8,1,5,3,2,4,7]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[1,6,7,5,3,2,4,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,5,1,2,4,8,3,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[7,8,1,6,4,2,3,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,1,2,5,6,3,7]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,7,3,6,5,2,4,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,3,7,2,6,4,5]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,3,2,6,5,1,8,4]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,8,4,2,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,7,4,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,3,6,5,1,7,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,9,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,9,8,7,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[5,9,8,7,6,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[4,9,8,7,6,5,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[3,9,8,7,6,5,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[2,9,8,7,6,5,4,3,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,10,9,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,9,7,8,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,10,9,8,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[4,8,6,5,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,9,8,6,7,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,10,9,8,7,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[3,8,7,5,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,5,6,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,9,8,7,5,6,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[5,10,9,8,7,6,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[2,8,7,6,4,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,4,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,9,8,7,6,4,5,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[4,10,9,8,7,6,5,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,8,7,6,5,3,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,7,6,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,9,8,7,6,5,3,4,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[3,10,9,8,7,6,5,4,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,8,7,6,5,2,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,9,8,7,6,5,4,2,3]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,10,9,8,7,6,5,4,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,2,8,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,8,5,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,2,8,5,1,7,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,4,7,2,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,4,3,1,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,4,1,3,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,6,1,5,3,7,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,1,8,5,2,7,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,4,1,2,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[6,8,3,5,4,1,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,5,8,3,6,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,5,6,3,4,2,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,6,8,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,3,8,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,6,4,8,3,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,5,7,4,2,6,3,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,2,3,1,7,8,5,6]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[5,2,8,4,1,7,6,3]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,6,3,4,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,3,4,5,1,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,2,1,5,4,7,6]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[6,3,7,1,5,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,5,1,8,4,3,7,6]=>[3,6,1,8,5,2,7,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[6,2,5,4,8,1,3,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,3,1,6,5,8,2,7]=>[7,3,2,5,4,8,1,6]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[6,1,3,4,5,8,2,7]=>[7,2,5,4,3,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,3,4,1,5,2,7,6]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,5,4,2,6,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,2,6,4,1,7,3,5]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[7,3,8,4,5,2,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,5,1,8,4,3,6]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[1,7,3,2,5,4,8,6]=>[1,8,4,3,6,5,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,2,1,5,3,4,6]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,6,1,5,8,7,4,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,6,4,5,1,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,6,8,1,2,7,3]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[6,4,7,2,3,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,8,4,1,3,5,7,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,4,7,8,6,2,5,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,1,3,5,7,8,6,2]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,5,1,8,4,7,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,3,1,8,4,7,6,2]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,2,7,4,6,1,3,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,7,3,2,8,1,6,5]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[6,3,1,4,7,2,8,5]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,7,3,6,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,3,6,8,2,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,4,7,3,8,5,6,1]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,8,6,1,5,7,3,4]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[7,8,2,5,4,3,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,3,4,2,7,6,5]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,5,3,7,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,3,2,4,1,8,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[2,8,3,4,7,1,5,6]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,1,3,6,7,8,2,5]=>[7,2,3,8,5,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,7,6,3,2,5,8,4]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,8,1,5,6,2,7,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[8,2,5,6,1,7,4,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[7,1,5,2,8,6,4,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,5,4,8,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,6,4,5,2,7,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,3,6,2,7,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,2,1,7,5,8,4]=>[4,8,3,1,6,5,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,5,4,1,8,7,6,3]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[4,7,2,6,5,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,8,1,4,2,7,3,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,3,4,7,1,8,2,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,4,7,8,2,5,6,1]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,8,2,4,5,6,7,3]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,2,4,1,6,8,7,3]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,2,5,7,6,1,8,4]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,3,5,6,1,8,7,2]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,3,4,1,7,6,8,2]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,1,4,6,5,7,8,2]=>[8,2,3,5,4,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,4,7,3,5,6,8,2]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,3,6,4,8,7,2]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,3,2,7,5,8,6,4]=>[1,3,2,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,5,8,3,7,6]=>[1,6,3,4,8,2,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,7,8,5,6,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,2,6,8,4,7,3]=>[8,2,3,6,7,4,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,2,6,5,8,4,7]=>[3,2,1,7,5,8,4,6]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[4,1,2,6,8,5,3,7]=>[7,2,3,6,8,4,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,5,2,4,8,7,6,3]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,4,8,7,5,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,4,8,6,5,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,7,5,8,4,6]=>[1,3,2,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,3,1,7,5,4,8,6]=>[3,2,1,8,6,5,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,2,8,5,7,4,6]=>[1,3,2,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,5,8,7,3,6]=>[1,7,3,4,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,4,8,7,3,6]=>[1,7,3,4,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,4,8,7,3,5]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,8,5,6,3,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,8,5,7,3,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,8,2,7,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,2,6,7,4,5]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,2,8,6,3,5]=>[1,7,8,4,6,5,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,8,2,5,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,8,3,7,5,4]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,8,2,3,6,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,7,8,4,6,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,2,8,3,6,5]=>[1,6,8,4,7,2,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,3,4,8,5,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,3,7,4,8,6,2]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,4,1,5,3,7,6]=>[4,8,6,1,5,3,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,8,4,1,5,7,2,6]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[1,3,6,4,2,8,7,5]=>[1,5,8,4,2,7,6,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,7,4,2,8,6,5]=>[1,5,8,4,2,7,6,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,4,2,7,6,5]=>[1,5,8,4,2,7,6,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,4,8,3,7,6]=>[1,6,3,4,8,2,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,4,5,7,2,3,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,3,5,2,7,4,6]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,3,5,1,4,7,6]=>[5,8,3,6,1,4,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,3,8,6,1,4,7,5]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,3,8,6,2,7,4,5]=>[1,5,8,7,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,8,6,7,2,3,5]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,8,7,2,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,8,5,3,7,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,8,5,3,6,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,8,7,3,6,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,8,7,3,5,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,8,6,3,5,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,8,5,2,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,8,6,2,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,6,8,2,3,5]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,7,6,2,8,4,5]=>[1,5,8,7,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,3,8,7,4,1,6,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,2,8,4,7,6,3,5]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,8,7,6,3,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,8,7,5,3,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,8,6,5,3,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,2,6,7,3,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,2,4,7,6,3,8,1]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,6,2,1,7,8,3,4]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,6,2,1,4,8,7,3]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[2,6,1,4,5,8,7,3]=>[3,8,1,5,4,7,6,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[5,4,2,7,6,3,8,1]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,3,7,6,4,5,8,1]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,6,1,7,5,8,3,4]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,6,1,7,4,8,5,3]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,6,1,7,4,8,3,5]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,6,4,1,7,8,2,5]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[5,4,6,1,3,8,7,2]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[3,6,4,1,5,8,7,2]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[2,6,1,5,4,8,7,3]=>[3,8,1,5,4,7,6,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,6,1,4,7,8,5,3]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[5,1,2,4,8,6,7,3]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,2,4,8,7,3,6]=>[7,2,3,4,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,2,4,8,7,6,3]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,3,8,5,4,7,6]=>[1,2,3,8,6,5,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,1,2,8,5,7,6]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[2,1,5,3,8,6,4,7]=>[2,1,7,4,8,6,3,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,3,8,5,6,4,7]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,8,6,4,5,7]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,8,6,5,4,7]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,8,5,4,6,7]=>[1,2,3,8,6,5,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,1,5,4,8,3,7]=>[3,7,1,5,4,8,2,6]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[5,1,2,4,8,6,3,7]=>[7,2,3,4,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,2,4,8,3,7,6]=>[6,2,3,4,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,6,3,1,4,8,2,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[2,5,4,3,1,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,4,6,3,1,8,7,2]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[3,6,4,5,1,8,7,2]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[3,6,5,4,1,8,7,2]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,2,6,1,7,8,4,3]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[5,1,6,2,8,7,3,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,1,3,7,8,6,4,5]=>[2,1,3,8,7,6,5,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,3,7,8,5,6,4]=>[2,1,3,8,7,6,5,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,2,4,1,7,8,6,3]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,3,1,2,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[5,1,4,2,8,6,7,3]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,1,3,6,8,5,7,4]=>[2,1,3,8,7,6,5,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,3,8,6,7,4,5]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,8,7,5,4,6]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,8,7,4,5,6]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,8,5,7,4,6]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,3,6,8,7,4,5]=>[2,1,3,8,7,6,5,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,4,1,2,8,7,6,3]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,1,6,2,8,7,5,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,2,3,4,5,9,6,7,8]=>[1,2,3,4,5,9,7,8,6]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,9,5,6,7,8]=>[1,2,3,4,9,6,7,8,5]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,9,4,5,6,7,8]=>[1,2,3,9,5,6,7,8,4]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,9,3,4,5,6,7,8]=>[1,2,9,4,5,6,7,8,3]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,5,6,7,10,8,9]=>[1,2,3,4,5,6,7,10,9,8]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,4,5,9,7,6,8]=>[1,2,3,4,5,9,8,7,6]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,5,6,10,7,8,9]=>[1,2,3,4,5,6,10,8,9,7]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,4,9,6,5,7,8]=>[1,2,3,4,9,7,6,8,5]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,5,10,6,7,8,9]=>[1,2,3,4,5,10,7,8,9,6]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,8,4,5,3,6,7]=>[1,2,8,6,5,4,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,9,5,4,6,7,8]=>[1,2,3,9,6,5,7,8,4]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,10,5,6,7,8,9]=>[1,2,3,4,10,6,7,8,9,5]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,8,3,4,2,5,6,7]=>[1,8,5,4,3,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,9,4,3,5,6,7,8]=>[1,2,9,5,4,6,7,8,3]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,10,4,5,6,7,8,9]=>[1,2,3,10,5,6,7,8,9,4]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,8,4,3,2,5,6,7]=>[1,8,5,4,3,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,9,3,2,4,5,6,7,8]=>[1,9,4,3,5,6,7,8,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,10,3,4,5,6,7,8,9]=>[1,2,10,4,5,6,7,8,9,3]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[8,4,7,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,7,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,7,4,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,3,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,7,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,7,2,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,7,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,7,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,7,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,7,1,6,5,4,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,1,7,2,6,5,4,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,7,6,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,7,6,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,7,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,7,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,7,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,1,5,2,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,1,3,2,5,4,7]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[6,8,1,4,2,5,3,7]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[7,8,3,6,1,4,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,2,5,3,6,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,2,5,1,4,3,6]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,8,1,4,3,6,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,1,4,3,7,2,6]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[6,8,2,5,1,4,3,7]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[6,8,2,5,3,7,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,2,5,4,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,4,7,6,8,1,3]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,5,3,7,6,8,1,4]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,5,1,4,3,7,6,8]=>[3,5,1,4,2,7,6,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,6,1,4,3,7,5,8]=>[3,7,1,5,4,6,2,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,6,5,8,1,4,3,7]=>[5,7,6,8,1,3,2,4]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,6,1,5,3,7,4,8]=>[3,7,1,5,4,6,2,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,6,3,7,4,8,1,5]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,6,4,7,5,8,1,3]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[5,8,3,6,4,7,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,2,6,4,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,2,6,3,7,1,5]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[4,8,1,5,3,7,2,6]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,8,1,5,2,6,3,7]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,8,3,7,1,5,2,6]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[6,8,3,7,1,4,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,1,3,2,6,4,7]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,8,4,7,1,3,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,8,4,7,1,3,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,7,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,6,8,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,6,8,1,3,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,7,5,8,1,3,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,7,1,3,2,6,5,8]=>[5,7,3,4,1,6,2,8]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,7,1,4,2,6,5,8]=>[5,7,3,4,1,6,2,8]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,7,5,8,1,4,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,7,6,8,1,4,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,7,6,8,2,5,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,7,6,8,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,5,8,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,5,8,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,5,8,2,6,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,7,4,8,2,6,1,5]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[3,7,4,8,1,5,2,6]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[3,7,2,6,5,8,1,4]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,7,3,6,5,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,6,5,8,4,7,1,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[2,6,5,8,4,7,1,3]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[2,6,5,8,3,7,1,4]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[7,6,4,2,8,5,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,4,3,8,2,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,4,8,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,4,3,7,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,4,3,5,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,7,3,5,4,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,8,3,7,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,8,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,3,5,8,2,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,3,5,2,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,6,4,2,5,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,6,2,8,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,3,8,2,4,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,3,4,8,2,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,3,7,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,3,5,8,4,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,8,3,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,3,6,7,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,4,8,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,8,4,7,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,8,4,1,7,5,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[6,2,7,4,1,5,3,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[6,3,4,7,5,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,3,5,7,8,4,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,3,6,8,2,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,8,3,7,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,7,3,4,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,6,7,8,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,8,3,5,7,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,3,5,6,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,7,3,5,8,2,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,4,7,8,2,1,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,3,8,2,4,1,6,7]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[5,3,4,8,2,6,1,7]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,8,3,6,2,5,7,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,8,3,5,7,2,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,3,5,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,7,8,3,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,8,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,3,6,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,3,7,2,5,6,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,3,4,8,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,3,8,2,4,1,7,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[5,2,8,4,1,7,3,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[6,4,2,5,1,8,7,3]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[6,4,3,5,8,2,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,3,5,8,7,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,3,7,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,3,4,8,2,1,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,8,4,2,3,1,6,7]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[5,8,4,2,3,1,7,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[6,4,5,3,8,2,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,4,8,5,3,7,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,3,8,5,7,2,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,4,2,8,5,3,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[6,4,2,7,3,1,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,4,3,7,8,5,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,5,3,7,1,8,2]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,7,4,2,3,1,6,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[5,6,3,7,1,8,2,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,3,4,7,1,8,2]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,6,3,4,8,2,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,3,5,7,4,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,3,5,4,7,8,2,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,4,3,5,7,1,8,2]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,4,2,5,1,7,3,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,3,7,2,4,1,6,8]=>[6,5,7,4,2,1,3,8]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[5,3,4,7,2,6,1,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,7,3,6,2,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,7,3,6,8,2,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,6,7,3,5,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,5,7,8,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,8,3,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,8,3,7,2,6,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[5,3,4,6,8,2,1,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,3,6,8,2,1,4,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[5,3,6,7,1,8,2,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,3,4,6,7,1,8,2]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,6,3,5,7,8,2,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,5,7,3,6,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,5,6,8,3,7,2,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,7,4,8,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,2,6,5,1,8,7,4]=>[5,2,8,4,1,7,6,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,5,6,7,2,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,6,9,8,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,5,4,9,8,7,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,8,5,9,7,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,7,8,9,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[5,8,4,3,9,7,6,2,1]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[5,4,7,6,9,8,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[5,7,8,4,9,6,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[5,6,7,8,9,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[4,7,8,3,2,9,6,5,1]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[4,6,7,8,3,9,5,2,1]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[4,5,6,7,8,9,3,2,1]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[3,2,1,6,5,4,9,8,7]=>[3,2,1,6,5,4,9,8,7]=>[3,2,1,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[8,7,10,9,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,6,5,10,9,8,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,9,6,10,8,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,5,4,3,10,9,8,7,2,1]=>[10,9,4,3,8,7,6,5,2,1]=>[10,9,4,3,8,7,6,5,2,1]=>[[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.]
[6,9,5,4,10,8,7,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,5,8,7,10,9,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,8,9,5,10,7,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[5,4,3,2,1,10,9,8,7,6]=>[5,4,3,2,1,10,9,8,7,6]=>[5,4,3,2,1,10,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[5,4,8,7,3,10,9,6,2,1]=>[10,9,8,5,4,7,6,3,2,1]=>[10,9,8,5,4,7,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[5,8,9,4,3,10,7,6,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[5,7,4,9,6,10,8,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[5,6,7,8,9,10,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[4,7,8,9,3,2,10,6,5,1]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[4,3,6,5,8,7,10,9,2,1]=>[10,9,4,3,6,5,8,7,2,1]=>[10,9,4,3,8,7,6,5,2,1]=>[[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.]
[4,6,7,8,9,3,10,5,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[1,6,8,2,5,3,7,4]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,5,3,4,7,6]=>[1,8,3,6,5,4,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,3,6,4,7,5]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,2,8,4,7,6]=>[1,4,6,2,8,3,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,7,3,4,6,5]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,2,3,7,4,6]=>[1,7,8,4,5,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,2,3,5,4,7]=>[1,7,8,4,5,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,3,6,1,2,4,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[7,1,5,8,4,2,3,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,5,7,4,2,3,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,4,5,8,2,3,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,1,6,2,8,3,5]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,1,7,2,6,3,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,4,7,5,2,3,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,5,4,7,2,3,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,1,7,5,8,3,4,6]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[7,1,5,4,8,2,3,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,4,8,5,2,3,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,1,7,2,3,8,5]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,8,3,1,2,4,6,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,7,1,6,4,2,3,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,1,7,4,2,3,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,1,8,4,2,3,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,3,8,1,2,4,6,5]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,3,7,1,2,4,6,5]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,3,6,1,2,4,7,5]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,3,7,5,1,2,4,6]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,3,6,1,2,4,8,5]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,7,1,8,4,2,3,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,1,7,4,2,3,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,8,5,4,2,3,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,4,5,2,3,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,1,7,8,5,3,4,6]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[7,6,3,1,2,4,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,1,2,3,8,7,5,4]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,8,1,4,2,3,7,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,3,1,2,7,4,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,7,3,1,2,8,4,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,7,1,4,2,3,8,5]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,3,6,8,5,7,1,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,1,2,5,4,8,3,7]=>[7,2,3,5,4,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,2,8,5,4,1,7,6]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[7,8,2,1,4,6,3,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,2,1,5,8,3,4,6]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,4,8,5,1,3,6,7]=>[5,6,8,4,1,2,7,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,5,6,1,8,4,2,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,3,6,8,7,4,2,5]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,5,7,3,4,6]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,1,5,8,3,4,7]=>[3,7,1,6,8,4,2,5]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[5,7,1,6,8,4,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,8,1,2,5,7,3,6]=>[7,8,3,4,5,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[8,4,6,2,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,6,4,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,1,4,7,2,5,6]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[1,7,8,4,6,2,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,4,8,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,1,6,5,4,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,7,3,1,5,8,4,6]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,7,4,6,8,1,3,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,7,5,8,6,4,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,2,6,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,1,6,4,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,8,2,7,4,1,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,5,2,8,7,4,6,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,4,2,7,8,1,6,5]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[4,1,3,7,5,6,8,2]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,3,8,1,7,4,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,8,7,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,1,7,3,8,5,2,6]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,6,1,4,5,8,2,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,6,7,4,5,3,8,2]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,7,3,5,4,8,2]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,3,1,2,5,8,4,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,4,7,2,8,5,3,6]=>[1,7,8,4,6,5,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,6,8,7,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,7,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,4,1,7,5,6,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[8,2,4,3,7,5,6,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,8,2,1,5,7,3,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,2,8,4,1,6,3,5]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,2,4,8,6,5,3,7]=>[1,2,7,8,6,5,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,5,6,8,4,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,7,8,1,4,6,3,5]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,8,2,5,7,1,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,1,6,8,5,3,7,2]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,2,6,4,8,3,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,7,1,3,4,5,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,3,6,5,2,8,4,7]=>[1,5,7,4,2,8,3,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,6,5,3,4,8,2]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,3,4,2,8,7,5,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,3,8,7,5,2,6,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,8,7,4,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,4,5,2,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[8,6,1,3,5,4,2,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,3,8,6,1,2,4,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[2,5,6,3,4,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[2,5,3,6,8,7,4,1]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,8,7,3,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,2,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,5,4,8,7,2,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,3,8,6,1,5,2,7]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[4,7,6,2,5,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,2,6,8,1,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,2,7,1,4,3,6]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,8,5,3,6,2,4,7]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,7,2,4,3,8,6]=>[6,2,8,4,5,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,5,3,4,8,6,2,7]=>[1,7,4,3,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,1,3,8,6,2,7]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[5,1,8,6,3,4,2,7]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,5,2,8,3,7,6,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,2,3,7,6,4,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,2,4,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,2,5,3,4,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,5,6,4,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,6,7,4,8,2,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,3,5,8,2,6,4]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,1,3,5,6,7,4]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,3,1,4,7,5,8,2]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,1,3,8,2,6,7,5]=>[5,2,3,8,1,7,6,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,8,3,6,7,5,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,1,7,2,8,5,4,6]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,6,1,4,7,2,8,5]=>[6,8,3,4,5,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[1,5,8,4,7,2,3,6]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,3,6,2,8,4,5]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,2,7,4,5,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,1,8,4,5,7,3,6]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,8,5,7,3,2,4,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,8,5,4,3,6,7]=>[2,1,8,6,5,4,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,7,4,1,5,3,8,6]=>[4,8,6,1,5,3,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[7,4,8,6,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,1,4,6,3,8,5]=>[3,8,1,6,5,4,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[4,7,5,6,8,1,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,1,3,2,8,5,4,6]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,8,5,4,1,3,6,7]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[5,1,7,4,2,3,8,6]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,8,6,5,1,4,2,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,1,8,6,5,3,2,7]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,8,5,2,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,8,5,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,8,4,3,7,6,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,4,7,5,2,3,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,2,8,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,4,3,6,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,7,5,1,2,8,3,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,2,6,8,3,4,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[7,6,2,4,5,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,6,8,4,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,3,8,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,3,8,4,7,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,3,6,5,8,4,1]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,2,7,5,8,3,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,3,6,4,5,7,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,1,5,6,8,3,7,4]=>[2,1,8,6,7,4,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,8,1,2,6,4,7,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,6,8,3,2,7,4,5]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,5,7,2,8,4,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,1,2,8,4,6,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,8,3,6,2,7,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[5,8,2,7,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,5,8,2,7,3,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,7,3,6,4,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,1,5,6,4,8,7,2]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,3,6,2,5,7,8,4]=>[1,4,8,2,5,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,3,5,7,8,2]=>[1,8,5,4,3,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,1,6,4,7,8,2]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,6,1,4,2,7,8,5]=>[5,8,3,4,1,6,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,3,6,5,2,7,8,4]=>[1,5,8,4,2,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,4,3,8,5,7]=>[1,2,7,5,4,8,3,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,3,5,1,8,4,7,6]=>[4,2,6,1,8,3,7,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,6,1,8,5,4,7]=>[4,2,7,1,8,6,3,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,2,7,4,6,8,3,5]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,3,7,5,1,8,4,6]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,7,2,5,3,8,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,1,7,5,4,8,6,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,7,6,4,8,5,3]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,3,6,8,5,4]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,3,6,1,8,5,7,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,1,5,4,8,7,6,2]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,5,8,4,7,3,6]=>[1,2,7,8,5,6,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,8,5,4,7,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,6,8,5,2,7,4]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,7,4,8,2,1,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[2,4,7,6,8,3,1,5]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,3,6,8,5,2,4,7]=>[1,6,7,8,5,2,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,8,5,4,3,7]=>[1,2,7,8,6,5,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,8,4,3,7,6]=>[1,2,6,8,5,3,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,8,2,4,7,6]=>[1,5,6,8,2,3,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,6,8,2,5,4,7]=>[1,5,7,8,2,6,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,8,3,2,5,7]=>[1,6,7,8,5,2,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,7,4,8,1,2,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[4,6,1,7,5,8,2,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,3,6,7,5,8,1,4]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,3,7,5,6,8,2,4]=>[1,7,8,5,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,3,6,5,8,1,7,4]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,4,6,2,8,1,7,5]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[3,5,4,6,8,2,1,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,5,4,6,8,1,2,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,2,4,7,5,8,3,6]=>[1,2,7,8,5,6,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,7,4,8,3,5]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,4,7,1,8,5,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,2,6,7,3,8,5,4]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,7,3,8,6,4]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,5,7,6,8,4,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,5,4,6,8,2,7,1]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,2,6,1,8,7,5,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,1,6,5,8,7,4,2]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,6,5,8,7,1,4]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,2,7,4,6,8,5,3]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,5,6,8,4,3]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,6,7,5,8,4,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,6,2,7,5,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,5,7,4,8,2,6,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[2,4,7,6,8,3,5,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,4,6,8,3,5,7,2]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,6,8,2,5,7,4]=>[1,5,8,7,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,8,2,7,4,6]=>[1,5,7,8,2,6,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,8,4,7,6,3]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,8,7,3,6,5]=>[1,2,6,8,7,3,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,8,7,4,3,6]=>[1,2,7,8,6,5,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,8,7,2,4,6]=>[1,6,7,8,5,2,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,3,7,6,8,5,1,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,7,1,2,8,6,4,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,1,7,6,8,5,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,6,8,5,7,4,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,8,7,4,6,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,8,7,6,3,5]=>[1,2,7,8,6,5,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,4,5,7,2,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,3,4,7,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,2,7,4,6,8,1,5]=>[7,2,8,4,5,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,3,6,2,7,1,4,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[2,6,3,4,7,1,5,8]=>[6,7,3,4,5,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,7,3,4,5,8,1,6]=>[7,8,3,4,5,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,7,4,5,6,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,5,7,3,6,8,1,4]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[4,7,6,2,3,8,1,5]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[7,3,5,2,4,8,1,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,6,2,4,5,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,5,2,3,4,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,3,1,2,8,4,7,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[6,5,2,3,7,1,4,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[5,2,1,7,3,4,6,8]=>[6,3,2,7,5,1,4,8]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[5,2,1,8,3,4,6,7]=>[6,3,2,8,5,1,7,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[6,3,2,8,4,5,7,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,3,1,2,8,4,6,5]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[6,4,1,3,8,5,7,2]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,2,3,1,8,4,7,5]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,3,5,2,7,1,4,6]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,6,2,4,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,2,3,6,1,4,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,1,7,3,4,5,6]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,6,3,7,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,6,2,3,4,5,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,2,7,3,4,5,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,6,2,3,4,5,7]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,3,4,5,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,1,7,2,4,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,5,7,2,3,6,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,5,8,2,3,6,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,1,8,3,4,5,6]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,3,8,2,4,5,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,8,3,4,5,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,7,8,3,4,5,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,8,3,6,7,2]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,7,1,8,3,6,4]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[6,2,7,1,8,4,5,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,7,1,3,8,5,6,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,6,2,8,4,5,7,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,3,6,8,2,7,5]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,3,4,6,8,2,7,1]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,6,3,8,7,1,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,4,5,8,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,4,8,7,1,2,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,2,8,7,1,4,6,5]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,1,8,7,2,4,6,5]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[5,3,7,6,1,2,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,8,3,7,2,4,5,6]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,8,1,7,2,4,5,6]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[6,8,2,3,5,1,4,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,7,8,2,6,1,3,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,2,8,7,1,4,5,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[3,8,7,1,4,5,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,6,1,3,4,5,7]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,7,6,1,3,4,5,8]=>[4,7,6,1,5,3,2,8]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,7,6,2,3,4,5,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,6,2,3,4,5,7]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,7,3,4,5,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,7,2,4,5,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,3,6,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,5,8,7,2,3,6,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,6,1,3,4,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,2,4,7,1,8,5]=>[6,8,3,4,5,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,4,7,2,5,1,8,6]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[2,1,6,4,8,5,3,7]=>[2,1,7,6,8,4,3,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[4,1,8,5,3,2,7,6]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,6,2,5,7,1,4,8]=>[6,7,3,4,5,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[1,2,8,3,7,5,4,6]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,3,2,8,5,4,7]=>[7,2,4,3,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,6,1,2,8,4,3,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,6,3,8,7,4,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,8,1,2,6,7,5]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[7,8,10,9,5,6,3,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,5,6,8,7,3,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[5,8,10,6,9,7,3,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[5,6,7,10,9,8,3,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,7,8,3,4,6,5,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,10,9,3,4,6,5,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,3,6,8,4,7,5,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[3,8,10,6,9,4,7,5,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[3,6,7,10,9,4,8,5,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,3,4,5,8,7,6,1,2]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[3,8,10,4,5,9,7,6,1,2]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[3,4,7,10,5,9,8,6,1,2]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[9,10,7,8,5,6,1,2,4,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,10,9,5,6,1,2,4,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,5,6,8,7,1,2,4,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[5,8,10,6,9,7,1,2,4,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[5,6,7,10,9,8,1,2,4,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,7,8,1,4,6,2,5,3]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,8,10,9,1,4,6,2,5,3]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[9,10,1,6,8,4,7,2,5,3]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[1,8,10,6,9,4,7,2,5,3]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,6,7,10,9,4,8,2,5,3]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[9,10,1,4,5,8,7,2,6,3]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[1,8,10,4,5,9,7,2,6,3]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,4,7,10,5,9,8,2,6,3]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[9,10,7,8,1,2,3,6,5,4]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,8,10,9,1,2,3,6,5,4]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[9,10,1,6,8,2,3,7,5,4]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[1,8,10,6,9,2,3,7,5,4]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,6,7,10,9,2,3,8,5,4]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,7,10,5,9,3,8,6,4]=>[1,2,10,9,8,7,6,5,4,3]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[9,10,1,2,3,4,8,7,6,5]=>[10,9,3,4,5,6,8,7,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[1,2,3,4,5,10,9,8,7,6]=>[1,2,3,4,5,10,9,8,7,6]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[11,12,9,10,7,8,5,6,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,12,11,7,8,5,6,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,8,10,9,5,6,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,10,12,8,11,9,5,6,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,8,9,12,11,10,5,6,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,5,6,8,7,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,12,11,5,6,8,7,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,5,8,10,6,9,7,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[5,10,12,8,11,6,9,7,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[5,8,9,12,11,6,10,7,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,5,6,7,10,9,8,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[5,10,12,6,7,11,9,8,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[5,6,9,12,7,11,10,8,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[5,6,7,8,12,11,10,9,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,7,8,3,4,6,5,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,12,11,7,8,3,4,6,5,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,8,10,9,3,4,6,5,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,10,12,8,11,9,3,4,6,5,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,8,9,12,11,10,3,4,6,5,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,3,6,8,4,7,5,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,12,11,3,6,8,4,7,5,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,3,8,10,6,9,4,7,5,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[3,10,12,8,11,6,9,4,7,5,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[3,8,9,12,11,6,10,4,7,5,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,3,6,7,10,9,4,8,5,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[3,10,12,6,7,11,9,4,8,5,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[3,6,9,12,7,11,10,4,8,5,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,3,4,5,8,7,6,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,12,11,3,4,5,8,7,6,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,3,8,10,4,5,9,7,6,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[3,10,12,8,11,4,5,9,7,6,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[3,8,9,12,11,4,5,10,7,6,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,3,4,7,10,5,9,8,6,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[3,10,12,4,7,11,5,9,8,6,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[3,4,9,12,7,11,5,10,8,6,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,7,8,5,6,1,2,4,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,12,11,7,8,5,6,1,2,4,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,8,10,9,5,6,1,2,4,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,10,12,8,11,9,5,6,1,2,4,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,8,9,12,11,10,5,6,1,2,4,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,5,6,8,7,1,2,4,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,12,11,5,6,8,7,1,2,4,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,5,8,10,6,9,7,1,2,4,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[5,10,12,8,11,6,9,7,1,2,4,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[5,8,9,12,11,6,10,7,1,2,4,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,5,6,7,10,9,8,1,2,4,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[5,10,12,6,7,11,9,8,1,2,4,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[5,6,9,12,7,11,10,8,1,2,4,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[5,6,7,8,12,11,10,9,1,2,4,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,7,8,1,4,6,2,5,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,12,11,7,8,1,4,6,2,5,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,8,10,9,1,4,6,2,5,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,10,12,8,11,9,1,4,6,2,5,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,8,9,12,11,10,1,4,6,2,5,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[1,10,12,8,11,6,9,4,7,2,5,3]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[1,8,9,12,11,6,10,4,7,2,5,3]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[1,10,12,6,7,11,9,4,8,2,5,3]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[1,6,9,12,7,11,10,4,8,2,5,3]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[1,6,7,8,12,11,10,4,9,2,5,3]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[1,10,12,8,11,4,5,9,7,2,6,3]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[1,8,9,12,11,4,5,10,7,2,6,3]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[1,10,12,4,7,11,5,9,8,2,6,3]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[1,4,9,12,7,11,5,10,8,2,6,3]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[1,4,7,8,12,11,5,10,9,2,6,3]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[11,12,9,10,7,8,1,2,3,6,5,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,12,11,7,8,1,2,3,6,5,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,8,10,9,1,2,3,6,5,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,10,12,8,11,9,1,2,3,6,5,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,8,9,12,11,10,1,2,3,6,5,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[1,10,12,8,11,6,9,2,3,7,5,4]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[1,8,9,12,11,6,10,2,3,7,5,4]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[1,10,12,6,7,11,9,2,3,8,5,4]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[1,6,9,12,7,11,10,2,3,8,5,4]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[3,1,2,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>[3,2,1,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[2,4,1,3,5,6,7,8,9]=>[3,4,1,2,5,6,7,8,9]=>[3,9,1,8,7,6,5,4,2]=>[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]
[3,6,8,7,1,2,5,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[6,2,8,5,4,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,7,2,4,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,4,1,6,5,8,7,2]=>[8,3,2,5,4,7,6,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,5,1,2,4,8,7,6]=>[4,5,3,1,2,8,7,6]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,8,5,2,7,4,1,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,2,8,4,7,3,1,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[5,2,7,4,1,3,6,8]=>[6,5,7,4,2,1,3,8]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[4,3,5,1,2,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,1,4,6,2,8,7,5]=>[5,2,3,8,1,7,6,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,4,6,5,2,8,7,3]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,4,5,6,1,8,7,2]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,4,5,8,7,2,1,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,4,7,2,6,3,5,8]=>[1,6,7,4,5,2,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,4,7,5,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,4,7,2,3,6,5]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,5,7,3,4,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,5,1,7,4,2,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,1,4,8,7,3,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,8,5,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,8,1,6,3,2,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,4,8,6,3,7,2,5]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,7,6,3,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,6,3,7,5,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,1,3,5,8,6,2,7]=>[7,2,3,4,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,7,4,3,8,1,2,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,4,8,3,7,6,5,2]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,8,2,1,6,5,7]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[3,8,4,2,7,1,5,6]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[3,1,2,5,7,6,4,8]=>[3,2,1,7,6,5,4,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,8,2,7,6,5,4,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,8,1,6,7,5,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,7,2,6,8,5,1,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[7,2,3,8,5,6,1,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,2,1,7,5,6,4,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,1,3,6,5,7,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,4,3,6,1,5,7]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,7,8,5,4,3,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,4,5,3,2,6,7]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,5,4,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,6,3,4,2,5,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,8,7,1,4,2,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,1,4,2,7,5,8]=>[5,7,3,4,1,6,2,8]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,4,1,8,5,7,6,2]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,6,5,1,2,8,4,7]=>[5,7,4,3,1,8,2,6]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,8,5,6,7,2,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,1,7,6,2,4,3,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,5,6,1,4,2,3,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,5,4,7,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,4,5,7,2,3,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,3,6,1,7,2,4,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,8,6,5,7,3,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,3,6,8,4,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,1,6,5,8,3,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,1,5,8,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,5,8,6,7,3,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,2,1,5,8,7,3,6]=>[7,3,2,4,8,6,1,5]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[5,2,4,6,1,7,3,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,5,3,6,8,7,4,2]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,4,6,1,8,2,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,1,5,7,6,8,2,4]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,4,5,6,8,7,2,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,3,7,2,8,5]=>[1,6,8,4,5,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,6,5,2,8,4]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,2,5,4,1,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,2,6,5,4,1,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,6,2,5,4,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,7,5,2,6,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,2,6,4,7,5,1,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,2,3,7,5,4,1,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,3,4,7,6,2,8,5]=>[1,6,3,8,5,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,3,6,1,7,5,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[8,7,2,5,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[3,8,2,6,5,1,7,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[7,8,2,5,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,5,2,6,1,7,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,1,3,7,2,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[6,1,3,7,5,2,8,4]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,3,6,2,8,5,4]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,3,6,2,7,5,4]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,4,7,3,8,6,5]=>[1,2,5,8,3,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,8,2,6,5,4,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,8,6,2,7,5,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,1,7,8,2,6,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,1,8,2,7,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,2,7,8,1,6,5,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[3,2,8,6,1,7,5,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[7,2,8,1,6,5,4,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[1,8,7,2,6,5,4,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,7,1,6,5,4,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,8,7,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,7,5,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,8,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,3,8,4,1,7,2]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[7,3,8,5,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,8,6,5,1,7,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,3,7,5,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,4,8,6,2,7,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,4,6,7,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,4,7,8,1,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,4,6,5,1,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[7,3,5,1,2,8,6,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,4,6,2,3,8,7,5]=>[1,5,8,4,2,7,6,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,7,4,8,6,5]=>[1,3,2,8,5,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,1,6,3,8,5,4]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,3,1,7,6,4,8,5]=>[3,2,1,8,6,5,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[4,5,2,1,7,3,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,6,7,1,2,8,4,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,7,5,1,2,8,6,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,7,1,6,2,8,5,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[7,6,1,2,8,5,4,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,7,1,3,8,6,5,4]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[8,6,1,2,7,5,4,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,7,2,3,8,6,5,4]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,1,2,6,5,4,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,1,2,6,5,4,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,1,6,2,7,5,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,8,5,1,2,7,6,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,8,1,2,7,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,1,3,7,4,8,6,5]=>[2,1,3,8,5,7,6,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[4,2,7,3,6,8,1,5]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[5,3,6,4,2,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,1,5,3,8,2,7,6]=>[6,2,4,3,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,2,6,4,7,3,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[2,6,3,4,7,5,1,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[2,6,3,5,4,8,1,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[2,7,4,3,5,8,1,6]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[7,3,6,4,2,8,1,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,6,4,5,2,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,4,3,1,8,2,7,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[6,5,4,2,7,3,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[5,4,1,7,2,6,3,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,4,1,8,3,2,6,7]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,5,2,8,3,4,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[7,4,2,1,8,3,6,5]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,5,3,4,8,2,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,1,5,3,8,2,7,4]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,6,3,1,8,2,7,5]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[5,8,4,2,7,3,1,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[8,2,6,4,7,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,2,5,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,3,2,6,4,1,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,1,7,2,5,4,6]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,5,2,6,4,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,1,6,2,5,4,3,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,1,7,3,5,6,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,1,7,4,5,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,3,7,2,6,5,4]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,6,8,3,2,4,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,5,8,4,2,6,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,3,8,4,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,8,5,3,4,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,8,4,3,2,5,7]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,1,7,4,2,5,3,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,7,8,4,3,5,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,2,8,3,5,7,4]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,1,6,8,2,7,5]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[5,7,4,8,3,2,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,4,8,2,7,3,1,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[5,2,8,7,3,4,1,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[6,4,7,5,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,8,3,7,6,2,4,5]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,3,2,6,4,1,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,8,2,4,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,8,2,6,4,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,6,8,2,7,3,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,6,8,7,3,4,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[7,2,8,6,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,1,7,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,7,4,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,6,4,3,5,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,7,6,3,5,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,7,6,5,2,4,3,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,6,5,3,2,4,7]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,8,7,4,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,3,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,8,6,5,2,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,7,5,3,2,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,2,5,4,3,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,3,2,5,4,7,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,4,5,2,3,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,5,7,8,4,3,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,8,1,5,4,7,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,2,1,8,5,4,7,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,6,5,7,4,1,3,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[2,5,6,8,4,3,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[2,4,7,5,8,1,6,3]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,5,4,7,1,8,6,3]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[5,2,1,8,7,6,4,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,8,5,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,6,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,5,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,4,8,2,1,7,3]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[5,8,4,7,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,5,7,4,8,2,6,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,3,2,8,6,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,3,2,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,2,1,4,3,6,7,8]=>[5,3,2,4,1,6,7,8]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,5,7,4,2,6,1,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[3,6,4,5,1,2,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,2,1,6,5,3,7,8]=>[6,3,2,5,4,1,7,8]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[4,3,5,1,7,6,2,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[3,5,4,7,1,6,2,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,4,7,5,6,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,4,5,8,6,7,1,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,5,4,6,1,8,7,2]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,3,5,1,6,8,7,2]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,3,2,1,7,6,5,9,8,10]=>[4,3,2,1,7,6,5,9,8,10]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[4,3,2,1,7,6,5,10,8,9]=>[4,3,2,1,7,6,5,10,9,8]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[4,3,2,1,10,6,5,9,7,8]=>[4,3,2,1,10,7,6,9,8,5]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[10,6,2,1,9,5,3,8,4,7]=>[10,9,4,3,8,7,6,5,2,1]=>[10,9,4,3,8,7,6,5,2,1]=>[[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.]
[2,1,4,3,6,5,10,9,7,8]=>[2,1,4,3,6,5,10,9,8,7]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,4,3,8,7,5,6,10,9]=>[2,1,4,3,8,7,6,5,10,9]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,4,3,10,9,8,5,6,7]=>[2,1,4,3,10,9,8,7,6,5]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,6,5,3,4,8,7,10,9]=>[2,1,6,5,4,3,8,7,10,9]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,6,5,3,4,10,9,7,8]=>[2,1,6,5,4,3,10,9,8,7]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,8,7,6,3,4,5,10,9]=>[2,1,8,7,6,5,4,3,10,9]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,10,9,6,3,8,4,5,7]=>[2,1,10,9,8,6,7,5,4,3]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,10,9,8,7,3,4,5,6]=>[2,1,10,9,8,7,6,5,4,3]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,3,1,2,6,5,8,7,10,9]=>[4,3,2,1,6,5,8,7,10,9]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[4,3,1,2,6,5,10,9,7,8]=>[4,3,2,1,6,5,10,9,8,7]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[4,3,1,2,8,7,5,6,10,9]=>[4,3,2,1,8,7,6,5,10,9]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[4,3,1,2,10,9,8,5,6,7]=>[4,3,2,1,10,9,8,7,6,5]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[6,5,4,1,2,3,8,7,10,9]=>[6,5,4,3,2,1,8,7,10,9]=>[6,5,4,3,2,1,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[6,5,4,1,2,3,10,9,7,8]=>[6,5,4,3,2,1,10,9,8,7]=>[6,5,4,3,2,1,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[10,9,4,1,6,2,8,3,5,7]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[10,9,4,1,8,7,2,3,5,6]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[8,7,6,5,1,2,3,4,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[10,7,6,5,1,2,3,9,4,8]=>[10,9,7,6,5,4,3,8,2,1]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[10,9,6,5,1,2,8,3,4,7]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[10,9,8,5,1,7,2,3,4,6]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[2,1,4,3,6,5,8,7,12,11,9,10]=>[2,1,4,3,6,5,8,7,12,11,10,9]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,6,5,10,9,7,8,12,11]=>[2,1,4,3,6,5,10,9,8,7,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,6,5,12,11,10,7,8,9]=>[2,1,4,3,6,5,12,11,10,9,8,7]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,8,7,5,6,10,9,12,11]=>[2,1,4,3,8,7,6,5,10,9,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,8,7,5,6,12,11,9,10]=>[2,1,4,3,8,7,6,5,12,11,10,9]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,10,9,8,5,6,7,12,11]=>[2,1,4,3,10,9,8,7,6,5,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,12,11,10,9,5,6,7,8]=>[2,1,4,3,12,11,10,9,8,7,6,5]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,6,5,3,4,8,7,10,9,12,11]=>[2,1,6,5,4,3,8,7,10,9,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,6,5,3,4,8,7,12,11,9,10]=>[2,1,6,5,4,3,8,7,12,11,10,9]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,6,5,3,4,10,9,7,8,12,11]=>[2,1,6,5,4,3,10,9,8,7,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,6,5,3,4,12,11,10,7,8,9]=>[2,1,6,5,4,3,12,11,10,9,8,7]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,8,7,6,3,4,5,10,9,12,11]=>[2,1,8,7,6,5,4,3,10,9,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,8,7,6,3,4,5,12,11,9,10]=>[2,1,8,7,6,5,4,3,12,11,10,9]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,10,9,8,7,3,4,5,6,12,11]=>[2,1,10,9,8,7,6,5,4,3,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,12,11,10,9,8,3,4,5,6,7]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[4,3,1,2,6,5,8,7,10,9,12,11]=>[4,3,2,1,6,5,8,7,10,9,12,11]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,3,1,2,6,5,8,7,12,11,9,10]=>[4,3,2,1,6,5,8,7,12,11,10,9]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,3,1,2,6,5,10,9,7,8,12,11]=>[4,3,2,1,6,5,10,9,8,7,12,11]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,3,1,2,6,5,12,11,10,7,8,9]=>[4,3,2,1,6,5,12,11,10,9,8,7]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,3,1,2,8,7,5,6,10,9,12,11]=>[4,3,2,1,8,7,6,5,10,9,12,11]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,3,1,2,8,7,5,6,12,11,9,10]=>[4,3,2,1,8,7,6,5,12,11,10,9]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,3,1,2,10,9,8,5,6,7,12,11]=>[4,3,2,1,10,9,8,7,6,5,12,11]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,3,1,2,12,11,10,9,5,6,7,8]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[6,5,4,1,2,3,8,7,10,9,12,11]=>[6,5,4,3,2,1,8,7,10,9,12,11]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[6,5,4,1,2,3,8,7,12,11,9,10]=>[6,5,4,3,2,1,8,7,12,11,10,9]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[6,5,4,1,2,3,10,9,7,8,12,11]=>[6,5,4,3,2,1,10,9,8,7,12,11]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[6,5,4,1,2,3,12,11,10,7,8,9]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[8,7,6,5,1,2,3,4,10,9,12,11]=>[8,7,6,5,4,3,2,1,10,9,12,11]=>[8,7,6,5,4,3,2,1,12,11,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[[[.,.],.],.],.]]
[8,7,6,5,1,2,3,4,12,11,9,10]=>[8,7,6,5,4,3,2,1,12,11,10,9]=>[8,7,6,5,4,3,2,1,12,11,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[[[.,.],.],.],.]]
[10,9,8,7,6,1,2,3,4,5,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[[.,.],.]]
[12,11,10,9,8,7,1,2,3,4,5,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,6,5,4,3,2,9,1,8]=>[8,6,5,4,3,2,9,1,7]=>[8,6,5,4,3,2,9,1,7]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[6,5,4,3,9,2,8,1,7]=>[8,6,4,3,9,2,7,1,5]=>[8,6,4,3,9,2,7,1,5]=>[[[[[[.,.],.],.],[.,.]],[.,.]],[.,.]]
[5,4,9,3,8,2,7,1,6]=>[8,6,9,4,7,2,5,1,3]=>[8,6,9,4,7,2,5,1,3]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]
[4,8,3,7,2,6,1,5,9]=>[7,8,5,6,3,4,1,2,9]=>[7,9,5,8,3,6,1,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],.]]
[3,6,2,5,1,4,7,8,9]=>[5,6,3,4,1,2,7,8,9]=>[5,9,3,8,1,7,6,4,2]=>[[[.,[.,.]],[.,.]],[[[[.,.],.],.],.]]
[8,7,6,5,4,3,2,10,1,9]=>[9,7,6,5,4,3,2,10,1,8]=>[9,7,6,5,4,3,2,10,1,8]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]
[7,6,5,4,3,10,2,9,1,8]=>[9,7,5,4,3,10,2,8,1,6]=>[9,7,5,4,3,10,2,8,1,6]=>[[[[[[[.,.],.],.],.],[.,.]],[.,.]],[.,.]]
[6,5,4,10,3,9,2,8,1,7]=>[9,7,5,10,3,8,2,6,1,4]=>[9,7,5,10,3,8,2,6,1,4]=>[[[[[[.,.],.],[.,.]],[.,.]],[.,.]],[.,.]]
[5,10,4,9,3,8,2,7,1,6]=>[9,10,7,8,5,6,3,4,1,2]=>[9,10,7,8,5,6,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[4,8,3,7,2,6,1,5,9,10]=>[7,8,5,6,3,4,1,2,9,10]=>[7,10,5,9,3,8,1,6,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[[[.,.],.],.]]
[3,6,2,5,1,4,7,8,9,10]=>[5,6,3,4,1,2,7,8,9,10]=>[5,10,3,9,1,8,7,6,4,2]=>[[[.,[.,.]],[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,1,3,5,6,7,8,9,10]=>[3,4,1,2,5,6,7,8,9,10]=>[3,10,1,9,8,7,6,5,4,2]=>[[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,7,3,8,4,6,5]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[4,1,8,2,7,3,6,5]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,1,7,2,8,3,6,5]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[7,1,3,2,8,4,6,5]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,2,4,3,6,5]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,2,5,3,6,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,5,2,8,3,6,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,7,2,8,3,6,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,8,2,7,3,6,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,8,2,4,3,7,6]=>[6,2,8,4,5,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,1,6,2,4,3,7,5]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,8,2,4,3,7,5]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,8,2,5,3,7,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,6,2,5,3,7,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,6,2,7,3,5,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,8,2,7,3,5,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,7,2,8,3,5,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,7,2,5,3,8,4]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,7,2,4,3,8,5]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,6,2,4,3,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[7,1,5,2,4,3,8,6]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,6,2,4,3,8,5]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,6,2,5,3,8,4]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,6,2,8,3,5,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,2,6,3,5,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,2,7,5,4,6,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,7,4,3,5,6]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,6,4,7,2,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,8,1,5,2,3,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,1,7,2,6,3,5,8]=>[6,2,7,4,5,1,3,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,1,7,4,3,6,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,5,8,3,2,4,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,5,4,3,6,2,7]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,4,3,7,2,6]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,4,7,2,6,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,4,2,5,3,7,6]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,4,2,6,7,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,8,2,1,3,5,6]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,1,7,3,2,5,6,8]=>[5,2,7,4,1,6,3,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[7,5,4,8,2,3,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,8,2,1,3,7,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,3,8,1,5,6,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,1,7,2,6,8,4,5]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[5,1,7,4,2,6,8,3]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,6,3,2,5,8,7]=>[5,2,6,4,1,3,8,7]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[5,4,3,7,1,2,8,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,3,1,6,2,5,7,8]=>[5,3,2,6,1,4,7,8]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[6,5,4,3,7,1,8,2]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,4,2,7,1,6,8,3]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,5,1,7,3,8,2,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,3,2,8,5,7,1,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,5,4,2,8,3,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,5,4,3,8,2,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,5,4,3,8,7,1,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,5,4,8,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,3,8,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,8,1,7,5,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,8,3,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,8,2,1,7,3,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[5,4,3,8,1,6,2,7]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,4,3,7,1,6,2,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,4,2,8,5,1,3,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[7,6,4,8,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,8,6,3,1,4,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,2,8,6,1,5,3,4]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[2,1,7,8,3,6,4,5]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,4,1,7,8,2,3,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,2,1,6,7,3,5,8]=>[6,3,2,7,5,1,4,8]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[4,3,1,5,2,7,6,8]=>[5,3,2,4,1,7,6,8]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[5,4,2,7,3,8,1,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,1,5,3,2,8,6,7]=>[5,2,4,3,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,1,6,2,8,7,4,5]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[6,3,1,7,8,5,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,1,7,8,2,6,3]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,4,2,6,1,8,7,3]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,5,4,1,7,8,3,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,5,4,2,7,8,3,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,4,2,6,3,8,7,1]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,3,1,5,2,6,8,7]=>[5,3,2,4,1,6,8,7]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[5,4,2,1,6,7,8,3]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,4,3,1,6,7,8,2]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[6,3,8,1,2,5,7,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[3,6,7,1,2,5,8,4]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[7,8,3,1,2,5,6,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,8,1,3,2,4,6,5]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,2,1,3,5,4,6]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,2,3,7,1,8,6,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,5,3,6,1,8,7,4]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,6,7,3,1,8,4,5]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,6,7,1,3,5,4,8]=>[4,7,6,1,5,3,2,8]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[6,2,8,3,1,7,4,5]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[3,2,5,7,1,8,4,6]=>[5,2,7,8,1,6,3,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,3,1,2,7,8,6,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[5,1,2,7,3,6,4,8]=>[7,2,3,6,5,4,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,4,7,8,2,3,6]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,3,4,7,8,6,1,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,5,4,6,8,7,1,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,5,4,6,8,2,3,7]=>[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,3,2,4,8,5]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,3,6,2,7,8,4]=>[1,8,5,4,3,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,2,4,7,8,1,6,3]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,2,5,7,6,1,8,3]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,5,2,8,6,1,7,3]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,3,1,8,2,6,7,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,1,8,3,2,4,7,5]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,3,5,7,6,8,1,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,1,5,7,6,2,3,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,5,1,8,6,2,3,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,2,1,8,3,6,4,7]=>[7,3,2,8,5,6,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[3,4,2,1,8,7,5,6]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[7,6,5,4,2,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,6,5,4,8,1,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,6,5,4,2,1,9,3]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[7,6,5,8,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,5,3,2,1,9,4]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[8,7,6,4,3,2,1,9,5]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[8,7,5,4,3,2,1,9,6]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[8,5,4,3,2,1,7,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,6,5,4,3,2,1,9,7]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[7,6,5,4,3,2,1,9,8]=>[7,6,5,4,3,2,1,9,8]=>[7,6,5,4,3,2,1,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[7,6,5,4,1,8,3,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,7,6,5,4,9,1,3,2]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[9,8,7,6,5,4,2,1,10,3]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[7,6,5,2,8,1,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,6,5,9,2,1,4,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,6,5,3,2,1,10,4]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[7,6,5,8,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,9,3,2,1,5,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,6,4,3,2,1,10,5]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[7,6,8,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,9,4,3,2,1,6,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,5,4,3,2,1,10,6]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[7,8,6,3,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,9,5,4,3,2,1,7,6]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,6,5,4,3,2,1,10,7]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[8,7,4,3,2,1,6,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[9,6,5,4,3,2,1,8,7]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[9,7,6,5,4,3,2,1,10,8]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[7,8,9,10,4,5,6,2,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,4,5,6,10,2,3,1]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[7,8,9,10,4,5,2,3,6,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,4,5,10,2,3,6,1]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,8,9,4,5,2,3,6,10,1]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[7,8,4,5,9,10,2,3,6,1]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,8,4,5,9,2,3,6,10,1]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[7,8,9,10,4,5,6,2,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,4,5,6,10,2,1,3]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[7,8,9,10,4,5,2,6,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,4,5,10,2,6,1,3]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,8,9,4,5,2,6,10,1,3]=>[10,9,7,6,5,4,3,8,2,1]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[7,8,4,5,9,10,2,6,1,3]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,8,4,5,9,2,6,10,1,3]=>[10,9,7,6,5,4,3,8,2,1]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[7,8,9,10,4,5,2,1,3,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,4,5,10,2,1,3,6]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,8,9,4,5,2,10,1,3,6]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[7,8,9,4,5,2,1,3,6,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[7,8,4,5,9,10,2,1,3,6]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,8,4,5,9,2,10,1,3,6]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[7,8,4,5,9,2,1,3,6,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[7,8,9,10,4,2,5,6,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,4,10,2,5,6,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,4,2,5,6,10,1,3]=>[10,9,7,6,5,4,3,8,2,1]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[7,8,4,9,10,2,5,6,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,4,9,2,5,6,10,1,3]=>[10,9,7,6,5,4,3,8,2,1]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[7,8,9,10,4,2,5,1,3,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,4,10,2,5,1,3,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,4,2,5,10,1,3,6]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[7,8,9,4,2,5,1,3,6,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[7,8,4,9,10,2,5,1,3,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,4,9,2,5,10,1,3,6]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[7,8,4,9,2,5,1,3,6,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[7,8,4,2,5,9,10,1,3,6]=>[10,9,8,5,4,6,7,3,2,1]=>[10,9,8,5,4,7,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[7,4,8,9,10,2,5,6,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,4,8,9,2,5,6,10,1,3]=>[10,9,7,6,5,4,3,8,2,1]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[7,4,8,9,10,2,5,1,3,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,4,8,9,2,5,10,1,3,6]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[7,4,8,9,2,5,1,3,6,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[7,4,8,2,5,9,10,1,3,6]=>[10,9,8,5,4,6,7,3,2,1]=>[10,9,8,5,4,7,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[7,8,2,4,5,1,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,7,2,5,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,8,1,3,2,4,5,6]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,4,1,5,2,3,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,2,3,6,1,4,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[2,5,3,6,1,4,7,8]=>[5,6,3,4,1,2,7,8]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,6,7,1,5,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,6,7,3,5,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,4,7,1,5,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,2,7,3,1,4,5,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[3,2,5,6,1,4,7,8]=>[5,2,6,4,1,3,7,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,5,2,6,1,4,7,8]=>[5,6,3,4,1,2,7,8]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[5,1,4,6,7,2,3,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,5,4,6,7,8,1,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,5,4,6,7,2,3,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,3,2,4,5,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,3,6,2,4,7,8]=>[1,6,5,4,3,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,3,6,2,4,7,8]=>[6,2,5,4,3,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,2,4,6,7,1,3,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[2,5,4,6,7,1,3,8]=>[6,7,3,4,5,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,6,7,4,5,1,3,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[6,2,7,4,5,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,2,5,6,7,1,3,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,5,2,6,7,1,3,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,3,1,6,2,4,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,1,7,3,2,4,5,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,1,7,4,5,2,3,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,3,7,4,5,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,4,1,6,7,2,3,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,2,1,6,3,4,7,8]=>[6,3,2,5,4,1,7,8]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[7,3,2,5,4,1,6,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,3,5,4,2,1,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,3,5,2,4,1,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,5,2,1,4,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,3,6,7,5,2,8,4]=>[1,6,8,5,4,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,3,4,1,6,2,5,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,3,4,1,6,5,2,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,3,4,1,5,6,2,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,3,2,5,1,6,4,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[7,6,5,4,1,3,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,3,4,1,5,2,6,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,7,4,6,2,8,5,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,1,7,2,6,8,5]=>[5,3,2,8,1,6,7,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[5,6,1,4,7,3,8,2]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,3,2,1,7,4,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,3,4,5,8,7,2,6]=>[1,7,3,4,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,4,5,8,1,7,2]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[2,4,5,1,6,8,7,3]=>[4,8,3,1,5,7,6,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,1,2,5,6,8,7,4]=>[3,2,1,8,5,7,6,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,7,5,4,6,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,1,4,6,5,8,2,7]=>[7,2,3,5,4,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,3,4,5,8,6,1,7]=>[7,2,3,4,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,3,4,5,8,1,7,6]=>[6,2,3,4,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,1,4,6,5,8,7,2]=>[8,2,3,5,4,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,7,5,4,6,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,1,4,7,2,8,3]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,1,4,6,7,8,5,2]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,7,5,2,6,8,1,4]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[3,7,5,2,6,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,1,2,7,4,8,3]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,3,5,2,4,7,8,1]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,3,2,1,4,7,8,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,3,1,4,2,7,8,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,3,1,2,4,7,8,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[7,1,5,2,6,8,4,3]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,5,2,6,8,3,4]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,4,6,5,8,3,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,4,6,1,8,3,5]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,7,4,6,1,8,5,3]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,3,6,7,5,1,8,4]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,3,2,6,7,1,8,5]=>[6,3,2,8,5,1,7,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[7,3,2,5,6,8,1,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,5,4,6,8,2,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,7,4,6,5,8,1,3]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[7,3,4,5,8,6,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,4,5,8,1,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,4,5,8,1,2,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,3,4,5,8,6,2,7]=>[1,7,3,4,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,5,8,2,7,6]=>[1,6,3,4,8,2,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,4,5,8,2,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,3,4,5,8,2,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,3,4,5,8,6,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,7,4,6,5,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,1,5,4,6,8,3,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,3,2,5,6,8,4,1]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,7,4,6,1,8,3,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,3,4,5,8,1,2,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,3,4,5,8,2,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,4,5,8,2,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,7,6,1,8,2,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,6,1,7,5,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,7,8,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,4,2,8,3,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,4,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,3,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,6,1,7,5,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,7,1,8,3,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,8,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,4,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,10,7,9,5,6,3,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,6,8,5,7,3,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,10,6,9,5,7,3,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,10,6,9,5,8,3,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,7,8,4,6,3,5,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,10,7,9,4,6,3,5,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,6,8,4,7,3,5,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,10,6,9,4,7,3,5,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,10,6,9,4,8,3,5,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,5,8,4,7,3,6,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,10,5,9,4,7,3,6,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,10,5,9,4,8,3,6,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,10,5,9,4,8,3,7,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,7,8,5,6,2,4,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,10,7,9,5,6,2,4,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,6,8,5,7,2,4,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,10,6,9,5,7,2,4,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,10,6,9,5,8,2,4,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,7,8,4,6,2,5,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,10,7,9,4,6,2,5,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,6,8,4,7,2,5,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,10,6,9,4,7,2,5,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,10,6,9,4,8,2,5,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,5,8,4,7,2,6,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,10,5,9,4,7,2,6,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,10,5,9,4,8,2,6,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,10,5,9,4,8,2,7,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,7,8,3,6,2,5,1,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,10,7,9,3,6,2,5,1,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,6,8,3,7,2,5,1,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,10,6,9,3,7,2,5,1,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,10,6,9,3,8,2,5,1,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,5,8,3,7,2,6,1,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,10,5,9,3,7,2,6,1,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,10,5,9,3,8,2,6,1,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,10,5,9,3,8,2,7,1,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,4,8,3,7,2,6,1,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,10,4,9,3,7,2,6,1,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,10,4,9,3,8,2,6,1,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,10,4,9,3,8,2,7,1,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,12,9,11,7,8,5,6,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,10,7,9,5,6,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,8,11,7,9,5,6,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,12,8,11,7,10,5,6,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,6,8,5,7,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,9,11,6,8,5,7,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,10,6,9,5,7,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,8,11,6,9,5,7,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,12,8,11,6,10,5,7,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,10,6,9,5,8,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,7,11,6,9,5,8,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,12,7,11,6,10,5,8,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,12,7,11,6,10,5,9,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,7,8,4,6,3,5,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,9,11,7,8,4,6,3,5,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,10,7,9,4,6,3,5,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,8,11,7,9,4,6,3,5,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,12,8,11,7,10,4,6,3,5,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,6,8,4,7,3,5,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,9,11,6,8,4,7,3,5,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,10,6,9,4,7,3,5,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,8,11,6,9,4,7,3,5,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,12,8,11,6,10,4,7,3,5,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,10,6,9,4,8,3,5,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,7,11,6,9,4,8,3,5,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,12,7,11,6,10,4,8,3,5,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,12,7,11,6,10,4,9,3,5,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,5,8,4,7,3,6,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,9,11,5,8,4,7,3,6,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,10,5,9,4,7,3,6,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,8,11,5,9,4,7,3,6,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,12,8,11,5,10,4,7,3,6,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,10,5,9,4,8,3,6,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,7,11,5,9,4,8,3,6,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,12,7,11,5,10,4,8,3,6,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,12,7,11,5,10,4,9,3,6,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,6,10,5,9,4,8,3,7,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,6,11,5,9,4,8,3,7,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,12,6,11,5,10,4,8,3,7,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,12,6,11,5,10,4,9,3,7,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,12,6,11,5,10,4,9,3,8,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,7,8,5,6,2,4,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,9,11,7,8,5,6,2,4,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,10,7,9,5,6,2,4,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,8,11,7,9,5,6,2,4,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,12,8,11,7,10,5,6,2,4,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,6,8,5,7,2,4,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,9,11,6,8,5,7,2,4,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,10,6,9,5,7,2,4,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,8,11,6,9,5,7,2,4,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,12,8,11,6,10,5,7,2,4,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,10,6,9,5,8,2,4,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,7,11,6,9,5,8,2,4,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,12,7,11,6,10,5,8,2,4,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,12,7,11,6,10,5,9,2,4,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,7,8,4,6,2,5,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,9,11,7,8,4,6,2,5,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,10,7,9,4,6,2,5,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,8,11,7,9,4,6,2,5,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,12,8,11,7,10,4,6,2,5,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,6,8,4,7,2,5,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,9,11,6,8,4,7,2,5,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,10,6,9,4,7,2,5,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,8,11,6,9,4,7,2,5,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,12,8,11,6,10,4,7,2,5,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,10,6,9,4,8,2,5,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,7,11,6,9,4,8,2,5,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,12,7,11,6,10,4,8,2,5,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,12,7,11,6,10,4,9,2,5,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,5,8,4,7,2,6,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,9,11,5,8,4,7,2,6,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,10,5,9,4,7,2,6,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,8,11,5,9,4,7,2,6,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,12,8,11,5,10,4,7,2,6,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,10,5,9,4,8,2,6,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,7,11,5,9,4,8,2,6,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,12,7,11,5,10,4,8,2,6,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,12,7,11,5,10,4,9,2,6,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,6,10,5,9,4,8,2,7,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,6,11,5,9,4,8,2,7,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,12,6,11,5,10,4,8,2,7,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,12,6,11,5,10,4,9,2,7,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,12,6,11,5,10,4,9,2,8,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,7,8,3,6,2,5,1,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,9,11,7,8,3,6,2,5,1,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,10,7,9,3,6,2,5,1,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,8,11,7,9,3,6,2,5,1,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,12,8,11,7,10,3,6,2,5,1,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,6,8,3,7,2,5,1,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,9,11,6,8,3,7,2,5,1,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,10,6,9,3,7,2,5,1,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,8,11,6,9,3,7,2,5,1,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,12,8,11,6,10,3,7,2,5,1,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,10,6,9,3,8,2,5,1,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,7,11,6,9,3,8,2,5,1,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,12,7,11,6,10,3,8,2,5,1,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,12,7,11,6,10,3,9,2,5,1,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,5,8,3,7,2,6,1,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,9,11,5,8,3,7,2,6,1,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,10,5,9,3,7,2,6,1,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,8,11,5,9,3,7,2,6,1,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,12,8,11,5,10,3,7,2,6,1,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,10,5,9,3,8,2,6,1,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,7,11,5,9,3,8,2,6,1,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,12,7,11,5,10,3,8,2,6,1,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,12,7,11,5,10,3,9,2,6,1,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,6,10,5,9,3,8,2,7,1,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,6,11,5,9,3,8,2,7,1,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,12,6,11,5,10,3,8,2,7,1,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,12,6,11,5,10,3,9,2,7,1,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,12,6,11,5,10,3,9,2,8,1,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,4,8,3,7,2,6,1,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,9,11,4,8,3,7,2,6,1,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,10,4,9,3,7,2,6,1,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,8,11,4,9,3,7,2,6,1,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,12,8,11,4,10,3,7,2,6,1,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,10,4,9,3,8,2,6,1,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,7,11,4,9,3,8,2,6,1,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,12,7,11,4,10,3,8,2,6,1,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,12,7,11,4,10,3,9,2,6,1,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,6,10,4,9,3,8,2,7,1,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,6,11,4,9,3,8,2,7,1,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,12,6,11,4,10,3,8,2,7,1,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,12,6,11,4,10,3,9,2,7,1,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,12,6,11,4,10,3,9,2,8,1,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,5,10,4,9,3,8,2,7,1,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,12,5,11,4,9,3,8,2,7,1,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,12,5,11,4,10,3,8,2,7,1,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,12,5,11,4,10,3,9,2,7,1,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,12,5,11,4,10,3,9,2,8,1,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[6,12,5,11,4,10,3,9,2,8,1,7]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[2,1,8,6,3,5,4,7]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,7,3,5,8,6,4]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[4,2,1,8,3,6,7,5]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[2,1,8,6,3,5,7,4]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,7,3,1,4,8,5,6]=>[4,8,3,1,5,7,6,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,2,1,6,4,5,7,8]=>[3,2,1,6,5,4,7,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,5,7,8,4,6]=>[3,2,1,7,8,6,4,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,1,7,3,6,8,4,5]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,7,3,1,5,6,8,4]=>[4,8,3,1,6,5,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,4,7,5,1,6,8,3]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[4,3,7,5,6,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,3,6,8,5,1,7,2]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[2,6,1,8,3,5,7,4]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,1,6,8,3,7,4,5]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,8,3,5,7,4,6]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,2,1,5,6,8,4,7]=>[3,2,1,7,5,8,4,6]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,5,7,4,6,8]=>[3,2,1,6,7,4,5,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,1,6,3,5,8,4,7]=>[2,1,7,4,5,8,3,6]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,2,4,1,7,5,6,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,8,4,7,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,3,6,1,7,5,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,2,1,7,3,5,4,6]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,6,1,8,3,5,4,7]=>[3,7,1,8,5,6,2,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[8,2,4,1,7,5,3,6]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[5,8,6,3,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,7,1,8,5,3,6]=>[4,7,8,1,6,5,2,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,4,8,5,1,6,3,7]=>[5,7,8,4,1,6,2,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[6,2,1,7,8,3,5,4]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,7,1,8,3,5,6,4]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,1,8,3,6,4,5,7]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,2,1,6,7,4,5,8]=>[3,2,1,7,6,5,4,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,7,4,5,6,8]=>[3,2,1,7,5,6,4,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,6,8,4,5,7]=>[3,2,1,7,8,6,4,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,1,8,3,7,4,5,6]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,8,3,6,7,4,5]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,8,5,1,6,7,3]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[4,3,8,5,6,1,7,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[3,2,1,8,4,5,6,7]=>[3,2,1,8,5,6,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,6,8,3,7,2,4,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,8,1,5,7,2,4,6]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[1,2,6,8,4,7,3,5]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,5,8,2,4,7,3]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,4,8,3,6,7,5]=>[1,2,5,8,3,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,7,8,3,6,5]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,5,7,4,8,6,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,8,4,7,6,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,1,2,5,4,6,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,1,2,3,7,6,4]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,2,8,4,3,5,7,6]=>[1,2,8,5,4,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,2,8,7,4,5,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,6,2,8,4,5,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,6,3,8,5,4,7]=>[1,2,7,4,8,6,3,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,5,3,6,4,7]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,3,8,5,4,6]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,4,2,7,3,5,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,6,3,2,4,5,7]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,7,8,6,2,4,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,8,7,2,4,5,6,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,7,3,5,6,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,8,7,4,5,6]=>[1,3,2,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,6,3,2,4,5,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,4,3,7,5,6]=>[1,2,8,5,4,7,6,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,5,1,7,2,4,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,3,8,7,4,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,6,4,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,8,2,7,4,5,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,5,3,8,6,4,7]=>[1,2,7,4,8,6,3,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,5,3,6,4,8]=>[1,2,7,6,5,4,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,7,5,4,8,6]=>[1,2,3,8,6,5,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,4,8,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,2,7,6,4,5,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,9,8,7,6,5,4,1,3]=>[8,9,7,6,5,4,3,1,2]=>[8,9,7,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[2,8,7,6,5,1,4,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[7,1,6,3,2,5,4,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,7,6,3,1,5,8,4]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[1,8,4,3,6,5,2,7]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,4,6,5,3,2,7]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,2,1,6,5,3,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,6,1,4,3,5,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,4,1,3,5,2,6,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,8,6,3,4,5,2,7]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,6,7,4,2,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,7,2,4,6,8,5]=>[4,2,8,1,5,6,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,4,7,1,5,2,8,6]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[3,6,7,4,1,5,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,3,2,7,1,5,8,6]=>[5,3,2,8,1,6,7,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,1,2,8,6,5,4,7]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[5,4,8,6,1,2,3,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[5,6,8,7,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,2,7,4,3,6,5]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,5,8,2,3,7,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,8,5,3,1,7,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,7,8,6,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,8,1,6,3,7,5]=>[4,6,8,1,7,2,5,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,1,2,8,6,4,7,5]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[5,3,2,6,4,8,1,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,1,6,3,5,8,2,7]=>[7,2,5,4,3,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,4,5,3,8,6,1,7]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,8,5,3,2,7,6,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,4,5,2,6,7,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,7,6,5,8,3]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,4,1,6,7,8,5,3]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[5,6,7,3,2,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,5,7,3,6,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,3,2,1,4,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,3,1,4,2,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[7,6,1,3,8,5,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,4,7,8,1,2,6,5]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[3,6,7,8,1,4,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,2,8,1,5,4,7]=>[5,7,3,8,1,6,2,4]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,3,6,8,5,1,4,7]=>[6,2,7,8,5,1,3,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,1,6,4,8,2,5,7]=>[6,2,7,4,8,1,3,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[7,3,2,6,8,5,1,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,3,5,8,4,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,2,8,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,5,8,2,1,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,5,2,4,6,3,7]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,4,2,3,5,7,6]=>[1,8,5,4,3,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,4,2,8,3,5,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[6,3,4,8,2,5,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[7,5,4,8,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,4,8,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,5,4,8,3,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,3,2,5,8,4,6,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,6,3,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,6,3,8,5,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,5,6,8,3,4,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[8,4,6,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,6,7,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,6,8,4,3,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[2,5,7,8,4,1,3,6]=>[6,7,8,5,4,1,2,3]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[6,5,7,8,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,6,8,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,6,2,8,5,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,3,2,6,8,5,1,7]=>[7,3,2,6,8,4,1,5]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[3,5,6,8,2,4,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[3,5,6,8,4,2,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[2,6,7,8,1,4,5,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[3,6,7,8,1,4,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,5,7,8,2,1,4,6]=>[6,7,8,5,4,1,2,3]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,6,7,8,1,4,3,5]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[6,5,7,8,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,7,8,3,1,4,6]=>[6,7,8,5,4,1,2,3]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,4,7,3,8,1,5,6]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[6,4,7,3,8,1,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,7,3,8,1,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,6,3,8,2,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,2,5,4,8,1,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,4,5,2,3,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,4,5,3,2,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,4,6,3,8,2,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[5,4,7,3,8,1,6,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[2,5,7,8,3,1,6,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[4,5,7,8,3,1,2,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,5,6,8,2,3,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[5,4,6,2,8,3,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[5,3,2,6,8,4,1,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,4,7,2,8,1,3,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[4,5,7,8,2,1,3,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,6,7,8,1,3,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,6,7,8,1,3,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,7,8,1,3,5,4]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,6,7,8,1,5,3,4]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[4,6,7,8,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,7,8,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,7,8,2,1,6,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,4,7,2,8,1,6,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[5,3,2,7,8,1,6,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,3,2,7,8,1,6,5]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[3,5,7,8,2,1,6,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[3,6,7,8,1,2,5,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[3,6,7,8,1,5,2,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,6,7,8,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,7,8,1,5,4,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,4,5,6,7,8,9,10,2,3]=>[1,10,9,4,5,6,7,8,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[4,2,7,1,5,3,8,6]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[4,2,8,6,1,5,3,7]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[4,7,2,1,5,8,6,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,2,1,3,5,8,6,4]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,3,6,4,7,1,5,8]=>[6,2,7,4,5,1,3,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,3,4,8,2,7,5,6]=>[1,5,3,8,2,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,4,8,2,6,7,5]=>[5,2,3,8,1,7,6,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[8,3,1,6,2,5,7,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,8,6,2,1,5,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,3,6,5,1,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,7,3,5,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,4,7,5,1,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,6,1,7,5,8,2,4]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[7,3,5,1,6,8,2,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,7,3,5,6,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,4,6,8,5,1,7,2]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[4,6,8,2,1,5,7,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,8,2,1,3,5,7,4]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,8,2,3,5,7,4,6]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,3,2,5,6,1,4,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,7,5,2,6,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,6,2,8,1,5,3,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[8,4,1,2,7,5,3,6]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,5,6,2,7,1,3,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[8,5,1,2,6,3,4,7]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,6,2,7,4,8,3,5]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,2,1,7,8,5,3,4]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,7,3,8,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,8,4,1,5,6,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,7,1,8,5,6,3,4]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[8,2,5,1,6,7,3,4]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,2,4,5,1,6,7,3]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[3,8,4,5,6,1,7,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,8,3,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,8,3,7,6,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,2,8,3,7,1,6,5]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[7,2,3,4,8,1,6,5]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,2,3,4,8,1,5,6]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,6,3,4,8,5,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,3,5,8,4,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,3,8,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,3,8,5,1,4,6]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,2,3,8,5,1,6,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,6,4,8,1,5,7,3]=>[5,8,6,7,1,3,4,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[7,2,3,8,4,1,5,6]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,2,3,5,8,1,4,6]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,8,2,3,6,1,4,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,2,3,6,1,5,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,2,6,3,7,1,5,8]=>[6,4,7,2,5,1,3,8]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[7,2,3,5,8,1,6,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,2,3,8,4,1,6,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,6,4,8,1,3,7,5]=>[5,8,6,7,1,3,4,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[3,6,4,8,1,7,5,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,6,5,1,2,3,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,6,5,1,4,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,6,4,5,1,8,7,3]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,5,6,4,1,2,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[7,8,5,4,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,6,4,1,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[7,6,5,1,4,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,5,1,2,4,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,5,1,2,4,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,6,5,1,3,2,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,6,5,1,3,2,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,5,1,3,4,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,2,3,4,5,1,8,6]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,6,4,3,1,5,8,7]=>[5,6,4,3,1,2,8,7]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[2,6,4,3,1,8,5,7]=>[5,7,4,3,1,8,2,6]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[2,6,4,3,1,8,7,5]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,5,8,4,1,2,7,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[3,5,8,4,1,2,6,7]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[3,5,8,4,1,6,2,7]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[4,2,8,3,6,1,7,5]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[3,5,8,4,1,6,7,2]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[2,5,8,4,1,7,3,6]=>[5,7,8,4,1,6,2,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,6,4,2,1,7,8,5]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,5,6,4,1,8,7,2]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[2,6,4,5,1,3,7,8]=>[5,6,4,3,1,2,7,8]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[7,6,5,1,4,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,6,5,1,2,8,4,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,6,5,1,2,8,3,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,6,5,1,8,2,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,5,1,8,2,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,5,1,8,3,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,5,1,4,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,6,4,5,1,7,2,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[2,5,6,4,1,7,8,3]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[7,8,5,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,4,5,1,7,8,2]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[7,6,5,1,4,8,3,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,6,5,1,8,3,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,5,1,8,4,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,1,7,6,2,8,5,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,8,6,2,1,3,5,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,6,1,2,8,4,5]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,6,5,3,1,4,8,7]=>[5,6,4,3,1,2,8,7]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[4,6,1,5,3,2,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,6,1,4,2,5,8,7]=>[5,6,3,4,1,2,8,7]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,6,4,5,7,8,1,3]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[8,7,1,6,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,5,6,8,1,3,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,1,3,4,2,8,7,5]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,4,5,6,1,8,7,3]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[8,4,1,6,5,7,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,8,3,4,7,5,1,6]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[6,8,2,7,4,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,8,5,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,6,4,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,6,1,7,3,2,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[8,7,3,2,1,5,4,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,8,5,1,7,2,4,6]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[6,8,7,1,3,2,4,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,5,1,8,7,4,6,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,7,1,8,4,5,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,2,3,8,4,7,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,4,3,1,7,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,7,4,6,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,3,8,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,5,8,6,7,4,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,2,1,8,6,5,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,6,7,2,5,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,6,2,5,3,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,5,4,2,8,3,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[5,4,3,1,8,7,2,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[6,1,4,3,8,5,2,7]=>[7,2,6,4,8,3,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,7,6,2,8,1,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,5,1,7,8,3,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,2,3,1,7,8,6,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,4,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[2,7,6,8,1,5,3,4]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[6,4,5,8,3,1,2,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[8,1,3,2,5,6,7,4]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,6,8,1,5,2,4,7]=>[6,7,8,4,5,1,2,3]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[3,2,8,7,4,5,1,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,3,8,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,6,8,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,4,8,7,5,3,6]=>[2,1,7,8,6,5,3,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,6,8,3,7,5,4]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,6,8,2,4,1,5,7]=>[6,7,8,4,5,1,2,3]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[6,2,8,1,7,5,4,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,6,5,4,8,1,3,7]=>[6,7,4,3,8,1,2,5]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[6,5,3,4,8,1,7,2]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[8,4,3,2,5,1,7,6]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,2,8,1,5,3,6,7]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[5,1,8,2,6,4,3,7]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,4,8,6,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,2,8,3,7,5,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[2,1,5,8,3,6,4,7]=>[2,1,7,8,5,6,3,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,8,5,3,6,7,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[7,8,5,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,4,1,6,3,7,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,1,3,5,7,6,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,1,4,5,6,2,7]=>[7,8,3,4,5,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[9,7,8,5,6,3,1,4,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,7,8,5,3,6,1,4,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,7,5,8,3,6,1,4,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,9,5,8,3,6,1,4,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,6,8,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,9,5,7,3,6,1,4,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,9,6,7,3,5,1,4,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,9,6,7,4,5,1,3,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,9,6,7,4,5,2,3,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,10,7,8,5,6,3,1,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,8,5,3,1,6,4,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,10,7,8,5,3,6,1,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,5,3,8,6,1,4,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,10,7,5,8,3,6,1,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,5,9,8,3,6,1,4,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,7,10,5,8,3,6,1,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,6,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,8,7,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[9,8,5,7,3,6,1,4,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,7,9,5,8,3,6,1,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,9,6,8,3,5,1,4,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,8,9,5,7,3,6,1,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,5,8,4,7,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,9,5,7,4,6,1,3,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,8,9,6,7,3,5,1,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,6,7,3,5,2,4,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,8,9,6,7,4,5,1,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,7,4,2,5,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,4,8,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,8,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,2,5,6,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,2,7,5,6,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,4,7,5,6,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,7,3,5,6,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,7,2,5,6,4,1,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,8,3,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,8,5,2,7,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,2,8,5,1,7,4,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[6,7,4,8,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,2,7,8,6,1,5,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,8,4,1,2,3,7,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,1,8,5,6,3,2,7]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,8,2,5,6,4,3,7]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,8,5,3,7,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,8,1,5,2,7,6,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[8,2,1,5,3,7,6,4]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,5,2,4,6,7,8,3]=>[1,8,3,4,5,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,6,5,3,7,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,4,6,3,2,8,5]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,6,4,1,7,8,5]=>[5,2,8,4,1,6,7,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[7,6,4,3,1,2,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,6,3,5,1,7,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,3,1,6,7,8,2]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,5,2,1,6,7,8,4]=>[4,8,3,1,5,6,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[5,2,3,1,6,7,8,4]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,5,3,2,6,7,8,4]=>[1,8,4,3,5,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,4,6,5,1,7,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,4,6,1,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,2,5,6,1,7,8,4]=>[5,2,8,4,1,6,7,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,2,8,7,6,1,4,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,8,4,7,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,5,6,1,2,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,2,7,5,6,1,3,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,8,6,5,1,7,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,4,6,2,3,8,5]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,4,2,1,5,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,7,4,6,1,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,6,4,7,3,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,4,3,7,1,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,5,4,2,7,1,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[8,6,4,1,3,5,2,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,4,1,5,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,4,1,2,6,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,7,4,2,3,6,8,5]=>[1,8,5,4,3,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,5,3,7,6,4]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,1,5,4,7,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,2,1,5,6,4,3,7]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,8,1,5,6,4,2,7]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[6,8,4,1,2,5,3,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,2,8,1,6,5,4,7]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,6,1,5,7,8,4]=>[4,2,8,1,5,6,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[7,6,4,1,5,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,6,1,5,4,7,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,5,1,4,6,7,8,2]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,2,1,4,6,7,8,3]=>[8,3,2,4,5,6,7,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[5,4,1,3,6,7,8,2]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,4,1,5,3,7,2,6]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,4,1,3,2,8,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,2,5,1,4,7,8,6]=>[4,2,5,1,3,8,7,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[7,1,4,3,5,2,8,6]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,3,5,4,7,2,6]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,8,2,5,7,4,6]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[8,3,2,6,1,4,7,5]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,8,1,6,4,3,7,5]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,6,1,3,8,7,5,4]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,5,7,1,3,8,6,4]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,6,8,1,5,7,4,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,7,1,5,8,4,6,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,7,1,6,4,8,3,5]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,7,1,6,5,3,8,4]=>[3,8,1,6,5,4,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,8,1,7,6,5,4,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[8,3,2,7,1,6,5,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,1,8,7,3,2,6,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,1,7,2,8,6,5,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,7,1,8,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,7,6,1,4,2,5,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[3,7,5,1,4,6,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,6,8,5,1,4,7,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,3,5,8,2,1,4,6]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,3,6,2,1,4,5,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[7,3,6,2,1,5,4,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[7,4,2,8,1,6,5,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,7,5,3,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,2,6,3,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,6,2,1,8,3,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,8,4,5,2,1,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,8,5,1,7,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,5,1,3,8,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,7,6,1,5,3,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,1,7,6,3,8,2,4]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,7,6,4,2,8,3]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,8,7,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,5,2,1,7,6,4,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,5,2,1,6,3,7,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,1,8,6,3,2,7,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,6,1,7,4,8,2,5]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,1,8,6,3,7,2,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,4,2,5,7,3,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,4,6,8,5,7,1,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,4,8,2,7,3,6,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[5,4,8,7,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,4,7,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,3,8,7,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,7,2,4,8,1,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,8,4,2,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,4,2,8,1,3,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,5,2,7,1,3,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,6,5,4,2,1,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,7,3,1,8,2,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,4,3,8,6,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,8,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,4,8,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,5,3,8,2,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,4,3,2,1,9,8,7]=>[6,5,4,3,2,1,9,8,7]=>[6,5,4,3,2,1,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]
[6,5,4,3,2,1,8,7,9]=>[6,5,4,3,2,1,8,7,9]=>[6,5,4,3,2,1,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]
[5,4,3,2,1,9,8,7,6]=>[5,4,3,2,1,9,8,7,6]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[5,4,3,2,1,8,7,6,9]=>[5,4,3,2,1,8,7,6,9]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[5,4,3,2,1,7,6,9,8]=>[5,4,3,2,1,7,6,9,8]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[5,4,3,2,1,7,6,8,9]=>[5,4,3,2,1,7,6,8,9]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[4,3,2,1,8,7,6,5,9]=>[4,3,2,1,8,7,6,5,9]=>[4,3,2,1,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[4,3,2,1,7,6,5,9,8]=>[4,3,2,1,7,6,5,9,8]=>[4,3,2,1,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[4,3,2,1,7,6,5,8,9]=>[4,3,2,1,7,6,5,8,9]=>[4,3,2,1,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[4,3,2,1,6,5,8,7,9]=>[4,3,2,1,6,5,8,7,9]=>[4,3,2,1,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[4,3,2,1,6,5,7,8,9]=>[4,3,2,1,6,5,7,8,9]=>[4,3,2,1,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,6,5,4,8,7,9]=>[3,2,1,6,5,4,8,7,9]=>[3,2,1,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[3,2,1,6,5,4,7,8,9]=>[3,2,1,6,5,4,7,8,9]=>[3,2,1,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[3,2,1,5,4,7,6,9,8]=>[3,2,1,5,4,7,6,9,8]=>[3,2,1,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[3,2,1,5,4,7,6,8,9]=>[3,2,1,5,4,7,6,8,9]=>[3,2,1,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[3,2,1,5,4,6,7,8,9]=>[3,2,1,5,4,6,7,8,9]=>[3,2,1,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]=>[2,1,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,4,3,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]=>[2,1,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,5,4,3,2,1,10,9,8]=>[7,6,5,4,3,2,1,10,9,8]=>[7,6,5,4,3,2,1,10,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[7,6,5,4,3,2,1,9,8,10]=>[7,6,5,4,3,2,1,9,8,10]=>[7,6,5,4,3,2,1,10,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[6,5,4,3,2,1,9,8,7,10]=>[6,5,4,3,2,1,9,8,7,10]=>[6,5,4,3,2,1,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[6,5,4,3,2,1,8,7,9,10]=>[6,5,4,3,2,1,8,7,9,10]=>[6,5,4,3,2,1,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[5,4,3,2,1,9,8,7,6,10]=>[5,4,3,2,1,9,8,7,6,10]=>[5,4,3,2,1,10,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[5,4,3,2,1,8,7,6,10,9]=>[5,4,3,2,1,8,7,6,10,9]=>[5,4,3,2,1,10,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[5,4,3,2,1,8,7,6,9,10]=>[5,4,3,2,1,8,7,6,9,10]=>[5,4,3,2,1,10,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[5,4,3,2,1,7,6,9,8,10]=>[5,4,3,2,1,7,6,9,8,10]=>[5,4,3,2,1,10,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[5,4,3,2,1,7,6,8,9,10]=>[5,4,3,2,1,7,6,8,9,10]=>[5,4,3,2,1,10,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[4,3,2,1,8,7,6,5,9,10]=>[4,3,2,1,8,7,6,5,9,10]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[4,3,2,1,7,6,5,10,9,8]=>[4,3,2,1,7,6,5,10,9,8]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[4,3,2,1,7,6,5,8,9,10]=>[4,3,2,1,7,6,5,8,9,10]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[4,3,2,1,6,5,8,7,9,10]=>[4,3,2,1,6,5,8,7,9,10]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[4,3,2,1,6,5,7,8,9,10]=>[4,3,2,1,6,5,7,8,9,10]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[3,2,1,6,5,4,9,8,7,10]=>[3,2,1,6,5,4,9,8,7,10]=>[3,2,1,10,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,1,6,5,4,8,7,10,9]=>[3,2,1,6,5,4,8,7,10,9]=>[3,2,1,10,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,1,6,5,4,8,7,9,10]=>[3,2,1,6,5,4,8,7,9,10]=>[3,2,1,10,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,1,6,5,4,7,8,9,10]=>[3,2,1,6,5,4,7,8,9,10]=>[3,2,1,10,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,1,5,4,7,6,9,8,10]=>[3,2,1,5,4,7,6,9,8,10]=>[3,2,1,10,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,1,5,4,7,6,8,9,10]=>[3,2,1,5,4,7,6,8,9,10]=>[3,2,1,10,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,1,5,4,6,7,8,9,10]=>[3,2,1,5,4,6,7,8,9,10]=>[3,2,1,10,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,4,3,6,5,7,8,9,10]=>[2,1,4,3,6,5,7,8,9,10]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[5,6,3,7,4,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,3,8,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,8,1,3,2,5,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[7,4,8,6,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,2,7,6,5,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,7,2,4,6,5,1,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,1,3,4,5,2,6,7]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,8,4,2,5,3,7]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,2,8,4,1,5,7,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[6,7,4,8,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,2,7,8,5,1,6,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,2,8,1,5,4,6,7]=>[4,2,8,1,6,5,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[6,1,4,8,5,3,7,2]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,4,8,5,2,6,7,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,8,4,3,7,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,7,1,4,2,5,8,6]=>[5,8,3,4,1,6,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[7,2,1,4,3,5,6,8]=>[7,3,2,5,4,6,1,8]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[4,1,5,3,6,8,2,7]=>[7,2,4,3,5,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,1,8,5,3,2,7,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,4,6,3,8,5,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,6,4,1,8,7,5]=>[5,2,8,4,1,7,6,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[7,6,4,3,1,8,2,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,5,2,1,8,7,6,4]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[1,5,3,2,8,6,4,7]=>[1,7,4,3,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,2,1,7,8,6,3]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,2,7,6,5,1,3,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,6,2,7,1,4,5,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,7,3,6,2,8,5,4]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,3,2,1,8,5,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,6,3,7,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,3,4,7,1,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[8,6,3,1,4,5,7,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,3,1,5,4,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,8,3,1,2,4,7,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[8,4,1,7,2,3,6,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,2,1,6,5,4,7,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,8,1,5,6,4,7,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,4,1,2,5,7,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,2,8,1,6,5,7,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[7,6,4,1,5,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,6,1,5,4,7,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,5,8,2,1,3,7,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[5,8,2,3,1,4,6,7]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[4,2,1,3,5,8,7,6]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[5,4,1,3,6,2,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[8,5,4,1,3,6,2,7]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,2,5,1,4,6,8,7]=>[4,2,5,1,3,6,8,7]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[8,1,4,3,5,6,7,2]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,3,5,4,6,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,1,3,2,5,7,6,8]=>[4,2,3,1,5,7,6,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,1,2,5,4,7,6,9,8]=>[3,2,1,5,4,7,6,9,8]=>[3,2,1,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[3,1,2,5,7,4,6,9,8]=>[3,2,1,6,7,4,5,9,8]=>[3,2,1,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[1,3,5,2,4,7,6,9,8]=>[1,4,5,2,3,7,6,9,8]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[3,1,2,5,4,7,6,9,8,10]=>[3,2,1,5,4,7,6,9,8,10]=>[3,2,1,10,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,2,4,5,1,3,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,6,7,2,5,1,4,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[4,6,7,3,1,5,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,8,1,2,4,7,3,6]=>[7,8,3,4,5,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[6,8,1,3,5,2,7,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,3,1,4,5,7,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,1,8,2,3,6,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,1,8,2,3,4,7,5]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,3,8,4,2,6,7,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,1,8,4,6,3,7,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,8,3,5,7,2,6]=>[7,2,8,4,5,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,4,7,2,6,1,8,5]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[4,5,7,3,2,6,8,1]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,5,7,2,3,6,8,1]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[2,6,3,4,7,5,8,1]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,6,4,2,7,5,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,5,2,7,1,6,8,3]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,4,1,6,5,8,2,7]=>[7,3,2,5,4,8,1,6]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[4,1,2,8,5,7,3,6]=>[7,2,3,8,5,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,4,8,6,2,7,3]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,3,1,4,8,5,6,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,6,3,1,7,4,2,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,3,4,1,8,5,2,6]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,4,2,8,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,4,8,1,5,3,6]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[2,6,3,7,5,1,4,8]=>[6,7,3,5,4,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[7,1,3,8,5,2,4,6]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,6,7,1,8,4,5]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,6,3,1,7,8,5,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,3,1,6,7,8,4,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,1,6,2,7,8,5,3]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,1,3,4,8,7,5,6]=>[2,1,3,4,8,7,6,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[4,5,6,7,8,9,1,2,3]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[4,5,6,7,8,9,2,3,1]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[5,6,7,8,9,1,2,3,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[5,6,7,8,9,2,3,4,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[5,6,7,8,9,3,4,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[5,6,7,8,9,3,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,7,8,9,2,3,4,5,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,7,8,9,3,4,5,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,7,8,9,3,4,5,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,7,8,9,4,5,2,3,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,7,8,9,4,5,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,8,9,4,5,6,2,3,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,8,9,4,5,6,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,8,9,5,6,3,4,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,8,9,5,6,3,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,8,9,5,6,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,9,6,7,4,5,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,9,6,7,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[5,6,7,8,9,10,1,2,3,4]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[5,6,7,8,9,10,2,3,4,1]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[5,6,7,8,9,10,3,4,1,2]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[5,6,7,8,9,10,3,4,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,8,9,10,3,4,5,6,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,10,3,4,5,6,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,10,4,5,6,1,2,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,10,4,5,6,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,10,5,6,3,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,10,5,6,3,4,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,10,5,6,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,5,6,7,2,3,4,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,5,6,7,3,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,5,6,7,3,4,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,5,6,7,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,6,7,4,5,2,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,6,7,4,5,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,6,7,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,7,8,5,6,3,4,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,7,8,5,6,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,7,8,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[4,8,3,7,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,8,7,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,8,7,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,7,6,1,5,4,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[5,2,8,7,6,1,4,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,2,8,7,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,8,2,6,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,8,7,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,8,7,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,8,2,6,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,2,8,7,1,5,4,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[4,2,8,1,7,6,5,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,8,2,7,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,2,1,6,5,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[6,5,8,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,1,7,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,1,8,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,4,8,1,7,5,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,4,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,3,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,8,1,7,5,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,1,8,7,6,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,2,1,6,5,4,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,5,3,1,8,7,4,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,4,3,1,8,7,5,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,4,3,1,8,7,6,2]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[7,5,2,1,8,6,4,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,4,2,1,8,7,6,3]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[7,3,2,1,8,6,5,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[6,3,2,1,8,7,5,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[9,7,5,3,1,10,8,6,4,2]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,7,5,3,1,10,9,6,4,2]=>[10,9,8,5,4,7,6,3,2,1]=>[10,9,8,5,4,7,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[9,6,5,3,1,10,8,7,4,2]=>[10,9,8,5,4,7,6,3,2,1]=>[10,9,8,5,4,7,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[8,6,5,3,1,10,9,7,4,2]=>[10,9,8,5,4,7,6,3,2,1]=>[10,9,8,5,4,7,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[9,7,4,3,1,10,8,6,5,2]=>[10,9,8,5,4,7,6,3,2,1]=>[10,9,8,5,4,7,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[8,7,4,3,1,10,9,6,5,2]=>[10,9,8,5,4,7,6,3,2,1]=>[10,9,8,5,4,7,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[9,6,4,3,1,10,8,7,5,2]=>[10,9,8,5,4,7,6,3,2,1]=>[10,9,8,5,4,7,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[8,6,4,3,1,10,9,7,5,2]=>[10,9,8,5,4,7,6,3,2,1]=>[10,9,8,5,4,7,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[6,5,4,3,1,10,9,8,7,2]=>[10,5,4,3,2,9,8,7,6,1]=>[10,5,4,3,2,9,8,7,6,1]=>[[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],.]
[9,7,5,2,1,10,8,6,4,3]=>[10,9,8,5,4,7,6,3,2,1]=>[10,9,8,5,4,7,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[8,7,5,2,1,10,9,6,4,3]=>[10,9,8,5,4,7,6,3,2,1]=>[10,9,8,5,4,7,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[9,6,5,2,1,10,8,7,4,3]=>[10,9,8,5,4,7,6,3,2,1]=>[10,9,8,5,4,7,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[8,6,5,2,1,10,9,7,4,3]=>[10,9,8,5,4,7,6,3,2,1]=>[10,9,8,5,4,7,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[9,7,4,2,1,10,8,6,5,3]=>[10,9,8,5,4,7,6,3,2,1]=>[10,9,8,5,4,7,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[8,7,4,2,1,10,9,6,5,3]=>[10,9,8,5,4,7,6,3,2,1]=>[10,9,8,5,4,7,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[9,6,4,2,1,10,8,7,5,3]=>[10,9,8,5,4,7,6,3,2,1]=>[10,9,8,5,4,7,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[8,6,4,2,1,10,9,7,5,3]=>[10,9,8,5,4,7,6,3,2,1]=>[10,9,8,5,4,7,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[6,5,4,2,1,10,9,8,7,3]=>[10,5,4,3,2,9,8,7,6,1]=>[10,5,4,3,2,9,8,7,6,1]=>[[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],.]
[6,5,3,2,1,10,9,8,7,4]=>[10,5,4,3,2,9,8,7,6,1]=>[10,5,4,3,2,9,8,7,6,1]=>[[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],.]
[9,4,3,2,1,10,8,7,6,5]=>[10,5,4,3,2,9,8,7,6,1]=>[10,5,4,3,2,9,8,7,6,1]=>[[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],.]
[8,4,3,2,1,10,9,7,6,5]=>[10,5,4,3,2,9,8,7,6,1]=>[10,5,4,3,2,9,8,7,6,1]=>[[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],.]
[7,4,3,2,1,10,9,8,6,5]=>[10,5,4,3,2,9,8,7,6,1]=>[10,5,4,3,2,9,8,7,6,1]=>[[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],.]
[6,4,3,2,1,10,9,8,7,5]=>[10,5,4,3,2,9,8,7,6,1]=>[10,5,4,3,2,9,8,7,6,1]=>[[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],.]
[10,9,7,5,3,1,12,11,8,6,4,2]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[11,8,7,5,3,1,12,10,9,6,4,2]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[10,8,7,5,3,1,12,11,9,6,4,2]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[11,9,6,5,3,1,12,10,8,7,4,2]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[10,9,6,5,3,1,12,11,8,7,4,2]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[11,8,6,5,3,1,12,10,9,7,4,2]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[10,8,6,5,3,1,12,11,9,7,4,2]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[8,7,6,5,3,1,12,11,10,9,4,2]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[11,9,7,4,3,1,12,10,8,6,5,2]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[10,9,7,4,3,1,12,11,8,6,5,2]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[11,8,7,4,3,1,12,10,9,6,5,2]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[10,8,7,4,3,1,12,11,9,6,5,2]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[11,9,6,4,3,1,12,10,8,7,5,2]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[10,9,6,4,3,1,12,11,8,7,5,2]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[11,8,6,4,3,1,12,10,9,7,5,2]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[10,8,6,4,3,1,12,11,9,7,5,2]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[8,7,6,4,3,1,12,11,10,9,5,2]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[8,7,5,4,3,1,12,11,10,9,6,2]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[11,6,5,4,3,1,12,10,9,8,7,2]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[10,6,5,4,3,1,12,11,9,8,7,2]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[9,6,5,4,3,1,12,11,10,8,7,2]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[8,6,5,4,3,1,12,11,10,9,7,2]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[11,9,7,5,2,1,12,10,8,6,4,3]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[10,9,7,5,2,1,12,11,8,6,4,3]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[11,8,7,5,2,1,12,10,9,6,4,3]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[10,8,7,5,2,1,12,11,9,6,4,3]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[11,9,6,5,2,1,12,10,8,7,4,3]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[10,9,6,5,2,1,12,11,8,7,4,3]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[11,8,6,5,2,1,12,10,9,7,4,3]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[10,8,6,5,2,1,12,11,9,7,4,3]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[8,7,6,5,2,1,12,11,10,9,4,3]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[11,9,7,4,2,1,12,10,8,6,5,3]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[10,9,7,4,2,1,12,11,8,6,5,3]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[11,8,7,4,2,1,12,10,9,6,5,3]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[10,8,7,4,2,1,12,11,9,6,5,3]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[11,9,6,4,2,1,12,10,8,7,5,3]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[10,9,6,4,2,1,12,11,8,7,5,3]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[11,8,6,4,2,1,12,10,9,7,5,3]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[10,8,6,4,2,1,12,11,9,7,5,3]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[8,7,6,4,2,1,12,11,10,9,5,3]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[8,7,5,4,2,1,12,11,10,9,6,3]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[11,6,5,4,2,1,12,10,9,8,7,3]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[10,6,5,4,2,1,12,11,9,8,7,3]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[9,6,5,4,2,1,12,11,10,8,7,3]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[8,6,5,4,2,1,12,11,10,9,7,3]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[8,7,6,3,2,1,12,11,10,9,5,4]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[8,7,5,3,2,1,12,11,10,9,6,4]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[11,6,5,3,2,1,12,10,9,8,7,4]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[10,6,5,3,2,1,12,11,9,8,7,4]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[9,6,5,3,2,1,12,11,10,8,7,4]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[8,6,5,3,2,1,12,11,10,9,7,4]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[11,9,4,3,2,1,12,10,8,7,6,5]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[10,9,4,3,2,1,12,11,8,7,6,5]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[11,8,4,3,2,1,12,10,9,7,6,5]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[10,8,4,3,2,1,12,11,9,7,6,5]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[9,8,4,3,2,1,12,11,10,7,6,5]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[11,7,4,3,2,1,12,10,9,8,6,5]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[10,7,4,3,2,1,12,11,9,8,6,5]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[9,7,4,3,2,1,12,11,10,8,6,5]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[8,7,4,3,2,1,12,11,10,9,6,5]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[11,6,4,3,2,1,12,10,9,8,7,5]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[10,6,4,3,2,1,12,11,9,8,7,5]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[9,6,4,3,2,1,12,11,10,8,7,5]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[8,6,4,3,2,1,12,11,10,9,7,5]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[6,1,4,2,3,5,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,6,1,4,2,3,5,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,1,4,2,3,5,7]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[8,1,4,2,3,6,5,7]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,8,2,3,6,5,7]=>[5,2,8,4,1,7,6,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[8,2,3,6,1,4,5,7]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,2,3,8,1,4,5,7]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,6,2,3,8,1,5,7]=>[6,7,4,3,8,1,2,5]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[4,8,2,3,6,1,5,7]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[8,2,3,6,4,1,5,7]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,4,3,6,2,1,5,7]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[6,2,3,8,4,1,5,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,4,2,3,6,1,5,7]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,4,2,3,8,1,5,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[2,6,4,3,8,1,5,7]=>[6,7,4,3,8,1,2,5]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[2,8,4,3,6,1,5,7]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[2,6,3,8,4,1,5,7]=>[6,7,3,8,5,1,2,4]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[6,3,8,4,2,1,5,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[2,6,3,8,1,4,5,7]=>[5,7,3,8,1,6,2,4]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,8,3,6,1,4,5,7]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[8,3,6,4,2,1,5,7]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,8,3,6,4,1,5,7]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[8,3,6,2,4,1,5,7]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,3,6,2,1,4,5,7]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,2,1,3,8,4,5,7]=>[7,3,2,4,8,6,1,5]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[8,2,1,3,6,4,5,7]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,3,8,2,4,1,5,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[6,2,4,3,8,1,5,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[3,6,4,7,8,5,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,6,4,2,7,5,8,3]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,2,5,6,8,3]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,4,8,5,3,7,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,5,4,2,7,8,3]=>[1,8,5,4,3,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,2,5,3,6,1,7,8]=>[6,4,3,2,5,1,7,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[7,1,5,3,6,2,8,4]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,5,2,4,8,7,3]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,1,4,2,5,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,4,8,5,2,1,6,7]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[4,8,5,3,1,6,2,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[6,1,3,5,8,2,7,4]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,8,7,4,2,3,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,8,5,7,3,6,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,6,8,7,5,2,4]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,5,4,7,6,3]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,2,4,5,8,6,3]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,7,3,5,8,6,4]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,2,1,7,5,3,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,6,3,7,8,5,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,2,3,7,8,1,5]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[4,6,3,7,1,2,8,5]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[4,2,1,3,5,7,8,6]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[7,3,2,4,5,1,8,6]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,8,2,5,4,1,7,6]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[7,8,4,2,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,2,6,3,8,7,1,5]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[5,8,2,7,4,3,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,3,8,5,1,7,2,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[4,3,6,8,1,2,7,5]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[6,4,3,5,2,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,5,3,8,4,2,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[6,1,7,8,9,10,2,3,4,5]=>[10,2,9,8,7,6,5,4,3,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[6,7,1,8,9,10,2,3,4,5]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[6,7,8,1,9,10,2,3,4,5]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[6,7,8,9,1,2,3,4,10,5]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[6,7,8,9,1,2,3,10,4,5]=>[10,9,7,6,5,4,3,8,2,1]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[6,7,8,9,1,2,10,3,4,5]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[6,7,8,9,1,10,2,3,4,5]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[3,8,1,7,5,6,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,2,5,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,6,7,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,5,8,7,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,8,6,2,3,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,7,6,1,3,5,4,8]=>[4,7,6,1,5,3,2,8]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[6,4,1,8,2,5,7,3]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,8,6,1,3,5,4,7]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,1,3,6,5,8,7,2]=>[8,2,3,5,4,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,1,6,3,5,8,7,4]=>[2,1,8,4,5,7,6,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,1,3,8,5,7,6]=>[3,4,1,2,8,6,7,5]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,1,3,5,8,7,6]=>[3,4,1,2,5,8,7,6]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[4,6,1,3,5,8,7,2]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,1,4,3,5,8,7,2]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,1,3,5,8,7,2]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,2,1,3,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,2,1,6,3,5,7,8]=>[5,3,2,6,1,4,7,8]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[6,2,1,8,3,5,7,4]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,2,1,3,8,5,7,4]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,1,4,3,8,5,7,2]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,3,6,5,7,2]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,1,3,6,5,7,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,2,1,3,6,5,7,4]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,2,1,6,3,5,7,4]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,2,1,4,3,5,7,8]=>[6,3,2,5,4,1,7,8]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[8,2,4,1,3,5,7,6]=>[8,4,5,2,3,6,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,2,6,1,3,5,7,4]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,4,6,1,3,5,7,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,1,6,3,5,7,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,4,6,3,5,7,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,4,6,3,5,7,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,4,8,3,5,7,2]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,4,1,8,3,5,7,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,4,8,1,3,5,7,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,2,8,1,3,5,7,4]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,6,8,1,3,5,7,4]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,6,8,1,3,5,7,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,6,1,8,3,5,7,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,1,6,8,3,5,7,2]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,6,1,3,8,5,7,2]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,1,6,8,3,5,7,4]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[4,1,3,6,8,5,7,2]=>[8,2,3,6,7,4,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,4,3,6,8,5,7,2]=>[1,8,3,6,7,4,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,3,8,6,5,7,2]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,1,8,3,6,5,7,4]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,6,1,4,3,5,7,8]=>[3,6,1,5,4,2,7,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,8,1,4,3,5,7,6]=>[3,8,1,5,4,6,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,8,1,6,3,5,7,4]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[4,8,1,3,6,5,7,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,4,8,3,6,5,7,2]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,8,6,3,5,7,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,8,6,3,5,7,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,8,1,6,3,5,7,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,8,6,1,3,5,7,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,6,1,3,5,7,4]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,8,4,1,3,5,7,6]=>[4,8,5,1,3,6,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,6,2,1,3,5,7,8]=>[5,6,4,3,1,2,7,8]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[6,8,1,4,3,5,7,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,1,8,4,3,5,7,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,8,4,3,5,7,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,6,4,3,5,7,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,6,4,3,5,7,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,1,4,3,5,7,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,4,1,3,5,7,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,2,1,3,5,7,4]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,4,2,1,3,5,7,6]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[7,8,6,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,4,1,8,6,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,4,2,8,3,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,6,4,2,7,3,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[5,7,1,4,6,3,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,8,1,4,6,3,7,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,7,4,5,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,5,7,4,6,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,8,4,1,7,2,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,4,6,1,7,8,3,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,6,4,1,8,7,3,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,5,8,4,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,8,4,5,7,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,8,4,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,1,4,5,3,7,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,1,4,5,3,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,7,1,5,4,6,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,8,1,5,4,6,7,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,7,1,5,4,6,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,7,1,4,5,3,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,7,1,4,6,3,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,6,4,2,7,3,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,4,7,2,8,3,1,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[5,4,7,2,8,3,6,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[5,6,4,2,8,3,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[5,8,1,4,6,3,2,7]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,8,1,5,4,6,2,7]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,6,1,5,4,2,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,6,1,5,4,8,2,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,8,3,1,4,2,5,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[7,3,8,1,4,2,5,6]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,7,3,1,4,2,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,6,1,5,4,7,8,2]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,4,1,2,7,6,5,8]=>[4,3,2,1,7,6,5,8]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,4,1,2,6,8,7,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[6,8,3,1,4,7,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,7,2,8,5,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,1,4,7,3,2,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[7,8,1,4,5,3,2,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,1,5,4,7,2,6]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,6,1,5,4,8,7,2]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,6,1,5,4,7,2,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,7,3,1,4,2,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,8,3,1,4,2,7,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,3,1,4,6,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,4,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,8,7,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,3,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,3,1,4,5,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,7,1,5,4,2,6,8]=>[6,7,3,5,4,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,8,1,5,4,2,7,6]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[5,8,1,4,7,3,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,4,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,7,2,8,5,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,7,1,4,8,5,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,8,3,1,4,7,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,7,1,5,4,8,6,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,4,1,2,8,5,7,6]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,4,1,2,5,8,7,6]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[3,7,1,5,4,2,8,6]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[6,7,3,1,4,5,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,3,8,1,4,5,2,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,8,1,4,5,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,3,1,4,5,2,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,8,1,5,4,2,6,7]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[9,8,7,6,5,4,2,1,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,6,5,3,2,1,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,7,6,3,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[9,8,7,6,4,3,2,1,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,7,4,6,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[9,8,7,5,4,3,2,1,6]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,5,7,4,3,2,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[9,8,6,5,4,3,2,1,7]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,7,6,5,4,3,2,1,8]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,6,5,4,1,3,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,9,8,7,6,5,4,2,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,8,7,6,5,2,4,1,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,9,8,7,6,5,3,2,1,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,8,7,6,3,5,2,1,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,9,8,7,6,4,3,2,1,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,7,6,2,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[9,8,7,4,6,3,2,1,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,9,8,7,5,4,3,2,1,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,5,4,7,3,2,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,3,6,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[9,8,5,7,4,3,2,1,6]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,9,8,6,5,4,3,2,1,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,5,8,4,3,2,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[8,4,7,6,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[9,6,8,5,4,3,2,1,7]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,9,7,6,5,4,3,2,1,8]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[5,8,7,4,3,2,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[10,8,7,6,5,4,3,2,1,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[5,8,6,2,3,4,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,2,7,3,1,8,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,8,2,6,3,5,7,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,3,7,8,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,1,7,2,5,8,6,3]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,8,2,1,5,6,4,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,6,2,5,8,4,3,7]=>[1,7,3,6,8,4,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,8,7,4,5,3,6]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[7,3,1,6,8,5,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,5,8,6,2,3,7,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,8,3,1,6,5,7]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[5,2,7,1,8,6,3,4]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,6,1,3,8,7,4,5]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[6,5,2,8,1,7,3,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[2,8,3,5,1,7,4,6]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[5,4,3,8,7,1,6,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,5,4,3,7,2,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,7,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,6,5,1,7,4,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[6,3,2,8,4,1,7,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,8,3,4,1,7,5,6]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[5,4,2,8,3,1,7,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[2,8,4,3,1,7,6,5]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[2,8,5,3,1,7,6,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,8,6,4,1,7,5,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[3,8,7,5,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,7,5,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,6,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,8,6,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,8,5,2,1,6,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,3,8,4,2,1,6,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,5,4,3,8,2,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,7,8,4,1,2,6,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[3,7,8,5,1,2,6,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[4,7,8,6,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,4,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,7,8,3,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,4,8,2,1,5,6]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[7,6,4,8,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,8,7,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,2,4,8,1,5,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[2,3,8,4,1,6,7,5]=>[5,2,8,4,1,7,6,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,8,5,1,6,7,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[6,4,8,7,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,4,7,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,4,7,2,5,6,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[3,4,8,7,1,5,6,2]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[2,4,8,6,1,5,7,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,5,8,6,1,4,7,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[8,3,5,7,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,6,7,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,8,7,1,3,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,8,5,1,3,7,4]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,6,8,4,1,3,7,5]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,5,8,3,1,4,7,6]=>[5,6,8,4,1,2,7,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[5,6,8,7,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,6,8,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,3,5,4,1,8,6,7]=>[5,2,4,3,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,6,4,8,1,5,7]=>[6,2,7,4,8,1,3,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,8,4,6,3,5,2,7]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,8,6,2,1,3,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[2,3,6,8,1,5,4,7]=>[5,2,7,8,1,6,3,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,5,6,1,4,7,8,3]=>[4,8,5,1,3,6,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[7,3,5,1,6,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,7,6,1,8,5,4,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,7,6,8,1,4,5,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,8,7,6,3,2,5,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,7,6,3,2,4,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,8,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,6,1,8,5,3,4]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[6,3,5,1,7,2,4,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[2,3,4,7,6,1,5,8]=>[6,2,3,7,5,1,4,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[7,3,5,8,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,4,5,2,7,3,6]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,4,5,2,7,6,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,3,5,8,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,6,4,8,5,1,3]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[7,3,5,4,6,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,3,5,4,7,1,8,2]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,3,5,4,7,1,2,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[3,7,1,6,8,5,2,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,3,1,8,6,4,7,5]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,8,6,4,5,7]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,7,1,6,8,5,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,3,5,4,7,2,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,3,5,4,6,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,7,6,4,8,5,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,8,4,5,2,6,3,7]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,4,8,5,3,1,2,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[7,3,5,8,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,3,4,6,5,8,1,7]=>[7,2,3,5,4,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,3,4,7,5,1,8,6]=>[6,2,3,8,5,1,7,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,4,7,5,1,6,8]=>[6,2,3,7,5,1,4,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,4,7,1,6,5,8]=>[5,2,3,7,1,6,4,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,4,7,1,6,8,5]=>[5,2,3,8,1,6,7,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,4,6,1,8,7,5]=>[5,2,3,8,1,7,6,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[6,3,5,8,4,2,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[7,4,8,5,3,2,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,4,5,2,3,6,7]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,8,5,3,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,5,8,4,2,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[5,2,4,6,8,3,7,1]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,5,7,4,6,3,2,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,2,8,4,6,3,7,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[3,8,5,4,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,3,4,5,7,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,7,4,6,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,4,1,7,8,3,2,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,4,2,7,8,3,6,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,1,4,6,8,3,2,7]=>[7,2,6,4,8,3,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,8,4,6,3,2,7]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,1,6,4,5,3,2,7]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,3,5,4,6,2,7]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,6,2,4,3,5,7]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,7,1,2,4,3,5,6]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,7,6,2,4,3,5,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,3,2,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,6,3,4,5,7,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,7,6,3,4,5,2,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,5,4,3,6,8]=>[1,7,3,6,5,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,2,4,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,2,4,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,3,2,4,7,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,1,3,4,5,2,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,6,3,4,5,2,7]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,5,4,3,6,7]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,4,8,7,5,2,6,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[3,2,8,6,1,5,4,7]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[8,6,1,2,4,3,5,7]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,3,6,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,2,5,4,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,2,4,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,6,2,4,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[3,5,2,8,6,1,4,7]=>[6,7,3,8,5,1,2,4]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,7,2,5,1,4,8,6]=>[5,8,3,6,1,4,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[5,1,8,6,2,3,4,7]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,5,4,1,8,6,3,7]=>[4,7,3,1,8,6,2,5]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,7,6,1,8,2,5,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[7,6,3,1,8,2,4,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,3,6,1,4,7,5]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,8,2,6,3,4,7,5]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,3,6,4,7,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,3,6,4,8,2,5]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,1,3,5,7,4,6]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,2,6,3,1,4,7,5]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[7,5,4,1,3,8,2,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,7,5,8,3,4,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[7,3,8,5,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,3,6,1,4,8,5]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,3,7,2,5,8,4,6]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,3,5,8,4,6]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,8,1,3,6,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,2,3,5,7,4,6]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,2,3,5,8,4,6]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,1,4,7,3,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,6,3,7,1,4,8,5]=>[5,8,3,6,1,4,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,6,3,8,1,4,7,5]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[7,5,4,8,1,3,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,4,7,1,3,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,3,1,8,5,4,6,7]=>[3,2,1,8,6,5,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[8,6,5,1,3,4,2,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,1,7,6,3,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,4,7,6,1,8,5,2]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[3,5,2,6,7,1,8,4]=>[6,8,3,4,5,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,2,8,4,7,5,1,6]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,4,7,5,1,3,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,1,6,5,2,7,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[6,1,2,8,3,4,7,5]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,8,3,1,7,2,4,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,7,2,5,6,1,8,4]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[6,8,4,2,5,1,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,5,3,8,4,1,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[8,3,1,4,7,2,6,5]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,3,2,1,5,7,4,6]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,8,3,6,4,7,1,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[7,3,6,4,8,1,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,6,4,7,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,2,8,3,5,7,4,6]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,5,1,7,4,2,8,3]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,3,6,4,8,2,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,6,1,7,3,5,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,6,1,7,3,4,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,1,7,3,4,2,8,5]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,3,8,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,7,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,1,7,4,2,8,6,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,8,1,7,6,5,3,4]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[4,2,8,6,5,1,7,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,4,2,8,5,1,7,3]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[8,6,4,7,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,4,8,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,6,4,2,3,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,2,3,8,7,5,1,6]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[3,8,7,1,6,5,2,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,4,3,8,1,6,7,5]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[2,4,3,7,1,6,8,5]=>[5,3,2,8,1,6,7,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,2,3,7,8,5,1,6]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[5,1,6,4,2,3,7,8]=>[6,2,5,4,3,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,4,7,8,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,4,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,7,8,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,8,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,2,4,7,8,1,5,6]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,2,4,8,7,1,5,6]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,8,7,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,6,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,5,7,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,6,7,4,2,3,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,7,4,8,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,6,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,2,4,7,1,5,6]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,3,2,4,8,1,5,6]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,4,6,7,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,6,8,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,6,8,4,2,3,7]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,2,3,7,5,1,6,8]=>[6,3,2,7,5,1,4,8]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[3,7,5,8,1,6,2,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,4,3,7,1,6,5,8]=>[5,3,2,7,1,6,4,8]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[2,4,7,1,5,8,6,3]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,2,4,7,6,1,5,8]=>[6,2,3,7,5,1,4,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,7,6,8,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,6,7,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,7,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,8,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,7,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,8,7,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,8,7,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,6,7,1,5,8,3]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,2,4,6,1,5,7,8]=>[5,2,3,6,1,4,7,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[6,7,8,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,6,5,1,4,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,1,7,5,4,2,8,6]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,1,8,5,4,6,3,7]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[4,1,8,5,2,3,6,7]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,4,1,2,6,3,7,5]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,2,7,1,5,3,4,6]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,2,7,1,5,8,4,6]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[6,3,7,1,5,4,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,3,8,1,5,4,2,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,1,5,3,8,4,2,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,5,1,3,6,8,2,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[3,6,8,1,5,4,2,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[6,8,3,1,5,4,2,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[7,6,3,1,5,4,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,6,2,1,5,3,4,7]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,8,2,1,7,5,3,6]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[2,3,8,1,5,7,4,6]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[7,1,3,2,8,6,4,5]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,6,2,8,3,4,5]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,7,1,2,6,3,8,5]=>[6,8,3,4,5,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,7,8,1,5,3,4,6]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[6,7,2,1,5,3,4,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,7,2,1,8,5,3,6]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[8,7,2,1,4,5,3,6]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,7,5,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,4,1,6,5,3,8]=>[4,7,6,1,5,3,2,8]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,7,1,4,5,6,8,2]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,1,6,4,5,8,3,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,5,1,4,7,6,8,2]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,6,4,1,7,5,3,8]=>[4,7,6,1,5,3,2,8]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[5,6,8,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,5,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,6,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,7,8,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,3,1,5,6,4,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[4,2,8,1,6,5,3,7]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[6,2,4,1,8,5,3,7]=>[7,4,6,2,8,3,1,5]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[8,3,1,4,5,6,7,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,3,1,4,8,6,7,2]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[7,5,1,6,3,4,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,1,5,8,4,3,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,8,1,6,4,3,7,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,3,1,8,4,6,7,2]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,3,1,5,4,6,7,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,2,6,1,4,5,3,7]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,2,8,1,4,5,3,7]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[7,2,6,1,5,3,4,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[2,8,6,1,5,3,4,7]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[7,1,2,5,8,3,4,6]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,4,5,6,8,3,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,5,6,7,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,8,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,7,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,7,1,4,5,3,8]=>[4,7,6,1,5,3,2,8]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,5,1,7,4,6,8,2]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,1,5,6,4,8,3,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,6,5,4,8,3,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,7,6,1,4,5,3,8]=>[4,7,6,1,5,3,2,8]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[5,7,6,8,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,6,5,1,4,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,1,6,5,8,7,2]=>[8,3,2,5,4,7,6,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[5,3,1,2,4,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,3,6,2,1,8,7,4]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,3,7,2,1,4,6,8]=>[6,5,7,4,2,1,3,8]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[5,3,7,2,8,4,1,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[7,2,4,5,8,3,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,4,5,1,3,6,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[6,2,4,5,1,8,7,3]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[3,1,4,5,2,8,7,6]=>[5,2,3,4,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,6,4,5,2,8,7,3]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,4,5,1,2,6,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[3,7,4,5,8,2,1,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,7,4,2,6,3,5,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,4,5,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,7,1,8,4,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,4,1,6,3,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,7,4,8,6,3,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,4,8,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,3,5,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,8,3,5,6,7,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,8,1,5,6,7,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,1,3,5,6,7,2,8]=>[7,2,3,4,5,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,8,4,3,6,1,2,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,3,8,4,1,7,2,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,5,8,4,6,7,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,8,3,6,7,5,2]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,8,2,1,7,5,6]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[3,8,4,2,6,1,5,7]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[1,8,2,5,6,7,4,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,8,1,5,6,7,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,2,5,6,7,1,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[8,2,1,5,6,7,4,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,1,3,5,6,7,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,4,3,6,2,5,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,8,4,3,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,1,8,5,7,6,2]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,3,1,6,8,7,5,2]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,3,1,8,2,7,4,5]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,3,5,8,2,7,1,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,5,4,8,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,4,8,6,2,3,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,5,4,1,6,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,4,5,8,1,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,6,4,5,8,2,3,7]=>[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,3,6,1,8,2,4,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,7,6,5,8,3,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,3,6,7,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,3,5,2,1,7,4,6]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,4,1,5,6,7,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,2,5,6,7,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,1,8,5,6,7,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,8,5,6,7,3,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,3,8,6,7,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,8,6,7,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,5,8,1,7,2,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,5,4,8,6,1,2,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,4,8,5,6,7,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,4,8,5,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,7,1,4,3,6,5,8]=>[3,7,1,5,4,6,2,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[4,3,7,2,5,6,8,1]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,6,3,1,4,5,8,7]=>[4,6,3,1,5,2,8,7]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,7,1,4,2,6,8,5]=>[5,8,3,4,1,6,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,7,1,5,6,2,8,4]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,7,1,5,6,8,2,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,2,6,7,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,2,6,3,7,1,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,4,2,3,5,7,1,6]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,7,3,2,5,6,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[5,3,4,6,2,8,1,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,3,7,4,2,8,1,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[6,4,7,2,3,8,1,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,5,7,2,8,3,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,7,2,4,8,6,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[2,6,5,1,8,3,4,7]=>[4,7,6,1,8,3,2,5]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[8,7,6,1,4,5,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,6,1,3,2,5,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,2,4,3,1,6,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,4,5,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,6,4,1,7,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,6,3,1,2,7,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,6,2,3,1,7,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,3,5,4,2,1,7,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,7,3,4,2,1,8,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[6,7,4,2,3,1,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,7,5,3,1,2,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,7,5,4,1,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,2,4,3,8,7,5,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,3,5,4,1,8,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,2,7,1,3,4,8,6]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[2,6,5,7,3,1,4,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[2,6,5,7,3,1,8,4]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[6,3,1,4,7,8,5,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,2,1,3,4,5,7]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[3,7,1,8,4,5,2,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[6,3,2,4,7,5,8,1]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,3,2,4,7,5,1,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,2,1,6,3,7,5,8]=>[5,3,2,7,1,6,4,8]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,2,1,6,3,7,8,5]=>[5,3,2,8,1,6,7,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[7,4,3,5,8,6,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,7,6,8,3,1,4,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[7,4,3,5,8,6,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,2,1,7,3,8,6,5]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,2,1,3,7,8,6,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[5,8,1,7,4,3,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,1,7,4,3,2,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,7,8,6,2,1,4,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[4,2,1,8,3,5,6,7]=>[5,3,2,8,1,6,7,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,2,1,3,6,7,5,8]=>[4,3,2,1,7,6,5,8]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,2,1,3,7,5,6,8]=>[4,3,2,1,7,6,5,8]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,2,1,3,6,8,7,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[7,3,2,4,8,6,5,1]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,2,1,6,3,8,7,5]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,2,1,7,3,5,6,8]=>[5,3,2,7,1,6,4,8]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,6,7,5,2,1,4,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[3,6,7,5,2,1,8,4]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[7,3,4,2,6,8,5,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,8,6,2,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,4,2,6,8,1,5]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,6,7,5,2,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,6,7,5,2,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,2,1,7,3,6,5,8]=>[5,3,2,7,1,6,4,8]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,2,1,7,3,6,8,5]=>[5,3,2,8,1,6,7,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,7,6,8,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,1,7,4,2,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,7,8,6,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,2,1,3,8,6,7,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,2,1,3,7,6,5,8]=>[4,3,2,1,7,6,5,8]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,2,1,3,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,2,1,3,5,8,6,7]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,8,1,7,3,6,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,7,8,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,2,1,8,3,7,6,5]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,2,1,3,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[7,8,2,4,1,3,6,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[2,6,1,5,4,7,8,3]=>[3,8,1,5,4,6,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[4,6,3,5,8,7,1,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,5,6,1,4,8,7,2]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[2,3,6,8,4,1,5,7]=>[6,2,7,8,5,1,3,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,7,5,1,8,3,4,6]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,7,5,2,1,3,6,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[3,5,6,2,4,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[2,5,6,1,4,8,3,7]=>[4,7,5,1,3,8,2,6]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[6,7,8,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,6,8,4,5,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,6,5,2,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,1,5,6,4,2,3,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,7,4,6,8,1,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,8,1,4,6,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,5,7,4,6,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,4,6,7,5,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,8,4,7,5,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,5,8,6,1,7,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,5,1,6,7,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,4,5,6,7,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,7,1,4,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,4,2,6,1,5,7,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,8,5,2,1,6,7,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,1,8,4,2,6,3,7]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,8,4,6,2,5,3,7]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,5,2,3,4,7,8]=>[6,2,5,4,3,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,3,1,4,6,2,5,7]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,1,8,2,5,6,4,7]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,5,1,8,2,6,4,7]=>[5,7,3,8,1,6,2,4]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,5,1,2,8,4,7,6]=>[4,6,3,1,8,2,7,5]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,3,5,8,6,1,7,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,2,4,3,6,7,1,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,2,8,5,7,1,6,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,6,2,8,5,1,7,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[6,2,1,8,4,7,5,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,8,7,1,4,6,5,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[8,2,7,1,5,4,6,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,2,5,3,6,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,3,1,5,6,2,4,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,7,5,1,6,2,4,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[2,7,3,6,5,8,1,4]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[8,7,2,4,1,6,5,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,8,7,2,3,6,5,4]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,2,6,4,3,5]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,8,2,6,4,5]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,5,8,3,2,4,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,2,8,4,3,7,5]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,7,2,4,6,5]=>[1,5,8,7,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,3,7,2,5,4,6]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,4,7,3,2,5,6]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,7,8,1,3,2,5,6]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[7,1,4,2,3,5,6,8]=>[7,2,5,4,3,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,2,1,4,7,3,5,6]=>[8,3,2,6,7,4,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,1,3,8,4,6,7,5]=>[2,1,3,8,5,7,6,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,3,4,8,5,7,6]=>[1,2,3,4,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,7,5,6,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,4,8,7,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,3,8,4,7,6,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,8,5,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,1,8,5,2,7,6,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[8,3,5,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,6,1,4,5,7,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,6,3,4,5,7,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,6,8,3,4,5,7,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[2,5,7,3,4,8,6,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[2,7,8,5,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,6,3,4,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,1,8,7,2,6,4,5]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[8,3,7,6,1,4,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,1,7,2,3,6,5]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,1,7,2,3,6,5,8]=>[5,2,7,4,1,6,3,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,7,1,8,2,6,4,5]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,1,7,8,2,5,6,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,1,6,5,8,2,7,4]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,3,5,8,7,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,8,5,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,6,1,4,8,5,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,8,3,6,1,4,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,8,1,2,3,6,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,7,4,6,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,1,2,3,4,8,6]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,4,6,1,2,8,3,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,4,1,2,8,5,7,3]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,7,1,2,3,6,4,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,6,8,1,2,7,4,5]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[4,8,6,1,2,3,7,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[8,4,6,1,2,3,7,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,8,1,5,2,7,3,6]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,1,2,5,3,8,7,6]=>[5,2,3,4,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,3,6,8,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,1,8,2,7,6,3]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,4,1,8,2,7,3,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[8,6,7,4,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,8,1,2,5,3,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[6,7,3,1,4,8,5,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,3,8,7,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,1,6,8,2,7,3]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,4,7,1,2,8,6,3]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,7,4,1,2,8,3,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,5,1,2,3,7,8,4]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,5,1,2,3,4,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[8,6,5,1,2,3,7,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,1,2,3,7,4,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,7,4,1,2,5,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,8,6,4,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,6,3,5,7,1,8]=>[7,4,5,2,3,6,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,4,6,3,7,2,5,8]=>[1,6,7,4,5,2,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,2,5,3,1,7,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,3,4,5,1,7,6]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,8,3,4,2,7,5,6]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,3,4,1,6,7,5]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[8,7,2,3,1,6,5,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,8,2,4,6,1,7,5]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[7,8,2,4,3,1,6,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,8,2,3,1,7,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[6,1,3,5,7,2,4,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,1,3,6,2,4,7,5]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,1,8,3,7,5,4,6]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[7,1,8,2,5,6,3,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,5,8,2,7,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,5,2,8,1,6,7,3]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,2,5,8,1,4,7,3]=>[8,5,6,7,2,3,4,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[3,2,8,5,1,6,7,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[8,2,7,1,4,6,5,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[1,3,8,2,5,7,4,6]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,7,1,6,4,5,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,8,7,1,5,6,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,4,8,5,6,1,7,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,3,7,4,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,4,8,6,2,7,3,5]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,4,5,7,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,6,8,4,1,7,2]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[6,2,3,1,5,4,7,8]=>[6,4,3,2,5,1,7,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[8,2,3,1,4,5,7,6]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,5,1,3,2,4,7,6]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,5,1,3,2,6,4,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[2,6,1,4,5,3,7,8]=>[3,6,1,5,4,2,7,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,6,4,1,5,2,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,5,6,1,3,2,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,5,7,1,2,6,3,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[6,7,1,4,2,5,3,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,6,1,2,4,3,7,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,1,2,5,3,6,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,4,1,2,5,7,6]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[1,2,6,7,5,3,8,4]=>[1,2,8,6,5,4,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,3,2,8,4,6]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,5,3,8,4,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,5,7,2,3,8,4]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,2,6,5,7,4]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,7,6,3,4,8]=>[1,2,7,6,5,4,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,8,2,5,7,6]=>[1,5,3,8,2,6,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,6,2,3,4,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,8,3,2,5,7,6]=>[1,5,8,4,2,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,8,3,5,7,6,2]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,8,3,5,7,6]=>[1,2,5,8,3,6,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,4,2,6,7,5]=>[1,5,8,4,2,7,6,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,8,2,3,5,7,6]=>[1,5,8,4,2,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,5,7,3,8,2,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,2,6,7,5,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,7,5,2,1,8,4,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,4,8,7,5,2,1,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,7,5,2,8,4,6,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,6,8,3,1,7,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,4,8,3,2,7,5]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,4,7,1,8,6,2,5]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[3,4,6,8,2,1,5,7]=>[6,5,7,8,2,1,3,4]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[3,8,2,5,6,1,4,7]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,5,2,8,6,4,1,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,2,5,7,3,8,6,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,4,2,5,3,8,1,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,1,2,8,5,6,4,7]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[5,2,1,6,8,3,4,7]=>[7,3,2,6,8,4,1,5]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[5,2,6,8,4,1,3,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[4,5,8,1,6,3,2,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[4,5,1,6,8,3,2,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,5,7,3,8,2,6,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,4,3,7,8,2,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,3,1,7,8,2,5]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,5,3,1,7,8,2,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[7,1,3,5,4,8,2,6]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,5,2,8,1,4,3,6]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,7,3,8,4,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,4,5,7,3,8,6,2]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,3,7,8,5,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,6,7,8,4,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,5,3,6,7,8,4,2]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,1,7,3,8,5,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,3,7,1,8,4,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,2,4,8,1,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,6,1,4,7,3,8,5]=>[3,8,1,6,5,4,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,2,5,6,7,8,1,4]=>[7,2,8,4,5,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,2,3,6,7,8,4,1]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,1,3,2,8,4,5]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,2,7,1,3,4,8,5]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[5,2,1,7,3,8,4,6]=>[7,3,2,8,5,6,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[6,4,2,7,1,8,3,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,2,6,3,7,8,1,5]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,2,6,3,7,8,5,1]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,7,3,8,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,2,7,4,1,8,5]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[6,7,3,2,1,4,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,1,8,3,4,2,5,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,4,1,8,3,5,6]=>[8,4,6,2,7,3,5,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,2,4,8,6,1,3,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,3,4,8,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,7,2,1,8,6,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[6,7,8,3,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,7,8,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,7,4,8,5,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,2,4,7,1,8,5,3]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,6,2,7,1,8,5,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,7,4,8,5,2,6,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,7,8,5,2,6,4]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,7,8,1,6,3,4]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[6,3,7,1,8,2,5,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,6,4,7,8,2,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,6,1,7,8,4,3]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[5,6,1,2,7,8,4,3]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,2,1,8,5,3,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,7,2,8,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,7,4,8,5,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,4,6,3,5,7]=>[1,8,3,6,7,4,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,8,3,5,1,4,6]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,3,7,4,6,2,5,8]=>[1,6,7,4,5,2,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,4,3,6,2,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,4,5,3,6,2,7]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,3,4,7,2,6]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,4,6,3,7,5]=>[1,8,3,6,7,4,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,5,4,6,7,3]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,8,1,2,4,7,5]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,3,7,4,6,2,8,5]=>[1,6,8,4,5,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,5,2,6,8,3]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,5,2,7,1,3,8,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,5,2,3,6,1,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,6,5,3,7,1,8,2]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[2,5,4,7,1,6,8,3]=>[5,8,3,6,1,4,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,2,3,8,6,7,1,5]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[6,2,4,8,5,1,7,3]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[5,2,4,8,1,3,7,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,2,5,4,8,3,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,4,3,5,8,2,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,2,3,4,8,1,6,7]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,5,2,4,7,1,6,8]=>[6,4,3,2,7,1,5,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,3,4,8,1,6,2,7]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,5,3,7,1,6,2,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,2,4,8,5,1,3,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[7,6,3,8,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,4,3,7,8,2,5,6]=>[1,6,3,8,7,2,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,2,6,7,3,8,1,5]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,5,7,4,2,8,6,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,7,2,8,6,4,5]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,5,2,7,1,8,6,3]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,3,6,5,7,8,1,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,2,6,4,7,8,3,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,2,6,7,3,8,5,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[3,2,5,6,8,1,7,4]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,4,5,2,3,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[8,4,6,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,5,2,3,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,4,2,5,3,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,4,2,5,3,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[8,6,4,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,2,7,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,2,5,8,7,3,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,6,2,5,3,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,6,5,2,3,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[6,8,7,4,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,6,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,4,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,2,7,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,4,7,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,2,4,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,2,4,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,2,6,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,4,6,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,6,7,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,7,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,4,5,8,7,3,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,6,4,8,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,2,8,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,4,6,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,4,8,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,2,6,8,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,2,6,5,8,7,3,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,2,4,5,8,7,3,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,2,6,7,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,7,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,5,2,8,7,3,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,2,3,6,8,7,5,1]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,4,5,8,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,7,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,6,7,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,8,7,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,8,7,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,8,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,8,7,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,5,8,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,6,8,7,4,5,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,6,8,7,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,8,6,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,2,8,6,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,8,4,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,6,4,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,8,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,8,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,8,4,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,8,7,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,5,8,2,7,3,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[2,1,6,8,4,7,5,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,8,6,4,7,5,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,8,7,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,6,4,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,6,2,7,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[9,8,7,3,6,2,5,1,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,6,3,5,1,2,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,4,8,3,7,2,6,1,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,4,7,3,6,1,2,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,2,4,6,1,3,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,4,6,1,2,3,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[5,9,4,8,3,7,1,2,6]=>[8,9,7,6,5,4,3,1,2]=>[8,9,7,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[9,5,8,2,4,7,1,3,6]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,5,8,4,7,1,2,3,6]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,3,5,7,1,2,4,6]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,5,7,1,2,3,4,6]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,9,3,5,8,1,2,4,7]=>[8,9,7,6,5,4,3,1,2]=>[8,9,7,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[6,9,5,8,1,2,3,4,7]=>[8,9,7,6,5,4,3,1,2]=>[8,9,7,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[9,6,8,1,2,3,4,5,7]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[10,9,8,7,6,5,2,4,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,3,6,2,5,1,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,6,3,5,1,2,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,4,8,3,7,2,6,1,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,4,7,3,6,1,2,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,2,4,6,1,3,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,4,6,1,2,3,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,5,9,4,8,3,7,1,2,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,5,8,2,4,7,1,3,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,5,8,4,7,1,2,3,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,3,5,7,1,2,4,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,5,7,1,2,3,4,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,10,5,9,2,4,8,1,3,7]=>[9,10,8,7,6,5,4,3,1,2]=>[9,10,8,7,6,5,4,3,1,2]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[6,10,5,9,4,8,1,2,3,7]=>[9,10,8,7,6,5,4,3,1,2]=>[9,10,8,7,6,5,4,3,1,2]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[10,6,9,3,5,8,1,2,4,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,6,9,5,8,1,2,3,4,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,4,6,8,1,2,3,5,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,6,8,1,2,3,4,5,7]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,10,2,4,6,9,1,3,5,8]=>[9,10,7,8,5,6,3,4,1,2]=>[9,10,7,8,5,6,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[7,10,4,6,9,1,2,3,5,8]=>[9,10,8,7,6,5,4,3,1,2]=>[9,10,8,7,6,5,4,3,1,2]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[4,2,5,6,3,8,1,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,2,5,7,4,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,2,1,4,7,6,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,7,3,2,5,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,2,6,4,8,1,5,7]=>[6,2,7,4,8,1,3,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,6,4,7,8,5,1]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,5,1,8,3,4,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,7,8,2,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,6,3,5,8,4,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,3,1,7,8,4,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,3,6,7,4,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,3,1,2,5,8,6,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,6,3,5,2,4,8,7]=>[1,6,5,4,3,2,8,7]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,4,8,2,7,5,1,6]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[6,3,2,8,5,7,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,4,7,2,5,6,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[2,4,8,1,5,3,7,6]=>[4,6,8,1,5,2,7,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,4,8,1,6,2,7,5]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[1,8,4,6,7,3,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,6,3,4,5,7,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,5,4,1,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,7,6,8,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,1,6,5,7,4,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[4,6,8,2,5,3,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,2,3,7,6,1,8,4]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,1,2,4,6,7,3,5]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,2,3,7,4,8,6,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,2,6,8,4,3,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[7,8,1,5,4,3,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,4,8,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,5,1,8,4,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,7,8,5,4,6,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,7,4,3,8,6,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,1,6,3,5,2,7]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[8,3,1,7,4,2,5,6]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,1,8,2,4,5,7,6]=>[4,2,8,1,5,6,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[8,1,3,7,6,2,4,5]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,6,8,7,1,4,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,3,2,8,5,7,1,6]=>[7,3,2,8,5,6,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[3,6,4,2,8,5,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,7,3,2,5,1,8,6]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[3,2,4,7,5,8,6,1]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,2,3,8,6,5,1,7]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[2,4,3,5,1,8,6,7]=>[5,3,2,4,1,8,7,6]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,2,8,1,4,6,5,7]=>[4,2,8,1,5,7,6,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,7,8,5,6,1,2,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,6,1,8,4,7,2,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,1,6,8,4,7,2,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,1,6,8,3,2,7,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,6,1,8,3,2,7,5]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,7,8,1,3,2,6,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[4,7,8,3,1,2,6,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,7,8,3,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,7,8,2,1,3,6,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[4,6,1,8,2,3,7,5]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,1,6,8,2,3,7,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,5,1,2,8,3,7,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,5,2,1,8,3,7,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,6,2,8,1,3,7,5]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[3,6,2,8,4,7,1,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,3,6,8,4,7,5,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,6,8,4,7,1,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,2,6,8,3,1,7,5]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[4,2,5,1,8,3,7,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,1,2,5,8,3,7,6]=>[6,2,3,4,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,1,2,4,3,8,7,6]=>[5,2,3,4,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[5,2,4,1,3,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,2,5,3,8,1,7,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,2,5,4,8,7,1,6]=>[7,2,4,3,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,5,2,4,8,7,1,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[5,4,2,1,3,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,1,4,2,3,8,7,6]=>[5,2,4,3,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[5,4,1,3,2,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,4,3,1,2,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,5,3,1,8,2,7,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,5,1,3,8,2,7,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,1,5,4,8,7,2,6]=>[7,2,4,3,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,5,1,4,8,7,2,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[3,5,4,1,8,7,2,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[3,6,5,8,7,1,2,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,5,6,8,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,5,1,8,7,2,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[3,4,1,5,8,7,2,6]=>[7,3,2,4,8,6,1,5]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[4,1,3,5,8,2,7,6]=>[6,2,3,4,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,3,6,8,2,1,7,5]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[2,4,6,8,3,7,5,1]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[3,4,5,2,8,7,1,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[5,3,1,4,2,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,1,3,4,2,8,7,6]=>[5,2,4,3,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[5,1,3,2,4,8,7,6]=>[5,2,4,3,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[5,3,2,1,4,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,4,2,5,8,7,1,6]=>[7,3,2,4,8,6,1,5]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[3,2,4,5,8,7,1,6]=>[7,2,3,4,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,2,3,1,4,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,2,1,3,4,8,7,6]=>[5,3,2,4,1,8,7,6]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[5,1,2,3,4,8,7,6]=>[5,2,3,4,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[8,6,2,5,4,1,3,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,7,4,2,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,7,5,3,8,2,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,1,6,3,4,5,7]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,3,5,6,2,4,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,2,1,3,5,4,7]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,1,2,3,4,6,5,7]=>[8,2,3,4,5,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,2,3,7,8,4,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,8,2,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,1,6,5,8,4,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,5,6,7,3,4,8,2]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,7,8,2,1,4,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,6,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,8,4,7,2,6,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,1,3,7,6,4,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,3,1,7,8,6,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,5,8,2,7,1,6,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[6,2,8,5,3,1,7,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,2,6,4,7,1,3,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[3,4,2,8,5,1,7,6]=>[6,3,2,8,5,1,7,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[3,8,6,5,2,1,7,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[8,3,7,4,2,5,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,5,7,2,1,3,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,4,1,8,2,6,7,5]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[8,4,6,3,7,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,3,4,1,5,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,7,6,2,8,4,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,8,2,5,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,5,6,7,1,3,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,5,7,6,3,1,8,4]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[2,5,7,3,8,4,6,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,2,7,1,8,5,3,6]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,2,1,8,7,5,6,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,3,6,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,3,7,5,8,6,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,8,4,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,4,5,8,3,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,5,7,1,4,8,6,2]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[7,2,8,5,1,4,6,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,6,5,3,8,4,2,7]=>[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,4,8,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,6,1,3,5,2,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[8,4,3,2,5,7,1,6]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,6,4,8,2,5,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[4,3,7,2,5,8,1,6]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[3,2,4,7,8,5,6,1]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,6,4,3,8,5,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[3,8,2,1,6,4,5,7]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[8,2,1,3,4,5,7,6]=>[8,3,2,4,5,6,7,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,6,8,3,2,1,5,7]=>[6,7,8,5,4,1,2,3]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[3,2,6,8,5,4,1,7]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,3,8,2,5,4,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,2,5,3,8,7,6,1]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,8,2,6,5,3,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,6,8,5,4,1,3,7]=>[6,7,8,5,4,1,2,3]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[3,1,8,6,5,4,2,7]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,4,8,7,3,2,6,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,4,8,3,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,3,6,2,1,8,5]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[5,4,3,7,1,8,2,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[7,3,8,5,1,4,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,8,7,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,1,5,7,4,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,8,5,7,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,5,4,8,3,7,6,2]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,8,3,6,7,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,8,3,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,5,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,1,3,8,7,5,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,2,1,7,4,5,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,7,1,6,4,2,8,5]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,1,2,7,5,6,8,4]=>[3,2,1,8,6,5,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,6,1,2,7,5,8,4]=>[4,8,3,1,6,5,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,7,6,2,5,8,1,4]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[3,6,2,5,8,7,4,1]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,2,3,6,7,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,7,2,6,3,8,1,5]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[6,3,2,4,8,7,5,1]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,7,2,4,6,1,8,5]=>[6,8,3,4,5,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[5,3,7,2,8,1,4,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[6,3,2,8,7,5,1,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,3,8,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,8,7,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,4,8,1,7,6,3]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[5,2,8,1,7,6,3,4]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,2,1,3,8,7,5,4]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,6,1,8,7,5,2,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,6,1,2,8,7,4,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,2,8,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[2,7,6,8,1,5,4,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[7,8,5,1,6,2,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,8,6,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,1,8,3,6,5,4]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[5,8,7,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[11,9,8,7,6,5,4,3,2,1,10]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[10,7,6,5,4,3,2,1,9,8]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[9,6,5,4,3,2,8,1,7]=>[9,8,6,5,4,3,7,2,1]=>[9,8,6,5,4,3,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[9,7,5,4,3,2,1,8,6]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,5,4,3,7,2,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,4,8,3,2,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[7,6,4,3,2,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,6,5,4,3,2,9,7,1]=>[9,8,6,5,4,3,7,2,1]=>[9,8,6,5,4,3,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[8,7,6,5,4,3,2,10,9,1]=>[10,7,6,5,4,3,2,9,8,1]=>[10,7,6,5,4,3,2,9,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.]
[7,3,1,4,8,2,5,6]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,4,1,2,5,8,3,6]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,4,2,5,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,7,2,4,6,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,7,5,1,6,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,7,4,6,3,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,1,4,3,2,8,6]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,6,4,2,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,7,1,3,8,5,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,4,2,7,3,1,6,8]=>[6,5,3,7,2,1,4,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,5,1,2,7,6,8,3]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,4,6,8,3,1,2,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[6,4,8,1,3,7,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,6,1,3,8,5,2,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,3,8,4,5,7,2,6]=>[1,7,8,4,5,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,7,4,5,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[2,6,8,4,3,5,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,3,7,4,2,8,5,6]=>[1,5,8,4,2,7,6,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,1,3,7,2,5,8]=>[6,7,3,4,5,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[7,5,8,6,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,1,3,6,5,4,7]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,8,7,3,5,4,1,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,4,2,6,8,7,1,5]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[7,4,2,3,6,1,8,5]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[8,4,2,3,6,5,7,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,3,8,4,1,2,6,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,8,3,2,7,1,5,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,5,6,3,7,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[7,4,2,5,8,1,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,7,8,3,4,5,1,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,7,1,2,4,6,5,8]=>[4,7,3,1,5,6,2,8]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[7,5,6,8,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,1,6,5,2,7,4,8]=>[5,2,7,4,1,6,3,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,8,6,5,3,4,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,4,6,2,8,5,7,1]=>[8,4,6,2,7,3,5,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,2,1,7,5,8,3,6]=>[7,3,2,8,5,6,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[4,7,2,6,5,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,7,4,1,2,5,8,6]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[4,7,1,6,5,2,8,3]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,7,3,6,5,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,3,7,1,6,8,5,2]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,2,6,8,7,3,1,5]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[3,4,6,1,8,5,2,7]=>[7,4,6,2,8,3,1,5]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,1,6,7,5,8,2,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,3,6,7,5,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,3,7,1,6,8,2,5]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,3,7,5,6,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,1,7,3,6,5,2,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,8,7,4,5,3,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,8,7,4,3,5,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,8,1,4,2,6,5,7]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,1,7,3,6,2,5,8]=>[6,2,7,4,5,1,3,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,8,7,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,6,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,1,7,2,6,8,5,3]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,2,7,3,6,1,8,5]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[4,2,7,3,6,5,8,1]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,8,2,4,5,6,7,1]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,2,4,1,6,7,5]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,8,5,6,2,4,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,8,6,5,3,7,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,8,6,5,1,4,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,2,1,4,6,7,5]=>[4,8,3,1,5,7,6,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,8,2,5,4,6,7,1]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,2,7,5,6,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,2,7,5,6,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,2,6,7,5,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,2,6,1,4,5,8,7]=>[4,2,6,1,5,3,8,7]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,8,7,3,4,5,1,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,8,1,2,4,6,5,7]=>[4,8,3,1,5,7,6,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[5,8,7,6,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,1,7,5,6,2,3,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,8,1,5,2,6,4,7]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,8,7,5,3,4,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,8,7,5,4,3,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,1,7,5,6,3,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,8,7,6,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,6,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,2,3,7,6,8,1]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[7,4,3,5,2,8,1,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,4,3,7,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,2,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,6,2,3,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,1,7,2,4,6,8,3]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,5,7,1,2,6,8,3]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,4,1,7,3,6,8,2]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,6,4,7,5,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,4,7,6,2,5,8,1]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,7,5,6,1,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,7,6,4,3,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,7,6,3,1,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,2,3,4,8,1,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,7,5,3,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,1,3,8,4,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,1,3,4,8,5,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,5,2,7,8,1,4]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[3,2,8,6,7,1,4,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,8,3,6,5,2,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,8,6,5,4,2,3,7]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,7,2,3,5,4,6]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,7,2,5,3,4,6]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,8,5,1,2,4,7]=>[6,7,8,5,4,1,2,3]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[3,7,5,1,8,2,6,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[7,1,2,8,3,5,6,4]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,7,8,2,5,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,7,5,2,8,1,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,1,4,5,8,6,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,6,4,2,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,6,1,2,8,4,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,5,7,6,8,2,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,6,8,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,6,8,4,2,7,3]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,8,2,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,8,4,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,7,8,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,4,8,5,1,2,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[3,7,4,8,1,2,5,6]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[7,4,3,8,2,6,5,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,6,8,3,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,1,3,5,4,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,8,3,4,2,6,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,8,3,1,4,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,1,4,8,2,5,7,6]=>[5,2,3,8,1,6,7,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,8,5,2,1,3,6,7]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[5,8,2,6,3,1,4,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,8,2,3,7,4,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,2,3,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,7,2,4,5,3,6]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,3,6,2,5,4,7]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,3,5,4,2,6,7]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,5,3,4,2,6,7]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,5,6,2,3,7,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,5,3,2,6,7]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,3,5,2,6,7]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,6,3,1,5,4,7,8]=>[4,6,3,1,5,2,7,8]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[6,3,2,1,5,4,7,8]=>[6,4,3,2,5,1,7,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[7,3,1,4,5,2,6,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,3,1,5,4,2,6,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,3,1,6,2,5,4,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,7,1,4,5,2,6,8]=>[6,7,3,4,5,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,6,2,1,5,4,7,8]=>[4,6,3,1,5,2,7,8]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,3,6,1,5,4,7,8]=>[4,2,6,1,5,3,7,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,5,2,4,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[6,3,4,1,5,2,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,2,5,1,3,7,4,8]=>[7,4,5,2,3,6,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[6,5,2,1,3,7,4,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[7,6,1,2,4,5,3,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,7,1,2,8,3,5,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,1,2,5,4,3,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,6,2,1,3,7,4,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,2,6,1,3,7,4,8]=>[7,4,5,2,3,6,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,7,1,3,5,2,6,8]=>[6,7,3,4,5,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,7,1,5,3,2,6,8]=>[6,7,3,5,4,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[5,7,1,4,2,6,3,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,7,1,6,2,3,8,4]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,6,3,1,2,7,4,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,2,5,3,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,3,6,1,2,7,4,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,5,1,8,7,3,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,2,7,5,4,1,3,6]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,8,5,2,3,4,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,6,8,7,1,5,3,4]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[8,5,6,2,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,1,2,7,8,4,3]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,7,6,1,5,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,7,6,4,1,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,6,2,4,5,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,1,7,5,3,8,4,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,7,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,2,7,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,6,1,5,3,8,4,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,6,2,4,7,8,1,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,4,6,1,7,8,5,2]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,4,8,6,7,1,5,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,8,5,6,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,4,1,2,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,1,7,2,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,7,3,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,1,7,2,6,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,5,7,2,6,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,2,5,6,3,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,8,7,2,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,2,1,6,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,1,5,2,6,7,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,7,8,5,1,6,2,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,5,2,7,8,1,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,1,2,8,5,6,3,4]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,7,2,1,5,6,3,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,6,7,1,5,2,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,1,7,8,5,2,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,5,6,2,1,8,4,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,7,5,2,1,6,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,3,5,8,6,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,5,3,6,8,2,7,1]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,6,3,4,8,1,7,2]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,6,7,8,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,3,1,2,6,7,5]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[8,5,1,6,3,4,7,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,1,8,6,3,4,7,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,6,8,1,5,3,7,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,4,5,8,3,2,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[3,6,4,8,7,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,8,1,3,4,7,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[5,6,8,3,1,2,7,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,1,8,3,5,2,7,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,8,3,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,1,3,5,2,7,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,1,3,5,6,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,8,3,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,8,1,2,6,7,5]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[5,8,2,4,3,6,7,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,8,2,3,1,6,7,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,8,2,3,5,1,7,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,2,3,5,6,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,5,1,4,3,7,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,4,8,6,1,3,7,5]=>[5,6,8,7,1,2,4,3]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[6,7,1,8,4,3,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,7,8,6,1,4,3,5]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,7,3,8,1,6,4,5]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[7,5,1,8,2,4,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,7,8,4,1,6,3,5]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,6,5,4,1,3,8,7]=>[5,6,4,3,1,2,8,7]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[4,1,7,6,3,8,2,5]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,8,2,5,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,4,6,5,1,8,2,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[2,6,5,3,4,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,6,1,5,2,3,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,2,3,5,1,4,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[2,6,7,5,1,8,4,3]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[8,6,1,2,5,3,4,7]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,2,5,1,8,3,4,7]=>[7,4,6,2,8,3,1,5]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[7,6,5,2,8,3,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,6,3,5,1,8,7,4]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,4,7,6,5,8,1,3]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[2,1,4,8,7,6,3,5]=>[2,1,7,8,6,5,3,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[7,4,6,8,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,3,5,7,4,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,8,7,5,1,6,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,8,5,1,6,7,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,5,1,6,7,2,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[7,8,6,1,3,5,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,7,2,8,1,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,5,1,8,6,7,4,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,5,1,8,6,7,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,2,3,8,6,7,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,5,4,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,1,3,8,6,7,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,5,8,6,7,4,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,2,1,5,3,8,7,4]=>[8,3,2,5,4,7,6,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[5,6,3,2,8,1,4,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[8,1,6,3,5,2,7,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,7,6,2,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,6,8,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,5,8,1,3,4,6]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[7,6,2,8,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,3,7,5,2,6,4]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,4,8,7,5,1,6,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,3,8,1,4,2,5,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[6,3,8,5,7,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,6,8,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,4,8,7,5,6,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[7,1,5,8,2,6,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,6,8,2,4,1,7,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[4,5,8,2,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,2,8,1,6,7,3,4]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,5,8,4,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,3,4,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,3,2,6,7,1,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,2,8,1,6,7,3,5]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[2,4,8,1,6,7,3,5]=>[4,7,8,1,6,5,2,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[5,1,8,2,6,7,3,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,4,8,7,2,1,5,6]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[7,8,5,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,5,7,4,1,3,6]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[5,8,4,1,6,7,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,1,4,6,7,2,5]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[8,2,3,4,6,7,1,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,2,7,3,8,4,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,3,2,8,5,1,6]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,3,2,8,4,6,1,7]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[8,4,2,6,5,3,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,2,5,3,1,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,3,6,2,5,4,1,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,4,8,3,2,6,1,7]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[3,5,8,2,4,6,1,7]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[6,4,7,8,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,3,6,4,2,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,8,6,2,5,3,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,6,4,3,2,8,7,5]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,4,3,1,2,6,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[2,8,7,3,5,1,4,6]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[7,3,8,6,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,2,7,3,8,5,4]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,1,7,4,3,8,6,5]=>[2,1,8,5,4,7,6,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,1,4,3,8,2,7,5]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,3,2,8,7,4,6]=>[7,2,4,3,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,8,4,2,7,6,5,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,3,7,2,6,5,4]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,4,8,3,7,2,6]=>[7,2,5,8,3,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,1,6,8,5,4,7,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,1,5,7,8,2,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,1,6,7,2,5,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,4,8,6,1,3,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,6,1,2,5,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,7,6,1,5,2,4,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,5,4,8,3,2,7,6]=>[1,6,5,8,3,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,3,6,1,2,5,4,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[5,4,7,1,3,2,6,8]=>[6,5,7,4,2,1,3,8]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[5,7,4,8,2,1,3,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,6,8,2,5,1,3,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[7,4,6,2,1,5,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,2,6,3,8,5,7,4]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,6,8,4,7,3]=>[1,8,3,6,7,4,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,2,3,8,1,4,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,4,7,5,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,8,5,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,3,6,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,4,2,1,7,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,2,1,5,8,6,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,6,4,1,8,5,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,6,4,8,7,5,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,1,2,8,4,7,5]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[7,5,1,3,2,8,6,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,7,1,2,5,8,6,3]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,4,1,2,7,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,8,1,2,6,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,8,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,2,1,7,3,6,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,6,1,8,2,4,7,5]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,3,8,7,6,2,5,4]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,1,8,7,3,2,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,5,1,8,7,2,4,6]=>[6,7,3,8,5,1,2,4]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,6,1,8,3,7,2,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,7,1,2,8,6,3,5]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,8,4,1,7,6,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,8,1,5,4,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,1,7,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,5,8,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,8,7,3,6,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,8,7,6,2,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,8,7,6,5,2,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,6,4,5,2,3,7,8]=>[1,6,5,4,3,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,5,2,3,6,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,5,2,4,6,8]=>[1,7,5,6,3,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,3,5,2,4,7,8]=>[1,6,5,4,3,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,3,4,2,5,7,8]=>[1,6,5,4,3,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,4,2,5,6,8]=>[1,7,5,4,3,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,6,7,3,4,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,7,3,4,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,4,2,6,5,8]=>[1,7,5,4,3,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,8,4,7,3,6]=>[1,7,3,8,5,6,2,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,8,5,7,3,6]=>[1,7,3,8,5,6,2,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,5,2,6,4,8]=>[1,7,5,6,3,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,4,7,3,5,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,6,2,5,4,8]=>[1,7,5,6,3,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,6,2,4,5,8]=>[1,7,5,6,3,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,6,2,3,5,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,6,2,3,4,7]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,6,2,4,3,7]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,8,5,6,4,7]=>[1,3,2,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,8,5,6,3,7]=>[1,7,3,8,5,6,2,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,8,4,6,3,7]=>[1,7,3,8,5,6,2,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,2,4,5,3,6,7]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[9,10,5,6,7,8,3,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[5,8,9,6,7,10,3,4,1,2]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[9,10,7,8,3,4,5,6,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,3,6,7,4,5,8,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[3,8,9,6,7,4,5,10,1,2]=>[10,9,7,6,5,4,3,8,2,1]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[3,6,7,8,9,4,5,10,1,2]=>[10,9,7,6,5,4,3,8,2,1]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[9,10,3,4,5,6,7,8,1,2]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[3,8,9,4,5,6,7,10,1,2]=>[10,9,7,6,5,4,3,8,2,1]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[7,8,9,10,5,6,1,2,3,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[5,8,9,6,7,10,1,2,3,4]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[9,10,7,8,1,4,5,2,3,6]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,8,9,10,1,4,5,2,3,6]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[9,10,1,6,7,4,5,2,3,8]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[1,8,9,6,7,4,5,2,3,10]=>[1,9,8,7,6,5,4,3,2,10]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,6,7,8,9,4,5,2,3,10]=>[1,9,8,7,6,5,4,3,2,10]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[9,10,1,4,5,6,7,2,3,8]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[1,8,9,4,5,6,7,2,3,10]=>[1,9,8,7,6,5,4,3,2,10]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[9,10,1,6,7,2,3,4,5,8]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[1,8,9,6,7,2,3,4,5,10]=>[1,9,8,7,6,5,4,3,2,10]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,6,7,8,9,2,3,4,5,10]=>[1,9,8,7,6,5,4,3,2,10]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[9,10,11,12,7,8,5,6,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,8,9,10,5,6,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,10,11,8,9,12,5,6,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,8,9,10,11,12,5,6,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,5,6,7,8,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,11,12,5,6,7,8,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,5,8,9,6,7,10,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,5,6,7,8,9,10,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,7,8,3,4,5,6,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,11,12,7,8,3,4,5,6,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,8,9,10,3,4,5,6,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,10,11,8,9,12,3,4,5,6,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,8,9,10,11,12,3,4,5,6,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,3,6,7,4,5,8,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,11,12,3,6,7,4,5,8,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,3,8,9,6,7,4,5,10,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,3,6,7,8,9,4,5,10,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,3,4,5,6,7,8,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,11,12,3,4,5,6,7,8,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,3,8,9,4,5,6,7,10,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,3,4,7,8,5,6,9,10,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,7,8,5,6,1,2,3,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,11,12,7,8,5,6,1,2,3,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,8,9,10,5,6,1,2,3,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,10,11,8,9,12,5,6,1,2,3,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,8,9,10,11,12,5,6,1,2,3,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,5,6,7,8,1,2,3,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,11,12,5,6,7,8,1,2,3,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,5,8,9,6,7,10,1,2,3,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,5,6,7,8,9,10,1,2,3,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,7,8,1,4,5,2,3,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,11,12,7,8,1,4,5,2,3,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,8,9,10,1,4,5,2,3,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,10,11,8,9,12,1,4,5,2,3,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,8,9,10,11,12,1,4,5,2,3,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,7,8,1,2,3,4,5,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,11,12,7,8,1,2,3,4,5,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,8,9,10,1,2,3,4,5,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,10,11,8,9,12,1,2,3,4,5,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[1,2,3,4,5,6,7,8,9,10,11,12]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[8,6,4,7,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,4,7,2,8,3,5]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,3,5,8,2,6]=>[1,7,8,4,5,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,4,6,2,3,5,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,8,2,3,6,1,7]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[7,4,8,5,2,3,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,6,2,4,5,1,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,8,6,2,3,5,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,7,5,3,4,8,2,6]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,6,4,8,2,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,7,4,1,2,3,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,8,5,3,4,1,2,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,8,3,7,2,1,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,1,6,3,7,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,1,3,7,4,8,2,5]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,7,3,5,8,2,6]=>[7,2,8,4,5,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,1,6,4,8,2,3,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,5,7,2,3,4,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,5,8,2,3,4,7]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,7,3,8,2,4,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,1,5,7,8,2,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,8,6,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,5,1,2,4,6]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[4,7,6,1,2,3,5,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[6,5,8,4,1,2,3,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[8,5,7,4,1,2,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,5,7,4,8,2,3,6]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,4,8,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,2,3,8,1,4,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,8,5,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,2,3,1,7,4,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,6,4,1,2,7,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,7,2,8,6,3,4,5]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,1,3,8,2,4,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,8,1,3,6,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,4,1,8,2,3,6,7]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,4,8,7,2,3,5,6]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,7,2,3,4,6]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,5,1,8,2,3,4,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,7,1,3,8,2,4,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[7,6,8,1,5,2,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,1,5,8,6,2,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,8,2,7,3,4,5]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,8,7,2,3,5,6]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,1,8,7,2,3,4,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,8,7,6,4,5,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[9,8,7,6,4,5,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[8,7,6,4,3,5,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[8,7,6,3,5,4,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,9,8,7,5,4,6,3,2]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,8,7,3,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,9,8,7,4,6,5,3,2]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,10,9,8,7,5,6,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[7,1,5,8,3,4,2,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,4,3,2,5,6,8]=>[7,2,5,4,3,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,4,2,3,8,5,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,4,2,7,5,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,4,1,7,5,8,3,6]=>[3,7,1,8,5,6,2,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[7,1,4,6,5,2,3,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,1,4,6,5,8,2,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,4,6,3,8,2,5]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,4,3,2,5,8,6]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,4,6,5,2,8,3]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,4,6,5,3,8,2]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,4,6,5,3,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,4,2,7,5,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,4,7,2,6,8,5,1]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,4,7,1,6,8,2,5]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[3,4,7,1,6,8,5,2]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,4,1,7,5,3,6,8]=>[3,6,1,7,5,2,4,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,4,1,7,8,6,2,5]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[6,4,2,3,8,5,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,4,2,7,5,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,4,2,7,5,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,4,7,2,6,8,1,5]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[5,4,7,3,6,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,4,7,2,6,5,1,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,8,3,2,5,6,1,7]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[4,8,7,3,5,1,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,8,7,1,3,5,2,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,8,3,1,2,6,5,7]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,4,7,1,6,2,5,8]=>[6,4,7,2,5,1,3,8]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[3,4,7,1,6,2,8,5]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[3,4,7,2,6,5,8,1]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,8,3,1,2,6,7,5]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[5,8,1,6,3,4,2,7]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[6,8,5,1,3,7,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,5,1,3,4,7,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,3,4,2,6,7,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,4,7,3,6,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,4,7,2,6,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,4,3,7,5,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,4,3,7,5,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,2,4,3,1,5,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[3,8,7,4,1,5,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,4,7,3,6,1,5,8]=>[6,4,7,2,5,1,3,8]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[5,8,3,2,1,6,4,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[5,8,7,4,3,1,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,4,7,3,6,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,3,8,2,1,6,5,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[7,4,3,8,5,2,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,2,8,4,3,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[4,3,2,8,6,5,1,7]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[4,3,8,7,5,1,6,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[3,2,5,8,6,1,4,7]=>[6,2,7,8,5,1,3,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,4,3,7,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,7,8,5,1,2,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[5,3,7,8,4,1,2,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[6,2,5,8,3,1,4,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[6,2,4,8,3,1,5,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[5,2,3,8,4,1,6,7]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,3,8,7,4,1,6,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,3,2,8,6,4,1,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,5,3,8,4,2,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,5,3,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,5,3,7,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,4,3,8,2,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,5,3,8,2,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,4,6,3,8,2,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,6,3,8,2,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,6,3,7,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,6,3,5,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,4,6,3,5,2,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,3,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,3,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,4,3,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,8,4,3,2,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,5,8,3,4,2,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,5,8,3,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,4,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,8,3,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,8,3,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,8,3,5,2,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,4,7,3,5,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,4,8,3,7,2,6,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,5,8,3,7,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,8,4,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,8,4,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,7,3,8,2,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,4,7,3,8,2,6,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[5,4,6,3,8,2,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,3,6,2,4,7,8,1]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,3,6,1,4,8,7,2]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,3,7,2,4,6,8,1]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,2,1,5,8,6,3,7]=>[7,3,2,4,8,6,1,5]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[4,2,1,5,8,6,7,3]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,2,1,5,8,7,6,3]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,3,1,5,7,8,6,2]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,3,1,7,5,8,6,2]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,7,3,1,4,8,2,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,3,7,1,4,8,2,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[4,3,1,5,7,8,2,6]=>[7,3,2,4,8,6,1,5]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[3,2,1,8,5,4,6,7]=>[3,2,1,8,6,5,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,8,5,7,4,6]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,8,7,5,4,6]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[5,2,7,1,8,4,3,6]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[6,7,2,1,8,4,3,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,7,2,1,8,4,5,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,2,1,8,5,6,4,7]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,8,6,5,4,7]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[4,3,1,6,7,8,5,2]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,2,1,6,8,7,5,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,2,1,6,8,5,7,3]=>[8,3,2,6,7,4,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,2,1,6,8,5,3,7]=>[7,3,2,6,8,4,1,5]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[5,2,6,1,8,4,3,7]=>[7,4,6,2,8,3,1,5]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[5,2,6,1,8,7,4,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[5,2,6,1,8,7,3,4]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[5,2,6,1,8,3,4,7]=>[7,4,6,2,8,3,1,5]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,2,1,6,8,3,7,5]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[4,3,1,6,7,8,2,5]=>[7,3,2,8,5,6,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[6,7,3,1,5,8,2,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,2,1,7,8,6,3,5]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[3,2,1,8,7,6,4,5]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,8,6,4,7,5]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,8,6,4,5,7]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,8,4,6,5,7]=>[3,2,1,8,5,7,6,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,8,4,6,7,5]=>[3,2,1,8,5,7,6,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,8,4,7,6,5]=>[3,2,1,8,5,7,6,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,8,7,4,6,5]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[4,2,1,7,8,3,6,5]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[5,2,7,1,8,3,6,4]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,7,2,1,8,3,5,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,2,7,1,8,3,4,6]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,2,1,7,8,3,5,6]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[3,2,1,8,4,5,7,6]=>[3,2,1,8,5,6,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[7,5,2,8,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,8,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,8,6,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,3,1,8,2,5,6]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,4,2,8,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,8,5,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,8,4,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,8,2,4,5,1,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[6,3,8,2,5,7,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,3,8,1,5,2,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[6,3,7,8,2,4,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,7,3,8,2,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,4,7,2,6,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,3,8,2,4,6,7,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,3,8,2,4,7,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,4,2,6,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,4,8,2,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,3,1,4,2,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,7,4,2,6,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,6,4,2,3,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,6,3,7,8,2,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,3,8,2,4,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[6,3,7,2,4,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,3,7,2,5,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,3,6,8,2,4,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[5,4,6,2,3,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,3,6,7,8,2,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,4,2,1,5,8,7]=>[5,6,4,3,1,2,8,7]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,5,8,6,4,2,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[5,8,6,3,4,2,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,6,3,4,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,3,4,2,1,5,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,6,4,2,1,3,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[2,5,4,1,7,8,6,3]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,7,8,5,4,1,6,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,8,5,4,1,6,3,7]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,6,3,8,5,4,1,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[2,8,6,3,5,4,1,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,8,6,4,2,1,3,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,2,1,5,7,8,6,3]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,7,8,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,8,5,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,2,1,8,4,3,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,1,8,5,6,4,3,7]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[4,2,1,8,5,6,3,7]=>[7,3,2,8,5,6,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[8,4,2,1,5,6,3,7]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,5,6,3,8,4,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,3,4,2,1,8,5,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[3,7,8,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,5,6,4,2,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,6,4,2,1,8,5,7]=>[5,7,4,3,1,8,2,6]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,8,6,4,2,1,5,7]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[3,7,8,6,4,2,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,5,3,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,2,4,1,8,5,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,4,1,7,6,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,2,3,8,5,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,1,7,8,6,4,3,5]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,6,4,3,7,8,5]=>[2,1,8,5,4,6,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,4,2,1,3,7,8,5]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[6,3,7,8,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,4,2,1,6,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,6,2,3,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,6,1,8,4,3,7,5]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,6,1,7,5,8,4,3]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[8,4,2,3,7,5,6,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,5,7,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,5,7,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,6,2,1,3,8,5]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[7,5,6,1,8,4,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,7,5,8,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,4,3,6,1,7,5]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[6,4,7,8,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,5,8,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[6,9,8,5,4,3,2,1,7]=>[8,9,7,6,5,4,3,1,2]=>[8,9,7,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[8,7,9,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[7,5,8,9,4,3,2,1,6]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,7,6,9,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[6,4,3,7,5,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,4,8,9,3,2,1,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,5,3,2,8,4,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,6,5,3,9,8,2,1,4]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[6,5,2,7,8,4,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,10,9,6,5,4,3,2,1,8]=>[9,10,8,7,6,5,4,3,1,2]=>[9,10,8,7,6,5,4,3,1,2]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[9,8,10,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[6,5,8,7,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[8,6,9,10,5,4,3,2,1,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,8,7,10,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[7,5,4,8,6,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[5,9,8,7,4,3,2,1,6]=>[8,9,7,6,5,4,3,1,2]=>[8,9,7,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[8,7,5,9,10,4,3,2,1,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,4,3,2,5,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[7,4,8,9,6,3,2,1,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,7,6,4,10,9,3,2,1,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,3,7,2,5,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,3,8,9,5,2,1,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,7,6,5,3,9,10,2,1,4]=>[10,9,8,5,4,6,7,3,2,1]=>[10,9,8,5,4,7,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[6,3,2,7,5,4,1,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,6,5,2,9,8,4,1,3]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[8,7,6,5,4,3,1,10,9,2]=>[10,7,6,5,4,3,2,9,8,1]=>[10,7,6,5,4,3,2,9,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.]
[9,8,7,6,5,4,3,2,1,10,11]=>[9,8,7,6,5,4,3,2,1,10,11]=>[9,8,7,6,5,4,3,2,1,11,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]
[8,4,2,6,3,1,7,5]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,5,3,7,4,2,8,6]=>[1,6,5,8,3,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,3,4,2,8,5]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,5,2,3,1,7,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,6,3,4,2,8,5]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,6,3,2,5,7,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,5,2,1,4,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,2,1,4,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,2,3,1,7,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,2,3,1,7,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,2,6,3,1,7,5]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[3,2,8,6,4,1,7,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,2,1,7,5,4,8,6]=>[3,2,1,8,6,5,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[4,1,3,7,5,2,8,6]=>[6,2,3,8,5,1,7,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,1,7,3,4,2,8,6]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[7,1,6,3,2,5,8,4]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,7,4,3,6,8,5]=>[1,2,8,5,4,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,8,2,4,5,7,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,8,3,2,6,7,4]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,8,7,1,5,6,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,8,2,7,1,5,6,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,8,7,2,1,4,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,7,1,3,4,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,6,1,3,4,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,7,8,2,4,5,6,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,7,1,3,4,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,8,1,3,4,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,8,2,3,1,7,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,6,8,3,2,5,7,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,3,8,2,6,7,4]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,4,2,7,1,5,6,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,4,2,8,1,5,6,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,4,2,8,3,1,7,5]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[5,4,2,3,8,1,7,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,5,2,3,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[7,4,2,1,3,6,8,5]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[8,4,2,1,3,6,7,5]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[1,5,3,2,4,7,8,6]=>[1,5,4,3,2,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,5,1,3,2,6,7,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,6,1,3,4,2,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,6,2,1,5,3,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,7,2,1,3,6,8,5]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[5,7,1,3,2,6,8,4]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,7,1,2,4,5,8,3]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,6,1,2,4,5,7,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,8,2,3,5,6,7,4]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,1,2,4,5,6,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,1,2,4,5,6,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,1,3,2,6,7,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,8,2,1,3,6,7,5]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[4,1,3,2,5,7,8,6]=>[4,2,3,1,5,8,7,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[5,1,2,4,3,7,8,6]=>[5,2,3,4,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[5,4,8,1,2,3,7,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[4,8,3,2,7,6,1,5]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[4,3,8,2,7,1,6,5]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[1,4,7,3,6,2,5,8]=>[1,6,7,4,5,2,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,2,8,1,7,6,5]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,1,8,3,7,2,5,6]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,1,8,7,3,2,5,6]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,7,8,1,2,5,3,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,4,7,6,2,1,8,5]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[3,4,2,7,1,6,8,5]=>[5,3,2,8,1,6,7,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[2,3,6,7,4,1,8,5]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,6,3,4,7,8,1,5]=>[7,8,3,4,5,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,6,7,8,3,4,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,1,7,8,4,2,5,6]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,1,3,2,8,7,5,6]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,7,8,2,6,4,1,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,2,3,8,1,6,7,5]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,3,1,8,2,5,7,6]=>[5,3,2,8,1,6,7,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,2,7,8,4,1,6,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,2,8,6,3,1,7,5]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[3,7,2,4,8,6,1,5]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,2,7,4,8,1,6,5]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,3,6,4,7,2,5,8]=>[1,6,7,4,5,2,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,4,7,1,8,6,5]=>[5,2,3,8,1,7,6,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,7,4,2,6,8,1,5]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[3,7,4,6,2,8,1,5]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[4,7,1,5,8,2,3,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,7,6,4,8,2,1,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,1,7,4,8,2,5,6]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,6,7,3,8,4,1,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,3,6,4,7,1,8,5]=>[6,2,8,4,5,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,7,5,2,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,5,2,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,8,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,6,7,8,5,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,2,6,4,7,5,8,3]=>[1,2,8,6,5,4,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,8,5,4,7,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,2,5,4,7,8,3]=>[1,8,3,5,4,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,5,6,3,7,4]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,3,1,4,2,5,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,1,5,2,3,6,7]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[7,4,1,5,2,3,6,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,6,1,8,4,3,2,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,1,8,6,4,3,2,7]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,6,3,8,7,2,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,2,5,8,3,7,4]=>[8,2,3,6,7,4,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,8,7,4,3,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,2,5,4,8,6,3]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,7,5,8,3,6,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,6,3,7,5,2,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,3,6,7,8,5,2,4]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,4,7,8,5,3]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,6,3,7,8,2,5]=>[7,2,8,4,5,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,1,6,4,8,2,7,5]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[7,8,4,1,6,3,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,1,6,3,8,7,2,5]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,5,1,8,4,3,2,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,5,1,7,4,3,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,1,8,5,2,3,7,6]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,1,6,8,3,7,2,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,4,6,1,3,8,2,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,5,8,1,4,3,2,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,3,5,7,6,8,2,4]=>[1,7,8,5,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,7,6,2,8,4]=>[1,6,8,5,4,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,7,4,6,2,8]=>[1,7,5,6,3,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,4,7,8,2,6]=>[1,7,4,3,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,7,4,2,8,6]=>[1,6,5,8,3,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,7,4,8,6,2]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,7,8,4,6,2]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,2,7,8,6,4]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,7,2,8,6,4]=>[1,5,8,7,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,7,8,2,6,4]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,3,2,7,4,8,5]=>[1,8,4,3,6,5,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,1,6,2,8,7,4]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,6,1,7,4,3,8,5]=>[3,8,1,6,5,4,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,4,7,3,5,2,8,6]=>[1,6,8,4,5,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,7,4,3,8,1,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[2,5,3,7,4,8,1,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,4,7,2,3,8,6,5]=>[1,5,8,4,2,7,6,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,7,3,1,8,6,5]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[1,4,6,3,8,2,7,5]=>[1,6,8,4,7,2,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,2,8,7,6,4]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,3,8,2,6,5]=>[1,6,8,4,7,2,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,1,7,8,4,6,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,2,6,7,8,1,5,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,3,6,7,8,2,1,5]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[3,5,2,7,8,4,1,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,5,7,4,8,3,2,6]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,1,6,8,4,7,3]=>[3,8,1,6,7,4,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[4,6,2,1,7,8,3,5]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[5,3,6,4,7,8,2,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,5,2,6,8,4,7,1]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,5,4,6,8,7,1,3]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[1,3,6,2,8,7,5,4]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,3,8,7,2,5]=>[1,7,8,4,6,5,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,7,4,3,8,6,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,5,7,2,4,8,6,3]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,3,7,2,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,3,6,7,8,2,5,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,4,7,3,8,6,2,5]=>[1,7,8,4,6,5,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,4,7,8,6,1,3]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,2,6,7,8,5,1,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,3,7,2,8,6,5,4]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,6,8,2,4,3,7]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,3,7,8,2,4,1,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[8,5,3,7,2,4,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,4,7,3,1,5,6]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[2,4,7,8,3,1,5,6]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[6,3,1,5,8,2,4,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,5,3,4,2,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,2,4,3,8,1,6,7]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,2,4,8,1,5,6,7]=>[5,2,3,8,1,6,7,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,2,4,6,8,1,5,7]=>[6,2,3,7,8,1,4,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,1,5,7,3,2,4,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,6,7,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,7,8,2,3,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[7,4,6,8,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,4,8,3,1,5,6]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[5,3,8,7,2,4,1,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[2,4,8,7,3,1,5,6]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[4,6,8,7,2,3,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,7,4,6,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,8,7,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,8,7,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,1,7,4,2,8,6,5]=>[5,2,8,4,1,7,6,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,2,8,4,1,7,6,5]=>[5,2,8,4,1,7,6,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[7,6,4,8,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,6,8,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,6,8,2,3,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,6,4,7,2,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,3,7,4,1,6,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,3,7,8,4,1,6,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,7,4,8,2,5,1,6]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[2,3,7,4,1,6,8,5]=>[5,2,8,4,1,6,7,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[8,1,6,4,2,3,7,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,7,8,6,2,3,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,3,1,7,4,2,8,5]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,5,7,6,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,6,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,6,4,2,3,8,5]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,7,6,4,2,8,5]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,8,7,6,2,3,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,8,7,5,2,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,6,1,5,8,7,2]=>[8,4,5,2,3,7,6,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,3,6,5,1,8,7,2]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,6,3,5,1,8,7,2]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,6,3,1,5,8,7,2]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,1,6,5,3,8,7,2]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,6,1,5,3,8,7,2]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,6,5,3,1,8,7,4]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[2,6,5,1,8,7,3,4]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,6,5,8,1,7,3,4]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,6,5,8,1,3,7,4]=>[5,8,6,7,1,3,4,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,6,5,8,3,1,7,4]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[2,6,5,3,8,1,7,4]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[4,6,1,5,8,3,7,2]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,1,6,5,8,3,7,2]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,6,5,8,7,3,2]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,6,5,3,8,7,1,4]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[6,4,3,8,7,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,8,3,7,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,8,5,3,7,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,6,8,1,5,7,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,6,1,8,5,7,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,1,6,8,5,7,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,4,6,8,5,7,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,8,5,3,7,2]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,1,8,5,3,7,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,6,8,5,3,1,7,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,6,8,5,1,7,3,4]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[4,6,8,3,5,1,7,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,6,8,3,1,5,7,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,6,3,1,8,5,7,2]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,6,3,8,1,5,7,2]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[4,6,3,8,5,7,1,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,3,6,8,1,5,7,2]=>[8,5,6,7,2,3,4,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[4,3,6,1,8,5,7,2]=>[8,4,6,2,7,3,5,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,3,1,6,8,5,7,2]=>[8,3,2,6,7,4,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,1,3,6,8,7,5,2]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,3,6,1,8,7,5,2]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,3,6,8,1,7,5,2]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[6,5,2,8,7,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,2,8,7,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,5,8,7,1,3,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,2,5,8,7,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,3,8,1,7,5,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,6,3,1,8,7,5,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,1,6,3,8,7,5,2]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,4,6,3,8,7,5,2]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,6,8,3,7,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,6,1,8,3,7,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,6,8,1,3,7,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,2,8,5,7,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,8,5,7,1,3,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,4,8,7,1,5,3,6]=>[5,7,8,6,1,4,2,3]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[4,2,8,7,5,3,1,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[6,4,1,8,7,5,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,1,4,8,7,5,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,4,8,7,3,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,4,1,8,7,3,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,2,8,7,5,1,3,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[2,4,8,7,3,5,1,6]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[2,3,4,7,1,8,6,5]=>[5,2,3,8,1,7,6,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,4,7,8,5,6,1]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,6,7,4,8,5,1]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,5,6,3,7,8,1,4]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[2,3,7,1,4,8,6,5]=>[4,2,8,1,5,7,6,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,6,1,3,7,8,5,4]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,5,6,7,4,8,1,3]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[2,3,7,8,4,5,6,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,6,7,3,4,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,5,3,2,6,4,7,8]=>[1,6,4,3,5,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,7,5,4,8,6]=>[1,3,2,8,6,5,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,5,2,4,3,7,1,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,4,2,5,3,7,1,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,4,7,6,2,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,6,4,8,2,1,5,7]=>[6,7,5,8,3,1,2,4]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[4,6,2,3,7,5,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,7,2,3,6,5,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,7,2,3,5,6,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[5,3,2,7,4,6,1,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,3,2,6,4,7,1,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,6,2,3,5,7,1,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,5,2,6,8,4,3,7]=>[1,7,3,6,8,4,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,2,8,4,3,6]=>[1,7,8,4,6,5,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,2,1,8,6,4,7]=>[4,7,3,1,8,6,2,5]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,6,8,4,2,1,5,7]=>[6,7,8,5,4,1,2,3]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[4,3,2,6,1,8,5,7]=>[5,3,2,7,1,8,4,6]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,5,8,2,7,4,3,6]=>[1,7,8,4,6,5,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,2,3,4,1,7,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,1,8,2,3,5,7,6]=>[5,2,8,4,1,6,7,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,1,8,4,5,7,6]=>[3,2,1,8,5,6,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[7,3,2,1,4,5,8,6]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[7,8,1,4,3,5,2,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,2,3,4,6,8,5]=>[8,2,3,4,5,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,2,3,4,8,7,5]=>[8,2,3,4,5,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,3,4,6,7,5]=>[8,2,3,4,5,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,7,1,4,3,5,2,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,2,1,4,5,7,6]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,8,2,1,5,6,4,7]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,8,2,1,6,5,4,7]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[1,7,8,3,5,4,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,1,8,3,5,2,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,1,7,3,5,2,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,4,6,2,1,5,7]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[8,4,2,5,3,1,6,7]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,5,2,4,3,1,6,7]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,3,2,5,4,1,6,7]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,3,2,5,1,8,6,7]=>[5,3,2,4,1,8,7,6]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,5,2,4,1,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[2,4,7,8,1,5,3,6]=>[5,7,8,6,1,4,2,3]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,8,7,3,5,4,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,8,2,7,4,3,6]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,7,2,8,4,3,6]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,3,2,1,8,4,5,7]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[7,3,2,8,4,5,1,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,7,8,4,3,5,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[7,1,8,3,5,4,2,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,8,2,3,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,1,3,4,8,2,5]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,1,3,4,7,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,7,2,3,4,6,8,5]=>[1,8,3,4,5,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,2,3,4,1,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,6,2,3,4,1,7,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,7,3,5,4,2,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,2,7,4,5,1,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,2,3,4,1,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,6,2,3,4,8,1,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,6,2,3,4,7,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,4,8,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,3,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,5,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,3,4,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,4,2,1,6,7,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,8,4,1,2,6,7,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,3,7,2,6,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,2,8,1,6,3,7,4]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[5,8,2,1,4,7,6,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,8,2,5,1,7,6,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,8,4,1,2,6,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,1,5,2,7,6,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,1,2,4,7,6,3]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,2,8,3,6,7,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,7,6,2,4,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,8,7,6,4,1,3,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[7,8,2,6,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,7,6,4,2,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,7,6,3,1,4,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[1,8,7,6,2,4,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,7,6,3,4,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,1,4,5,6,7,3]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,1,7,3,6,5,8,4]=>[2,1,8,4,6,5,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,1,7,2,6,5,8,4]=>[4,2,8,1,6,5,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,2,7,1,6,5,8,4]=>[4,2,8,1,6,5,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[6,1,2,8,5,7,3,4]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,2,1,8,5,7,3,4]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,3,1,8,5,7,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,4,2,1,7,5,8,3]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,1,3,8,5,2,7,4]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,7,1,6,8,5,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,3,7,2,6,8,5,4]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,2,6,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,2,6,7,5,8,1,4]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,2,7,5,6,3,8,4]=>[1,2,8,6,5,4,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,7,6,4,3,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,8,7,6,1,2,5,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[3,8,7,6,2,1,5,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[4,8,7,6,2,1,3,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,8,7,6,1,3,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,8,7,6,4,1,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[7,8,3,6,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,3,7,5,6,8,1,4]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,8,7,6,4,2,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,1,4,6,8,2,3,7]=>[7,2,6,4,8,3,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,7,6,3,5,4,8,2]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,7,2,6,5,1,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[3,4,6,1,5,7,2,8]=>[7,4,5,2,3,6,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,6,8,5,7,3,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,1,2,5,8,3,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,6,7,2,1,4,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,8,6,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,3,6,5,7,8,2,4]=>[1,7,8,4,5,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,8,5,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,2,4,1,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,3,1,6,8,5,7,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[7,3,2,5,1,4,8,6]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,1,4,2,3,6,8,5]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,5,8,3,4,6,7,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,3,1,2,4,7,6,5]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,3,8,1,6,5,4,7]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[8,1,4,7,2,5,3,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,5,2,4,1,7,8,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,4,7,8,6,2,1,5]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[3,4,8,6,2,7,1,5]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[5,8,2,1,6,7,3,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,7,2,8,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,2,7,5,3,8,4]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,3,2,8,6,4,1,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,7,8,4,6,3,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[7,3,5,2,6,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,5,2,3,6,1,7,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,6,3,5,7,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,8,6,4,3,7,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,3,2,6,4,7,1,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,3,8,7,6,5,1,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,2,8,7,3,6,5,4]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,2,8,7,3,6,1,5]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[4,5,8,7,1,2,6,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,5,8,7,3,2,6,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,5,8,7,3,2,1,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[2,6,8,1,7,5,4,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,6,8,4,7,2,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,5,8,3,7,6,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,2,8,4,7,6,1,5]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,5,8,3,7,2,6,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,8,4,7,2,1,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[5,6,8,2,3,7,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,8,4,2,7,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,4,2,7,6,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,2,3,7,6,4]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,8,4,3,7,6,5]=>[2,1,8,5,4,7,6,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,5,8,4,3,7,1,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[5,6,8,4,1,2,7,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,6,8,1,3,2,7,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,6,8,4,3,2,7,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,6,8,4,3,2,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[7,1,2,8,6,5,4,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,4,8,6,2,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,3,1,8,6,2,5,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,2,4,8,3,6,1,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,1,4,8,3,2,6,5]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,5,8,3,2,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,2,8,7,5,4,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,4,8,7,2,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,4,8,7,2,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,2,5,8,7,6,1,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,1,5,8,7,2,6,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,1,4,8,7,2,6,5]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,6,4,8,2,7,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,8,2,7,6,3]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,5,8,3,7,1,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,6,5,8,1,2,7,3]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,6,4,8,3,2,7,5]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,8,3,2,7,6]=>[1,6,5,8,3,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,1,4,8,2,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,1,3,8,2,5,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,3,4,8,2,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,5,1,8,6,4,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,2,5,3,8,6,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,1,4,8,6,5,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,2,1,3,8,6,5,4]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,2,3,4,8,6,1,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,3,5,4,8,2,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,6,5,1,8,7,4,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,3,5,4,8,7,1,6]=>[7,2,4,3,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,6,5,4,8,2,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,6,5,2,3,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,6,1,4,2,8,5,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,1,2,3,8,5,4]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,2,4,3,8,1,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,1,5,4,2,8,6,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,5,2,3,8,6,4]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,2,4,3,8,6,5]=>[8,2,3,5,4,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,6,5,4,3,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[7,6,1,4,3,2,8,5]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,1,5,4,3,2,8,6]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,4,2,6,7,8,1,5]=>[7,3,2,8,5,6,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[3,1,4,2,6,8,7,5]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[8,3,4,2,6,1,7,5]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[2,6,7,3,5,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[2,7,8,3,5,4,1,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,6,8,3,5,4,1,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[4,7,1,2,8,5,3,6]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,8,1,2,7,5,3,6]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,7,1,3,6,8,4,5]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[6,7,3,2,8,1,4,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,4,2,6,1,8,5]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,4,1,2,8,5,3,6]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,4,2,1,5,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,1,2,6,5,3,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,4,3,1,5,6,8,2]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,7,4,1,5,8,3,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,7,5,1,6,8,3,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,5,3,1,7,6,8,2]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,6,1,2,7,5,3,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,1,8,2,6,5,3,7]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,6,1,2,8,5,3,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,4,3,1,5,6,7,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,5,3,1,8,6,7,2]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,8,5,6,3,1,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,3,4,8,6,7,2]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,4,3,8,1,6,7,2]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,5,3,4,1,6,7,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,4,8,2,1,5,3,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[6,7,3,2,5,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,8,3,2,5,1,4,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,7,1,4,6,8,3,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,1,3,4,7,6,8,2]=>[8,2,4,3,6,5,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,4,2,7,5,3,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,4,3,7,1,6,8,2]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,7,5,4,1,8,3,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,6,4,2,1,5,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,2,7,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,8,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,9,7,6,5,4,3,2]=>[9,2,8,7,6,5,4,3,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[2,10,9,8,7,6,5,4,1,3]=>[9,10,8,7,6,5,4,3,1,2]=>[9,10,8,7,6,5,4,3,1,2]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[9,2,8,7,6,5,4,1,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[3,9,8,7,6,5,4,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,7,2,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,2,8,7,6,5,1,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,8,7,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,9,1,7,6,5,4,3,2]=>[9,8,3,7,6,5,4,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[7,3,8,6,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,9,7,6,5,4,3,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,1,10,8,7,6,5,4,3,2]=>[10,2,9,8,7,6,5,4,3,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[4,8,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,7,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,6,1,3,2,4,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,1,5,3,2,4,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,1,5,3,2,4,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,7,5,3,2,4,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,1,4,5,2,3,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,3,1,5,2,4,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,6,1,5,2,3,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,2,1,5,4,3,7]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,5,2,6,1,4,3,7]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,5,2,1,7,4,3,6]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,8,2,1,5,4,3,6]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,8,3,1,5,2,4,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,7,5,1,3,4,6]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[8,4,1,7,5,2,3,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,2,7,1,5,4,3,6]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,2,6,1,7,4,3,5]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,1,7,4,3,2,6,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,5,7,3,2,6,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,8,1,3,2,6,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,6,1,5,7,3,4]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[5,8,1,6,7,2,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,7,6,1,8,2,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,2,5,1,8,3,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,1,6,8,2,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,5,7,1,8,2,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,3,8,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,4,1,8,2,3,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,1,4,8,2,3,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,6,4,7,2,3,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,5,8,1,3,2,4,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,4,1,3,2,5,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,7,4,1,2,5,6]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,5,1,7,3,2,4,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,1,7,3,2,4,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,8,4,3,6,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,3,1,8,6,4,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,1,7,4,6,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,5,1,7,2,3,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,8,1,7,2,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,8,1,2,7,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,1,8,5,6,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,2,7,8,3,1,5,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,8,1,7,3,2,6,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,1,7,3,2,6,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,3,4,7,1,2,6,5]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[8,2,7,4,1,3,6,5]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[7,4,8,2,1,3,6,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,4,3,8,1,2,6,5]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[8,2,3,6,7,1,5,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,6,8,7,1,5,4,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[7,8,5,2,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,5,2,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,2,3,4,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,2,6,8,1,4,7]=>[6,7,3,4,8,1,2,5]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,5,2,4,6,8,1,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[2,4,5,7,3,6,8,1]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,4,5,3,6,8,1,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[5,2,4,6,8,1,3,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,1,3,4,6,8,2,7]=>[7,2,4,3,5,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,3,5,2,6,8,1,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[4,3,5,7,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,3,5,7,2,6,8,1]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,6,3,7,2,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,6,3,1,7,8,2,5]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[4,3,5,1,7,8,2,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[5,7,1,3,4,8,2,6]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,7,1,3,4,6,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,5,7,1,3,6,8,2]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,3,6,7,1,5,8,2]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,6,3,5,1,7,8,2]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,6,3,5,7,2,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[3,5,6,4,1,7,8,2]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[3,1,5,6,7,4,8,2]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,6,7,3,4,8,2]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,7,1,3,5,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,6,7,3,4,5,8,2]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,7,4,5,8,1,3]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[2,6,7,4,8,1,3,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[5,3,6,1,2,7,8,4]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[3,5,2,6,1,7,8,4]=>[5,8,3,4,1,6,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,5,2,6,7,4,8,1]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,2,3,6,7,4,8,1]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,2,3,6,1,7,8,4]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,2,6,1,3,7,8,4]=>[8,4,5,2,3,6,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,2,6,7,3,5,8,1]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,3,7,2,4,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,5,7,2,8,1,4,6]=>[6,7,8,4,5,1,2,3]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[3,7,2,4,8,1,5,6]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[7,2,4,6,8,1,3,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,1,3,4,6,8,2,5]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,7,2,4,6,8,1,5]=>[7,8,3,4,5,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,5,7,2,6,8,1,4]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[6,3,7,2,5,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,3,5,7,2,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,3,5,7,2,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,2,4,5,7,3,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,2,4,5,1,7,8,3]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,7,1,2,5,6,8,3]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,6,7,5,8,1,3,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[4,6,7,1,2,5,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,6,2,4,7,3,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,4,2,6,7,3,8,1]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,4,2,6,1,7,8,3]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,5,4,6,2,7,8,3]=>[1,8,5,4,3,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,6,4,1,2,7,8,3]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[6,4,5,1,2,7,8,3]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[6,3,5,1,7,8,2,4]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,5,7,2,8,1,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,7,1,3,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,6,4,7,1,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,4,6,3,1,7,8,2]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[7,5,3,2,4,8,1,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,4,5,2,6,1,3,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,4,2,1,6,3,7]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,3,4,1,6,2,7]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,4,5,3,1,6,2,7]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,4,2,1,8,3,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,4,2,1,6,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,4,5,3,1,6,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,4,3,5,6,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,6,3,7,4,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,6,7,3,1,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,7,3,4,1,5,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,7,4,2,1,5,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,6,7,3,1,8,2,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,3,7,8,1,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,3,7,2,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,6,7,2,3,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,4,5,2,8,1,3,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,3,2,4,8,1,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,6,4,2,1,3,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,6,3,4,1,2,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,6,3,2,4,1,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,7,3,2,5,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,5,3,2,7,8,1,4]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,5,3,2,7,4,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,4,5,2,7,3,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,4,5,2,7,8,1,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,4,5,2,6,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,4,5,6,1,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,6,2,1,3,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,7,3,5,1,2,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,6,7,4,1,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,6,7,2,4,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,6,4,2,7,8,1,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,5,7,2,1,8,3,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,5,7,2,1,4,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,4,6,7,3,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,7,8,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,8,5,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,8,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,8,5,6,3,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,8,6,3,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,5,8,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,5,8,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,3,8,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,8,5,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,5,8,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,7,8,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,5,7,8,6,3,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,8,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,7,8,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,7,8,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,5,8,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,8,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,1,5,6,3,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,8,5,6,3,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,5,8,6,3,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,7,8,3,6,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,7,8,5,6,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,3,7,8,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,7,5,8,6,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,7,3,8,6,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,5,3,8,6,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,5,8,3,6,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,8,1,5,3,6,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,3,5,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,5,8,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,7,1,8,6,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,5,7,1,8,6,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,7,5,3,8,6,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,3,1,8,6,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,3,8,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,5,8,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,5,8,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,5,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,8,5,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,3,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,6,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,1,6,3,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,8,1,3,6,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,7,8,1,5,6,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,7,8,3,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,8,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,1,8,5,6,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,7,1,8,3,6,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,7,1,8,6,3,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,1,8,6,3,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,8,1,6,3,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,5,1,6,3,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,5,1,3,6,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,8,1,3,6,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,1,8,3,6,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,1,3,8,6,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,7,1,3,8,6,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,7,1,5,8,6,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,7,3,5,8,6,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,3,7,8,6,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,1,7,8,6,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,3,1,7,8,6,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,3,1,5,8,6,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,3,1,8,5,6,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,3,8,1,5,6,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,3,1,5,6,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,1,3,5,6,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,8,3,5,6,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,3,8,5,6,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,3,5,8,6,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,5,7,8,6,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,3,4,6,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,3,4,8,6,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,3,4,8,1,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,3,4,1,8,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,3,4,1,6,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,7,3,4,6,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,3,5,6,1,2,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,7,3,1,4,6,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,7,3,1,4,6,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,7,3,1,4,8,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,3,1,4,8,2,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[5,3,7,4,1,2,8,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[5,3,7,4,1,2,6,8]=>[6,5,7,4,2,1,3,8]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[5,3,7,1,4,2,6,8]=>[6,5,7,4,2,1,3,8]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[5,3,7,1,4,2,8,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[3,7,5,1,2,8,6,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[7,8,3,5,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,8,5,1,2,6,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,3,5,8,1,2,6,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[3,7,5,1,2,6,8,4]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[6,1,4,3,5,2,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,5,7,3,8,4,1,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[5,4,7,8,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,6,2,8,3,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,7,2,5,8,3,1,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,2,4,5,1,3,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,1,4,6,3,2,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,5,6,2,4,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[3,8,6,7,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,7,8,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,3,4,8,1,7,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[8,7,1,2,5,3,4,6]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,1,8,2,3,4,7,6]=>[6,2,8,4,5,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,4,7,6,2,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,7,8,1,5,4,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,1,3,4,6,8,5,2]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,6,5,7,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,1,4,6,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,7,6,1,8,3,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,7,2,6,3,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,1,8,4,6,7,3,5]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[4,7,8,6,3,1,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,8,1,5,6,7,2,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[6,7,2,4,8,5,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,3,6,7,5,1,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[8,2,1,7,6,3,5,4]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,2,4,5,8,1,7,6]=>[6,2,3,4,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[7,4,6,3,2,1,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,7,3,2,1,8,6,5]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[6,4,7,5,2,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,4,8,1,7,3,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,7,2,3,1,5,6]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[4,2,3,1,8,7,5,6]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[7,6,8,1,3,5,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,5,2,3,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,7,2,6,5,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,4,2,1,8,5,7,3]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,2,1,5,6,8,4,3]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,7,2,6,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,8,2,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,7,3,6,8,5,4]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,5,7,8,4,6,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,5,7,8,3,6,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,4,1,5,7,2,8,3]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,4,8,1,2,5,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,2,7,8,6,3,5,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,1,7,4,3,2,8,5]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,8,3,4,2,1,7,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,2,6,1,5,7,8,3]=>[8,4,5,2,3,6,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,4,6,7,3,5,8,1]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,5,8,3,7,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,4,8,3,5,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,8,7,5,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,6,3,1,5,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,8,2,5,7,6,1]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,6,8,7,2,5,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,5,7,2,8,6,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,5,7,4,8,6,1,3]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,6,3,7,5,2,8,4]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,3,7,5,1,8,4]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,6,4,8,7,5,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,3,7,2,8,5,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,2,5,8,7,1,4]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,2,8,4,7,6,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,4,8,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,4,8,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,5,8,7,6,1,3]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,3,5,7,6,1,8,4]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,3,4,6,2,8,7,5]=>[1,5,3,8,2,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,2,3,6,1,8,7,4]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,2,7,3,8,1,6,5]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[6,1,3,8,7,2,5,4]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,5,6,2,8,7,4]=>[5,2,8,4,1,7,6,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,2,4,6,3,8,7,5]=>[1,2,5,8,3,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,5,2,8,7,6,3]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,4,2,8,6,5,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,3,7,2,8,6,4]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,5,3,2,8,7,6]=>[5,2,4,3,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,6,1,4,3,8,7,5]=>[3,8,1,5,4,7,6,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,6,2,4,1,8,7,5]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[7,2,3,5,1,8,6,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,3,4,1,8,6,5,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,3,4,1,8,7,5,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,4,5,1,8,7,6,2]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,6,4,2,8,7,5,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,6,3,1,8,7,4,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,4,2,5,1,8,6,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,3,6,2,8,1,7,4]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,6,2,7,5,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,5,2,6,1,8,7,3]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,5,3,6,2,8,7,4]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,3,2,7,6,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,8,3,1,7,6,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[4,5,8,2,1,7,6,3]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[3,6,2,5,1,4,8,7]=>[5,6,3,4,1,2,8,7]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[5,2,8,4,1,3,7,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[2,4,8,7,1,3,6,5]=>[5,6,8,7,1,2,4,3]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,5,8,1,3,7,6,4]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,3,8,1,4,7,6,5]=>[4,2,8,1,5,7,6,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,4,1,7,2,8,6,5]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,5,2,1,7,4,8,6]=>[4,6,3,1,8,2,7,5]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[6,3,1,7,2,8,5,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,5,1,2,8,6,4,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,6,1,2,8,7,5,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,6,2,3,8,7,5,4]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,3,8,7,6,4]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,5,1,2,8,7,6,3]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[6,4,1,2,8,7,5,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,4,1,2,8,6,5,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,3,1,7,2,8,6,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,2,8,1,3,7,6,4]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,1,2,8,3,7,6,5]=>[5,2,3,8,1,7,6,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,7,5,6,8,3,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,4,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,2,6,4,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,6,3,7,5,8,4,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,7,4,5,8,6,2]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,6,3,4,1,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,3,7,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,4,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,5,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,6,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,5,2,1,4,3,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,3,2,1,4,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,7,6,4,5,1,3,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[5,7,2,6,4,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,1,3,7,5,8,4,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,7,3,6,8,5,2]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,6,4,3,7,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,1,7,4,8,6,3,5]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,8,6,3,7,5,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,7,3,6,5,4]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,3,8,4,7,5,6]=>[2,1,3,8,5,7,6,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,1,2,7,4,3,6,5]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,3,1,6,8,4,7,2]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,2,8,7,1,4,3,5]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[8,7,2,1,5,4,3,6]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,2,3,1,4,6,5,7]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,4,2,7,1,5,6,8]=>[5,3,2,7,1,6,4,8]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,7,3,8,2,1,5,6]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[5,2,7,3,1,4,6,8]=>[6,5,7,4,2,1,3,8]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[8,3,7,2,1,5,4,6]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,3,7,2,8,4,6,5]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,5,8,6,7,3]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,5,3,8,2,1,4,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[5,4,6,2,7,1,3,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,6,3,1,8,4,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,2,1,8,5,3,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,7,5,8,6,4,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,5,1,2,8,3,7,4]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,6,1,4,3,7,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,4,1,3,7,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,7,1,3,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,8,3,1,7,4,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,1,7,5,4,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,3,8,7,4,6,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,7,6,3,5,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,1,7,6,4,3,5]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,3,1,8,7,4,5,6]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,4,1,8,5,7,3,6]=>[3,7,1,8,5,6,2,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[5,8,2,1,7,6,3,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,2,7,1,8,5,3,4]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,7,1,6,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,8,3,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,8,7,5,6,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,2,8,9,4,5,6,7]=>[3,2,1,9,8,6,7,5,4]=>[3,2,1,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[2,1,7,8,4,6,3,5]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,5,8,7,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,2,7,1,6,4,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[2,1,6,4,5,8,3,7]=>[2,1,7,5,4,8,3,6]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,6,3,7,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,3,8,5,2,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[4,6,3,7,5,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,5,7,8,2,6,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,6,2,4,1,3,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[7,6,3,8,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,3,4,6,1,5,7]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,2,3,4,6,1,8,5]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,2,3,4,7,5,1,6]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,3,4,6,8,5,1]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,3,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,2,3,6,1,5,8,7]=>[5,3,2,6,1,4,8,7]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,8,3,7,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,3,4,7,8,6,1]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,2,3,4,7,1,6,5]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,2,3,4,8,7,1,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[5,2,3,4,6,8,1,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[4,2,8,5,7,6,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,7,6,4,5,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,8,6,4,5,1,2,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,7,3,6,5,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,8,3,7,5,2,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,7,3,6,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,7,5,1,6,3,4]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[4,2,7,5,8,6,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,1,7,3,6,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,2,7,8,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,8,3,7,6,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,7,3,1,6,4,5]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,8,3,2,5,7,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,3,8,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,3,4,7,5,8,1]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,2,3,4,8,5,1,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,2,3,4,1,7,5,6]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,2,3,4,1,8,5,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,2,3,4,8,7,5,1]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,3,1,5,7,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,3,4,1,8,6,5]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,2,3,4,1,5,8,6]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,2,3,4,8,7,5,6]=>[1,2,3,4,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,5,3,4,6,7]=>[1,2,8,6,5,4,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,4,2,3,5,6,7]=>[1,8,5,4,3,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,7,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,6,7,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,8,4,6,5,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,7,1,5,4,6,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,7,1,4,6,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,8,5,1,7,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,5,7,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,1,5,6,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,1,4,5,6,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,4,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,5,1,4,6,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,2,5,1,4,6,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,8,7,2,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,4,8,5,2,7,3]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,1,4,2,5,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,5,1,2,4,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,1,8,5,6,2,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,8,7,1,2,5,6,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,5,8,7,1,2,6,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,3,8,5,7,1,6,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,8,7,1,5,6,2,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,5,8,7,1,6,2,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,3,8,6,7,5,1,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,2,8,6,7,5,1,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,1,8,6,2,7,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,7,4,1,2,6,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,3,8,6,7,5,2,4]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,1,8,2,6,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,8,7,1,5,6,3,4]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[8,7,1,5,2,4,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,8,2,4,6,5,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,2,8,4,7,5,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,5,7,2,6,4]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,3,7,2,5,6,4]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,7,1,3,5,6,4]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[5,7,1,8,2,3,6,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,8,2,3,5,6,4]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,3,7,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,2,8,6,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,2,7,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,3,6,1,7,5,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,3,4,7,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,7,4,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,4,2,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,5,1,6,2,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,2,4,1,5,6,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,8,6,1,7,2,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,7,1,8,2,6,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,2,8,6,7,1,5,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,7,4,1,2,5,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,7,1,6,3,4,5]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,2,7,1,3,6,4,5]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,8,3,6,7,1,5,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[8,7,2,1,3,5,6,4]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,8,7,2,3,6,4,5]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,7,2,6,3,4,5]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,7,3,6,1,4,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,8,7,3,6,2,4,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,7,6,3,4,5]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,7,4,1,5,6,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[8,2,1,7,5,6,3,4]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,7,3,1,5,6,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,7,3,5,6,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[8,3,1,6,7,5,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,2,1,6,7,4,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,5,2,8,6,7,4,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,6,7,5,3,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,3,6,7,5,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,3,6,7,5,1,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,7,2,5,6,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,3,7,5,6,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,1,2,7,5,6,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,4,2,6,7,5,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,8,6,7,3,5,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,2,7,3,6,4,5]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,3,6,2,4,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,2,6,3,4,5]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,2,3,6,4,5]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,3,7,2,5,6,4]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,3,6,7,2,5,4]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,2,3,6,5,4]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,3,7,1,2,5,6,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,7,1,2,3,6,4,5]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,8,5,7,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,1,8,5,7,4,2,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,3,5,7,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,6,2,4,5,7,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,6,4,3,5,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,8,3,5,4,7,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[2,7,5,8,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,2,7,6,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,1,7,6,3,2,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,7,1,8,6,2,5,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,1,7,6,4,5,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,1,7,5,8,4,2,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,1,6,8,7,5,2,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,3,8,7,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,5,8,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,6,4,2,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,8,3,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,8,2,1,6,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,4,6,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,2,1,4,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,2,3,1,4,8,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,4,6,2,3,8,1,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,4,2,5,8,3,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,6,5,8,1,3,2,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[4,7,1,5,3,8,2,6]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,7,8,1,3,6,2,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,7,1,3,4,6,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,7,1,4,2,3,6,8]=>[6,7,3,5,4,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[5,8,1,3,2,4,6,7]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,8,6,1,3,2,7,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[8,4,6,2,1,3,7,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,4,8,7,2,3,6,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,4,8,7,3,1,2,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[6,8,3,7,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,6,8,2,3,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[5,7,4,2,8,3,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,7,2,1,8,3,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,5,3,4,1,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,8,5,4,1,3,2,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,4,3,7,1,5,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[9,8,7,6,5,2,3,1,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,6,3,4,2,1,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,4,5,3,2,1,6]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,5,6,4,3,2,1,7]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,6,7,5,4,3,2,1,8]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,4,2,6,1,5,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,2,5,6,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,4,2,8,1,5,7,3]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[6,3,7,8,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,5,6,4,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,3,1,5,6,2,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,4,5,2,6,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,3,7,2,8,6,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,8,2,6,7,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,8,2,5,4,7,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,4,8,2,1,5,7,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,4,3,1,8,2,7,5]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,3,7,8,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,8,5,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,7,6,8,2,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,8,4,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,4,3,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,6,4,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,8,6,2,7,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,5,8,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,8,7,2,4,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,8,7,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,8,6,7,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,7,8,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,6,4,8,2,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,4,6,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,2,8,1,7,3,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,5,2,4,3,7,8,1]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,4,6,2,8,7,1,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,6,3,8,7,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,4,3,1,8,2,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,4,3,6,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,3,8,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,8,6,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,8,5,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,8,3,7,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,6,8,2,7,1,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[3,6,7,8,2,5,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,7,8,2,6,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,8,5,7,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,4,8,6,2,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,2,5,7,8,1,4]=>[7,8,3,4,5,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,2,7,4,6,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,2,4,5,8,6,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,6,7,1,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,2,5,6,7,1,8,3]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,2,3,7,5,1,6,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,2,6,3,5,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,1,3,6,7,2,4,5]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,2,5,6,3,7]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,2,7,5,3,6]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,3,8,2,7,4,5]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,6,2,4,1,7,8,5]=>[5,8,3,4,1,6,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[6,2,7,3,1,5,8,4]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,3,4,1,8,5,7,2]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,3,4,1,5,8,6,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,7,5,2,8,6,3,4]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,4,1,8,5,6,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,6,3,1,7,8,4,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,6,4,8,1,5,7,2]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,5,8,4,2,6,3,7]=>[1,7,8,5,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,7,4,1,6,8,2]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,5,1,8,2,3,7,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,7,1,8,2,6,3,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[6,3,1,8,5,2,4,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,5,2,1,8,4,6,7]=>[4,6,3,1,8,2,7,5]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[7,5,1,2,3,8,6,4]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,4,1,2,7,3,8,5]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,2,6,1,3,4,8,7]=>[6,4,5,2,3,1,8,7]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[7,8,4,5,1,3,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,1,3,2,5,4,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,7,1,4,3,5,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,8,2,3,1,5,4,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,8,2,4,3,5,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,2,4,1,5,3,6]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,4,2,6,5,7,3,8]=>[1,7,3,5,4,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,6,1,4,2,7,3,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,7,2,4,1,5,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,2,4,3,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,2,3,1,5,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,3,5,4,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,4,1,6,5,7,3,8]=>[3,7,1,5,4,6,2,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,5,2,6,4,7,3,8]=>[1,7,3,5,4,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,1,6,4,7,3,8]=>[3,7,1,5,4,6,2,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,6,5,7,4,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,2,4,3,7,1,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,5,2,6,1,7,3,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,5,1,6,3,7,2,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,5,3,6,1,7,2,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,6,3,4,1,7,2,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,6,1,4,3,7,2,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,6,1,3,2,7,4,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,6,4,7,1,3,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,4,5,1,3,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,5,8,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,1,3,2,7,6,8]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,6,5,7,1,3,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,6,1,3,2,7,5,8]=>[5,7,3,4,1,6,2,8]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,4,3,6,2,7,5,8]=>[1,5,3,7,2,6,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,4,1,6,5,7,2,8]=>[7,3,2,5,4,6,1,8]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[4,5,2,3,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,5,3,7,6,8,1,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,6,5,7,3,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,6,5,7,2,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,5,4,6,1,7,2,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,5,1,6,4,7,2,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,5,3,6,4,7,2,8]=>[1,7,5,4,3,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,3,6,2,7,4,8]=>[1,7,5,4,3,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,2,6,1,7,4,8]=>[5,7,3,4,1,6,2,8]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,5,2,6,4,7,1,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,4,2,6,1,7,5,8]=>[5,3,2,7,1,6,4,8]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[2,4,3,6,1,7,5,8]=>[5,3,2,7,1,6,4,8]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[2,5,3,6,4,7,1,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[2,5,3,6,1,7,4,8]=>[5,7,3,4,1,6,2,8]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,6,2,7,3,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,6,2,7,5,4,8,1]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,6,1,7,3,8,2,5]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,4,7,1,3,8,6,5]=>[4,5,8,1,2,7,6,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[5,2,6,7,4,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,5,2,7,6,4,8,1]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,5,7,4,3,8,2,6]=>[1,7,8,5,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,7,3,1,8,6,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[1,5,7,2,8,3,6,4]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,7,3,1,8,4,6]=>[5,7,8,4,1,6,2,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[1,5,7,3,4,8,2,6]=>[1,7,8,5,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,2,6,7,1,8,4,3]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,3,7,2,8,5,6,4]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,3,1,5,8,4,7,6]=>[3,2,1,6,8,4,7,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,1,5,6,8,4,3,7]=>[2,1,7,6,8,4,3,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,3,1,5,8,6,4,7]=>[3,2,1,7,8,6,4,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,4,7,3,1,8,5,6]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[1,3,7,2,8,5,4,6]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,3,1,6,8,5,4,7]=>[3,2,1,7,8,6,4,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[4,6,2,7,1,8,3,5]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,6,4,5,7,8,3,2]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,1,7,8,6,3,4]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,3,6,2,8,7,4,5]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,5,6,8,4,7,3]=>[2,1,8,6,7,4,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,1,7,8,5,6,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,3,6,2,8,4,7,5]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,5,6,8,7,3,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,6,5,2,7,8,4,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,2,4,7,5,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,5,7,8,4,2,6,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,4,1,8,6,2,5]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[3,4,6,8,5,7,2,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,2,5,7,3,1,8,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,5,6,2,8,7,3,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,5,6,8,1,7,4,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[4,5,6,1,8,7,3,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,5,6,3,1,8,7,2]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,6,3,1,7,5,2,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,5,3,7,6,1,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,5,1,7,3,8,6,2]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,5,7,1,4,3,8,6]=>[4,6,8,1,5,2,7,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,3,5,7,6,1,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,3,6,1,7,5,2,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,3,2,6,1,7,5,8]=>[5,3,2,7,1,6,4,8]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[5,3,2,1,6,4,7,8]=>[6,4,3,2,5,1,7,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,3,1,6,2,7,4,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,1,6,3,2,7,4,8]=>[7,2,5,4,3,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,6,1,7,4,2,5,8]=>[6,7,3,5,4,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,6,1,7,5,3,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,1,6,3,7,4,2,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,3,6,4,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,3,2,6,4,1,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,2,1,6,3,7,4,8]=>[7,3,2,5,4,6,1,8]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[5,2,6,3,1,7,4,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[3,6,2,7,4,1,5,8]=>[6,7,3,5,4,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,5,7,2,8,6,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,4,7,1,3,6,5,8]=>[4,5,7,1,2,6,3,8]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,6,1,7,5,2,4,8]=>[6,7,3,5,4,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[5,1,6,2,7,4,3,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,2,6,4,3,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,2,1,6,4,3,7,8]=>[6,3,2,5,4,1,7,8]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[5,4,2,1,6,3,7,8]=>[6,4,3,2,5,1,7,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,4,2,6,3,1,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,4,1,6,2,7,3,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,1,6,4,2,7,3,8]=>[7,2,5,4,3,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,6,1,7,5,4,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,6,1,5,4,3,7,8]=>[3,6,1,5,4,2,7,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,1,6,2,5,4,7,8]=>[4,2,6,1,5,3,7,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[5,1,6,4,3,2,7,8]=>[6,2,5,4,3,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,4,1,6,3,2,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,4,3,1,6,2,7,8]=>[6,4,3,2,5,1,7,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[7,3,1,6,5,4,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,2,8,1,5,4,3,6]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,2,7,6,5,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,8,2,6,5,4,1,7]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[7,3,2,1,5,4,6,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[7,2,8,6,1,4,3,5]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[5,2,7,6,8,4,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,2,8,7,6,5,9,1,3]=>[9,8,6,5,4,3,7,2,1]=>[9,8,6,5,4,3,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[3,8,7,2,5,4,1,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[8,4,1,7,6,5,9,3,2]=>[9,8,3,6,5,4,7,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[7,5,1,6,8,4,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,4,2,1,5,6,3,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,2,8,6,5,1,3,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,3,2,6,7,4,1,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,2,8,7,6,9,4,1,3]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[4,3,7,2,5,6,1,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,2,9,8,7,6,5,10,1,3]=>[10,9,7,6,5,4,3,8,2,1]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[6,7,1,4,3,2,5,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,4,2,6,7,1,5,8]=>[6,3,2,7,5,1,4,8]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[3,7,1,6,5,2,4,8]=>[6,7,3,5,4,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,5,6,2,4,7,1,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[3,5,8,7,2,4,6,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,7,8,2,5,4,3,6]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,2,5,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,1,6,3,5,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,5,3,8,7,2,6,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,4,5,3,7,8,2,6]=>[1,7,4,3,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,8,2,7,6,3,5]=>[1,7,8,4,6,5,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,7,3,5,1,8,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,7,3,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,8,7,4,6,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,4,2,1,7,8,3,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[4,7,8,3,5,2,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,7,6,2,1,8,3,5]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,4,6,7,3,5,8,2]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,3,6,2,1,7,5,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,3,7,6,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,3,1,8,4,7,6,5]=>[3,2,1,8,5,7,6,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,7,4,8,6,5,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,6,5,1,4,7,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,4,1,7,3,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,7,2,8,5,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,6,3,8,2,7,5,4]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,3,8,2,6,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,2,7,4,1,8,5,3]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,6,3,2,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,7,5,1,3,8,6,4]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,7,6,4,3,8,2,5]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,2,4,8,6,5,1]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,4,2,8,7,6,1,5]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[5,1,4,3,2,7,8,6]=>[5,2,4,3,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,7,8,5,2,4,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,7,6,2,4,1,8,5]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,6,8,2,5,7,4,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,7,2,5,8,4,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,2,7,8,4,3,1,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[5,3,1,7,8,4,2,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[2,7,6,4,1,3,8,5]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[4,1,7,6,3,2,8,5]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,4,2,7,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,1,7,5,2,8,4]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,2,7,5,3,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,5,8,2,7,4,6,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,2,8,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,3,1,8,4,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,7,3,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,8,5,7,4,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,5,2,1,7,4,8,3]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,7,4,6,2,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,6,4,8,3,7,2,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,7,1,8,3,4,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,3,5,1,4,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,2,7,1,8,3,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,7,2,4,3,8,1,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,4,3,8,6,7,1,5]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[1,8,2,7,4,5,3,6]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,4,8,3,6,1,7]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[2,3,1,8,5,6,4,7]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,8,5,6,4,7,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,3,6,4,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,2,3,1,6,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,7,2,4,3,6,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,6,2,7,1,5,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,7,1,6,2,5,3,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,7,1,5,3,6,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,6,3,5,1,7,2,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,7,3,5,1,4,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,6,3,7,1,4,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,7,1,6,3,4,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,8,5,6,3,4,2,7]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,6,4,7,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,1,6,4,8,2,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,6,5,8,1,7,2,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[3,7,1,4,2,8,5,6]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,5,1,4,2,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,6,5,8,3,7,1,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,6,5,8,2,3,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[3,4,2,6,5,8,1,7]=>[7,3,2,5,4,8,1,6]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[3,5,4,6,2,8,1,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,8,3,5,4,7,2,6]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,4,2,7,1,8,5,6]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,7,2,3,1,8,5,6]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[2,4,3,8,1,7,5,6]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[2,5,3,8,4,7,1,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[2,6,3,8,1,7,4,5]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,7,1,8,3,6,4,5]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,2,8,7,4,6,3,5]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,4,8,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,1,8,7,6,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,5,2,8,7,6,3,4]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,2,8,7,6,3,4]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,5,8,7,6,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,6,8,7,4,5,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,7,8,6,4,5,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,5,7,8,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,6,8,2,7,3,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,2,6,8,3,7,4,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[3,1,6,8,7,4,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,4,8,7,2,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,8,4,7,3,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,8,3,4,7,1,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,3,5,7,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,1,7,8,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,2,7,8,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,7,8,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,5,2,8,6,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,8,4,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,4,5,2,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,2,5,3,7,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,8,4,2,7,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,5,3,8,6,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,4,7,5,8,6,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,7,4,8,5,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,4,2,8,5,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,7,5,2,8,6,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,7,5,3,8,6,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,2,8,3,7,4,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,7,8,3,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,8,3,2,7,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,8,4,2,7,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,5,8,2,7,3,6,4]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,4,7,2,3,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,8,1,3,7,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,4,8,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,2,8,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,4,8,6,2,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,2,8,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,3,7,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,2,3,7,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,3,8,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,2,3,8,6,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,7,4,5,8,6,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,3,4,8,5,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,4,7,8,5,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,2,7,8,5,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,2,5,8,6,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,1,8,3,4,7,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,8,4,2,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,3,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,5,8,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,4,7,8,5,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,1,7,3,4,5,8,2]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,2,3,4,1,8,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[2,7,1,8,4,5,6,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,6,8,3,4,5,1,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[2,8,9,3,4,5,6,7,1]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[7,1,8,3,4,5,6,9,2]=>[9,2,7,6,5,4,3,8,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[6,1,2,7,4,5,8,3]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,7,2,3,1,5,8,6]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[2,7,1,3,8,5,6,4]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,6,7,8,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,1,9,4,5,6,7,3]=>[3,9,1,8,7,6,5,4,2]=>[3,9,1,8,7,6,5,4,2]=>[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]
[2,5,8,3,4,1,6,7]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[6,7,8,3,4,5,2,9,1]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[5,6,2,7,4,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,6,7,3,2,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,6,7,3,8,5,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,6,1,8,4,5,3,7]=>[3,7,1,8,6,5,2,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,5,7,8,4,3,6,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,7,8,9,4,5,6,3,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[3,6,8,4,5,7,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,8,4,7,2,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,7,8,2,6,3]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,4,5,7,8,6,1,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,4,5,7,6,8,1,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,7,4,8,5,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,4,5,6,8,7,1,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,2,5,8,3,6,4,7]=>[1,2,7,8,5,6,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,1,4,6,2,3,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,6,7,4,8,2,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,8,6,2,7,3]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,8,3,4,7,6]=>[1,2,6,8,5,3,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,2,3,5,8,4]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,1,2,3,5,4,6]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,6,7,2,3,5,4,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,7,6,2,3,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,7,3,6,4,8]=>[1,2,7,6,5,4,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,7,3,6,8,4]=>[1,2,8,6,5,4,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,2,3,5,7,4]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,4,5,2,3,7]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,4,5,2,7,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,2,3,4,7,5]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,2,3,7,4,5]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,7,6,2,8,3]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,1,4,5,2,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,1,2,3,4,6,5]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,1,2,3,6,4,5]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,6,7,2,3,8,5,4]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,6,3,8,7,4]=>[1,2,8,5,4,7,6,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,2,1,6,5,3,8,7]=>[6,3,2,5,4,1,8,7]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[8,2,4,3,1,6,5,7]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[6,2,4,3,1,8,7,5]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,2,6,3,5,1,8,7]=>[6,4,5,2,3,1,8,7]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[4,6,2,1,5,8,7,3]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,6,5,2,1,8,7,3]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[2,1,6,4,3,8,7,5]=>[2,1,8,5,4,7,6,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[4,8,2,1,6,7,3,5]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[6,8,2,1,4,3,7,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,6,2,4,3,1,5,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,2,4,3,1,7,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,7,2,4,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,8,4,6,5,3,7]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,6,4,8,5,7,3]=>[2,1,8,6,7,4,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[4,6,5,2,8,3,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[2,6,4,5,8,3,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,4,2,8,3,5,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[8,4,2,6,3,5,1,7]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,2,4,8,5,3,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[4,2,6,3,5,8,7,1]=>[8,4,5,2,3,7,6,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,2,6,3,8,7,5,1]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,2,4,3,8,5,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[8,2,4,3,6,5,1,7]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,2,1,4,6,5,3,7]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,2,1,4,8,5,7,3]=>[8,3,2,6,7,4,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,2,1,8,7,4,3,5]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,2,1,8,4,3,7,5]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,4,6,5,2,1,3,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,8,5,2,1,7,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,4,8,5,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,8,7,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,4,8,6,7,3,5]=>[2,1,7,8,6,5,3,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,6,8,7,4,5,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,4,8,6,7,5,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,2,8,6,5,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,6,4,5,1,3,7]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,4,6,2,1,5,3,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,8,7,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,5,8,2,1,7,3]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[2,1,6,8,4,3,7,5]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,8,7,4,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,6,4,7,1,3,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[4,8,6,2,1,7,3,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,8,5,3,1,4,6,7]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,7,4,8,3,5,1,6]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[2,7,4,8,3,5,6,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,2,8,4,3,5,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,2,1,5,3,6,7]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[8,5,1,4,2,3,6,7]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,4,1,5,3,2,6,7]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,7,3,8,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,3,8,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,8,4,3,5,2,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,8,4,3,5,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,4,8,3,5,2,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,8,1,5,6,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,1,8,4,3,5,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,7,3,1,8,4,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,3,8,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,1,4,8,3,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,4,1,3,8,2,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,6,7,8,4,3,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,1,8,4,5,3,6]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,2,7,1,8,4,3,5]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,2,7,8,4,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,7,8,4,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,7,4,8,3,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,6,7,4,8,3,1,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[7,8,1,3,6,2,4,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,2,7,8,6,3,4,5]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,7,1,8,5,3,4]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,6,7,8,5,3,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,6,7,8,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,7,8,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,1,8,4,5,6,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,7,2,8,4,5,6,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,8,1,5,6,2,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,3,7,8,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,1,2,8,5,3,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,6,7,8,4,2,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,7,6,5,8,4]=>[3,2,1,8,6,5,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[6,1,2,4,7,3,8,5]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,5,3,6,4,8,2]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,2,6,7,4,8,3]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,6,1,7,3,2,5,8]=>[6,7,3,5,4,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,6,1,8,3,2,5,7]=>[6,7,3,8,5,1,2,4]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,7,1,8,3,5,2,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,1,7,8,6,2,3,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,6,5,7,8,3,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,5,8,7,3,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,8,7,6,2,3,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,8,1,7,3,5,2,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,8,1,6,3,2,5,7]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,7,1,6,3,2,5,8]=>[6,7,3,5,4,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[6,1,2,3,7,5,4,8]=>[7,2,3,4,6,5,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,8,1,5,3,7,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,5,2,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,5,7,3,4,8,6,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,3,4,7,6,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,5,2,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,2,3,5,6,4,8]=>[7,2,3,4,6,5,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,1,2,3,5,6,4,7]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,4,6,3,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,8,2,4,3,1,5,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,7,2,4,3,1,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,8,1,2,4,5,7,6]=>[4,8,3,1,5,6,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,7,1,8,6,4,2,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[1,6,4,3,7,5,8,2]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,6,7,5,8,4]=>[3,2,1,8,6,5,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,8,1,7,6,4,2,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[7,6,2,4,3,1,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,7,2,4,3,5,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,7,4,6,3,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,6,5,3,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,5,7,3,4,6,8,2]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,2,5,3,6,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,2,3,5,8,4,7]=>[7,2,3,4,5,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,1,2,3,5,7,4,8]=>[7,2,3,4,5,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,2,3,7,6,4,8]=>[7,2,3,4,6,5,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,2,3,8,6,4,7]=>[7,2,3,4,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,5,6,3,4,7,8,2]=>[1,8,5,4,3,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,5,2,4,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,2,5,3,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,4,5,2,3,8,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,2,3,7,4,5,1,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,7,3,2,5,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,6,3,1,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,6,2,3,1,5,8,7]=>[5,6,4,3,1,2,8,7]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[7,2,3,4,5,8,6,1]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,2,3,4,5,7,1,6]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,3,4,6,8,5,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,7,3,2,8,6,1,5]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[3,7,4,5,1,8,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,8,2,6,7,4,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,8,1,5,6,7,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,2,4,6,7,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,1,3,4,2,7,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,2,4,3,1,7,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[2,1,7,6,8,5,3,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,7,6,1,8,5,2,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,7,2,3,8,5,1,6]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[7,1,3,6,4,8,5,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,1,4,8,5,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,2,3,7,8,5,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,2,3,8,4,5,1,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,2,3,6,8,4,1,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,2,3,5,7,1,4,6]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,4,8,3,5,1,7,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,4,8,3,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,5,1,8,4,6,7,2]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,6,1,8,4,5,2,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,6,8,3,5,2,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,7,8,3,2,4,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,8,2,3,5,6,1,7]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[6,8,2,3,1,4,5,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[5,2,7,4,8,3,1,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[3,7,8,2,1,4,6,5]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,7,5,2,8,4,1,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,3,2,4,1,8,7,5]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,2,3,4,8,5,1,6]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,7,3,1,4,2,6,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[3,7,4,1,8,2,5,6]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[6,3,7,4,8,1,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,7,4,2,6,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,4,1,5,6,2,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,8,3,2,4,5,7,6]=>[1,8,4,3,5,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,4,1,6,3,7,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,4,2,1,6,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,5,2,7,4,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,5,3,8,7,6,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,4,8,1,3,6,5]=>[8,5,6,7,2,3,4,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,2,8,7,5,6,3,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,8,6,7,5,2,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,4,8,6,5,7,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,5,4,8,2,3,7]=>[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,6,8,3,4,2,7]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,2,5,1,7,4,3,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[5,2,1,8,7,4,3,6]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[5,2,6,3,8,1,4,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[5,2,8,3,4,6,1,7]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[6,2,8,4,3,1,7,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,2,8,1,3,6,5,4]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,3,8,1,4,6,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,7,8,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,4,6,3,7,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,3,8,4,1,2,7,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[5,8,4,3,6,2,1,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,8,3,6,5,2,7,4]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,4,7,6,5,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,8,1,4,6,7,5,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,2,5,1,7,6,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,3,8,2,5,1,6,7]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[8,2,4,3,5,1,7,6]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[8,2,1,4,6,5,7,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,1,3,4,5,7,6,2]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,5,2,4,7,8,3]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,8,5,2,7,6,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,8,5,1,3,6,2,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[3,6,1,5,7,2,8,4]=>[6,8,3,4,5,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[6,3,1,2,8,5,7,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,1,8,2,3,7,5,6]=>[5,2,8,4,1,7,6,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[5,3,8,7,2,1,4,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[6,7,3,5,1,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,4,7,5,8,2,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,8,4,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,7,6,2,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,4,1,6,8,3,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,8,4,5,7,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,4,6,1,7,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,1,4,7,8,3,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,6,7,2,4,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,3,7,4,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,3,6,7,4,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,3,2,8,6,7,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,8,2,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,4,8,6,2,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,8,5,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,8,5,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,8,5,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,8,2,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,3,8,4,7,2,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,6,3,5,8,7,2,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,6,3,2,8,7,5,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,6,3,8,2,7,4,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[3,6,5,8,7,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,6,8,2,7,4,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,3,7,2,8,6,5,1]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[5,4,7,2,6,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,3,2,7,6,8,4,1]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,3,8,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,2,7,5,4,8,1]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,4,7,2,5,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,2,7,5,1,4,8,3]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[2,7,8,5,3,6,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,3,7,8,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,7,8,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,7,8,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,2,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,8,4,3,7,6,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[2,6,8,4,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,4,8,6,2,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,6,4,8,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,4,8,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,3,7,5,8,6,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,7,3,8,6,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,5,6,8,4,7,2,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,3,1,8,7,5,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,8,1,7,6,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,4,1,7,6,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,4,1,8,6,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,4,1,7,6,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,8,2,5,6,3,4,7]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,8,4,5,1,3,6]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,6,7,4,3,5,2,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,2,3,7,4,6]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,5,3,6,7,4]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,8,4,3,5,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,5,8,3,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,8,4,1,5,6,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[7,5,8,1,2,6,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,6,7,4,3,2,8,5]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,6,4,7,8,3]=>[1,8,3,5,4,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,4,6,2,3,7,8]=>[1,6,5,4,3,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,2,5,7,1,4,8,3]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,5,4,3,8,1,7,2]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,3,6,8,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,8,3,6,5,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,7,8,5,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,5,8,3,4,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[2,6,5,7,3,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,2,5,7,4,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,2,5,8,4,1,3,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[2,7,8,4,6,1,3,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[6,1,2,8,3,7,4,5]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,2,8,5,4,7,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,2,5,7,8,1,3,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[2,6,5,7,3,8,1,4]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,6,2,7,5,8,4,3]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,7,8,5,6,4]=>[1,3,2,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,2,4,8,7,3,5]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,5,2,1,8,7,3,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,6,5,3,7,8,4,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,2,5,3,8,4,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,5,2,3,8,7,1,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,4,1,2,3,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,1,4,2,3,7,8,6]=>[5,2,4,3,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[5,1,6,3,8,2,7,4]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[9,8,7,6,5,4,3,1,2,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[8,7,6,5,4,2,1,3,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[8,7,6,5,4,1,3,2,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,9,8,7,6,5,3,2,4]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,8,7,6,2,5,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,9,8,7,6,5,2,4,3]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,10,9,8,7,6,5,4,2,3]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[2,1,9,8,7,6,5,4,3]=>[2,1,9,8,7,6,5,4,3]=>[2,1,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,9,8,7,6,5,4,3]=>[1,2,9,8,7,6,5,4,3]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[3,2,1,9,8,7,6,5,4]=>[3,2,1,9,8,7,6,5,4]=>[3,2,1,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[1,3,2,9,8,7,6,5,4]=>[1,3,2,9,8,7,6,5,4]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,9,8,7,6,5,4]=>[1,2,3,9,8,7,6,5,4]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,3,2,1,9,8,7,6,5]=>[4,3,2,1,9,8,7,6,5]=>[4,3,2,1,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[1,4,3,2,9,8,7,6,5]=>[1,4,3,2,9,8,7,6,5]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,4,3,9,8,7,6,5]=>[2,1,4,3,9,8,7,6,5]=>[2,1,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,3,9,8,7,6,5]=>[1,2,4,3,9,8,7,6,5]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,9,8,7,6,5]=>[1,2,3,4,9,8,7,6,5]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,5,4,3,2,9,8,7,6]=>[1,5,4,3,2,9,8,7,6]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,5,4,3,9,8,7,6]=>[2,1,5,4,3,9,8,7,6]=>[2,1,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,4,3,9,8,7,6]=>[1,2,5,4,3,9,8,7,6]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,3,2,5,4,9,8,7,6]=>[1,3,2,5,4,9,8,7,6]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,5,4,9,8,7,6]=>[1,2,3,5,4,9,8,7,6]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,5,9,8,7,6]=>[1,2,3,4,5,9,8,7,6]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,3,2,6,5,4,9,8,7]=>[1,3,2,6,5,4,9,8,7]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,6,5,4,9,8,7]=>[1,2,3,6,5,4,9,8,7]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,4,3,6,5,9,8,7]=>[2,1,4,3,6,5,9,8,7]=>[2,1,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,3,6,5,9,8,7]=>[1,2,4,3,6,5,9,8,7]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,6,5,9,8,7]=>[1,2,3,4,6,5,9,8,7]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,5,4,7,6,9,8]=>[1,2,3,5,4,7,6,9,8]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,5,7,6,9,8]=>[1,2,3,4,5,7,6,9,8]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,10,9,8,7,6,5,4,3]=>[1,2,10,9,8,7,6,5,4,3]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[3,2,1,10,9,8,7,6,5,4]=>[3,2,1,10,9,8,7,6,5,4]=>[3,2,1,10,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,10,9,8,7,6,5,4]=>[1,3,2,10,9,8,7,6,5,4]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,10,9,8,7,6,5,4]=>[1,2,3,10,9,8,7,6,5,4]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,4,3,2,10,9,8,7,6,5]=>[1,4,3,2,10,9,8,7,6,5]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,4,3,10,9,8,7,6,5]=>[1,2,4,3,10,9,8,7,6,5]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,4,10,9,8,7,6,5]=>[1,2,3,4,10,9,8,7,6,5]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,5,4,3,2,10,9,8,7,6]=>[1,5,4,3,2,10,9,8,7,6]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[2,1,5,4,3,10,9,8,7,6]=>[2,1,5,4,3,10,9,8,7,6]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,5,4,3,10,9,8,7,6]=>[1,2,5,4,3,10,9,8,7,6]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,3,2,5,4,10,9,8,7,6]=>[1,3,2,5,4,10,9,8,7,6]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,5,4,10,9,8,7,6]=>[1,2,3,5,4,10,9,8,7,6]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,6,5,4,3,10,9,8,7]=>[1,2,6,5,4,3,10,9,8,7]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[3,2,1,6,5,4,10,9,8,7]=>[3,2,1,6,5,4,10,9,8,7]=>[3,2,1,10,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,6,5,4,10,9,8,7]=>[1,3,2,6,5,4,10,9,8,7]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,6,5,4,10,9,8,7]=>[1,2,3,6,5,4,10,9,8,7]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,4,3,6,5,10,9,8,7]=>[1,2,4,3,6,5,10,9,8,7]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,4,6,5,10,9,8,7]=>[1,2,3,4,6,5,10,9,8,7]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,4,5,6,10,9,8,7]=>[1,2,3,4,5,6,10,9,8,7]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,4,3,2,7,6,5,10,9,8]=>[1,4,3,2,7,6,5,10,9,8]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[2,1,4,3,7,6,5,10,9,8]=>[2,1,4,3,7,6,5,10,9,8]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,4,3,7,6,5,10,9,8]=>[1,2,4,3,7,6,5,10,9,8]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,4,7,6,5,10,9,8]=>[1,2,3,4,7,6,5,10,9,8]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,3,2,5,4,7,6,10,9,8]=>[1,3,2,5,4,7,6,10,9,8]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,5,4,7,6,10,9,8]=>[1,2,3,5,4,7,6,10,9,8]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,4,5,7,6,10,9,8]=>[1,2,3,4,5,7,6,10,9,8]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,4,5,6,7,10,9,8]=>[1,2,3,4,5,6,7,10,9,8]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,4,3,6,5,8,7,10,9]=>[1,2,4,3,6,5,8,7,10,9]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,4,6,5,8,7,10,9]=>[1,2,3,4,6,5,8,7,10,9]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,4,5,6,8,7,10,9]=>[1,2,3,4,5,6,8,7,10,9]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[5,2,7,4,1,6,3,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[4,7,3,1,5,6,2,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[5,8,3,4,1,6,7,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,7,8,4,5,6,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,4,2,6,7,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,3,8,5,2,7,4]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,2,3,7,1,6,4,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,2,3,7,5,1,4,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,7,3,4,8,6,2,5]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,2,3,4,8,1,7,5]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,7,3,2,1,6,5,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,7,6,3,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,1,7,2,3,4,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[9,8,7,6,5,2,1,4,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,3,2,1,6,5,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,6,3,1,5,2,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,4,3,1,7,6,2,5]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[9,8,7,2,1,4,3,6,5]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[9,8,7,4,1,6,2,3,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,9,8,7,6,5,2,1,4,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,3,2,1,6,5,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,6,3,1,5,2,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,4,3,2,1,8,7,6,5]=>[10,9,6,5,4,3,8,7,2,1]=>[10,9,6,5,4,3,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.]
[10,9,8,4,3,1,7,6,2,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,2,1,4,3,6,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,4,1,6,2,3,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,5,2,1,8,4,3,7,6]=>[10,9,8,5,4,7,6,3,2,1]=>[10,9,8,5,4,7,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[10,9,5,4,1,8,7,2,3,6]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[10,9,8,3,1,5,2,7,4,6]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[10,6,5,1,9,8,2,3,4,7]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[10,9,2,1,4,3,6,5,8,7]=>[10,9,4,3,6,5,8,7,2,1]=>[10,9,4,3,8,7,6,5,2,1]=>[[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.]
[10,9,6,1,8,2,3,4,5,7]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[2,4,8,5,3,7,1,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[2,4,1,8,5,3,7,6]=>[3,6,1,8,5,2,7,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,8,6,3,1,7,5]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[3,4,6,8,2,1,7,5]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[8,1,4,5,3,2,7,6]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,4,1,5,2,8,7,6]=>[5,3,2,4,1,8,7,6]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,4,6,2,1,8,7,5]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[3,5,6,2,1,7,8,4]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,4,6,2,7,8,1,5]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[8,1,4,6,3,7,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,6,3,7,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,5,6,7,3,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,5,6,7,3,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,4,1,6,8,7,2,5]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[3,5,6,1,8,7,2,4]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[2,1,3,8,6,7,4,5]=>[2,1,3,8,7,6,5,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,1,3,2,6,7,5,4]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,8,6,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,4,1,8,6,7,5,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,5,8,6,1,7,4,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[3,5,6,1,8,7,4,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,4,1,6,8,7,5,2]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,4,6,8,7,1,5,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,1,4,6,2,7,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,5,1,6,7,8,4,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,5,6,1,7,8,3,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,5,6,1,7,3,8,2]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[3,5,1,6,7,4,8,2]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,1,5,6,7,4,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,5,6,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,5,1,6,7,4,2,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,5,6,1,7,3,2,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,5,8,7,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,2,7,8,5,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,1,4,8,7,5,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,4,8,7,5,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,6,2,4,7,3,5]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,6,2,4,7,3,5]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,2,1,4,8,3,5]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,4,1,7,8,5,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,1,2,4,8,3,5]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,1,3,4,8,2,5]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,6,3,4,7,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,6,3,4,7,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,5,4,8,3,6]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,2,5,4,8,3,6]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,7,1,5,4,8,3,6]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,8,6,3,4,7,1,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,8,6,1,4,7,3,5]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[7,2,1,5,4,8,3,6]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,2,7,5,4,8,3,6]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,7,5,4,8,1,6]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,5,8,4,7,3,1,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[2,3,7,5,4,8,1,6]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,8,3,2,4,7,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,7,2,5,4,8,1,6]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,1,7,5,4,8,2,6]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,3,7,5,4,8,2,6]=>[1,7,8,5,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,4,7,3,2,6]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,8,4,7,3,2,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,8,2,4,7,3,1,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,8,4,3,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,5,6,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,2,4,7,3,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,5,4,7,3,2,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,5,4,7,3,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,5,4,8,2,6]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,3,1,4,7,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,4,2,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,4,1,7,2,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,7,4,6,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,1,3,2,7,8,5,6]=>[4,2,3,1,8,7,6,5]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,4,3,2,7,8,5,6]=>[1,4,3,2,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,3,1,7,8,5,6]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[2,7,3,5,4,8,1,6]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,8,5,4,7,3,1,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,7,3,4,6,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,2,5,4,7,3,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,3,5,4,8,1,6]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,2,1,4,7,8,5,6]=>[3,2,1,4,8,7,6,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[8,1,7,6,4,3,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,4,5,2,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,8,6,4,3,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,2,5,1,6,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,3,6,5,2,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,3,6,5,2,1,7,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,3,6,5,2,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,8,6,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,2,8,1,3,7,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,8,2,6,4,1,3,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,4,2,5,1,8,3,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,3,5,2,1,4,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[2,5,8,6,3,1,4,7]=>[6,7,8,5,4,1,2,3]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,3,5,8,1,4,7,6]=>[5,2,6,8,1,3,7,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,6,8,1,5,7,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[6,3,8,5,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,7,5,2,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[2,5,7,6,3,1,4,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[2,8,7,6,3,1,5,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,5,8,7,6,3,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,4,8,1,6,5,7,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,8,7,3,6,1,4,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[7,3,5,2,1,4,6,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[8,4,2,5,1,3,7,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,3,6,8,1,4,7,5]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,7,8,6,3,1,4,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[7,3,8,5,2,1,4,6]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,3,6,1,8,4,7,5]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,8,6,3,1,4,5,7]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[8,3,5,2,1,4,6,7]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[2,4,8,1,3,7,5,6]=>[4,5,8,1,2,7,6,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,5,8,1,7,3,6,4]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,8,1,5,7,3,6,4]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[8,3,6,1,4,7,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,6,1,4,7,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,6,8,1,5,7,3,4]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,7,1,5,8,3,4,6]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,7,1,6,3,8,4,5]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[4,7,6,1,8,5,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,7,5,8,1,2,6,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[7,3,6,1,2,8,4,5]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[7,4,8,1,6,5,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,6,1,8,2,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,5,8,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,4,5,1,7,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,8,5,1,7,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,7,6,2,3,8,4]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,7,6,2,8,3,4]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,8,7,6,2,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,5,1,7,6,2,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,1,6,2,7,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,1,8,4,7,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,6,1,8,7,5,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,6,1,7,5,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,5,1,7,2,3,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,5,1,8,7,2,3,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,4,8,7,1,2,5,6]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[5,8,4,1,7,2,3,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[8,6,4,7,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,8,7,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,8,3,7,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,7,1,2,8,5,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,5,1,2,7,3,8,4]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,5,1,8,2,7,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,5,1,2,7,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,5,1,7,2,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,1,8,7,2,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,5,1,7,2,8,3,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,5,1,7,2,3,8,4]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,7,4,1,8,2,3,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,6,8,7,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,7,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,8,1,5,2,4,6]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,1,7,5,3,6,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,8,4,2,3,6,7,5]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,8,3,4,6,7,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,1,7,2,3,6,8,5]=>[5,2,8,4,1,6,7,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,6,2,1,5,7,8,3]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,5,2,3,1,7,8,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,2,6,7,4,1,8,5]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,6,2,7,1,4,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,2,3,8,1,7,4,5]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,6,8,3,4,7,1,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,6,2,7,5,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[2,6,3,1,8,4,5,7]=>[4,7,3,1,8,6,2,5]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,4,3,7,8,1,5,6]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[5,3,2,7,4,8,1,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,1,2,7,6,8,4,3]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,6,3,1,8,7,4,5]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,5,6,4,7,8,1,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,3,6,4,2,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,4,2,3,7,8,6,1]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,1,8,2,5,7,3,6]=>[7,2,8,4,5,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,1,8,4,7,2,5,6]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,2,3,8,4,1,7,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,6,4,1,5,3,8,7]=>[4,6,5,1,3,2,8,7]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,2,7,6,4,1,8,5]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,5,4,1,7,6,8,3]=>[4,8,3,1,6,5,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[6,2,1,4,7,8,3,5]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,6,5,1,7,8,3,4]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,7,5,2,1,6,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,2,3,7,8,1,6,5]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[5,8,3,1,7,2,4,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,8,3,1,5,2,4,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,2,7,1,6,3,5,8]=>[6,4,7,2,5,1,3,8]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[5,1,7,4,2,6,3,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,8,4,2,1,5,3,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,8,5,2,1,7,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,2,1,4,7,3,6]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[6,8,3,2,5,1,7,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,4,3,1,5,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,4,2,1,5,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,3,2,1,4,5,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[5,2,1,8,3,6,7,4]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,3,8,1,6,2,7,5]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[5,4,7,2,1,6,8,3]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,2,1,7,3,4,8,6]=>[6,3,2,8,5,1,7,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[6,4,3,1,7,5,8,2]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,3,1,7,2,6,8,4]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,2,1,7,6,4,8,5]=>[3,2,1,8,6,5,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[4,2,1,6,5,8,3,7]=>[7,3,2,5,4,8,1,6]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[4,2,1,8,5,7,3,6]=>[7,3,2,8,5,6,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[7,4,3,1,8,5,6,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,4,2,1,8,5,6,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,3,2,1,7,4,5,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[6,4,2,1,7,5,3,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,5,2,1,8,6,3,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,1,8,4,2,7,3,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,2,1,8,3,7,4,5]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[5,3,2,7,6,1,4,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,3,2,8,6,1,4,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,3,2,8,7,1,4,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,2,8,1,7,3,5,6]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[4,3,8,7,2,1,5,6]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[2,1,5,8,4,7,3,6]=>[2,1,7,8,5,6,3,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[4,3,1,6,2,7,5,8]=>[5,3,2,7,1,6,4,8]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,3,1,7,2,8,5,6]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[5,4,1,7,2,8,6,3]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,5,3,1,7,8,4,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,4,2,1,7,8,3,5]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,4,2,1,7,8,5,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,3,2,6,8,1,7,4]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,2,1,4,8,7,5,6]=>[3,2,1,4,8,7,6,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,4,6,8,5,7]=>[3,2,1,4,7,8,5,6]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[4,3,2,6,1,7,8,5]=>[5,3,2,8,1,6,7,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[5,3,2,1,6,7,8,4]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,6,1,4,5,7,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,6,4,5,7,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,8,3,7,4,6,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,2,8,5,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,6,3,7,4,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,6,5,7,2,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,2,8,4,3,6,7,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,4,2,7,3,6,1,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,4,2,8,3,6,1,7]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,5,3,8,4,7,2,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,2,8,4,3,7,1,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[6,2,8,3,7,4,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,4,2,7,3,1,8,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,4,3,7,1,2,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,4,3,8,1,2,7,5]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[7,6,3,8,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,8,5,1,6,3,4]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[7,2,8,4,3,1,5,6]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,5,3,8,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,2,7,3,1,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,4,8,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,8,1,2,5,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,1,7,8,4,6,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,3,2,7,8,4,6,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,4,1,6,3,8,7,2]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,5,1,7,8,2,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,3,1,7,8,4,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,1,7,3,8,2,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,3,2,7,8,4,1,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,1,5,4,3,2,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,7,6,1,3,5,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,6,5,7,3,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,1,5,7,6,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,6,2,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,3,5,2,8,4,7]=>[7,2,5,4,3,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,1,3,7,4,2,5,6]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,3,8,7,5,2,1,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[6,7,1,8,5,3,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,7,6,4,8,3,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,2,7,1,4,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,4,6,1,3,2,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,2,1,3,8,4,6]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,4,7,6,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,1,5,6,3,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,4,7,5,6,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,4,7,5,6,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,4,1,7,6,2,8,3]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,5,6,7,1,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,7,6,1,3,4,8,5]=>[4,8,6,1,5,3,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[5,7,2,1,6,3,8,4]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,7,2,5,6,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,6,2,5,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,4,5,3,8,1,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[6,8,7,1,3,2,5,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,6,5,7,1,4,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[5,8,4,3,2,6,7,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,8,5,6,2,4,7,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,5,6,2,4,7,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,8,1,3,2,7,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[2,3,1,7,8,6,4,5]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,5,7,6,2,8,1,4]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[4,5,6,1,2,8,7,3]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,4,1,2,8,6,7,3]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,4,5,2,1,6,7,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,1,2,6,8,4,7,5]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[5,1,3,2,7,8,4,6]=>[7,2,4,3,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,5,4,2,7,8,3,6]=>[1,7,4,3,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,7,8,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,2,8,4,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,8,6,3,4,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,6,8,4,3,2,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,3,8,1,7,2,4,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[3,6,7,8,4,2,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,5,1,8,4,3,7,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,3,8,4,2,1,7,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,5,8,3,1,6,7,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,5,8,1,2,6,7,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,2,8,1,5,6,7,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,5,8,3,2,6,7,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,6,2,4,7,5]=>[1,5,8,7,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,7,8,4,6,1,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,8,3,4,6,7,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,8,7,2,1,6,3,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,8,1,6,3,4,7,5]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[8,3,4,2,1,6,5,7]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[6,4,7,2,5,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,4,5,2,6,3,1,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,4,5,8,3,6,1,7]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,5,8,1,2,6,4,7]=>[5,7,8,4,1,6,2,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[8,6,1,3,5,2,4,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,1,2,6,4,3,7]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,6,1,3,4,2,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,8,4,6,1,3,2,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[7,3,4,5,2,8,1,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,4,3,6,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,6,4,3,7,8,5,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,4,1,8,3,2,5,6]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,2,1,7,8,4,5,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,6,3,1,5,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,4,6,5,1,7,8,3]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[1,4,7,5,6,8,2,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,6,5,8,2,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,5,2,4,6,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,6,1,7,4,2,8,3]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,7,4,8,1,2,6,5]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[6,3,5,7,8,1,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,5,7,1,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,4,7,8,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,3,8,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,8,3,4,6,1,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[7,5,8,4,1,3,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,5,8,3,1,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,6,7,4,8,1,2,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,7,3,1,6,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,7,3,1,8,6,4,5]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,8,4,3,1,5,7,6]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[4,8,1,2,3,5,7,6]=>[5,8,3,4,1,6,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[7,6,8,1,2,4,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,8,5,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,5,4,6,1,7,3]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[8,4,5,2,7,6,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,6,4,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,1,3,5,2,8,4]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,7,2,3,6,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,3,2,7,6,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,4,6,7,5,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,4,5,7,6,1,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,6,4,5,7,8,3,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,8,5,1,6,2,7,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[5,4,6,1,3,7,8,2]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[6,3,5,7,1,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,3,4,6,8,1,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,2,8,4,1,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,6,4,1,8,2,5]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[3,7,8,4,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,5,4,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,8,6,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,1,6,7,3,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,2,5,1,8,4,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,8,2,1,6,7,4,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,5,2,8,6,3,7,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,4,5,8,2,3,7,6]=>[1,6,5,8,3,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,4,5,8,3,7]=>[1,2,7,5,4,8,3,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,4,6,8,3,7]=>[1,7,3,4,5,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,1,5,8,2,4,7]=>[6,7,3,4,8,1,2,5]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,6,5,1,4,8,3,7]=>[4,7,5,1,3,8,2,6]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[5,2,6,1,4,8,3,7]=>[7,4,5,2,3,8,1,6]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[2,5,1,8,4,7,3,6]=>[3,7,1,8,5,6,2,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,7,1,4,3,6,8,5]=>[3,8,1,5,4,6,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,3,7,5,8,2,4,6]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,1,5,7,3,4,6]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,5,4,8,1,3,7,6]=>[5,6,3,8,1,2,7,4]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,4,1,3,8,6,7,5]=>[3,4,1,2,8,7,6,5]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[8,4,3,7,1,2,6,5]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,7,3,5,8,2,6,4]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,4,2,6,7,3,5]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,6,8,7,2,4,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[7,2,1,6,8,3,4,5]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,1,7,6,8,2,4,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,1,7,2,6,8,3,5]=>[7,2,8,4,5,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,7,2,3,6,8,4]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,6,1,7,3,5,8,4]=>[3,8,1,6,5,4,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[7,1,2,5,3,6,8,4]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,4,1,2,7,8,3,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[7,3,1,2,4,6,8,5]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,5,8,1,2,7,4,6]=>[5,7,8,4,1,6,2,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,6,8,1,2,4,7,5]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[4,1,3,8,7,2,6,5]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,3,7,4,8,2,6,5]=>[1,6,8,4,7,2,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,8,2,3,7,5]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,8,1,7,2,4,6]=>[6,7,8,4,5,1,2,3]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,6,8,1,7,3,4,5]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[6,1,5,8,2,3,7,4]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,7,2,8,5,6,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,6,7,3,8,1,5,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[8,4,1,7,3,6,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,7,2,8,6,1,5,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[6,2,3,8,7,1,5,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,1,7,8,4,2,6,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,8,7,4,2,6,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,7,2,8,3,6,5,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,1,7,8,5,3,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,7,4,8,3,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,8,7,5,3,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,8,2,7,3,6,5,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,7,2,6,3,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,8,2,4,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,2,4,3,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,8,2,7,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,2,4,1,5,6]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[3,7,8,2,4,1,5,6]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[3,6,8,2,4,5,7,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[3,6,7,2,4,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,5,1,4,2,3,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[8,6,1,7,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,6,1,2,3,5,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,4,3,1,6,2,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[8,3,4,7,1,6,2,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,3,4,1,8,5,2,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[3,8,5,2,7,1,6,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,8,6,7,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,8,7,3,6,4,5]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,6,5,8,2,4,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[5,2,1,8,7,3,4,6]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[6,5,2,7,4,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,6,5,2,7,3,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,2,7,1,8,3,5,4]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,7,5,4,8,3,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,5,1,2,6,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,3,2,7,1,6,5]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,1,6,2,3,8,5,4]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,8,1,3,2,7,5,6]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,8,1,4,7,5,2,6]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[6,3,8,7,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,4,8,5,2,3,7]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,5,7,4,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,7,8,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,4,6,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,1,3,5,2,8,4]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,8,3,2,4,6,1,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[8,2,6,5,3,1,7,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,8,7,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,8,6,4,3,7,5]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,7,6,5,3,8,4]=>[2,1,8,6,5,4,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,7,6,1,3,5,8,4]=>[4,8,6,1,5,3,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[7,2,5,4,6,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,7,6,1,2,5,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,4,1,7,6,8,5,3]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,4,1,7,8,5,6,2]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,5,4,3,1,8,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,6,2,7,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,2,5,6,1,7,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,5,4,1,7,8,2]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,1,3,6,7,5,8,2]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,5,3,8,2,4,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,4,5,8,3,6]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,5,3,1,6,4,7]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,7,4,5,8,3,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,4,7,8,3,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,6,4,7,8,3,1,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,2,6,4,7,8,3,5]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,4,5,8,1,3,6]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,7,5,3,1,8,4,6]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[6,1,4,7,8,3,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,6,4,7,8,1,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,3,6,7,1,8,5,2]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,3,6,7,1,8,2,5]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[3,6,4,7,8,1,2,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,3,6,4,1,7,8,5]=>[5,2,8,4,1,6,7,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,7,2,1,5,3,8,6]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[3,7,4,5,2,1,8,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,3,6,4,7,2,8,5]=>[1,6,8,4,5,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,4,7,2,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,1,3,4,2,7,8,6]=>[5,2,4,3,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[5,4,2,1,3,7,8,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[6,1,7,3,8,2,5,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,7,3,8,2,5,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,4,7,8,5,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,3,2,1,7,8,5,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[6,2,7,3,1,8,5,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,2,4,7,8,1,5,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[2,6,7,3,1,8,5,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[8,6,5,1,3,2,4,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,7,8,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,4,7,1,2,5,6]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[8,6,1,2,5,4,3,7]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,8,6,1,5,3,2,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,8,6,4,1,3,2,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,3,6,4,5,2,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,3,8,7,1,6,4,5]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,3,7,8,1,6,2,5]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[3,5,8,7,4,1,2,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[7,3,8,4,1,2,5,6]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,8,1,2,7,3,5,6]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[6,8,1,2,7,4,5,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,6,8,4,1,3,7,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,5,4,7,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,8,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,8,7,5,6,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,7,4,8,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,8,7,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,5,2,4,6,7,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,1,8,4,6,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,3,8,7,2,1,4,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,3,7,8,5,6,1,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,7,6,8,5,1,2,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,6,7,8,5,1,3,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,4,7,8,1,6,3,5]=>[5,7,8,6,1,4,2,3]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[5,4,7,8,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,3,4,1,5,7,6]=>[5,8,3,4,1,6,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[6,8,3,4,1,2,7,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,7,1,5,2,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,3,2,7,6,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,5,3,1,8,6,7,4]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[4,5,3,2,8,6,7,1]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,5,8,6,1,4,7,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,8,5,6,1,4,7,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[4,8,6,1,5,2,7,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,2,3,7,6,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,6,8,5,3,2,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,6,4,8,5,1,7,3]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[7,6,4,8,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,8,6,5,2,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[3,4,8,7,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,3,2,8,6,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,5,1,3,8,6,7,4]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[4,5,1,2,8,6,7,3]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,4,8,1,3,6,7,2]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,3,5,4,1,6,7,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,3,4,8,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,5,7,2,4,8,3]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,5,1,2,3,8,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,4,3,1,2,8,5,6]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[8,4,7,6,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,6,5,7,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,1,4,5,8,3,6]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,4,1,6,3,5,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,5,7,6,4,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,7,5,2,1,3,8,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[5,7,2,3,6,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,6,2,3,7,1,4,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,2,4,8,3,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,7,2,4,8,6,3,5]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,1,5,4,8,3,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,7,3,2,1,8,5,6]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,1,7,2,5,8,4,6]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,8,7,6,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,6,1,3,2,5,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,6,7,4,1,3,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[5,8,6,4,2,3,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,8,3,1,6,5,4,7]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,8,1,2,5,7,4,6]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[6,8,5,4,2,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,3,1,2,4,5,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[4,6,8,7,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,3,7,8,4,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,1,3,8,7,5,6,2]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,2,7,4,8,1,3,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,4,5,2,1,6,3,7]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,3,2,6,8,1,7,5]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[7,1,5,6,3,8,2,4]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,2,4,7,8,3,6]=>[7,2,3,4,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,5,4,2,8,1,6,7]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[6,2,8,7,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,8,4,3,6,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,6,8,7,4,1,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,6,8,1,7,3,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,1,6,8,7,4,2,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,4,6,8,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,8,4,3,1,2,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[2,5,8,3,6,7,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,1,3,7,4,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,5,8,3,7,4,2,6]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,8,2,7,1,5,6,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[5,8,2,3,6,4,1,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,8,2,3,4,7,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,5,8,7,4,2,6,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,5,1,8,4,2,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,8,5,2,7,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,6,5,4,8,3,7]=>[2,1,7,5,4,8,3,6]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,7,8,4,6,5,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,7,4,3,5,8,6]=>[2,1,8,5,4,6,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,5,7,8,4,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,2,8,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,2,3,5,7,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,2,4,3,1,5,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,3,8,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,7,1,3,5,8,4]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,1,8,2,3,5,4,7]=>[7,2,8,4,5,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,2,4,1,6,3,8,5]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,4,3,1,7,5,2,6]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,3,1,4,6,8,5,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,3,8,5,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,8,7,1,6,5,2]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[4,7,1,8,5,2,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,3,2,4,7,8,6,1]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,3,4,2,8,7,1,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[5,2,4,3,6,8,1,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[3,8,6,5,4,1,2,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,7,5,6,3,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,8,5,7,2,3,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,2,7,5,8,3,6,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[3,8,5,7,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,2,7,3,4,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,2,5,4,3,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,7,2,4,5,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,7,2,8,3,6,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,3,6,4,2,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,1,8,7,4,6,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,8,3,7,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,3,4,7,5,8,2]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,3,2,1,4,8,5,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[6,2,3,1,4,7,8,5]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[6,2,1,4,8,7,5,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,2,8,3,5,7,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,1,8,3,5,4,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,2,4,8,5,6,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,1,3,4,5,8,6]=>[8,3,2,4,5,6,7,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,7,3,5,4,2,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,6,5,3,2,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,6,4,3,2,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,3,7,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,3,6,4,7,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,2,1,7,5,8,3,4]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,3,8,7,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,2,1,5,8,4,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[9,1,8,7,6,5,4,3,2]=>[9,2,8,7,6,5,4,3,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[7,6,8,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,1,9,8,6,5,4,3,2]=>[9,2,8,7,6,5,4,3,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[6,1,9,8,7,5,4,3,2]=>[9,2,8,7,6,5,4,3,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[5,4,8,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,9,8,7,6,4,3,2]=>[9,2,8,7,6,5,4,3,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[4,1,9,8,7,6,5,3,2]=>[9,2,8,7,6,5,4,3,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[3,1,9,8,7,6,5,4,2]=>[9,2,8,7,6,5,4,3,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[10,1,9,8,7,6,5,4,3,2]=>[10,2,9,8,7,6,5,4,3,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[9,8,1,7,6,5,4,3,2]=>[9,8,3,7,6,5,4,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[7,6,1,8,5,4,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,9,1,6,5,4,3,2]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[8,1,10,9,7,6,5,4,3,2]=>[10,2,9,8,7,6,5,4,3,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[6,5,8,1,7,4,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,9,8,1,5,4,3,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,1,10,9,8,6,5,4,3,2]=>[10,2,9,8,7,6,5,4,3,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[6,5,9,8,7,1,4,3,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,1,10,9,8,7,5,4,3,2]=>[10,2,9,8,7,6,5,4,3,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[6,5,8,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,9,8,7,6,1,3,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[5,1,10,9,8,7,6,4,3,2]=>[10,2,9,8,7,6,5,4,3,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[4,3,9,8,7,6,5,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[4,1,10,9,8,7,6,5,3,2]=>[10,2,9,8,7,6,5,4,3,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[3,2,9,8,7,6,5,4,1]=>[9,2,8,7,6,5,4,3,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[3,1,10,9,8,7,6,5,4,2]=>[10,2,9,8,7,6,5,4,3,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[1,8,3,5,6,2,4,7]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,8,5,6,2,3,7]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,5,3,7,4,6]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,4,8,2,3,5,7]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,7,2,5,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,2,5,4,7,3,6]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,4,1,2,3,8,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,7,4,2,5,3,8,6]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,7,4,2,1,3,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,4,3,8,5,7,1,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,4,3,6,2,1,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,2,5,3,4,1,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,3,7,4,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,4,2,3,1,5,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,7,5,2,4,1,6,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[7,1,3,2,8,4,5,6]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,1,7,4,8,3,5,6]=>[2,1,8,6,7,4,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,2,8,6,1,3,4,7]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[2,8,3,1,4,5,6,7]=>[4,8,3,1,5,6,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[7,4,8,2,3,1,5,6]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,3,7,2,1,4,5,6]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,5,2,4,7,1,3,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,5,7,4,1,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,6,4,5,1,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,6,4,1,3,7,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,3,1,8,2,5,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,4,1,2,8,3,5,6]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,8,1,3,5,7,2,6]=>[7,8,3,4,5,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[7,8,4,1,3,6,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,8,1,3,7,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,6,1,8,2,4,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,7,3,1,8,2,5,6]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[8,3,1,7,2,4,5,6]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,8,1,4,7,3,5,6]=>[3,8,1,6,7,4,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,1,8,5,4,7,6,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,5,8,3,7,6,2]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,5,3,8,7,6,2]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,5,1,8,2,7,6,3]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,8,5,3,1,7,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,5,2,8,1,7,6,3]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,5,2,1,8,7,6,3]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,6,2,7,8,1,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,6,2,8,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,6,3,7,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,6,3,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,8,2,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,2,8,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,2,7,4,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,6,7,2,3,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,6,7,2,8,3,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,7,2,1,8,3,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,7,2,1,3,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,6,1,7,8,2,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,6,1,7,2,4,8,3]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,1,6,7,8,3,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,6,8,7,3,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,8,6,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,6,8,7,5,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,6,7,4,8,3,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,1,7,8,4,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,6,8,1,7,5,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,6,1,7,5,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,7,1,8,3,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,7,1,3,8,2,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,7,1,3,2,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,6,7,3,1,2,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,6,7,3,8,1,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,8,7,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,7,3,8,2,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,6,2,3,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,4,8,6,3,2,5,7]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,1,6,3,8,5,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,3,1,5,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,4,2,5,7,3,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,2,5,7,6,3,1,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,4,5,6,1,8,3,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,1,5,8,6,3,2,7]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,2,7,6,1,8,5,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,7,5,1,6,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,6,5,1,2,7,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,2,5,1,4,8,7,6]=>[4,2,5,1,3,8,7,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[8,5,4,1,3,2,7,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,4,2,3,6,8,7,5]=>[1,4,3,2,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,8,3,7,1,6,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,7,1,8,2,5,3,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[6,4,1,8,5,3,7,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,4,6,1,3,5,2,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,2,5,4,7,8,1,6]=>[7,2,4,3,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,2,4,3,7,8,1,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[8,1,6,7,2,5,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,7,6,5,8,2,4]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,2,7,5,6,8,3,4]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,4,7,2,8,3,5]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,1,7,6,8,4,5]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,8,6,4,7,1,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,8,4,6,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,6,5,3,7,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,5,3,6,7,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,5,2,7,6,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,7,5,3,1,8,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,5,3,6,8,1,7,2]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,5,2,6,1,8,7,4]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,6,3,5,7,2,8,4]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,4,6,7,8,2,3]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,4,6,5,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,5,2,6,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,4,2,6,8,7,1,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,4,3,1,2,6,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,1,4,3,2,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,6,4,5,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,7,4,1,3,8,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,4,2,3,8,1,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,2,6,7,3,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[2,4,3,8,6,1,5,7]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[7,8,1,3,5,6,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,3,1,5,6,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,1,3,8,5,6,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,8,3,5,6,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,7,8,3,4,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,5,7,8,3,4,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,1,5,8,6,2,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[1,3,7,8,2,5,6,4]=>[1,5,8,7,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,7,8,5,2,6,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,3,7,5,8,2,6,4]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,7,5,8,2,6,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,5,7,1,8,4,6,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[3,5,7,8,1,4,6,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,3,7,8,4,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,7,8,4,1,6,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,3,7,8,1,4,6,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,3,7,1,8,4,6,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[5,1,3,7,8,4,2,6]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,6,2,1,4,5,8,7]=>[4,6,3,1,5,2,8,7]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[4,6,2,5,1,3,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,4,2,5,1,3,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[8,6,1,7,3,2,4,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,5,8,1,7,3,4,6]=>[4,7,8,1,6,5,2,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[6,8,2,7,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,2,3,7,1,4,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,2,7,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,8,1,7,3,4,6]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,2,3,8,1,5,6,7]=>[5,3,2,8,1,6,7,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[5,2,8,3,7,1,4,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[5,2,8,4,6,1,3,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[2,1,5,8,4,3,6,7]=>[2,1,6,8,5,3,7,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,8,3,2,7,1,4,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,1,3,8,2,5,6,7]=>[5,2,3,8,1,6,7,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,5,8,2,7,1,4,6]=>[6,7,8,4,5,1,2,3]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[4,5,8,2,6,1,3,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[2,6,8,3,7,1,4,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[5,1,8,3,7,2,4,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,8,4,6,2,3,7]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,8,4,1,6,2,3,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,5,8,1,6,2,3,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[5,4,8,1,6,2,3,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[4,8,5,1,6,2,3,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,1,5,4,8,3,6,7]=>[2,1,6,4,8,3,7,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,3,8,1,5,6,7]=>[5,3,2,8,1,6,7,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,1,8,4,2,5,6,7]=>[5,2,8,4,1,6,7,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,8,4,2,1,5,6,7]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[2,3,8,4,1,5,6,7]=>[5,2,8,4,1,6,7,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,4,2,8,1,5,6,7]=>[5,3,2,8,1,6,7,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,8,5,2,7,1,4,6]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[4,8,5,2,6,1,3,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,1,4,8,5,3,6,7]=>[2,1,6,8,5,3,7,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,2,8,4,1,5,6,7]=>[5,2,8,4,1,6,7,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,8,4,3,1,5,6,7]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[4,1,7,5,6,2,8,3]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,4,3,8,1,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,4,3,8,2,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,4,2,6,7,5,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,8,4,1,6,7,5,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,1,7,5,2,8,4,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,4,3,2,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[2,6,7,5,3,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,7,4,8,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,6,7,5,3,8,4]=>[2,1,8,6,5,4,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,8,4,2,1,6,7,5]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[5,7,4,3,8,2,1,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,7,4,8,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,5,8,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,4,8,3,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,3,4,8,2,5,7]=>[7,2,6,4,8,3,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,2,3,4,8,1,5,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,7,5,8,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,5,8,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,8,1,5,7,6,2]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,5,7,6,1,4,8,3]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[6,7,4,8,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,4,8,1,3,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,7,5,1,3,8,4]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[6,3,1,4,8,2,5,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,7,4,8,1,3,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,5,8,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,4,8,2,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,4,8,1,2,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,5,6,3,4,8,2,7]=>[1,7,5,4,3,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,3,6,5,8,2,7]=>[1,7,3,5,4,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,3,4,7,2,6,5]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,7,3,4,8,2,6]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,7,8,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,2,3,7,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,3,4,7,5,6,1]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,8,3,4,7,6,2,5]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,2,3,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,1,7,5,2,6,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,8,1,6,7,2,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,1,3,8,4,6,5,7]=>[2,1,3,8,5,7,6,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,2,1,7,4,3,6,5]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,3,2,8,5,4,6,7]=>[1,3,2,8,6,5,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,3,1,5,7,2,6,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,4,5,1,7,2,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,5,6,8,7,4,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,4,5,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,4,8,5,7,6,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,8,5,7,3,6,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,3,8,6,5,7,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,2,8,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,7,8,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,2,8,6,7,3,5,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[3,2,8,7,5,4,6,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,8,7,5,6,2,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,1,8,6,7,5,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,7,8,6,4,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,7,1,8,5,4,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,3,2,6,1,4,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,4,8,2,6,1,7,5]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[7,8,4,1,5,6,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,1,4,5,6,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,1,2,6,3,4,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,5,1,4,6,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,4,5,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,8,4,1,6,7,2]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,2,4,8,1,5,3,7]=>[7,5,6,8,2,3,1,4]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[3,4,8,5,1,6,7,2]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[3,5,8,1,4,6,7,2]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,4,8,2,6,3,7,5]=>[1,6,8,4,7,2,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,3,8,1,4,6,7,2]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,2,6,8,1,5,3,7]=>[7,5,6,8,2,3,1,4]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[7,4,2,8,1,5,3,6]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,1,7,5,8,4,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,2,1,8,4,5,3,7]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[1,2,7,8,5,3,4,6]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,7,8,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,5,7,8,4,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,5,6,8,4,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,8,4,5,6,7,2]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,1,4,8,6,5,3,7]=>[2,1,7,8,6,5,3,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,1,8,6,5,3,7]=>[3,7,1,8,6,5,2,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[4,2,1,8,6,5,3,7]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[3,2,7,8,5,1,4,6]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,7,8,5,1,4,6]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,7,3,8,5,1,4,6]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,6,2,8,5,1,4,7]=>[6,7,3,8,5,1,2,4]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[7,3,6,8,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,1,8,5,3,4,6]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,2,6,8,4,5,3,7]=>[1,2,7,8,6,5,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,6,5,8,4,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,5,7,1,8,4,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,6,1,8,4,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,1,5,8,4,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,3,8,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,2,8,4,5,3,6]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,1,5,8,4,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,6,1,8,4,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[9,10,7,8,5,6,2,1,3,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,7,8,4,3,5,6,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,7,8,4,2,5,1,3,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,7,8,3,2,1,4,5,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,6,5,7,8,3,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,6,5,7,8,2,1,3,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,6,4,7,3,5,8,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,6,4,7,2,5,1,3,8]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,6,3,7,2,1,4,5,8]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,5,4,3,6,7,8,1,2]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[9,10,5,4,2,6,7,1,3,8]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[9,10,5,3,2,6,1,4,7,8]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,7,9,10,5,6,3,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,7,9,10,5,6,2,1,3,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,7,9,10,4,3,5,6,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,7,9,10,4,2,5,1,3,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,7,9,10,3,2,1,4,5,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,6,9,5,7,10,3,4,1,2]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,6,9,5,7,10,2,1,3,4]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,6,9,4,7,3,5,10,1,2]=>[10,9,7,6,5,4,3,8,2,1]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[8,6,9,3,7,2,1,4,5,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[8,5,9,4,3,6,7,10,1,2]=>[10,9,7,6,5,4,3,8,2,1]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[8,5,9,4,2,6,7,1,3,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[8,5,9,3,2,6,1,4,7,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[7,6,5,8,9,10,3,4,1,2]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,6,5,8,9,10,2,1,3,4]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,6,4,8,9,3,5,10,1,2]=>[10,9,7,6,5,4,3,8,2,1]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[7,6,4,8,9,2,5,1,3,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[7,6,3,8,9,2,1,4,5,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[6,5,4,3,7,8,9,10,1,2]=>[10,9,4,3,5,6,7,8,2,1]=>[10,9,4,3,8,7,6,5,2,1]=>[[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.]
[11,12,9,10,7,8,5,6,2,1,3,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,7,8,4,3,5,6,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,7,8,4,2,5,1,3,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,7,8,3,2,1,4,5,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,6,5,7,8,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,6,5,7,8,2,1,3,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,6,4,7,3,5,8,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,6,4,7,2,5,1,3,8]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,6,3,7,2,1,4,5,8]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,5,4,3,6,7,8,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,5,4,2,6,7,1,3,8]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,5,3,2,6,1,4,7,8]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,4,3,2,1,5,6,7,8]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,7,9,10,5,6,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,7,9,10,5,6,2,1,3,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,7,9,10,4,3,5,6,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,7,9,10,4,2,5,1,3,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,7,9,10,3,2,1,4,5,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,6,9,5,7,10,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,6,9,5,7,10,2,1,3,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,6,9,4,7,3,5,10,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,6,9,4,7,2,5,1,3,10]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,6,9,3,7,2,1,4,5,10]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,5,9,4,3,6,7,10,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,5,9,4,2,6,7,1,3,10]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,5,9,3,2,6,1,4,7,10]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,6,5,8,9,10,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,6,5,8,9,10,2,1,3,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,6,4,8,9,3,5,10,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,6,4,8,9,2,5,1,3,10]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,6,3,8,9,2,1,4,5,10]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,5,4,8,3,6,9,10,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,5,4,8,2,6,9,1,3,10]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,5,3,8,2,6,1,4,9,10]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,9,11,12,7,8,5,6,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,9,11,12,7,8,5,6,2,1,3,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,9,11,12,7,8,4,3,5,6,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,9,11,12,7,8,4,2,5,1,3,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,9,11,12,7,8,3,2,1,4,5,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,9,11,12,6,5,7,8,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,9,11,12,6,5,7,8,2,1,3,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,9,11,12,6,4,7,3,5,8,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,9,11,12,6,4,7,2,5,1,3,8]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,9,11,12,6,3,7,2,1,4,5,8]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,9,11,12,5,4,3,6,7,8,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,9,11,12,5,4,2,6,7,1,3,8]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,9,11,12,5,3,2,6,1,4,7,8]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,9,11,12,4,3,2,1,5,6,7,8]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,8,11,7,9,12,5,6,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,8,11,7,9,12,5,6,2,1,3,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,8,11,7,9,12,4,3,5,6,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,8,11,7,9,12,4,2,5,1,3,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,8,11,7,9,12,3,2,1,4,5,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,8,11,6,9,4,7,2,5,1,3,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[10,8,11,6,9,3,7,2,1,4,5,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[10,8,11,5,9,4,2,6,7,1,3,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[10,8,11,5,9,3,2,6,1,4,7,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[10,8,11,4,9,3,2,1,5,6,7,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[10,7,11,6,4,8,9,2,5,1,3,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[10,7,11,6,3,8,9,2,1,4,5,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[10,7,11,5,4,8,2,6,9,1,3,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[10,7,11,5,3,8,2,6,1,4,9,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[10,7,11,4,3,8,2,1,5,6,9,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[9,8,7,10,11,12,5,6,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,8,7,10,11,12,5,6,2,1,3,4]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,8,7,10,11,12,4,3,5,6,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,8,7,10,11,12,4,2,5,1,3,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,8,7,10,11,12,3,2,1,4,5,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,8,6,10,11,4,7,2,5,1,3,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[9,8,6,10,11,3,7,2,1,4,5,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[9,8,5,10,11,4,2,6,7,1,3,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[9,8,5,10,11,3,2,6,1,4,7,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[6,5,4,3,2,1,7,8,9,10,11,12]=>[6,5,4,3,2,1,7,8,9,10,11,12]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[7,1,6,5,3,2,4,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,8,7,5,3,2,4,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,7,4,2,5,3,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,4,2,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,6,4,2,5,3,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,1,5,3,6,4,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,3,7,1,6,4,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,3,6,4,2,7,1,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[7,4,2,8,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,6,1,8,7,4,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,1,5,3,8,7,4,2]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,8,7,5,4,6,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,3,1,8,7,5,4,6]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[5,3,8,7,4,2,1,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[7,4,2,1,8,6,3,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,6,3,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,6,3,5,7,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,8,5,2,1,7,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,6,3,7,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,6,4,7,5,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,1,8,6,3,7,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,3,7,4,1,8,5,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,2,6,3,7,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,8,7,4,2,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,3,7,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,6,3,2,4,7,5]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,3,2,4,7,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,1,8,6,3,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,1,8,7,5,3,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,3,2,8,7,6,1,5]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[2,4,5,1,3,8,7,6]=>[4,5,3,1,2,8,7,6]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[7,5,8,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,5,8,6,3,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,2,5,8,6,3]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,3,1,7,4,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,4,2,5,3,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,1,8,7,4,2,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,1,8,7,5,3,2,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,8,6,4,1,3,7,5]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[4,1,8,6,3,2,7,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[7,4,2,8,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,1,8,5,2,7,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,5,2,6,3,1,7,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,8,5,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,5,2,7,4,6,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,5,2,7,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,6,3,1,8,5,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,3,1,7,4,8,5,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,3,1,5,7,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,1,7,5,8,6,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,1,7,5,8,6,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[7,4,8,5,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,2,1,7,4,6,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,7,4,6,3,8,5,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,5,2,1,4,8,7]=>[5,6,4,3,1,2,8,7]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,5,6,2,1,4,8,7]=>[5,6,4,3,1,2,8,7]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,5,7,8,1,4,2,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,1,8,5,7,3,2,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,1,7,5,8,3,2,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,1,5,8,7,4,3,6]=>[2,1,7,8,6,5,3,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,5,7,8,4,3,6]=>[2,1,7,8,6,5,3,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,1,7,4,8,3,2,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,7,2,8,3,6,1,5]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[4,6,2,7,3,1,8,5]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[3,7,8,2,4,1,6,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[3,8,7,2,4,1,6,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[3,8,6,2,4,1,7,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,3,1,6,5,4,10,9,8,7]=>[3,2,1,6,5,4,10,9,8,7]=>[3,2,1,10,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[4,7,3,8,6,2,10,9,5,1]=>[10,9,6,5,4,3,8,7,2,1]=>[10,9,6,5,4,3,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.]
[6,2,8,4,1,7,3,5]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[7,3,4,8,1,6,2,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,3,4,8,1,7,2,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,3,4,8,1,2,7,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,3,5,8,1,2,7,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,8,5,4,2,3,7,6]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,4,8,1,2,7,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,5,3,8,1,2,7,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,4,3,8,1,7,2,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,4,3,8,1,6,2,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,5,3,8,7,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,3,8,7,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,3,8,1,7,2,5]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[2,6,8,4,1,7,3,5]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,8,7,4,2,6,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,3,8,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,5,8,6,1,2,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,7,8,5,6,1,3,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[1,8,7,5,6,2,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,8,5,7,1,3,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[5,3,6,8,7,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,5,8,7,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,8,5,6,1,3,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,2,8,6,7,1,3,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,2,8,7,6,1,3,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,2,8,7,5,1,3,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[3,4,7,8,1,6,2,5]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[1,8,5,7,6,2,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,8,7,6,1,3,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[7,4,6,5,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,7,8,5,1,2,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,6,8,7,5,1,3,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[1,8,6,7,5,2,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,8,6,5,1,3,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[5,7,6,4,8,1,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,8,7,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,7,4,1,3,5,6]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[5,4,8,7,1,3,2,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,8,6,1,3,2,5,7]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[5,4,2,7,6,8,1,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,8,7,1,4,5,3,6]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,2,1,8,7,3,5,6]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[5,1,6,3,2,8,7,4]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,6,1,8,7,3,2,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[8,7,2,3,5,4,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,1,4,8,7,2,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[4,3,5,2,8,7,1,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[3,4,2,8,6,1,5,7]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[3,7,6,8,1,5,2,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,1,4,2,3,6,7,5]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,7,2,1,8,6,4,5]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,8,6,1,7,3,5,4]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,7,6,3,5,8,2,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,5,1,6,8,2,4]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[3,6,5,8,1,4,7,2]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[8,1,5,6,4,7,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,6,7,4,1,8,2,5]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,7,4,6,8,2,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,5,8,2,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,1,6,5,4,8,3]=>[3,8,1,6,5,4,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[7,3,2,6,1,8,5,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,4,7,2,3,1,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,3,1,8,4,6,2,7]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,8,1,6,7,4,2,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,7,4,3,6,8,1,5]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[2,8,4,6,1,5,3,7]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[8,4,1,6,3,2,5,7]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,7,3,8,5,2,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,1,7,4,8,5,2,6]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,4,1,6,3,2,8,5]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,8,6,2,7,4,1,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[7,3,1,4,5,2,8,6]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,1,4,8,5,3,2,7]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,1,2,4,6,7,5,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,3,6,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,5,2,3,8,6,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,2,4,1,3,7,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,7,5,1,8,6,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,7,3,2,8,5,6,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,4,5,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,4,2,3,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,4,6,1,7,5,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[3,7,4,6,5,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,2,7,6,1,5,8,3]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,3,1,4,5,7,6,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,5,1,6,8,4,7,2]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,1,5,7,3,8,4,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,8,4,7,3,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,6,5,8,4,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,2,5,1,6,7,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,6,8,3,7,4,1,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[8,1,5,6,4,7,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,5,8,1,6,4,7,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[7,4,1,8,3,2,6,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,3,7,4,2,1,6,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,2,6,8,3,1,7,4]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[3,6,5,8,4,1,7,2]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[7,3,6,1,8,4,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,7,3,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,8,2,5,6,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,3,1,6,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,7,4,2,3,6,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,1,5,4,2,3,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,7,1,5,2,8,6,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[8,7,2,5,4,1,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,2,5,3,1,4,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,8,7,1,4,3,6]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[7,1,8,6,2,4,3,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,6,2,7,5,3,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,6,2,8,5,3,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,3,4,1,7,2,8,5]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,2,4,3,5,1,8,6]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,1,7,2,3,8,6,4]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,3,5,1,7,6,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,6,3,1,4,8,2,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,1,8,2,7,5,3,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,8,1,6,5,3,4]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,2,6,4,3,8,1,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,1,7,4,3,8,2,6]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,3,1,7,4,8,2,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[7,4,8,2,1,5,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,4,1,6,3,7,5]=>[8,4,6,2,7,3,5,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,2,7,5,1,6,4,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[6,1,7,3,2,8,5,4]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,7,2,1,6,3,8,5]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[6,2,1,5,3,8,4,7]=>[7,3,2,5,4,8,1,6]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[5,3,1,6,2,8,4,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,1,5,2,8,4,3,7]=>[7,2,6,4,8,3,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,4,3,8,1,5,2,6]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,4,8,1,5,3,2,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,1,5,3,2,8,4,7]=>[7,2,5,4,3,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,3,2,8,4,1,5,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,3,4,2,8,5,1,6]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,1,6,3,4,2,8,5]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,5,1,3,7,4,2,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,6,1,5,2,7,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[8,6,1,3,7,5,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,8,5,6,1,7,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,1,3,8,5,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,7,1,5,2,8,4]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[7,1,3,8,4,2,6,5]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,2,7,1,3,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,6,2,8,1,3,7,4]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[6,1,8,3,7,5,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,2,1,5,8,3,6]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,4,1,5,8,3,2,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,3,2,6,4,8,1,5]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,4,2,7,3,8,1,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,1,8,3,7,4,2,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,4,8,3,1,5,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,1,7,4,8,3,6]=>[7,3,2,8,5,6,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[6,1,8,4,5,2,7,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,6,4,5,2,8,3]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,5,2,7,1,6,8,4]=>[5,8,3,6,1,4,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,5,7,3,1,6,8,2]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,5,7,2,8,6,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,5,1,7,2,6,8,4]=>[5,8,3,6,1,4,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,5,7,2,8,1,3,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[4,6,7,2,1,5,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,6,7,1,3,8,5,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,6,1,5,7,8,4,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,6,7,1,5,8,3,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,1,3,7,4,8,5,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,1,7,4,8,5,6]=>[3,2,1,8,5,7,6,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[4,1,5,2,7,6,3,8]=>[7,2,4,3,6,5,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,5,1,4,3,8,6,7]=>[3,5,1,4,2,8,7,6]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,7,2,1,5,8,6,4]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[6,2,7,1,4,8,5,3]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,7,4,2,1,8,5,6]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[7,2,5,3,1,8,6,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[7,5,1,4,2,8,6,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,4,1,3,8,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,3,2,1,7,6,4,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[6,3,2,8,1,5,7,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,4,3,2,8,1,6,5]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,6,2,4,8,3,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,6,4,8,1,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,7,5,3,8,1,4,6]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[1,8,5,3,6,4,2,7]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,2,3,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,3,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,2,7,1,6,4,5]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,2,6,1,5,4,3,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[8,5,7,4,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,2,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,6,7,1,3,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,5,6,1,4,3,7]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[7,2,6,8,4,1,5,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,6,4,8,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,8,1,4,2,7,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,5,8,4,1,3,7,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,4,8,3,2,1,7,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[2,5,8,1,4,3,7,6]=>[4,6,8,1,5,2,7,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,6,8,2,1,5,7,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[5,7,4,8,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,1,4,8,2,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,7,4,1,8,3,6,5]=>[4,8,6,1,7,3,5,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,5,1,8,4,2,7,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,2,5,8,3,1,7,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,1,2,7,8,3,5,4]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,3,1,8,6,4,2,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,1,8,4,7,5,2,6]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,2,8,7,3,5,1,6]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[4,8,1,7,6,2,3,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[6,8,1,4,7,5,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,3,8,1,6,4,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,7,8,1,5,3,2,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[7,1,8,6,2,5,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,8,7,1,3,6,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,7,2,1,6,4,5]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,8,7,1,6,3,5,4]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,7,6,1,5,4,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,8,7,6,1,3,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,2,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,1,7,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,3,8,6,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,4,3,1,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,8,6,4,3,2,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,7,3,6,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,4,2,5,3,7,8]=>[6,2,5,4,3,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,3,7,5,4,2,8,6]=>[1,6,8,5,4,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,3,5,4,2,7,8]=>[6,2,5,4,3,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,1,2,5,4,7,3,8]=>[7,2,3,5,4,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,6,3,4,7,8,2]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,2,6,3,4,7,1,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[3,4,7,5,8,6,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,4,7,1,5,3,8,6]=>[4,6,8,1,5,2,7,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,3,6,7,4,8,1,5]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,3,6,7,4,8,5,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,6,5,3,1,8,4]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[5,2,6,1,4,7,8,3]=>[8,4,5,2,3,6,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,7,6,5,2,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,3,6,2,4,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,7,4,2,1,3,6,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[6,3,1,5,4,7,8,2]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,3,6,1,4,2,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,7,4,2,6,3,8,5]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,4,1,2,3,6,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[6,4,1,2,5,3,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,7,6,3,8,5,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,7,6,5,2,8,1,4]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[3,7,6,5,1,2,8,4]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[4,7,2,6,1,3,8,5]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[2,7,1,6,8,3,5,4]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,7,6,5,8,1,4,3]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[9,1,2,3,4,5,6,8,7]=>[9,2,3,4,5,6,7,8,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[10,1,2,3,4,5,6,7,9,8]=>[10,2,3,4,5,6,7,8,9,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[2,11,10,9,8,7,6,5,4,3,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[3,2,10,9,8,7,6,5,4,1]=>[10,2,9,8,7,6,5,4,3,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[3,9,2,8,7,6,5,4,1]=>[9,8,3,7,6,5,4,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[4,2,9,8,7,6,5,3,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[5,2,8,7,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,7,6,1,5,4,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[8,4,1,7,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[9,3,1,8,7,6,5,4,2]=>[9,8,3,7,6,5,4,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[10,2,1,9,8,7,6,5,4,3]=>[10,3,2,9,8,7,6,5,4,1]=>[10,3,2,9,8,7,6,5,4,1]=>[[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.]
[4,5,6,2,3,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,5,3,2,7,8,1,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[6,5,7,3,8,4,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,7,2,4,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,2,7,4,5,8,1,6]=>[7,2,8,4,5,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,8,1,5,2,4,3,7]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[8,3,4,6,1,5,2,7]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[2,3,4,7,5,8,1,6]=>[7,2,3,8,5,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,3,4,7,8,2,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,7,4,8,6,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,6,4,1,7,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,3,7,4,8,6,2,5]=>[1,7,8,4,6,5,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,8,5,4,1,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,4,3,1,7,8,2,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[5,7,6,2,8,4,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,1,7,5,8,3,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,5,6,4,1,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,5,6,8,4,7,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,3,7,6,5,8,2]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,4,1,7,5,8,6,2]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,5,7,4,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,1,7,2,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,4,1,3,7,6,5]=>[8,4,5,2,3,7,6,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,8,3,6,2,1,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,7,4,2,3,6,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,7,2,3,5,6,4]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,3,1,6,7,5,4]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[8,2,3,1,5,7,6,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,8,4,1,2,7,6,5]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[5,4,7,2,3,6,8,1]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,3,2,1,8,4,7,5]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,3,7,4,1,8,5,6]=>[5,2,8,4,1,7,6,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[6,4,1,3,2,7,8,5]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,7,8,5,1,3,6,4]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[8,2,5,6,7,1,3,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,8,5,4,7,6,1,3]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,7,1,5,8,2,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,8,7,6,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,1,5,3,2,6,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,5,7,3,8,2,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,4,7,2,5,6,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,3,4,6,1,5,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,3,4,5,7,1,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,2,6,8,3,1,5,7]=>[6,5,7,8,2,1,3,4]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[3,7,6,2,4,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[2,3,6,5,8,1,4,7]=>[6,2,7,4,8,1,3,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,5,8,6,1,4,7]=>[6,2,7,8,5,1,3,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,2,3,8,6,1,5,7]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[6,4,1,2,8,3,5,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,2,3,7,4,6,8,5]=>[1,2,3,8,5,6,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,7,1,4,5,8,6]=>[4,2,8,1,5,6,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,1,5,3,8,7,4,6]=>[2,1,7,4,8,6,3,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,8,3,2,4,1,6,7]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[4,2,7,1,8,3,5,6]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[4,1,8,2,7,3,5,6]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,2,7,5,3,8,4,6]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,7,1,4,8,5,6]=>[4,2,8,1,5,7,6,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,2,3,7,6,8,4,5]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,6,8,7,4,5]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,7,8,4,6,5]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,6,8,4,7,5]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,7,8,6,4,5]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,2,8,3,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,2,8,3,7,5,6,1]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,3,4,8,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,4,8,7,2,6,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,3,5,8,7,2,6,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,6,3,8,5,7,2,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,5,3,8,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,8,3,7,4,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,8,4,3,7,5,6,2]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,8,3,7,4,6,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,4,3,8,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,4,8,7,2,6,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,5,3,8,6,7,2,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,7,8,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,8,5,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,5,6,4,7,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,8,6,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,6,5,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,7,8,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,7,8,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,8,6,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,2,8,6,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,2,8,6,7,4,5,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,8,7,5,4,6,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,2,7,4,5,6,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,8,6,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,8,4,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,8,4,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,2,8,5,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,3,6,8,5,7,2,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[3,4,6,8,7,2,5,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,3,5,8,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,3,5,7,4,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,8,4,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,5,8,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,4,6,8,3,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,5,8,4,7,2,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[2,6,8,4,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,2,7,1,3,8,5,6]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[4,2,5,1,3,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,3,6,1,7,2,4,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[3,7,1,2,5,8,6,4]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,7,4,1,2,8,5,6]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[7,5,1,3,4,8,6,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,1,2,4,8,6,3]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,4,2,3,7,1,5,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,6,3,8,1,2,5,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,2,3,8,1,6,5]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,7,5,2,8,1,3,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[8,2,6,3,7,1,4,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,6,1,2,7,4,5,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,7,1,2,3,6,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,5,7,1,2,4,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,7,1,3,4,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,2,7,1,3,5,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[3,8,5,6,1,2,4,7]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[3,7,5,8,1,2,4,6]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[7,6,4,8,1,3,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,8,1,2,4,7,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[3,6,8,1,2,5,7,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,7,2,4,8,1,6,5]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,6,3,8,1,2,5,7]=>[6,7,5,8,3,1,2,4]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[4,6,3,7,1,2,5,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[4,1,7,8,2,3,6,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,3,8,1,6,2,4,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[6,1,8,5,2,3,4,7]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,1,7,5,2,3,4,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,8,1,3,7,4,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,8,1,6,3,4,5]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,7,8,2,5,1,3,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,8,2,7,1,4,5,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,8,7,1,3,5,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,7,1,2,4,6,5]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[4,8,7,1,2,3,6,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[5,8,7,1,2,4,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,7,1,3,4,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,1,8,6,2,3,5,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,8,6,4,1,2,3,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[7,8,4,1,2,5,3,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,1,2,6,5,3,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,4,8,2,7,5,3,6]=>[1,7,8,4,6,5,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,3,4,7,2,5,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,8,2,1,6,3,5,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,1,2,7,5,4,3,8]=>[7,2,3,6,5,4,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,2,8,7,5,4,3,6]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,7,3,6,4,8,2]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,2,3,7,4,1,5,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,4,8,7,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,3,8,7,4,1,5,6]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,7,3,8,6,4,1,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[1,8,3,7,6,4,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,2,7,1,4,6,8,3]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,6,7,5,2,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,3,1,4,5,7,8,2]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,3,1,4,6,2,7,8]=>[6,4,3,2,5,1,7,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,7,4,1,2,6,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,8,1,2,6,7,3,5]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,1,7,8,2,6,3,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,2,8,7,6,5,3,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,4,6,8,7,5]=>[3,2,1,4,8,7,6,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,1,8,4,5,7,6,2]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,8,5,4,7,1,6]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,2,8,1,5,3,7,6]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[4,3,8,5,7,6,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,2,1,6,3,7,5]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[3,8,6,5,2,7,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,8,5,6,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,7,8,1,2,6,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[3,7,8,5,2,1,6,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[3,7,2,8,4,1,6,5]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,8,1,7,4,6,5,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,8,7,5,1,6,4,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,8,6,7,5,1,4,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[8,2,4,1,7,3,5,6]=>[8,4,6,2,7,3,5,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,6,1,4,2,3,7,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,1,4,2,8,7,5]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,6,8,4,3,7,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,7,4,3,8,2,5]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,7,4,3,6,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,1,3,8,2,6,5]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,8,2,3,1,5,7,6]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[4,8,6,2,1,3,7,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,7,4,1,8,3,5,6]=>[4,8,6,1,7,3,5,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,7,8,4,2,3,6,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,7,1,3,8,2,6,5]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[8,7,1,3,4,2,6,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,7,4,3,6,2,8,5]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,8,6,4,5,2,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,8,4,6,5,2,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,4,3,7,5,8,1,6]=>[7,3,2,8,5,6,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[1,4,7,3,6,2,8,5]=>[1,6,8,4,5,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,3,4,2,6,7,5]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,4,1,3,7,2,8,5]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,1,4,3,6,2,7,5]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,2,3,8,5,7,1,6]=>[7,3,2,8,5,6,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[2,8,5,7,3,4,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,8,2,6,4,3,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[7,2,5,8,4,3,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,2,3,5,8,7,1,6]=>[7,3,2,4,8,6,1,5]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[8,2,3,5,4,7,1,6]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,1,8,3,4,2,7,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,6,4,2,3,7,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,8,4,5,6,2,1,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,4,3,5,7,8,1,6]=>[7,3,2,4,8,6,1,5]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[3,8,6,5,4,2,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,3,1,4,2,8,7,5]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,3,8,1,2,6,4,5]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[7,1,4,5,3,2,6,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,8,4,2,6,5,3,7]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,4,8,6,3,2,7]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,3,1,8,4,7,2,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,3,8,1,5,7,2,6]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[7,1,4,2,6,5,3,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,8,4,1,6,5,2,7]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[7,5,3,6,4,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,3,6,4,5,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,7,2,4,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,5,4,8,6,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,7,5,4,8,6,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,1,8,7,5,3,6,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,8,3,7,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,7,4,2,6,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,3,1,8,4,7,2]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,7,1,4,8,6,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,5,7,4,8,6,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,6,7,4,5,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,1,7,4,5,8,3,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,3,7,4,8,6,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,3,6,1,4,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,3,6,8,2,7,1]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,5,3,7,4,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,8,4,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,8,4,5,1,6,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[5,7,3,8,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,3,8,1,4,7,2]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[8,4,1,2,5,6,7,3]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,7,8,4,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,3,1,2,5,7,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,1,7,2,6,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,1,4,5,2,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,3,1,5,2,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,1,8,2,6,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,3,1,5,4,2,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,2,1,5,4,8,7]=>[4,6,3,1,5,2,8,7]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[5,4,2,6,1,3,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,2,6,5,1,4,8,7]=>[5,2,6,4,1,3,8,7]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,5,8,1,7,4,3,6]=>[4,7,8,1,6,5,2,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[6,8,2,7,4,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,2,3,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,2,5,4,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,6,5,1,8,4,3,7]=>[4,7,6,1,8,3,2,5]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,2,7,3,1,8,5,6]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[4,2,3,7,1,5,8,6]=>[5,3,2,8,1,6,7,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[5,2,7,3,8,6,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,1,5,8,4,3,7,6]=>[2,1,6,8,5,3,7,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,8,4,2,6,7,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,2,4,8,1,5,7,6]=>[5,2,3,8,1,6,7,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,4,8,3,1,7,5,6]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[4,8,3,2,1,7,6,5]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[4,1,3,7,2,6,8,5]=>[5,2,3,8,1,6,7,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,4,8,2,1,6,5,7]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[6,8,3,7,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,8,1,7,2,6,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[5,1,7,4,6,8,3,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,4,8,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,7,1,8,2,6,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[2,7,6,3,8,1,4,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,1,7,6,4,8,3,5]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,5,4,8,7,3,6]=>[2,1,7,4,8,6,3,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,4,8,7,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,3,8,7,1,5,6]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[3,4,1,8,6,2,7,5]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[3,8,5,4,2,1,7,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[4,8,6,5,2,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,2,8,7,5,4,1,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,8,6,5,4,3,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,4,2,6,3,1,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,5,2,1,3,4,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[8,5,2,7,3,1,4,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,6,5,2,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,6,2,3,4,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,7,5,3,1,4,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,5,3,8,4,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,7,2,3,5,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,7,6,4,2,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,1,7,6,4,8,5,3]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,8,7,4,3,5,6]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,8,3,7,2,1,4,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,8,7,4,2,1,5,6]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[7,8,2,3,5,1,4,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,6,3,1,4,7,5]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[8,1,6,3,2,4,5,7]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,1,4,8,3,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,1,7,5,4,8,3,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,3,7,5,8,4,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,1,5,8,3,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,7,5,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,2,6,1,7,3,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,4,2,6,8,3,7,1]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,5,2,8,1,4,3,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[7,4,2,8,1,3,6,5]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[2,7,8,4,5,1,3,6]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[5,7,3,8,4,1,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,4,8,1,5,6,3,7]=>[4,7,8,1,5,6,2,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,4,8,1,5,2,7,6]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[3,6,8,4,1,2,7,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[4,8,1,2,5,3,6,7]=>[6,8,3,4,5,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[8,1,2,4,3,5,6,7]=>[8,2,3,5,4,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,8,7,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,9,6,8,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[5,8,4,7,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,9,8,5,7,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,8,5,4,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,9,8,7,4,6,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[3,8,7,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,9,8,7,6,3,5,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[4,8,7,6,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,9,8,7,6,5,2,4,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[3,8,7,6,5,2,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,6,9,7,4,5,2,3,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,6,9,4,7,5,2,3,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,6,9,4,7,2,5,3,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,6,9,4,7,3,5,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,6,9,5,7,3,4,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,7,9,5,6,3,4,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,7,10,8,5,6,3,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,6,4,9,7,5,2,3,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,7,10,5,8,6,3,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,6,9,4,2,7,5,3,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,7,10,5,8,3,6,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,6,9,4,7,2,1,5,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,5,8,4,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,9,4,7,3,5,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,7,10,5,8,3,6,2,4,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,6,9,5,7,2,4,1,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,7,10,5,8,4,6,2,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,6,8,2,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,9,4,6,3,5,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,7,10,6,8,4,5,2,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,6,8,5,7,3,4,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,10,6,7,4,5,2,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[3,5,2,4,7,6,1,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[3,5,4,7,2,6,1,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,5,4,7,6,1,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,5,4,7,6,1,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,5,7,4,6,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,5,7,4,6,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,5,7,4,6,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,5,2,7,6,4,1,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,5,7,2,6,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,3,7,6,2,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,3,7,6,1,2,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,3,7,6,1,4,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,3,7,6,4,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,5,7,2,6,1,4,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[3,5,2,7,6,1,4,8]=>[6,7,3,5,4,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[5,3,7,6,4,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,7,5,4,1,8,2,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[3,7,5,4,1,8,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,7,5,1,4,8,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,7,5,1,4,8,2,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[3,5,7,1,2,6,8,4]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,5,7,2,1,6,8,4]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[5,3,7,1,6,2,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,5,7,1,4,6,8,2]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[3,5,7,1,4,6,2,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[3,5,7,1,4,2,6,8]=>[6,5,7,4,2,1,3,8]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[3,5,7,2,1,4,6,8]=>[5,6,7,4,1,2,3,8]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,5,2,7,1,4,6,8]=>[5,6,3,7,1,2,4,8]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,5,2,7,4,1,6,8]=>[6,5,3,7,2,1,4,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,5,7,4,2,1,6,8]=>[6,5,7,4,2,1,3,8]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[3,5,7,4,1,2,6,8]=>[6,5,7,4,2,1,3,8]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[3,5,4,7,1,6,8,2]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,5,4,7,1,2,6,8]=>[6,5,3,7,2,1,4,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,5,4,7,2,1,6,8]=>[6,5,3,7,2,1,4,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,5,4,2,7,1,6,8]=>[6,4,3,2,7,1,5,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,5,4,7,2,1,8,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,5,4,7,1,2,8,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,7,6,3,1,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,6,3,1,8,2,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,5,7,4,1,2,8,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[3,5,7,4,2,1,8,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[3,2,5,7,1,4,8,6]=>[5,2,6,8,1,3,7,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,5,2,7,1,4,8,6]=>[5,6,3,8,1,2,7,4]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,5,7,2,1,4,8,6]=>[5,6,8,4,1,2,7,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,5,7,1,4,2,8,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[3,7,5,2,1,8,6,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,7,2,5,1,8,6,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,2,7,5,1,8,6,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,2,7,5,1,8,4,6]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,7,2,5,1,8,4,6]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,7,5,2,1,8,4,6]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[6,1,2,5,7,4,8,3]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,3,2,7,4,1,8,5]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,1,7,5,8,4,6,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,7,3,6,8,4,1,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,1,8,3,4,7,5,6]=>[2,1,8,4,5,7,6,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,1,7,2,4,8,3,6]=>[7,2,8,4,5,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,4,2,6,7,1,8,5]=>[6,3,2,8,5,1,7,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[3,5,8,7,2,1,6,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[1,3,4,5,6,7,9,2,8]=>[1,8,3,4,5,6,9,2,7]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,4,5,6,7,8,9,3]=>[2,1,9,4,5,6,7,8,3]=>[2,1,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,3,4,1,7,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,8,7,2,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,6,4,1,7,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,5,6,8,1,7,2]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,7,6,4,1,8,5,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,7,4,1,8,6,5,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,8,4,1,7,6,5,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,2,7,6,1,5,4,8]=>[5,2,7,6,1,4,3,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,2,8,7,6,1,5,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,7,8,2,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,2,5,8,1,6,7,3]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,2,5,8,1,7,3,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,8,2,4,1,6,3,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[8,4,2,6,5,1,3,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,2,6,8,1,5,4,7]=>[5,2,7,8,1,6,3,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[8,3,2,5,6,1,4,7]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,2,8,6,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,2,6,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,2,6,7,1,5,4,8]=>[5,2,7,6,1,4,3,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[8,7,3,2,5,6,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,8,1,5,3,6,4]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,4,2,7,5,1,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,2,8,5,1,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,4,1,8,3,6,5]=>[8,4,6,2,7,3,5,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,2,8,5,7,1,4,6]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,6,5,7,1,8,3,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,5,1,8,7,4,3,6]=>[3,7,1,8,6,5,2,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[8,1,4,6,3,5,2,7]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,5,4,1,6,2,7]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,6,3,4,1,5,2,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,7,6,8,2,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,1,8,2,3,7,6,5]=>[5,2,8,4,1,7,6,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,1,8,5,3,4,7,6]=>[2,1,8,6,5,4,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,2,4,6,8,7,3,1]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,6,8,3,4,5,7,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,4,8,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,2,6,7,8,1,3]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,4,2,7,3,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,4,1,8,3,5,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,5,4,8,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,4,2,1,3,6,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,1,3,2,5,6,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,2,3,1,7,5,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,4,3,2,6,8,5,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,7,4,3,8,5,6,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,3,7,2,1,5,6,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,7,8,2,4,3,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,4,7,3,2,6,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,1,6,7,4,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,2,5,7,4,8,1,6]=>[7,2,5,8,3,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,2,7,3,4,1,5,6]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,1,6,3,5,8,2,4]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,8,5,6,7,1,4,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[1,5,2,7,8,6,4,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,8,5,1,4,7,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,4,2,8,6,5,7,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,1,6,8,7,2,4]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,7,6,2,1,3,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,5,8,7,4,1,6,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[4,1,7,5,2,6,8,3]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,2,4,5,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,3,4,2,5,8,6,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,7,4,2,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,4,5,2,6,7,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,2,4,8,6,7,1,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,6,2,1,3,7,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,2,1,5,6,7,8,3]=>[8,3,2,4,5,6,7,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,4,6,5,1,7,8,2]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[7,3,5,2,4,6,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,3,7,2,4,6,1,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[3,7,5,2,4,6,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,7,3,2,4,6,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,7,3,2,1,4,6,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[5,7,3,2,4,1,6,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[3,7,2,5,4,1,6,8]=>[6,7,3,5,4,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[5,1,3,2,4,7,6,8]=>[5,2,4,3,1,7,6,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[7,1,3,2,5,4,6,8]=>[7,2,4,3,6,5,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,2,7,5,1,4,6,8]=>[5,2,7,6,1,4,3,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[5,7,3,1,2,4,6,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[5,3,2,7,4,1,6,8]=>[6,5,3,7,2,1,4,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,3,2,4,7,1,6,8]=>[6,4,3,2,7,1,5,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,3,2,1,4,7,6,8]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,3,2,1,7,4,6,8]=>[6,4,3,2,7,1,5,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[7,3,1,2,5,4,6,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[5,3,1,2,7,4,6,8]=>[6,4,3,2,7,1,5,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,3,1,2,4,7,6,8]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,2,5,1,4,7,6,8]=>[4,2,5,1,3,7,6,8]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[7,3,1,5,2,4,6,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[7,5,1,3,2,4,6,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,7,1,3,2,4,6,8]=>[6,7,3,5,4,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,2,1,7,5,4,6,8]=>[3,2,1,7,6,5,4,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,1,2,7,5,4,6,8]=>[3,2,1,7,6,5,4,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,1,7,5,2,4,6,8]=>[5,2,7,6,1,4,3,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[7,1,5,3,2,4,6,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,7,5,3,2,4,6,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,4,5,7,9,6,8]=>[1,2,3,4,5,8,9,6,7]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,6,9,5,7,8]=>[1,2,3,4,7,9,5,8,6]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,5,9,4,6,7,8]=>[1,2,3,6,9,4,7,8,5]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,4,9,3,5,6,7,8]=>[1,2,5,9,3,6,7,8,4]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,3,9,2,4,5,6,7,8]=>[1,4,9,2,5,6,7,8,3]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,9,8,7,6,2,5,4,3]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[3,9,8,7,6,5,2,1,4]=>[8,9,7,6,5,4,3,1,2]=>[8,9,7,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[1,10,9,8,7,6,5,2,4,3]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[4,9,8,7,6,1,2,5,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[1,10,9,8,7,6,2,5,4,3]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,8,7,4,2,6,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,9,8,7,1,2,6,4,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[2,8,5,1,7,6,4,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[6,9,8,2,1,7,5,4,3]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[6,8,5,1,2,7,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,10,1,9,8,7,6,5,4,3]=>[3,10,1,9,8,7,6,5,4,2]=>[3,10,1,9,8,7,6,5,4,2]=>[[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]]
[3,10,9,8,7,6,5,2,1,4]=>[9,10,8,7,6,5,4,3,1,2]=>[9,10,8,7,6,5,4,3,1,2]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[1,11,10,9,8,7,6,5,2,4,3]=>[1,11,10,9,8,7,6,5,4,3,2]=>[1,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,9,8,7,6,3,2,5,4]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,10,9,8,7,6,1,2,5,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,11,10,9,8,7,6,2,5,4,3]=>[1,11,10,9,8,7,6,5,4,3,2]=>[1,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,9,8,7,4,2,6,5,3]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,9,8,7,6,3,2,1,5]=>[8,9,7,6,5,4,3,1,2]=>[8,9,7,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[5,10,9,8,7,1,2,6,4,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[2,8,1,4,7,6,5,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[5,9,8,7,4,1,2,6,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,10,9,8,2,1,7,5,4,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,8,7,4,3,2,6,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,9,8,5,1,2,7,4,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,10,9,1,2,8,6,5,4,3]=>[10,9,8,4,5,7,6,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[1,8,5,4,2,7,6,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,9,6,2,1,8,5,4,3]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[9,2,1,10,8,7,6,5,4,3]=>[10,3,2,9,8,7,6,5,4,1]=>[10,3,2,9,8,7,6,5,4,1]=>[[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.]
[1,2,11,10,9,8,7,6,5,4,3]=>[1,2,11,10,9,8,7,6,5,4,3]=>[1,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[7,5,3,4,2,8,1,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,3,6,2,4,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,6,3,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,6,2,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,3,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,2,3,6,8,5,4]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,6,4,8,2,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[3,5,1,4,8,2,7,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,7,5,4,8,2,6,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,5,1,6,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,7,5,4,8,1,3,6]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,7,5,4,8,6,1,3]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,7,5,4,8,6,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,4,2,8,7,1,5]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[3,5,2,4,8,1,6,7]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,5,6,4,8,1,2,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,5,6,4,8,7,2,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,4,1,8,7,2,5]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[3,6,4,5,8,7,2,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,6,4,3,8,5,2,7]=>[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,3,4,5,8,2,6]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,1,4,5,3,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,6,1,3,5,4,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,1,3,2,5,8,4,6]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,4,2,8,5,3,7]=>[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,5,8,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,5,8,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,4,3,8,1,7,5]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[2,6,4,3,8,5,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,2,3,1,5,8,6,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[7,1,5,6,3,8,4,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,3,6,5,1,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,2,6,5,3,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,2,3,1,4,8,6,5]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[7,2,3,5,4,8,6,1]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,6,4,5,8,1,7,3]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[2,5,6,4,8,3,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[3,5,6,1,4,7,8,2]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[7,6,1,3,4,5,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,6,1,5,3,4,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,6,1,5,4,3,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,6,4,5,8,3,2,7]=>[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,5,8,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,6,8,7,2,1,5]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[3,5,6,8,2,1,7,4]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[4,2,1,5,3,7,8,6]=>[5,3,2,4,1,8,7,6]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,2,5,6,3,1,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,5,6,8,1,7,2,4]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[4,1,5,6,3,2,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,5,3,1,7,2,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,1,3,5,2,7,8,6]=>[5,2,3,4,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,5,4,7,3,8,6,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,5,7,1,8,4,2,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[4,1,5,3,2,7,8,6]=>[5,2,4,3,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,5,3,7,1,2,8,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,1,3,2,4,6,7,8]=>[5,2,4,3,1,6,7,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,6,1,7,4,5,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,1,3,4,2,6,7,8]=>[5,2,4,3,1,6,7,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[5,3,1,4,2,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,5,2,3,7,1,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,6,2,1,7,4,8,5]=>[4,8,3,1,6,5,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,1,4,7,6,5,2,8]=>[7,2,3,6,5,4,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,6,2,7,1,5,8,4]=>[5,8,3,6,1,4,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,6,2,7,1,3,5,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[3,5,7,1,8,2,6,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[5,1,4,2,3,6,7,8]=>[5,2,4,3,1,6,7,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,6,1,7,2,5,8,4]=>[5,8,3,6,1,4,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,6,5,3,4,7,8,1]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[3,6,1,7,5,4,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,1,4,3,2,6,7,8]=>[5,2,4,3,1,6,7,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[5,4,1,3,2,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[6,4,2,5,3,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,6,2,3,5,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,2,4,5,1,8,3,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[8,2,6,7,1,4,5,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[8,2,6,7,4,1,5,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,6,2,3,5,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[2,6,4,1,5,8,3,7]=>[4,7,5,1,3,8,2,6]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,8,1,6,7,4,5,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[6,8,4,5,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,6,1,4,7,5,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,8,1,6,4,7,5,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,6,1,4,8,5,3,7]=>[3,7,1,6,8,4,2,5]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[6,4,5,2,8,3,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,2,3,6,1,8,5,7]=>[5,3,2,7,1,8,4,6]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,2,3,1,6,8,5,7]=>[4,3,2,1,7,8,5,6]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,2,3,8,6,1,7,5]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[6,4,5,8,2,3,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[8,6,7,2,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,8,5,2,3,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,2,8,3,1,6,7,5]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[2,4,8,1,3,6,7,5]=>[4,5,8,1,2,7,6,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,4,1,8,3,6,7,5]=>[3,5,1,8,2,7,6,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,1,4,8,6,3,7,5]=>[2,1,6,8,7,3,5,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,4,8,2,5,3,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,6,2,4,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,8,2,3,5,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,6,8,4,1,5,7,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,6,8,1,4,5,7,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,1,6,8,4,5,7,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,8,1,4,6,7,3,5]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[4,8,6,2,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,2,6,7,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,4,5,1,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,6,7,5,3,4,8,2]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,2,3,8,4,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,6,7,5,8,2,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,2,5,8,3,4,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[6,2,3,8,7,4,1,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,4,7,3,5,8,6,1]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,5,3,7,1,8,4,6]=>[5,7,3,8,1,6,2,4]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[5,2,8,3,1,4,6,7]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[4,8,2,3,6,5,7,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,8,1,3,6,4,7,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,1,4,3,6,2,7]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,8,4,1,3,7,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,4,5,3,8,1,7,2]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,6,5,3,7,1,2,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,5,1,3,6,2,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,2,6,5,1,7,3,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,3,5,7,2,1,6,8]=>[6,5,3,7,2,1,4,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,4,7,6,8,1,2,5]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[3,4,6,2,5,8,7,1]=>[8,4,5,2,3,7,6,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,5,2,4,6,1,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,2,5,1,6,8,3,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,8,2,3,6,5,7,4]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,2,8,3,5,7,1,6]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,3,8,6,5,7,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,3,8,4,1,7,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[7,5,3,4,8,2,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,8,3,4,1,5,6]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,4,3,8,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,2,7,3,1,5,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[7,6,3,8,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,8,5,1,3,4,6]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,5,3,7,6,8,4,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,3,7,8,2,4,5]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,2,6,5,7,8,3,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,2,6,7,5,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,2,6,7,8,1,4,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,1,8,3,6,4,7,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,6,8,5,7,2,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,1,3,8,7,6,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,8,5,6,1,7,2,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,4,8,1,7,6,2,5]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,7,6,8,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,4,8,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,6,8,7,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,4,6,7,2,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,2,8,3,7,1,6,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,4,5,8,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,6,8,7,1,5,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,4,8,3,1,7,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,5,8,7,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,4,8,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,4,8,2,7,3,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,6,8,3,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,3,8,2,7,5,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,3,8,1,7,2,6,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,5,8,1,3,7,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,3,8,2,7,4,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,4,8,1,3,7,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,2,8,3,4,7,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,3,1,4,2,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,5,4,3,7,8,2,6]=>[1,7,4,3,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,4,2,5,3,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,2,7,8,5,3,1,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,2,5,3,1,7,8,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,2,8,7,6,3,1,5]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,2,7,6,3,1,5,8]=>[6,5,7,4,2,1,3,8]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[6,3,1,7,5,2,4,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,3,1,8,7,5,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,3,1,7,5,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,2,7,6,3,1,8,5]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[7,6,3,1,8,4,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,4,2,1,8,3,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,8,2,7,6,4,3,5]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,3,5,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,2,5,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,2,4,8,6,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,5,2,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,2,4,6,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,2,8,6,3,7,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,5,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,6,4,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,2,7,5,3,6,4]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,5,2,1,8,3,6,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,5,2,6,3,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,2,7,4,1,8,6,3]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,2,8,7,4,1,6,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,7,4,1,5,2,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,1,5,2,8,6,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,3,1,4,2,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,2,8,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,5,2,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,2,1,3,6,4,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[8,7,5,2,1,3,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,2,1,3,8,6,4]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,3,7,6,5,8,2,4]=>[1,7,8,5,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,4,7,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,8,7,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,7,5,2,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,3,1,4,7,5,2,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,3,1,4,8,7,5,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,3,1,4,7,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,7,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,2,5,7,6,4,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,6,4,7,5,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,5,2,1,6,4,8,3]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,3,8,7,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,7,4,1,5,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,1,6,3,5,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,4,1,8,6,3,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,6,3,1,7,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,7,5,2,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,6,4,7,5,3,8,2]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,3,5,2,7,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,5,2,8,7,4,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,3,5,2,7,4,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,5,7,2,6,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,5,8,4,6,1,7,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,4,7,3,5,2,6,8]=>[1,6,7,4,5,2,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,4,2,6,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,2,6,3,5,7,1,8]=>[7,4,5,2,3,6,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[2,4,5,8,1,6,7,3]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[8,3,4,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,2,5,7,8,1,6,3]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,3,4,6,5,1,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,1,7,3,5,2,6,8]=>[6,2,7,4,5,1,3,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,1,3,7,4,2,5,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,1,6,8,2,7,4,5]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[6,1,3,8,2,5,4,7]=>[7,2,5,8,3,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,8,2,3,1,6,7,5]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,2,6,8,1,5,7,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[8,2,6,1,5,4,7,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,6,2,7,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,6,8,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,4,2,8,1,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,7,2,8,1,5,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,5,2,8,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,3,8,1,5,6,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,6,8,5,2,4,3,7]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,5,7,2,8,1,6,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,5,6,8,3,1,7,2]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[8,4,6,5,3,1,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,4,8,3,1,7,2]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[4,8,1,6,2,3,7,5]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,5,3,1,7,2,6,8]=>[6,4,3,2,7,1,5,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,2,7,1,3,6,4,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[7,8,1,2,4,3,6,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,1,6,2,3,7,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,8,3,1,2,5,7,6]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[4,1,3,6,5,7,8,2]=>[8,2,3,5,4,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,3,4,2,8,5,7]=>[7,2,5,4,3,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,1,4,2,5,7,6,3]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,3,5,7,6,2]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,2,4,1,3,7,8,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[2,6,5,3,1,7,8,4]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[8,3,2,1,5,7,6,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,7,4,3,6,8,2,5]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,6,3,1,8,4,5]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,8,4,6,3,7,5,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,7,1,3,6,5,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,8,5,7,4,2,6,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,8,6,5,7,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,6,2,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,5,3,8,2,1,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,1,5,3,8,4,2,7]=>[7,2,6,4,8,3,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,1,5,4,7,2,6,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,1,4,7,5,8,3,6]=>[2,1,7,8,5,6,3,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,3,5,8,7,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,2,8,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,4,8,7,3,5,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,7,6,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,6,8,5,7,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,6,8,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,2,8,6,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,5,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,7,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,7,6,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,7,2,5,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,6,7,4,8,1,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,5,7,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,4,7,8,2,6,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,7,8,1,6,5,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[4,2,6,8,7,1,5,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[3,1,7,8,2,6,5,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[6,1,3,8,2,7,5,4]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,8,4,2,7,6,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,6,1,7,5,4,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,8,3,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,3,8,1,6,5,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,7,3,8,2,6,5,4]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,8,4,1,7,5,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[4,5,8,6,3,1,7,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,6,7,1,2,8,5,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,6,1,8,2,7,5,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[5,7,4,1,2,8,6,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,3,7,1,2,8,5,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,2,1,8,3,7,5,4]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,1,5,6,3,2,4,7]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,8,3,5,2,4,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,5,3,7,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,2,4,8,5,3,6]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,5,4,3,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,8,7,4,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,2,6,7,8,4,3,5]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,5,8,4,1,3,6]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,1,7,8,4,5,3,6]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,7,8,2,1,5,4,6]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[8,5,1,4,7,3,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,7,5,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,4,6,7,3,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,5,8,6,7,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,8,4,7,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,1,3,6,8,2,5]=>[7,8,3,4,5,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,7,6,4,8,1,2,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,1,7,5,6,8,2,4]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,3,6,5,7,1,8,4]=>[6,2,8,4,5,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,7,5,4,2,1,8,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,3,6,7,4,2,8,5]=>[1,6,8,5,4,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,4,8,2,7,5,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,4,6,3,2,7,8,5]=>[1,5,8,4,2,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,1,5,6,3,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,6,7,5,3,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,8,6,5,3,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,2,4,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,8,2,6,4,5,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,2,5,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,2,5,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,3,2,1,5,6,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,2,6,7,3,1,5,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,7,2,8,5,6,4,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,1,8,4,6,5,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,7,8,2,1,6,5,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[8,7,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,1,2,3,7,5,6]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,8,2,3,6,5,4,7]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,8,4,7,2,6,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,8,5,4,6,2,3,7]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,8,5,4,6,1,2,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,8,5,1,6,4,2,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,8,5,4,6,1,3,7]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,8,5,4,6,3,1,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,8,5,4,6,3,2,7]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,8,4,7,3,6,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[3,6,4,2,7,8,5,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,5,4,1,6,2,7,8]=>[6,4,3,2,5,1,7,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,5,8,1,7,6,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,5,8,4,7,1,6,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,5,8,4,7,3,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,4,1,7,8,5,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,6,4,8,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,4,3,7,8,5,2]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,3,4,8,6,5,2]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,1,3,8,4,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,6,4,2,7,8,3,5]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,4,3,7,1,8,5]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[2,6,4,1,7,8,3,5]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[7,2,3,4,8,6,5,1]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,3,1,8,6,4,5]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[7,2,3,4,1,6,8,5]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,2,4,3,8,5,7,6]=>[1,2,4,3,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,3,8,6,1,4,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,8,6,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,3,1,5,6,8,4]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[7,2,3,8,1,6,5,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,2,3,8,5,6,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,6,4,8,7,1,5,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[1,5,8,4,7,6,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,8,1,6,7,2,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[7,6,1,3,5,8,2,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,3,2,5,6,8,4]=>[8,2,4,3,6,5,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,3,8,2,6,5,4]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,1,8,5,4,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,1,6,5,8,2,7,3]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,6,5,8,4,7,2]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,6,5,8,4,7,1]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,3,7,1,6,5,8,2]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[5,2,6,4,8,3,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,1,6,4,8,3,7,2]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,6,4,8,2,7,3]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,2,6,4,8,1,7,3]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,3,7,5,8,1,6,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,3,7,5,8,2,6,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[5,3,7,4,8,2,6,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[5,3,7,4,8,1,6,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[5,4,8,1,6,2,7,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,3,7,2,6,1,8,5]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[4,3,7,1,5,2,8,6]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[4,3,7,1,6,2,8,5]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[5,4,8,2,6,3,7,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[5,4,8,1,6,3,7,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,1,7,8,6,3,2,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,7,2,8,3,5,1,6]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,2,6,8,3,7,4,5]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,3,2,1,4,7,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,2,4,1,6,5,8,3]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,5,8,4,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,2,4,1,3,7,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[2,8,4,7,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,2,7,5,8,4,3]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,2,7,3,8,5,6,1]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,5,2,6,8,3,7,1]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,8,3,2,5,7,6,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,2,4,3,8,5,6,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,8,5,3,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,6,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,4,1,5,3,7,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,4,7,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,3,5,2,6,7,4]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,3,5,1,4,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,4,2,3,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,2,4,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,2,1,3,5,6,4,7]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,2,1,3,5,4,7,6]=>[8,3,2,4,6,5,7,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,1,3,4,2,6,5,7]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,3,4,2,5,7,6]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,3,2,5,6,4,7]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,4,5,3,7,6]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,4,3,6,7,5]=>[8,2,3,5,4,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[10,2,1,4,3,6,5,8,7,9]=>[10,3,2,5,4,7,6,9,8,1]=>[10,3,2,9,8,7,6,5,4,1]=>[[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.]
[12,2,1,4,3,6,5,8,7,10,9,11]=>[12,3,2,5,4,7,6,9,8,11,10,1]=>[12,3,2,11,10,9,8,7,6,5,4,1]=>[[[[.,.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]],.]
[6,5,3,8,4,2,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[7,4,5,1,6,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,7,3,5,6,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,7,8,4,1,3,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,1,6,8,4,7,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,6,1,5,7,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,2,7,5,8,6,1,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,5,4,7,8,1,6,3]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,4,6,7,8,1,5,3]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,4,6,8,1,7,5,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[7,4,3,8,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,7,8,3,5,6,1]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[3,2,7,6,1,8,4,5]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,2,6,8,1,7,4,5]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,3,6,2,1,8,5,7]=>[5,4,7,2,1,8,3,6]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[3,6,4,2,5,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,6,2,3,7,5,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,8,4,2,3,6,7,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,4,5,3,2,1,7,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,8,3,4,2,1,7,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[6,8,4,2,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,8,3,2,7,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,3,7,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,6,4,7,1,8,3]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[2,5,4,8,1,6,7,3]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[6,4,7,3,8,2,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,4,3,2,1,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,4,3,7,2,1,5,6]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,2,6,5,8,7,3,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,8,4,6,7,3]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,7,4,6,8,3]=>[1,8,3,6,5,4,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,2,7,3,6,8,4]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,2,8,3,6,7,4]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,3,4,8,7,2,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,5,3,4,8,7,2,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,1,2,8,3,6,7,5]=>[5,2,3,8,1,7,6,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,1,2,7,3,6,8,5]=>[5,2,3,8,1,6,7,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[7,5,3,8,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,3,7,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,1,2,3,4,7,6]=>[6,8,3,4,5,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[7,1,2,8,3,6,4,5]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,8,2,3,5,7,4]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,7,2,3,5,8,4]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,8,2,4,5,7,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,8,7,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,2,7,4,6,5,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,6,2,3,5,8,4]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,6,2,3,5,7,4]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,2,3,5,6,4]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,8,3,7,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,7,3,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,7,2,4,5,3,6]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,1,2,3,4,6,5]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,1,2,3,4,7,5]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,6,2,3,5,4,7]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,6,2,4,5,3,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,7,4,6,3,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,7,5,1,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,2,5,8,7,3,6,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,8,3,5,7,2,6,4]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,3,4,6,8,5,7,1]=>[8,2,3,6,7,4,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,5,7,4,8,6,1]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,4,6,3,7,8,5,1]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,5,7,1,8,6,3,4]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[8,2,4,5,1,3,7,6]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[2,6,7,1,8,4,5,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[5,8,3,1,4,2,6,7]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[3,8,4,2,6,7,1,5]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[2,4,1,8,5,6,3,7]=>[3,7,1,8,5,6,2,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,6,2,7,8,5,3,4]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,2,6,7,8,4,1]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,5,1,6,7,3,8,2]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,8,4,1,7,5,3,6]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[8,5,3,1,7,4,2,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,2,8,7,1,5,3,6]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[5,2,6,8,1,7,4,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[5,7,3,2,6,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,4,7,3,1,6,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,1,2,3,5,8,4]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,1,6,7,8,4,2,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,1,4,8,5,6,2,7]=>[7,2,3,8,5,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,3,1,4,5,7,2,6]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,6,7,8,9,2,3,4,5]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[6,7,8,9,1,2,3,4,5,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,7,8,9,2,3,4,5,6]=>[1,9,8,7,5,6,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,7,8,9,10,2,3,4,5,6]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[6,7,8,9,10,1,2,3,4,5,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[5,6,7,8,9,1,2,3,4,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,6,7,8,2,9,3,4,5]=>[1,9,8,7,5,6,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,6,7,8,9,10,2,3,4,5]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,7,8,9,10,11,2,3,4,5,6]=>[1,11,10,9,8,7,6,5,4,3,2]=>[1,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[8,6,2,3,5,1,4,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,4,5,7,3,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,6,3,8,7,5,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,2,3,7,5,4,1,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,2,6,3,5,4,1,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,1,5,2,4,3,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,2,4,1,5,3,7]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,4,1,6,5,3,2,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,6,1,5,4,2,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,2,6,5,4,1,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,2,5,7,4,1,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,1,7,5,4,2,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,2,7,4,1,5,3,6]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[6,1,3,8,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,6,1,8,7,5,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,1,5,7,6,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,5,2,8,7,6,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,4,8,2,7,6,5,1]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,4,8,7,1,6,5,2]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[8,1,3,5,7,6,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,8,5,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,7,1,4,5,6,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,1,7,3,4,6,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,1,7,2,6,5,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,8,2,4,7,6,5,1]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,8,3,7,4,6,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,2,3,7,1,6,5,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,2,7,1,3,6,5,4]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,1,7,2,6,4,3,5]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,5,2,4,3,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,3,7,4,6,1,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,4,8,5,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,4,3,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,2,7,3,5,1,4,6]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,2,7,4,3,1,5,6]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,2,7,3,1,5,6,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,2,1,5,7,6,4,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,2,1,8,7,5,4,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,1,8,2,7,5,4,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,3,5,2,6,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,5,2,7,6,4,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,2,4,6,5,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,4,1,7,6,5,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,2,8,3,7,6,5,1]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,8,2,1,7,6,5,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,1,8,7,2,6,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,8,1,3,7,6,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,2,5,4,1,7,6,3]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,1,4,8,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,3,7,6,5,2]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,8,1,3,7,6,5,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,3,8,1,7,6,5,2]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[5,8,6,3,2,1,7,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,6,3,2,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,5,7,2,4,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,7,1,3,2,8,6,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,1,3,2,7,4,6]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[8,5,1,3,2,4,6,7]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,5,1,3,2,4,8,6]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,5,8,2,1,4,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,1,2,5,4,8,3]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,8,1,2,5,7,4,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,2,3,8,6,4,5]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,6,4,2,3,5,7]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,5,4,8,2,3,7,6]=>[1,6,5,8,3,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,2,3,5,6,4]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,5,8,2,3,1,4,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,1,2,6,8,3,5]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,2,8,1,5,7,3,4]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,2,5,4,1,8,6,3]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[7,3,5,4,2,1,8,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,3,2,8,5,6,1,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,7,4,3,6,8,5,2]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,7,6,5,2,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,7,6,5,1,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,4,6,8,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,4,2,1,8,5,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,7,3,2,1,8,5,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,7,6,3,2,8,4,5]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,2,1,7,3,6,8]=>[6,4,3,2,7,1,5,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[6,5,8,1,7,3,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,8,2,3,7,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,8,3,4,1,7,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,1,2,8,5,3,6,7]=>[6,2,3,8,5,1,7,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,7,4,1,6,5,2,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[3,5,8,2,6,1,7,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[3,7,6,1,5,2,8,4]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,7,6,2,5,8,4,3]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,6,5,8,4,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,6,5,8,1,2,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,7,6,2,8,4,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,3,6,8,5,1,2,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[2,7,1,5,8,4,3,6]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,7,6,1,8,4,3,5]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[7,1,2,6,3,5,4,8]=>[7,2,3,6,5,4,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,2,6,3,4,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,8,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,2,5,7,8,4,3]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,7,3,1,2,6,8,5]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,7,6,1,5,8,2,4]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[3,8,5,6,4,2,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,2,6,4,7,8,5,1]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,2,7,5,8,3,1,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[4,2,7,1,3,8,6,5]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[5,2,1,4,7,8,3,6]=>[7,3,2,4,8,6,1,5]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[5,6,2,7,3,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,1,3,8,5,4,7,2]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,7,6,8,5,1,3,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,7,6,8,5,3,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,5,8,6,4,2,3,7]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,8,6,4,1,7,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[4,7,2,3,1,6,8,5]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[6,7,3,1,5,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,4,6,2,8,3,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,5,1,4,8,2,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,4,6,5,1,2,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[7,5,4,3,8,6,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,3,8,2,6,7,5,1]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,3,8,2,5,7,1,6]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,1,6,2,5,3,7,8]=>[6,2,5,4,3,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,1,8,6,4,7,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,8,5,6,3,7,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,2,6,1,5,3,8,7]=>[6,4,5,2,3,1,8,7]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[6,7,2,3,1,5,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,2,3,8,1,6,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,2,3,8,4,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,1,7,6,3,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,1,7,5,2,3,4,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,3,1,4,2,5,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,1,6,2,8,7,3]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,8,3,6,1,7,2,5]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[6,2,7,8,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,3,4,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[4,2,3,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,4,6,8,9,7,5,3]=>[1,2,9,8,7,6,5,4,3]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,4,6,8,10,9,7,5,3]=>[1,2,10,9,8,7,6,5,4,3]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[2,1,7,5,8,6,3,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[4,7,3,8,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,8,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,3,6,5,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,5,8,7,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,6,7,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,2,7,6,5,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,6,7,8,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,3,8,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,8,5,4,1,7,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,4,7,2,5,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,3,8,7,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,6,4,1,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,8,4,3,5,7,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,4,8,7,6,1,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,2,4,5,1,8,6,7]=>[5,2,3,4,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,2,5,1,7,8,3,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[2,5,4,1,3,8,6,7]=>[4,5,3,1,2,8,7,6]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[5,1,8,2,4,3,6,7]=>[6,2,8,4,5,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,5,4,8,2,3,6,7]=>[1,6,5,8,3,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,1,4,7,8,2,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[4,8,3,1,6,7,2,5]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[3,4,8,2,6,5,7,1]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,6,2,4,8,7,1,5]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,7,3,2,6,8,1,5]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[7,3,4,6,8,1,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,7,2,5,8,1,4]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,5,6,8,3,7,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,5,8,3,4,7,2]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,8,1,3,4,7,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[2,8,5,6,3,4,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,1,3,5,4,7,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,6,3,5,4,7,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,7,3,6,4,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,2,5,8,4,6,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,2,4,8,1,7,3,5]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[3,1,7,8,5,4,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,2,7,4,8,5,3]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,1,8,4,3,5,6]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[6,7,1,8,3,2,4,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,7,6,3,5,8,1,4]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[2,7,5,6,8,1,3,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[6,7,2,8,1,3,4,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,1,6,8,7,2,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,5,7,6,8,2,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,6,8,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,5,7,8,3,6,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[4,6,2,5,7,1,8,3]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[3,8,6,7,5,1,2,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,7,5,8,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,8,3,2,5,4,7]=>[1,7,8,5,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,5,1,3,2,6,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,6,8,1,5,4,7,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,5,4,7,6,2,8,3]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,3,7,6,5,1,8,4]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,1,5,8,3,2,7,4]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,2,4,8,5,7,6]=>[3,2,1,4,8,6,7,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,5,8,4,6,3,1,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[7,1,5,4,8,3,2,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,1,7,5,3,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[2,7,6,4,8,1,5,3]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[7,2,5,4,8,1,6,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,7,2,5,3,8,6,4]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,3,8,6,1,5,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,3,2,5,8,1,6,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,3,8,4,1,2,6,7]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[2,4,8,3,7,1,5,6]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[5,2,8,4,1,6,3,7]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[7,6,5,2,1,8,4,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,7,5,1,8,3,6,4]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[5,1,8,7,4,3,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,8,7,2,4,6,1,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,7,1,3,2,4,8,6]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,2,7,6,3,5,8,1]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,4,7,6,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,7,4,2,3,5,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,5,1,3,8,7,4,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,7,8,3,2,5,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,1,8,5,3,7,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,6,8,3,7,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,5,1,7,4,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,4,1,3,5,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,2,3,7,1,4,5,6]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,8,3,7,1,4,5,6]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[5,6,2,7,4,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,6,2,7,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,8,2,6,1,4,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[3,7,8,5,2,1,4,6]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[6,8,4,7,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,6,5,1,2,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,6,5,1,2,3,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,4,5,1,7,6,8,2]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,8,7,6,5,1,2,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,4,6,7,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,2,6,1,8,4,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,2,6,1,3,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,8,2,6,1,4,7,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[3,8,7,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,4,7,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,6,5,1,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,7,3,4,5,2,8,6]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,8,2,1,3,5,6,7]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[1,7,2,5,4,3,8,6]=>[1,8,3,6,5,4,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,7,3,4,8,1,5]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[2,1,5,7,4,3,8,6]=>[2,1,6,8,5,3,7,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[4,1,8,7,5,6,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,5,8,7,4,3,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,4,1,3,8,7,5,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,1,7,4,6,8,3,5]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,7,2,4,6,8,3,5]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,4,2,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,6,1,2,3,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,8,6,2,7,3,5,4]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,6,2,3,5,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,8,3,5,7,6,4]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,5,8,1,7,6,2,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,8,1,3,6,7,5,4]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[7,2,4,8,6,1,5,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,4,1,5,6,7,8,9,10,3]=>[3,10,1,4,5,6,7,8,9,2]=>[3,10,1,9,8,7,6,5,4,2]=>[[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,5,6,7,8,9,10,3]=>[10,2,3,4,5,6,7,8,9,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[6,4,3,2,8,1,7,5]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,2,4,3,8,1,7,5]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,8,4,3,1,6,7,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[10,5,2,4,7,9,6,8,1,3]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[10,9,2,8,5,7,4,6,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,7,2,6,5,9,4,8,1,3]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[6,10,5,9,8,7,2,4,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,3,5,8,2,4,7,6,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,7,3,6,2,5,4,10,1,9]=>[9,7,6,5,4,3,2,10,1,8]=>[9,7,6,5,4,3,2,10,1,8]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]
[3,6,10,9,8,2,5,7,4,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,3,6,2,5,4,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[4,8,3,7,6,5,2,10,1,9]=>[9,7,6,5,4,3,2,10,1,8]=>[9,7,6,5,4,3,2,10,1,8]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]
[4,6,10,3,5,9,8,7,2,1]=>[10,9,8,5,4,7,6,3,2,1]=>[10,9,8,5,4,7,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[10,9,4,8,3,7,6,5,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[5,10,4,9,8,7,6,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[12,11,10,9,2,4,6,8,1,3,5,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,2,10,7,9,4,6,8,1,3,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,2,8,7,11,4,6,10,1,3,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,12,7,11,10,9,2,4,6,1,3,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,9,8,7,2,4,6,1,3,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,6,10,5,9,2,4,8,1,3,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,9,2,8,5,7,4,6,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[6,8,12,5,7,11,10,9,2,4,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,6,10,5,9,8,7,2,4,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,7,6,12,5,11,10,9,2,4,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,12,6,11,10,9,8,5,2,4,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,9,8,7,6,5,2,4,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,9,4,8,3,7,2,6,1,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,9,3,5,8,2,4,7,6,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,3,6,10,9,8,2,5,7,4,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[3,12,7,11,10,9,6,8,2,5,4,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,9,8,7,3,6,2,5,4,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,5,10,4,9,3,8,2,7,6,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,4,6,10,3,5,9,8,7,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[4,7,12,11,10,3,6,9,8,5,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,9,4,8,3,7,6,5,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,5,10,4,9,8,7,6,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[6,12,5,11,10,9,8,7,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[4,2,8,1,5,7,6,3]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,3,7,2,5,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,4,7,3,2,6,8,1]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,7,2,6,3,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,7,5,4,6,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,8,3,2,1,7,4,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,8,1,7,5,3,2,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,4,3,7,2,8,6,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,6,5,7,2,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,6,5,3,8,2,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[2,6,5,8,7,3,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,3,8,4,1,7,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,8,1,6,4,3,5]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,2,8,7,6,4,1,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,2,6,4,3,5,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,2,8,6,3,7,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,8,7,5,3,1,4,6]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,5,6,3,1,4,8,7]=>[5,6,4,3,1,2,8,7]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[2,4,7,8,5,3,1,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[6,5,3,2,4,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,5,8,7,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,4,7,8,5,3,6]=>[2,1,7,8,6,5,3,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,3,1,6,5,7,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,6,7,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,5,3,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,3,1,4,6,7,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,1,6,4,3,7,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,1,4,3,7,8,2,5]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,2,7,5,8,3,4]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,7,3,1,4,6,8,5]=>[4,8,3,1,5,6,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,8,3,1,6,5,7,4]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,8,5,6,7,1,2,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,5,1,2,8,4,7,3]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,5,8,1,4,6,7,3]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,1,8,7,5,4,6,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[7,8,3,4,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,3,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,5,2,3,7,1,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,7,2,8,6,3,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,7,5,2,3,8,1,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[6,4,7,5,2,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,1,3,6,4,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,5,2,3,7,8,4,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,2,6,3,1,5,8,4]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,6,3,8,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,4,1,5,7,6,3]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,8,4,2,5,7,6,3]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,5,4,1,7,6,3]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,5,8,3,7,1,6,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[1,8,5,2,4,7,6,3]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,2,8,7,5,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,2,4,1,6,5,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[2,4,6,1,8,7,5,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,8,4,5,1,7,6,3]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,5,8,2,7,6,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,1,6,8,7,5,3,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,8,2,4,5,7,6,3]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,3,5,7,6,4]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,2,5,7,6,4]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,3,8,1,5,7,6,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,6,1,8,7,5,3,4]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,6,2,8,7,5,3,4]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,3,8,7,5,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,3,8,7,5,1,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,2,8,1,5,7,6,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,1,8,2,5,7,6,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,8,1,4,5,7,6,3]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[7,8,2,1,4,6,5,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,3,6,8,7,5,1,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,1,6,8,7,2,5,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,8,4,5,1,6,2,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[6,1,4,5,7,2,3,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,1,4,7,6,3,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,1,6,4,7,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,3,8,6,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,6,1,5,7,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,6,3,1,2,5,7]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,8,1,4,5,2,3,7]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[1,5,8,4,6,2,3,7]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,6,5,3,8,4,7]=>[2,1,7,5,4,8,3,6]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,6,8,1,4,2,3,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[5,7,4,8,1,2,3,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,2,1,5,3,7,4,6]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,7,8,1,2,6,3,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[8,7,1,5,6,2,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,6,5,8,7,2,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,1,6,2,4,8,5]=>[5,8,3,6,1,4,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[5,1,2,7,6,8,3,4]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,7,2,5,8,3,4]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,6,5,8,2,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,5,7,2,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,5,1,2,6,8,3,4]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,1,5,2,7,8,3,4]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,3,8,7,2,4,5]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,2,4,6,8,5]=>[1,8,4,3,5,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,3,1,4,2,5,7,6]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,1,2,7,8,4,6,5]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[5,1,2,6,8,7,3,4]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,6,2,5,7,3,4]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,8,1,2,6,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,5,7,6,2,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,6,8,5,2,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,7,1,2,8,4,6,5]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[8,3,1,2,7,6,4,5]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,5,8,7,6,2,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,6,1,5,2,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,9,3,4,5,6,7,8,2]=>[1,9,8,4,5,6,7,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,9,8,4,5,6,7,3,2]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,10,3,4,5,6,7,8,9,2]=>[1,10,9,4,5,6,7,8,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,10,9,4,5,6,7,8,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[7,8,6,3,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,1,3,4,5,2,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,7,4,8,2,5,3,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,8,6,1,4,2,7,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[7,1,8,2,4,6,3,5]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,8,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,2,8,1,5,4,6]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,5,4,1,7,2,6,8]=>[6,4,3,2,7,1,5,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[6,4,7,3,2,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,5,3,8,4,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,5,7,8,1,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,7,4,1,6,8,5,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,1,2,7,6,8,5,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[6,3,2,8,4,5,1,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,1,8,3,5,4,2,7]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,8,5,2,4,6,1,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,5,4,8,6,3,7,2]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,8,2,5,3,7,1,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[3,8,4,5,2,6,7,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,1,8,6,5,3,7,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,8,4,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,2,8,6,4,7,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,8,1,2,7,4,3,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,7,3,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,2,3,4,8,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,3,5,4,2,8,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,1,3,2,4,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[2,5,1,3,7,8,6,4]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[4,3,7,2,1,8,6,5]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[4,6,7,2,1,3,5,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[4,6,2,3,1,5,7,8]=>[5,6,4,3,1,2,7,8]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,6,4,2,5,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[3,1,6,4,7,5,2,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,6,2,7,5,4,1,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[2,4,7,5,3,6,1,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[2,5,7,3,4,1,6,8]=>[6,5,7,4,2,1,3,8]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[2,3,5,8,6,4,7,1]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,4,7,3,8,6,5,1]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,4,2,7,5,8,6,1]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,1,5,4,7,8,6,2]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,5,7,2,3,1,8,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[3,7,8,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,5,8,7,4,1,3,6]=>[6,7,8,5,4,1,2,3]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,6,4,7,5,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,2,4,7,1,3,8,5]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[7,3,5,1,4,2,8,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,4,7,1,3,2,8,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[6,1,4,7,5,3,8,2]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,7,4,3,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,1,4,3,5,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,1,8,4,7,3,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,7,3,6,1,2,8,5]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[5,2,1,7,4,3,8,6]=>[6,3,2,8,5,1,7,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[4,7,6,2,3,1,8,5]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[7,6,8,2,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,3,6,1,8,7,5,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,6,8,7,5,3,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,4,1,7,5,2,8,3]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,7,8,2,3,6,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,1,2,5,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,7,4,1,5,6,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[8,6,2,1,5,7,4,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,8,6,7,5,2,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,1,3,7,5,8,2,4]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,7,3,1,8,5,6,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,6,7,5,3,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,6,4,5,7,3,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,1,4,5,8,3,7,2]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,8,5,3,4,7,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,5,6,8,3,7,2]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,1,8,7,2,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,5,7,2,6,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,3,8,5,2,7,4,6]=>[1,5,8,7,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,6,7,2,4,5]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,3,7,6,1,4,5]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,2,7,8,6,1,3,5]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,3,8,7,6,2,4,5]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,6,8,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,3,6,8,2,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,2,6,7,8,1,3,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,5,6,8,1,2,7,3]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[3,5,8,6,1,2,7,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[4,2,6,8,7,1,3,5]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,4,6,8,7,2,3,5]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,5,3,8,1,7,2,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,5,8,4,1,7,2,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,6,5,7,8,2,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,6,4,8,2,3,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[6,5,4,8,1,3,7,2]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[7,6,4,8,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,6,5,8,1,3,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,3,7,5,2,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,1,2,7,4,5,3,6]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,5,7,4,6,1,3,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[6,1,7,4,5,3,8,2]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,7,3,1,5,4,6]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[2,6,4,8,3,1,7,5]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[8,1,3,7,5,6,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,5,3,8,6,7,4]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,6,5,7,8,2,3]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,3,7,4,2,8,5]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,7,2,4,1,3,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,3,8,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,3,4,2,7,1,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,3,8,2,5,6,7,4]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,6,7,2,5,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,8,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,7,3,8,5,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,3,4,8,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,7,2,4,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,6,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,7,5,2,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,4,6,7,8,1,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,6,7,8,1,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,7,6,8,4,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,3,2,8,6,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,4,8,6,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,8,6,3,1,2,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,5,7,3,6,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,5,6,3,8,2,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,4,8,7,2,1,3,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[2,5,4,7,8,1,3,6]=>[6,7,3,8,5,1,2,4]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[5,3,6,4,8,2,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,3,7,4,6,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,2,6,3,7,4,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,4,7,3,5,6,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,2,6,5,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,6,2,7,3,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,4,6,1,5,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,4,6,2,8,3,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[8,4,6,1,7,2,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,2,1,6,3,8,7,4]=>[8,3,2,5,4,7,6,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,5,6,3,7,1,8,2]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,3,2,8,5,4,1,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,3,1,5,2,8,6,7]=>[5,3,2,4,1,8,7,6]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[8,5,4,1,3,2,6,7]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,8,4,1,5,2,6,7]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[2,5,4,3,8,1,6,7]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[2,5,7,4,3,1,6,8]=>[6,5,7,4,2,1,3,8]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[5,3,4,2,7,1,6,8]=>[6,4,3,2,7,1,5,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,7,5,4,1,2,6,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[4,2,5,1,3,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,3,5,1,2,7,6,8]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,3,4,1,7,2,6,8]=>[6,4,3,2,7,1,5,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,1,6,3,5,2,7,8]=>[6,2,5,4,3,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,2,1,8,6,3,7,5]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[3,7,5,4,2,1,6,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[3,7,2,4,1,6,5,8]=>[5,7,3,4,1,6,2,8]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[7,3,2,1,6,4,5,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[2,8,6,1,7,4,3,5]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,5,4,6,1,3,7,8]=>[5,6,3,4,1,2,7,8]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,5,6,4,1,3,7,8]=>[5,6,4,3,1,2,7,8]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[8,5,2,6,1,3,7,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,1,5,6,3,2,4,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,1,2,5,4,6,3,8]=>[7,2,3,6,5,4,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,4,1,6,5,3,7,8]=>[3,6,1,5,4,2,7,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[4,1,2,7,5,6,3,8]=>[7,2,3,6,5,4,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,1,2,6,5,4,3,8]=>[7,2,3,6,5,4,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,2,1,5,6,3,7,4]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,8,5,1,6,4,7,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[6,1,4,5,3,2,7,8]=>[6,2,5,4,3,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,1,6,5,4,2,7,8]=>[6,2,5,4,3,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,1,4,6,5,2,7,8]=>[6,2,3,5,4,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,4,1,5,3,2,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[2,1,8,6,3,7,5,4]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,8,3,1,7,6,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,3,2,8,5,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,3,8,7,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,6,8,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,8,5,7,2,6,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,3,8,5,4,1,2,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[6,3,8,4,5,1,2,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[5,2,3,1,4,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,4,1,3,2,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,1,3,4,2,8,6,7]=>[5,2,4,3,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[5,2,1,4,3,8,6,7]=>[5,3,2,4,1,8,7,6]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,2,7,3,8,5,1,6]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,7,3,2,8,5,1,6]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[4,3,7,2,8,5,6,1]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[5,3,1,2,4,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,4,3,1,2,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,3,4,1,2,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,2,3,4,1,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,1,7,3,4,6,8,2]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,8,7,4,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,1,3,4,5,7,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,5,2,8,1,6,7,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,1,7,8,2,5,4,6]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[6,2,3,7,4,1,8,5]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,3,7,4,1,2,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,2,6,8,4,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,2,8,6,5,1,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,6,7,5,1,2,4,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[7,4,5,1,8,2,3,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,3,1,8,4,5,6]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,1,4,8,3,7,5,6]=>[2,1,5,8,3,7,6,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[4,8,1,6,7,3,2,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[1,2,7,8,4,3,6,5]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,1,4,3,2,7,6]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,8,1,3,5,6,2,7]=>[7,8,3,4,5,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,3,7,8,4,2,6,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,3,7,8,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,2,4,3,1,7,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,4,2,3,1,8,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,5,6,4,8,1,7,2]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[3,5,4,6,7,1,8,2]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,4,2,6,5,8,7,3]=>[1,8,3,5,4,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,6,4,8,7,5]=>[1,3,2,8,5,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,5,3,8,7,6]=>[1,5,3,4,2,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,6,4,8,7,3]=>[1,8,3,5,4,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,2,5,3,8,7,4]=>[1,8,3,5,4,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,1,4,3,8,7,6]=>[3,5,1,4,2,8,7,6]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,7,3,5,4,8,6,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,6,3,7,5,4]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,3,6,4,7,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,6,4,8,5,3]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,6,3,8,5,4]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,7,4,8,6,3]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,8,5,7,6,3]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,8,1,3,2,6,5,7]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,5,3,8,4,7,6,2]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,4,7,3,6,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,3,8,1,5,4,7]=>[5,7,3,8,1,6,2,4]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[8,3,1,4,2,6,5,7]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,8,7,3,5,2,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,8,7,3,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,5,1,2,6,4,7]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,6,3,1,5,4,2,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,4,1,5,3,2,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,5,4,1,3,2,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,8,7,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,3,8,7,4,6,1,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,3,5,7,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,5,3,1,2,7,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[6,8,7,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,4,1,3,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,8,7,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,5,1,6,2,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,3,8,7,5,6,1,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,8,7,1,3,6,4,5]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[8,5,4,7,2,1,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,7,3,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,8,6,4,2,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,8,4,1,5,2,7,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,2,1,7,5,3,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,8,4,6,1,2,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,8,6,5,1,7,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[4,8,7,6,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,5,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,2,1,8,6,7,3]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,5,8,3,1,6,7,2]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,7,2,8,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,3,2,4,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,2,8,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,2,6,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,7,8,4,1,3,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[2,7,8,6,4,1,3,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[7,6,3,5,2,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,2,7,4,8,5,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,5,1,7,2,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,5,1,7,3,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,6,8,3,7,4,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,6,3,4,8,2,7]=>[7,2,5,4,3,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,5,2,6,4,8,1,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,5,2,4,8,1,7,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[6,3,8,2,4,1,7,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,6,3,8,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,8,7,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,4,2,1,7,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,6,4,3,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,5,3,1,4,8,2,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[3,1,7,8,6,4,2,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,8,1,7,6,2,5,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[8,1,7,6,4,2,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,6,3,8,5,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,8,6,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,5,8,2,4,3,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,5,2,4,8,3,7]=>[7,2,5,4,3,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,5,6,3,8,2,4,7]=>[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,1,3,6,5,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,6,7,4,3,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,2,4,7,3,8,6,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,5,8,7,2,4,6,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,8,7,3,6,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,3,7,2,5,1,6,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[3,7,2,8,1,5,4,6]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,2,6,1,5,8,4,7]=>[4,2,7,1,5,8,3,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[7,2,1,5,8,4,3,6]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,2,8,1,4,3,6,5]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[1,7,8,3,2,6,5,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,8,3,2,6,5]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,4,8,3,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,5,4,3,8,2,7]=>[7,2,5,4,3,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,7,4,5,6,8,2,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,4,2,3,5,7,8]=>[1,6,5,4,3,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,7,2,3,4,5,6]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,6,2,3,4,7]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,5,7,2,3,4,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,6,2,3,4,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,7,6,4,5,8]=>[1,2,3,7,6,5,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,4,2,3,8,6,7]=>[1,5,4,3,2,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,8,6,4,5,7]=>[1,3,2,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,8,2,3,4,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,7,5,2,3,4,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,5,8,6,3,7,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,5,8,4,6,1,7,3]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,5,3,8,6,1,7,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,6,3,5,8,1,7,4]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[6,3,2,5,8,1,7,4]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,3,2,8,6,1,7,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,8,4,6,1,3,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,8,6,1,4,7,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,6,5,4,8,1,7,3]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[8,3,5,7,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,6,8,5,3,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[2,4,8,1,7,6,5,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,3,8,1,5,7,6,2]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,8,4,1,5,7,6,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,3,6,8,5,2,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[8,5,4,7,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,8,5,4,2,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[3,6,4,8,5,2,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[3,6,4,1,8,2,7,5]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[3,6,4,1,5,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,8,6,5,1,3,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,3,5,6,7,1,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,6,2,4,7,1,8,3]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[2,7,5,4,6,1,8,3]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[2,3,7,4,6,1,8,5]=>[6,2,8,4,5,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,6,7,4,1,3,8,5]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[6,5,7,4,1,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,4,6,3,5,7,8,1]=>[8,4,5,2,3,6,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,1,6,3,5,7,8,2]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,6,4,2,5,7,8,1]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[2,3,6,1,5,7,8,4]=>[4,2,8,1,5,6,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,3,6,2,5,7,8,1]=>[8,4,5,2,3,6,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,6,1,2,5,7,8,3]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,6,4,1,5,7,8,3]=>[4,8,5,1,3,6,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,4,1,6,5,7,8,3]=>[3,8,1,5,4,6,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[7,5,4,2,6,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,7,3,1,8,6,5,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,6,4,2,7,1,8,3]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,2,7,5,3,1,8,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[5,3,6,4,8,2,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,3,2,5,4,1,8,6]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,3,2,5,1,8,6,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,6,3,8,7,2,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,7,6,3,8,2,1,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,7,3,8,6,2,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,7,3,2,6,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,7,3,2,6,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[2,7,5,3,1,8,6,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[7,5,2,8,4,3,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,2,4,1,8,6,5]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,4,3,2,7,5,1,6]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,3,7,5,8,2,1,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[4,3,7,5,2,6,1,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[8,4,5,3,7,2,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,3,5,2,8,6,1,7]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[4,5,3,6,8,2,1,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,2,3,4,5,9,7,8,6]=>[1,2,3,4,5,9,8,7,6]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,9,6,7,8,5]=>[1,2,3,4,9,8,7,6,5]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,5,6,10,8,9,7]=>[1,2,3,4,5,6,10,9,8,7]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,4,9,7,6,8,5]=>[1,2,3,4,9,8,7,6,5]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,5,10,7,8,9,6]=>[1,2,3,4,5,10,9,8,7,6]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,8,6,4,5,7,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,3,4,6,7,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,9,4,3,5,6,7,8,2]=>[1,9,8,4,5,6,7,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[3,5,6,7,8,9,4,2,1]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[7,8,4,1,6,3,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,5,6,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,2,3,4,6,8,5,7,9]=>[1,2,3,4,7,8,5,6,9]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[3,2,6,4,1,8,5,7]=>[5,2,7,4,1,8,3,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,8,6,5,3,1,4,7]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[5,4,8,6,2,3,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,8,7,5,2,3,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,2,4,7,6,8,3,1]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,4,2,8,7,5,1,6]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[8,5,7,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,1,8,7,3,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,8,5,4,2,7,3,6]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,6,1,5,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,6,5,8,2,7,4,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,3,2,7,4,6,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,8,4,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,6,2,3,8,4,5]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,7,1,3,2,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,1,3,8,7,2,6,4]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,7,1,6,2,5,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,5,2,4,7,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,1,5,2,4,8,3,6]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,8,5,1,4,7,2,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[7,2,5,4,1,3,8,6]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[7,5,8,1,6,3,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,1,4,8,5,6,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,6,1,3,2,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,4,5,7,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,2,6,7,3,1,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,1,7,5,3,6,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,2,8,3,6,1,4,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[5,2,6,3,1,7,8,4]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,3,5,1,6,7,8,2]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,7,6,1,2,3,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,6,7,5,1,2,8,4]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,7,6,8,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,6,8,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,3,7,1,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,3,2,1,8,6,4,7]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[3,8,6,4,5,7,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[9,8,7,5,6,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[2,1,9,8,6,7,5,4,3]=>[2,1,9,8,7,6,5,4,3]=>[2,1,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,8,7,5,4,6,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,4,6,5,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[2,1,9,8,6,5,7,4,3]=>[2,1,9,8,7,6,5,4,3]=>[2,1,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,9,8,5,7,6,4,3]=>[2,1,9,8,7,6,5,4,3]=>[2,1,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,10,9,8,6,7,5,4,3]=>[2,1,10,9,8,7,6,5,4,3]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,11,10,9,8,7,6,5,4,3]=>[2,1,11,10,9,8,7,6,5,4,3]=>[2,1,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,8,7,6,5,4,3,2,9]=>[1,8,7,6,5,4,3,2,9]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,9,8,7,6,5,4,3,2,10]=>[1,9,8,7,6,5,4,3,2,10]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[2,1,8,7,6,5,4,3,9]=>[2,1,8,7,6,5,4,3,9]=>[2,1,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,9,7,6,5,4,3,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,8,6,1,4,5,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,8,5,4,6,7,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,5,8,3,7,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,3,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,3,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,4,3,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,4,3,2,6,7,5]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,3,8,2,1,7,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,4,8,3,2,1,7,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,8,4,3,2,7,6,5]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,5,8,3,1,2,7,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,8,6,7,3,2,4,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,6,1,3,2,4,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,8,4,3,2,7,5,6]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,3,8,2,1,6,7]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,8,4,3,2,5,7,6]=>[1,8,5,4,3,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,3,8,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,4,2,3,5,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,2,3,6,1,4,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,2,3,8,6,4,7,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,2,3,7,4,8,1,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[8,6,3,2,5,4,7,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,3,4,5,8,1,6]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,8,1,5,3,4,6]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,8,6,4,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,8,6,4,5,7,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[4,8,2,5,7,3,1,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,8,2,3,4,7,1,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[6,3,4,7,8,2,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,5,1,4,7,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,8,5,1,3,6,7,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,6,8,5,2,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,8,5,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,6,2,7,4,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,4,7,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,6,2,8,1,5,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,1,5,2,3,7,6,4]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,2,3,7,8,5,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,4,2,3,6,7,1,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,5,8,3,7,2,1,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[3,7,2,8,4,5,1,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,5,1,8,4,6,2,7]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,1,2,6,5,8,3,7]=>[7,2,3,5,4,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,1,8,3,2,6,7,5]=>[5,2,8,4,1,7,6,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,2,7,5,8,1,3,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[4,6,2,7,8,3,1,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,6,1,3,8,2,5,7]=>[6,7,3,4,8,1,2,5]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,3,6,2,1,8,7,5]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[3,7,4,5,1,6,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,6,4,5,8,2,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,1,4,5,2,8,7,3]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,4,5,1,6,3,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[7,5,4,1,6,3,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,4,8,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,7,5,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,3,7,4,1,6,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,4,1,6,3,2,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,7,4,2,6,5,3,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,1,5,6,7,3,4]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,3,1,8,4,7,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,4,8,6,3,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,8,5,6,7,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,4,8,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,6,8,2,7,1,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,3,7,4,8,2,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,6,1,4,7,2,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,3,6,8,2,7,1,5]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[5,3,7,4,8,2,1,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[5,3,8,4,1,6,2,7]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[5,3,8,1,4,7,2,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[5,8,4,1,6,3,2,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[7,3,8,4,1,6,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,5,8,3,6,7,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,5,6,7,3,4]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,4,1,6,5,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,8,1,5,7,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,1,2,5,7,4,6]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,1,4,2,6,5,3,7]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,3,7,4,8,2,6]=>[7,2,5,8,3,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,3,4,7,8,2,6]=>[7,2,4,3,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,5,8,7,4,3,6,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,1,7,8,3,4,2,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,5,4,8,3,7,6,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,6,8,2,3,4,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,5,2,3,8,6,1,7]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[3,7,4,5,8,1,2,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,7,8,1,4,5,2,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,8,2,1,6,3,4,7]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[4,8,1,3,7,5,2,6]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,4,7,8,5,3,6,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,3,1,4,7,2,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,3,8,5,1,2,7,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[2,4,7,5,8,3,6,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,3,5,8,2,1,7,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,8,5,3,7,1,2,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,8,5,7,3,1,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,8,7,5,1,3,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,2,8,5,1,3,6,7]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[3,7,8,4,1,5,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,4,7,5,8,2,1,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,8,5,7,2,4,3,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,4,2,3,6,7]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,3,8,2,7,4,5]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,7,5,8,3,6]=>[1,7,3,8,5,6,2,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,3,6,7,5,4]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,6,8,2,7,5,4]=>[1,5,8,7,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,5,4,3,8,2,7]=>[1,7,5,4,3,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,3,4,5,6,2,7]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,3,6,2,4,5,7]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,8,4,5,3,6]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,8,4,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,8,5,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,3,8,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,8,7,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,8,4,3,7,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,8,4,3,1,7,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[1,4,7,3,2,6,8,5]=>[1,5,8,4,2,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,3,6,2,8,4]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,4,8,3,7,6]=>[1,2,6,4,8,3,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,3,5,8,2,7,6]=>[1,6,3,4,8,2,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,3,7,6,8,2,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,4,5,7,8,2,3]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,2,6,5,7,8,1,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,2,5,7,6,8,1,4]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,3,2,6,8,4,7,1]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,1,8,6,4,7,2,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,1,6,8,5,4,2,7]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,3,2,8,7,6,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,3,8,2,7,6,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,4,8,3,7,2,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,8,5,1,3,7,2,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[4,3,8,7,2,6,5,1]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[2,7,5,1,8,4,6,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[7,8,5,2,1,6,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,4,8,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,4,8,3,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,4,7,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,5,6,2,7,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,4,5,8,7,3,1,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[2,4,5,8,6,7,1,3]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,1,5,8,6,7,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,3,7,6,1,2,8,5]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[4,7,5,6,1,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,3,7,5,6,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,5,1,8,6,7,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,4,5,8,6,7,2,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,1,5,8,6,7,4,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,4,5,8,7,1,2,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,7,1,5,6,2,8,3]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,6,4,7,1,3,8,5]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[5,3,8,6,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,1,5,7,8,3,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,4,7,2,1,8,5]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[3,8,4,6,1,7,2,5]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[3,8,5,6,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,4,5,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,6,5,2,7,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,5,2,1,4,6]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[3,8,6,5,1,7,2,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,4,1,7,3,2,8,5]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,1,4,6,7,2,8,3]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,5,4,7,1,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,1,6,5,3,7,8,4]=>[2,1,8,5,4,6,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,1,4,7,2,3,8,5]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,1,3,4,5,6,7,9,8]=>[2,1,3,4,5,6,7,9,8]=>[2,1,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,4,5,6,7,8,10,11,9]=>[1,2,3,4,5,6,7,8,11,10,9]=>[1,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,3,2,4,5,6,8,9,7]=>[1,3,2,4,5,6,9,8,7]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,3,4,5,6,7,8,10,9]=>[2,1,3,4,5,6,7,8,10,9]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,6,2,5,4,8,3,7]=>[1,7,3,5,4,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,7,5,8,3,6]=>[7,2,3,8,5,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,1,3,5,8,2,4,7]=>[7,2,6,4,8,3,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,6,4,3,1,8,2,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,2,3,5,8,1,4,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,7,2,3,8,4,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,2,1,3,8,4,5]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,7,4,1,8,3,2,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,1,7,5,8,3,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,7,1,3,8,4,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,6,7,4,3,8,5,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,7,4,2,8,5,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,1,6,7,4,3,8,5]=>[2,1,8,6,5,4,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,7,3,2,1,8,4,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,5,7,3,1,4,8,6]=>[5,6,8,4,1,2,7,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[6,7,3,2,8,4,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,2,6,7,4,3,8,5]=>[1,2,8,6,5,4,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,1,8,4,6,3,5]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,7,5,8,1,6,3,4]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[6,7,1,8,4,5,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,7,6,1,2,5,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,7,3,4,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,5,7,1,4,6,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[8,2,4,7,1,5,6,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[8,2,3,4,7,1,5,6]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,7,3,5,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,4,6,5,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,6,7,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,6,7,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,5,7,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,3,6,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,3,4,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,4,6,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,5,2,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,3,7,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,6,7,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,6,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,2,7,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,4,2,7,5,6,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,4,7,6,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,5,2,7,4,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,2,6,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,3,7,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,2,5,7,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,2,4,7,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,2,3,7,4,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,3,2,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,1,5,4,3,2,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,4,5,8,3,1,6,7]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[2,7,4,6,1,5,8,3]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,4,3,8,5,1,6,7]=>[6,3,2,8,5,1,7,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[7,8,3,2,5,4,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,5,6,7,3,8,2,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,5,4,8,3,2,7]=>[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,5,8,4,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,1,6,4,8,5,3]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,5,8,3,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,2,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,3,7,6,4,8,5,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,8,7,6,4,2,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,1,8,7,5,4,2,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,1,7,6,5,4,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,7,1,6,5,3,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,8,1,6,5,3,2,7]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[8,4,1,7,6,3,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,1,8,6,3,2,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,4,1,7,6,3,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,4,1,8,5,3,2,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,4,1,7,5,3,2,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,4,1,6,5,3,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,5,6,1,4,3,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,5,6,1,4,3,2,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,7,1,4,3,2,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,6,1,4,3,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,8,6,1,4,3,2,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,7,5,1,4,3,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,7,5,1,4,3,2,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,5,1,4,3,2,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,1,7,2,5,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,8,6,3,4,2,5,7]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,6,4,5,8,7,2]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,6,4,5,2,7,8]=>[6,2,5,4,3,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,1,6,4,5,8,2,7]=>[7,2,5,4,3,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,1,6,4,5,7,2,8]=>[7,2,5,4,3,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,6,8,7,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,3,8,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,7,6,1,4,3,5]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[5,2,7,8,1,4,3,6]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[5,6,3,8,4,1,2,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[8,2,7,6,1,4,5,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[5,2,3,4,7,1,6,8]=>[6,4,3,2,7,1,5,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,2,3,7,1,6,8,4]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,2,3,4,7,8,1,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[8,7,5,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,4,7,8,5,2,3,6]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,3,7,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,1,7,2,4,8,3]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,6,7,1,4,2,5,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[4,7,5,8,2,1,3,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,1,2,7,5,4,3,6]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,5,1,8,3,7,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,8,7,5,3,2,6,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,1,5,4,2,3,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,7,5,1,4,6,3,8]=>[4,7,6,1,5,3,2,8]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,4,6,8,1,5,7,2]=>[8,5,6,7,2,3,4,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[5,7,6,1,4,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,8,1,7,5,4,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,3,1,2,8,5,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,3,5,7,1,4,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,2,6,7,4,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,7,5,2,6,4,8,3]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,3,6,8,2,4,5]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,5,7,8,4,6,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,7,5,4,8,6]=>[3,2,1,8,6,5,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[6,7,4,1,3,2,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,7,2,8,4,3,5,6]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,3,5,7,8,2,4]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,1,7,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,4,1,8,3,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,1,6,5,2,7,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,5,3,4,7,8,2,6]=>[1,7,4,3,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,2,1,5,7,8,3,6]=>[7,3,2,4,8,6,1,5]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[5,4,1,6,7,8,2,3]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,1,4,6,7,8,2,3]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,5,3,7,8,2,6]=>[7,2,4,3,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,1,4,6,5,2,7,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,5,4,6,3,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,2,1,6,7,5,4,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,2,4,7,6,3,8,5]=>[1,2,6,8,5,3,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,7,4,1,8,5,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,4,1,5,7,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,2,4,3,7,1,6,8]=>[6,4,3,2,7,1,5,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[6,1,5,4,8,3,2,7]=>[7,2,6,4,8,3,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,2,8,7,4,3,6,5]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,1,7,5,8,4,6]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,3,6,4,7,8,2,5]=>[1,7,8,4,5,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,5,1,3,7,8,2,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[5,2,3,1,7,8,4,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,6,4,3,7,8,2,5]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,4,3,1,5,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,4,6,1,3,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,4,6,5,1,2,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,5,6,3,7,8,2,4]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,2,3,4,5,8,9,10,6]=>[10,2,3,4,5,6,7,8,9,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[6,1,2,3,4,7,8,9,10,5]=>[10,2,3,4,5,6,7,8,9,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[5,1,2,3,6,7,8,9,10,4]=>[10,2,3,4,5,6,7,8,9,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[6,8,3,5,7,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,5,2,4,3,8,7,6]=>[1,5,3,4,2,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,5,7,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,3,8,4,5,7,2]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,5,4,2,6,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,8,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[9,7,6,5,4,3,1,2,8]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[2,3,8,4,7,5,6,1]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,7,2,8,6,4,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,3,7,5,8,2,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,3,7,8,6,2,5,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[3,8,1,7,5,2,4,6]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,4,7,8,6,1,5,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,4,8,5,1,7,3,6]=>[5,7,8,4,1,6,2,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,8,3,5,1,6,4,7]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[8,2,4,6,3,7,5,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,5,3,8,2,1,7,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,8,3,2,5,1,6,7]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[5,2,7,1,3,8,6,4]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,5,6,7,8,9,2,1,3]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[5,6,7,8,9,2,1,3,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,7,8,9,2,1,3,4,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,8,9,2,1,3,4,5,6]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[1,4,6,2,7,5,3,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,7,5,1,4,6,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,7,4,6,8,3,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,1,4,5,6,7,3]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,3,1,2,5,6,4,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[7,2,4,1,5,8,6,3]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,8,2,1,5,4,6,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,4,8,5,2,6,3,7]=>[1,7,8,5,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,3,2,6,4,7]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,4,1,3,2,5,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,2,3,7,8,1,6,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,2,8,6,3,1,7,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,2,3,5,1,8,7,4]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,6,3,4,2,8,1,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,2,4,5,7,8,1,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,6,3,2,5,7,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,2,5,3,7,1,8,4]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[8,5,3,6,7,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,7,8,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,2,8,4,3,6,7,5]=>[1,2,8,5,4,7,6,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,5,3,4,6,8]=>[1,2,7,6,5,4,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,4,5,3,8,6]=>[1,2,8,6,5,4,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,7,1,4,3,5,6]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,2,1,3,6,8,4,5]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,2,1,7,8,3,4,5]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,7,8,1,6,5,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,5,8,6,1,4,2,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,8,4,2,7,6,3,5]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,8,1,6,5,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,8,2,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,1,3,8,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,3,7,6,5,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,4,1,8,7,3,6,5]=>[3,6,1,8,7,2,5,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[7,3,8,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,1,7,8,2,6,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[5,4,7,8,2,1,6,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,3,6,1,8,4,2,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,3,8,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,4,7,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,7,1,5,3,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,4,6,2,1,8,5,7]=>[5,4,7,2,1,8,3,6]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[4,5,7,2,1,6,3,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[5,6,4,8,3,2,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[5,7,4,8,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,5,8,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,4,2,6,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,7,4,1,6,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,8,7,3,1,4,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,6,1,7,3,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,1,6,7,8,3,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,5,2,6,1,3,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[8,4,6,7,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,6,7,2,5,8,1]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[7,1,4,6,8,3,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,7,1,2,4,8,5,3]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,6,3,4,7,8,5,2]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,3,6,4,7,5,8,1]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,8,1,3,4,5,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,8,2,6,7,3,4,5]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,7,3,2,8,1,5,6]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[7,1,2,6,3,8,5,4]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,6,3,7,5,4]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,7,6,3,5,4]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,8,7,3,1,6,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,7,8,3,1,6,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[7,4,3,1,6,2,8,5]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,4,3,1,8,6,2,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,7,6,2,4,8,1,5]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[4,3,7,2,8,6,1,5]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[6,1,2,7,4,3,8,5]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,2,6,3,8,7,4]=>[8,2,3,5,4,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,2,7,3,8,6,4]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,2,7,3,5,8,4]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,6,2,1,7,4,5]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,1,2,8,3,5,7,4]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,5,3,2,1,8,6,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,2,1,5,3,6,7,8]=>[5,3,2,4,1,6,7,8]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[8,6,4,3,2,1,9,7,5]=>[9,8,6,5,4,3,7,2,1]=>[9,8,6,5,4,3,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[8,6,4,2,1,9,7,5,3]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[7,4,1,8,5,2,9,6,3]=>[9,8,3,6,5,4,7,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[9,7,5,4,3,2,1,10,8,6]=>[10,9,7,6,5,4,3,8,2,1]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[9,7,5,3,2,1,10,8,6,4]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[6,2,5,4,1,8,7,3]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,6,3,2,1,8,7,5]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[6,5,3,2,1,8,7,4]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[8,4,3,2,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,5,8,4,7,6,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,7,4,8,6,1,5]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,4,3,2,8,6,1,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,8,3,7,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,4,3,2,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,4,3,8,5,2,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[8,2,5,4,7,6,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,5,4,8,6,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,3,2,8,6,1,7]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[3,2,5,4,8,6,1,7]=>[7,2,4,3,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,2,8,6,5,4,1,7]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,4,3,6,5,2,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,3,7,5,2,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,2,7,8,5,4,1,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,8,7,4,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,1,4,8,7,2,5]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,8,1,3,7,2,6,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,7,5,1,8,2,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,2,1,8,7,4,5]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[6,2,3,1,8,7,4,5]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,4,7,1,8,5,6,2]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,4,8,1,7,5,6,2]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,2,5,1,8,3,6,4]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,2,1,5,8,4,6,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,2,8,1,7,5,6,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,3,6,4,1,7,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,1,5,2,8,6,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,1,6,4,2,8,5,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,7,4,1,5,8,6,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,8,6,1,2,7,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,1,4,3,7,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,1,4,3,8,5,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,7,1,5,3,8,6,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,1,2,4,7,5,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,6,4,8,3,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,4,1,3,7,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,3,6,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,1,4,5,8,6,3]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,5,6,1,2,7,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,2,5,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,3,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,2,1,4,3,6,7]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[2,8,4,1,3,6,7,5]=>[4,8,5,1,3,7,6,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[8,1,2,4,5,6,7,3]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,4,3,2,7,8,5]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,3,6,7,2,4,5]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,3,7,4,6,5]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,6,5,4,3,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,7,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,3,5,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[12,10,9,8,7,6,5,4,3,2,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[4,6,7,2,1,8,3,5]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[3,7,1,8,2,5,4,6]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,5,8,6,1,3,7,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,5,8,6,2,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,7,1,5,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,6,7,2,1,8,5,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,2,5,6,7,8,3,1]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,1,3,5,6,7,8,2]=>[8,2,3,4,5,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,7,8,4,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,8,3,2,7,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,6,8,2,3,7,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,8,1,7,4,5,2,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,5,8,3,7,1,2,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[3,7,8,4,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,1,5,7,8,2,4]=>[7,8,3,4,5,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,8,2,5,4,7,1,6]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,8,6,2,5,1,7,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[4,5,8,6,2,1,7,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,5,8,6,1,2,7,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,6,8,5,2,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,8,5,2,6,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,7,8,5,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,8,5,3,1,7,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,8,2,3,5,4,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,1,3,7,6,4,8,2]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,6,5,2,7,8,1,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,6,5,2,3,4,8,7]=>[1,6,5,4,3,2,8,7]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,5,1,7,3,8,2]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,7,3,1,2,4,8,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[6,3,2,5,1,7,4,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,1,2,4,8,5,3,7]=>[7,2,3,6,8,4,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,3,1,7,2,5,8,4]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,7,2,8,5,1,4,6]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,6,5,2,4,7,1,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[3,6,5,8,1,7,2,4]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,5,6,7,9,8,10]=>[1,2,3,4,5,6,7,9,8,10]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[5,2,7,3,4,6,1,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,3,5,8,6,4,7,2]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,8,6,7,2,4]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,7,4,8,5,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,4,1,3,6,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,4,3,1,6,5,8,2]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[8,6,1,7,5,3,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,1,4,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,6,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,1,7,6,3,4,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,2,7,3,8,5,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,2,7,5,3,4,8,6]=>[1,2,8,6,5,4,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,8,3,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,2,7,8,3,1,4,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,7,8,2,5,3,4,6]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,8,1,2,5,6,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[1,2,8,7,3,4,6,5]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,7,4,5,1,6,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[3,8,1,5,7,2,6,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[7,5,4,8,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,8,6,4,5,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,7,5,1,4,3,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,5,7,8,3,4,2,6]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,4,3,1,7,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,1,3,7,5,6,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,8,1,3,7,5,6,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,8,5,7,4,2,3,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,6,8,5,3,4,7]=>[2,1,7,8,6,5,3,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[4,5,1,3,8,6,7,2]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,2,6,8,5,3,4,7]=>[1,2,7,8,6,5,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,6,8,7,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,5,3,8,1,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,2,3,4,7,1,8,5]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,8,5,7,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,6,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,2,4,7,1,8,5]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,7,8,3,6,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,5,8,6,2,4,3,7]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,8,6,2,4,3,7]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,8,6,3,7,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,5,2,4,8,6,7,3]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,6,3,8,1,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,6,8,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,7,5,3,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,7,2,1,5,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,6,1,4,8,2,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,8,1,6,5,3,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,3,2,1,4,6,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,3,5,1,7,4,2,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,5,6,8,4,2,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[5,8,2,6,4,3,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,6,3,4,1,7,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[4,3,6,2,8,5,7,1]=>[8,4,6,2,7,3,5,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[1,7,2,3,5,8,6,4]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,2,3,5,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[2,8,3,7,5,1,6,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[6,4,8,7,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,2,3,7,5,6,4]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,4,3,6,7,1,5]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[7,3,2,5,6,1,8,4]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,6,7,8,2,4,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,2,8,5,3,7,6]=>[6,2,3,8,5,1,7,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,8,4,2,5,1,7,6]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[1,8,5,6,4,3,2,7]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,3,5,6,4,1,7]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,1,5,7,6,8,2,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,8,3,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,8,1,6,4,5,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,7,1,4,5,3,8,6]=>[3,8,1,6,5,4,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,5,2,7,4,3,6,8]=>[1,6,3,7,5,2,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,3,8,4,6,2,7]=>[7,2,5,8,3,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,5,8,7,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,3,5,1,6,8,4]=>[5,8,3,6,1,4,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[5,7,6,8,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,3,6,5,2,7,4,8]=>[1,5,7,4,2,6,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,5,3,4,7,8]=>[1,2,6,5,4,3,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,5,6,8,3,4]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,4,8,3,5,6]=>[1,8,3,6,7,4,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,2,4,5,3,7,8]=>[1,6,3,5,4,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,2,4,3,5,7]=>[1,7,8,4,6,5,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,2,5,3,4,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,3,6,7,4,5]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,5,3,4,8,6]=>[1,8,3,6,5,4,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,1,5,6,7,8,9,10,2]=>[10,3,2,4,5,6,7,8,9,1]=>[10,3,2,9,8,7,6,5,4,1]=>[[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.]
[10,9,4,5,6,7,8,1,2,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,3,8,5,6,7,1,9,2,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,1,5,6,2,3,8,4]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,1,4,6,7,3,5]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,2,6,1,3,4,8,5]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,1,3,7,2,5,8,6]=>[5,2,3,8,1,6,7,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[6,2,7,5,1,3,8,4]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,7,5,6,2,3,8,4]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,6,1,2,4,8,5]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[8,6,1,3,5,7,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,1,5,3,4,8,2,7]=>[7,2,5,4,3,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,6,7,5,2,8,1,4]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[7,8,4,1,5,6,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,1,3,6,7,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,8,4,3,7,1,5,6]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[3,8,4,6,7,1,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,3,8,4,7,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,2,5,4,8,3,6,7]=>[1,2,6,4,8,3,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,3,8,2,4,5,6]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,3,7,2,4,5,6]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,5,4,7,8,1,2,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,3,1,4,7,2,5,6]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,6,4,7,8,2,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,2,3,6,7,8,1,4]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,2,7,3,8,5,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,3,7,8,5,6,2,4]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,6,7,5,1,3,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,1,7,4,6,2,3,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,5,8,4,7,1,3,6]=>[6,7,8,4,5,1,2,3]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[4,5,8,7,1,2,3,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,1,8,5,7,2,3,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,8,7,4,6,2,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,5,4,1,8,3,7]=>[5,7,4,3,1,8,2,6]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[6,2,5,1,4,8,3,7]=>[7,4,5,2,3,8,1,6]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[6,5,4,1,3,8,2,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,3,5,4,2,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,3,8,7,4,2,6,5]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,4,3,1,5,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,5,1,4,6,7,3]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,8,4,5,1,6,7,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,4,1,3,6,7,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,3,1,7,5,6,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,7,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,4,5,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,4,1,8,5,7,6,3]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[8,2,1,4,7,6,3,5]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,3,1,7,4,2,6,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,2,7,3,1,6,5,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,8,4,2,3,7,6,5]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,8,7,4,6,5]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[8,5,1,2,4,3,7,6]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,8,3,7,4,1,6,5]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[8,4,5,7,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,3,1,8,7,6,4,5]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[4,2,8,7,3,1,5,6]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[1,3,4,8,7,2,5,6]=>[1,6,3,8,7,2,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,3,4,6,7,2,5]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,4,8,2,6,7,1,5]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[3,6,8,2,5,1,7,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[3,8,2,5,7,4,6,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,2,1,7,5,6,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,2,7,5,6,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,8,5,4,1,7,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,8,5,4,1,7,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,1,5,7,6,3,4]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,1,8,2,7,5,6,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[8,5,7,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,4,7,3,6,5,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,4,7,2,1,6,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,4,7,6,5,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,8,1,7,4,6,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,4,7,1,3,6,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,3,9,5,6,7,1,4]=>[9,8,3,7,6,5,4,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[8,2,9,4,5,6,7,1,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,9,3,4,5,6,7,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[4,2,3,1,9,8,7,6,5]=>[4,3,2,1,9,8,7,6,5]=>[4,3,2,1,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,9,8,6,7,5,4]=>[3,2,1,9,8,7,6,5,4]=>[3,2,1,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[9,2,10,4,5,6,7,8,1,3]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[2,3,4,7,6,8,1,5]=>[7,2,3,8,5,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,8,1,2,5,6,4,7]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[8,5,2,1,4,6,7,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,8,1,6,5,2,7,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,2,6,3,8,5,7,1]=>[8,4,6,2,7,3,5,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,5,2,6,7,1,8,3]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,7,4,1,6,3,5,8]=>[4,7,6,1,5,3,2,8]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[8,3,5,4,2,7,1,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,8,6,4,7,3,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,1,8,6,5,2,7,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,3,1,5,2,6,7,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,8,2,4,1,5,7,6]=>[5,8,3,4,1,6,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[5,8,3,2,4,1,7,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[7,2,6,8,4,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,3,2,4,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,2,4,6,1,3,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[7,2,3,4,6,8,1,5]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,4,6,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,3,4,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,1,3,4,7,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,1,5,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,7,4,6,8,2,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,7,1,6,8,3,2,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,5,2,8,1,7,3,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,7,5,2,8,6,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,8,5,2,6,7,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,4,8,6,1,2,7,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,4,6,5,2,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,6,4,7,5,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,2,7,6,4,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,6,2,3,5,1,7,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,5,7,4,1,3,6]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,2,4,5,6,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,1,3,5,6,2,8,4]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,5,8,4,6,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,3,8,4,7,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,4,3,2,8,5,6]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,3,6,1,4,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,7,2,1,4,3,8,6]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[7,1,8,3,5,2,4,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,4,8,1,5,6,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[7,1,8,4,2,5,6,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,2,5,8,1,7,3]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[2,1,7,5,8,3,6,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[7,3,8,5,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,4,8,1,5,6,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[7,4,8,3,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,5,8,3,7,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,6,3,5,8,7,4,1]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,5,3,7,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,5,3,7,2,1,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[7,4,8,6,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,8,5,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,4,1,3,5,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,3,4,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,1,8,2,5,6,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,2,3,8,1,5,6,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,4,8,7,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,4,8,6,3,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,4,8,2,3,1,7,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,2,1,8,3,5,6,4]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[5,1,6,3,8,2,4,7]=>[7,2,6,4,8,3,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,6,5,1,4,8,7,2]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[7,3,6,2,8,4,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,1,8,4,7,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,4,8,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,5,8,7,1,2,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,5,6,8,1,4,2,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[4,3,5,8,2,1,6,7]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,4,7,2,3,1,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,8,1,5,4,2,7,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,6,3,1,4,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,6,3,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,8,5,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,8,4,7,2,3,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,4,3,7,1,8,2]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,5,3,7,2,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,6,2,8,4,3,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[4,1,2,6,8,3,7,5]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[7,1,3,6,5,8,4,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,4,3,6,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,6,2,7,8,3,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,1,2,4,6,7,8,3]=>[8,2,3,4,5,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,6,3,5,2,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,6,3,4,8,2,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,2,6,4,1,7,8,3]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,8,4,6,3,2,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,3,8,6,2,7,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,7,8,2,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,2,4,8,3,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,4,7,8,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,5,2,4,8,1,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[4,7,5,2,3,8,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,4,7,3,2,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,7,3,2,8,4,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,7,2,8,4,6,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,3,7,2,5,8,6,1]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,7,3,2,5,8,6,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,7,3,2,6,8,5,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,5,3,2,6,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,5,2,6,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,2,6,3,7,5,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,4,6,2,3,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,6,2,8,3,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,6,2,8,3,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,7,6,2,3,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,6,3,2,5,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,6,4,2,5,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[9,8,4,5,6,7,1,2,10,3]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[9,3,8,5,6,7,1,2,10,4]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[9,7,4,5,6,1,8,2,10,3]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[6,3,8,5,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,3,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,4,2,3,5,6,7,8,9]=>[1,4,3,2,5,6,7,8,9]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,3,2,4,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[2,4,6,3,8,7,5,1]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,4,6,1,8,7,3,5]=>[4,7,8,1,6,5,2,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,4,3,6,8,7,1,5]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[2,4,6,3,8,7,1,5]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[2,4,6,5,8,7,1,3]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[2,4,6,8,5,7,3,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[2,4,6,8,5,7,1,3]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[2,4,6,8,3,7,1,5]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[2,4,6,8,1,7,3,5]=>[5,7,8,6,1,4,2,3]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,4,6,5,1,8,7,3]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[2,4,6,5,8,3,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[2,4,6,5,8,1,7,3]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[2,4,6,8,5,1,7,3]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[2,4,6,8,7,3,5,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,4,6,8,7,1,5,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,4,6,8,7,1,3,5]=>[6,7,8,5,4,1,2,3]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,4,6,8,5,1,3,7]=>[6,7,5,8,3,1,2,4]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[2,4,6,5,1,8,3,7]=>[5,7,4,3,1,8,2,6]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[2,4,6,5,1,3,8,7]=>[5,6,4,3,1,2,8,7]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[2,4,6,5,3,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[2,4,6,5,8,3,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[2,4,6,8,5,3,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[2,4,6,8,7,3,1,5]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[2,4,6,8,7,5,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,8,7,5,2,1,3,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,1,4,7,5,8,2,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,6,5,3,2,7,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,3,5,8,2,4,7]=>[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,1,7,8,5,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,1,2,7,8,4,5,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,3,2,7,8,5,4]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,3,1,7,4,8,2]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,8,3,7,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,7,2,6,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,3,2,1,7,6,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,4,3,8,1,7,6,2]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,5,3,8,7,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,8,2,7,6,5,1]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,8,2,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,2,6,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,6,2,5,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,8,3,7,2,1,6,5]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[8,6,3,1,7,5,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,3,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,3,7,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,2,7,6,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,2,1,7,6,5,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,6,4,2,5,3,7,8]=>[1,6,5,4,3,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,6,2,7,3,4,5]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,3,2,4,5,7,8]=>[1,6,4,3,5,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,6,4,3,7,8]=>[1,6,3,5,4,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,4,6,3,7,8]=>[1,6,3,4,5,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,6,2,3,7,4,5]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,6,8,2,7,4,5]=>[1,5,8,7,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,3,8,2,5,6,7]=>[1,5,3,8,2,6,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,3,8,5,4,6]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,4,2,5,6,7]=>[1,5,8,4,2,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,3,8,6,4,5]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,8,2,5,6,3,7]=>[1,7,8,4,5,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,3,2,8,4,6]=>[1,7,8,5,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,3,6,8,4,5]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,3,6,8,4,5]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,8,3,2,5,6,7]=>[1,5,8,4,2,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,5,8,3,4,6]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,2,3,4,1,7,9,8,6]=>[5,4,3,2,1,9,8,7,6]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[6,2,3,5,8,1,7,4]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,2,3,1,6,9,7,8,5]=>[4,3,2,1,9,8,7,6,5]=>[4,3,2,1,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[5,2,4,8,1,6,7,3]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,2,1,5,9,6,7,8,4]=>[3,2,1,9,8,6,7,5,4]=>[3,2,1,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[1,3,9,4,5,6,7,8,2]=>[1,9,8,4,5,6,7,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,6,4,5,7,3,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[2,5,6,3,4,7,1,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,3,7,5,6,8,4,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,6,7,4,5,8,2]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,3,4,2,7,8]=>[1,6,5,4,3,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,3,4,7,2,8]=>[1,7,5,4,3,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,3,6,4,2,7,8]=>[1,6,5,4,3,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,6,8,3,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,6,3,8,4,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,7,5,2,8,6,4]=>[1,5,8,7,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,7,2,5,8,6,4]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,3,7,4,6,2,8]=>[1,7,5,6,3,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,3,7,6,4,2,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,3,6,7,4,2,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,3,7,4,2,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,6,3,4,8,2]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,3,6,4,8,2]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,7,5,6,2,8,4]=>[1,6,8,5,4,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,7,4,1,3,8,6]=>[5,6,8,4,1,2,7,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[6,7,3,1,8,5,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,1,5,8,7,2,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,5,1,7,6,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,6,3,5,8,2,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,2,4,8,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,3,6,4,1,8,7,5]=>[5,2,8,4,1,7,6,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[7,4,5,2,1,8,6,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,7,5,2,1,8,6,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,3,6,2,1,7,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,7,3,1,2,8,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[4,5,1,8,3,2,7,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,7,4,6,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,6,1,2,4,8,7,5]=>[4,8,3,1,5,7,6,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,5,3,8,4,1,7,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[8,6,2,3,1,7,5,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,2,3,1,8,6,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,3,1,2,4,8,7,5]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,7,5,2,3,6,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,6,8,4,5,1,2,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[5,2,3,7,6,4,1,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,2,7,3,5,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,2,6,5,3,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,2,6,5,4,1,3,7]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,2,8,4,5,1,3,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[2,3,1,7,8,5,6,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[7,2,8,5,1,4,3,6]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[8,6,7,1,4,2,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,7,1,4,3,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,2,5,3,1,4,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,7,8,5,1,4,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,8,7,3,1,2,5,6]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[4,8,6,2,3,1,5,7]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[3,8,5,4,2,1,6,7]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[4,5,3,8,2,1,6,7]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,7,4,1,8,2,6,5]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[3,8,4,1,7,6,2,5]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[3,7,2,1,8,4,6,5]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[8,7,1,6,5,2,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,1,2,7,6,3,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,2,1,7,6,4,5]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,5,7,8,2,4,6,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,8,2,5,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,3,7,8,2,6,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,5,4,7,3,6,2,8]=>[1,7,5,6,3,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,6,8,4,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,8,2,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,6,3,5,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,8,3,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,7,8,4,6,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,7,5,6,2,1,4,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,2,6,4,7,5,3,8]=>[1,2,7,6,5,4,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,5,6,3,8,4,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,4,2,1,6,7,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,6,8,4,7,5,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,7,5,1,4,8,3,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,4,1,6,5,3,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,8,2,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,5,7,3,8,4,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,8,4,2,7,3]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,5,4,1,8,2,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,1,8,2,7,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,5,3,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,5,1,7,6,4,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,7,4,3,8,2,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,4,2,7,8,6,1,5]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[7,8,6,1,4,3,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,4,7,8,6,1,3,5]=>[6,7,8,5,4,1,2,3]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[3,7,8,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,2,7,8,6,3,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,6,2,5,3,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,1,5,6,3,2,7,8]=>[6,2,5,4,3,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,6,7,5,4,1,3,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[4,1,6,7,5,3,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,7,4,3,1,5,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,7,5,6,4,3,2,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,5,3,1,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,8,6,4,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,1,7,8,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,5,7,3,8,6,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,5,3,7,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,1,5,8,2,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,7,6,2,1,8,4,5]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,7,5,8,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,8,2,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,4,8,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,8,1,6,5,2,7]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[2,3,6,5,7,8,1,4]=>[7,2,8,4,5,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,3,4,1,2,6,7,5]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[7,3,4,8,5,2,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,8,4,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,4,5,1,8,3,6]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[7,3,1,2,8,5,6,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,8,2,3,5,7,6,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,5,2,3,8,6,7,1]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[6,7,4,8,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,5,6,1,7,8,2]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,5,2,6,4,7,8,1]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,1,2,8,5,7,6,3]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,5,6,4,7,8,2]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,4,6,7,5,8,2]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,6,4,5,8,1,3,7]=>[6,7,4,3,8,1,2,5]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[6,4,1,3,5,8,2,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,4,1,7,2,6,8,5]=>[5,3,2,8,1,6,7,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[2,4,7,5,8,1,3,6]=>[6,7,8,4,5,1,2,3]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[3,1,6,4,8,7,5,2]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,7,6,2,1,5,8,4]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[8,5,4,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,4,6,7,1,3,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[5,8,2,1,4,6,7,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,4,6,1,2,5,7,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,7,8,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,2,8,7,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,3,8,4,5,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,8,1,4,3,5,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,7,2,8,1,5,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,6,7,1,3,5,8,4]=>[4,8,6,1,5,3,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,6,7,1,8,2,5,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[3,4,1,8,7,2,6,5]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[3,1,5,7,2,8,6,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,8,1,4,7,2,6,5]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,8,1,3,2,7,6,5]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,1,8,3,2,7,6,5]=>[5,2,8,4,1,7,6,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,3,8,1,2,7,6,5]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[4,3,8,2,1,7,6,5]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[3,8,4,2,7,1,6,5]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[2,8,4,3,7,6,1,5]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[3,8,2,4,7,1,6,5]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,2,4,8,7,1,6,5]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,2,5,7,1,8,6,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,2,8,3,1,7,6,5]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[4,8,2,1,3,7,6,5]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[4,2,8,1,3,7,6,5]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[5,6,4,7,1,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,6,7,5,8,2,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,7,1,6,8,3,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,2,7,6,8,1,4,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,5,1,7,6,8,2,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,2,8,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,3,1,2,8,4,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,2,7,8,4,1,3,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,3,7,8,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,2,4,1,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,2,3,1,8,4,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,2,5,1,3,7,8,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,5,1,4,2,7,8,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,4,1,7,8,5,2,6]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[4,3,1,8,5,2,7,6]=>[6,3,2,8,5,1,7,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[3,1,8,5,4,2,7,6]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[7,6,3,5,8,4,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,1,3,2,7,8,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,1,3,2,4,7,8,6]=>[5,2,4,3,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,7,8,5,4,1,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,3,5,6,1,7,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,8,1,2,6,7,3]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,3,6,7,8,2,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,3,4,8,6,2,7,5]=>[1,6,3,8,7,2,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,4,1,3,8,5,6]=>[8,4,5,2,3,7,6,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,8,2,5,4,1,6,7]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[8,4,5,2,6,1,7,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,6,8,2,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,7,2,3,6,1,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[2,7,3,4,1,5,6,8]=>[5,7,3,4,1,6,2,8]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[6,7,2,3,4,8,1,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,5,2,4,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,2,6,3,5,7,8,1]=>[8,4,5,2,3,6,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,3,1,5,4,6,7,8,9]=>[3,2,1,5,4,6,7,8,9]=>[3,2,1,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[1,4,8,5,6,2,7,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,8,5,6,1,7,3]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[6,3,5,8,4,7,1,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[2,8,7,4,5,1,6,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[1,3,8,5,2,6,7,4]=>[1,5,8,7,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,8,4,5,1,6,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,2,3,5,1,7,8,4]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,6,2,4,1,5,7,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,6,4,3,2,7,8,5]=>[1,8,5,4,3,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,5,3,2,1,6,7,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,7,5,2,3,6,8,4]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,5,2,3,6,8,4]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,5,3,6,7,4]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,1,6,3,7,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,5,3,8,2,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,2,6,8,3,7,1,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,2,5,8,6,7,1,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,6,3,4,1,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,2,4,1,8,6,5]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,4,7,8,5,1,3,6]=>[6,7,8,5,4,1,2,3]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,5,3,8,4,1,6,7]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,7,6,8,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,1,7,4,5,6,2,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,4,8,3,5,7,1,6]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[8,1,7,2,4,3,5,6]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,3,7,2,4,6,5,8]=>[1,4,7,2,5,6,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,3,7,4,2,5,6]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,3,1,4,2,5,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,4,3,5,7,1,6]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[3,2,8,7,4,1,5,6]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,2,1,7,4,6,5,8]=>[3,2,1,7,5,6,4,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,6,5,1,7,8,4]=>[5,2,8,4,1,6,7,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[5,3,2,6,7,1,8,4]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,2,8,6,7,4,1,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,4,6,2,7,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,8,6,7,2,1,5]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,3,6,2,8,7,1,5]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[3,8,4,7,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,4,2,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,2,7,8,6,4,5,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,7,5,6,8,4,1]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,8,6,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,4,2,1,7,8,3]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,4,2,1,7,6,3,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[4,1,6,5,2,7,8,3]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,4,1,6,7,2,8,3]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,8,5,3,1,7,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,6,3,8,7,1,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,6,1,7,3,4,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,8,3,6,7,4,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,3,5,2,7,8,4]=>[1,8,5,4,3,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,3,2,6,4,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,6,7,2,4,3,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,4,8,2,7,3,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,2,4,8,3,7,1,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,7,2,6,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,7,6,5,2,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,5,6,8,2,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,7,1,5,2,4,8,3]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,6,1,5,2,4,3,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,1,6,3,5,4,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,6,7,3,5,4,8,2]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,5,6,8,4,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,3,6,4,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,7,6,4,5,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,7,4,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,5,7,6,4,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[7,4,5,1,6,8,3,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,1,7,5,6,8,3,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,7,4,3,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,7,8,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,4,6,2,5,3,7,8]=>[1,6,5,4,3,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,3,2,5,4,7,8]=>[1,6,4,3,5,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,2,5,4,7,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,4,2,6,3,7,8]=>[1,6,4,3,5,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,4,3,5,7,8]=>[1,2,6,5,4,3,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,2,7,5,4,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,3,2,6,8,5]=>[1,8,5,4,3,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,7,6,2,8,5,4]=>[1,5,8,7,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,6,2,8,4,3,5]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,8,4,3,7,6]=>[1,6,3,8,5,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,4,3,6,5,7]=>[1,2,8,5,4,7,6,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,5,6,3,4,7]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,5,2,8,6,4]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,2,5,8,4,3]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,3,2,7,4,6]=>[1,7,8,5,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,6,4,8,2,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,8,6,5,2,7,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,2,6,5,4,7]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,6,3,8,2,4,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,7,6,4,8,3]=>[1,8,3,6,5,4,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,3,8,7,5,6]=>[1,2,4,3,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,3,8,7,2,5,6]=>[1,6,3,8,7,2,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,6,2,4,5,7]=>[1,5,8,7,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,5,4,2,6,7]=>[1,6,8,5,4,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,4,8,6,5,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,5,3,2,8,7,4]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,8,7,5,4,6]=>[1,3,2,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,6,5,4,3,7]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,3,4,6,5,2,7]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,1,4,6,5,2,7]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,3,1,2,6,4,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[4,8,1,7,5,2,3,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,8,1,7,5,2,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,1,4,2,6,3,7]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,1,3,5,6,2,7]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,3,2,1,6,4,7]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,1,5,4,2,6,3,7]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,5,2,4,1,6,3,7]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,8,7,1,5,2,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,7,1,5,2,3,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[7,6,8,4,1,3,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,8,4,1,3,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,5,4,1,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,8,2,7,5,1,3,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[7,6,8,4,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,1,5,2,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,1,4,8,6,3,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,6,5,3,4,7,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,2,5,3,4,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,5,1,3,4,7,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,5,1,3,6,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,1,5,3,6,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,1,3,5,4,7,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,4,8,3,6,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,8,5,2,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,8,2,5,4,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,2,5,3,7,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,8,1,5,3,7,6,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,4,8,2,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,8,2,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,3,1,6,4,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,3,1,6,4,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,3,1,4,6,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,3,2,7,5,6,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,4,1,7,8,5,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,3,4,1,8,5,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,7,3,1,6,2,5,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,6,4,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,2,4,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,7,3,5,6,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,7,5,2,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,7,5,4,6,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,7,3,2,6,1,5,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,1,7,6,4,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,8,6,4,2,9,7,5,3]=>[1,9,8,7,5,6,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[9,7,5,3,1,8,6,4,2,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[8,6,4,2,1,7,5,3,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[8,7,5,3,1,6,4,2,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[7,5,3,2,1,6,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,5,3,1,4,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,8,6,4,3,2,7,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,9,7,5,3,2,8,6,4]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,8,7,6,4,2,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,9,8,6,4,2,7,5,3]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,10,8,6,4,2,9,7,5,3]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[8,4,6,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,4,8,6,7,5,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,2,5,8,4,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,7,3,6,8,5,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,2,5,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,3,6,8,5,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,3,6,7,5,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,7,6,4,5,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,6,4,5,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,2,7,4,5,3,8]=>[1,7,3,6,5,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,6,4,3,5,7]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,6,4,3,5,8]=>[1,7,3,6,5,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,5,4,6,3,8]=>[1,7,3,6,5,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,5,7,2,8,3,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,7,2,8,1,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,2,7,5,8,1,4,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,7,2,5,8,1,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,7,3,8,1,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,7,4,8,2,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,7,4,8,1,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,2,7,4,8,1,5,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,7,6,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,4,6,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,4,5,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,5,1,4,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,8,5,1,4,3,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,7,6,8,3,5,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[7,2,1,5,3,8,6,4]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[5,8,2,7,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,8,7,3,4,2,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,2,3,6,7,1,4,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,2,3,1,5,8,6,7]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[6,3,5,1,2,4,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]
[8,6,5,4,3,2,1,7,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[3,1,2,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,10,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,5,1,2,4,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[9,7,6,5,4,3,2,1,8,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[10,8,6,9,4,7,2,5,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[2,4,8,7,5,3,1,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[2,6,8,7,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,5,1,4,3,8,7]=>[4,6,5,1,3,2,8,7]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[6,5,1,2,4,3,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,6,5,3,1,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,8,7,5,3,1,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,6,8,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,7,5,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,5,6,3,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,3,4,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,4,8,7,3,6,5]=>[2,1,6,8,7,3,5,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[4,8,7,3,1,2,6,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[8,7,3,4,1,2,6,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,3,1,6,5,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,3,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,7,3,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,7,3,6,5,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,8,7,1,6,5,3,4]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[8,7,1,2,6,5,3,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,1,2,4,3,6,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,1,8,7,3,4,6,5]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,7,5,1,2,4,3,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,7,1,4,3,6,5]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,8,7,3,4,1,6,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,8,7,5,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,8,7,3,1,6,5]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[2,8,7,3,1,4,6,5]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,4,3,1,8,7,5,6]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[4,3,1,2,6,8,7,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[2,8,7,5,6,3,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,8,7,5,3,1,6,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,8,7,5,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,7,5,6,1,4,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,6,8,7,5,1,4,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[6,8,7,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,5,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,1,2,4,6,5,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,4,8,7,3,6,5,1]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[8,7,2,4,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,1,2,6,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,5,3,1,2,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,5,3,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,1,4,3,6,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,3,4,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,2,3,5,4,6,8]=>[7,2,3,4,6,5,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,9,2,3,4,5,6,8,7]=>[1,9,3,4,5,6,7,8,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[7,1,2,6,4,5,3,8]=>[7,2,3,6,5,4,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,1,2,4,3,5,6,8]=>[7,2,3,5,4,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,10,2,3,4,5,6,7,9,8]=>[1,10,3,4,5,6,7,8,9,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[4,7,3,6,5,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,4,2,8,3,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,6,1,5,2,4,7]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[3,1,6,8,5,7,2,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,7,2,1,8,4,6,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,2,8,6,4,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,8,7,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,3,2,8,4,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,1,3,2,4,5,7]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,3,7,4,2,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,1,7,3,5,8,6,2]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,7,3,5,2,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,8,1,3,2,6,7]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[4,5,8,2,1,3,6,7]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[1,8,3,5,7,2,4,6]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,8,6,2,4,5]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,2,1,3,7,5,4]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,1,4,2,7,6,3,5]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,3,4,5,6,7,8,10,2,9]=>[1,9,3,4,5,6,7,10,2,8]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,5,7,3,6,8,2,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,4,6,2,5,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,3,4,7,6,8,2,5]=>[1,7,3,8,5,6,2,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,3,6,7,4,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,4,7,8,5,3,6]=>[1,2,7,8,6,5,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,4,7,6,8,2,5]=>[7,2,3,8,5,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,1,3,7,6,8,2,5]=>[7,2,3,8,5,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,7,3,6,8,2,4]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,7,8,2,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,2,4,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,2,6,5,7,1,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,8,3,6,7,4,1,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[8,7,2,5,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,1,6,4,3,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,8,2,7,5,4,3,6]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,8,1,7,5,4,2,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,8,6,1,7,3,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,1,2,8,4,3,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,1,3,8,6,5,4,7]=>[2,1,3,8,7,6,5,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,2,1,7,5,4,3,6]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,3,2,8,6,5,4,7]=>[1,3,2,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,4,1,7,6,8,2,5]=>[7,3,2,8,5,6,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[2,5,7,1,8,4,3,6]=>[4,7,8,1,6,5,2,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,5,7,1,6,8,2,4]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[4,5,7,6,1,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,4,7,6,8,3,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,5,7,8,6,3,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,4,6,7,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,7,5,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,4,8,6,7,3,2,5]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,8,6,7,3,1,5]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[5,2,7,8,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,3,8,7,5,4,1,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,3,8,7,5,4,2,6]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,7,6,4,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,7,6,4,3,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,8,6,7,3,2,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,8,7,5,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,8,1,7,4,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,6,9,8,7,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,4,9,8,7,6,5,3,2]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,3,9,8,7,6,5,4,2]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[8,7,1,9,6,5,4,3,2]=>[9,8,3,7,6,5,4,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[1,8,10,9,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[6,7,9,1,8,5,4,3,2]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[1,7,10,9,8,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[5,6,9,8,1,7,4,3,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[4,1,8,7,3,6,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,8,4,1,7,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,9,8,7,1,6,3,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[1,5,10,9,8,7,6,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[4,5,8,7,3,1,6,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,4,10,9,8,7,6,5,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[9,8,1,10,7,6,5,4,3,2]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[1,9,11,10,8,7,6,5,4,3,2]=>[1,11,10,9,8,7,6,5,4,3,2]=>[1,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,7,6,9,8,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[7,8,10,1,9,6,5,4,3,2]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[1,8,11,10,9,7,6,5,4,3,2]=>[1,11,10,9,8,7,6,5,4,3,2]=>[1,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,6,9,5,8,7,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[8,7,6,1,9,5,4,3,2]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[6,7,10,9,1,8,5,4,3,2]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[3,1,8,4,7,6,5,2]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,9,8,4,7,6,3,2]=>[9,2,8,7,6,5,4,3,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[6,7,9,5,1,8,4,3,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,5,10,9,8,1,7,4,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,6,11,10,9,8,7,5,4,3,2]=>[1,11,10,9,8,7,6,5,4,3,2]=>[1,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,4,9,8,7,3,6,5,2]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[5,6,9,8,4,1,7,3,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[4,5,10,9,8,7,1,6,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,5,11,10,9,8,7,6,4,3,2]=>[1,11,10,9,8,7,6,5,4,3,2]=>[1,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,5,8,4,3,7,6,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,11,10,9,8,7,6,5,4,2]=>[1,11,10,9,8,7,6,5,4,3,2]=>[1,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[8,1,7,2,5,6,4,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,3,5,2,7,6,4]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,7,1,5,4,8,6,3]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[8,6,2,4,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,1,6,7,5,8,3]=>[3,8,1,6,5,4,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[8,1,4,5,6,3,7,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,5,6,2,7,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,7,6,2,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,5,1,7,8,6,4,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,5,6,2,8,7,4,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,3,1,5,6,4,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,3,2,5,6,7,1,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,5,3,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,4,5,6,2,8,1,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,7,4,2,8,5,1,6]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[7,3,4,1,6,8,2,5]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,6,3,1,4,7,5,8]=>[4,7,3,1,5,6,2,8]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[7,3,4,1,6,5,8,2]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[3,7,4,2,5,8,6,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,3,5,1,4,8,7,6]=>[4,2,5,1,3,8,7,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,7,1,3,6,8,5,4]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,7,1,3,8,4,6,5]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,8,7,1,6,2,5,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[3,8,7,1,4,5,2,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,7,4,2,1,8,6,5]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[4,8,5,7,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,5,7,3,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,7,2,4,1,5,6]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,6,7,2,1,4,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,7,5,1,2,6,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,3,4,6,2,1,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,7,4,6,1,5,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,4,7,6,1,2,8,5]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[4,5,8,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,3,7,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,3,5,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,3,8,1,4,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,2,7,6,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,3,1,4,5,2,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,7,2,1,5,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,4,2,5,1,6,7,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,3,1,6,4,7,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,3,1,4,5,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,4,1,5,6,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,4,1,7,5,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,3,1,7,4,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,3,1,6,7,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,3,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,3,8,1,4,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,8,2,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,7,3,1,5,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,5,3,1,6,4,2,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,4,1,5,2,3,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,5,1,2,6,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,4,1,2,7,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,4,1,2,5,3,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,5,1,2,3,6,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,3,7,4,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,7,2,5,3,6,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,8,3,4,5,2,6,7]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,6,4,2,5,3,7]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,6,4,1,5,7,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[7,8,3,4,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,5,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,4,8,3,2,5,7]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,1,8,5,3,2,6,7]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,1,6,4,2,7,3,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,7,4,2,5,8,6]=>[5,2,8,4,1,6,7,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,2,7,4,3,5,6,8]=>[1,2,7,5,4,6,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,8,5,2,4,3,7]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,8,2,5,1,4,7,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,5,2,1,6,8,7,3]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[7,2,8,6,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,4,8,6,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,2,6,1,4,5,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,7,8,6,2,4,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,3,1,2,5,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,5,3,1,2,4,7,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,2,1,6,5,3,4,7]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,8,1,5,6,2,4,7]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[6,8,4,1,5,2,3,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,2,8,1,6,4,5,7]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[5,4,1,2,8,3,7,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,8,4,1,2,3,7,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[7,1,2,5,3,4,6,8]=>[7,2,3,6,5,4,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,6,7,3,2,8,4,5]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,6,3,2,7,4,5]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,2,8,5,3,7]=>[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,2,8,4,3,7]=>[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,4,8,6,5,7,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,2,4,7,3,6,5,8]=>[1,2,5,7,3,6,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,7,4,3,6,8]=>[1,2,6,7,5,3,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,7,4,6,8,3]=>[1,2,8,6,5,4,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,7,6,8,3,5]=>[1,2,7,8,5,6,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,8,6,1,7,2,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,3,6,8,1,7,4,5]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,7,1,8,6,4,5]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,6,1,7,8,5,3,4]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,4,8,5,6,7,1,3]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,4,8,5,6,7,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,1,6,8,4,7,5]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[4,8,3,1,6,5,7,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,6,8,5,4,2,7,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,5,8,4,2,1,7,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,7,4,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,3,5,4,2,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,6,4,2,5,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[2,1,5,8,6,4,7,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[4,2,8,5,6,3,7,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[5,3,7,2,6,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,2,3,4,6,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,8,7,3,2,5,6,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,1,2,3,8,6,4]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,6,2,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,8,4,6,1,5,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,4,6,2,8,1,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,1,5,8,2,3,6,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,4,8,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,8,4,2,3,5,7]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,3,6,2,1,8,5,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,8,6,4,2,5,7,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,6,2,1,8,4,7,3]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[2,8,1,6,5,7,3,4]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[5,1,6,4,3,8,7,2]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,4,6,8,1,3,7,2]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[3,7,1,6,4,5,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,3,8,7,5,4,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,4,5,7,9,8,6]=>[1,2,3,4,5,9,8,7,6]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,6,8,9,7,5]=>[1,2,3,4,9,8,7,6,5]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,6,9,8,7,5]=>[1,2,3,4,9,8,7,6,5]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,5,7,9,8,6,4]=>[1,2,3,9,8,7,6,5,4]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,5,9,8,7,6,4]=>[1,2,3,9,8,7,6,5,4]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,4,6,9,8,7,5,3]=>[1,2,9,8,7,6,5,4,3]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,4,9,8,7,6,5,3]=>[1,2,9,8,7,6,5,4,3]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,3,5,7,9,8,6,4,2]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,3,5,9,8,7,6,4,2]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,5,6,8,10,9,7]=>[1,2,3,4,5,6,10,9,8,7]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,4,5,7,9,10,8,6]=>[1,2,3,4,5,10,9,8,7,6]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,4,5,7,10,9,8,6]=>[1,2,3,4,5,10,9,8,7,6]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,4,6,8,10,9,7,5]=>[1,2,3,4,10,9,8,7,6,5]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,4,6,10,9,8,7,5]=>[1,2,3,4,10,9,8,7,6,5]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,5,7,9,10,8,6,4]=>[1,2,3,10,9,8,7,6,5,4]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,5,7,10,9,8,6,4]=>[1,2,3,10,9,8,7,6,5,4]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,5,10,9,8,7,6,4]=>[1,2,3,10,9,8,7,6,5,4]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,4,6,10,9,8,7,5,3]=>[1,2,10,9,8,7,6,5,4,3]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,4,10,9,8,7,6,5,3]=>[1,2,10,9,8,7,6,5,4,3]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,3,5,7,9,10,8,6,4,2]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,3,5,7,10,9,8,6,4,2]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,3,5,10,9,8,7,6,4,2]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,3,10,9,8,7,6,5,4,2]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[6,7,3,4,8,5,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,1,8,2,5,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,1,7,2,5,6,8,4]=>[4,2,8,1,6,5,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[6,4,1,7,2,8,5,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,3,1,6,2,8,5,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,8,2,5,3,1,6,7]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[5,1,3,4,8,2,6,7]=>[6,2,4,3,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,1,4,5,7,8,2,3]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,3,4,7,1,8,5,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,8,5,1,3,4,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,1,3,4,5,6,8,2]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,5,2,7,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,3,5,6,2,7,4]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,3,2,5,6,1,7,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,2,5,1,6,8,7,3]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,4,2,7,8,6,1,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,7,2,1,3,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,6,8,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,8,5,2,6,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,1,2,5,3,8,4]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,8,7,2,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,2,4,8,1,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,5,7,3,8,6,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,7,5,1,8,2,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,1,2,4,3,8,5]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,7,2,1,5,3,8,4]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,3,2,8,7,1,6,5]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[4,8,3,2,7,1,6,5]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[4,8,3,1,7,6,5,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,3,8,7,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,3,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,8,2,1,7,6,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[3,8,7,2,6,5,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[7,4,1,8,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,2,8,1,7,6,3]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,8,4,2,1,7,6,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,8,4,7,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,8,3,1,7,6,2]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,5,6,1,4,7,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,4,1,2,5,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,6,7,4,2,5,8,3]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,7,5,8,1,2,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,6,7,5,8,3,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,8,6,5,7,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,6,5,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,2,1,6,8,4,7,3]=>[8,3,2,6,7,4,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,5,8,7,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,7,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,7,5,8,2,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,7,5,3,8,1,2,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,7,5,3,6,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,7,5,3,1,6,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[2,7,5,3,6,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,7,5,3,8,1,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,7,5,8,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,5,6,8,3,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,7,5,6,8,3,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,7,5,3,6,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,7,5,6,3,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,7,5,3,6,8,1,4]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[8,7,5,3,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,5,3,1,4,8,6]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,7,5,3,4,8,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,6,2,8,3,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,1,6,3,2,4,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,7,6,1,8,3,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,7,2,1,5,4,6]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[6,1,7,2,8,4,3,5]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,8,5,6,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,6,2,8,5,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,1,7,3,8,5,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,3,2,5,4,6]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,7,8,3,1,5,4,6]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[4,8,5,6,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,2,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,6,7,8,5,1,3]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,4,6,7,8,3,1,5]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[4,7,6,2,8,5,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,7,3,2,4,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,6,5,8,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,1,7,2,6,4,5]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,5,1,2,8,7,3,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[5,6,1,2,8,3,7,4]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,8,7,1,6,2,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,5,1,7,6,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,1,4,8,2,7,5]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,5,6,1,7,2,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,6,1,3,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,6,1,3,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,7,1,4,2,8,5,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,1,6,4,8,3,7,5]=>[2,1,8,6,7,4,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[7,4,5,1,3,8,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,5,7,8,4,2,3,6]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,6,4,2,5,7,8]=>[1,5,6,4,2,3,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,7,8,3,6,2]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,8,3,6,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,8,2,4,3,6]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,4,7,3,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,4,2,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,4,6,3,2,7,5]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,4,8,5,3,2,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[3,5,6,1,4,2,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,6,3,8,4,2,7,5]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,5,7,8,3,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,1,8,2,6,7,5,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,6,7,8,2,1,4,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,5,7,1,6,3,4,8]=>[4,7,6,1,5,3,2,8]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,2,8,3,6,5,1,7]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[6,3,8,7,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,1,8,2,4,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,5,6,3,4,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,2,4,7,8,6,1,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,4,5,7,1,8,6,3]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[8,1,6,2,3,4,7,5]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,4,2,5,7,8,3]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,7,2,4,3,5,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,3,4,5,2,7,6]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,3,6,4,7,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,2,5,6,3,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,3,5,8,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,8,6,7,2,1,5]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[3,4,8,2,5,1,7,6]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[1,7,2,5,8,4,3,6]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,7,8,3,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,5,1,6,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,8,7,4,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,7,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,7,8,4,6,5,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,7,8,5,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,5,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,7,4,6,1,5,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[4,8,7,2,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,8,5,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,8,1,5,7,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,6,8,3,5,2,7,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,5,8,6,3,7,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,7,8,4,5,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,1,2,8,4,7,5,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,7,1,8,5,6,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,7,1,8,2,6,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,1,8,6,4,5,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[5,3,8,4,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,5,8,1,7,4,6,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,5,8,3,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,7,2,8,6,4,5,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,7,8,1,6,2,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,4,7,8,5,6,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,1,7,8,5,6,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,5,8,6,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,8,5,7,6,1,3]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,6,3,8,5,1,7,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,1,5,8,6,7,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,5,8,2,6,3,1,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[5,3,4,7,6,1,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,2,1,4,8,3,7,5]=>[8,3,2,6,7,4,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,8,5,4,1,3,7,6]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[4,2,8,7,1,3,5,6]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[5,4,6,3,1,7,2,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,3,6,5,1,8,2,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,5,6,8,7,3,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,8,3,6,5,2,7]=>[1,7,8,4,6,5,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,6,4,7,2,5]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,6,4,3,7,5]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,5,1,8,7,3,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,1,7,6,8,3,2,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,1,4,5,7,3,2,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,4,7,6,2,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,3,2,6,1,7,4,5]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,6,3,7,4,5,2,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,3,7,4,8,5,1]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,6,1,7,8,2,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,3,8,4,5,6,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,2,6,7,8,3,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,8,1,2,7,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,1,8,7,2,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,4,3,7,2,1,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,1,2,8,7,3,4,5]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,3,2,8,4,6,1,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,5,1,7,6,2,8,3]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,5,2,7,6,3,4,8]=>[1,7,3,6,5,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,6,8,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,1,7,6,2,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,8,6,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,1,8,7,6,5,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,5,2,8,4,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,1,8,7,4,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,1,8,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,1,7,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,3,7,6,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,6,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,7,5,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,3,1,8,7,2,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[3,4,8,1,5,2,6,7]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[8,6,5,7,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,5,8,6,2,7,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,8,5,7,2,6,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,8,5,3,4,2,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,5,2,6,4,3,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,4,5,2,1,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,2,6,1,4,7,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[2,7,5,8,1,4,6,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[3,2,6,7,1,8,5,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,4,6,7,8,2,1,5]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[3,2,6,7,8,4,1,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,2,7,4,8,5,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,1,3,8,5,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,1,8,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,2,6,7,8,5,3,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,7,8,3,2,5]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,2,4,5,3,7,8]=>[6,2,3,5,4,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,1,7,3,2,6,4,5]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,4,1,2,3,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[7,3,4,6,1,2,5,8,9]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[7,9,4,6,1,8,2,3,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[5,4,1,2,3,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,10,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[7,3,4,6,1,2,5,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,10,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[7,9,4,6,1,8,2,3,5,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[6,8,10,1,7,2,9,3,5,4]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[8,10,4,5,7,1,9,2,3,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,7,2,1,5,4,6,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,7,4,8,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,5,2,4,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,6,4,3,1,5,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,1,8,7,2,3,5,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,1,2,7,3,4,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,8,2,7,1,5,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,8,6,1,4,5,7,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[6,8,7,2,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,2,6,4,8,7,5,1]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,7,2,8,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,1,8,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,7,4,8,3,6,1,5]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[4,7,3,8,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,6,8,7,2,5,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,3,8,2,5,7,6,1]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,1,2,6,8,7,5,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,6,4,8,7,2,5]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,1,6,8,7,5,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,8,1,4,5,7,2,6]=>[7,8,3,4,5,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,8,1,4,2,5,7,6]=>[5,8,3,4,1,6,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,1,8,3,5,2,7,6]=>[6,2,8,4,5,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,8,1,2,5,4,7,6]=>[4,8,3,1,6,5,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[4,2,3,6,8,7,1,5]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[4,2,8,3,5,1,7,6]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[4,2,8,3,5,7,6,1]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,8,2,4,5,7,6,1]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,2,5,1,4,7,6]=>[5,8,3,6,1,4,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,2,8,5,7,1,3,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[3,8,1,5,2,4,7,6]=>[5,8,3,6,1,4,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[7,5,6,4,1,3,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,8,6,4,1,3,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,4,2,5,6,3,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,6,1,4,3,2,5,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,4,1,3,5,6,2,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,6,2,1,5,8,7,4]=>[4,8,3,1,5,7,6,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,3,6,1,5,8,7,4]=>[4,2,8,1,5,7,6,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,4,7,1,5,6,8,2]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,6,7,4,1,2,8,5]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[4,3,2,7,1,6,8,5]=>[5,3,2,8,1,6,7,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[7,3,2,8,1,6,4,5]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,4,8,1,5,6,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,6,8,1,5,3,7,4]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[6,8,2,1,5,3,7,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,8,2,5,3,6,7,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,5,8,2,3,6,7,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[2,4,8,5,3,6,7,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,3,2,6,4,8,7,1]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,4,5,3,8,6,7,1]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,3,5,2,8,6,7,1]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,8,5,3,2,6,7,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,5,4,2,8,6,7,1]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,1,2,7,5,6,8,3]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,7,4,2,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,5,7,4,6,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,2,4,3,8,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,8,1,2,5,4,7,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,4,1,8,5,2,7,3]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,6,1,8,5,4,7,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[7,1,2,8,5,6,4,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,3,2,6,8,5,7,1]=>[8,3,2,6,7,4,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,7,6,4,8,5,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,1,6,8,5,4,7,2]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,5,8,4,6,7,1]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,5,2,8,4,6,7,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,4,5,8,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,4,2,8,3,6,7,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,3,4,8,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,5,4,8,3,6,7,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,3,2,5,8,4,7,1]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,1,8,3,5,4,7,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,4,8,3,2,6,7,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,8,2,3,4,6,7,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,2,1,7,8,5,4,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,4,6,8,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,5,2,7,1,6,8]=>[6,4,3,2,7,1,5,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[7,5,6,1,2,3,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,5,7,6,3,2,8,4]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,4,6,7,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,6,2,3,1,5,7]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,5,2,1,4,3,8,6]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[3,1,7,8,5,4,2,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,4,5,2,1,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[7,6,4,8,3,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,8,5,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,8,5,1,3,4,7]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[3,2,7,8,6,1,4,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,8,2,5,1,3,7,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,7,4,2,1,5,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,7,4,1,3,6,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,2,7,5,1,8,3,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[4,1,6,5,3,8,2,7]=>[7,2,5,4,3,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,5,4,6,3,8,2,7]=>[1,7,5,4,3,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,6,4,7,3,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,7,1,8,6,3,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,8,1,7,3,6,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,3,8,6,2,1,7,5]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[8,3,6,2,4,1,7,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,8,3,2,4,6,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,8,5,3,1,6,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,5,4,8,7,3,6,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,4,2,8,7,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,8,1,7,4,2,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[7,8,6,3,1,4,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,6,1,7,5,2,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,7,5,4,8,3,1,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,8,7,5,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,2,8,5,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,5,7,6,2,8,4,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,5,2,7,8,4,3]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,7,8,5,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,8,5,6,1,4,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[6,7,8,4,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,8,1,2,5,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,4,1,2,5,7,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,1,4,7,2,5,8,3]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,7,8,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,8,2,1,5,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,3,2,7,4,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[2,6,4,3,7,5,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,2,3,6,1,8,4,5]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,4,6,5,7,1,2,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,6,2,3,5,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,5,2,4,3,6,1,7]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,7,2,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,7,5,8,1,4,3]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[7,4,8,2,1,5,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,3,6,7,8,5,1,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,3,7,1,6,4,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,1,7,6,5,3,4]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[5,7,4,1,6,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,5,1,2,8,3,4,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,6,8,1,3,7,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,7,4,8,6,1,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,6,8,5,3,2,4,7]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,1,6,7,4,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,8,4,6,1,3,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,2,7,4,3,8,1,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,7,8,4,6,2,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,8,4,6,2,3,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,6,5,4,7,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,6,8,7,3,2,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,4,6,7,3,8,2]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,3,4,6,2,8,5]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,4,1,2,6,5,8,7,9]=>[4,3,2,1,6,5,8,7,9]=>[4,3,2,1,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[4,7,2,8,5,3,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,7,1,4,6,3,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,5,2,8,4,7,1,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,4,7,5,8,6,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,8,3,4,7,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,6,3,5,2,7,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,1,3,5,4,2,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,7,1,6,8,3,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,5,2,8,4,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[8,2,5,6,3,1,7,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,1,8,4,2,5,3,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,4,8,7,5,2,6,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,4,2,3,7,8]=>[1,6,5,4,3,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,3,6,8,4,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,7,4,2,1,3,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,1,5,2,7,8,6,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,8,7,3,2,5,4,6]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,4,8,7,3,6]=>[1,2,7,4,8,6,3,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,8,6,3,5,7]=>[1,2,6,8,7,3,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,4,7,3,8,6]=>[1,6,3,4,8,2,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,3,5,7,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,3,2,1,4,7,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,2,7,6,8,4,3,5]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,3,2,5,7,8,4]=>[1,8,4,3,5,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,4,2,6,8,5]=>[1,8,5,4,3,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,3,5,8,4,2,7]=>[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,3,2,8,4,7]=>[1,7,5,4,3,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,8,4,6,3,7]=>[1,2,7,8,5,6,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,3,2,7,8,4,6]=>[1,7,4,3,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,8,6,2,3,7,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[7,5,8,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,6,4,3,8,5,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,7,6,3,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,3,6,8,5,2]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,3,5,7,8,4,2]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,3,2,7,8,4]=>[1,8,5,4,3,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,6,8,4,5,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,4,7,5,3,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,5,2,1,7,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,2,6,8,4,3,7,5]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,3,7,2,6,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,3,8,2,6,1,7,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,6,2,5,3,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,2,4,5,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,2,4,3,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,2,3,5,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,4,2,7,1,6,3,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,6,3,2,8,1,7,5]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[8,7,6,1,5,3,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,6,1,4,3,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,6,1,3,5,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,6,1,5,4,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,2,7,1,5,3,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,3,7,2,8,1,6,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,3,5,4,2,1,6,7]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,8,4,3,1,5,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,3,7,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,1,2,5,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,6,1,2,5,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,6,1,4,2,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,7,5,8,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,7,3,8,4,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,5,4,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,7,1,5,3,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,6,1,3,4,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,7,8,1,3,4,2,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[7,8,5,1,3,4,2,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,8,3,4,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,1,3,4,2,6,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,7,1,3,4,2,8,6]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[7,3,5,6,4,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,7,3,8,2,5,6,4]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,3,7,8,4,6,2]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,3,8,2,6,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,5,3,6,2,4,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,7,3,5,8,4,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,7,5,8,6,2,4]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,5,3,6,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,8,3,4,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,5,6,3,4,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,3,5,6,4,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,7,5,8,4,1,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[7,5,6,8,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,4,7,8,1,2,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,3,7,6,8,1,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,7,1,2,5,8,4,6]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,1,2,7,5,8,4,6]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,1,2,5,7,8,6,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[7,3,1,5,4,6,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,3,5,1,2,6,4,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[3,7,1,2,8,5,6,4]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[5,3,1,7,4,6,8,2]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,3,7,1,2,6,8,4]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[7,4,8,3,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,7,3,5,6,1,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[5,7,6,4,2,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,8,2,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,2,4,6,1,3,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,1,4,8,5,2,7,3]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,4,5,8,1,6,7,2]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,8,7,4,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,8,4,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,1,6,8,5,2,7,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,8,1,5,6,4,7]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[5,4,8,1,2,6,7,3]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,1,8,2,4,6,7,3]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,8,2,3,6,7,5]=>[5,2,8,4,1,7,6,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[5,2,3,8,1,7,4,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[2,3,5,7,1,6,4,8]=>[5,2,7,6,1,4,3,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,5,3,8,2,4,6,7]=>[1,6,5,8,3,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,2,7,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,1,8,6,3,5,4]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[5,7,6,1,3,2,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,1,7,5,3,6,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,5,3,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,4,6,1,7,8,2]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,1,5,4,6,3,7,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,6,3,1,7,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,2,5,6,3,7,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,2,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,7,2,8,6,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,5,6,4,1,7,2,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[2,5,6,1,7,4,3,8]=>[4,7,6,1,5,3,2,8]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,7,1,8,6,5,4,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,7,6,1,8,5,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,4,2,1,3,5,7,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[8,6,4,2,9,1,3,5,7]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,6,4,2,7,1,3,5,8]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,7,4,2,5,1,3,6,8]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,7,5,2,3,1,4,6,8]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,7,5,3,1,2,4,6,8]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,8,6,4,2,1,3,5,7,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,8,6,2,1,4,3,5,7,9]=>[10,9,8,5,4,7,6,3,2,1]=>[10,9,8,5,4,7,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[6,4,2,7,1,3,5,8,9]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[8,6,4,2,9,1,3,5,7,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[6,2,8,3,1,4,5,7]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[8,9,4,2,5,1,3,6,7]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,6,4,2,7,1,3,5,8,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[2,7,8,3,1,4,5,6]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[9,6,7,2,3,1,4,5,8]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,7,4,2,5,1,3,6,8,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[9,7,4,5,1,2,3,6,8]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,7,5,2,3,1,4,6,8,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[9,7,5,3,1,2,4,6,8,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,8,5,3,2,6,7,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,5,6,3,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,7,3,2,8,4]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,2,3,4,8,6]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,2,4,8,6,3]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,8,3,2,4,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,8,6,2,3,5,7]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,4,5,6,7,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,6,3,4,5,7]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,6,3,5,7,4]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,8,4,3,5,6]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,6,7,4,2,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,8,4,2,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,8,3,4,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,2,3,8,5,6]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,4,2,3,5,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,5,6,2,8,4]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,3,4,2,5,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,7,8,5,4,6]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,4,6,3,8,5]=>[1,2,8,6,5,4,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,5,2,3,8,6]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,4,5,2,3,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,3,4,5,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,4,5,6,3,7]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,4,5,6,2,3,7]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,2,7,3,4,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,8,7,2,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,5,2,6,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,8,7,3,2,5,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,3,8,1,6,7,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,2,1,3,7,6,4]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,1,8,2,6,4,7,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,8,3,6,7,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,8,4,6,2,7,5]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,4,1,6,5,2,3,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,8,7,6,4,3,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,8,7,5,3,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,8,7,3,2,4,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,3,7,5,6,8,4,1]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,4,7,5,8,1,6]=>[7,2,3,8,5,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,8,7,6,4,5,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,8,7,6,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,2,4,7,6,8,1]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,3,2,6,4,7,8,1]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,3,2,6,7,4,8,1]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,3,2,7,6,4,8,1]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,3,5,2,8,4,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,5,2,7,4,6,8,1]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,2,7,5,4,8,6,1]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,7,5,2,4,8,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,3,7,5,4,8,6,1]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,5,1,6,4,7,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,5,6,1,3,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,7,6,8,2,5,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[5,2,8,4,1,3,6,7]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[3,8,5,2,1,4,6,7]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[7,6,4,1,8,2,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,4,2,1,6,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,1,6,7,3,4,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,1,6,7,4,3,5]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[5,2,8,6,3,7,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,8,1,2,5,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,2,9,3,4,5,6,8,7]=>[1,2,9,4,5,6,7,8,3]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,9,5,6,8,7]=>[1,2,3,4,9,6,7,8,5]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,3,4,8,5,7,6]=>[2,1,3,4,8,6,7,5]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,2,3,4,5,9,6,8,7]=>[1,2,3,4,5,9,7,8,6]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,10,3,4,5,6,7,9,8]=>[1,2,10,4,5,6,7,8,9,3]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,4,10,5,6,7,9,8]=>[1,2,3,4,10,6,7,8,9,5]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,4,5,10,6,7,9,8]=>[1,2,3,4,5,10,7,8,9,6]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,4,5,6,9,10,7,8]=>[1,2,3,4,5,6,10,9,8,7]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[5,7,1,2,6,8,3,4]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,2,3,8,5,4,6,9,7]=>[1,2,3,9,6,5,7,8,4]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,3,2,4,5,6,9,8,7]=>[1,3,2,4,5,6,9,8,7]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,5,6,7,8,11,10,9]=>[1,2,3,4,5,6,7,8,11,10,9]=>[1,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[3,5,7,4,1,8,2,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[8,6,4,7,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,4,1,2,5,3,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,4,3,1,6,5,7]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,8,4,6,1,5,2,7]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[8,3,5,6,1,4,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,7,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,1,2,8,5,7,4,6]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[7,3,1,2,5,8,4,6]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,1,2,8,4,6,9,5,7]=>[3,2,1,9,5,8,7,6,4]=>[3,2,1,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[8,3,5,7,2,1,4,6]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,1,3,8,5,7,4,6]=>[2,1,3,8,7,6,5,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[7,3,1,2,8,4,5,6]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[7,2,4,5,3,8,1,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,4,2,5,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,4,1,6,3,7,8,2]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,5,1,3,6,7,8,2]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,1,7,6,3,4,8,2]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,7,5,4,8,2,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,7,2,1,6,8,4,5]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[1,5,8,2,4,7,6,3]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,1,6,4,7,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,6,5,7,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,1,4,7,3,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,6,8,2,7,4,5,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,2,1,8,4,3,6]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[5,7,1,6,8,3,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,6,2,1,8,3,4,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,4,1,7,3,8,2,5]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,2,5,6,7,1,4,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,2,4,6,8,3,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,2,4,7,8,1,3,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,1,4,3,2,8,5,7]=>[7,2,5,4,3,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,7,4,8,6,1,5,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,4,8,6,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,8,6,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,8,4,7,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,7,3,6,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,4,7,8,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,4,7,2,6,8,5,3]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,2,3,5,7,1,4,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,8,1,2,5,6,4,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,3,6,8,5,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,2,8,5,1,6,3,7]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[6,5,8,1,4,2,3,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[3,8,2,4,5,1,6,7]=>[6,8,3,4,5,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,6,2,4,1,5,7,8]=>[5,6,3,4,1,2,7,8]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,3,8,4,1,6,5,7]=>[5,2,8,4,1,7,6,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,5,7,3,1,6,2,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[2,3,1,4,8,5,7,6]=>[3,2,1,4,8,6,7,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[4,2,6,1,5,8,7,3]=>[8,4,5,2,3,7,6,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,5,1,8,4,3,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,1,8,5,7,6,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,8,7,4,6,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,4,8,7,5,1,3,6]=>[6,7,8,5,4,1,2,3]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[3,5,7,6,1,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,5,7,6,2,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,1,4,3,8,7,5,2]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,3,1,8,7,4,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,3,6,2,8,7,4,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,3,5,2,1,8,7,4]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[2,8,4,1,3,7,6,5]=>[4,8,5,1,3,7,6,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,8,1,4,7,6,5,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,2,3,8,7,5,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,1,3,5,8,7,6,2]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,4,7,5,8,1,2,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[2,7,8,3,4,1,5,6]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,8,6,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,6,8,1,4,3,5]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[5,3,6,2,8,4,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[8,1,6,3,7,4,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,4,3,7,1,8,6,5]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[2,6,5,7,3,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,8,2,7,4,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,7,8,5,3,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,6,5,4,7,1,8,3]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[5,8,3,4,6,1,7,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,1,7,4,2,5,8,3]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,8,7,1,5,4,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,3,1,5,7,6,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,3,8,2,7,1,6,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,3,4,5,2,7,1,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,2,6,7,1,5,3,4]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[7,1,5,2,6,3,4,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,7,1,5,2,6,8,4]=>[5,8,3,6,1,4,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[6,7,1,8,3,4,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,7,1,6,8,4,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,5,2,6,7,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,8,3,4,7,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,1,6,5,2,8,4]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[8,3,5,2,7,1,6,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,1,8,4,6,3,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,8,6,4,7,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,1,4,8,6,5,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,7,1,4,5,2,8,6]=>[6,8,3,4,5,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,3,7,6,5,8,1,4]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,7,8,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[6,5,7,8,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[7,8,9,5,4,3,2,1,6]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,8,9,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[6,7,8,9,4,3,2,1,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,6,8,9,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[6,5,7,8,9,3,2,1,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,6,5,8,9,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[6,5,4,7,8,9,2,1,3]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[2,1,4,3,6,5,8,7,11,12,9,10]=>[2,1,4,3,6,5,8,7,12,11,10,9]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,6,5,9,10,7,8,12,11]=>[2,1,4,3,6,5,10,9,8,7,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,6,5,10,11,12,7,8,9]=>[2,1,4,3,6,5,12,11,10,9,8,7]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,7,8,5,6,10,9,12,11]=>[2,1,4,3,8,7,6,5,10,9,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,7,8,5,6,11,12,9,10]=>[2,1,4,3,8,7,6,5,12,11,10,9]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,8,9,10,5,6,7,12,11]=>[2,1,4,3,10,9,8,7,6,5,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,9,10,11,12,5,6,7,8]=>[2,1,4,3,12,11,10,9,8,7,6,5]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,5,6,3,4,8,7,10,9,12,11]=>[2,1,6,5,4,3,8,7,10,9,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,5,6,3,4,8,7,11,12,9,10]=>[2,1,6,5,4,3,8,7,12,11,10,9]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,5,6,3,4,9,10,7,8,12,11]=>[2,1,6,5,4,3,10,9,8,7,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,5,6,3,4,10,11,12,7,8,9]=>[2,1,6,5,4,3,12,11,10,9,8,7]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,6,7,8,3,4,5,10,9,12,11]=>[2,1,8,7,6,5,4,3,10,9,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,6,7,8,3,4,5,11,12,9,10]=>[2,1,8,7,6,5,4,3,12,11,10,9]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,7,8,9,10,3,4,5,6,12,11]=>[2,1,10,9,8,7,6,5,4,3,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,8,9,10,11,12,3,4,5,6,7]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[3,4,1,2,6,5,8,7,10,9,12,11]=>[4,3,2,1,6,5,8,7,10,9,12,11]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[3,4,1,2,6,5,8,7,11,12,9,10]=>[4,3,2,1,6,5,8,7,12,11,10,9]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[3,4,1,2,6,5,9,10,7,8,12,11]=>[4,3,2,1,6,5,10,9,8,7,12,11]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[3,4,1,2,6,5,10,11,12,7,8,9]=>[4,3,2,1,6,5,12,11,10,9,8,7]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[3,4,1,2,7,8,5,6,10,9,12,11]=>[4,3,2,1,8,7,6,5,10,9,12,11]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[3,4,1,2,7,8,5,6,11,12,9,10]=>[4,3,2,1,8,7,6,5,12,11,10,9]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[3,4,1,2,8,9,10,5,6,7,12,11]=>[4,3,2,1,10,9,8,7,6,5,12,11]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[3,4,1,2,9,10,11,12,5,6,7,8]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,5,6,1,2,3,8,7,10,9,12,11]=>[6,5,4,3,2,1,8,7,10,9,12,11]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[4,5,6,1,2,3,8,7,11,12,9,10]=>[6,5,4,3,2,1,8,7,12,11,10,9]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[4,5,6,1,2,3,9,10,7,8,12,11]=>[6,5,4,3,2,1,10,9,8,7,12,11]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[4,5,6,1,2,3,10,11,12,7,8,9]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[5,6,7,8,1,2,3,4,10,9,12,11]=>[8,7,6,5,4,3,2,1,10,9,12,11]=>[8,7,6,5,4,3,2,1,12,11,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[[[.,.],.],.],.]]
[5,6,7,8,1,2,3,4,11,12,9,10]=>[8,7,6,5,4,3,2,1,12,11,10,9]=>[8,7,6,5,4,3,2,1,12,11,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[[[.,.],.],.],.]]
[6,7,8,9,10,1,2,3,4,5,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[[.,.],.]]
[3,5,7,6,8,2,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,2,5,3,7,6,1,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[6,2,4,3,7,5,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,3,6,4,7,5,2,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,5,3,6,4,1,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,5,3,6,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,2,5,3,7,4,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,2,6,3,7,5,1,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[5,2,7,3,6,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,3,6,2,5,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,3,8,2,5,4,1,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[7,3,1,4,6,5,2,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,3,7,2,5,4,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,2,8,3,6,4,1,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[3,2,8,4,6,5,1,7]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,4,7,3,6,5,2,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,5,4,1,6,3,7]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,2,6,4,1,5,3,7]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,4,8,3,7,5,2,6]=>[1,7,8,4,6,5,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,2,1,4,8,5,3,7]=>[7,3,2,6,8,4,1,5]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[5,2,1,4,8,6,3,7]=>[7,3,2,4,8,6,1,5]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[3,2,1,5,8,6,4,7]=>[3,2,1,7,8,6,4,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[4,2,8,3,7,5,1,6]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[5,2,8,3,7,4,1,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[8,3,7,2,6,4,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,1,4,8,5,2,6]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,3,7,4,8,5,2,6]=>[1,7,8,4,6,5,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,6,3,7,4,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,6,3,8,4,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,2,7,3,8,4,1,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[3,2,7,4,8,5,1,6]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,2,6,3,8,4,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,2,5,3,8,4,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,2,5,3,8,4,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,5,3,7,4,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,3,6,4,8,5,2,7]=>[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,4,8,6,2,7]=>[1,7,4,3,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,4,3,7,5,1,6]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,2,4,3,8,5,1,6]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,2,4,3,8,5,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[5,2,4,3,8,6,1,7]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[4,2,5,3,8,6,1,7]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[4,2,5,3,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[6,2,4,3,1,7,5,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[7,2,4,3,1,6,5,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[8,5,1,3,6,4,2,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,1,3,6,5,2,7]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,5,3,1,6,4,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[6,2,5,3,1,7,4,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[3,2,6,4,1,7,5,8]=>[5,2,7,4,1,6,3,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,2,7,4,1,6,5,8]=>[5,2,7,4,1,6,3,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[5,2,7,3,1,6,4,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[6,2,7,3,1,5,4,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[7,2,6,3,1,5,4,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,5,2,4,8,6,3,7]=>[1,7,3,4,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,4,1,3,7,5,2,6]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,2,1,5,3,7,4,8]=>[7,3,2,5,4,6,1,8]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[3,2,1,6,4,7,5,8]=>[3,2,1,7,5,6,4,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,2,8,5,1,6,4,7]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[6,2,8,4,1,5,3,7]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[8,3,7,4,1,5,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,3,2,5,6,4,8]=>[7,2,4,3,6,5,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,3,5,2,4,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,7,2,8,1,4,3,6]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[5,8,2,7,1,4,3,6]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[4,8,3,1,5,2,7,6]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[7,1,5,3,2,6,8,4]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,5,7,8,6,2,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,7,6,5,3,2,1,4,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[8,7,6,4,3,2,1,5,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[8,7,5,4,3,2,1,6,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[8,7,6,5,4,1,2,3,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[9,8,7,6,5,4,2,1,3,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[8,7,6,5,2,3,1,4,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[9,8,7,6,5,3,2,1,4,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[8,7,6,3,4,2,1,5,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[9,8,7,6,4,3,2,1,5,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[8,7,4,5,3,2,1,6,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[9,8,7,5,4,3,2,1,6,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[8,5,6,4,3,2,1,7,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[9,8,6,5,4,3,2,1,7,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[6,7,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[8,6,2,3,1,5,7,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,5,1,7,4,8,6,3]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[8,6,7,3,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,4,2,7,3,6,8,5]=>[1,5,3,8,2,6,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,1,7,8,5,4,6]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[7,3,4,2,1,5,8,6]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[1,7,6,3,2,4,8,5]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,6,4,7,8,5,3]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,6,3,2,4,7,8,5]=>[1,8,4,3,5,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,7,5,8,4,6]=>[1,2,3,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,3,2,4,7,6]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,7,8,1,5,6,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,7,1,8,4,2,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,7,3,8,4,5,6,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,4,3,8,5,6,2]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,2,7,8,3,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,1,8,5,6,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,5,8,1,6,3,4]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[6,4,8,1,5,7,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,7,4,1,3,6,8,5]=>[4,8,5,1,3,6,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[5,2,1,8,4,6,7,3]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,8,7,9,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[5,8,7,6,9,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[4,8,7,6,5,9,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[3,8,7,6,5,4,9,2,1]=>[9,8,6,5,4,3,7,2,1]=>[9,8,6,5,4,3,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[2,8,7,6,5,4,3,9,1]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[2,6,1,5,4,7,3,8]=>[3,7,1,5,4,6,2,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,2,8,5,4,6,3,7]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,6,8,4,5,7,2]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,3,5,7,8,1,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,7,6,5,1,4,8,3]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,7,4,8,1,3,6,5]=>[5,8,6,7,1,3,4,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,3,6,8,4,1,7,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,2,6,8,4,7,5,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,8,6,3,5,4]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,3,8,5,4,7,1,6]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,6,1,4,8,3,7,5]=>[3,8,1,6,7,4,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,7,6,5,2,1,4,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[2,5,6,1,4,8,7,3]=>[4,8,5,1,3,7,6,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[8,4,2,3,7,1,6,5]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,2,4,8,7,3,1,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,3,2,6,7,4,1,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,2,4,6,7,8,1,5]=>[7,2,3,8,5,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,2,6,8,1,3,7,4]=>[8,5,6,7,2,3,4,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[4,8,1,6,3,7,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,5,2,6,4,3,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,3,5,2,6,1,4,7]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,8,5,6,2,7,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,3,2,4,6,7,1,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,2,7,6,1,8,5,3]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[7,2,4,8,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,2,1,8,5,4,6]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[7,3,2,1,6,4,8,5]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,6,5,2,1,8,4,7]=>[5,7,4,3,1,8,2,6]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[6,7,2,4,3,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,5,3,7,2,1,6,8]=>[6,5,3,7,2,1,4,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,3,2,8,1,6,7,5]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,5,8,3,2,7,1,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[6,8,5,2,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,7,8,2,3,6,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,3,8,2,1,6,7,5]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[3,6,7,4,5,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,5,7,4,6,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,3,7,6,2,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,6,7,2,5,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,4,7,8,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,3,1,5,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,1,7,6,4,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,6,7,1,8,3,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,1,8,6,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,5,1,7,6,4,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,5,8,2,6,4,7,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,4,6,8,3,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,5,6,8,3,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,6,7,4,8,1,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,2,6,4,5,7,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,8,1,7,2,5,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,6,7,1,5,4,8,3]=>[4,8,6,1,5,3,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,2,7,6,5,8,1,4]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,7,3,4,5,8,2,6]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,8,4,5,6,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,3,4,5,6,7,8,11,9,10]=>[1,2,3,4,5,6,7,8,11,10,9]=>[1,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,8,3,4,5,6,9,2,7]=>[1,9,8,4,5,6,7,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,7,4,5,8,3,6]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,9,4,5,6,7,3,2]=>[9,2,8,7,6,5,4,3,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[7,9,3,4,5,6,1,8,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[1,9,3,4,5,6,7,10,2,8]=>[1,10,9,4,5,6,7,8,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[7,8,3,4,5,2,9,1,6]=>[9,8,6,5,4,3,7,2,1]=>[9,8,6,5,4,3,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[6,7,3,2,5,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,1,3,9,5,6,7,4,2]=>[9,2,8,7,6,5,4,3,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[6,1,8,4,5,3,7,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,8,9,4,5,6,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,1,10,4,5,6,7,8,3,2]=>[10,2,9,8,7,6,5,4,3,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[6,9,3,4,5,1,7,8,2]=>[9,8,6,5,4,3,7,2,1]=>[9,8,6,5,4,3,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[8,10,3,4,5,6,7,1,9,2]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[4,6,2,5,1,8,7,3]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,1,4,6,2,8,7,3]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,3,5,2,1,6,8,4]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,5,1,2,6,3,7,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,5,8,7,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,2,1,3,6,8,4]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[3,7,2,6,8,1,5,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[7,4,8,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,6,8,5,1,4,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[1,6,4,5,7,3,8,2]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,4,7,8,6,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,3,1,6,8,2,5,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,1,6,8,5,2,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,5,8,7,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,5,7,8,6,2,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,2,1,4,7,8,5]=>[4,8,3,1,5,6,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[6,8,2,7,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,1,7,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[10,7,1,2,3,4,9,5,6,8]=>[10,9,3,4,5,6,8,7,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[9,10,1,2,3,4,8,5,6,7]=>[10,9,3,4,5,6,8,7,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[8,6,3,2,1,5,4,7]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,3,2,4,1,7,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,2,4,3,6,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,5,1,4,6,3,2,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,1,6,3,4,2,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,3,6,1,5,2,7]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,4,3,5,2,1,7,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,4,3,2,8,7,1,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,5,1,4,3,7,2,6]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,4,2,1,3,7,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,7,3,6,1,8,5,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,6,2,4,1,5,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,1,6,3,7,4,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,3,8,2,6,7,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,5,1,7,6,3,4]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,2,4,6,3,7,1,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,2,6,4,3,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,3,6,2,4,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,3,7,2,1,4,6,5]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[7,6,4,1,3,2,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,3,8,2,1,5,6,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,2,5,7,4,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,2,5,4,8,7,1,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,2,4,8,5,1,6,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,2,7,6,8,5,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,1,6,2,8,5,4,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,6,3,8,5,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,6,8,1,3,5,4]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[7,2,8,5,1,3,6,4]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[7,1,8,5,3,2,6,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,2,5,6,4,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,5,8,7,2,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,5,7,4,8,3,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,5,7,8,3,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,6,7,3,1,8,5,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,2,6,3,1,8,7,5]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[6,1,4,2,5,8,7,3]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,3,5,8,4,1,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,4,2,8,5,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,7,6,4,8,5,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,4,2,1,5,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,3,5,1,4,6,7]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,7,4,1,3,2,6,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,1,4,8,3,6,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,8,5,7,6,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,7,5,8,4,2,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,1,5,8,3,4,2,7]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,7,5,1,3,2,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,2,6,1,7,3,4,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,2,6,8,3,7,1,5]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[6,8,5,1,4,2,3,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[7,8,4,5,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,8,5,3,4,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,3,6,4,7,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,8,1,4,2,7,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,8,1,5,6,3,7,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,8,2,6,5,3,7,4]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,8,1,7,2,6,5,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[7,3,8,1,2,6,5,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,1,4,2,3,5,7,6]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,4,6,5,7,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,8,3,7,4,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,7,1,5,4,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,7,1,5,3,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,5,3,4,6,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,4,2,5,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,8,4,3,6,2,7,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,7,2,6,3,4,8,5]=>[1,8,3,6,5,4,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,5,1,6,3,2,4,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,1,2,6,3,4,5,8]=>[7,2,3,6,5,4,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,2,5,1,6,3,4,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[7,3,1,4,6,2,5,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,1,6,5,4,2,3,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,8,4,3,1,7,2,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[3,6,8,5,2,4,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,7,8,4,3,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,3,8,4,7,2,6,5]=>[1,6,8,4,7,2,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,1,4,5,8,6,7]=>[3,2,1,4,5,8,7,6]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[6,7,1,3,2,8,5,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,3,1,7,2,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,7,6,5,8,2,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,4,2,8,6,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,4,3,7,8,2,6,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,8,5,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,3,6,8,7,2,5,4]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,7,1,4,2,3,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,5,1,2,4,7,8,3]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,6,8,4,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,6,5,3,2,4,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,6,5,4,1,3,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[6,2,3,5,8,4,1,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,7,6,1,5,8,3,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[9,8,7,6,5,4,2,3,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[2,3,9,8,7,6,5,4,1]=>[9,2,8,7,6,5,4,3,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[6,8,7,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,4,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[9,8,7,1,6,5,4,3,2]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[9,8,7,6,1,5,4,3,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,6,5,1,4,3,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,10,1,8,7,6,5,4,3,2]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[10,9,1,8,7,6,5,4,3,2]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[10,9,8,1,7,6,5,4,3,2]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[10,9,8,7,1,6,5,4,3,2]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[10,9,8,7,6,1,5,4,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,6,5,1,4,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,6,5,4,1,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[2,4,3,6,5,8,7,10,9,1]=>[10,3,2,5,4,7,6,9,8,1]=>[10,3,2,9,8,7,6,5,4,1]=>[[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.]
[7,2,6,1,5,8,3,4]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,7,3,8,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,3,6,8,2,1,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,4,7,3,8,2,1,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[8,7,2,4,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,5,7,2,6,1,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,7,2,8,5,4,3,6]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,8,3,6,2,1,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[6,8,2,5,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,6,2,7,5,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,8,4,2,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,7,3,4,5,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,5,2,4,6,3,7]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,1,3,4,5,7,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,1,2,4,6,7,3]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,6,8,7,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,8,5,6,4,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,3,1,2,4,6,7,5]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,1,7,5,8,2,4,6]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,1,5,6,4,2,3,7]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,6,5,4,3,2,7]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,6,8,1,5,4,3,7]=>[4,7,8,1,6,5,2,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,5,8,2,1,4,7,6]=>[5,6,8,4,1,2,7,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[4,2,8,5,3,7,6,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,2,7,5,3,8,6,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,4,5,1,8,3,2,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[5,4,7,8,3,1,2,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,5,8,1,3,7,2,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,5,3,6,8,7,2,4]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,2,8,1,4,3,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,7,2,6,8,3,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,2,8,7,4,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,4,3,8,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,1,5,8,7,6,2,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,2,1,6,5,7,3,4]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,1,8,6,5,7,2,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,2,7,6,4,5,8,3]=>[1,2,8,6,5,4,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,6,5,1,8,3,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,2,8,5,6,3,1,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[6,4,2,1,8,7,3,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,2,5,3,8,7,1,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[7,2,5,3,8,4,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,8,1,7,4,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,3,2,5,4,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,6,1,8,3,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,6,2,7,3,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[5,3,4,7,1,6,2,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,5,1,4,6,8,2,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[8,5,7,4,2,1,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,3,7,4,1,8,6,5]=>[5,2,8,4,1,7,6,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,4,5,1,8,6,3,7]=>[4,7,3,1,8,6,2,5]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[6,3,7,1,5,2,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,1,3,7,8,2,6,5]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[7,1,4,8,6,5,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,4,2,1,7,5,6]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,6,2,7,5,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,3,2,5,1,8,4,6]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,8,1,4,2,3,5,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,5,2,4,8,7,1,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,5,2,4,1,3,7,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,1,2,4,3,6,8,7]=>[5,2,3,4,1,6,8,7]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[5,2,1,4,3,7,6,8]=>[5,3,2,4,1,7,6,8]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[8,6,2,7,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,1,5,8,3,4,7]=>[7,3,2,6,8,4,1,5]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[2,3,8,7,1,5,4,6]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,3,8,1,5,2,6,7]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[4,1,3,6,7,2,8,5]=>[6,2,3,8,5,1,7,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[7,1,4,5,8,2,6,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,3,2,4,5,8,7]=>[6,2,4,3,5,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[7,8,1,6,5,2,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,4,8,6,5,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,8,6,5,1,2,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,4,5,7,2,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,8,2,7,3,1,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[6,5,8,2,7,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,8,2,7,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,1,3,6,4,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,3,8,2,7,5,1,6]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,5,7,8,3,2,1,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[5,7,3,4,2,6,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,7,4,2,3,6,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,4,7,3,2,8,1,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[6,8,3,2,4,5,1,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,8,3,4,6,1,2,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,4,3,8,5,1,2,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[6,4,8,2,3,5,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[5,4,6,8,2,3,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[5,6,8,4,1,2,3,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[6,4,8,5,1,2,3,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[7,4,8,3,1,2,5,6]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,7,8,2,3,1,4,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,4,7,8,2,1,3,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[5,8,6,3,1,2,4,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,8,5,2,1,3,4,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,6,1,3,2,4,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[8,1,5,4,6,2,7,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,6,3,2,8,5,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,3,7,2,1,8,6,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[7,4,3,2,5,1,8,6]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,4,8,3,7,2,1,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[3,6,8,5,2,1,7,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[6,1,5,4,7,2,8,3]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,3,6,5,8,2,7,4]=>[1,6,8,4,7,2,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,8,3,2,7,1,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[5,4,3,7,2,1,6,8]=>[6,5,3,7,2,1,4,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,4,3,7,8,2,1,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,4,8,6,3,2,7,5]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,8,6,2,5,7,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,7,2,5,3,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,3,4,8,1,2,7,5]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[6,2,8,1,7,4,5,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,6,3,1,5,8,7,4]=>[4,8,3,1,5,7,6,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[7,1,3,2,6,5,8,4]=>[8,2,4,3,6,5,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,7,6,4,5,3,2,9,1]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[2,9,8,7,5,6,4,3,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,1,3,5,8,7,4,2]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,5,8,7,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,7,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,6,8,4,2,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[5,1,6,8,4,7,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,2,8,3,4,1,5,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[2,4,1,8,7,6,3,5]=>[3,7,1,8,6,5,2,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,3,8,7,5,1,6,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,5,4,7,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,2,4,1,3,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,1,3,5,6,2,8,7]=>[6,2,3,4,5,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,3,8,5,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,4,6,1,3,7,5]=>[8,5,6,7,2,3,4,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[6,4,8,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,3,5,6,1,4,7]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,3,5,6,8,2,7,1]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,2,3,4,6,1,7,5]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,7,4,3,5,2,8,6]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,4,3,8,1,5,6]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[3,8,2,7,6,4,1,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,3,6,2,1,8,4,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,3,8,6,2,7,1,5]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[8,2,1,4,6,3,7,5]=>[8,3,2,6,7,4,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,1,6,8,2,7,5,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[5,3,8,6,7,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,2,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,5,2,8,7,6,4,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,7,1,2,6,5,8,3]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,2,5,6,8,7,3,1]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,5,8,3,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,5,1,6,3,7,4]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,3,4,5,1,6,7,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,8,1,5,6,3,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,7,8,3,2,5,4,6]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,1,3,2,5,6,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,1,3,5,4,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,1,3,5,2,4,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,3,7,8,5,2,4,6]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,3,5,2,6,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,3,2,5,6,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,8,5,4,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,7,6,4,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,3,7,8,5,4,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,7,8,5,4,2,6]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,7,8,2,5,4,6]=>[1,5,8,7,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,7,8,5,4,6]=>[1,3,2,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,6,8,3,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,4,7,8,6,1,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,5,7,6,8,4,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,5,7,6,8,3,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,7,4,6,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,5,8,4,3,7,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,3,1,5,2,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,2,4,1,8,3,6,7]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[2,1,7,4,3,8,5,6]=>[2,1,8,5,4,7,6,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[7,2,3,8,5,4,1,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,1,5,7,6,3,8,2]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,2,1,10,9,8,4,5,6,7]=>[3,2,1,10,9,8,7,6,5,4]=>[3,2,1,10,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,2,3,1,10,9,6,7,8]=>[5,4,3,2,1,10,9,8,7,6]=>[5,4,3,2,1,10,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[7,4,2,6,3,5,1,10,8,9]=>[7,6,5,4,3,2,1,10,9,8]=>[7,6,5,4,3,2,1,10,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[7,6,5,2,3,4,1,10,8,9]=>[7,6,5,4,3,2,1,10,9,8]=>[7,6,5,4,3,2,1,10,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[9,8,5,2,7,3,4,6,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[9,8,7,6,2,3,4,5,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,10,7,6,2,3,9,4,5,8]=>[1,10,9,8,5,6,7,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,10,9,8,7,2,3,4,5,6]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[3,2,1,12,11,10,9,4,5,6,7,8]=>[3,2,1,12,11,10,9,8,7,6,5,4]=>[3,2,1,12,11,10,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[5,4,2,3,1,12,11,10,6,7,8,9]=>[5,4,3,2,1,12,11,10,9,8,7,6]=>[5,4,3,2,1,12,11,10,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,2,6,3,5,1,12,11,8,9,10]=>[7,6,5,4,3,2,1,12,11,10,9,8]=>[7,6,5,4,3,2,1,12,11,10,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[[[[.,.],.],.],.],.]]
[7,6,5,2,3,4,1,12,11,8,9,10]=>[7,6,5,4,3,2,1,12,11,10,9,8]=>[7,6,5,4,3,2,1,12,11,10,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[[[[.,.],.],.],.],.]]
[9,8,5,2,7,3,4,6,1,12,10,11]=>[9,8,7,6,5,4,3,2,1,12,11,10]=>[9,8,7,6,5,4,3,2,1,12,11,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[[[.,.],.],.]]
[11,10,5,2,7,3,9,4,6,8,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[11,10,5,2,9,8,3,4,6,7,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[9,8,7,6,2,3,4,5,1,12,10,11]=>[9,8,7,6,5,4,3,2,1,12,11,10]=>[9,8,7,6,5,4,3,2,1,12,11,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[[[.,.],.],.]]
[11,10,7,6,2,3,9,4,5,8,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[11,10,9,6,2,8,3,4,5,7,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[11,10,9,8,7,2,3,4,5,6,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[1,12,11,10,9,8,2,3,4,5,6,7]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[1,4,8,2,3,6,5,7]=>[1,5,8,4,2,7,6,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,7,3,5,2,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,8,2,6,7,5,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,2,4,5,8,6]=>[1,8,4,3,5,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,4,3,2,5,7,8]=>[1,6,5,4,3,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,2,6,5,3,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,2,1,6,8,7,4,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,3,5,8,6,2,7,4]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,3,8,4,1,7,6,5]=>[5,2,8,4,1,7,6,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,7,8,5,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,2,7,5,6,1,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,3,8,5,7,4,2,6]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,7,5,4,6,8]=>[1,2,3,7,6,5,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,8,6,3,5,7]=>[1,6,3,8,7,2,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,6,3,5,7,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,1,8,2,5,3,4,7]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,8,6,4,2,7,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,1,5,2,3,4,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,5,2,1,7,3,4,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[3,1,2,4,8,6,7,5]=>[3,2,1,4,8,7,6,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,1,2,5,8,7,4,6]=>[3,2,1,7,8,6,4,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[6,5,2,1,8,4,7,3]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,6,2,4,3,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[3,7,5,2,8,1,4,6]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,3,5,4,8,6,1,7]=>[7,2,4,3,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,3,6,4,7,5,1,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,3,5,7,4,8,1,6]=>[7,2,5,8,3,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,3,2,4,1,7,6,5]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,7,6,1,2,5,8,4]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[4,7,1,6,8,5,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,1,8,6,3,5,2,7]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,1,5,8,6,2,3,7]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,3,4,6,2,8,7,1]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,4,8,6,3,7,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,3,4,8,2,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,4,2,7,8,3,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,5,2,3,7,4,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,5,2,3,1,8,7,4]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[6,5,3,7,4,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,4,7,5,3,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,6,4,8,3,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,4,8,3,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,1,4,7,5,2,8,6]=>[6,2,3,8,5,1,7,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,3,5,1,8,7,2,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[2,5,3,6,1,8,4,7]=>[5,7,3,4,1,8,2,6]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,5,6,8,3,1,7,4]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[7,1,4,5,3,6,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,7,2,4,5,3,6,8]=>[1,7,3,6,5,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,5,3,2,6,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,4,7,3,5,2,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,6,4,8,2,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,6,4,7,5,2,3,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,6,7,4,3,8]=>[1,7,3,6,5,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,5,6,1,4,3,7,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,5,4,7,8,3,1,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,4,5,8,2,3,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[8,6,1,3,2,5,7,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,8,1,4,6,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,2,6,7,8,1,5,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[3,4,6,7,8,1,5,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,7,3,8,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,2,7,5,8,1,6]=>[7,3,2,8,5,6,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[4,8,5,3,2,6,1,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[2,8,4,5,3,6,1,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[8,1,5,3,2,4,7,6]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,8,4,1,3,6,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,1,3,2,7,4,5]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,3,8,2,4,1,6,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,2,3,7,8,1,5,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,3,7,8,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,3,7,8,1,5,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[7,5,8,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,4,3,7,5,6,2]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,4,8,5,3,2,6,7]=>[1,6,8,5,4,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,7,6,4,1,5,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,7,4,3,8,5,1,6]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[6,8,2,7,3,1,5,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,6,3,4,1,7,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,1,2,8,5,3,7,4]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,5,8,3,6,7,2]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,5,2,8,1,6,3,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,8,5,7,1,3,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,8,2,7,1,3,6,5]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[5,2,1,8,7,4,6,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,2,1,7,4,6,3,5]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,2,5,8,3,6,7,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,1,6,8,3,2,7,4]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,5,6,8,2,7,3]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,8,2,4,1,3,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,5,2,8,7,3,1,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,8,5,3,1,6,7,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,2,3,1,7,8,5,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,2,3,6,8,4,7,1]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,2,1,7,8,4,3,5]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[5,2,7,8,4,1,6,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,2,7,8,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,8,6,4,1,7,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,1,2,8,4,3,7,6]=>[6,2,3,8,5,1,7,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,7,8,3,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,2,6,4,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,2,3,4,7,8,5,1]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,1,8,4,3,5,6]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,2,1,3,7,5,8,4]=>[8,3,2,4,6,5,7,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,8,7,3,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,3,7,8,1,4,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,4,3,2,5,8,1,6]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,2,4,3,5,8,1,6]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,7,6,4,2,3,5,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,4,7,2,8,5,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,5,8,4,2,3,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,2,4,8,5,3]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,2,4,3,6,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,7,3,4,6,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,8,3,6,1,7,4,5]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,3,1,8,5,2,6,7]=>[6,3,2,8,5,1,7,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,8,4,5,6,2,7,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,3,8,2,1,4,5,6]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,2,5,3,1,7,4,6]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,3,5,8,1,7,4,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[3,5,4,8,6,1,7,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,5,2,3,8,4,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,7,5,1,4,8,3,6]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[5,7,6,1,2,8,3,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,4,6,5,1,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,1,3,2,6,8,4,5]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,3,5,2,8,1,6,7]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,7,3,8,2,4,6,5]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,4,8,5,3,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,1,3,8,4,2,7,5]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,4,1,8,6,2,7,3]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,4,6,8,1,3,2,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[3,6,1,5,8,4,7,2]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,4,8,3,5,7,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,8,2,4,1,7,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[7,2,8,4,1,3,6,5]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[5,8,1,2,4,3,6,7]=>[6,8,3,4,5,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[8,4,3,5,7,2,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,1,5,2,3,8,7,6]=>[5,2,4,3,1,8,7,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[6,3,5,8,2,4,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[2,8,7,1,4,6,3,5]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,8,5,3,7,4,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,5,6,2,8,4,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,6,2,8,1,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,8,1,2,5,4,7]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[7,6,4,8,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,5,3,8,4,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,5,4,2,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,6,9,7,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,5,4,8,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,5,9,6,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,7,6,4,9,5,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,6,5,3,2,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,7,6,5,3,9,4,2,1]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[8,7,6,5,4,2,9,3,1]=>[9,8,6,5,4,3,7,2,1]=>[9,8,6,5,4,3,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[3,2,1,10,7,6,9,8,5,4]=>[3,2,1,10,9,8,7,6,5,4]=>[3,2,1,10,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,3,6,5,2,1,10,9,8]=>[7,6,5,4,3,2,1,10,9,8]=>[7,6,5,4,3,2,1,10,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[9,4,3,8,7,6,5,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[9,8,5,4,7,6,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,10,5,4,7,6,9,8,3,2]=>[1,10,9,8,6,5,7,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,10,5,4,9,8,7,6,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,10,7,6,5,4,9,8,3,2]=>[1,10,9,8,6,5,7,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,10,9,6,5,8,7,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[3,2,1,12,7,6,11,10,9,8,5,4]=>[3,2,1,12,11,10,9,8,7,6,5,4]=>[3,2,1,12,11,10,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[3,2,1,12,11,8,7,10,9,6,5,4]=>[3,2,1,12,11,10,9,8,7,6,5,4]=>[3,2,1,12,11,10,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[3,2,1,12,11,10,9,8,7,6,5,4]=>[3,2,1,12,11,10,9,8,7,6,5,4]=>[3,2,1,12,11,10,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[5,4,3,2,1,12,9,8,11,10,7,6]=>[5,4,3,2,1,12,11,10,9,8,7,6]=>[5,4,3,2,1,12,11,10,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,3,2,1,12,11,10,9,8,7,6]=>[5,4,3,2,1,12,11,10,9,8,7,6]=>[5,4,3,2,1,12,11,10,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,3,6,5,2,1,12,11,10,9,8]=>[7,6,5,4,3,2,1,12,11,10,9,8]=>[7,6,5,4,3,2,1,12,11,10,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[[[[.,.],.],.],.],.]]
[9,4,3,8,7,6,5,2,1,12,11,10]=>[9,8,7,6,5,4,3,2,1,12,11,10]=>[9,8,7,6,5,4,3,2,1,12,11,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[[[.,.],.],.]]
[11,4,3,10,7,6,9,8,5,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[11,4,3,10,9,8,7,6,5,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[7,6,5,4,3,2,1,12,11,10,9,8]=>[7,6,5,4,3,2,1,12,11,10,9,8]=>[7,6,5,4,3,2,1,12,11,10,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[[[[.,.],.],.],.],.]]
[9,8,5,4,7,6,3,2,1,12,11,10]=>[9,8,7,6,5,4,3,2,1,12,11,10]=>[9,8,7,6,5,4,3,2,1,12,11,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[[[.,.],.],.]]
[11,10,5,4,7,6,9,8,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[11,10,5,4,9,8,7,6,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[1,12,5,4,11,8,7,10,9,6,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[1,12,5,4,11,10,9,8,7,6,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[9,8,7,6,5,4,3,2,1,12,11,10]=>[9,8,7,6,5,4,3,2,1,12,11,10]=>[9,8,7,6,5,4,3,2,1,12,11,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[[[.,.],.],.]]
[11,10,7,6,5,4,9,8,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[11,10,9,6,5,8,7,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[1,12,11,6,5,8,7,10,9,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[1,12,11,6,5,10,9,8,7,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[1,12,11,8,7,6,5,10,9,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[1,12,11,10,7,6,9,8,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[1,5,7,2,4,3,6,8]=>[1,6,7,4,5,2,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,5,3,2,4,7,8]=>[1,6,5,4,3,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,4,6,5,3,8]=>[1,7,3,6,5,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,2,6,5,3,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,8,7,4,3,5]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,4,3,5,8,6]=>[1,2,8,5,4,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,2,8,7,4,3,5]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,2,3,5,8,6]=>[1,8,5,4,3,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,2,3,6,4,7]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,8,5,2,3,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,5,2,8,6,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,3,7,4,2,8,5]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,2,7,4,3,6]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,8,7,5,3,2,6]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,8,6,3,7,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,7,5,8,6,3]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,7,6,2,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,8,7,6,2,4]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,7,5,3,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,7,4,3,8,6]=>[1,2,6,8,5,3,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,6,8,7,5,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,6,3,2,7,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,2,6,3,4,7]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,6,3,2,8,5]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,3,2,8,5,4,7]=>[1,7,4,3,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,6,4,2,5,7]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,4,2,3,8,6]=>[1,6,8,5,4,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,7,5,4,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,2,6,3,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,8,2,7,5,4,1,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,4,8,6,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,3,6,8,5,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,7,2,8,1,6,4,5]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[8,5,2,4,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,5,8,7,1,4,3,6]=>[5,7,8,6,1,4,2,3]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[3,4,6,5,8,2,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,2,4,1,6,7,8,3]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,2,7,1,6,8,3,5]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[5,2,8,6,4,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,3,4,7,2,8,5]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,7,2,5,3,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,4,5,2,1,7,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,6,1,4,7,3,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,3,6,7,2,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,3,6,7,2,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,6,4,2,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,1,4,7,5,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,5,8,2,6,7,4,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,3,6,5,2,8,4]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,1,4,5,7,6,3]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,4,7,5,2,3,8,6]=>[1,6,8,5,4,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,7,5,4,2,8,3]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,7,3,6,5,1,8,4]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[8,6,5,1,3,7,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,6,2,4,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,7,5,6,4,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,6,8,1,3,5,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,4,6,1,7,5,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,8,6,4,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,1,4,6,5,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,5,8,6,7,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,2,4,6,8,5,3,7]=>[1,2,7,6,8,4,3,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,5,8,6,2,4,7]=>[6,2,7,8,5,1,3,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,5,4,6,8,1,3,7]=>[6,7,3,4,8,1,2,5]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[6,5,2,4,7,8,1,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,2,5,8,6,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,8,3,4,7,6,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[2,4,3,8,7,1,6,5]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,5,8,7,4,2,6,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,7,5,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,4,8,6,2,7,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,4,5,8,6,2,7,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,4,2,3,6,1,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,1,7,4,3,6,8,2]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,3,7,6,8,2,1,5]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[8,1,4,7,2,3,5,6]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,8,5,2,7,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,7,2,6,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,1,6,4,5,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,1,3,7,2,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[8,3,4,7,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,1,8,7,5,2,4,6]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,5,8,7,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,6,5,8,2,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,6,3,2,8,5,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,2,6,8,7,1,4,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,3,7,1,8,5,2,6]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[3,2,8,5,6,7,1,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,3,2,1,4,7,5,6]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,7,3,1,8,5,2,6]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[3,7,8,2,5,6,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[7,5,1,4,2,3,6,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,8,6,1,2,4,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,1,2,4,7,8,6,3]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,7,8,6,2,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,5,1,6,7,2,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,1,2,4,6,8,3]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,1,5,2,7,3,4,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,1,2,6,4,5,8,3]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,3,6,4,5,8,2]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,3,6,4,5,7,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,6,2,7,3,4,5]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,6,2,5,3,4,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,1,6,2,5,3,4,7]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,2,5,3,4,6]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,7,4,5,6,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,3,7,4,5,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,6,7,5,2,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,3,1,2,6,4,5,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[3,1,2,8,5,6,7,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[6,3,1,2,7,4,5,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[6,1,7,4,2,3,5,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,7,3,4,6,8,5,2]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,8,4,5,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,8,2,5,3,4,6]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,7,2,5,3,4,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,7,2,6,3,4,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,8,2,6,3,4,7]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,6,3,7,4,5,8,2]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,7,3,5,1,6,8]=>[6,4,7,2,5,1,3,8]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[2,4,8,6,3,5,1,7]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[3,4,6,2,1,5,8,7]=>[5,4,6,2,1,3,8,7]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[2,6,8,3,5,1,4,7]=>[6,7,8,4,5,1,2,3]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,3,6,1,5,8,4,7]=>[4,2,7,1,5,8,3,6]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,7,1,6,5,8,4]=>[4,2,8,1,6,5,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,4,7,1,3,6,8,5]=>[4,5,8,1,2,6,7,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[5,4,7,8,1,3,2,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[2,5,7,1,4,6,3,8]=>[4,7,6,1,5,3,2,8]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,4,7,1,6,3,5,8]=>[4,6,7,1,5,2,3,8]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,5,7,1,4,3,6,8]=>[4,6,7,1,5,2,3,8]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,5,7,3,1,4,6,8]=>[5,6,7,4,1,2,3,8]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[4,6,3,7,1,5,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,7,3,2,8,1,4,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,6,5,7,1,8,4,3]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,6,8,5,4,1,7,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,4,7,8,1,3,6,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,5,7,1,4,6,8,3]=>[4,8,6,1,5,3,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,4,7,1,6,3,8,5]=>[4,6,8,1,5,2,7,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,4,7,1,6,8,3,5]=>[4,7,8,1,5,6,2,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,4,8,3,1,7,6,5]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[8,6,5,1,2,4,3,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,1,4,2,3,5,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,5,1,4,8,3,2,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,7,1,4,3,2,5,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,5,1,4,2,3,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,1,2,5,3,6,7]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,7,5,1,4,2,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,1,4,2,5,3,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,1,4,3,2,6,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,6,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,3,7,4,5,6,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,5,2,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,9,1,8,7,6,5,4,3]=>[3,9,1,8,7,6,5,4,2]=>[3,9,1,8,7,6,5,4,2]=>[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]
[4,2,5,7,3,1,6,8]=>[6,5,3,7,2,1,4,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[8,2,4,5,3,1,6,7]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,4,5,1,3,2,6,7]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,3,7,5,2,1,6,8]=>[6,5,7,4,2,1,3,8]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[1,6,7,4,3,2,5,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,1,4,7,2,6,8]=>[6,4,3,2,7,1,5,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,3,7,1,5,2,6,8]=>[6,4,7,2,5,1,3,8]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[3,5,1,6,4,2,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,4,3,1,7,2,5,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,2,7,4,3,1,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[2,6,4,1,7,3,5,8]=>[4,7,6,1,5,3,2,8]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[6,3,2,7,4,5,1,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,2,4,1,3,6,8,5]=>[8,4,5,2,3,6,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,3,2,5,7,1,4,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,2,6,5,7,1,4,8]=>[6,2,7,4,5,1,3,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,1,7,3,5,6,8,4]=>[2,1,8,4,6,5,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,6,3,5,7,8,4]=>[2,1,8,4,5,6,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,4,6,5,2,7,3,8]=>[1,7,5,4,3,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,6,2,1,4,3,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[2,5,1,6,4,3,7,8]=>[3,6,1,5,4,2,7,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,5,4,1,6,3,7,8]=>[4,6,3,1,5,2,7,8]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[4,6,1,5,2,7,3,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,6,5,3,7,2,4,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,4,7,3,6,8]=>[1,2,6,4,7,3,5,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,3,4,8,7,6]=>[1,2,5,4,3,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,2,7,6,1,8,4,3]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,8,2,6,1,7,4,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,7,8,2,4,6,5,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,3,6,2,7,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,7,1,4,5,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,2,6,4,7,3,8,5]=>[1,2,8,6,5,4,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,8,3,5,6,4]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,8,7,6,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,4,5,8,1,6,3]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,6,1,8,5,4,3,7]=>[3,7,1,8,6,5,2,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[5,8,6,2,3,4,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,8,6,2,1,4,3,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,5,8,6,2,1,3,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[6,4,7,5,8,2,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,7,4,2,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,2,1,5,8,4,3,7]=>[7,3,2,6,8,4,1,5]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[7,5,6,2,4,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,6,2,5,7,3,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,2,8,5,3,6,1,7]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[8,1,7,4,5,6,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,1,7,8,4,5,6,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,2,1,4,3,7,6,5]=>[8,3,2,5,4,7,6,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,6,5,3,1,2,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,4,1,6,2,8,3,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,2,3,1,7,8,4,5]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,1,8,6,7,2,4,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,2,5,1,8,6,7,3]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,5,3,7,1,6,8,2]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,2,8,5,3,6,7,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[2,8,6,3,5,4,7,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,5,2,8,6,4,7,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,3,5,1,6,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,8,2,5,6,4,7,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,1,4,8,5,6,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,8,4,6,1,3,7,5]=>[5,8,6,7,1,3,4,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[8,4,6,2,5,3,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,7,6,2,1,5,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,5,2,7,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,2,7,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,7,6,2,5,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,8,6,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[9,8,7,6,1,2,3,4,5,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[2,6,3,7,5,4,8,1]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,4,7,1,3,8,6,2]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[2,8,5,1,4,7,3,6]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[8,1,7,6,3,4,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,2,5,7,3,6]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,6,5,8,4,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,4,8,5,6,2,7,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[5,8,2,3,4,6,1,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[6,1,3,4,2,5,7,8]=>[6,2,5,4,3,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,5,6,3,2,4,7,8]=>[1,6,5,4,3,2,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,5,2,4,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[7,8,3,5,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,5,7,3,6,1,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[2,5,3,1,6,4,7,8]=>[4,6,3,1,5,2,7,8]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[6,5,1,3,4,2,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,7,4,3,2,6,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,8,7,4,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,7,8,4,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,8,4,5,3,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,8,5,3,4,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,4,2,1,6,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,8,6,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,6,3,5,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,6,5,8,7,4,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,3,8,7,5,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,2,1,8,3,5,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,1,3,6,8,2,5,4]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,5,6,8,2,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,7,5,8,2,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,7,4,5,2,8,6,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,5,4,2,1,8,6,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,6,7,4,2,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,6,3,2,7,8,5,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,6,1,3,4,2,5,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,8,2,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,5,4,6,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,1,2,4,5,6,3,8]=>[7,2,3,6,5,4,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,3,2,1,5,6,4,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[2,1,6,4,7,5,3,8]=>[2,1,7,6,5,4,3,8]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[7,2,8,5,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,8,5,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,8,4,6,5,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,8,6,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,1,4,5,3,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,1,5,6,4,3,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,1,3,8,6,2,7,5]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,1,2,8,4,6,7,3]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,3,2,8,1,7,4]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[8,2,6,3,1,5,7,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,2,5,6,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,5,3,4,7,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,3,2,4,1,8,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,1,2,3,6,8,4,5]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,7,2,8,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,1,8,4,6,5,7,2]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,2,3,8,4,7,5]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,6,7,4,2,3,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,6,4,5,2,3,7]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,6,4,5,2,7,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,4,7,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,4,1,2,3,7,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,1,4,2,5,7,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,7,4,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,4,2,5,3,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,4,2,5,3,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,4,2,7,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,4,1,5,7,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,4,2,1,5,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,4,2,1,7,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,1,4,7,2,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,4,1,5,2,3,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,7,1,4,5,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,4,5,2,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,7,4,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,4,7,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,4,2,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,4,2,5,1,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,4,2,5,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,7,5,8,2,6,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,7,1,4,6,5,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,7,6,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,8,6,4,1,7,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,4,5,1,2,8,6,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,4,7,1,8,5,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,4,2,3,8,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,8,2,5,1,7,4,6]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[5,8,4,2,3,7,1,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[4,8,5,2,1,7,3,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[8,5,7,6,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,7,5,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,6,8,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,1,6,8,5,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,3,1,7,4,8,6,2]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,3,1,8,6,4,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,4,1,7,3,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,6,8,3,7,1,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,5,2,8,4,7,1,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,4,8,3,7,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,2,8,7,4,1,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[6,8,4,2,7,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[9,8,2,3,4,5,6,7,1]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[8,9,2,3,4,5,6,7,1]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[9,8,7,6,4,5,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[5,6,7,9,8,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[5,6,7,8,9,1,4,3,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[3,4,7,8,5,1,2,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,7,3,2,5,6,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[3,2,7,6,4,5,8,1]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,3,6,8,4,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,3,6,5,1,8,7,4]=>[5,2,8,4,1,7,6,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[8,3,1,2,6,4,7,5]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,7,8,2,4,3,5,6]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,4,7,1,2,8,5]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[5,7,4,8,1,3,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,3,7,8,1,5,2,6]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[8,5,4,2,6,1,7,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,2,6,8,7,4,1,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,3,7,5,1,8,6,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[6,3,1,2,8,7,4,5]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,2,1,3,8,7,6,4]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,2,1,5,3,8,4,6]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,5,8,2,4,3,6,7]=>[1,6,8,4,5,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,6,8,1,5,2,7]=>[7,5,6,8,2,3,1,4]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[5,4,6,8,3,1,7,2]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[3,6,8,4,5,1,7,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,6,1,7,2,4,3,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,3,1,2,8,6,4,5]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,3,7,6,1,8,5,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,2,7,8,6,4,1,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,2,8,3,1,4,7,5]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[3,1,2,8,7,4,5,6]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,1,3,8,7,4,6,5]=>[2,1,3,8,7,6,5,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,3,8,7,4,5,6]=>[2,1,3,8,7,6,5,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,6,8,3,2,4,7,5]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,5,1,7,2,4,3,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,1,7,3,2,5,6]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,3,1,6,2,7,5,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,3,2,8,7,6,4,5]=>[1,3,2,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,3,8,7,6,4,5]=>[2,1,3,8,7,6,5,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,3,1,6,5,8,7,10,9]=>[4,3,2,1,6,5,8,7,10,9]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,6,3,7,2,5,4,8]=>[1,7,5,6,3,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,4,6,3,5,8]=>[1,7,3,6,5,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,2,8,4,1,3,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,6,2,8,4,1,3,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[2,4,8,3,1,6,7,5]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[3,5,8,4,2,1,6,7]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[2,5,8,3,1,4,6,7]=>[5,6,8,4,1,2,7,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,8,1,3,5,7,4,6]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[5,4,7,8,3,2,6,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[3,4,8,5,7,1,2,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[3,6,8,2,5,1,4,7]=>[6,7,8,4,5,1,2,3]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[3,6,8,7,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,6,5,8,2,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[2,4,6,7,8,3,5,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,4,2,6,8,5,3,7]=>[1,7,3,6,8,4,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,8,3,5,4,7]=>[1,2,7,8,5,6,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,3,5,4,2,7]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,7,6,3,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,6,3,2,4,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,6,4,3,5,8]=>[1,2,7,6,5,4,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,7,5,2,4,6,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,2,4,6,3,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,2,5,3,6,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,4,7,5,2,6,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,2,3,6,4,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,2,6,3,4,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,3,7,4,2,5,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,5,2,6,3,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,6,4,8,7,5,2]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,4,8,5,7,6]=>[1,3,2,4,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,7,5,2,4,6]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,3,2,7,5,8]=>[1,5,7,4,2,6,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,3,2,8,7,5]=>[1,5,8,4,2,7,6,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,6,4,2,3,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,3,5,2,7,4,8]=>[1,7,5,4,3,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,3,5,2,8,7,4]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,3,7,5,2,4,6]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,4,9,5,2,10,6,3,1]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[6,4,7,1,5,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,3,8,2,6,4,7,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,3,8,2,6,5,7,1]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,6,1,8,3,4,7,5]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[5,7,1,4,8,2,3,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[6,5,7,1,4,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,8,3,5,7,6,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,6,1,2,4,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,8,3,5,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,3,4,2,8,5,7,6]=>[1,4,3,2,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,6,2,4,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,7,5,2,3,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,7,5,3,8,4,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,2,1,4,8,5,7,6]=>[3,2,1,4,8,6,7,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[7,3,1,4,2,6,5,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[7,4,1,6,2,5,3,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,4,1,8,2,6,3,7]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,3,1,8,2,6,4,7]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,7,1,5,2,6,3,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,5,1,4,2,7,3,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,8,7,3,4,5,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,9,3,4,5,6,7,2]=>[1,9,8,7,5,6,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,8,7,4,5,2,3,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,8,7,3,4,5]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,7,8,4,5,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,4,2,3,1,6,5,7]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[6,4,5,2,8,1,7,3]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,8,6,2,3,1,7,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[6,4,2,1,8,5,3,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,2,6,1,5,8,3,7]=>[7,4,5,2,3,8,1,6]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[6,4,2,3,5,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[2,8,6,4,5,1,7,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[8,2,4,6,7,1,5,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,6,3,1,7,4,8,5]=>[4,8,3,1,6,5,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[6,5,1,8,3,2,7,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,4,3,7,2,8,6,5]=>[1,5,3,8,2,7,6,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,7,4,5,3,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,3,1,4,5,7,6]=>[4,8,3,1,5,6,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[6,1,7,2,8,4,5,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,2,1,5,6,7,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,2,6,7,8,4,5,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,4,6,3,8,2,5]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,6,4,1,3,8,2,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,5,3,1,8,7,6,2]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[6,3,4,2,7,8,5,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,7,4,5,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,7,8,1,3,5,4]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[5,1,8,4,3,7,2,6]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,2,8,1,4,5,6,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[1,4,8,2,5,6,7,3]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,4,3,6,5,8,10,9,7]=>[2,1,4,3,6,5,10,9,8,7]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,4,3,6,8,7,5,10,9]=>[2,1,4,3,8,7,6,5,10,9]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,4,3,8,10,7,9,5,6]=>[2,1,4,3,10,9,8,7,6,5]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,4,6,5,3,8,7,10,9]=>[2,1,6,5,4,3,8,7,10,9]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,4,6,5,3,8,10,9,7]=>[2,1,6,5,4,3,10,9,8,7]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,6,8,5,7,3,4,10,9]=>[2,1,8,7,6,5,4,3,10,9]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,8,5,10,6,7,9,3,4]=>[2,1,10,9,8,7,6,5,4,3]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,4,3,1,6,5,8,10,9,7]=>[4,3,2,1,6,5,10,9,8,7]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[2,4,3,1,6,8,7,5,10,9]=>[4,3,2,1,8,7,6,5,10,9]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[2,4,3,1,8,10,7,9,5,6]=>[4,3,2,1,10,9,8,7,6,5]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[4,6,3,5,1,2,8,7,10,9]=>[6,5,4,3,2,1,8,7,10,9]=>[6,5,4,3,2,1,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[4,6,3,5,1,2,8,10,9,7]=>[6,5,4,3,2,1,10,9,8,7]=>[6,5,4,3,2,1,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[6,3,8,4,5,7,1,2,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[8,5,10,4,7,6,2,9,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[2,7,10,4,8,6,9,5,1,3]=>[9,10,8,7,6,5,4,3,1,2]=>[9,10,8,7,6,5,4,3,1,2]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[2,1,4,3,6,5,8,7,10,12,11,9]=>[2,1,4,3,6,5,8,7,12,11,10,9]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,6,5,8,10,9,7,12,11]=>[2,1,4,3,6,5,10,9,8,7,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,6,5,10,12,9,11,7,8]=>[2,1,4,3,6,5,12,11,10,9,8,7]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,6,8,7,5,10,9,12,11]=>[2,1,4,3,8,7,6,5,10,9,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,6,8,7,5,10,12,11,9]=>[2,1,4,3,8,7,6,5,12,11,10,9]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,8,10,7,9,5,6,12,11]=>[2,1,4,3,10,9,8,7,6,5,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,10,7,12,8,9,11,5,6]=>[2,1,4,3,12,11,10,9,8,7,6,5]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,6,5,3,8,7,10,9,12,11]=>[2,1,6,5,4,3,8,7,10,9,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,6,5,3,8,7,10,12,11,9]=>[2,1,6,5,4,3,8,7,12,11,10,9]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,6,5,3,8,10,9,7,12,11]=>[2,1,6,5,4,3,10,9,8,7,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,6,5,3,10,12,9,11,7,8]=>[2,1,6,5,4,3,12,11,10,9,8,7]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,6,8,5,7,3,4,10,9,12,11]=>[2,1,8,7,6,5,4,3,10,9,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,6,8,5,7,3,4,10,12,11,9]=>[2,1,8,7,6,5,4,3,12,11,10,9]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,8,5,10,6,7,9,3,4,12,11]=>[2,1,10,9,8,7,6,5,4,3,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,10,7,12,6,9,8,4,11,3,5]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,4,3,1,6,5,8,7,10,9,12,11]=>[4,3,2,1,6,5,8,7,10,9,12,11]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,4,3,1,6,5,8,7,10,12,11,9]=>[4,3,2,1,6,5,8,7,12,11,10,9]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,4,3,1,6,5,8,10,9,7,12,11]=>[4,3,2,1,6,5,10,9,8,7,12,11]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,4,3,1,6,5,10,12,9,11,7,8]=>[4,3,2,1,6,5,12,11,10,9,8,7]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,4,3,1,6,8,7,5,10,9,12,11]=>[4,3,2,1,8,7,6,5,10,9,12,11]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,4,3,1,6,8,7,5,10,12,11,9]=>[4,3,2,1,8,7,6,5,12,11,10,9]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,4,3,1,8,10,7,9,5,6,12,11]=>[4,3,2,1,10,9,8,7,6,5,12,11]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,4,3,1,10,7,12,8,9,11,5,6]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,6,3,5,1,2,8,7,10,9,12,11]=>[6,5,4,3,2,1,8,7,10,9,12,11]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[4,6,3,5,1,2,8,7,10,12,11,9]=>[6,5,4,3,2,1,8,7,12,11,10,9]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[4,6,3,5,1,2,8,10,9,7,12,11]=>[6,5,4,3,2,1,10,9,8,7,12,11]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[4,6,3,5,1,2,10,12,9,11,7,8]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[6,3,8,4,5,7,1,2,10,9,12,11]=>[8,7,6,5,4,3,2,1,10,9,12,11]=>[8,7,6,5,4,3,2,1,12,11,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[[[.,.],.],.],.]]
[6,3,8,4,5,7,1,2,10,12,11,9]=>[8,7,6,5,4,3,2,1,12,11,10,9]=>[8,7,6,5,4,3,2,1,12,11,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[[[.,.],.],.],.]]
[8,5,10,4,7,6,2,9,1,3,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[[.,.],.]]
[10,7,12,4,8,6,9,5,2,11,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,1,6,7,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,5,2,3,6,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,1,4,6,5,3,2,7]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,7,6,5,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,7,6,5,4,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,5,8,1,6,7,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,2,8,6,1,5,7,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,7,2,5,8,4,6,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,8,4,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,8,3,5,1,4,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[6,2,7,4,5,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,8,2,5,3,4,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,8,7,5,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,5,6,1,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,3,5,2,8,1,7,4]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,1,8,7,4,5,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,8,7,1,6,3,2,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,8,2,7,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,3,2,6,8,7,4,5]=>[1,3,2,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,2,5,8,7,3,4]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,7,2,3,5,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,7,2,5,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,4,8,3,6,7]=>[1,6,3,4,8,2,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,5,8,6,3,7]=>[1,2,7,4,8,6,3,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,5,2,4,8,3]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,4,7,2,3,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,2,5,8,3,6]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,4,3,7,5,2,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,5,4,7,2,3,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,2,6,4,8,5]=>[1,8,4,3,6,5,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,2,3,6,7,4]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,5,4,2,3,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,4,2,3,6,5,7]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,7,5,3,8,6]=>[1,6,3,8,5,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,6,2,4,3,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,4,7,3,2,6,5]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,4,2,6,5,7]=>[1,5,8,4,2,7,6,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,2,6,5,8,3]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,5,8,3,7,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,8,3,2,5,6]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,8,3,2,7,5,6]=>[1,5,8,4,2,7,6,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,3,6,4,5,2,7]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,4,7,3,2,8,5]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,3,7,4,5,6,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,7,2,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,2,1,6,8,3,4]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,6,1,5,4,8,2,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,3,2,1,8,4,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,8,7,3,4,6,1,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,5,1,3,7,2,8,4]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,1,7,3,4,5,2,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,3,4,5,2,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,8,7,3,4,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,1,2,4,5,6]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[1,8,5,3,4,6,2,7]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,6,5,4,3,8,2]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,3,6,4,5,8,2]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,5,3,6,4,8,2]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,5,3,7,8,2,4]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,8,7,1,2,6,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,2,3,4,7,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,1,7,3,8,6,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,2,1,3,4,7,8,5]=>[8,3,2,4,5,6,7,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,5,6,1,7,8,9,10,2,3]=>[10,9,4,3,5,6,7,8,2,1]=>[10,9,4,3,8,7,6,5,2,1]=>[[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.]
[1,3,5,2,6,7,8,9,4]=>[1,4,9,2,5,6,7,8,3]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[3,2,5,8,7,4,1,6]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,2,5,8,7,3,1,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,3,4,1,6,5,2,7]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,4,8,5,7,2,1,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[3,6,4,8,5,7,2,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,8,4,7,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,2,8,7,3,1,6,5]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[6,5,8,2,1,7,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,4,3,8,7,2,5]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,3,8,7,2,4,5]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,8,4,5,7,3,6]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,2,1,8,7,6,3,5]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[3,2,5,8,7,1,4,6]=>[6,2,7,8,5,1,3,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,6,3,8,7,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,8,4,7,1,6,3]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[1,6,2,4,8,5,7,3]=>[1,8,3,6,7,4,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,6,5,8,7,2,4]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,8,5,3,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,8,5,3,4,7,6,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,7,3,5,4,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,6,3,2,5,4,7]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,4,8,5,7,1,6]=>[7,2,3,8,5,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,1,2,4,7,5,6,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,5,8,3,1,7,2]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[8,6,2,1,5,7,3,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,6,2,8,5,3,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[8,7,2,4,1,5,3,6]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,5,3,4,8,6,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,3,1,4,6,7,5]=>[4,8,3,1,5,7,6,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[4,3,6,5,1,2,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,8,3,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,3,8,7,6,5,2,4]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,8,7,2,6,3,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,8,7,2,6,3,5,4]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,2,1,4,3,5,6]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,8,7,1,6,3,4,5]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,2,8,7,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,2,7,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,7,5,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,2,5,7,4,8,6,3]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,2,1,8,7,5,3,4]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,3,8,7,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,5,3,2,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[2,8,3,4,1,5,6,7]=>[5,8,3,4,1,6,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,3,7,5,4,8,6,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,5,6,3,1,8,2,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,2,1,4,3,6,8,7]=>[5,3,2,4,1,6,8,7]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,5,6,3,8,4,2,7]=>[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,5,3,8,4,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[5,7,3,8,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,6,2,8,4,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[2,3,6,5,4,8,1,7]=>[7,2,5,4,3,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,7,5,4,8,2,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,7,1,2,8,4,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[6,3,8,7,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,7,6,1,5,3,4]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[9,7,8,5,4,3,2,1,6]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[6,8,4,1,7,5,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,4,6,7,5,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,6,8,1,4,7,5,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[6,4,8,1,2,7,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,4,6,7,2,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,1,6,7,4,5,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,2,6,1,7,4,5,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,2,8,1,6,7,5,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,1,2,6,4,7,5,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,1,6,2,7,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,8,1,2,6,7,5,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,8,2,1,6,7,5,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,1,6,2,4,7,5,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,4,6,1,7,5,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[8,3,9,5,1,7,4,10,6,2]=>[10,9,7,6,5,4,3,8,2,1]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[8,3,9,5,6,7,1,10,4,2]=>[10,9,7,6,5,4,3,8,2,1]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[6,3,4,5,7,8,9,10,1,2]=>[10,9,4,3,5,6,7,8,2,1]=>[10,9,4,3,8,7,6,5,2,1]=>[[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.]
[5,4,7,6,3,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,6,4,8,1,5,2,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[3,6,8,4,1,5,2,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[8,7,1,4,2,3,5,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,6,4,1,5,2,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,2,6,5,7,1,3,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,6,1,3,2,8,7,5]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[7,1,4,8,2,3,6,5]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,5,3,6,7,1,8,2]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,4,7,8,3,5,2,6]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,1,3,5,2,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,1,2,5,4,8,7,3]=>[8,2,3,5,4,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,1,7,3,5,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,1,2,5,7,3,6]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,4,5,6,8,3,1,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,4,5,8,6,2,1,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,5,1,8,6,3,7,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,3,7,2,1,6,5,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,4,7,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,3,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,5,6,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,5,6,2,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,8,7,5,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,7,5,6,4,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,3,7,8,2,4,5,9,1]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[7,8,4,5,9,2,3,6,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,5,8,3,6,2,4,9,1]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[8,6,4,9,3,7,2,5,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,6,5,4,3,9,2,7,1]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[4,3,2,5,6,7,8,9,10,1]=>[10,3,2,4,5,6,7,8,9,1]=>[10,3,2,9,8,7,6,5,4,1]=>[[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.]
[6,7,8,9,2,3,4,5,10,1]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[7,8,9,10,1,3,4,5,6,2]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,3,8,9,10,2,4,5,6,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,5,9,3,6,10,2,4,7,1]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,9,6,7,4,5,2,3,10,1]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[8,6,4,9,3,7,2,5,10,1]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[9,7,5,4,10,3,8,2,6,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,6,5,4,3,10,2,8,1]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[2,6,3,8,4,7,1,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,6,3,5,7,8,1,4]=>[7,8,3,4,5,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[1,5,6,3,7,2,8,4]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,3,6,2,8,4]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,3,4,2,8,6]=>[1,6,8,5,4,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,3,4,2,7,6]=>[1,6,8,5,4,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,5,1,4,2,7,8,3]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,5,1,4,2,8,7,3]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,7,5,4,2,8,6,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,6,8,3,7,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,10,7,6,3,4,9,5,8,2]=>[1,10,9,8,6,5,7,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,10,9,6,3,8,4,5,7,2]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,10,9,8,7,3,4,5,6,2]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[3,1,2,10,7,5,9,6,8,4]=>[3,2,1,10,9,8,7,6,5,4]=>[3,2,1,10,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,10,9,8,5,6,7,4]=>[3,2,1,10,9,8,7,6,5,4]=>[3,2,1,10,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,1,2,3,10,9,7,8,6]=>[5,4,3,2,1,10,9,8,7,6]=>[5,4,3,2,1,10,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[7,6,5,1,2,3,4,10,9,8]=>[7,6,5,4,3,2,1,10,9,8]=>[7,6,5,4,3,2,1,10,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[1,12,11,6,3,8,4,10,5,7,9,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[1,12,11,6,3,10,9,4,5,7,8,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[1,12,11,8,7,3,4,10,5,6,9,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[1,12,11,10,7,3,9,4,5,6,8,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[1,12,11,10,9,8,3,4,5,6,7,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[3,1,2,12,11,8,5,10,6,7,9,4]=>[3,2,1,12,11,10,9,8,7,6,5,4]=>[3,2,1,12,11,10,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[3,1,2,12,11,10,9,5,6,7,8,4]=>[3,2,1,12,11,10,9,8,7,6,5,4]=>[3,2,1,12,11,10,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[5,4,1,2,3,12,9,7,11,8,10,6]=>[5,4,3,2,1,12,11,10,9,8,7,6]=>[5,4,3,2,1,12,11,10,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,1,2,3,12,11,10,7,8,9,6]=>[5,4,3,2,1,12,11,10,9,8,7,6]=>[5,4,3,2,1,12,11,10,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,5,1,2,3,4,12,11,9,10,8]=>[7,6,5,4,3,2,1,12,11,10,9,8]=>[7,6,5,4,3,2,1,12,11,10,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[[[[.,.],.],.],.],.]]
[9,8,7,6,1,2,3,4,5,12,11,10]=>[9,8,7,6,5,4,3,2,1,12,11,10]=>[9,8,7,6,5,4,3,2,1,12,11,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[[[.,.],.],.]]
[11,10,9,8,7,1,2,3,4,5,6,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[3,8,5,2,1,4,7,6]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,5,4,8,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,4,7,1,8,6,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,4,8,2,6,5,3,7]=>[1,7,8,4,6,5,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,5,1,3,6,2,4,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,1,8,3,4,2,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,2,8,1,7,4,3,6]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,4,8,2,6,7,3,5]=>[1,7,8,4,6,5,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,6,8,7,3,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,8,2,7,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,7,3,4,1,8,5]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,6,5,7,8,2,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,7,2,8,4,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,6,1,8,2,4,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[1,5,8,6,7,3,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,5,8,7,2,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,6,2,8,3,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,8,6,7,4,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,5,7,3,8,4]=>[1,2,8,6,5,4,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,8,6,4,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,5,8,1,2,7,4]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[5,4,7,8,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,6,8,1,3,7,4]=>[5,8,6,7,1,3,4,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[5,3,6,8,1,2,7,4]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[4,6,5,8,3,2,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[4,5,6,8,2,3,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[2,5,8,7,1,6,4,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[4,7,5,8,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,6,8,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,6,7,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,5,7,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,7,8,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,8,7,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,7,8,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,4,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,4,7,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,9,2,3,4,5,1,6,7]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[5,6,7,4,8,9,1,2,3]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[7,8,9,2,3,1,4,5,6]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,5,7,8,9,1,2,3,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,6,1,2,3,5,4,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[2,8,7,5,1,6,3,4]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[8,7,6,4,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,5,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,5,1,2,6,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[5,8,3,7,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,4,2,6,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,3,2,4,7,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,3,4,7,2,6,5,8]=>[1,5,3,7,2,6,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,1,4,3,6,7,8]=>[3,5,1,4,2,6,7,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[5,3,8,2,4,6,1,7]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[4,5,8,3,2,6,1,7]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[5,8,2,1,4,6,3,7]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[4,1,5,8,3,6,2,7]=>[7,2,5,8,3,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,5,8,3,6,1,2,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[3,2,7,1,8,5,4,6]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,7,8,5,2,3,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,2,7,8,1,5,3,4]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[2,7,1,3,8,5,4,6]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,6,7,8,4,1,3,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,6,7,8,4,3,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[7,1,2,6,3,8,4,5]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,6,5,3,7,4]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,5,4,6,1,2,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,1,8,2,5,3,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,1,8,3,6,4,5]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,8,7,3,1,2,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,8,3,1,2,6,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,4,5,3,1,6,7,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,2,3,1,6,7,4,5]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,2,1,7,4,3,5,6]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,2,6,8,4,1,3,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,2,5,1,6,8,3,4]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,2,1,7,4,8,3,5]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,7,4,3,2,5,6,8]=>[1,7,5,4,3,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,3,6,2,5,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,5,8,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,1,6,3,4,8,7]=>[6,3,2,5,4,1,8,7]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[5,1,3,4,6,2,8,7]=>[6,2,4,3,5,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,8,4,5,7,2,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,4,7,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,2,8,6,3,7,5,1]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[4,1,7,6,3,8,5,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,1,8,5,3,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,5,6,8,4,7,1,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,4,1,8,6,7,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,2,8,4,5,3,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,5,2,1,8,7,3,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[4,7,3,8,2,6,5,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,7,3,1,8,6,2,5]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[6,2,1,3,7,4,8,5]=>[8,3,2,4,6,5,7,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,3,7,1,2,5,8,4]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,1,4,7,8,2,6,3]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,5,8,1,3,6,4]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[8,3,6,7,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,5,2,1,6,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[3,8,5,6,2,7,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,5,8,4,2,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[6,8,3,2,5,7,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,1,5,6,8,7,3,2]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,2,3,6,7,5,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,1,2,4,5,7,8,3]=>[8,2,3,5,4,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,5,1,3,7,6,8,2]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,5,4,8,6,2,7,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,6,2,4,5,8,7,1]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,1,3,7,4,5,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,5,3,6,4,7,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,6,4,8,3,1,5,7]=>[6,7,5,8,3,1,2,4]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[2,6,4,1,5,8,7,3]=>[4,8,5,1,3,7,6,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,5,1,4,6,2,7,8]=>[6,4,3,2,5,1,7,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[7,6,5,2,4,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,6,4,5,2,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[8,1,5,4,7,3,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,5,4,1,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,6,4,1,5,7,2,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[8,1,5,4,7,6,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,5,1,4,6,7,3,8]=>[3,7,1,4,5,6,2,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,6,4,1,5,7,8,2]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[7,6,5,2,8,4,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,1,6,5,2,8,7,4]=>[5,2,8,4,1,7,6,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,7,2,4,3,5,8,6]=>[1,8,3,5,4,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,8,1,7,4,2,6,5]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[8,1,7,4,3,5,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,8,2,4,5,3,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,5,3,6,1,7,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,3,1,4,7,5,6]=>[4,8,3,1,5,7,6,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[8,6,3,2,7,4,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,7,3,1,8,4,5,6]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[1,2,8,3,5,6,4,7]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,7,4,8,1,6,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[3,1,2,6,5,4,10,9,8,7]=>[3,2,1,6,5,4,10,9,8,7]=>[3,2,1,10,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,8,6,3,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,8,4,1,2,5,7]=>[6,7,8,5,4,1,2,3]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[4,7,8,5,2,1,3,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,1,5,2,8,7,3,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,3,5,7,4,2,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,8,5,4,7,2,6]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,1,6,4,8,5,2,7]=>[7,2,6,4,8,3,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,3,4,2,6,8,7]=>[5,2,4,3,1,6,8,7]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,2,6,4,1,5,7,8]=>[5,2,6,4,1,3,7,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[5,4,2,1,8,3,6,7]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,2,5,1,8,7,3,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[6,8,2,7,1,4,3,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,8,4,7,3,2,5,6]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,3,1,5,7,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,3,1,4,7,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,2,5,4,7,8,3,6]=>[1,2,7,4,8,6,3,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,7,1,2,5,3,6,8]=>[6,7,3,4,5,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[6,8,4,1,3,7,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,2,6,1,7,8,5,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[7,6,4,1,8,3,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,4,1,6,7,3,2,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,4,1,6,5,8,2,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,4,1,6,7,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,6,2,3,5,7,8,4]=>[1,8,3,4,5,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,8,5,2,6,7]=>[1,6,3,8,5,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,4,6,1,7,3,5]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,5,7,2,3,6,8,4]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,3,1,4,2,5,8,6]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,2,5,7,8,4,1,6]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,3,5,1,6,2,7,8]=>[6,4,3,2,5,1,7,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[8,6,3,5,4,1,2,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,2,6,1,5,4,7]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,5,1,7,4,6,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,8,1,7,6,3,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,1,7,4,3,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,7,6,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,8,3,1,7,2,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[4,8,1,7,6,5,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,3,8,7,2,6,1,5]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[3,8,7,2,6,4,1,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[8,2,5,7,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,4,6,1,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,7,6,3,5,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,4,7,6,1,5,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,5,4,8,3,1,7,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,4,8,2,1,3,7,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[3,8,7,2,6,1,5,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[1,8,4,7,6,3,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,3,7,6,5,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,3,8,7,2,6,5]=>[1,6,3,8,7,2,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,5,4,6,2,3,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,4,1,3,6,2,5,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,4,3,1,7,6,2,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[4,1,3,7,5,6,2,8]=>[7,2,3,6,5,4,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,6,8,3,1,7,4,5]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,5,4,8,1,7,3,6]=>[5,7,3,8,1,6,2,4]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[7,5,2,4,8,3,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,2,6,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,6,5,8,3,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,3,1,4,2,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[2,6,5,3,4,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[2,6,1,5,3,4,7,8]=>[3,6,1,5,4,2,7,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,6,2,7,4,5,1,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,4,7,8,5,1,6,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[3,6,2,4,7,8,5,1]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,3,6,4,8,7,2,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,5,4,8,6,2,7,3]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,5,2,7,6,3,8,1]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,8,3,1,2,7,6,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,6,2,5,3,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,4,6,1,3,7,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,5,1,2,3,6,7]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[8,6,2,4,5,1,3,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,1,3,8,6,2,7]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[7,4,2,3,6,8,5,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,1,6,7,4,8,3,5]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[7,8,1,3,6,4,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,6,8,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,6,8,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,1,6,2,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,8,1,6,3,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,6,8,5,1,4,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,5,2,4,8,3,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,3,1,6,2,5,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,8,4,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,3,6,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,8,1,6,4,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,7,5,8,2,4,6,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,5,2,8,1,4,6,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[3,7,8,2,6,5,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,7,8,2,1,6,4,5]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[7,8,1,6,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,8,2,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,8,3,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,1,6,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,6,1,4,3,8,2,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,1,6,8,3,4,7,2]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,6,8,5,4,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,8,1,2,3,7,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,8,1,2,7,6,5,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,6,1,2,8,5,7,3]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,4,7,3,5,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,7,8,4,2,1,3,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,4,8,3,5,2,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[3,1,6,2,5,7,8,4]=>[4,2,8,1,5,6,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,6,4,5,2,7,3,8]=>[1,7,5,4,3,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,3,2,5,6,8]=>[1,5,7,4,2,6,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,2,1,4,5,3,7,8]=>[6,3,2,5,4,1,7,8]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,2,3,4,5,8,9,6,7]=>[1,2,3,4,5,9,8,7,6]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,7,9,5,8,6]=>[1,2,3,4,9,8,7,6,5]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,4,6,8,3,7,5]=>[1,2,6,8,7,3,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,8,2,6,7,4]=>[1,5,8,7,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,9,2,5,6,7,8,3]=>[1,9,8,4,5,6,7,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[6,1,3,7,2,8,5,4]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,5,8,3,7,1,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,1,4,3,6,7,2,5]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,6,8,4,3,1,7,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[8,1,5,2,6,4,3,7]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,7,4,2,8,3,5]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,4,3,6,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,7,4,3,2,6]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,2,3,6,8,5]=>[1,5,8,4,2,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,6,7,8,5,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,8,1,6,4,2,7,5]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[1,6,3,4,7,8,2,5]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,5,7,6,2,8,4]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,3,1,4,2,7,8,5]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,4,3,7,6,1,8,5]=>[6,3,2,8,5,1,7,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[3,1,7,6,5,2,8,4]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,4,7,6,8,3,2,5]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,1,8,6,2,7,5]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[3,1,5,2,8,7,6,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,2,8,4,3,7,6,5]=>[1,2,8,5,4,7,6,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,1,8,7,4,3,5]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[7,5,1,8,3,2,6,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,7,6,3,1,8,2,5]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[5,3,1,8,6,2,4,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,1,8,6,3,2,4,7]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,5,4,2,8,6,3,7]=>[1,7,4,3,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,8,5,3,7,6]=>[1,6,3,8,5,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,3,1,6,4,2,5,7]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,7,4,8,3,5,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,3,2,4,8,5,1,6]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,7,8,1,4,2,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,6,3,8,1,7,5,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,5,1,8,6,3,7,4]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,8,6,4,1,7,3,5]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,8,4,2,7,5,3,6]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,5,1,7,2,8,4,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,8,1,7,5,3,6,4]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,2,8,7,6,4,3,5]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,7,8,6,3,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,5,7,8,4,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,8,7,6,3,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,8,2,6,3,5,1,7]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[4,3,5,7,1,6,2,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,1,8,5,3,6,2,7]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,4,2,5,3,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[3,1,5,8,2,7,4,6]=>[5,2,7,8,1,6,3,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[6,4,1,5,3,2,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[6,2,1,5,4,3,7,8]=>[6,3,2,5,4,1,7,8]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[3,1,8,5,4,6,2,7]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,1,8,4,5,3,2,7]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,5,2,7,1,6,3,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,3,5,7,1,6,8,2]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,1,8,5,3,6,7,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,3,8,4,5,1,7,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[3,1,6,8,5,7,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,6,1,8,5,7,4,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[6,3,8,4,5,2,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[6,5,8,7,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,8,4,5,2,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,1,6,8,5,3,7,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,2,6,8,5,4,7,1]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,8,5,2,6,3,7]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,1,6,8,5,2,4,7]=>[6,2,7,8,5,1,3,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,5,8,7,4,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,8,7,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,8,7,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,8,4,5,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,8,4,5,7,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,2,7,3,5,8,6,1]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,6,2,4,8,5,7,1]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,7,5,4,3,8,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,5,1,8,4,7,6,2]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,6,1,8,5,4,7,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,4,8,3,7,6,5,1]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,6,8,2,5,7,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,6,8,5,4,3,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[3,6,8,2,5,4,7,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,6,8,3,2,5,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,6,2,8,3,5,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[3,6,1,8,5,7,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,2,6,8,4,1,7,3]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[4,6,3,8,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,8,2,7,4,6,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[2,6,8,5,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,8,7,6,3,5,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,5,1,6,3,2,8,4]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,7,6,3,4,1,8,5]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[5,7,6,3,1,2,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,8,2,1,7,5,6,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,3,8,5,7,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,1,7,5,3,6,4]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[8,2,1,6,7,3,5,4]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,2,8,1,7,5,3,4]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,5,1,8,7,6,2,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,6,2,7,8,1,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,7,3,5,6,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,7,8,3,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,2,3,4,5,6,7,8,10,9,11]=>[1,2,3,4,5,6,7,8,10,9,11]=>[1,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[3,2,5,6,8,4,7,1]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,5,2,6,3,7,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,5,6,4,8,3,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,3,2,4,7,8,1,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[4,2,5,7,3,8,1,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,7,3,1,6,8,2,5]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[4,2,7,6,8,1,3,5]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,7,4,6,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,3,6,5,8,7,10,9,12,11,1]=>[12,3,2,5,4,7,6,9,8,11,10,1]=>[12,3,2,11,10,9,8,7,6,5,4,1]=>[[[[.,.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]],.]
[4,7,2,5,6,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,4,1,3,7,8,2,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[6,1,5,8,3,7,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,3,5,7,8,2,6]=>[7,2,3,4,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,1,5,8,4,3,2,7]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,2,1,6,8,3,5,4]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[5,6,4,1,8,3,2,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,5,2,1,7,8,3,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[2,3,7,8,5,1,6,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,1,7,6,2,3,8,5]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,2,6,7,4,3,5,8]=>[1,2,7,6,5,4,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,6,3,4,1,2,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,9,7,3,4,5,1,2,8]=>[8,9,7,6,5,4,3,1,2]=>[8,9,7,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[6,2,3,1,8,5,4,7]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[5,1,2,6,4,8,3,7]=>[7,2,3,5,4,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,6,2,3,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,9,1,2,3,4,5,6]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[7,10,8,3,4,5,6,1,2,9]=>[9,10,8,7,6,5,4,3,1,2]=>[9,10,8,7,6,5,4,3,1,2]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[4,5,2,8,6,1,3,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,4,8,2,5,6,1,7]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[9,7,2,3,8,5,6,1,4]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[2,8,3,6,7,4,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,2,7,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,2,5,8,4,1,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,6,7,2,8,4,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,3,6,4,1,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,8,5,2,7,1,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[2,8,4,5,1,6,3,7]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,2,5,8,4,7,1,6]=>[7,2,5,8,3,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,5,8,1,3,4,7,6]=>[4,6,8,1,5,2,7,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,5,1,8,7,4,2,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,6,1,3,8,2,7,5]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[8,6,1,2,3,5,7,4]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,1,7,8,3,2,4,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,1,7,6,2,8,5,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[5,3,6,7,4,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,4,2,8,6,7,3,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,1,4,2,8,7,3,5]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,7,2,6,8,4,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,6,5,2,7,8,3,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,4,6,2,7,8,3,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,1,8,6,4,2,7,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,2,1,8,5,7,4,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[5,4,6,2,3,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,5,7,8,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,7,6,8,4,5,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,4,7,2,8,3,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,2,7,8,4,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,4,8,2,7,6,5,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,7,8,9,4,5,6]=>[1,2,3,9,8,7,6,5,4]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,8,9,6,7,4,5]=>[1,2,3,9,8,7,6,5,4]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,5,8,9,2,6,7,3,4]=>[1,9,8,7,5,6,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,7,9,5,8,3,6,4]=>[1,2,9,8,7,6,5,4,3]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,7,9,1,5,8,2,6,3]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[1,8,9,6,7,4,5,2,3]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,6,9,4,8,2,7,5,3]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[5,9,3,8,1,7,6,4,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[3,9,1,8,7,6,5,4,2]=>[9,8,3,7,6,5,4,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[1,2,3,4,8,9,10,5,6,7]=>[1,2,3,4,10,9,8,7,6,5]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,4,5,8,10,6,9,7]=>[1,2,3,4,5,10,9,8,7,6]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,7,8,9,10,3,4,5,6]=>[1,2,10,9,8,7,6,5,4,3]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,4,9,10,7,8,5,6]=>[1,2,3,4,10,9,8,7,6,5]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,8,10,6,9,4,7,5]=>[1,2,3,10,9,8,7,6,5,4]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[5,6,9,10,1,2,7,8,3,4]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[1,8,9,10,5,6,7,2,3,4]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,9,10,7,8,5,6,3,4]=>[1,2,10,9,8,7,6,5,4,3]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[7,8,10,4,5,9,1,2,6,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[4,7,10,1,5,9,2,8,6,3]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[1,6,10,4,9,2,8,7,5,3]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[5,10,3,9,1,8,7,6,4,2]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[4,7,3,1,5,2,8,6]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[2,1,4,7,5,3,8,6]=>[2,1,6,8,5,3,7,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[4,7,3,6,5,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,7,6,3,1,5,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,4,7,3,8,5,1,6]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[2,7,3,1,8,5,4,6]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,8,3,1,7,4,5,6]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[6,7,5,2,1,4,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,6,8,9,1,2,3,4,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[5,4,6,7,8,9,1,2,3]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[1,2,6,8,3,4,7,5]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,7,3,5,6,4]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,8,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,3,5,7,4,8,2]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,8,5,2,6,1,7,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[3,7,4,8,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,2,6,5,3,4,7]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,7,4,2,5,6,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,8,7,1,3,4,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,4,2,8,6,7,5,1]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,7,8,6,1,4,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,6,1,5,2,7,8,4]=>[5,8,3,4,1,6,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[7,1,6,8,3,4,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,6,3,5,7,4]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,2,8,4,7,1,3,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[3,7,8,4,2,5,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,2,8,5,1,6,7]=>[6,3,2,8,5,1,7,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,4,3,2,5,6,7,8,9]=>[1,4,3,2,5,6,7,8,9]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[6,8,2,7,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,4,3,7,6,2,5]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,8,7,1,2,6,5]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[1,8,4,5,7,6,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,8,5,7,1,6,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,3,4,8,7,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,8,4,7,1,6,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[5,2,8,7,1,4,6,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[3,2,8,7,1,6,4,5]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,7,8,3,1,6,4,5]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,7,8,5,1,4,6,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[3,5,8,7,4,1,6,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,4,6,8,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,8,1,3,6,4,5]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,7,8,1,5,4,6,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,7,8,1,4,5,6,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,6,7,8,2,4,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,5,7,8,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,6,8,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,8,6,7,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,6,8,2,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,6,8,2,4,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,4,7,8,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,7,8,2,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,6,8,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,3,4,2,1,6,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[6,1,5,3,8,4,7,2]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,6,2,5,4,7,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,8,4,1,7,5,2,6]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[6,2,7,4,8,3,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,5,1,4,3,7,6]=>[4,8,6,1,5,3,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[6,8,2,7,5,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,4,5,6,1,7,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,6,4,7,2,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,2,6,5,7,3,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[5,4,6,2,7,3,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[3,2,6,5,8,4,1,7]=>[7,2,6,4,8,3,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,2,6,5,8,7,1,4]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,2,6,5,8,7,1,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,2,6,4,8,7,1,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,4,7,6,8,2,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,7,5,8,3,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,2,7,5,8,6,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,2,7,5,8,4,1,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,3,7,2,8,5,1,6]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,3,6,2,8,5,1,7]=>[7,4,6,2,8,3,1,5]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,3,7,6,8,5,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,7,6,8,2,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,7,2,8,6,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,2,6,4,8,7,1,5]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,2,7,3,8,6,1,5]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[5,2,7,6,8,3,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,2,7,6,8,4,1,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,2,7,6,8,5,1,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,2,7,5,8,4,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,1,7,3,2,5,6]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,7,4,8,2,1,5,6]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[3,7,8,2,5,4,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,7,5,8,3,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,1,3,2,5,8,4]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,7,6,4,1,5,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,5,2,6,4,7,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,5,3,4,8,1,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,2,5,3,7,8,6,1]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,3,6,2,4,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[7,8,6,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,2,6,3,7,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,2,3,7,5,6,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,5,6,2,3,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,7,5,6,4,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,8,4,3,7,5,6,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,8,5,7,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,6,3,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,6,3,8,5,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,2,5,6,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,2,7,5,3,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,4,8,3,7,5,6,1]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,8,3,7,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,5,8,3,7,4,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,7,3,8,2,5,6,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,2,5,6,3,7,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,3,7,1,2,6,8]=>[6,5,3,7,2,1,4,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[8,5,6,4,1,3,2,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,2,8,4,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,3,2,8,4,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,7,8,3,1,5,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,5,8,1,3,2,6,7]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[4,7,8,1,6,3,2,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,7,1,3,8,6,5,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,6,7,4,3,8,1,5]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[3,7,6,4,5,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,2,8,3,4,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,2,8,5,6,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,1,5,8,6,4,7,2]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,8,6,4,5,7,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,8,6,4,7,5,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,6,2,8,7,4,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,5,6,1,8,7,3,4]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,6,2,8,4,7,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,3,8,5,7,4,6,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,8,6,7,5,4,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,5,6,3,1,4,2,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,5,1,6,4,2,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,8,3,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,1,8,6,4,2,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,5,3,8,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,3,8,6,4,2,7]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,5,8,3,6,4,2,7]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,5,8,3,6,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,5,8,6,3,4,2,7]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,5,8,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,1,4,6,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,3,7,8,4,2,6,5]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,2,5,3,4,7,8]=>[6,2,3,5,4,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,1,2,5,4,3,7,8]=>[6,2,3,5,4,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,1,4,6,7,3,2,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,4,6,5,7,2,3,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,7,3,5,4,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,1,6,7,3,5,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,4,1,6,5,3,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,2,5,1,3,7,6,8]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,3,2,6,8,4,7,5]=>[1,3,2,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,5,4,1,6,7,3]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,1,7,5,4,2,6,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,6,4,7,3,5,8]=>[1,2,7,6,5,4,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,4,3,7,2,5,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,8,3,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,5,1,3,7,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,6,4,3,7,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,6,8,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,7,5,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,1,8,6,5,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,7,3,1,4,8,6,5]=>[4,8,3,1,5,7,6,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,1,6,5,7,8,4,2]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,3,1,5,8,7,6,2]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,7,1,3,2,5,6,8]=>[5,7,3,4,1,6,2,8]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,1,6,7,3,2,8,5]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,7,2,5,6,8,4,3]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,7,6,8,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,8,6,1,7,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,4,7,1,8,6,2]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,1,5,4,2,3,6,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,1,3,6,4,5,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,1,3,8,4,5,2,7]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,1,8,7,3,6,5,4]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,8,6,3,1,2,7,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,2,7,1,3,6,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[2,6,5,4,1,3,7,8]=>[5,6,4,3,1,2,7,8]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[4,1,5,7,6,3,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,3,4,2,1,8,7,5]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,5,1,7,6,3,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,4,2,1,8,7,3,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[6,2,1,5,4,3,8,7]=>[6,3,2,5,4,1,8,7]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,4,2,6,7,8,5,3]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,3,6,7,8,4,1]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,8,6,2,4,3,5,7]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,4,5,7,8,1,6]=>[7,2,3,4,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,3,4,7,5,8,6,1]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,5,2,8,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,4,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,2,8,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,3,2,6,5,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,6,3,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,7,2,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,2,7,8,4,5,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,2,7,5,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,8,2,7,5,3,4]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,3,2,8,1,5,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,1,7,4,3,8,6,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,3,7,2,4,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,8,6,4,2,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,8,6,4,1,3,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,7,6,4,3,2,8,5]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,6,3,4,2,5,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,4,3,8,6,5]=>[1,2,8,5,4,7,6,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,4,2,3,8,7,6]=>[1,5,4,3,2,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,4,2,3,7,8,6]=>[1,5,4,3,2,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,6,3,5,8,4]=>[1,2,8,6,5,4,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,3,2,6,5,7,4]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,3,7,2,8,1,6,5]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[3,2,7,5,6,1,8,4]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[7,5,6,1,3,2,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,3,4,1,8,2,6,5]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,4,5,1,6,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,6,1,4,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,2,7,6,8,3,5,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[3,2,6,4,8,5,7,1]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,2,8,3,6,5,7,1]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,1,4,3,5,2,7,6]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,2,8,5,7,1,4,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,4,8,5,7,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,4,1,6,2,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[6,5,7,3,4,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,2,7,6,8,1,4,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,5,6,1,8,2,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,6,1,8,2,5,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,2,8,1,6,3,5,4]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[10,5,9,4,8,3,7,2,6,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,3,6,5,4,1,2,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,5,8,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,5,7,1,2,8,3,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,1,4,2,3,8,6,5]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,7,5,6,8,1,2,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[8,1,2,5,3,7,6,4]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,5,2,4,1,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,5,2,4,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,8,5,2,4,3,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,4,2,8,6,7,1,5]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[3,7,1,6,2,5,8,4]=>[5,8,3,6,1,4,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,6,7,2,5,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,6,2,5,1,7,8,4]=>[5,8,3,4,1,6,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,4,2,7,8,1,5,6]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[3,8,5,2,4,7,1,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[7,1,4,2,5,8,6,3]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,8,5,1,2,4,3,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,1,4,3,6,7,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,3,8,6,4,1,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,2,3,8,7,4,1,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,7,6,3,1,2,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,6,2,7,8,1,3,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,2,3,7,1,4,5,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,6,7,8,2,1,3,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,6,3,2,1,7,5,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,3,4,1,7,8,2,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[8,6,4,9,7,5,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,8,5,9,6,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,6,4,2,9,7,5,3,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,8,5,3,9,6,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,4,8,5,9,6,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,7,8,4,9,5,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,8,5,3,1,9,6,4,2]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[7,4,8,5,2,9,6,3,1]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[6,7,8,4,2,9,5,3,1]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[6,7,3,8,4,9,5,2,1]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[5,6,7,8,3,9,4,2,1]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[6,7,3,8,4,1,9,5,2]=>[9,8,6,5,4,3,7,2,1]=>[9,8,6,5,4,3,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[5,6,7,8,3,1,9,4,2]=>[9,8,6,5,4,3,7,2,1]=>[9,8,6,5,4,3,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[9,7,10,8,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,5,10,8,6,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,6,10,7,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,5,3,10,8,6,4,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,6,4,10,7,5,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,5,9,6,10,7,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,5,10,6,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,6,4,2,10,7,5,3,1]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,5,9,6,3,10,7,4,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,8,9,5,3,10,6,4,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,8,4,9,5,10,6,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[6,7,8,9,4,10,5,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,5,9,6,3,1,10,7,4,2]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[7,8,9,5,3,1,10,6,4,2]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[8,5,2,9,6,3,10,7,4,1]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[6,7,8,9,4,2,10,5,3,1]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[7,3,8,4,9,5,10,6,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[6,7,8,3,9,4,10,5,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[5,6,7,8,9,3,10,4,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[7,3,8,4,9,5,1,10,6,2]=>[10,9,7,6,5,4,3,8,2,1]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[6,7,8,3,9,4,1,10,5,2]=>[10,9,7,6,5,4,3,8,2,1]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[5,6,7,8,9,3,1,10,4,2]=>[10,9,7,6,5,4,3,8,2,1]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[6,1,3,4,2,5,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,1,3,6,2,4,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,5,7,6,8,2,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,1,3,8,4,2,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,6,1,4,3,7,8,5]=>[3,8,1,5,4,6,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[5,3,7,6,1,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,5,6,3,7,8,4,2]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,6,3,8,4,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,3,5,6,1,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,3,6,1,5,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,6,3,7,8,5,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,6,3,5,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,5,6,1,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,2,8,4,7,3,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,7,6,3,4,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,7,5,4,6,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,3,4,7,6,8,1,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,3,7,4,6,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,3,5,4,6,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,8,3,5,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,5,4,1,2,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,7,6,3,4,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,5,4,1,2,7,6,8]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,7,6,1,3,2,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,3,4,1,2,7,6,8]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[7,8,3,1,2,5,4,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,8,5,1,3,2,4,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,6,1,3,2,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,1,3,8,6,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,3,8,2,5,4,6]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,6,1,3,8,2,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,6,3,8,1,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,1,3,7,6,2,4,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,6,3,7,2,4,5,8]=>[1,7,5,6,3,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,3,2,4,8,1,7,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[6,8,5,3,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,7,2,6,5,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,6,2,7,1,3,8,5]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[3,4,6,5,1,8,7,2]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[8,7,1,5,3,2,6,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,5,1,4,7,2,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,1,4,8,7,3,2,6]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,1,4,3,6,5,9,7,8]=>[2,1,4,3,6,5,9,8,7]=>[2,1,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,4,3,6,5,8,10,7,9]=>[2,1,4,3,6,5,9,10,7,8]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,4,3,6,8,5,10,7,9]=>[2,1,4,3,7,9,5,10,6,8]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,4,6,3,8,5,10,7,9]=>[2,1,5,7,3,9,4,10,6,8]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[6,1,3,4,2,7,8,5]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,5,2,3,7,8,1,4]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,5,3,8,4,2,7,6]=>[1,6,5,8,3,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,2,1,8,3,7,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[3,1,7,4,2,6,8,5]=>[5,2,8,4,1,6,7,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[7,4,8,2,3,5,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,1,3,2,6,7,5]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,1,7,3,2,5,6,4]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,5,2,7,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,1,6,8,4,2,7,5]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,5,2,8,3,6,7,4]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,6,2,3,7,4,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,2,4,7,3,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,4,8,5,3,6,7,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,6,3,1,8,4,7]=>[5,7,4,3,1,8,2,6]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[4,5,1,2,7,8,6,3]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,8,5,1,2,6,7,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,6,7,5,1,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,2,8,1,4,5,3,6]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,1,4,7,3,8,2,5]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,6,3,4,8,2,5]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,8,4,6,3,1,5,7]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[8,2,6,3,5,1,4,7]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[3,7,4,1,5,8,2,6]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[3,8,4,1,7,2,5,6]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[6,7,5,1,3,8,2,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,1,3,6,7,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,6,2,4,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,4,1,3,6,7,5]=>[8,4,5,2,3,7,6,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,1,3,6,2,5,7,4]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,1,3,7,2,8,4]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,6,1,8,2,3,7,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,6,1,2,8,4,7,3]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,7,8,1,6,4,2,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,7,8,6,3,4,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,8,6,4,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,1,8,6,4,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,1,5,6,4,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,8,5,6,4,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,5,8,6,4,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,3,5,6,4,2,7]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,3,8,5,6,4,2,7]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,8,6,4,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,6,5,3,4,7]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,1,5,2,3,4,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,1,6,2,3,4,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,1,2,3,8,4,5]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,7,8,4,1,3,5,6]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[6,8,1,2,3,7,4,5]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,3,5,6,7,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,5,3,4,7,6]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,7,6,2,5,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,2,7,3,4,8,1,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[8,6,4,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,4,6,5,1,8,3]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[6,8,7,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,6,3,5,1,4,7]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[1,2,8,6,4,5,3,7]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,7,6,3,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,8,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,4,8,5,7,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,5,2,7,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,5,4,2,3,7]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,8,5,2,7,6]=>[1,6,3,8,5,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,8,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,3,7,4,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,1,6,4,2,5,8,7]=>[5,2,6,4,1,3,8,7]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,6,1,4,5,7,8,2]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,8,4,7,2,3,6,5]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,8,2,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,2,3,6,8,1,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[3,8,1,6,4,2,5,7]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[7,3,2,1,8,6,4,5]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,7,2,4,1,3,6,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,2,6,3,5,7,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,8,3,7,4,6,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,3,1,7,4,5,6]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,1,7,8,6,2,5,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,8,1,2,6,5,7,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,6,1,8,3,7,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,8,1,6,5,3,7,4]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,1,5,7,6,3,8,4]=>[2,1,8,6,5,4,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[4,3,5,1,7,8,6,2]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,8,5,2,3,4,7,6]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,2,3,4,7,6]=>[1,6,8,4,5,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,8,4,5,6,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,4,5,6,9,7,10,8]=>[1,2,3,4,5,6,10,8,9,7]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[4,3,8,7,6,2,5,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,4,8,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,2,5,6,4,8,1,7]=>[7,2,5,4,3,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,3,6,4,1,7,5,8]=>[5,2,7,4,1,6,3,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,3,7,1,5,8,4,6]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,6,1,7,5,8,4]=>[4,2,8,1,6,5,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,3,6,5,1,7,4,8]=>[5,2,7,4,1,6,3,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,6,4,2,1,5,7,8]=>[5,6,4,3,1,2,7,8]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[4,3,2,6,5,8,1,7]=>[7,3,2,5,4,8,1,6]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[4,6,5,2,1,7,8,3]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,6,1,7,5,8,3,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,2,6,5,1,7,8,3]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,1,5,7,6,8,3,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,5,6,2,1,4,7,8]=>[5,6,4,3,1,2,7,8]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[4,2,5,7,6,8,3,1]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,3,6,5,2,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,3,6,5,1,7,8,2]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[3,6,4,5,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[3,5,6,4,2,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,6,5,3,1,7,8,2]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[1,2,3,4,5,7,6,8,9,10]=>[1,2,3,4,5,7,6,8,9,10]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,5,4,6,7,8,9,10]=>[1,2,3,5,4,6,7,8,9,10]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[5,8,1,4,2,3,6,7]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,5,8,2,3,1,6,7]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[3,5,4,8,1,7,2,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,3,6,8,1,4,7,2]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[3,5,1,8,6,4,7,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,7,2,8,3,1,6,5]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[5,3,8,4,6,2,7,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,4,8,1,5,2,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,2,1,6,5,7,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,1,5,6,8,7,2,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,5,6,8,4,7,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,6,8,1,2,4,7,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,8,1,4,5,7,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,3,5,1,8,6,7,2]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,6,8,2,3,4,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[9,8,7,4,5,6,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,5,1,2,4,8,7,3]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,8,7,2,1,3,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,7,2,8,6,3,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,5,3,4,8,7,2]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,8,6,3,2,1,4,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,7,1,6,3,5,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,2,1,7,8,6,4,5]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[8,6,7,1,2,5,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,5,6,4,2,8,7,3]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,5,1,4,8,2,3,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,2,8,1,7,5,6,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[8,4,3,1,7,5,6,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,1,7,8,4,2,3,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,3,1,8,5,2,6]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,8,1,6,3,4,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,1,7,3,4,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,5,6,7,8,9,2,3,4]=>[1,9,8,7,5,6,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,8,9,10,2,3,4,5,6,7]=>[1,10,9,8,5,6,7,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,5,6,7,8,9,10,2,3,4]=>[1,10,9,8,5,6,7,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[3,4,2,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[4,3,1,2,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[3,4,2,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[4,5,2,1,3,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[5,3,1,2,4,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[4,3,5,1,2,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[4,3,1,2,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[4,6,5,3,8,2,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,5,6,3,8,1,7,2]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,8,3,5,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,7,5,2,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,2,4,5,7,3,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,8,1,5,6,4,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,3,7,5,1,4,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,1,7,3,4,2,5,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,1,7,2,5,8,6,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,8,7,6,3,5,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,8,7,1,5,6,4,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,5,6,2,8,1,7,4]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[5,3,1,8,6,2,7,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,1,4,6,8,2,7,5]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,1,5,7,3,8,2,6]=>[7,2,5,8,3,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,2,5,8,4,7,3,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,2,8,5,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,6,8,2,5,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,6,5,7,8,4,1,3]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,6,5,7,4,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,6,5,7,4,2,3,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,4,7,5,2,1,8,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[3,6,7,5,8,4,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,4,7,2,5,6,8,1]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,5,3,7,8,6,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,8,4,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,3,8,5,4,7,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,4,3,1,2,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[6,5,4,3,1,2,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]
[6,5,4,3,1,2,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[7,6,5,4,3,1,2,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,10,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[6,8,7,3,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,6,1,4,5,7,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,8,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,6,3,8,5,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,3,1,8,4,6,5,7]=>[3,2,1,8,5,7,6,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,7,6,8,4,5]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,1,8,4,6,7,5]=>[3,2,1,8,5,7,6,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[4,2,3,5,1,8,6,7]=>[5,3,2,4,1,8,7,6]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[5,8,7,2,6,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,1,7,4,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,5,2,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,8,6,5,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,8,2,6,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,2,8,1,7,5,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>[2,1,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,8,7,1,3,5,4]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[5,3,8,7,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,6,1,4,5,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,1,6,2,7,5,3,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,6,2,5,3,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,3,1,7,6,2,5,8]=>[6,3,2,7,5,1,4,8]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[4,5,3,1,2,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[2,4,5,3,1,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,7,6,2,3,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,1,3,7,5,2,6,8]=>[6,2,3,7,5,1,4,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,1,6,3,2,7,5,8]=>[5,2,7,4,1,6,3,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[7,5,4,1,3,2,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[2,4,8,5,6,3,1,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[2,5,7,4,1,3,6,8]=>[5,6,7,4,1,2,3,8]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[5,7,4,1,3,2,6,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[2,6,8,4,5,3,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[5,2,3,7,4,1,6,8]=>[6,5,3,7,2,1,4,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,5,1,6,3,2,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,1,6,3,2,4,7,8]=>[6,2,5,4,3,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,2,5,1,6,3,7,8]=>[6,4,3,2,5,1,7,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,1,6,2,4,3,7,8]=>[6,2,5,4,3,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,3,4,8,7,6,2,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,1,6,7,5,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,6,5,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,2,6,7,4,5,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,5,7,2,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,3,6,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,5,3,6,7,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,5,2,7,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,4,5,2,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,2,4,7,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,5,1,4,6,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,8,5,4,2,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,4,7,2,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,1,7,3,6,4,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,5,3,4,2,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,8,4,3,1,5,2,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,4,5,8,3,2,6,7]=>[1,6,5,8,3,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,4,7,8,6,3]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,2,7,4,3,8,6,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[2,7,3,4,8,5,6,1]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,7,6,8,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,4,5,3,8,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,2,3,7,4,5,8,1]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,6,3,2,7,5,8,4]=>[1,8,4,3,6,5,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,3,5,2,6,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,4,2,7,1,5,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,5,3,6,4,7,8,1]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,2,5,3,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,6,5,2,4,7,3,8]=>[1,7,5,4,3,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,7,2,4,6,3,5]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,7,2,5,4,3,6]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,4,2,8,7,3,6]=>[1,7,4,3,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,3,5,2,4,7]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,6,2,3,5,8,4]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,3,6,5,4,7]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,6,5,2,4,7]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,3,2,8,6,5]=>[1,5,8,4,2,7,6,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,6,5,2,4,7,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,4,3,2,5,7]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,3,2,6,4,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,5,3,8,4,7]=>[1,2,7,5,4,8,3,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,3,7,2,4,6,5]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,2,8,7,6,1,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,3,2,5,7,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,2,1,6,5,8,4]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[7,3,2,6,1,5,8,4]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,8,5,2,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,2,5,1,7,4,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,8,5,7,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,8,2,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,1,7,5,8,4,3]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,6,4,8,5,3,7,2]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,6,2,8,7,1,4]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[1,6,5,3,4,7,8,2]=>[1,8,5,4,3,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,2,6,7,8,1,3,5]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[4,6,5,1,3,7,8,2]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,1,7,2,6,4,8,3]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,7,6,5,8,2,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,2,3,6,7,8,1,5]=>[7,3,2,8,5,6,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[4,7,2,1,6,5,8,3]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[2,7,6,4,1,5,8,3]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,4,3,6,7,8,1,5]=>[7,3,2,8,5,6,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[6,8,5,2,7,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,2,4,1,8,3,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,5,1,3,7,8,2,4]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,1,2,4,3,7,8,5]=>[8,2,3,5,4,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,5,4,2,3,6,7]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,2,4,6,3,8,5]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,2,6,5,3,8,4]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,5,6,1,2,4,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,1,4,5,2,3,6,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,1,4,8,7,2,3,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,8,5,7,2,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,7,5,8,3,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,7,5,8,2,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,4,7,8,2,3,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,3,7,5,4,6]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,8,6,1,2,4,7,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,6,8,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,8,7,5,2,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,1,2,4,6,5,7]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,3,1,2,4,5,7,6]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[6,7,1,4,2,3,5,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,1,7,4,8,2,3,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,7,8,5,1,2,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,5,4,3,2,7,9,1]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[8,9,5,4,3,2,1,6,7]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,6,5,4,3,2,7,1,8]=>[9,8,6,5,4,3,7,2,1]=>[9,8,6,5,4,3,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[4,3,8,5,6,2,7,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,3,8,6,7,2,5,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,6,8,1,5,3,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,6,1,5,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,3,8,1,7,2,5,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,1,5,4,8,2,7,3]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,2,5,4,7,1,8,3]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[2,6,3,4,8,7,5,1]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,7,4,5,1,8,3,6]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[8,4,5,7,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,5,7,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,3,4,6,7,5,2]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,7,6,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,6,7,5,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,1,6,5,7,4,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,7,1,8,5,6,4,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,7,8,6,1,5,3,4]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[4,6,8,2,3,5,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[6,8,2,1,3,5,4,7]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[3,5,1,6,4,8,2,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,5,8,6,2,1,4,7]=>[6,7,8,5,4,1,2,3]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,4,8,5,6,1,3,7]=>[6,7,8,4,5,1,2,3]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[4,8,2,5,6,1,3,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,3,8,4,2,7,6,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[2,8,5,3,1,4,7,6]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[1,7,8,4,6,3,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,2,4,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,3,2,1,6,4,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,8,3,4,6,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,3,6,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,1,2,8,6,5,7,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[3,8,2,7,5,4,6,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,1,4,5,3,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,8,7,4,6,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,7,4,6,3,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,3,4,1,2,5,7,6]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[8,4,1,3,2,5,7,6]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,3,8,6,2,1,4,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,2,8,4,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,4,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,2,6,5,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,6,8,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,5,2,4,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,1,2,7,5,6,3,4]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,7,3,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,5,4,8,1,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,5,6,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,6,2,4,3,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,8,1,3,4,2,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[6,8,4,5,1,3,2,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,4,8,7,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,1,4,3,2,8,5]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,2,5,1,4,8,3,6]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[5,8,1,3,4,2,7,6]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[1,5,6,3,2,8,7,4]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,7,6,8,4,2,5]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,3,2,8,5,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,7,6,8,4,5,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,3,8,5,2,7,6,4]=>[1,5,8,7,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,4,1,5,2,8,7,3]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,6,5,3,1,8,2,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,5,1,4,7,3,6,8]=>[3,6,1,4,7,2,5,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,1,6,5,7,2,4,8]=>[6,2,7,4,5,1,3,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,6,1,5,7,4,8,3]=>[3,8,1,6,5,4,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,5,7,1,6,3,8,4]=>[4,8,6,1,5,3,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,1,6,5,2,4,7,8]=>[5,2,6,4,1,3,7,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,6,5,1,4,2,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[3,6,5,2,1,4,7,8]=>[5,6,4,3,1,2,7,8]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[5,4,3,6,1,7,2,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,5,2,7,6,1,3,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,6,5,3,1,2,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,4,1,6,3,7,2,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,4,2,6,3,7,8,1]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,6,5,7,1,4,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,6,5,1,4,7,2,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,3,6,5,7,1,2,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,2,6,5,1,3,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,1,6,5,3,7,8,2]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,2,5,7,6,1,3,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,4,7,6,1,2,5,8]=>[6,5,7,4,2,1,3,8]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[4,2,5,7,6,3,8,1]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,1,6,5,2,7,3,8]=>[7,2,5,4,3,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,6,5,7,2,1,4,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[3,5,7,6,2,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,4,2,6,3,7,1,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,6,5,2,7,3,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,6,5,2,1,7,3,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[3,5,8,2,1,4,6,7]=>[5,6,8,4,1,2,7,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,5,8,2,4,6,7,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,3,8,2,1,4,6,7]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[5,3,1,8,2,4,6,7]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,5,8,4,2,3,6,7]=>[1,6,8,5,4,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,2,1,4,3,6,7]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[5,8,2,4,1,6,7,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,8,2,4,6,3,1,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,8,2,4,3,6,1,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[5,8,1,4,6,2,3,7]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[1,5,8,4,6,7,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,8,4,6,7,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,8,2,4,6,3,7,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,4,6,7,2,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,8,4,6,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,3,6,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,3,6,7,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,2,4,5,3,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,6,4,5,7,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,2,4,5,3,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,6,4,2,3,5,7]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,8,1,6,2,4,5,7]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,8,6,2,1,4,5,7]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,8,6,2,4,1,5,7]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[3,8,6,2,4,5,7,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,6,2,4,5,1,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,3,6,2,4,5,7]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,6,7,2,1,4,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[3,8,6,7,2,1,4,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[8,2,6,4,5,1,7,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,8,4,6,7,5,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,4,6,2,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,2,1,3,6,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,7,1,6,3,5,8,4]=>[3,8,1,6,5,4,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[8,4,2,1,5,3,7,6]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[8,2,1,4,7,3,6,5]=>[8,3,2,6,7,4,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,6,2,5,8,4,7,3]=>[1,8,3,6,7,4,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,1,7,4,5,8,6]=>[3,2,1,8,5,6,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,6,8,5,1,7,4,3]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,1,5,8,7,3,6,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,2,1,6,7,4,8,5]=>[3,2,1,8,6,5,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[4,3,1,7,8,5,2,6]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[5,6,8,2,4,3,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,8,5,3,6,4,7,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,2,8,6,4,7,3,5]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,3,2,7,8,6,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,2,7,8,3,5,6,1]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[2,8,3,7,1,4,6,5]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,8,7,1,5,3,6,4]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[7,3,5,6,4,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,8,4,2,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,8,3,2,7,5,6,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,2,4,8,7,5,6,1]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,6,8,1,5,3,4,7]=>[4,7,8,1,6,5,2,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,2,5,6,8,1,4,7]=>[6,2,7,4,8,1,3,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,8,1,6,4,5,2,7]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[8,1,3,6,5,4,2,7]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,3,6,2,1,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,2,4,8,6,3,7,5]=>[1,2,6,8,7,3,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,2,3,1,4,8,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[7,1,5,2,4,6,8,3]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,2,7,3,5,6,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,8,6,4,7,5,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,1,5,8,6,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,5,8,7,3,1,2,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,3,8,7,6,4,2,5]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,5,1,7,4,6,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,8,6,4,7,5,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,4,6,3,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,2,8,6,4,7,5,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,8,6,3,7,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,3,1,6,2,5,7]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,5,4,3,8,1,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,1,6,2,8,7,4]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,5,4,1,7,8,2,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[6,4,2,1,5,7,3,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[3,1,5,8,7,2,4,6]=>[6,2,7,8,5,1,3,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,2,5,7,8,4,6,1]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,3,7,4,2,6,8,1]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,3,7,4,2,6,1,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[5,3,8,4,2,1,6,7]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[5,2,8,4,3,1,6,7]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[5,1,8,4,3,2,6,7]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,2,7,4,3,6,1,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[5,2,7,4,3,6,8,1]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,3,7,4,1,6,8,2]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[3,1,5,7,8,4,6,2]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,5,7,8,4,2,6]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,2,7,4,1,3,8,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[6,2,3,7,4,8,5,1]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,2,3,7,4,8,1,5]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,2,3,7,4,5,1,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,1,3,7,4,5,8,2]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,8,6,4,3,5,7]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,3,7,4,5,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,8,6,3,5,4,2,7]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,1,8,5,3,4,7]=>[3,7,1,8,6,5,2,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[4,5,7,8,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,7,8,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,2,7,5,3,4,6]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,4,1,8,6,7,3]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[5,6,8,3,4,2,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,1,5,3,8,6,7,2]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,3,5,1,4,8,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,8,7,1,4,2,5,6]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[5,1,7,8,2,4,3,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,5,4,6,1,7,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,2,1,4,6,8,7]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,3,2,4,8,1,6,7]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,3,2,4,7,1,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[8,4,5,3,7,1,2,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,1,7,3,5,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,3,2,4,6,8,1,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[2,7,6,3,1,4,8,5]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,7,4,5,6,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,7,1,4,2,5,3,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,6,8,3,7,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,3,5,8,1,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,3,5,7,1,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,7,6,4,2,5,3,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,4,2,8,3,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,2,4,3,7,1,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,1,4,3,7,6,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,4,1,3,6,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,6,7,2,5,1,8,4]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[2,6,5,7,1,4,8,3]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,5,1,7,8,4,6,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,1,2,4,7,6,5,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,4,1,8,6,7,5,2]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,3,8,5,1,7,6,2]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,1,3,2,8,5,7,4]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,5,3,2,4,7,1,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,7,4,2,5,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,4,2,6,3,1,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,2,1,6,4,3,7]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,4,6,5,1,3,2,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,3,8,4,7,5,2,6]=>[1,7,8,4,6,5,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,3,7,1,4,6,8,2]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,7,2,6,1,4,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,8,5,7,6,1,2,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,4,7,5,2,1,3,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,6,4,7,2,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,2,7,4,6,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,8,6,3,7,2,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,8,3,1,7,6,4,5]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,5,6,4,8,1,7,3]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[5,7,2,1,6,8,3,4]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,7,8,5,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,2,1,6,7,8,3]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,5,6,3,1,7,8,2]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[3,5,6,7,4,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,5,1,4,2,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,5,1,4,2,6,8,7]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,5,1,4,2,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,3,8,4,6,2,5,7]=>[1,6,8,4,7,2,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,4,2,3,7,5,6]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,8,3,2,7,6,5]=>[1,5,8,4,2,7,6,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,6,7,5,4,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,4,3,2,6,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,9,10,1,5,6,7,3,4,2]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[8,9,10,5,6,7,1,3,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,1,5,6,3,4,7,2]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[8,9,10,5,6,1,3,4,7,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,5,6,3,4,7,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,5,6,10,1,3,4,7,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,5,6,10,3,4,7,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,1,5,6,7,3,2,4]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[8,9,10,5,6,7,1,3,2,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,1,5,6,3,7,2,4]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[8,9,10,5,6,1,3,7,2,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,5,6,3,7,1,2,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,5,6,10,1,3,7,2,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,5,6,10,3,7,1,2,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,1,5,6,3,2,4,7]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[8,9,10,5,6,1,3,2,4,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,5,6,3,1,2,4,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,5,6,3,2,4,7,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,5,6,10,1,3,2,4,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,5,6,10,3,1,2,4,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,5,6,10,3,2,4,7,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,1,5,3,6,7,2,4]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[8,9,10,5,1,3,6,7,2,4]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,9,10,5,3,6,7,1,2,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,5,10,1,3,6,7,2,4]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,9,5,10,3,6,7,1,2,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,1,5,3,6,2,4,7]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[8,9,10,5,1,3,6,2,4,7]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,9,10,5,3,6,1,2,4,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,5,3,6,2,4,7,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,5,10,1,3,6,2,4,7]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,9,5,10,3,6,1,2,4,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,5,10,3,6,2,4,7,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,5,3,6,10,1,2,4,7]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,9,5,3,6,10,2,4,7,1]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,5,9,10,1,3,6,7,2,4]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,5,9,10,3,6,7,1,2,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,5,9,10,1,3,6,2,4,7]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,5,9,10,3,6,1,2,4,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,5,9,10,3,6,2,4,7,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[3,8,5,7,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,2,4,5,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,7,4,5,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,2,4,1,3,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[7,6,3,2,5,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,2,7,8,3,6,1,5]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[4,6,3,7,5,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,2,5,7,8,6,3,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,8,4,5,2,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[8,2,5,7,3,6,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,2,5,8,7,6,3,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,2,4,5,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,2,7,8,3,6,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,8,3,1,6,4,5]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[7,2,3,4,1,8,5,6]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,4,7,8,1,3,6,5]=>[5,6,8,7,1,2,4,3]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[8,5,1,2,3,7,4,6]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,2,8,3,1,4,7,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[8,7,2,5,1,4,3,6]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,4,1,3,2,7,6,5]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,3,5,1,2,4,7,6]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,6,5,1,7,4,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,4,5,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,6,2,7,1,5,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[3,4,8,2,1,7,6,5]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[3,8,4,2,1,7,6,5]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[8,3,1,7,5,6,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,1,7,5,2,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,2,7,5,3,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,3,7,5,1,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,6,4,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,6,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,1,4,7,6,2,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,5,7,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,4,6,8,2,5,7,3]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,2,4,8,1,7,5]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[7,3,8,2,4,6,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,5,2,6,8,3,7,4]=>[1,8,3,6,7,4,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,5,3,1,8,2,6,7]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,1,7,8,3,6,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,8,4,1,3,5,6]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[6,1,7,3,2,8,4,5]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,2,1,7,3,8,4,5]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[5,8,2,1,3,4,6,7]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[4,2,5,1,8,3,6,7]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[7,4,2,8,3,1,5,6]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[7,4,2,8,3,5,1,6]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,7,8,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,2,7,8,4,3,5]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[10,1,9,5,6,7,8,2,3,4]=>[10,2,9,8,7,6,5,4,3,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[9,1,10,8,6,7,2,3,4,5]=>[10,2,9,8,7,6,5,4,3,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[8,1,9,10,7,2,3,4,5,6]=>[10,2,9,8,7,6,5,4,3,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[7,3,4,1,8,6,2,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,7,6,3,5,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,7,6,5,2,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,4,7,8,6,2,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,8,3,2,5,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,7,8,4,6,5]=>[1,3,2,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,2,3,5,7,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,1,4,6,2,8,3]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,3,1,4,7,8,2,5]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[9,8,7,6,5,1,3,4,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,6,1,4,5,3,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,7,1,5,4,6,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[9,8,7,1,5,6,4,3,2]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[9,8,1,6,7,5,4,3,2]=>[9,8,3,7,6,5,4,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[9,1,7,8,6,5,4,3,2]=>[9,2,8,7,6,5,4,3,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[4,5,7,1,8,6,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,3,8,6,5,2,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,3,8,6,5,1,7,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,4,7,3,1,2,6,8]=>[6,5,7,4,2,1,3,8]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[7,6,2,1,5,4,3,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[3,1,2,6,5,7,8,4]=>[3,2,1,8,5,6,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[7,3,2,6,1,4,8,5]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,2,5,6,8,4,1,7]=>[7,2,6,4,8,3,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,2,6,8,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,5,6,2,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,2,5,1,3,7,6,9,8]=>[5,4,3,2,1,7,6,9,8]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[4,2,5,1,3,6,8,7]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,2,5,1,3,8,9,6,7]=>[5,4,3,2,1,9,8,7,6]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[4,2,5,1,3,7,6,9,8,10]=>[5,4,3,2,1,7,6,9,8,10]=>[5,4,3,2,1,10,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[5,3,4,2,7,1,8,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,6,8,2,1,3,4,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[6,5,2,1,3,8,4,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,3,2,4,8,5,1,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,3,1,2,7,8,4,5]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,4,7,1,2,5,3,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,6,1,8,5,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,6,7,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,6,3,8,4,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,8,4,2,3,1,7,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,6,2,8,3,5,4]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,5,6,3,2,8,4]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,3,8,5,2,7,6]=>[6,2,3,8,5,1,7,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,8,5,4,7,2,3,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,5,6,4,3,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,3,8,6,5,1,7]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[3,1,4,5,8,6,2,7]=>[7,2,3,4,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,8,3,2,5,4,6,7]=>[1,8,4,3,6,5,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,7,3,2,8,4,6]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,7,8,1,3,2,4,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[8,2,4,1,6,7,3,5]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,7,3,6,2,4,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,4,8,3,6,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,6,1,3,5,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,7,5,8,4,3,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,1,2,7,8,5,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,2,7,5,3,4,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,1,2,8,7,5,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,4,7,2,6,3,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,2,5,7,8,3,6,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,3,4,2,1,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,4,6,2,3,7,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,5,8,1,7,2,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,3,4,2,7,8,1,5]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,6,3,7,8,2,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,3,4,7,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,8,6,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,6,2,7,8,3,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,5,6,2,7,1,8,3]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,5,6,2,1,7,8,3]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,5,6,2,1,7,3,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,8,7,2,3,1,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,1,6,7,3,2,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[2,5,1,8,3,7,4,6]=>[3,7,1,8,5,6,2,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[5,7,2,1,3,8,4,6]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[3,7,5,4,1,6,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,1,5,4,2,6,3,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,5,6,3,7,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,5,4,3,1,2,9,8]=>[7,6,5,4,3,2,1,9,8]=>[7,6,5,4,3,2,1,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[9,8,7,6,5,4,3,2,1,11,10]=>[9,8,7,6,5,4,3,2,1,11,10]=>[9,8,7,6,5,4,3,2,1,11,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]
[8,7,6,5,4,3,1,2,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[7,6,5,4,2,1,3,9,8]=>[7,6,5,4,3,2,1,9,8]=>[7,6,5,4,3,2,1,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[7,6,5,4,1,3,2,9,8]=>[7,6,5,4,3,2,1,9,8]=>[7,6,5,4,3,2,1,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[9,8,7,6,5,3,2,4,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,6,5,2,4,3,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,9,8,7,6,5,4,2,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[2,7,4,5,6,8,1,3]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[2,3,4,6,8,1,7,5]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,5,8,1,6,7,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,4,7,5,6,8,1,3]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[7,3,4,6,2,8,1,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,7,6,5,2,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,3,5,8,6,7,9,2,1]=>[9,8,3,6,5,4,7,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[2,5,4,8,6,7,3,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,4,1,6,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,2,1,7,6,3,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,7,3,6,4,1,8,5]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[7,2,1,8,5,6,4,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[3,6,5,1,4,8,2,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,3,5,4,8,1,2,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[2,5,1,4,6,3,8,7]=>[3,6,1,4,5,2,8,7]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,1,5,6,4,2,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,5,6,4,3,1,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,5,6,7,1,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,4,7,3,6,8,5]=>[2,1,5,8,3,6,7,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,3,7,6,4,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,7,6,4,2,8,1,5]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[8,6,1,4,3,7,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,7,5,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,5,3,7,8,6,4]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,1,4,7,6,8,2,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,1,3,7,6,5,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,4,1,6,7,5,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,1,4,2,6,5,7,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,4,3,7,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,1,4,3,2,6,7]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[5,6,4,3,8,2,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,7,4,1,3,2,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,8,1,4,3,2,5,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,8,4,5,3,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,3,1,8,6,5,7,2]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,3,2,7,5,1,8,6]=>[6,3,2,8,5,1,7,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[5,2,3,7,4,1,8,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[2,1,7,4,3,6,8,5]=>[2,1,8,5,4,6,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[7,1,2,4,5,6,8,3]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,8,7,1,4,5,6,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[8,7,1,3,4,5,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,3,1,4,6,7,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,7,2,5,4,6,8,3]=>[1,8,3,6,5,4,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,3,8,1,6,7,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,6,4,2,5,7,8,3]=>[1,8,5,4,3,6,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,5,3,4,1,7,8,2]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,6,3,4,1,7,8,2]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[2,5,3,1,4,7,8,6]=>[4,5,3,1,2,8,7,6]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[6,8,2,3,1,5,7,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,3,1,5,2,7,8,6]=>[5,3,2,4,1,8,7,6]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[5,2,3,1,4,7,8,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[7,2,1,3,5,6,8,4]=>[8,3,2,4,6,5,7,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,3,6,4,5,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,4,3,7,5,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,2,4,7,8,6,3,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,8,7,2,3,1,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[8,1,4,5,3,6,2,7]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,5,1,4,6,2,7]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,8,2,1,7,4,3,6]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[6,5,7,2,1,8,4,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,5,4,7,3,8,6,2]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,1,3,8,5,6,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,8,4,1,7,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,1,8,4,7,6,3,5]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,7,5,6,8,4,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,5,2,4,7,8,6,1]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[7,5,6,3,8,2,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,6,2,7,4,5,8,3]=>[1,8,3,6,5,4,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,2,6,1,5,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,4,1,6,2,5,7,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,3,4,5,1,6,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,3,2,5,4,7,6,9,8,11,10]=>[1,3,2,5,4,7,6,9,8,11,10]=>[1,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[8,4,2,7,6,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,1,2,6,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,7,6,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,2,1,5,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,1,6,2,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,9,6,8,4,5,2,3,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,9,5,8,4,6,2,3,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,9,5,8,3,6,2,4,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,8,4,7,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,9,5,8,3,6,4,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,9,5,8,6,3,4,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,9,8,5,6,3,4,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,9,5,8,4,7,2,3,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,9,4,8,3,6,2,5,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,9,5,8,2,6,1,4,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,8,2,7,1,5,4,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,9,5,8,3,6,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,10,6,9,4,7,2,5,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,8,7,4,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,9,5,8,6,3,1,4,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,10,6,9,4,7,5,2,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,9,8,5,3,6,4,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,10,6,9,7,4,5,2,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,5,8,6,3,4,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,10,9,6,7,4,5,2,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,8,4,5,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,4,2,5,1,3,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,5,3,7,6,4,8,1]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,1,5,7,6,4,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,1,6,5,4,7,2,8]=>[7,2,5,4,3,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,5,6,8,3,4,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[4,1,3,6,5,2,7,8]=>[6,2,3,5,4,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,6,2,4,5,7,1,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,6,2,5,4,7,1,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,5,1,7,6,4,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,6,1,4,5,7,2,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,3,1,6,5,2,7,8]=>[6,3,2,5,4,1,7,8]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[4,1,2,6,5,3,7,8]=>[6,2,3,5,4,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,6,1,3,5,2,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,6,4,2,5,7,1,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[3,4,7,6,5,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,5,2,7,1,3,6,8]=>[6,5,3,7,2,1,4,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,6,1,2,5,3,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[2,6,5,1,4,8,7,3]=>[4,8,5,1,3,7,6,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[5,8,4,7,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,7,1,3,5,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,8,1,3,5,7,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,3,2,7,4,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,3,1,5,4,7,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,1,2,5,3,7,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,2,8,3,4,6,7,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,2,7,1,6,4,8,3]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,5,2,6,1,3,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,3,5,8,6,1,7,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,1,3,6,7,4,2,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,2,8,3,6,7,5,1]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,1,7,8,5,6,2,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,7,1,8,5,2,4,6]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,2,8,6,7,1,3,5]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[6,1,2,4,7,3,5,8]=>[7,2,3,6,5,4,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,3,1,6,4,7,2,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,2,4,5,8,7,3,6]=>[1,2,7,4,8,6,3,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,4,7,5,8,6,2]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,3,7,8,6,4]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,2,8,1,6,5,7,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[5,6,1,4,8,3,2,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,6,4,1,7,2,8,5]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[7,8,9,3,2,1,4,5,10,6]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[5,2,6,3,7,8,4,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,4,1,3,7,8,6,5]=>[3,4,1,2,8,7,6,5]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,6,1,5,7,8,4,3]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[5,1,6,4,7,8,2,3]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,6,3,7,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,6,8,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,4,8,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,7,5,8,1,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,7,5,6,8,2,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,7,1,6,8,4,5,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,5,4,7,2,6,3,8]=>[1,7,5,6,3,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,5,8,3,1,7,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,4,7,5,8,3,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,8,7,3,5,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,7,8,6,2,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,3,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,6,3,5,4,2,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,8,1,6,5,7,2]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[5,8,7,1,4,6,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,2,5,1,3,4,8,7]=>[6,4,5,2,3,1,8,7]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[2,6,5,1,3,4,8,7]=>[4,6,5,1,3,2,8,7]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,6,5,1,2,7,3,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,6,4,1,2,7,3,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[8,1,5,6,2,4,3,7]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,5,1,2,7,3,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,4,6,1,3,2,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[5,7,1,4,3,2,6,8]=>[6,7,3,5,4,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[7,8,5,3,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,2,6,7,8,4,5,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,4,8,2,7,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,2,3,7,1,8,4,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[7,2,3,1,8,4,6,5]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,4,1,7,3,2,8,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[7,3,4,5,1,8,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,5,6,7,4,8,2,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,2,5,7,4,8,1]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,7,3,8,1,2,4,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,5,2,7,6,3,1,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,5,2,1,7,6,3,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[2,6,7,8,3,1,4,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[6,3,2,5,1,7,8,4]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,6,3,7,8,2,1,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,6,7,1,8,4,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,7,8,4,6,5,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,1,2,8,6,5,4]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,7,8,1,6,5,3,4]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,5,8,1,7,6,3,4]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[8,1,5,7,3,4,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,8,2,7,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,4,7,6,3,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,8,2,4,7,6,3,5]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,5,8,7,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,2,4,6,7,5,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,1,8,4,7,6,3]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,4,2,8,1,7,6,5]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[2,4,5,8,1,7,6,3]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,1,8,2,6,7,5,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[2,6,8,1,4,3,7,5]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,1,8,2,6,7,3,5]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,6,5,2,8,7,3,4]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,1,5,8,7,3,4]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[8,1,7,3,5,2,4,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,3,2,7,6,4,5]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,3,4,8,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,1,6,2,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,4,5,3,1,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,5,3,2,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,2,5,3,8,1,4,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,6,1,3,5,2,4,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,2,4,5,3,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,1,5,4,7,2,3,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,8,5,4,7,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,8,4,2,5,7,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,5,8,1,3,4,2,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,4,2,8,3,5,7,6]=>[1,5,3,8,2,6,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,5,4,8,7,2,6]=>[1,7,4,3,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,2,4,8,3,7,5]=>[1,8,3,6,7,4,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,5,4,2,6,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,2,8,6,4,7,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,5,2,7,4,8,3]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,6,7,4,2,8,3]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,8,1,5,2,3,7,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,8,5,4,6,2,7,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,4,6,2,8,3]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,4,1,6,2,7,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,5,1,7,2,8,3]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,8,1,3,7,6,2,5]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,5,3,1,2,8,7,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[6,4,2,3,1,8,7,5]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[6,5,2,1,3,8,7,4]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[7,6,1,8,2,5,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,2,3,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,7,8,1,2,4,3,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,7,6,8,3,5,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,6,4,2,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,5,7,4,1,3,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,6,1,8,3,5,2,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,1,6,8,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,7,1,8,3,2,5,6]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,8,3,6,1,5,2,7]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,7,8,6,4,5,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,8,6,4,5,1,7]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,4,3,6,2,5,1,7]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,6,8,7,4,3,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,2,6,8,7,5,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[5,7,4,2,1,8,6,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,6,5,7,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,6,1,8,5,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,6,3,8,1,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,8,1,6,3,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,8,3,6,2,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,8,2,3,5,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,6,8,2,5,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,8,2,5,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,4,5,8,3,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,8,2,4,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,6,2,7,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,4,2,7,1,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,2,4,1,7,3,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,5,1,6,2,4,8,3]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,2,5,7,1,6,8,3]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,4,8,5,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,2,3,8,7,1,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[2,5,4,7,6,1,3,8]=>[6,7,3,5,4,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[5,2,3,7,6,1,4,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,2,3,7,6,1,5,8]=>[6,3,2,7,5,1,4,8]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[4,2,7,3,5,1,6,8]=>[6,4,7,2,5,1,3,8]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[5,6,2,3,8,4,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,6,2,3,1,7,8,4]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,7,2,3,4,1,6,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[6,2,7,3,5,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,2,6,3,5,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,5,2,3,1,7,8,4]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[6,5,2,3,8,4,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,5,2,1,4,6,8,3]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[8,5,2,3,1,6,4,7]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,6,2,3,1,5,4,7]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,2,6,3,1,7,4,5]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,6,3,4,2,7,5,8]=>[1,7,5,4,3,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,5,2,7,3,4,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,2,4,5,6,8,3]=>[1,8,3,6,5,4,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,8,1,4,6,3,5]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,7,8,1,5,6,3,4]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[6,8,2,3,1,5,4,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[5,8,2,3,1,6,4,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[5,7,2,1,4,6,8,3]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,2,7,1,5,6,8,3]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,2,3,8,1,7,5,6]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,2,1,5,3,7,6,8]=>[5,3,2,4,1,7,6,8]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[5,1,3,8,4,6,7,2]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,3,4,2,7,6,8]=>[5,2,4,3,1,7,6,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[6,1,3,4,2,7,5,8]=>[7,2,5,4,3,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,2,1,3,5,8,4,6]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,8,7,2,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[10,9,11,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[1,9,8,10,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[2,8,7,9,6,5,4,3,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[3,7,2,8,1,4,5,6]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[5,2,3,7,4,6,1,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[2,5,3,7,4,6,1,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[2,6,7,3,4,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,2,7,3,4,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,8,4,5,2,1,6,7]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[2,7,6,3,4,5,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[2,8,7,5,1,3,4,6]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[4,5,1,2,3,9,6,7,8]=>[5,4,3,2,1,9,7,8,6]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[4,5,7,2,8,3,6,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[9,7,5,3,1,8,6,4,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,6,3,8,5,2,7,4,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,5,2,9,6,3,7,4,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,5,1,8,4,7,3,6,2]=>[9,8,3,7,6,5,4,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[8,4,7,3,6,2,9,5,1]=>[9,8,6,5,4,3,7,2,1]=>[9,8,6,5,4,3,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[7,3,8,4,6,2,9,5,1]=>[9,8,6,5,4,3,7,2,1]=>[9,8,6,5,4,3,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[9,4,7,2,5,8,3,6,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,4,6,1,8,3,5,7,2]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[8,3,5,7,2,9,4,6,1]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[7,2,8,3,9,4,5,6,1]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[8,3,7,2,9,4,5,6,1]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[5,8,3,7,2,9,4,6,1]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[9,3,6,5,4,7,1,8,2]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[8,2,9,3,6,5,4,7,1]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[9,2,7,4,5,6,3,8,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,8,6,4,2,9,7,5,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,7,4,1,8,5,2,9,6,3]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[9,6,3,8,5,2,10,7,4,1]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[9,5,1,7,3,10,6,2,8,4]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[10,6,2,7,3,8,4,9,5,1]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[10,5,8,3,6,1,9,4,7,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,4,7,2,10,5,8,3,6,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,5,7,2,8,3,9,4,6,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,3,10,5,7,2,9,4,6,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,3,9,4,7,2,10,5,6,1]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[10,4,6,8,2,9,3,5,7,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,4,5,6,7,1,8,2,9,3]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[8,2,9,3,10,4,5,6,7,1]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[9,3,8,2,10,4,5,6,7,1]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[9,2,7,6,5,4,10,3,8,1]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[10,3,7,6,5,4,8,1,9,2]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[9,2,10,3,7,6,5,4,8,1]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[5,2,1,3,6,7,8,4]=>[8,3,2,4,5,6,7,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,6,5,7,2,8,3,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,5,2,6,1,8,4,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,1,5,2,7,8,4,3]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,5,7,2,8,4,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,4,6,2,8,7,3]=>[1,8,5,4,3,7,6,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,4,6,2,8,3,7]=>[1,7,5,4,3,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,4,8,2,3,7]=>[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,2,1,5,8,4,7,3]=>[8,3,2,6,7,4,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,5,6,8,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,7,5,1,4,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,5,7,3,6,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,2,6,4,5,1,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,3,7,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,6,2,7,1,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,2,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,3,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,2,3,6,4,7,5]=>[8,2,3,4,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,2,3,5,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,5,3,7,8,1,6,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,4,2,8,1,6,7,5]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[8,3,4,1,5,7,6,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,3,7,5,1,6,2,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[3,5,2,8,6,7,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,3,7,4,2,8,6,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[7,4,8,2,3,5,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,2,8,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,3,5,2,7,8,1]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,1,6,3,5,7,2,8]=>[7,2,5,4,3,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,2,5,8,6,1,4,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,3,6,1,5,7,8,2]=>[8,4,5,2,3,6,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,5,4,1,2,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,3,1,4,6,7,8,2]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,6,7,1,3,5,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,6,1,3,4,7,2,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[2,5,3,7,8,4,6,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,6,2,1,3,7,8,5]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[3,6,2,4,1,7,5,8]=>[5,7,3,4,1,6,2,8]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,2,6,7,4,8,5,1]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,3,8,4,5,2,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,3,4,6,2,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,3,2,7,5,8,4,1]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,2,7,1,4,5,3,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,2,6,1,5,7,3,8]=>[7,4,5,2,3,6,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[6,5,2,7,4,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,5,7,3,1,4,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,7,4,3,1,5,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,1,6,7,8,4,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,5,6,2,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,4,5,2,7,1,8,3]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[3,7,5,6,2,1,8,4]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,7,6,3,8,4,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,4,1,2,7,8,3,5]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,4,1,3,5,2,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,1,8,3,4,6,2,7]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,5,8,2,3,7,1,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[7,3,4,8,2,5,1,6]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,8,1,5,4,2,3,7]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,7,2,5,1,6,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,5,4,7,2,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,2,4,6,5,8,1,7]=>[7,2,3,5,4,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,5,4,8,7,1,6,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,5,2,1,6,3,4,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,3,1,7,4,2,5,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,7,2,1,5,3,6,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,8,5,3,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,8,1,5,6,4,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,3,6,4,1,5,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,6,1,4,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,2,6,3,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,4,1,2,3,6,7,5]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,6,4,2,1,8,3,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,8,1,3,2,7,5,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,7,3,6,4,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,2,4,3,8,1,5,6]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[2,5,4,6,1,3,8,7]=>[5,6,3,4,1,2,8,7]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[5,8,2,6,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,5,3,8,1,4,7]=>[6,7,4,3,8,1,2,5]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[6,1,2,4,3,5,7,8]=>[6,2,3,5,4,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,5,8,2,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,6,8,4,3,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,6,5,3,8,2,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,2,4,3,5,8,7]=>[6,2,3,5,4,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,6,1,3,7,8,5,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,1,5,2,6,7,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,5,6,3,8,7,2,4]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,3,2,6,8,7,1,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,3,5,2,7,1,4,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[8,5,2,6,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,8,7,1,4,2,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[6,4,5,3,1,8,7,2]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[8,5,1,2,3,6,7,4]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,8,6,1,5,4,7,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[8,3,2,6,1,5,7,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,8,6,4,7,1,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,8,7,5,4,3,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,4,7,1,3,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,1,4,7,6,2,5,8]=>[6,2,3,7,5,1,4,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,3,4,1,6,2,7,8]=>[6,4,3,2,5,1,7,8]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[7,3,1,6,5,2,4,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,1,5,2,4,6,3,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,1,4,5,2,7,3,8]=>[7,2,5,4,3,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,1,5,8,2,7,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,2,3,6,4,5,8]=>[7,2,3,4,6,5,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,3,1,8,5,4,7,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,1,3,8,7,4,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,8,4,6,5,1,7,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[7,4,1,3,6,5,2,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,7,2,8,1,3,6,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,4,1,2,6,3,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[6,5,1,4,7,3,2,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[2,7,8,4,1,3,6,5]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[2,4,6,5,7,8,1,3]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[2,4,6,7,5,8,1,3]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[2,4,6,3,7,8,1,5]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[2,4,5,6,8,7,1,3]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,4,5,6,8,3,7,1]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,4,5,6,3,8,1,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[2,3,4,6,8,5,1,7]=>[7,2,3,6,8,4,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,2,8,3,4,1,6,7]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[3,6,4,1,2,7,8,5]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[4,1,7,3,8,6,2,5]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,4,1,2,5,3,7,6]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,5,2,7,6,8,4,3]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,7,6,8,3,1,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,8,2,7,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,2,8,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,5,2,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,8,2,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,2,1,6,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,2,1,6,5,8,4,7]=>[3,2,1,7,5,8,4,6]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,6,4,8,5,7,3,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,3,1,4,5,8,2,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,4,8,5,2,1,7,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[4,8,7,1,3,2,6,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[5,8,7,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,1,8,7,6,2,5]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[1,3,5,6,8,7,2,4]=>[1,7,8,4,6,5,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,7,5,4,1,6,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[8,1,5,7,4,2,6,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,8,7,3,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,1,3,2,8,5,7]=>[5,7,3,4,1,8,2,6]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,6,5,8,3,1,4,7]=>[6,7,5,8,3,1,2,4]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[6,7,8,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,2,8,4,5,7,1,6]=>[7,2,8,4,5,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,1,8,2,4,5,3,7]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,3,6,4,2,7,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,3,8,4,7,6,2,5]=>[1,7,8,4,6,5,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,3,7,5,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,4,7,8,5,1,3]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,4,3,7,6,1,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,6,3,7,1,4,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,1,2,8,7,6,4,5]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[8,5,4,1,2,3,7,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,3,2,1,6,4,7,5]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,3,8,4,1,7,5,6]=>[5,2,8,4,1,7,6,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,6,1,3,2,7,8,5]=>[5,8,3,4,1,6,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[6,7,2,5,8,4,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,1,7,8,2,5,6,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,4,6,7,1,5,8,2]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[3,4,5,7,8,1,6,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,8,7,4,3,5,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,5,8,1,3,7,6]=>[5,6,3,8,1,2,7,4]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,7,8,6,5,3,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,3,1,5,8,4,2,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[2,8,3,5,6,1,4,7]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[1,3,6,4,2,7,5,8]=>[1,5,7,4,2,6,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,3,7,5,8,1,4,6]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,2,8,5,6,1,4,7]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[7,2,5,8,1,4,6,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[4,7,5,8,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,5,8,1,2,3,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,4,7,5,2,8,1,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[4,3,2,5,7,8,1,6]=>[7,3,2,4,8,6,1,5]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[2,4,7,5,8,3,1,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[2,5,4,7,3,8,1,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,7,8,4,2,1,6,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[8,5,4,7,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,5,4,8,7,6,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,4,5,8,1,6,7]=>[6,2,3,4,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,6,8,4,2,7,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,8,3,7,6,2,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,4,7,6,3,8,2,5]=>[1,7,8,5,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,5,1,7,2,8,4]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[7,4,1,6,2,8,5,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,3,6,8,2,4,7,5]=>[1,5,8,7,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,4,3,8,2,5]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,3,1,6,5,2,8,4]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,5,4,1,6,2,7,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,7,2,8,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,6,2,1,5,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,2,7,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,3,8,7,5,6,4]=>[2,1,3,8,7,6,5,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,1,7,3,6,5,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,4,7,3,8,5,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,4,5,6,8,10,7,9]=>[1,2,3,4,5,6,9,10,7,8]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[4,8,1,6,3,7,2,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[8,5,4,1,6,3,7,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,7,6,2,4,8,5,3]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,3,2,4,8,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,6,8,5,4,3,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[2,8,4,6,3,5,1,7]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[2,7,8,3,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,1,4,6,5,2,7]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,7,5,4,1,8,3,6]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[4,6,1,8,5,3,2,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,8,5,2,1,6,4,7]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[5,1,4,8,2,6,3,7]=>[7,2,5,8,3,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,5,8,1,3,7,6,2]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,6,7,1,4,3,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,4,7,8,6,3,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,5,2,6,3,4,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,6,1,2,7,4,5]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[3,8,6,1,2,5,7,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,7,6,2,1,8,5,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[4,3,7,6,1,8,5,2]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,6,3,2,7,1,5,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,1,5,4,7,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,2,5,4,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,6,2,4,8,5,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,6,8,7,3,1,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,7,5,2,6,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,5,6,2,8,1,4,7]=>[6,7,4,3,8,1,2,5]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[8,9,10,4,5,6,2,3,1,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,4,5,6,10,2,3,1,7]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,9,10,4,5,2,3,6,1,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,4,5,10,2,3,6,1,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,4,5,2,3,6,10,1,7]=>[10,9,7,6,5,4,3,8,2,1]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[8,9,10,4,5,6,2,1,3,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,4,5,6,10,2,1,3,7]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,9,10,4,5,2,6,1,3,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,4,5,10,2,6,1,3,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,4,5,2,6,10,1,3,7]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[8,4,5,9,10,2,6,1,3,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,4,5,9,2,6,10,1,3,7]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[8,9,10,4,5,2,1,3,6,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,4,5,10,2,1,3,6,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,4,5,2,10,1,3,6,7]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,9,4,5,2,1,3,6,10,7]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[8,9,10,4,2,5,6,1,3,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,4,10,2,5,6,1,3,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,4,2,5,6,10,1,3,7]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[8,4,9,10,2,5,6,1,3,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,4,9,2,5,6,10,1,3,7]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[8,9,10,4,2,5,1,3,6,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,4,10,2,5,1,3,6,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,4,2,5,10,1,3,6,7]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,9,4,2,5,1,3,6,10,7]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[4,8,9,10,2,5,6,1,3,7]=>[9,10,8,7,6,5,4,3,1,2]=>[9,10,8,7,6,5,4,3,1,2]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[6,1,8,2,4,3,5,7]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,6,8,2,5,3,4,7]=>[1,7,8,4,6,5,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,5,2,7,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,2,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,8,7,1,2,6,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,5,6,4,3,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[8,7,3,5,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,3,5,2,1,4,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,3,5,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,2,7,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,3,8,5,2,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[8,7,1,4,5,6,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,1,3,8,5,6,2,7]=>[7,2,3,8,5,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,2,8,3,1,6,7,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,7,8,6,3,2,5,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,2,4,5,6,1,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,2,8,1,5,7,4,6]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,4,6,7,2,1,5,8]=>[6,5,7,4,2,1,3,8]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[2,6,7,1,4,3,8,5]=>[4,8,6,1,5,3,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[5,7,6,2,1,8,3,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,2,5,3,8,6,7,1]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,2,7,4,8,5,6,1]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,5,1,6,3,8,4]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,8,9,10,5,6,7,2,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,10,2,5,6,3,4,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[5,8,9,10,2,6,7,3,4,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[2,8,9,10,3,6,7,4,5,1]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[5,6,9,10,2,7,8,3,4,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[2,6,9,10,3,7,8,4,5,1]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,8,9,10,4,5,6,1,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[4,8,9,10,5,6,7,1,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,10,3,5,6,1,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[5,8,9,10,3,6,7,1,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[3,8,9,10,4,6,7,1,5,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[5,6,9,10,3,7,8,1,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[3,6,9,10,4,7,8,1,5,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,10,1,5,6,2,4,3]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[5,8,9,10,1,6,7,2,4,3]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[4,8,9,10,1,6,7,2,5,3]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[5,6,9,10,1,7,8,2,4,3]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[4,6,9,10,1,7,8,2,5,3]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,8,9,10,3,4,6,1,5,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,8,9,10,3,4,7,1,5,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[3,8,9,10,4,5,7,1,6,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,7,9,10,3,4,8,1,5,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[3,7,9,10,4,5,8,1,6,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,10,1,4,6,2,5,3]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[6,8,9,10,1,4,7,2,5,3]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[4,8,9,10,1,5,7,2,6,3]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[6,7,9,10,1,4,8,2,5,3]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[4,7,9,10,1,5,8,2,6,3]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[6,7,8,10,3,4,9,1,5,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[3,7,8,10,4,5,9,1,6,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,7,8,10,1,4,9,2,5,3]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[4,7,8,10,1,5,9,2,6,3]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[6,3,8,5,4,2,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,4,6,1,3,5,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,5,3,8,7,4,6,2]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,3,8,7,4,6,2]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,5,3,8,7,4,1,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,8,3,5,1,2,7,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,2,7,4,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,2,8,3,7,1,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[7,8,5,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,5,1,6,4,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,8,3,1,2,7,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[4,6,8,3,2,1,7,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[4,6,8,3,5,1,2,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,4,6,3,7,5,2,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,5,2,6,8,7,3,1]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,7,6,3,8,5,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,7,4,5,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,3,1,8,4,5,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,2,8,7,4,5,6,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,2,4,3,7,5,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,4,2,5,1,7,8,3]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[3,8,2,1,5,7,6,4]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[1,3,2,8,7,4,6,5]=>[1,3,2,8,7,6,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,5,2,8,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,2,7,3,8,6,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,6,3,7,8,1,2,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[8,3,5,4,7,1,2,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,2,5,4,1,7,8,3]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,1,5,6,3,8,7,2]=>[8,2,5,4,3,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,5,1,6,3,2,4,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,7,4,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,5,4,6,7,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,8,5,1,3,7,6,4]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,4,5,8,3,7,6,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,6,4,1,8,2,7,3]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,4,5,1,3,8,7,2]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[6,1,3,5,4,8,2,7]=>[7,2,5,4,3,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,3,8,7,2,5,6,4]=>[1,5,8,7,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,4,1,8,3,7,6]=>[4,6,3,1,8,2,7,5]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[5,1,4,8,3,7,6,2]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,1,2,7,6,5,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,8,3,2,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,8,7,3,4,6,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,1,2,6,5,8,7,9]=>[4,3,2,1,6,5,8,7,9]=>[4,3,2,1,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[6,5,3,1,2,4,8,7,9]=>[6,5,4,3,2,1,8,7,9]=>[6,5,4,3,2,1,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]
[8,7,5,3,1,2,4,6,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[7,5,3,1,2,4,6,9,8]=>[7,6,5,4,3,2,1,9,8]=>[7,6,5,4,3,2,1,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[5,3,1,2,4,7,6,9,8]=>[5,4,3,2,1,7,6,9,8]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[6,5,3,1,2,4,8,7,10,9]=>[6,5,4,3,2,1,8,7,10,9]=>[6,5,4,3,2,1,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[8,7,5,3,1,2,4,6,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[10,9,7,5,3,1,2,4,6,8]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[5,3,1,2,4,6,8,7]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[8,5,7,3,1,2,4,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,3,1,2,4,6,8,9]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[3,1,2,8,7,5,4,6]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[5,3,1,2,4,9,7,6,8]=>[5,4,3,2,1,9,8,7,6]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[7,5,3,1,2,4,6,9,8,10]=>[7,6,5,4,3,2,1,9,8,10]=>[7,6,5,4,3,2,1,10,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[5,3,1,2,4,7,6,9,8,10]=>[5,4,3,2,1,7,6,9,8,10]=>[5,4,3,2,1,10,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,4,3,8,5,7,2,6]=>[1,7,3,8,5,6,2,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,7,1,5,2,8,4,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,5,3,7,6,4,8,2]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,8,1,3,6,2,7,5]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,7,3,4,8,6,5,1]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,8,2,4,7,3,6,5]=>[1,8,3,6,7,4,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,1,6,5,8,3,4]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[6,2,3,8,1,5,7,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,5,7,4,8,3,6,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,5,6,2,4,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,5,6,7,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,5,7,3,6,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,3,7,1,2,8,5,6]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[2,7,6,4,3,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,8,6,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,1,6,2,5,3,7]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[1,8,4,2,5,7,3,6]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,3,1,2,4,6,7]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,4,8,5,2,3,6,7]=>[1,6,8,5,4,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,8,5,2,3,7,6]=>[1,6,8,5,4,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,4,2,6,8,3,5]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,5,8,7,2,4,3,6]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,7,3,5,4,6]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,1,3,2,5,4,6]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,7,4,2,8,1,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,1,6,8,7,2,3,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,7,5,6,2,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,4,3,6,7,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,5,2,8,4,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,4,3,2,7,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,7,3,5,8,2,4]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,3,7,6,4,8,2,5]=>[1,7,8,5,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,4,8,7,3,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,1,8,7,3,5,4,6]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,1,5,8,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,8,5,7,4,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,5,1,4,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,3,7,2,4,6,5]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,6,7,3,5,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,6,7,3,5,8,1,4]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[5,3,1,6,4,8,2,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[2,5,6,7,1,4,8,3]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[4,7,5,3,2,8,1,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[4,7,5,2,8,6,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,6,7,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,1,2,7,4,3,6]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[6,3,1,8,2,4,5,7]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,6,3,7,8,1,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,1,8,4,5,2,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[2,1,4,7,5,8,6,3]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[7,6,2,4,8,3,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,8,1,4,3,7,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,1,4,2,7,5,6,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,8,9,2,3,10,4,5,6]=>[1,10,9,8,5,6,7,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[7,1,8,9,10,2,3,4,5,6]=>[10,2,9,8,7,6,5,4,3,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[7,8,1,9,10,2,3,4,5,6]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[7,8,9,1,2,10,3,4,5,6]=>[10,9,8,4,5,7,6,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[7,8,9,1,10,2,3,4,5,6]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[1,8,9,10,11,12,2,3,4,5,6,7]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[8,6,3,5,2,1,7,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,3,1,2,5,4,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[5,8,6,4,7,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,1,8,7,3,4,6]=>[3,7,1,8,6,5,2,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[7,2,4,3,8,6,1,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,7,6,5,4,3,2,9,8]=>[1,7,6,5,4,3,2,9,8]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[6,8,4,3,5,1,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,4,7,3,6,8,2,5]=>[1,7,8,4,5,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,1,4,6,8,2,5]=>[7,8,3,4,5,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,4,7,3,6,8,1,5]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[8,5,7,6,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,5,6,1,8,4,3]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[1,2,6,7,4,5,8,3]=>[1,2,8,6,5,4,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,5,2,8,7,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,3,6,8,1,4,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,4,1,8,3,2,5,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,8,1,4,2,7,3,6]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,3,1,6,8,7,4,5]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[6,4,8,2,1,7,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,3,1,8,7,5,6,4]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,5,6,7,2,4,3,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,3,7,1,2,5,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,6,4,1,5,3,7]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,5,7,3,6,2,4,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,7,4,5,1,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,6,5,3,8,2,4,7]=>[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,6,1,2,4,8,3,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[8,7,4,5,1,3,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,1,2,7,4,3,6]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,1,8,7,2,5,3,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,6,3,8,4,1,7,5]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,2,4,6,1,8,7,5]=>[5,2,3,8,1,7,6,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,6,7,4,1,2,5,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,4,7,5,8,2,3,6]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,4,7,3,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,7,5,4,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,5,7,2,6,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,1,5,7,4,6,8,3]=>[2,1,8,6,5,4,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,3,5,7,8,1,6,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,4,7,5,3,6,8,1]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,1,7,2,4,6,3,5]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,4,7,8,6,3,5]=>[1,2,7,8,6,5,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,7,8,3,5,1,6]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[1,3,6,2,5,8,4,7]=>[1,4,7,2,5,8,3,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,3,6,8,2,4,7]=>[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,8,1,2,6,3,7,5]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[5,8,1,2,6,3,7,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,1,2,6,5,7,8,3]=>[8,2,3,5,4,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,7,5,2,3,8,6,4]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,4,7,3,5,2,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,3,6,1,7,2,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[2,6,1,8,3,7,4,5]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[8,4,2,1,3,7,5,6]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[2,5,1,7,6,8,3,4]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[5,3,1,8,2,4,7,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,1,8,3,2,4,7,6]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,8,5,7,3,1,4,6]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[2,6,8,7,3,1,4,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[7,4,2,1,3,8,5,6]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[7,2,1,3,8,5,4,6]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,1,7,3,8,6,4,5]=>[2,1,8,4,7,6,5,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,7,5,3,2,4,8,6]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,7,6,5,8,3]=>[1,8,3,6,5,4,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,7,3,4,1,5,6]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[5,7,6,2,3,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,5,7,6,2,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,1,8,7,5,2,6,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,5,6,8,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,3,1,5,4,7,6]=>[4,8,3,1,6,5,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,8,4,1,5,2,7,6]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[5,1,7,8,3,2,6,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,6,2,4,3,7,5]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,8,3,1,6,2,7,5]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[2,8,3,1,6,4,7,5]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[6,2,7,1,5,8,4,3]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[1,7,8,9,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,6,7,8,9,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,5,6,7,8,9,4,3,2]=>[1,9,8,7,5,6,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,4,5,6,7,8,9,3,2]=>[1,9,8,4,5,6,7,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,8,9,10,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,7,6,8,9,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,7,8,9,10,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,6,5,7,8,9,4,3,2]=>[1,9,8,7,5,6,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,6,7,8,9,10,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,5,4,6,7,8,9,3,2]=>[1,9,8,4,5,6,7,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,5,6,7,8,9,10,4,3,2]=>[1,10,9,8,5,6,7,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,4,5,6,7,8,9,10,3,2]=>[1,10,9,4,5,6,7,8,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[4,8,5,1,3,2,6,7]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[5,4,3,1,2,7,6,8]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,1,6,5,2,3,7,8]=>[6,2,5,4,3,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[7,1,5,2,3,6,4,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,1,6,3,7,2,5,8]=>[6,2,7,4,5,1,3,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,6,1,2,8,3,7,5]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[4,1,3,6,7,2,5,8]=>[6,2,3,7,5,1,4,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,6,7,4,3,1,5,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[6,5,3,7,2,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[2,3,6,7,1,5,4,8]=>[5,2,7,6,1,4,3,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,7,5,8,1,3,6,4]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[5,1,6,7,3,2,4,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,6,1,4,7,2,3,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,2,5,7,8,6,3,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,7,4,5,3,8]=>[1,2,7,6,5,4,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,8,4,6,3,5]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,5,2,1,7,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,8,6,7,1,5,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,3,2,4,7,1,6,5]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,3,2,8,6,1,5,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,5,8,2,6,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,8,2,7,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,1,2,6,5,8,3]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,2,7,4,6,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,4,1,2,3,6,8,5]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,4,8,6,3,2,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[8,4,6,7,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,8,5,1,2,7,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,1,3,6,8,5,2,7]=>[7,2,3,6,8,4,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,3,5,7,1,2,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,8,5,3,2,4,6,7]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,3,4,2,5,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,3,4,2,5,7]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,7,5,3,4,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,5,3,4,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,6,8,4,2,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,6,4,3,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[9,8,7,6,5,2,1,3,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,6,4,7,2,5,1,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[5,1,7,8,4,2,3,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,8,2,1,6,7,5,4]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,8,3,1,7,5,6,4]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[8,5,6,2,1,4,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[9,10,6,4,2,1,3,5,8,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,7,8,4,2,1,3,6,5,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,10,4,2,1,3,6,8,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,4,2,1,3,7,6,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,8,5,6,2,1,4,3,7,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,5,6,2,1,4,3,8,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,7,5,8,2,1,4,6,3,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,5,10,2,1,4,6,8,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,5,10,2,1,4,7,6,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,6,7,8,2,1,5,4,3,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,6,7,10,2,1,5,4,8,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,6,9,10,2,1,5,7,4,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,10,2,1,6,5,4,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,8,6,3,4,2,1,5,7,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,6,3,4,2,1,5,8,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,7,8,3,4,2,1,6,5,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,10,3,4,2,1,6,8,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,3,4,2,1,7,6,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,8,5,3,6,2,4,1,7,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,5,3,6,2,4,1,8,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,7,5,3,8,2,4,6,1,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,5,3,10,2,4,6,8,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,5,3,10,2,4,7,6,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,6,7,3,8,2,5,4,1,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,6,7,3,10,2,5,4,8,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,6,9,3,10,2,5,7,4,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,3,10,2,6,5,4,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,8,4,5,6,3,2,1,7,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,4,5,6,3,2,1,8,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,7,4,5,8,3,2,6,1,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,4,5,10,3,2,6,8,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,4,5,10,3,2,7,6,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,6,4,7,8,3,5,2,1,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,6,4,7,10,3,5,2,8,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,6,4,9,10,3,5,7,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,4,9,10,3,6,5,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,5,6,7,8,4,3,2,1,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,5,6,7,10,4,3,2,8,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,5,6,9,10,4,3,7,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,5,8,9,10,4,6,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[12,10,8,6,4,2,1,3,5,7,9,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,6,4,2,1,3,5,7,10,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,10,6,4,2,1,3,5,8,7,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,12,6,4,2,1,3,5,8,10,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,11,12,6,4,2,1,3,5,9,8,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,7,8,4,2,1,3,6,5,9,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,8,4,2,1,3,6,5,10,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,7,10,4,2,1,3,6,8,5,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,12,4,2,1,3,6,8,10,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,11,7,12,4,2,1,3,6,9,8,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,8,9,10,4,2,1,3,7,6,5,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,8,9,12,4,2,1,3,7,6,10,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,8,11,12,4,2,1,3,7,9,6,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,11,12,4,2,1,3,8,7,6,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,8,5,6,2,1,4,3,7,9,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,5,6,2,1,4,3,7,10,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,10,5,6,2,1,4,3,8,7,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,12,5,6,2,1,4,3,8,10,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,11,12,5,6,2,1,4,3,9,8,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,7,5,8,2,1,4,6,3,9,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,5,8,2,1,4,6,3,10,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,7,5,10,2,1,4,6,8,3,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,5,12,2,1,4,6,8,10,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,11,7,5,12,2,1,4,6,9,8,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,8,9,5,10,2,1,4,7,6,3,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,8,9,5,12,2,1,4,7,6,10,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,8,11,5,12,2,1,4,7,9,6,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,11,5,12,2,1,4,8,7,6,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,6,7,8,2,1,5,4,3,9,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,6,7,8,2,1,5,4,3,10,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,6,7,10,2,1,5,4,8,3,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,6,7,12,2,1,5,4,8,10,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,11,6,7,12,2,1,5,4,9,8,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,8,6,9,10,2,1,5,7,4,3,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,8,6,9,12,2,1,5,7,4,10,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,8,6,11,12,2,1,5,7,9,4,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,6,11,12,2,1,5,8,7,4,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,7,8,9,10,2,1,6,5,4,3,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,7,8,9,12,2,1,6,5,4,10,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,7,8,11,12,2,1,6,5,9,4,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,7,10,11,12,2,1,6,8,5,4,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,9,10,11,12,2,1,7,6,5,4,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,8,6,3,4,2,1,5,7,9,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,6,3,4,2,1,5,7,10,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,10,6,3,4,2,1,5,8,7,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,12,6,3,4,2,1,5,8,10,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,11,12,6,3,4,2,1,5,9,8,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,7,8,3,4,2,1,6,5,9,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,8,3,4,2,1,6,5,10,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,7,10,3,4,2,1,6,8,5,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,12,3,4,2,1,6,8,10,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,11,7,12,3,4,2,1,6,9,8,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,8,9,10,3,4,2,1,7,6,5,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,8,9,12,3,4,2,1,7,6,10,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,8,11,12,3,4,2,1,7,9,6,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,11,12,3,4,2,1,8,7,6,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,8,5,3,6,2,4,1,7,9,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,5,3,6,2,4,1,7,10,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,10,5,3,6,2,4,1,8,7,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,12,5,3,6,2,4,1,8,10,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,11,12,5,3,6,2,4,1,9,8,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,7,5,3,8,2,4,6,1,9,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,5,3,8,2,4,6,1,10,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,7,5,3,10,2,4,6,8,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,5,3,12,2,4,6,8,10,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,11,7,5,3,12,2,4,6,9,8,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,8,9,5,3,10,2,4,7,6,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,8,9,5,3,12,2,4,7,6,10,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,8,11,5,3,12,2,4,7,9,6,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,11,5,3,12,2,4,8,7,6,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,6,7,3,8,2,5,4,1,9,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,6,7,3,8,2,5,4,1,10,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,6,7,3,10,2,5,4,8,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,6,7,3,12,2,5,4,8,10,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,11,6,7,3,12,2,5,4,9,8,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,8,6,9,3,10,2,5,7,4,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,8,6,9,3,12,2,5,7,4,10,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,8,6,11,3,12,2,5,7,9,4,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,6,11,3,12,2,5,8,7,4,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,7,8,9,3,10,2,6,5,4,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,7,8,9,3,12,2,6,5,4,10,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,7,8,11,3,12,2,6,5,9,4,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,7,10,11,3,12,2,6,8,5,4,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,9,10,11,3,12,2,7,6,5,4,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,8,4,5,6,3,2,1,7,9,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,8,4,5,6,3,2,1,7,10,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,10,4,5,6,3,2,1,8,7,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,12,4,5,6,3,2,1,8,10,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,11,12,4,5,6,3,2,1,9,8,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,7,4,5,8,3,2,6,1,9,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,7,4,5,8,3,2,6,1,10,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,7,4,5,10,3,2,6,8,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,4,5,12,3,2,6,8,10,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,11,7,4,5,12,3,2,6,9,8,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,8,9,4,5,10,3,2,7,6,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,8,9,4,5,12,3,2,7,6,10,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,8,11,4,5,12,3,2,7,9,6,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,11,4,5,12,3,2,8,7,6,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,6,4,7,8,3,5,2,1,9,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,6,4,7,8,3,5,2,1,10,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,6,4,7,10,3,5,2,8,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,6,4,7,12,3,5,2,8,10,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,11,6,4,7,12,3,5,2,9,8,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,8,6,4,9,10,3,5,7,2,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,8,6,4,9,12,3,5,7,2,10,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,8,6,4,11,12,3,5,7,9,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,6,4,11,12,3,5,8,7,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,7,8,4,9,10,3,6,5,2,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,7,8,4,9,12,3,6,5,2,10,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,7,8,4,11,12,3,6,5,9,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,7,10,4,11,12,3,6,8,5,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,9,10,4,11,12,3,7,6,5,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,5,6,7,8,4,3,2,1,9,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,5,6,7,8,4,3,2,1,10,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,5,6,7,10,4,3,2,8,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,5,6,7,12,4,3,2,8,10,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,11,5,6,7,12,4,3,2,9,8,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,8,5,6,9,10,4,3,7,2,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,8,5,6,9,12,4,3,7,2,10,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,8,5,6,11,12,4,3,7,9,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,5,6,11,12,4,3,8,7,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,7,5,8,9,10,4,6,3,2,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,7,5,8,9,12,4,6,3,2,10,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,7,5,8,11,12,4,6,3,9,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,7,5,10,11,12,4,6,8,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,9,5,10,11,12,4,7,6,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,6,7,8,9,10,5,4,3,2,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,6,7,8,9,12,5,4,3,2,10,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,6,7,8,11,12,5,4,3,9,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,6,7,10,11,12,5,4,8,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,6,9,10,11,12,5,7,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[2,7,4,1,5,8,3,6]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,1,6,4,7,8,3,5]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,7,8,3,4,2,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,7,5,3,8,2,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,6,4,7,8,5,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,4,5,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,1,8,4,6,7,3]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[5,2,8,4,6,7,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,5,8,3,4,2,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,3,5,8,4,6,7,2]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,4,5,8,2,1,6,7]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[8,2,7,6,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,7,3,2,1,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,8,2,7,1,5,6]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[7,2,6,1,4,8,3,5]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,8,1,2,4,6,3,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,8,3,4,5,1,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,1,8,3,4,2,5,7]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,5,1,2,4,3,8,6]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,6,8,1,4,2,3,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,4,3,7,8,5,6,1]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,1,7,6,3,4,5,8]=>[2,1,7,6,5,4,3,8]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,3,5,2,1,8,4,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,1,5,3,8,2,4,7]=>[7,2,6,4,8,3,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,3,6,8,5,1,7,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,2,4,8,6,1,7,5]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,1,3,8,4,5,7,6]=>[2,1,3,8,5,6,7,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,1,2,8,5,4,7,6]=>[3,2,1,8,6,5,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,1,3,7,8,4,6,5]=>[2,1,3,8,7,6,5,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,1,3,8,4,7,6,5]=>[2,1,3,8,5,7,6,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,1,2,8,4,5,7,6]=>[3,2,1,8,5,6,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,2,8,7,5,4,6,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,7,2,3,8,1,5]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[3,2,6,5,7,8,1,4]=>[7,2,8,4,5,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,2,7,5,6,8,1,4]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,1,8,7,4,6,5,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,1,5,8,4,7,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,4,6,8,5,7,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,5,1,6,4,3,7]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[2,4,7,1,8,3,6,5]=>[4,6,8,1,7,2,5,3]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[6,1,5,4,2,3,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,4,5,1,2,8,3,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[8,4,1,5,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,6,3,5,2,4,7]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,6,2,5,3,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,6,5,2,1,8,3,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,8,4,3,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,2,1,5,3,4,7]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[2,5,3,8,6,7,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,2,6,5,1,8,4,7]=>[5,2,7,4,1,8,3,6]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[7,4,5,8,1,6,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,8,1,6,7,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,1,8,4,6,7,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,5,3,8,1,7,2,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,3,7,1,6,2,4,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,1,4,6,5,7,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,5,6,4,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,1,5,3,7,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,3,6,8,1,5,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,6,3,7,8,1,4,5]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[6,3,8,7,2,1,5,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,2,5,6,3,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,2,8,6,3,1,5,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,2,4,5,8,6,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,8,4,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,3,6,8,5,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,8,5,4,1,3,6]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,4,5,2,8,1,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,4,2,8,1,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,3,2,8,4,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,3,6,8,4,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,5,4,8,3,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,8,3,6,1,4,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,4,5,2,8,3,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,1,6,7,4,5,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,1,5,4,7,6,2,8]=>[7,2,4,3,6,5,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,3,6,8,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,3,2,4,6,8,7]=>[5,2,4,3,1,6,8,7]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[8,4,2,5,1,7,3,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,4,2,5,7,3,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,7,8,4,2,3,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,5,2,8,3,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,5,2,4,3,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[6,5,3,4,1,8,2,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,4,5,3,8,1,2,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[5,6,4,8,3,1,2,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[7,2,4,6,3,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,8,3,7,6,1,5,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[5,4,2,6,8,7,3,1]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,7,2,5,8,6,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,6,5,3,8,1,7,2]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[2,4,8,7,6,1,5,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[3,2,8,7,4,6,5,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,6,5,1,4,3,7]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[4,8,5,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,6,5,7,1,3,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[3,8,4,7,2,1,6,5]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[4,8,5,1,7,6,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,1,7,6,2,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,4,6,2,5,7,1,8]=>[7,4,5,2,3,6,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,7,5,2,6,8,3,4]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,7,2,4,6,3,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,8,2,1,3,4,7,5]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,4,8,3,6,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,8,5,1,7,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,8,1,3,6,7,4]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,3,2,7,4,5,8,1]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,4,3,8,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,1,8,7,4,5,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,2,1,8,7,3,5,4]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,2,6,8,5,7,1,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,6,4,3,2,7,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,3,4,7,8,2,6,5]=>[1,6,3,8,7,2,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,4,3,8,7,2,6]=>[1,7,4,3,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,5,8,4,3,6,7]=>[1,2,6,8,5,3,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,2,6,4,3,7]=>[1,7,8,4,6,5,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[10,9,8,6,4,2,1,3,5,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,8,7,6,4,2,1,3,5,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,7,9,6,4,2,1,3,8,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,6,4,2,1,3,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,8,6,5,4,2,1,3,7,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,6,5,4,2,1,3,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,8,5,7,4,2,1,6,3,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,5,9,7,4,2,1,6,8,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,5,7,4,2,1,6,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,8,7,6,5,4,2,1,3,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,7,9,6,5,4,2,1,8,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,6,9,8,5,7,2,1,4,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,8,6,4,3,2,1,5,7,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,6,4,3,2,1,5,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,8,7,6,4,3,2,1,5,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,7,9,6,4,3,2,1,8,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,8,6,3,5,2,4,1,7,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,6,3,5,2,4,1,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,8,3,7,5,2,4,6,1,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,3,9,7,5,2,4,6,8,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,3,7,5,2,4,6,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,8,7,6,3,5,2,4,1,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,7,9,6,3,5,2,4,8,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,3,8,6,5,2,7,4,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,6,3,5,2,4,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,8,6,5,4,3,2,1,7,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,8,5,7,4,3,2,6,1,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,5,9,7,4,3,2,6,8,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,5,7,4,3,2,6,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,8,4,7,6,3,5,2,1,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,4,9,7,6,3,5,2,8,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,4,9,6,8,3,5,7,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,4,7,6,3,5,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,7,9,6,5,4,3,2,8,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,6,9,8,5,4,3,7,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,5,9,8,7,4,6,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[12,11,10,8,6,4,2,1,3,5,7,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,9,8,6,4,2,1,3,5,7,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,11,8,6,4,2,1,3,5,10,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,9,8,6,4,2,1,3,5,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,8,7,6,4,2,1,3,5,9,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,8,7,6,4,2,1,3,5,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,7,9,6,4,2,1,3,8,5,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,7,11,9,6,4,2,1,3,8,10,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,7,9,6,4,2,1,3,8,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,9,8,7,6,4,2,1,3,5,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,11,8,7,6,4,2,1,3,10,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,8,11,10,7,9,4,2,1,3,6,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,9,8,7,6,4,2,1,3,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,8,6,5,4,2,1,3,7,9,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,8,6,5,4,2,1,3,7,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,9,8,6,5,4,2,1,3,7,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,11,8,6,5,4,2,1,3,10,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,9,8,6,5,4,2,1,3,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,8,5,7,4,2,1,6,3,9,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,8,5,7,4,2,1,6,3,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,5,9,7,4,2,1,6,8,3,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,5,11,9,7,4,2,1,6,8,10,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,5,9,7,4,2,1,6,8,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,9,8,5,7,4,2,1,6,3,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,11,8,5,7,4,2,1,6,10,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,5,10,8,7,4,2,1,9,6,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,9,8,5,7,4,2,1,6,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,8,7,6,5,4,2,1,3,9,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,8,7,6,5,4,2,1,3,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,7,9,6,5,4,2,1,8,3,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,7,11,9,6,5,4,2,1,8,10,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,7,9,6,5,4,2,1,8,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,6,9,8,5,7,2,1,4,3,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,6,11,9,8,5,7,2,1,4,10,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,6,11,8,10,5,7,2,1,9,4,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,6,9,8,5,7,2,1,4,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,9,8,7,6,5,4,2,1,3,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,11,8,7,6,5,4,2,1,10,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,8,11,10,7,6,5,9,2,1,4,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,7,11,10,9,6,8,5,2,1,4,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,9,8,7,6,5,4,2,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,8,6,4,3,2,1,5,7,9,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,8,6,4,3,2,1,5,7,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,9,8,6,4,3,2,1,5,7,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,11,8,6,4,3,2,1,5,10,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,9,8,6,4,3,2,1,5,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,8,7,6,4,3,2,1,5,9,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,8,7,6,4,3,2,1,5,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,7,9,6,4,3,2,1,8,5,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,7,11,9,6,4,3,2,1,8,10,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,7,9,6,4,3,2,1,8,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,9,8,7,6,4,3,2,1,5,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,11,8,7,6,4,3,2,1,10,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,8,11,10,7,9,4,3,2,1,6,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,9,8,7,6,4,3,2,1,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,8,6,3,5,2,4,1,7,9,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,8,6,3,5,2,4,1,7,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,9,8,6,3,5,2,4,1,7,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,11,8,6,3,5,2,4,1,10,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,9,8,6,3,5,2,4,1,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,8,3,7,5,2,4,6,1,9,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,8,3,7,5,2,4,6,1,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,3,9,7,5,2,4,6,8,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,3,11,9,7,5,2,4,6,8,10,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,3,9,7,5,2,4,6,8,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,9,8,3,7,5,2,4,6,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,11,8,3,7,5,2,4,6,10,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,3,10,8,7,5,2,4,9,6,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,9,8,3,7,5,2,4,6,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,8,7,6,3,5,2,4,1,9,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,8,7,6,3,5,2,4,1,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,7,9,6,3,5,2,4,8,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,7,11,9,6,3,5,2,4,8,10,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,7,9,6,3,5,2,4,8,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,9,3,8,6,5,2,7,4,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,11,3,8,6,5,2,7,4,10,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,3,8,10,6,5,2,7,9,4,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,9,3,8,6,5,2,7,4,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,9,8,7,6,3,5,2,4,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,11,8,7,6,3,5,2,4,10,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,8,11,10,7,6,3,5,2,9,4,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,3,9,7,6,8,2,5,4,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,9,8,7,6,3,5,2,4,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,8,6,5,4,3,2,1,7,9,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,8,6,5,4,3,2,1,7,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,9,8,6,5,4,3,2,1,7,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,11,8,6,5,4,3,2,1,10,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,9,8,6,5,4,3,2,1,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,8,5,7,4,3,2,6,1,9,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,8,5,7,4,3,2,6,1,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,5,9,7,4,3,2,6,8,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,5,11,9,7,4,3,2,6,8,10,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,5,9,7,4,3,2,6,8,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,9,8,5,7,4,3,2,6,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,11,8,5,7,4,3,2,6,10,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,5,10,8,7,4,3,2,9,6,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,9,8,5,7,4,3,2,6,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,8,4,7,6,3,5,2,1,9,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,8,4,7,6,3,5,2,1,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,4,9,7,6,3,5,2,8,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,4,11,9,7,6,3,5,2,8,10,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,4,9,7,6,3,5,2,8,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,4,9,6,8,3,5,7,2,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,4,11,9,6,8,3,5,7,2,10,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,4,11,6,10,8,3,5,7,9,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,4,9,6,8,3,5,7,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,9,8,4,7,6,3,5,2,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,11,8,4,7,6,3,5,2,10,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,8,11,10,4,7,6,3,5,9,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,4,10,7,9,6,3,8,5,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,9,8,4,7,6,3,5,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,8,7,6,5,4,3,2,1,9,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,8,7,6,5,4,3,2,1,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,7,9,6,5,4,3,2,8,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,7,11,9,6,5,4,3,2,8,10,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,7,9,6,5,4,3,2,8,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,6,9,8,5,4,3,7,2,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,6,11,9,8,5,4,3,7,2,10,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,6,11,8,10,5,4,3,7,9,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,6,9,8,5,4,3,7,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,5,9,8,7,4,6,3,2,1,11]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,5,11,9,8,7,4,6,3,2,10,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,5,11,8,10,7,4,6,3,9,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,5,11,7,10,9,4,6,8,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,10,5,9,8,7,4,6,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,11,8,7,6,5,4,3,2,10,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,8,11,10,7,6,5,4,3,9,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,7,11,10,9,6,5,4,8,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,6,11,10,9,8,5,7,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[3,5,6,2,4,7,8,1]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[3,5,6,7,2,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,5,7,6,8,2,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,5,7,2,6,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,5,2,7,6,8,4,1]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,5,7,4,2,6,8,1]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[3,5,4,7,2,6,8,1]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,4,5,7,2,6,8,1]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,4,5,7,2,8,6,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,5,4,7,8,2,6,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,5,4,7,2,8,6,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,2,5,7,4,8,6,1]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,5,7,4,2,8,6,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[3,5,7,8,4,2,6,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,3,5,7,8,4,6,1]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,5,2,7,8,6,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,5,7,8,2,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,7,8,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,2,5,6,7,3,8,1]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,6,1,4,3,5,2,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,1,8,4,3,5,2,7]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,6,4,8,2,3,7]=>[7,2,6,4,8,3,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,1,4,2,5,3,6,7]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,8,4,1,5,3,6,7]=>[4,8,6,1,5,3,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[8,4,1,3,5,2,6,7]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,1,8,3,5,2,6,7]=>[6,2,8,4,5,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,3,1,2,5,4,6,7]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,1,8,2,5,4,6,7]=>[4,2,8,1,6,5,7,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,2,5,1,8,7,6,3]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,2,4,8,1,7,6,3]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,3,2,4,6,8,1,5]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,4,8,6,7,2,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,8,1,2,5,3,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[3,5,6,8,2,1,4,7]=>[6,7,5,8,3,1,2,4]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[8,2,5,4,1,3,7,6]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[2,4,5,8,6,3,1,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,4,8,2,3,1,7,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[4,7,5,8,2,3,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,6,7,5,1,8,3,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,7,3,6,5,8,2,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,3,4,2,6,7,1,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,5,3,8,6,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,1,8,2,6,5,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,6,7,5,2,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,8,7,2,4,3,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,1,2,8,6,7,3,4]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,5,7,8,6,1,4,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[7,2,6,8,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,7,6,8,2,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,6,7,2,1,5,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,7,6,2,4,3,8,5]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,6,2,4,5,3,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,7,1,6,2,3,4,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,2,5,8,3,4,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[5,6,8,7,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,3,6,5,8,4,7]=>[2,1,3,7,5,8,4,6]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,8,6,5,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,6,5,7,4,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,5,2,7,4,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,5,2,8,4,3,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[7,5,8,3,4,2,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,8,5,2,4,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,7,2,4,1,8,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[5,1,2,8,6,3,7,4]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,5,7,2,4,3,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,1,8,2,6,5,7,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,4,7,8,5,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,5,7,8,4,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,8,3,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,1,5,7,2,8,3]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,5,8,4,6,3,7,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,1,6,5,2,7,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,8,1,5,2,7,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,5,8,2,3,7,6,1]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,6,2,7,4,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,3,1,8,2,6,7,5]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[4,8,1,3,2,5,7,6]=>[5,8,3,4,1,6,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,7,5,3,8,6,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,3,8,1,4,7,6]=>[5,6,3,8,1,2,7,4]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,2,5,8,1,3,7,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[8,1,2,4,3,5,7,6]=>[8,2,3,5,4,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,4,3,8,1,5,7,6]=>[5,3,2,8,1,6,7,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[3,1,7,4,8,6,5,2]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,5,3,2,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[2,7,3,8,5,1,6,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[8,7,3,2,5,6,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,1,8,2,6,5,4,7]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[7,6,2,8,1,4,5,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[2,3,8,4,1,5,7,6]=>[5,2,8,4,1,6,7,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[8,4,2,3,1,5,7,6]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[8,2,3,4,1,5,7,6]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,1,6,2,4,8,3,5]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,7,8,1,4,3,6,5]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[6,5,8,1,3,2,4,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[2,1,8,5,3,4,6,7]=>[2,1,8,6,5,4,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,4,1,3,2,5,6,7]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,6,1,2,3,5,4,7]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,1,5,2,4,6,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,8,6,3,1,5,4,7]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[5,7,2,8,4,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,6,3,8,1,4,7]=>[6,7,4,3,8,1,2,5]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[7,4,5,6,8,1,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,8,1,4,5,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,1,8,4,6,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,7,8,5,6,4,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,1,7,4,5,3,6]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[7,3,6,2,5,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,6,2,3,5,8,4,7]=>[1,7,3,4,5,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,6,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,8,4,5,1,7,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[4,6,5,7,8,1,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,5,8,6,4,7,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,3,2,1,7,8,4,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[8,4,1,3,6,7,2,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,2,3,5,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,2,5,3,4,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,2,5,3,4,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[2,6,5,3,4,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,3,4,8,1,7,2,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,1,3,4,8,7,2,6]=>[7,2,4,3,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,5,3,4,8,7,2,6]=>[1,7,4,3,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,3,8,4,7,6,2]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,3,8,1,4,7,6,2]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,3,5,8,1,7,6,2]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,6,5,4,8,1,2,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[3,6,5,4,8,2,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[3,5,2,4,8,7,6,1]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,5,3,6,8,4,1,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,6,2,5,1,7,8,3]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[2,3,6,5,8,4,1,7]=>[7,2,6,4,8,3,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,3,1,7,4,8,6,5]=>[3,2,1,8,5,7,6,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[2,3,8,7,6,4,1,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,6,3,7,4,1,5,8]=>[6,7,3,5,4,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[7,5,2,3,1,6,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,8,3,6,4,2,7,5]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,7,4,8,5,3,6]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,1,7,3,2,5,4,6]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,8,5,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,2,8,1,3,6,7,5]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[8,1,2,5,7,4,6,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,6,3,1,2,5,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,4,1,3,7,2,5,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,2,5,3,6,1,4,7]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[3,7,5,1,4,6,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,8,7,4,1,5,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,4,7,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,2,4,7,8,3,5]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,4,6,5,7,1,8,3]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[4,2,6,7,8,5,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,2,4,7,8,5,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,5,2,1,7,8,6,4]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[4,2,7,8,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,2,7,8,6,4,5,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,8,1,2,6,5,3,7]=>[7,8,3,4,6,5,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[7,1,6,3,2,4,8,5]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,8,1,2,3,7,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[7,4,1,3,6,8,5,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,8,3,2,6,5,4]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,5,1,6,4,3,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[5,2,7,1,4,6,3,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[6,3,8,5,7,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,3,8,5,7,1,6]=>[7,3,2,8,5,6,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[2,8,3,1,4,6,5,7]=>[4,8,3,1,5,7,6,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[4,5,7,6,1,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,7,1,6,5,8,2,4]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[7,4,3,6,8,2,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,5,4,7,6,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,4,6,8,7,3,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,5,1,3,8,7,2]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,4,6,2,1,8,7,3]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[3,5,4,1,2,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[5,3,8,1,4,2,6,7]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[5,3,8,1,4,2,7,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[1,4,7,5,8,6,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,5,7,6,3,4,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,2,6,1,4,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,4,5,1,8,3,7,6]=>[4,6,3,1,8,2,7,5]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[7,2,8,5,3,4,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,5,3,1,7,8,2]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[7,3,5,6,4,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,4,7,6,8,5,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,3,1,7,8,9,4,5,6]=>[3,2,1,9,8,7,6,5,4]=>[3,2,1,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[2,1,6,7,8,9,3,4,5]=>[2,1,9,8,7,6,5,4,3]=>[2,1,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,6,3,4,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,6,2,1,5,8,3,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,6,7,2,3,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,3,5,8,7,4,1,6]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,3,5,8,7,4,6,1]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,5,3,7,8,1,2,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[2,3,5,8,1,6,4,7]=>[5,2,7,8,1,6,3,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,7,4,5,8,3,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,1,5,4,2,7,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,8,5,6,3,1,4,7]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[4,8,2,6,1,5,7,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[2,3,7,8,1,5,4,6]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[5,2,6,7,8,3,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,2,7,8,3,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,3,7,5,8,4,6,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,7,8,5,1,4,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,6,7,1,8,4,3]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[8,5,3,6,4,2,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,3,7,8,5,4,6,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,7,8,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,1,2,3,6,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,2,8,7,4,6,5,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,4,8,7,3,6,2]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,3,1,8,7,5,6,2]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,3,2,7,6,1,5,8]=>[6,3,2,7,5,1,4,8]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[7,2,6,5,3,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,3,8,2,7,4,6,5]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,7,1,6,4,3,5]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[4,3,2,8,1,7,5,6]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[7,5,4,1,6,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,6,5,3,2,4,8,7]=>[1,6,5,4,3,2,8,7]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,7,2,5,1,6,8]=>[6,4,7,2,5,1,3,8]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[5,1,4,3,2,6,8,7]=>[5,2,4,3,1,6,8,7]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[8,3,7,5,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,8,7,5,2,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,6,1,8,5,2,7]=>[7,4,6,2,8,3,1,5]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,4,8,7,3,6,2,5]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,5,7,6,3,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,6,7,5,1,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,6,5,1,4,7,8,2]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,6,7,3,1,5,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,4,1,8,7,3,6,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,2,4,7,5,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,2,5,1,8,7,3,4]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,2,6,1,5,8,7,4]=>[4,2,8,1,5,7,6,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[6,2,3,5,7,4,1,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,6,3,8,4,7,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,5,2,4,7,3,6]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,5,8,1,4,2,3,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,3,4,8,5,6,2,7]=>[1,7,3,8,5,6,2,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,7,1,8,6,5,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,3,8,5,6,7,2,4]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,2,4,1,5,7,8,3]=>[8,4,5,2,3,6,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[5,8,4,1,3,6,7,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,7,2,3,8,1,4,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,2,7,4,8,1,5,6]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,2,8,1,7,4,6,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,5,4,7,3,1,8,6]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,6,3,1,2,5,7,8]=>[5,6,4,3,1,2,7,8]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[7,4,6,8,3,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,4,7,3,1,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,2,1,5,4,8,6]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,5,6,4,8,1,3,7]=>[6,7,4,3,8,1,2,5]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[5,4,1,6,2,3,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,3,6,5,2,4,7,8]=>[1,5,6,4,2,3,7,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,4,5,1,2,8,7,3]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,4,1,2,7,6,3,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[5,8,7,3,1,2,4,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,7,8,1,4,5,3,6]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,1,2,8,7,3,6,5]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,1,2,4,3,8,7,5]=>[8,2,3,5,4,7,6,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,7,8,1,2,4,6,5]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[7,3,4,1,2,6,8,5]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[8,4,3,1,2,6,5,7]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[3,8,2,7,4,5,1,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[8,6,2,3,5,4,1,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,6,1,3,5,4,7]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,4,3,7,2,5,6,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,3,1,7,4,5,2,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,2,4,5,1,7,3,6]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,8,2,4,5,1,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,8,1,7,5,6,2]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,4,3,7,1,5,6,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,3,4,7,2,6,5,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,1,3,7,6,4,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,7,1,4,5,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,3,6,1,2,5,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,7,6,2,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,2,3,6,1,5,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,7,1,3,4,6,5]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[5,1,8,4,2,3,7,6]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,2,4,7,3,1,6,5]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[8,2,7,6,3,1,4,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,8,1,4,7,3,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,7,2,6,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,2,7,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,2,6,7,5,4,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,1,7,5,6,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,2,4,7,6,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,7,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,2,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,4,7,3,6,5,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,1,7,6,4,5,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,2,7,6,4,5,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,4,7,3,6,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,1,9,8,7,6,5,4]=>[3,2,1,9,8,7,6,5,4]=>[3,2,1,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[3,4,2,1,9,8,7,6,5]=>[4,3,2,1,9,8,7,6,5]=>[4,3,2,1,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[4,5,3,2,1,9,8,7,6]=>[5,4,3,2,1,9,8,7,6]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[5,6,4,3,2,1,9,8,7]=>[6,5,4,3,2,1,9,8,7]=>[6,5,4,3,2,1,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]
[6,7,5,4,3,2,1,9,8]=>[7,6,5,4,3,2,1,9,8]=>[7,6,5,4,3,2,1,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[2,8,1,5,3,7,6,4]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,8,2,4,7,5,6,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,3,8,4,7,1,6,5]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,8,2,3,5,6,4,7]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,6,2,3,8,4,5]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,3,7,6,4,5]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,8,6,2,5,4]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,2,3,7,4,1,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,2,8,3,7,6,1,5]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,3,5,6,4,8,2,7]=>[1,7,5,4,3,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,7,8,5,2,4,6]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,6,1,8,2,7,5,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,3,5,2,8,4,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,6,3,5,2,8,4,7]=>[1,7,5,4,3,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,8,6,3,7,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,5,8,1,3,7,2]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[6,3,5,1,8,4,7,2]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[2,5,4,8,6,3,1,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[2,5,4,8,6,3,7,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,2,5,4,8,6,3,7]=>[1,2,7,4,8,6,3,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,4,5,8,2,1,7,3]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[5,3,4,1,2,6,8,7]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,4,3,5,2,8,6,7]=>[1,5,3,4,2,8,7,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,4,8,2,6,1,7]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,6,4,5,1,2,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,3,5,1,8,6,2,7]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[3,5,4,8,1,6,2,7]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,4,8,5,6,1,2,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[3,4,8,5,6,2,1,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[3,5,4,8,1,6,7,2]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,4,3,1,5,8,6,7]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,7,6,2,5,4,8,3]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,6,1,7,4,3,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,7,2,1,5,6,8,4]=>[4,8,3,1,6,5,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,1,5,6,4,2,7,8]=>[6,2,5,4,3,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,3,4,1,6,5,7,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,1,6,4,3,5,2,7]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,3,7,8,2,6,4,5]=>[1,5,8,7,2,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,6,5,3,8,7,4]=>[2,1,8,5,4,7,6,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,4,2,5,6,7,8,9,10,1]=>[10,3,2,4,5,6,7,8,9,1]=>[10,3,2,9,8,7,6,5,4,1]=>[[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.]
[3,7,5,6,4,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,1,4,3,7,5,8,2]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,8,6,4,5,2,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,8,6,2,3,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,6,8,5,3,7,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,7,2,8,6,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,7,4,5,1,6,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,6,8,1,2,5,7,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,6,8,5,1,3,7,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[3,7,4,5,2,8,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,7,8,4,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,7,2,1,6,8,3]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,5,1,6,8,3,7,2]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,3,5,4,6,1,2,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,7,4,5,2,6,8,3]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,5,8,4,6,2,7]=>[7,2,5,8,3,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,2,6,3,4,1,5,7]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,6,5,8,2,1,3,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,4,8,3,5,6,2,7]=>[1,7,8,4,5,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,7,4,2,3,6,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,7,9,8,1,3,4,2,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[4,3,1,8,5,7,2,6]=>[7,3,2,8,5,6,1,4]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[7,3,2,4,8,1,6,5]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,7,2,4,5,8,1,6]=>[7,8,3,4,5,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,2,7,4,6,1,8,5]=>[6,2,8,4,5,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,3,2,4,6,1,7,5]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,3,2,4,5,7,1,6]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,4,6,2,1,3,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,6,7,2,4,1,8,5]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[8,4,7,2,3,5,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,6,7,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,2,8,6,1,5,7]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[4,1,6,3,2,5,7,8]=>[5,2,6,4,1,3,7,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[5,7,1,8,4,3,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,8,7,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,6,3,1,5,2,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,1,5,2,4,7,8]=>[5,6,3,4,1,2,7,8]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,7,6,2,5,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,4,5,1,2,7,6,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,2,3,8,7,1,6,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,5,2,4,1,3,8,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,2,6,8,5,1,3,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,6,5,4,1,3,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,3,4,1,6,7,5]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,2,3,4,1,9,6,8,7]=>[5,4,3,2,1,9,7,8,6]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[3,2,1,9,4,6,7,8,5]=>[3,2,1,9,5,8,7,6,4]=>[3,2,1,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[7,4,3,8,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,5,1,4,3,8,7,2]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,7,6,2,5,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,3,2,4,5,8,1,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[2,6,4,5,8,3,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[3,7,4,8,6,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,5,2,8,1,4,6]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,5,8,7,4,2,3,6]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,4,5,8,6,3]=>[1,8,3,7,5,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,8,7,2,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,2,7,5,3,4,8]=>[1,7,3,6,5,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,5,2,4,8,3,7]=>[1,7,5,4,3,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,8,4,2,5,6]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,2,4,7,5,8,3]=>[1,8,3,6,5,4,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,2,7,4,3,8,5]=>[1,8,3,6,5,4,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,2,3,6,4,7]=>[1,7,8,4,5,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,3,6,7,1,4,8]=>[6,7,3,4,5,1,2,8]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[6,4,1,5,7,2,3,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,4,1,5,7,3,8,2]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,2,7,3,8,5,6,4]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,1,6,3,8,2,5]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,5,7,4,3,8,6,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,3,1,4,5,8,6]=>[4,8,3,1,5,6,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[6,5,8,3,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,3,1,7,6,5,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,2,6,7,5,3,4,8]=>[1,2,7,6,5,4,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,8,7,4,5,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,4,5,6,8,2,7,1]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,5,6,7,3,4,2,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,8,5,2,1,7,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,6,7,8,2,4,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,7,8,2,1,3,5,6]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[5,7,8,3,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,2,3,1,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,4,2,1,9,8,7,6]=>[5,4,3,2,1,9,8,7,6]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[6,5,3,4,2,1,9,8,7]=>[6,5,4,3,2,1,9,8,7]=>[6,5,4,3,2,1,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]
[7,6,4,5,3,2,1,9,8]=>[7,6,5,4,3,2,1,9,8]=>[7,6,5,4,3,2,1,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[4,5,2,7,8,6,1,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,3,5,8,7,2,6,4]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,4,1,8,5,7,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,1,6,7,2,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,7,2,1,5,8,4]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,5,6,1,3,8,7,4]=>[4,8,5,1,3,7,6,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[3,8,5,7,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,1,4,5,2,8,3]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,2,5,6,1,3,8,4]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,4,1,2,5,8,3,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,6,3,5,7,1,8,2]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,7,3,5,2,6,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,3,5,4,7,1,8,6]=>[6,2,4,3,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,8,4,1,5,7,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,6,2,3,7,5,4]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,8,9,6,1,2,3,4,10,5]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[8,9,7,5,6,1,2,3,10,4]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[7,8,9,5,1,2,3,4,10,6]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[2,8,3,6,4,1,7,5]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[5,1,8,7,3,2,6,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,5,3,4,8,2,1,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[5,4,8,7,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,5,1,2,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[5,2,7,6,8,3,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,5,2,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,7,4,5,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,3,4,2,8,5,6,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,3,6,5,8,2,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[8,2,7,4,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,8,4,5,3,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,8,2,7,4,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,2,8,4,7,5,6,1]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,6,2,7,4,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,2,3,5,6,7,8,9,10,1]=>[10,3,2,4,5,6,7,8,9,1]=>[10,3,2,9,8,7,6,5,4,1]=>[[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.]
[1,7,8,4,3,6,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,3,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,4,5,8,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,1,7,2,4,3,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,5,7,3,8,1,4,6]=>[6,7,8,4,5,1,2,3]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[8,3,5,2,1,6,7,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[2,6,4,7,1,8,5,3]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[1,6,5,7,3,8,2,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,3,7,6,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,4,2,3,8,7,5,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,5,1,3,8,4,2,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,1,4,2,7,8,3,5]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,5,1,3,7,8,4,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,1,3,2,7,8,6,4]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,8,2,4,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,4,2,3,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,8,7,3,2,4,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,3,2,6,8,4,7]=>[7,2,4,3,5,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,7,1,4,6,8,2,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,4,3,7,6,2,8,5]=>[1,6,3,8,5,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,2,5,7,3,8,4]=>[1,8,3,6,5,4,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,3,8,2,5,7,6]=>[1,5,3,8,2,6,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,3,6,4,2,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,7,2,4,8,3,5]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,2,8,4,1,5,6]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[5,3,4,1,7,8,6,2]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,7,6,5,8,2,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,3,8,4,5,7,1,6]=>[7,2,8,4,5,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,1,8,3,2,6,5,7]=>[5,2,8,4,1,7,6,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,2,6,8,4,3,5,7]=>[1,2,7,8,6,5,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,6,3,1,8,4,5]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,8,4,1,3,7,2,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[3,4,2,1,6,8,5,7]=>[4,3,2,1,7,8,5,6]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[8,1,3,5,6,4,7,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,4,7,1,5,6,2,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,8,2,6,5,3,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,2,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,4,7,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,2,3,1,6,7,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,8,6,3,5,1,7,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[8,3,2,6,4,1,7,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,4,1,5,3,6,7,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,5,1,4,6,7,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,1,3,4,6,7,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,6,2,5,4,7,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,4,6,5,2,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,7,4,2,5,3,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,2,5,1,4,7,6]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,4,5,1,2,6,7,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,1,5,3,2,6,7,4]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,5,2,4,6,7,3]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,2,6,4,1,3,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[7,1,3,5,2,8,6,4]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,4,7,1,3,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,4,3,2,1,7,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,8,5,4,3,7,6]=>[2,1,8,6,5,4,7,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,2,8,5,4,1,3,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[6,4,8,5,3,2,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[9,10,6,7,4,5,2,3,1,8]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,5,4,6,2,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,4,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,7,3,4,8,1,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[5,2,4,7,8,1,3,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,5,9,3,6,1,2,4,7]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,7,1,5,8,3,6,2,4]=>[9,8,3,7,6,5,4,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[9,7,5,4,1,3,8,2,6]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,9,4,5,10,1,2,3,6,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,6,10,1,3,7,8,2,4,5]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[9,10,6,7,4,5,1,2,3,8]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,6,4,10,3,7,1,2,5,8]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,1,8,9,6,7,4,5,2,3]=>[10,2,9,8,7,6,5,4,3,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[10,8,6,1,4,9,3,7,2,5]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[10,8,6,5,4,1,3,9,2,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,8,7,6,5,4,3,1,2,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[4,8,5,6,1,2,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,6,8,7,1,4,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[1,7,8,5,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,8,1,5,2,7,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[5,3,8,1,2,6,7,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,2,3,6,4,1,7,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,3,7,5,8,6,1,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,8,5,1,2,4,7,6]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[1,3,6,4,8,2,7,5]=>[1,6,8,4,7,2,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,7,6,2,8,5,3,4]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,6,4,7,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,6,2,8,1,7,3,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,8,4,5,1,3,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,3,8,1,4,6,7]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,6,8,3,2,4,5,7]=>[1,7,8,5,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[9,6,5,4,3,2,1,7,8]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[10,7,6,5,4,3,2,1,8,9]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[9,8,5,4,3,2,1,6,7]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,6,5,2,4,3,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,5,3,7,4,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[8,5,4,2,6,3,7,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,3,2,6,4,7,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,6,5,8,2,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,6,5,8,2,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,6,4,8,2,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,5,4,8,2,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,6,8,4,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,5,7,4,2,8,3]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,4,8,5,6,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,7,4,8,5,1,3]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[3,2,7,5,8,4,6,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,5,8,6,4,3,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,4,2,5,7,1,8,3]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[2,7,5,4,6,8,1,3]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[8,1,4,7,3,5,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,7,2,4,5,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,4,5,7,3,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[9,3,8,2,4,5,6,7,1]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[5,6,3,4,2,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[2,5,7,4,6,8,1,3]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[2,5,6,4,1,3,8,7]=>[5,6,4,3,1,2,8,7]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[4,6,1,3,5,7,2,8]=>[7,5,3,4,2,6,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,2,7,5,8,1,6,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,3,6,8,5,2,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[4,5,3,2,1,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,6,5,8,1,7,4,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[4,1,6,8,5,2,3,7]=>[7,2,6,8,5,3,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,5,2,8,6,7,1,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,5,2,8,6,7,3,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,5,8,6,2,4,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,5,1,6,4,8,3,7]=>[3,7,1,5,4,8,2,6]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,2,4,5,8,6,1,7]=>[7,2,3,4,8,6,1,5]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,5,2,1,3,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,2,3,6,8,5,1,7]=>[7,3,2,6,8,4,1,5]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[4,5,1,3,2,8,6,7]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,4,5,8,6,1,7,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,4,5,8,6,1,2,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,4,1,3,7,8,2,5]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,3,1,2,5,4,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[7,3,1,2,5,4,8,6]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,2,6,4,1,3,7,5]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,5,8,2,4,3,7,6]=>[1,6,8,4,5,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,3,7,8,2,6,5,1]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[3,8,5,1,2,6,7,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,4,7,8,3,6,5,1]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[5,4,7,8,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,1,3,2,5,7,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,4,8,5,7,2,3,6]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,7,3,2,4,5,6]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,2,7,3,4,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,2,7,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,3,2,8,7,1,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,1,6,7,8,3,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,5,6,3,7,2,4,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,7,4,2,3,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,6,7,3,4,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,6,1,7,3,4,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,5,1,7,4,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,2,3,5,7,6,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,8,5,2,3,1,6,7]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[5,4,8,3,1,2,6,7]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[8,4,7,3,2,5,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,5,1,7,3,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,2,7,3,8,1,4,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,4,2,6,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,8,3,6,5,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,7,5,1,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,5,2,6,8,7,4,1]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,3,6,8,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,2,3,7,5,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,3,7,5,1,2,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,2,5,4,8,6,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,2,3,8,7,4,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,2,8,4,6,5,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,5,8,1,2,7,6,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[1,4,3,6,8,5,2,7]=>[1,7,3,6,8,4,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,2,8,5,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,3,5,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,7,6,4,1,3,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,3,7,5,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,7,1,4,2,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,2,5,6,3,7,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,5,7,4,6,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,7,1,5,6,3,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,5,7,1,6,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,7,1,4,8,3,6,5]=>[3,8,1,6,7,4,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,7,1,5,6,8,4,3]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,3,1,8,7,4,6,5]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[4,6,8,2,1,5,3,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[5,6,8,4,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,7,3,6,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,5,8,2,6,1,7,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[3,4,5,7,2,1,6,8]=>[6,5,3,7,2,1,4,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,5,6,8,3,2,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[4,5,7,2,6,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,6,5,7,2,3,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,6,7,2,5,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,3,6,7,4,8,1,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,2,7,8,3,6,5,1]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[4,2,7,8,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,3,7,8,1,6,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,5,7,8,4,2,1,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,6,7,3,2,8,1,5]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[4,6,5,3,7,8,1,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,6,2,4,7,8,3,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,6,3,2,8,4,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,6,2,8,3,4,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[3,7,4,8,1,6,5,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,2,4,8,6,7,3,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,2,6,4,8,7,3,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,4,7,8,6,5,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,5,6,7,8,9,1,4,2]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[4,5,6,7,8,9,1,3,2]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[5,2,6,7,8,1,4,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,8,2,7,5,3,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,2,4,6,5,8,3,7]=>[1,2,7,5,4,8,3,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,2,3,1,7,8,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,5,8,1,7,4,2,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[5,8,6,1,7,2,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,1,4,3,8,2,6,7]=>[6,2,4,3,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,4,7,5,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,6,7,5,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,5,4,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,2,8,7,3,6,5,1]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[3,7,8,6,1,4,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,7,8,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,6,3,8,1,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,1,4,6,2,5,7]=>[6,8,3,4,7,1,5,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,4,5,3,8,7,1,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[4,7,5,6,2,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,7,5,1,6,3,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,6,2,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,4,6,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,1,6,7,8,2,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,3,4,1,2,7,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,8,4,6,1,3,7]=>[6,7,8,4,5,1,2,3]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[4,7,8,6,5,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,6,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,4,7,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,5,8,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,3,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,4,2,8,1,7,5]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[3,4,8,6,2,1,7,5]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[8,4,6,2,1,7,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,6,2,1,7,4,5]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[3,1,8,2,4,6,5,7]=>[4,2,8,1,5,7,6,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[8,1,7,6,2,5,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,5,4,3,7,6,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,1,3,6,7,5,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,5,8,6,1,7,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,4,7,5,2,6,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,4,8,6,7,3,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,6,7,8,5,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,7,8,6,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,1,5,7,2,3,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,8,5,3,2,7,1,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[5,4,8,1,3,7,2,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[8,4,5,3,1,7,2,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,4,5,3,1,8,6,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,6,8,7,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,6,4,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,7,5,1,3,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,8,2,6,7,5,1,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,7,6,3,8,2,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,4,1,8,2,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,6,8,3,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,4,2,8,1,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,4,8,7,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,4,8,1,6,3,5]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[5,3,1,6,7,8,2,4]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,4,7,8,6,1,2,5]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[2,1,4,7,8,6,3,5]=>[2,1,7,8,6,5,3,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,4,5,8,1,6,3,7]=>[5,7,3,8,1,6,2,4]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,4,6,8,2,5,7,1]=>[8,5,6,7,2,3,4,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,8,5,6,4,2,3,7]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,7,6,2,4,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,4,8,5,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,4,7,2,5,8,3]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,5,1,8,6,3,4]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[4,7,1,6,5,3,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,7,5,6,4,8,2,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,8,5,7,3,1,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[8,3,1,4,6,2,7,5]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,2,6,4,5,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,2,5,4,6,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,6,7,8,9,1,2,3,5]=>[8,9,7,6,5,4,3,1,2]=>[8,9,7,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[5,7,8,9,1,2,3,4,6]=>[8,9,7,6,5,4,3,1,2]=>[8,9,7,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[2,7,1,5,3,8,6,4]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,5,7,2,8,4,1,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[2,4,3,8,5,1,7,6]=>[6,3,2,8,5,1,7,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[7,3,2,1,4,8,6,5]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[2,8,3,4,1,7,6,5]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,7,6,8,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,7,1,4,5,8,3]=>[4,8,6,1,5,3,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[8,7,1,6,3,5,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,7,2,6,1,5,3,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,1,3,8,2,6,4,5]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,2,5,3,4,7,1,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[2,7,3,4,1,5,8,6]=>[5,8,3,4,1,6,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[2,5,8,1,6,7,3,4]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[6,2,8,3,4,5,1,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[7,3,4,6,8,2,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,1,3,7,2,8,4,6]=>[7,2,5,8,3,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,2,4,6,1,7,8,3]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,8,4,6,1,5,7,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[8,7,3,2,5,1,6,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,4,1,2,5,8,7]=>[5,6,4,3,1,2,8,7]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[5,2,7,1,4,3,6,8]=>[6,4,7,2,5,1,3,8]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[6,3,1,4,2,5,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[5,2,3,1,4,6,8,7]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[3,5,4,1,6,2,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,5,7,2,8,3,1,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[3,5,1,7,6,2,8,4]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[8,3,6,2,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,2,6,5,3,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,2,7,1,8,6,3]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,1,7,6,5,3,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,3,6,7,1,8,5,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,6,1,2,7,8,5,4]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[4,5,1,8,7,6,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,5,2,7,6,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,1,3,6,7,5,2,8]=>[7,2,3,6,5,4,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,1,4,5,7,6,2,8]=>[7,2,3,4,6,5,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,5,1,3,6,8,7,2]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,8,5,1,2,4,6,7]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[8,5,1,2,4,3,6,7]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,8,4,1,2,3,6,7]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[3,5,8,1,4,2,7,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[2,8,5,7,1,4,3,6]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[4,8,7,5,1,2,3,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,1,2,4,6,3,7,5]=>[8,2,3,6,7,4,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,1,4,2,3,8,5]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,1,2,7,8,4,3,5]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,8,1,2,5,3,4,6]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,8,4,7,5,2,3,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,4,7,2,1,6,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,8,2,1,6,7,3]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[7,4,2,5,3,6,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,4,2,5,3,6,7,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,8,1,5,3,6,7,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,1,7,5,2,6,3,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,1,4,6,3,7,8,2]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,5,3,6,8,2,4]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,5,3,6,7,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,6,5,2,4,7,8,1]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[1,7,5,4,6,8,2,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,7,8,2,5,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,5,4,6,7,1,3]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[9,6,1,3,4,2,7,8,5]=>[9,8,3,6,5,4,7,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[10,9,5,1,8,2,4,3,6,7]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[4,5,2,6,1,8,3,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,1,8,6,7,3,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,8,3,2,4,1,5,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,5,2,4,1,7,8,3]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,4,8,2,1,3,6,7]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[1,4,8,3,2,6,5,7]=>[1,5,8,4,2,7,6,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,4,2,7,5,6]=>[1,5,8,4,2,7,6,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,8,3,1,4,5,6]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,1,3,2,7,5,4,6]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[9,8,7,5,6,4,3,2,10,1]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[8,7,5,4,6,3,2,9,1]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[8,7,4,6,5,3,2,9,1]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[2,5,6,7,8,9,4,3,1]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[2,3,1,7,8,9,6,5,4]=>[3,2,1,9,8,7,6,5,4]=>[3,2,1,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[2,1,6,7,8,9,5,4,3]=>[2,1,9,8,7,6,5,4,3]=>[2,1,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[9,7,10,2,4,6,8,1,3,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,7,2,4,6,1,3,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,9,5,10,2,4,6,8,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[5,8,9,10,7,2,4,6,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,6,7,5,10,2,4,8,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,6,10,5,7,2,4,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,10,6,5,2,4,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,3,4,7,2,6,1,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[5,7,3,8,2,4,6,10,1,9]=>[9,7,6,5,4,3,2,10,1,8]=>[9,7,6,5,4,3,2,10,1,8]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]
[8,5,9,10,3,7,2,4,6,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[3,6,7,8,5,2,4,10,1,9]=>[9,7,6,5,4,3,2,10,1,8]=>[9,7,6,5,4,3,2,10,1,8]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]
[9,3,6,7,5,10,2,4,8,1]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[6,8,3,9,10,5,7,2,4,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,10,3,6,5,2,4,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[4,8,5,9,10,3,7,2,6,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,7,4,8,3,5,2,10,1,9]=>[9,7,6,5,4,3,2,10,1,8]=>[9,7,6,5,4,3,2,10,1,8]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]
[8,6,9,4,10,3,5,7,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,4,8,9,10,6,3,5,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[5,6,7,8,4,3,2,10,1,9]=>[9,7,6,5,4,3,2,10,1,8]=>[9,7,6,5,4,3,2,10,1,8]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]
[9,5,6,7,4,3,10,2,8,1]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[8,9,5,6,4,10,3,7,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,8,9,5,10,4,6,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[11,9,12,2,4,6,8,10,1,3,5,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,11,12,9,2,4,6,8,1,3,5,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,11,7,12,2,4,6,8,10,1,3,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,10,11,12,9,2,4,6,8,1,3,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,8,9,7,12,2,4,6,10,1,3,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,11,8,12,7,9,2,4,6,1,3,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,11,12,8,7,2,4,6,1,3,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,5,6,9,12,2,4,8,10,1,3,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,11,12,5,6,9,2,4,8,1,3,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,9,11,5,12,2,4,6,8,10,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,7,11,12,5,9,2,4,6,8,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,5,8,9,7,12,2,4,6,10,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,10,5,11,12,7,9,2,4,6,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,11,12,5,8,7,2,4,6,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[6,10,7,11,12,5,9,2,4,8,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,8,11,6,12,5,7,9,2,4,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,6,10,11,12,8,5,7,2,4,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,11,7,8,6,12,5,9,2,4,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,11,7,12,6,8,5,2,4,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,9,10,11,12,7,6,5,2,4,1,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,11,8,12,3,4,7,9,2,6,1,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,11,12,8,3,4,7,2,6,1,5]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,5,7,11,12,3,9,2,4,6,8,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,10,11,5,12,3,7,9,2,4,6,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[5,9,10,11,12,8,3,7,2,4,6,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[6,10,3,7,11,12,5,9,2,4,8,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,6,8,3,11,12,5,7,9,2,4,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,6,10,11,12,3,8,5,7,2,4,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,11,7,12,3,6,8,5,2,4,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,9,10,11,12,7,3,6,5,2,4,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,10,4,5,11,12,3,9,2,6,8,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[4,8,10,11,5,12,3,7,9,2,6,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,10,6,11,4,12,3,5,7,9,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[6,9,4,10,11,12,8,3,5,7,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,7,10,4,11,12,6,8,3,5,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[4,8,9,10,11,12,7,6,3,5,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,5,10,6,11,12,4,8,3,7,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,10,7,11,5,12,4,6,8,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,9,5,10,11,12,7,4,6,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,9,10,11,6,12,5,7,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[7,6,1,8,2,5,4,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,1,6,7,3,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,4,2,1,6,3,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[7,6,4,1,2,5,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,4,2,8,1,6,3,7]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[8,7,2,6,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,8,4,3,6,1,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,5,4,8,6,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,8,6,3,5,2,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,8,6,3,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,6,3,2,4,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,7,3,2,8,6,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,1,6,8,2,7,3]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,9,7,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,6,7,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[8,7,9,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,7,8,6,5,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[4,3,7,1,6,2,5,8]=>[6,4,7,2,5,1,3,8]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[4,3,1,6,7,2,5,8]=>[6,3,2,7,5,1,4,8]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[6,3,1,5,7,2,4,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,7,5,4,3,6,9,2,1]=>[9,8,6,5,4,3,7,2,1]=>[9,8,6,5,4,3,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[8,7,6,9,5,3,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,7,9,6,5,4,2,3,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[5,2,1,4,8,6,7,3]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,5,2,1,3,7,6,8]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[8,2,7,4,1,6,5,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[3,2,8,4,1,6,5,7]=>[5,2,8,4,1,7,6,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[3,7,6,4,1,5,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,1,6,5,4,2,8,3]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,4,2,3,6,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,7,6,4,5,1,8,3]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[4,6,8,1,7,3,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,8,1,5,7,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,3,1,6,7,4,5]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[4,5,6,8,2,1,7,3]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[4,5,6,8,1,3,7,2]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[4,5,8,3,2,1,7,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[4,5,1,3,2,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,7,8,3,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,1,3,5,6,2,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,8,3,2,1,6,7,5]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[5,2,8,1,4,6,7,3]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[5,6,3,7,8,1,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,7,1,4,3,6,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,2,3,7,1,5,4,8]=>[7,5,3,6,2,4,1,8]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,2,8,1,5,4,7,3]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,1,3,4,5,2,7,8]=>[6,2,5,4,3,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[7,1,3,4,5,6,2,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,2,5,1,3,6,4,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[6,5,2,7,8,4,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,5,3,6,4,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[2,3,6,5,8,4,7,1]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,5,2,6,8,7,3,4]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,3,2,1,7,8,9,6]=>[5,4,3,2,1,9,7,8,6]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[8,5,6,3,4,1,2,9,7]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[6,5,4,3,2,1,8,9,7]=>[6,5,4,3,2,1,9,8,7]=>[6,5,4,3,2,1,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]
[6,9,4,7,2,5,1,3,8]=>[8,9,7,6,5,4,3,1,2]=>[8,9,7,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[2,5,1,3,6,7,8,9,10,4]=>[3,10,1,4,5,6,7,8,9,2]=>[3,10,1,9,8,7,6,5,4,2]=>[[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]]
[8,9,4,5,6,1,2,3,10,7]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[5,9,10,2,6,7,1,3,4,8]=>[9,10,8,7,6,5,4,3,1,2]=>[9,10,8,7,6,5,4,3,1,2]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[7,6,5,4,3,2,1,9,10,8]=>[7,6,5,4,3,2,1,10,9,8]=>[7,6,5,4,3,2,1,10,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[10,7,8,5,6,3,4,1,2,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[5,3,4,7,2,1,6,8]=>[6,5,3,7,2,1,4,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,8,5,7,1,2,3,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,2,3,7,6,1,8,5]=>[6,3,2,8,5,1,7,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[4,2,6,3,1,5,7,8]=>[5,4,6,2,1,3,7,8]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[2,1,8,7,4,3,6,5,10,9]=>[2,1,8,7,6,5,4,3,10,9]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[6,5,2,1,4,3,12,11,8,7,10,9]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[4,6,3,2,5,8,7,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[5,8,4,3,2,6,1,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,5,7,4,8,6,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,5,7,3,8,2,4]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,7,8,6,4,3,5]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,1,7,8,6,2,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,2,4,1,7,6,8,3]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,3,2,5,4,7,6,9,10,8]=>[1,3,2,5,4,7,6,10,9,8]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,4,3,6,7,5,9,10,8]=>[1,2,4,3,7,6,5,10,9,8]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[2,9,4,5,6,7,8,3,1]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[9,3,4,5,6,7,8,2,1]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[2,3,1,9,6,7,8,5,4]=>[3,2,1,9,8,7,6,5,4]=>[3,2,1,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[2,1,9,5,6,7,8,4,3]=>[2,1,9,8,7,6,5,4,3]=>[2,1,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,9,4,5,6,7,8,3,2]=>[1,9,8,7,5,6,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[5,4,3,8,1,7,2,6]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[5,4,9,1,8,2,7,3,6]=>[8,6,9,4,7,2,5,1,3]=>[8,6,9,4,7,2,5,1,3]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]
[5,4,6,3,9,1,8,2,7]=>[8,6,4,3,9,2,7,1,5]=>[8,6,4,3,9,2,7,1,5]=>[[[[[[.,.],.],.],[.,.]],[.,.]],[.,.]]
[5,7,3,9,1,8,2,6,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,4,9,1,8,2,7,3,5]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[4,5,9,1,8,2,7,3,6]=>[8,6,9,4,7,2,5,1,3]=>[8,6,9,4,7,2,5,1,3]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]
[6,4,5,3,9,1,8,2,7]=>[8,6,4,3,9,2,7,1,5]=>[8,6,4,3,9,2,7,1,5]=>[[[[[[.,.],.],.],[.,.]],[.,.]],[.,.]]
[5,6,4,10,1,9,2,8,3,7]=>[9,7,5,10,3,8,2,6,1,4]=>[9,7,5,10,3,8,2,6,1,4]=>[[[[[[.,.],.],[.,.]],[.,.]],[.,.]],[.,.]]
[5,4,7,3,6,2,9,1,8]=>[8,6,5,4,3,2,9,1,7]=>[8,6,5,4,3,2,9,1,7]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[5,6,4,7,3,10,1,9,2,8]=>[9,7,5,4,3,10,2,8,1,6]=>[9,7,5,4,3,10,2,8,1,6]=>[[[[[[[.,.],.],.],.],[.,.]],[.,.]],[.,.]]
[7,3,1,5,6,8,4,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,9,1,3,4,5,6,7,10,8]=>[3,10,1,4,5,6,7,8,9,2]=>[3,10,1,9,8,7,6,5,4,2]=>[[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,3,1,6,8,4,5]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,1,8,2,5,6,3,7]=>[7,2,8,4,5,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,7,8,1,6,2,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,6,4,2,7,3,8,5]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,5,8,6,3,7]=>[1,7,3,4,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,4,3,2,1,8,9,7,6]=>[5,4,3,2,1,9,8,7,6]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[4,3,2,1,8,9,7,6,5]=>[4,3,2,1,9,8,7,6,5]=>[4,3,2,1,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[3,2,1,8,9,7,6,5,4]=>[3,2,1,9,8,7,6,5,4]=>[3,2,1,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[2,1,8,9,7,6,5,4,3]=>[2,1,9,8,7,6,5,4,3]=>[2,1,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[4,8,2,1,5,7,3,6]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[5,2,7,1,6,3,4,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,8,2,5,1,6,3,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[5,8,1,2,4,6,3,7]=>[7,8,3,4,5,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,1,7,3,6,4,2,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,3,1,7,5,4,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[9,8,3,4,5,6,7,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,2,3,4,5,6,1,7]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[6,2,8,7,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[9,4,5,6,7,8,2,1,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,3,4,5,6,7,2,1,8]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[10,9,3,4,5,6,7,8,1,2]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,2,9,8,3,4,5,6,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,2,3,4,5,1,6,7]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[7,3,4,8,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[9,5,6,7,8,2,1,3,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,3,6,8,4,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,3,9,4,5,6,7,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,4,5,6,7,8,9,2,1,3]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[5,6,2,8,3,1,7,4]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,4,7,5,6,2,8,3]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,8,3,5,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,3,1,4,8,6,2,7]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[5,2,4,8,3,1,6,7]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[8,7,3,5,4,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,5,1,8,6,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,5,7,6,3,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,6,7,5,3,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,8,3,1,6,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,5,3,7,6,2,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,8,7,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,4,2,3,5,7,8]=>[6,2,5,4,3,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,5,1,8,3,7,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,4,3,8,6,5,2]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,5,4,1,7,3,2,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,3,8,1,7,6,2]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[4,7,6,3,2,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,6,3,8,2,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,8,4,7,1,2,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,3,7,6,8,4,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,5,7,2,8,3,4]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,7,2,5,6,3,4]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,6,7,4,3,5]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,4,8,7,6,1,3]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[1,8,7,6,3,5,4,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,7,6,4,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,4,1,8,5,3,6]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[7,3,2,1,4,6,8,5]=>[8,4,3,2,5,6,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[4,7,2,6,1,8,3,5]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[8,7,3,5,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,3,2,1,6,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,8,1,3,4,2,5,7]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[3,6,1,4,7,8,2,5]=>[7,8,3,4,5,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[2,5,7,1,3,6,4,8]=>[4,7,6,1,5,3,2,8]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,4,7,2,5,3,6,8]=>[1,6,7,4,5,2,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,5,3,1,2,6,8,7]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[4,5,1,3,8,2,6,7]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[4,1,5,3,2,7,6,8]=>[5,2,4,3,1,7,6,8]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[7,3,5,1,4,2,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[2,4,3,6,7,1,5,8]=>[6,3,2,7,5,1,4,8]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[7,3,5,2,1,6,4,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[4,6,5,2,1,3,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[6,1,5,3,7,2,4,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,6,5,4,1,7,2,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[10,9,3,8,7,6,5,4,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,7,6,4,5,3,2,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,8,7,5,4,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,8,7,3,2,4,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,5,4,6,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,8,2,4,6,3,5]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,5,4,8,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,1,8,4,3,7,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,8,2,6,7,5,4,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,5,1,6,8,3,4]=>[4,8,7,1,5,6,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[8,5,4,2,7,3,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,8,6,1,2,4,5,7]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[1,8,5,3,2,7,4,6]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,4,7,2,3,5,6]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,8,1,7,5,4,6]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,4,5,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[7,1,5,6,2,3,4,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,5,1,7,2,3,4,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,6,8,2,7,3,4,5]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,7,3,4,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,3,6,7,8,5,2]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,1,5,6,8,3,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,1,2,6,7,8,5,3]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,7,8,2,1,4,5,6]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[6,3,7,1,8,2,4,5]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[3,7,8,1,5,2,6,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[2,1,4,3,10,9,7,5,6,8]=>[2,1,4,3,10,9,8,7,6,5]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,8,7,5,3,4,6,10,9]=>[2,1,8,7,6,5,4,3,10,9]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,10,7,5,9,4,3,6,8]=>[2,1,10,9,8,7,6,5,4,3]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,10,8,5,3,6,4,9,7]=>[2,1,10,9,8,6,7,5,4,3]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,10,9,4,6,7,3,5,8]=>[2,1,10,9,8,7,6,5,4,3]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[8,5,3,7,2,1,4,6,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[10,6,3,9,4,2,7,1,5,8]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,7,2,4,5,1,3,6,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[10,7,2,4,5,9,3,1,6,8]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[10,9,7,4,2,6,3,1,5,8]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,1,8,4,9,6,2,3,5,7]=>[10,2,9,8,7,6,5,4,3,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[10,9,2,3,5,6,7,1,4,8]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[2,1,4,3,6,5,12,11,9,7,8,10]=>[2,1,4,3,6,5,12,11,10,9,8,7]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,10,9,7,5,6,8,12,11]=>[2,1,4,3,10,9,8,7,6,5,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,12,9,7,11,6,5,8,10]=>[2,1,4,3,12,11,10,9,8,7,6,5]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,12,11,6,8,9,5,7,10]=>[2,1,4,3,12,11,10,9,8,7,6,5]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,8,7,5,3,4,6,10,9,12,11]=>[2,1,8,7,6,5,4,3,10,9,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,10,7,5,9,4,3,6,8,12,11]=>[2,1,10,9,8,7,6,5,4,3,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,12,8,5,11,6,4,9,3,7,10]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,10,9,4,6,7,3,5,8,12,11]=>[2,1,10,9,8,7,6,5,4,3,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,12,11,9,6,4,8,5,3,7,10]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[6,5,3,1,2,4,8,7,10,9,12,11]=>[6,5,4,3,2,1,8,7,10,9,12,11]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[6,5,3,1,2,4,12,11,9,7,8,10]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[8,5,3,7,2,1,4,6,10,9,12,11]=>[8,7,6,5,4,3,2,1,10,9,12,11]=>[8,7,6,5,4,3,2,1,12,11,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[[[.,.],.],.],.]]
[10,6,3,9,4,2,7,1,5,8,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[[.,.],.]]
[8,7,2,4,5,1,3,6,10,9,12,11]=>[8,7,6,5,4,3,2,1,10,9,12,11]=>[8,7,6,5,4,3,2,1,12,11,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[[[.,.],.],.],.]]
[10,9,7,4,2,6,3,1,5,8,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[[.,.],.]]
[12,11,8,4,9,6,2,3,5,1,7,10]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,9,3,5,6,2,8,4,1,7,10]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[1,5,4,7,8,3,6,2]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,2,4,7,8,3,6,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,1,4,7,8,3,6,2]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,8,1,5,6,2,3,7]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[5,6,4,1,7,3,8,2]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,3,7,8,2,5,1,6]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[3,7,8,5,4,2,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,7,4,5,6,8,3,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,4,5,6,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,7,4,5,6,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,4,7,8,3,1,6,5]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[5,4,3,6,8,1,7,2]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,7,4,5,8,1,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,4,3,5,6,8,2,7]=>[1,7,3,4,5,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,1,7,3,2,8,5]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[1,7,3,6,4,2,8,5]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,7,3,5,1,2,8,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,6,4,2,3,5,8,7]=>[1,6,5,4,3,2,8,7]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,8,3,5,2,1,6,7]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[10,9,7,6,5,4,3,8,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,6,8,4,7,5,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,3,1,5,2,6,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,7,1,6,8,2,3,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,6,5,8,2,3,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[7,1,8,2,4,5,3,6]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,8,2,3,4,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,2,3,8,7,1,4,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[11,10,9,8,6,7,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[8,7,1,3,2,6,4,5]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,7,6,4,8,3,1,5]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,6,3,7,5,8,4,1]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,5,1,2,3,8,4,6]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,2,1,3,7,4,5]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,2,3,6,8,5,7,1]=>[8,3,2,6,7,4,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[4,7,3,2,6,5,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,3,7,8,2,1,6,5]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[4,8,7,2,1,5,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,8,2,5,1,6,4]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,5,3,8,6,1,2,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,3,5,8,4,1,2,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[7,3,8,4,5,1,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,5,1,2,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,4,6,1,3,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,7,5,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,3,6,8,1,2,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,8,6,2,1,4,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,6,3,1,2,5,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,6,4,1,5,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,2,8,4,7,1,3,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[7,3,1,2,8,6,5,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,7,1,3,2,4,5,6]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,1,3,6,5,7,2,8]=>[7,2,3,5,4,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,1,3,5,7,2,8,6]=>[6,2,3,4,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,1,8,2,4,6,3,7]=>[7,2,8,4,5,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,8,2,1,4,5,3,7]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[4,2,7,3,6,8,5,1]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,1,5,8,6,7,2,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,8,2,1,4,5,7,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,1,4,3,10,9,6,5,8,7]=>[2,1,4,3,10,9,8,7,6,5]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,10,7,4,9,6,3,8,5]=>[2,1,10,9,8,7,6,5,4,3]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,10,9,4,3,6,7,8,5]=>[2,1,10,9,6,5,8,7,4,3]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,1,10,9,4,5,6,3,8,7]=>[2,1,10,9,8,6,7,5,4,3]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[6,5,2,1,4,3,8,7,10,9]=>[6,5,4,3,2,1,8,7,10,9]=>[6,5,4,3,2,1,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[8,5,2,7,4,1,6,3,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[10,5,2,7,4,9,6,1,8,3]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[10,7,2,9,4,5,6,1,8,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,2,1,8,5,4,7,6,3]=>[10,9,4,3,8,7,6,5,2,1]=>[10,9,4,3,8,7,6,5,2,1]=>[[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.]
[10,7,2,3,4,9,6,1,8,5]=>[10,9,8,4,5,7,6,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[10,9,6,3,2,5,4,1,8,7]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[2,1,4,3,6,5,12,11,8,7,10,9]=>[2,1,4,3,6,5,12,11,10,9,8,7]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,10,9,6,5,8,7,12,11]=>[2,1,4,3,10,9,8,7,6,5,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,12,9,6,11,8,5,10,7]=>[2,1,4,3,12,11,10,9,8,7,6,5]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,4,3,12,11,6,5,8,9,10,7]=>[2,1,4,3,12,11,8,7,10,9,6,5]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,8,7,4,3,6,5,10,9,12,11]=>[2,1,8,7,6,5,4,3,10,9,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,10,7,4,9,6,3,8,5,12,11]=>[2,1,10,9,8,7,6,5,4,3,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,10,9,4,3,6,7,8,5,12,11]=>[2,1,10,9,6,5,8,7,4,3,12,11]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,12,9,4,11,6,7,8,3,10,5]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[2,1,12,11,4,3,10,7,6,9,8,5]=>[2,1,12,11,6,5,10,9,8,7,4,3]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[6,5,2,1,4,3,8,7,10,9,12,11]=>[6,5,4,3,2,1,8,7,10,9,12,11]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[8,5,2,7,4,1,6,3,10,9,12,11]=>[8,7,6,5,4,3,2,1,10,9,12,11]=>[8,7,6,5,4,3,2,1,12,11,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[[[.,.],.],.],.]]
[10,7,2,9,4,5,6,1,8,3,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[[.,.],.]]
[12,9,2,11,8,5,4,7,6,1,10,3]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,2,1,8,5,10,7,4,9,6,3]=>[12,11,4,3,10,9,8,7,6,5,2,1]=>[12,11,4,3,10,9,8,7,6,5,2,1]=>[[[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]],.],.]
[12,11,2,1,10,5,6,7,4,9,8,3]=>[12,11,4,3,10,9,8,7,6,5,2,1]=>[12,11,4,3,10,9,8,7,6,5,2,1]=>[[[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]],.],.]
[12,11,2,1,4,9,6,5,8,7,10,3]=>[12,11,4,3,10,9,8,7,6,5,2,1]=>[12,11,4,3,10,9,8,7,6,5,2,1]=>[[[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]],.],.]
[12,11,6,3,8,5,2,7,4,1,10,9]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[4,3,1,2,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[7,1,4,5,8,3,6,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,5,8,1,2,4,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,1,5,2,8,7,4,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,6,3,1,2,7,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[3,8,6,4,1,5,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,1,4,5,2,3,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,6,4,5,1,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,6,4,5,1,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,4,6,3,1,2,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,6,2,5,7,8,1,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,6,3,5,7,1,2,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[4,7,3,5,8,6,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,3,5,7,1,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,3,5,6,1,2,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,7,2,5,6,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,8,2,5,6,7,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,4,7,2,6,5,8,3]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,2,6,4,8,3]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,4,6,1,8,3,5]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,2,7,8,3,5,4,6]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,6,2,8,5,4,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,8,3,4,6,5]=>[1,2,8,7,5,6,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,6,8,3,4,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,4,1,7,8,6,5,2]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,4,8,6,5,7,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,1,3,4,8,2,7,6]=>[6,2,4,3,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,7,3,6,1,4,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,1,8,3,4,7,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,2,1,5,6,4,7,3]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,5,6,1,3,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,7,2,4,6,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,1,5,6,3,8,7,4]=>[2,1,8,5,4,7,6,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[3,2,7,5,8,6,4,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,4,5,3,8,1,7,6]=>[6,4,3,2,8,1,7,5]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[7,2,5,4,3,8,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,3,1,2,6,7,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,2,5,1,3,6,8,4]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,4,7,3,1,2,6,5]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,8,7,3,5,2,6,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,8,3,6,5,7,1]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[3,1,8,2,6,5,7,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[4,6,7,8,5,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,2,1,8,6,5,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,6,2,8,4,1,7,3]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[5,7,2,4,8,6,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,2,4,8,5,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,7,3,2,8,5,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,3,1,8,6,5,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[7,2,8,3,5,6,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,3,8,4,6,1,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,7,3,4,8,5,2,6]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,3,8,5,4,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,8,4,5,3,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,6,4,3,1,7,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[1,5,8,3,4,6,2,7]=>[1,7,8,5,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,4,2,5,7,6]=>[1,5,8,4,2,6,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,6,2,3,8,5]=>[1,6,8,5,4,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,4,6,7,2,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,3,7,8,6,5]=>[1,4,3,2,8,7,6,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,1,6,4,8,3,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,4,5,8,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,3,6,5,8,2,4,7]=>[1,6,7,4,8,2,3,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,3,2,8,5,7]=>[1,5,7,4,2,8,3,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,4,1,5,7,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,2,6,7,4,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,5,6,4,1,7,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,3,1,6,4,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,8,2,6,3,1,7,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,8,1,6,3,7,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,1,4,6,2,5,7,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,5,8,1,6,2,7,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[5,2,6,8,1,4,3,7]=>[7,5,6,8,2,3,1,4]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[6,7,3,8,2,1,4,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,3,5,4,1,8,6]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,6,3,7,4,1,8,5]=>[6,8,3,5,4,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,1,4,8,5,3,7,6]=>[2,1,6,8,5,3,7,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[2,7,3,8,4,1,6,5]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[2,6,3,1,5,4,8,7]=>[4,6,3,1,5,2,8,7]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[1,5,8,3,4,7,2,6]=>[1,7,8,5,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,3,8,1,4,6,2,7]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[4,5,8,1,3,6,2,7]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[7,4,6,5,2,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,1,3,8,5,7,6,2]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,3,7,2,8,6,5]=>[5,2,3,8,1,7,6,4]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,6,3,1,7,2,8,5]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[7,2,6,3,1,8,5,4]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[4,8,7,2,5,3,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,8,1,7,5,4,6,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[6,8,3,1,5,7,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,7,3,1,2,5,6,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,4,5,1,2,6,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,4,3,6,1,7,8,2]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,2,7,8,5,6,1,4]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,8,3,2,1,7,5,6]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[5,1,2,6,4,7,8,3]=>[8,2,3,5,4,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,9,8,7,6,4,3,2,5]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,9,8,7,5,4,3,2,6]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,9,8,6,5,4,3,2,7]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,9,7,6,5,4,3,2,8]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,9,8,7,6,5,2,3,4]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,10,9,8,7,6,5,3,2,4]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,9,8,7,6,3,4,2,5]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,10,9,8,7,6,4,3,2,5]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,9,8,7,4,5,3,2,6]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,10,9,8,7,5,4,3,2,6]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,9,8,5,6,4,3,2,7]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,10,9,8,6,5,4,3,2,7]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,8,4,5,6,3,2,7]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,9,6,7,5,4,3,2,8]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,10,9,7,6,5,4,3,2,8]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,7,8,6,5,4,3,2,9]=>[1,8,7,6,5,4,3,2,9]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,10,8,7,6,5,4,3,2,9]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[4,7,6,1,5,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,5,1,7,4,6,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,4,8,1,6,7,2,5]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[3,6,7,8,4,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,3,7,8,4,6,1,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,3,7,8,4,6,2,5]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,7,8,4,6,2,5]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,3,8,1,6,7,2,5]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,8,7,3,6,1,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,8,4,3,7,1,2,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,1,8,3,7,5,2,6]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,4,8,3,6,7,1,5]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,6,5,8,7,3,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,6,4,8,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,6,8,3,5,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,8,6,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,3,7,6,1,2,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[2,8,4,7,1,3,6,5]=>[5,8,6,7,1,3,4,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[8,9,2,3,4,5,6,1,7]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[7,8,9,2,3,4,5,1,6]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,7,8,9,2,3,4,1,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[5,6,7,8,9,2,3,1,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,9,10,2,3,4,5,6,1,7]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,8,9,2,3,4,1,5,6]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,8,9,10,2,3,4,5,1,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,7,8,9,2,3,1,4,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[5,6,7,8,9,10,2,3,1,4]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[6,8,3,4,5,2,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,7,1,4,5,6,2,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[7,9,3,4,5,6,2,1,8]=>[8,9,7,6,5,4,3,1,2]=>[8,9,7,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[3,6,1,4,5,2,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[3,8,2,4,5,1,7,6]=>[6,8,3,4,5,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,6,8,1,5,4,7,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[3,8,9,1,5,6,7,4,2]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[1,7,4,6,3,5,2,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,6,5,7,2,4,8]=>[1,6,7,4,5,2,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,5,6,4,3,8]=>[1,7,3,6,5,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,7,8,4,3,1,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[6,8,5,3,2,4,1,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,6,8,5,3,2,7,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,1,8,7,5,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,3,7,6,8,5,2,4]=>[1,7,8,6,5,4,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,7,8,6,5,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,4,3,7,6,1,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,7,6,1,2,3,8,5]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[4,5,2,6,7,8,1,3]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,8,7,6,5,4,3,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[2,1,4,9,8,7,6,5,3]=>[2,1,9,8,7,6,5,4,3]=>[2,1,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,6,5,4,2,1,9,8]=>[7,6,5,4,3,2,1,9,8]=>[7,6,5,4,3,2,1,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[3,2,1,6,9,8,7,5,4]=>[3,2,1,9,8,7,6,5,4]=>[3,2,1,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[4,6,5,3,2,1,9,8,7]=>[6,5,4,3,2,1,9,8,7]=>[6,5,4,3,2,1,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]
[1,7,6,2,3,8,5,4]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,5,1,3,7,6,2,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[7,2,3,8,6,4,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,5,4,3,8,6,2,7]=>[1,7,4,3,8,6,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,7,5,8,4,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,1,5,3,4,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,3,5,4,1,6,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,5,7,1,6,4,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[3,7,5,6,1,4,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,7,5,6,3,4,8,2]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,3,1,2,7,8,4,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[5,1,3,7,8,2,6,4]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,8,1,2,7,6,4,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,6,7,4,5,3,2,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,2,6,7,5,3,8]=>[1,7,3,6,5,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,2,4,6,5,3,7]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,8,7,2,3,6,5]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,3,6,5,8,2,7]=>[7,2,3,5,4,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,3,7,1,5,8,2,6]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,8,6,5,2,7,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,6,2,7,4,3,5]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,6,4,1,8,5,3]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,4,1,8,3,7,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,5,8,7,3,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,4,1,7,8,6,2]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[6,8,7,2,1,5,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,9,8,7,6,5,2,1,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[5,9,8,7,6,2,1,4,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,9,8,7,2,1,5,4,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,9,8,2,1,6,5,4,3]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[8,1,6,3,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,5,1,3,7,6,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,6,5,4,2,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,1,3,5,7,2,8,4]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,8,1,5,6,4,3,7]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,6,7,5,8,4,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,1,6,5,2,8,3]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,4,2,8,6,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,4,7,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,3,2,1,6,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,7,2,6,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,7,3,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,5,6,8,3,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,6,5,7,8,3,2,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,6,7,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,8,6,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,6,4,2,1,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,8,5,2,7,3,1,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[6,4,3,1,8,5,2,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,4,3,1,5,8,6,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,4,8,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,5,2,6,7,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,2,1,8,5,6,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[6,7,8,1,9,2,3,4,5]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[5,6,7,8,1,9,2,3,4]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[1,5,7,2,4,3,8,6]=>[1,6,8,4,5,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,7,5,8,4,3,6]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,3,8,2,7,4,6]=>[7,2,5,8,3,6,1,4]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,7,1,3,2,8,4,6]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[7,1,6,3,2,8,4,5]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,7,2,3,6,5,4]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,2,6,4,3,8,5]=>[8,2,3,6,5,4,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,4,7,8,3,2,5,6]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,1,3,2,4,6,5]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,6,3,2,4,7,5]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,2,7,6,3,5,4]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,6,3,2,7,4,5]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,1,7,6,3,4,5]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,8,4,3,5,1,2,7]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[8,7,3,5,4,1,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,8,5,7,2,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,3,6,4,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,7,4,6,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,7,2,3,5,1,4,6]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,6,3,4,1,8,2,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,3,5,2,8,1,4,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[6,4,5,3,1,7,2,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[8,7,2,4,3,1,5,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,6,2,3,1,4,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,7,6,2,3,1,5,8]=>[6,7,5,4,3,1,2,8]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[4,7,6,1,3,2,8,5]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[7,2,6,5,4,3,1,9,8]=>[7,6,5,4,3,2,1,9,8]=>[7,6,5,4,3,2,1,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[3,2,1,9,5,8,7,6,4]=>[3,2,1,9,8,7,6,5,4]=>[3,2,1,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[6,3,5,4,2,1,9,8,7]=>[6,5,4,3,2,1,9,8,7]=>[6,5,4,3,2,1,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]
[4,3,2,1,9,7,8,6,5]=>[4,3,2,1,9,8,7,6,5]=>[4,3,2,1,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[2,8,1,3,5,6,4,7]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,6,3,4,7,8,5,1]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,6,3,1,8,5,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,1,3,6,8,5,4]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,6,3,8,1,5,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,4,7,8,5,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,5,8,6,1,3,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[4,1,3,6,2,5,8,7]=>[5,2,3,6,1,4,8,7]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[7,1,4,6,3,2,5,8]=>[7,2,6,5,4,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,4,5,8,6,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,7,2,3,8,4,1,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,7,8,1,5,4,3,6]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,5,2,6,8,7,4,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,3,7,5,2,6,4]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,3,6,5,2,7,4]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,3,8,5,2,6,4]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,7,1,5,2,6,8,3]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,4,1,5,2,6,8,3]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,1,6,7,5,2,8,4]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[8,6,2,4,5,1,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,7,5,2,1,4,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,4,5,2,6,8,3]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,6,2,3,8,7,5]=>[5,2,8,4,1,7,6,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,1,7,6,5,2,8,3]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,4,1,5,6,2,7,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,5,3,6,1,7,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,4,7,3,5,6,1]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,5,4,8,3,2,6,7]=>[1,6,5,8,3,2,7,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,6,3,8,2,4]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,3,1,7,8,4,5]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,1,7,8,3,5,4,6]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,5,8,6,7,4,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,1,3,5,2,6,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,7,8,2,5,4,1,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[4,7,6,5,8,1,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,7,8,6,2,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,6,3,2,1,7,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[5,1,4,7,6,8,3,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,6,4,7,1,8,3,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,3,7,4,6,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,1,5,7,8,6,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,6,7,1,5,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,6,4,7,5,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,1,7,3,2,4,5,6]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[10,2,1,3,4,5,6,7,9,8]=>[10,3,2,4,5,6,7,8,9,1]=>[10,3,2,9,8,7,6,5,4,1]=>[[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.]
[6,4,7,1,5,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,8,1,3,5,2,7,6]=>[6,8,3,4,5,1,7,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[1,6,5,2,8,7,4,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,1,7,2,5,8,3,6]=>[7,2,8,4,5,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[3,2,5,8,6,1,7,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,5,1,7,2,8,6,3]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,8,5,3,6,7,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,5,2,6,7,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,8,6,3,4,7,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,9,5,3,6,7,8,4,1]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[9,4,2,5,6,7,8,3,1]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[4,7,1,8,5,3,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,4,7,2,5,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,1,4,3,6,8,2,5]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,3,1,5,4,8,7,2]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[7,1,3,8,5,4,2,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,8,7,3,5,1,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,8,7,1,6,2,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,1,6,2,8,7,5]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[5,2,6,7,4,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,5,1,6,4,3,2,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,3,5,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,6,2,1,5,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,2,1,6,4,7,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,7,2,8,5,4,6,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,7,1,4,8,5,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,3,2,8,5,1,4,6]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,1,7,3,2,8,5,6]=>[5,2,8,4,1,7,6,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[8,3,5,2,4,7,1,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,3,7,8,6,1,5,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,2,6,3,7,8,5,4]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,3,7,8,5,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,7,9,1,4,5,6,2,3]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[9,8,10,1,4,5,6,7,2,3]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[3,6,8,5,4,2,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[2,6,4,7,5,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,6,3,7,2,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[4,5,1,8,6,2,7,3]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,6,1,8,7,2,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,5,1,6,8,7,3,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,8,6,1,5,2,4,7]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[3,2,8,1,5,6,4,7]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[5,8,7,3,2,1,4,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[3,4,7,6,8,2,1,5]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[2,8,1,3,7,5,6,4]=>[3,8,1,4,7,6,5,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,8,7,2,5,6,4,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,6,1,2,5,8,4,3]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,4,7,1,5,8,2,6]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,2,7,1,5,8,3,6]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,1,6,2,5,8,3,7]=>[7,2,5,4,3,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,8,2,5,7,3,4,6]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,6,3,8,5,2,7]=>[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,5,6,3,1,7,2,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,4,6,5,8,2,3,7]=>[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,8,3,7,6,2,5]=>[1,7,8,4,6,5,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,7,6,8,3,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,1,6,7,2,8,5,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[6,5,1,3,8,4,7,2]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,7,4,8,5,3,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,3,1,6,8,4,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,1,4,6,7,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,4,7,5,6,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,4,7,8,5,2,6,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,4,2,3,6,5,1,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,2,4,3,1,5,6,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,3,1,4,8,5,7,2]=>[8,6,3,4,7,2,5,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,3,5,4,8,7,1,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,8,1,7,5,6,3,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,5,7,2,8,4,6,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,7,2,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,5,1,2,3,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,8,7,5,2,6,3,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,6,3,4,5,8,2]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,7,4,5,6,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,7,3,6,4,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,5,8,2,6,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,2,3,6,5,8]=>[1,5,7,4,2,6,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,5,6,3,4,8]=>[1,7,3,6,5,4,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,6,5,8,3,4,7]=>[1,2,7,6,8,4,3,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,8,2,6,3,4,7]=>[1,7,8,4,6,5,2,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,3,2,7,5,1,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,6,8,1,2,5,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,7,2,1,3,6,4,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[3,5,6,7,2,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,4,7,5,2,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,5,6,4,8,3,2,7]=>[1,7,6,4,8,3,2,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,5,6,4,8,3,7]=>[2,1,7,5,4,8,3,6]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,1,4,7,8,6,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,7,2,8,5,4,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,3,2,1,7,8,6,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[7,4,3,8,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,7,1,5,8,6,2]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,2,4,5,3,1,7,6]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,4,3,2,7,5,8,6]=>[1,4,3,2,8,6,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,8,7,2,6,1,3,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[4,5,8,2,1,7,3,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[6,8,4,1,7,3,2,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,6,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]
[5,6,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[4,5,3,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[6,7,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,10,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[6,7,4,3,2,1,5,8,9]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[7,5,4,3,1,2,6,8,9]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[6,7,9,8,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,6,8,9,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,11,10,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[7,8,10,9,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,7,5,9,8,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[5,7,9,8,6,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,6,8,5,9,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,5,8,9,7,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,7,9,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,3,1,8,2,7,5,4]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,4,1,3,2,5,7,8]=>[6,5,3,4,2,1,7,8]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,1,7,8,3,2,5,6]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[5,4,7,1,3,6,2,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[7,6,2,8,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,2,1,3,6,4,7]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[7,6,4,3,5,2,1,9,8]=>[7,6,5,4,3,2,1,9,8]=>[7,6,5,4,3,2,1,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[7,6,3,5,4,2,1,9,8]=>[7,6,5,4,3,2,1,9,8]=>[7,6,5,4,3,2,1,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[8,5,1,7,3,4,6,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,7,6,3,4,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,8,9,10,1,5,6,3,4,2]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[1,8,3,5,2,6,4,7]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,4,6,1,8,5,7,2]=>[8,4,6,2,7,3,5,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,3,8,7,4,5,1,6]=>[7,2,8,6,5,4,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,8,3,5,7,4,2,6]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,5,8,4,6,7,1,3]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[9,8,6,1,2,3,4,5,7]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[9,8,7,5,1,2,3,4,6]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,6,4,1,2,3,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,6,5,3,1,2,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,1,2,6,4,3,5,8]=>[7,2,3,6,5,4,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[7,1,2,6,5,3,4,8]=>[7,2,3,6,5,4,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,7,8,6,2,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,2,4,8,6,5,3]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,7,5,6,4,8,1,3]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[2,8,3,6,5,7,1,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[9,8,4,7,6,5,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,3,7,6,5,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,3,8,7,6,5,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,2,8,7,6,5,4,3,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,9,8,5,7,6,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,8,4,6,5,7,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,8,3,6,5,4,7,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,9,4,8,7,6,5,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,3,7,6,5,4,8,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,2,7,6,5,4,3,8,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,3,9,8,7,6,5,4,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,2,9,8,7,6,5,4,3,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,4,3,1,6,5,2,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[3,5,1,2,6,8,7,4]=>[4,8,3,1,5,7,6,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,1,2,4,8,7,5,6]=>[3,2,1,4,8,7,6,5]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[5,4,1,2,3,7,8,6]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,6,7,2,5,8,3,4]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,5,6,2,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,8,6,2,4,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[2,7,4,6,3,8,1,5]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[5,4,7,8,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,4,8,3,1,5,6]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[8,2,1,3,7,4,6,5]=>[8,3,2,4,7,6,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[6,5,8,2,3,4,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,8,2,3,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,2,7,5,3,4,6]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,2,8,1,3,7,5,6]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[7,5,1,8,2,3,4,6]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,2,4,1,3,7,5,6]=>[8,4,5,2,3,7,6,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,1,6,2,3,7,4,5]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,2,3,6,4,5]=>[8,2,7,4,5,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,2,6,7,5,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,7,2,5,3,8,1,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[3,5,7,4,2,8,1,6]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[2,4,7,6,3,8,1,5]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[4,6,8,5,1,2,3,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[4,6,5,7,1,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,6,5,7,1,3,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,4,7,6,1,8,2,5]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[8,5,2,1,6,3,4,7]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,1,8,5,3,2,4,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[9,10,2,1,6,4,3,5,7,8]=>[10,9,4,3,8,7,6,5,2,1]=>[10,9,4,3,8,7,6,5,2,1]=>[[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.]
[2,9,1,10,7,4,3,5,6,8]=>[3,10,1,9,8,7,6,5,4,2]=>[3,10,1,9,8,7,6,5,4,2]=>[[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]]
[10,8,5,2,1,6,3,4,7,9]=>[10,9,8,5,4,7,6,3,2,1]=>[10,9,8,5,4,7,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[10,7,2,1,8,5,3,4,6,9]=>[10,9,4,3,8,7,6,5,2,1]=>[10,9,4,3,8,7,6,5,2,1]=>[[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.]
[9,2,1,10,7,5,3,4,6,8]=>[10,3,2,9,8,7,6,5,4,1]=>[10,3,2,9,8,7,6,5,4,1]=>[[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.]
[10,8,6,3,1,4,2,5,7,9]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[10,8,5,1,6,3,2,4,7,9]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[10,7,1,8,5,3,2,4,6,9]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[9,1,10,7,5,3,2,4,6,8]=>[10,2,9,8,7,6,5,4,3,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[10,7,1,8,4,2,5,3,6,9]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[9,1,10,7,4,2,5,3,6,8]=>[10,2,9,8,7,6,5,4,3,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[11,12,8,2,1,6,4,3,5,7,9,10]=>[12,11,10,5,4,9,8,7,6,3,2,1]=>[12,11,10,5,4,9,8,7,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],.],.],.]
[11,12,2,1,9,6,4,3,5,7,8,10]=>[12,11,4,3,10,9,8,7,6,5,2,1]=>[12,11,4,3,10,9,8,7,6,5,2,1]=>[[[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]],.],.]
[10,11,2,1,4,3,12,7,5,6,8,9]=>[12,11,4,3,6,5,10,9,8,7,2,1]=>[12,11,4,3,10,9,8,7,6,5,2,1]=>[[[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]],.],.]
[12,10,8,5,2,1,6,3,4,7,9,11]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[12,10,7,2,1,8,5,3,4,6,9,11]=>[12,11,10,5,4,9,8,7,6,3,2,1]=>[12,11,10,5,4,9,8,7,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],.],.],.]
[12,9,2,1,10,7,5,3,4,6,8,11]=>[12,11,4,3,10,9,8,7,6,5,2,1]=>[12,11,4,3,10,9,8,7,6,5,2,1]=>[[[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]],.],.]
[11,2,1,12,9,7,5,3,4,6,8,10]=>[12,3,2,11,10,9,8,7,6,5,4,1]=>[12,3,2,11,10,9,8,7,6,5,4,1]=>[[[[.,.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]],.]
[8,6,1,3,2,7,5,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,7,5,2,4,6,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,7,5,4,1,6,3]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,6,1,2,7,3,5,4]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,2,8,5,7,1,6,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,8,7,4,5,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,6,7,4,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,5,8,1,7,3,2,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,8,1,5,2,3,7]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[7,2,4,1,6,3,5,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,2,1,3,6,5,8,7,9]=>[4,3,2,1,6,5,8,7,9]=>[4,3,2,1,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[4,2,1,3,6,5,8,7,10,9]=>[4,3,2,1,6,5,8,7,10,9]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[2,6,1,5,3,4,8,7]=>[3,6,1,5,4,2,8,7]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,8,7,5,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,8,2,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,7,3,1,4,5,6]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[5,6,1,2,4,7,8,3]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[9,8,4,5,7,6,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,5,4,6,7,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,9,8,6,5,7,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[11,10,9,8,5,7,6,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[10,9,8,4,5,7,6,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,8,4,5,3,7,6,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,3,5,7,6,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,5,4,6,3,7,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,4,3,6,7,5,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,9,8,5,4,6,7,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[11,10,9,8,6,5,7,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[3,8,6,7,5,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,5,1,4,6,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,7,5,4,6,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,6,3,1,2,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,7,1,3,2,8,5]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[6,4,7,5,3,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,4,6,3,1,5,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,1,4,5,6,8,2]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,7,3,4,2,1,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,4,8,3,1,5,7,2]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,4,2,3,5,1,8,6]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[3,1,6,5,2,4,8,7]=>[5,2,6,4,1,3,8,7]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,5,3,8,6,4,1,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,7,1,5,4,3,2,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,8,4,1,3,2,7,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[5,3,4,7,6,1,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,5,2,1,6,3,8,7]=>[6,4,3,2,5,1,8,7]=>[6,4,3,2,8,1,7,5]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[5,3,8,6,2,4,7,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[2,5,1,6,4,3,8,7]=>[3,6,1,5,4,2,8,7]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,6,2,8,5,7,1,4]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[4,6,8,1,5,7,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,1,2,5,7,6,3,8]=>[7,2,3,4,6,5,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,6,5,8,1,7,3,2]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[2,1,3,6,4,8,7,5]=>[2,1,3,8,5,7,6,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[4,8,1,2,7,5,6,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,6,4,3,8,7,5,2]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,5,1,6,8,7,2,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,4,7,2,5,8,6,1]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,5,1,8,6,4,7,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,5,8,7,3,1,4,6]=>[6,7,8,5,4,1,2,3]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[9,8,7,4,3,2,1,5,6]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,6,3,2,1,4,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[3,8,7,2,6,1,4,5]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[8,4,5,1,6,7,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,7,3,1,5,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,1,8,3,6,4,7]=>[3,7,1,8,5,6,2,4]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[5,8,4,7,3,2,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,6,8,4,2,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,8,6,1,2,5,7]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[4,8,6,5,7,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,3,5,6,8,4,1]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,1,3,4,7,2,6]=>[7,8,3,5,4,6,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[8,3,4,2,7,6,1,5]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,7,5,6,4,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,4,2,3,6,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,2,3,7,6,5,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,2,4,5,3,1,6,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,6,3,1,4,5,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,7,4,6,2,1,8,5]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[5,4,1,7,8,6,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,3,4,7,8,1,6,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,3,7,6,5,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,2,8,5,4,1,6,7]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[7,8,9,1,3,4,5,6,2]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[8,1,2,7,3,5,4,6]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,1,2,6,3,4,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,2,7,5,6,3,4,8]=>[1,2,7,6,5,4,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,8,1,2,3,6,5,7]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,3,4,2,5,6,7,8,9]=>[1,4,3,2,5,6,7,8,9]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,3,5,7,8,6,4,2,9]=>[1,8,7,6,5,4,3,2,9]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[6,2,3,8,7,1,4,5]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,2,3,6,4,7,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,3,6,4,8,1,5]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,5,1,3,2,6,8,7]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[6,4,7,5,1,3,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,3,1,6,2,7,8,4]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,7,2,4,1,8,3,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,1,6,3,2,7,8,4]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,2,1,6,4,7,3,8]=>[7,3,2,5,4,6,1,8]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[5,4,1,6,2,7,8,3]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,7,2,5,4,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,1,3,5,4,2,8,6]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,8,2,4,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,2,8,6,5,1,3,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[3,8,5,4,7,1,2,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,4,8,3,6,2,7,5]=>[1,6,8,4,7,2,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,2,4,8,7,1,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,2,7,4,1,5,6]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,3,2,6,5,8,1,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,6,2,5,7,4,8,1]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,7,1,5,8,6,4,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[7,2,4,1,6,8,5,3]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,4,7,2,3,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,1,8,5,7,4,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,4,3,6,5,8,2]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,5,6,3,4,8,2]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,8,5,4,7,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,1,5,4,2,8,3]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,1,6,8,7,2,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,6,7,5,3,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,3,2,6,8,7,4,1]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,4,6,2,8,7,3,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,5,8,6,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,7,6,1,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,6,5,7,2,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,3,5,7,10,8,9,6,4,1]=>[10,2,9,8,7,6,5,4,3,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[2,4,7,5,10,8,9,6,3,1]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[2,4,6,9,7,8,5,3,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[2,6,5,8,9,7,10,4,3,1]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[3,7,4,5,10,9,8,1,6,2]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[3,6,4,8,9,7,1,10,5,2]=>[10,9,7,6,5,4,3,8,2,1]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[3,7,4,5,10,8,9,6,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[3,6,4,9,7,8,5,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[3,5,6,8,9,7,10,4,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[7,4,8,6,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,4,3,6,1,8,5]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[6,3,7,1,4,2,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,3,2,1,7,6,5,9,10,8]=>[4,3,2,1,7,6,5,10,9,8]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[4,6,3,5,1,8,2,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[8,5,7,6,2,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,6,7,8,9,2,4,1]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[3,4,6,7,8,2,5,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[2,5,6,7,3,8,1,4]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[5,8,4,6,2,1,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,4,7,5,8,6,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,6,8,3,4,2,7,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,7,6,2,8,3,5]=>[7,2,8,5,4,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,1,8,2,7,5,3,6]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,1,7,2,8,5,3,6]=>[7,2,8,4,6,5,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[2,5,6,3,7,4,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[2,6,5,3,8,4,7,1]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[2,6,5,3,7,4,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,1,6,3,5,4,8,2]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,3,2,8,4,1,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[2,8,6,1,7,5,3,4]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[8,1,5,2,7,4,3,6]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,4,2,8,5,3,6]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,6,8,1,7,5,3,4]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,4,6,5,3,8,2,7]=>[1,7,5,4,3,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,4,5,8,7,1,3,6]=>[6,7,3,8,5,1,2,4]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,1,6,8,7,5,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,8,7,5,6,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,1,8,7,6,3,4,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,7,5,3,6,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,2,3,1,5,6,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,8,5,7,6,1,3,4]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[1,8,7,2,6,4,5,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,2,1,6,4,5,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,8,4,7,6,2,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,7,1,6,4,3,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,4,1,7,3,6,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,3,6,2,1,5,4,7]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,7,3,6,8,2,5,4]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,5,1,8,7,3,6,2]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,8,5,2,6,7,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,3,8,5,2,6,1,7]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[3,6,4,7,5,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,7,4,1,2,6,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,8,6,7,5,3,1,4]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[7,4,5,2,6,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[8,6,3,4,5,1,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,3,5,4,1,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,4,5,1,3,6,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,2,5,3,1,4,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,3,1,2,5,6]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,7,3,5,1,6,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,3,2,6,1,7,5]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[4,3,7,6,1,5,2,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[7,5,4,3,6,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,6,8,5,3,1,2,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[5,6,8,4,3,7,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,4,2,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,4,8,7,6,2,5,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,4,1,5,3,8,6]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[8,5,3,4,1,7,2,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,8,5,4,3,6,1,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[8,6,5,3,1,2,7,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,6,5,3,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,6,7,2,3,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,4,2,6,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,4,2,8,5,6,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,2,1,7,4,6,8,5]=>[3,2,1,8,5,6,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[6,2,5,7,1,4,3,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[4,8,5,3,1,2,6,7]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[8,5,2,4,6,1,3,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,6,1,5,7,3,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,7,2,1,3,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,7,3,1,2,4,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,1,8,7,6,2,5,4]=>[6,2,8,7,5,1,4,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,3,8,6,7,2,5,4]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,2,3,6,1,8,4,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[3,2,6,4,7,1,5,8]=>[6,2,7,4,5,1,3,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[3,6,2,5,7,8,4,1]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,7,4,6,8,3,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,7,6,8,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,5,7,6,8,4,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,4,6,8,5,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,7,6,8,5,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,3,8,6,2,4,5]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,7,1,8,6,5,3,4]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[8,1,5,2,6,4,7,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,6,7,5,1,2,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,3,4,7,6,2,1,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,1,8,5,7,2,6,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,8,2,7,5,6,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,8,2,4,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,5,3,8,1,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,6,1,4,2,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[8,7,2,6,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,2,3,4,8,5,6,9,7]=>[1,2,3,4,9,6,7,8,5]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,7,8,5,9,6]=>[1,2,3,4,9,7,6,8,5]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,6,4,8,3,5,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,4,8,5,3,2,7,6]=>[1,6,8,5,4,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,5,8,4,6,7,1,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,2,4,8,5,7,3,6]=>[1,2,7,8,5,6,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,3,4,1,8,2,5,6]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[5,6,3,1,8,2,4,7]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,3,6,5,1,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,2,1,4,8,6,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,6,3,5,2,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,1,4,6,8,5,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,5,1,6,4,8,3]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[2,7,1,5,6,4,8,3]=>[3,8,1,6,5,4,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,5,7,8,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,8,5,7,6,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,1,5,6,4,7,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[3,7,2,8,1,5,6,4]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[7,3,2,5,1,6,8,4]=>[8,5,3,6,2,4,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,7,2,1,3,6,5,4]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,3,2,8,1,4,6,5]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,6,2,1,8,4,7,5]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,5,1,7,6,4,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,7,4,2,1,6,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,7,6,2,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,5,2,8,7,1,6,4]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[3,7,6,5,4,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,6,5,3,1,8,7,2]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,5,2,6,7,3,8,1]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,6,7,4,3,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,7,1,8,5,3,2,6]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[8,6,7,1,4,3,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,7,2,1,3,5,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,5,6,1,7,4,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,1,2,5,7,8,3]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,1,5,4,2,7,3,8]=>[7,2,5,4,3,6,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,4,2,3,1,7,5,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[3,4,6,1,8,2,7,5]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[5,3,1,4,7,6,2,8]=>[7,4,3,2,6,5,1,8]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[6,4,5,2,7,1,3,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[7,4,3,5,1,6,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,5,3,6,2,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,4,3,7,1,8,2,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,1,2,7,6,4,5,8]=>[3,2,1,7,6,5,4,8]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[5,1,2,7,6,3,4,8]=>[7,2,3,6,5,4,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[5,6,1,7,2,4,3,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[3,5,6,8,1,2,7,4]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[2,6,5,3,4,1,7,8]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[2,6,1,3,5,4,7,8]=>[3,6,1,4,5,2,7,8]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[4,6,1,5,2,8,7,3]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,1,5,4,2,7,8,3]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,6,1,5,2,7,8,3]=>[8,5,3,4,2,6,7,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[2,8,6,5,1,3,7,4]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[5,1,8,6,2,7,4,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,6,8,2,7,5,1,4]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[5,6,4,1,7,2,8,3]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[3,8,6,1,5,7,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,6,3,4,2,5,7]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,2,3,1,6,8,5]=>[8,5,4,3,2,6,7,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[6,4,2,3,7,8,1,5]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,3,6,2,5,8,1,7]=>[7,4,5,2,3,8,1,6]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[9,8,10,7,6,5,4,3,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,7,9,6,5,4,2,1,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,9,7,6,5,4,2,1,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,9,7,6,5,4,2,3,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,7,1,2,3,4,8,9,5,6]=>[10,9,3,4,5,6,8,7,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[1,6,4,5,7,3,2,8]=>[1,7,6,4,5,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,4,5,7,2,8,3]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,6,4,8,3,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,6,7,3,2,4,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,4,3,1,7,5,6]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[8,2,1,4,3,7,5,6]=>[8,3,2,5,4,7,6,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[7,6,8,2,1,5,3,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,2,5,1,3,7,4]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[7,1,6,8,3,2,4,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,2,6,4,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,5,6,1,3,8,2,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[6,3,5,7,4,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,6,4,8,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,1,6,4,7,3,5]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,3,8,6,5,2,7,4]=>[1,6,8,7,5,2,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,3,8,5,6,4,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,2,8,5,7,4,6,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,5,4,7,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,1,8,3,2,6,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,1,3,8,6,4,7,5]=>[2,1,3,8,7,6,5,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[8,2,5,4,3,7,1,6]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,8,4,3,7,6,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,1,5,3,4,7,2,6]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,8,7,4,5,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,5,8,6,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,6,4,2,1,7,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,1,8,4,7,5,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[5,3,8,6,1,2,7,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[5,8,1,4,6,2,7,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,7,6,2,1,4,8,5]=>[5,8,6,4,1,3,7,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[4,6,2,3,7,1,8,5]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[6,8,7,5,1,3,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,3,2,7,8,5,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,7,6,1,5,3,8,4]=>[4,8,6,1,5,3,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[7,8,6,4,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,5,8,7,1,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,1,7,8,3,2,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,4,3,8,7,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,4,7,2,1,3,8,6]=>[6,5,8,4,2,1,7,3]=>[6,5,8,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[1,8,9,3,4,5,6,2,7]=>[1,9,8,7,5,6,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[2,6,4,5,7,1,8,3]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[3,7,4,6,1,5,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,4,6,5,2,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,6,7,5,8,2,1,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,5,7,6,4,1,8,3]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[5,1,4,6,2,7,8,3]=>[8,2,5,4,3,6,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,5,3,7,8,6,4]=>[1,2,8,4,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,8,3,5,1,2,7,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[6,1,3,7,2,8,4,5]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,8,5,4,1,7,2,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[3,1,5,8,2,6,7,4]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,8,5,3,1,7,4,6]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[6,5,2,3,7,1,8,4]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[7,2,1,6,4,8,3,5]=>[8,3,2,7,5,6,4,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[2,1,3,7,5,8,4,6]=>[2,1,3,8,7,6,5,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,2,4,5,7,1,8,3]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[2,3,8,7,1,4,6,5]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,2,7,5,6,8,1,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,8,2,5,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,6,3,8,4,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,6,8,2,3,1,7,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[4,7,2,3,5,1,8,6]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[6,4,2,1,3,7,5,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,3,2,7,6,1,8,4]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,6,4,2,8,7,1,3]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,7,4,2,6,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,4,7,1,6,2,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,5,8,7,6,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,7,1,2,3,8,5]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[10,6,9,5,4,3,8,2,7,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,2,6,10,9,5,4,3,7,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[4,10,8,2,5,6,7,1,9,3]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[9,3,10,4,5,7,1,8,2,6]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[4,9,3,10,5,7,1,8,2,6]=>[9,10,7,8,5,6,3,4,1,2]=>[9,10,7,8,5,6,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[10,5,7,1,9,4,2,6,8,3]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[10,5,7,1,8,3,9,4,2,6]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[10,7,1,8,3,9,4,2,5,6]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[6,1,7,3,8,4,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,3,1,6,4,7,5]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,8,7,2,3,4,6,5]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,3,7,6,2,5,4]=>[1,8,6,7,5,3,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,2,5,6,4,7]=>[1,4,8,2,7,6,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,8,4,6,2,7,5]=>[1,6,8,4,7,2,5,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,2,3,6,7,4,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,6,4,2,1,7,3,8]=>[7,5,4,3,2,6,1,8]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[2,5,7,6,3,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[6,4,7,1,2,5,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,2,7,5,8,6,3,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,9,8,7,6,5,3,4]=>[2,1,9,8,7,6,5,4,3]=>[2,1,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,9,8,7,6,4,3,5]=>[2,1,9,8,7,6,5,4,3]=>[2,1,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,9,8,7,6,3,5,4]=>[2,1,9,8,7,6,5,4,3]=>[2,1,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,10,9,8,7,6,5,3,4]=>[2,1,10,9,8,7,6,5,4,3]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[7,4,5,1,6,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,7,8,4,2,6,3,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,2,5,7,4,1,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,2,5,1,3,8,7,4]=>[8,4,5,2,3,7,6,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,2,8,5,1,3,7,4]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[10,9,7,3,6,1,2,4,8,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,4,10,9,7,3,6,1,2,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,8,4,9,7,3,6,1,2,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,3,8,4,10,9,6,1,2,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,3,10,8,4,9,6,1,2,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,7,3,8,4,9,6,1,2,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,6,1,3,7,2,4,8,5]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[6,1,3,10,8,4,9,7,2,5]=>[10,2,9,8,7,6,5,4,3,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[8,4,10,9,6,1,3,7,2,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,8,4,9,6,1,3,7,2,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,3,6,1,4,10,9,7,2,5]=>[10,9,8,4,5,7,6,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[10,8,3,6,1,4,9,7,2,5]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[10,9,6,1,4,8,3,7,2,5]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[9,6,1,4,10,8,3,7,2,5]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[8,3,9,6,1,4,10,7,2,5]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[9,4,10,8,3,7,2,6,1,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,3,9,4,10,7,2,6,1,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[12,11,9,5,10,7,1,2,4,8,3,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,5,12,10,7,1,2,4,8,3,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,5,11,8,3,7,1,2,4,10,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,9,4,8,3,7,1,2,5,10,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,5,12,11,9,4,8,3,7,1,2,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,5,11,9,4,8,3,7,1,2,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,4,10,5,12,11,8,3,7,1,2,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,4,12,10,5,11,8,3,7,1,2,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,4,10,5,11,8,3,7,1,2,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,3,9,4,10,5,12,11,7,1,2,6]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[8,3,9,4,12,10,5,11,7,1,2,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,3,12,9,4,10,5,11,7,1,2,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,8,3,9,4,10,5,11,7,1,2,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,8,2,4,9,5,10,7,1,3,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,5,11,8,2,4,10,7,1,3,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,9,4,8,2,5,10,7,1,3,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,4,12,11,8,2,5,10,7,1,3,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,8,2,5,12,9,4,10,7,1,3,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,4,10,5,12,11,7,1,3,8,2,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[9,4,12,10,5,11,7,1,3,8,2,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,9,4,10,5,11,7,1,3,8,2,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,5,12,11,9,3,7,1,4,8,2,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,10,5,11,9,3,7,1,4,8,2,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[12,11,5,10,4,9,3,8,2,7,1,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,5,12,10,4,9,3,8,2,7,1,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[10,4,11,5,12,9,3,8,2,7,1,6]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[4,1,7,8,3,6,5,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,2,1,7,3,5,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[5,8,4,2,1,3,6,7]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,7,5,8,4,3,6,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,1,6,4,7,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,4,7,5,1,8,6,3]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,3,7,1,8,5,6,4]=>[4,2,8,1,7,6,5,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[6,5,1,2,7,4,8,3]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,6,5,7,8,2,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,6,5,1,8,7,4,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[7,8,1,2,5,4,3,6]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,8,4,3,5,1,7,6]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[5,2,4,7,6,8,1,3]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,1,5,7,4,8,6,2]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,7,6,8,2,5,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,6,4,1,5,3,8]=>[7,5,6,4,2,3,1,8]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[7,3,5,6,1,4,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,8,3,1,6,7,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,5,8,1,7,3,6,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,7,1,6,8,5,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,8,7,1,6,4,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,7,3,8,2,5,4,6]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,4,1,3,6,7,5,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,3,1,8,6,7,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,7,1,6,4,2,8,3]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[2,7,1,6,5,8,4,3]=>[3,8,1,7,5,6,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[2,7,1,4,8,6,5,3]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[6,7,5,4,1,3,2,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,2,7,1,4,3,5,8]=>[7,4,6,2,5,3,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[8,3,2,6,5,1,7,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,3,2,6,5,1,4,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[2,6,8,4,7,1,3,5]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[7,8,6,3,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,8,6,3,1,4,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[2,8,5,6,4,1,7,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[1,4,7,3,5,8,6,2]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,8,2,5,1,6,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[8,6,1,4,3,2,7,5]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,3,8,2,4,1,5,6]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,3,7,8,1,2,5,4]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,6,1,5,2,3,8,4]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[5,1,8,6,7,2,3,4]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,1,6,8,2,3,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,4,2,1,7,3,5]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,2,8,1,7,4,5]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[6,4,1,3,7,8,5,2]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,5,4,3,7,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,4,8,3,1,2,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[6,1,2,4,8,3,7,5]=>[8,2,3,6,7,4,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,5,6,8,1,4,7,3]=>[5,8,6,7,1,3,4,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[7,4,1,6,5,2,3,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,1,6,5,2,3,8,7]=>[6,2,5,4,3,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,5,1,7,8,6,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,5,7,3,4,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,7,4,3,5,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,7,5,3,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,8,6,2,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,6,2,5,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,4,7,5,3,2,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,5,3,2,7,4,8]=>[1,7,5,4,3,6,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,7,4,5,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,4,3,2,8,6]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,5,3,2,8,6]=>[1,6,8,5,4,2,7,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,4,6,8,5,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,7,2,3,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,7,6,1,8,2,4,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,6,5,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,7,8,5,1,4,3,6]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[8,5,6,2,4,7,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,8,4,2,6,1,7]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[8,1,3,6,4,5,2,7]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,5,3,1,9,8,6,4,2]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[5,3,1,9,8,7,6,4,2]=>[9,8,3,7,6,5,4,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[7,5,3,1,10,9,8,6,4,2]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[5,3,1,10,9,8,7,6,4,2]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[4,3,1,6,2,5,8,7]=>[5,3,2,6,1,4,8,7]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[7,5,2,1,8,4,3,6]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[5,3,1,4,7,8,2,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[7,1,2,4,8,3,5,6]=>[8,2,3,6,7,4,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,6,1,3,5,7,4,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,5,8,2,3,4,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,6,8,5,1,4,2,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[5,2,4,1,6,8,3,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,3,2,5,4,7,6,10,8,9]=>[1,3,2,5,4,7,6,10,9,8]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[2,5,3,4,6,8,1,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[4,7,1,2,5,6,3,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[6,7,3,1,8,2,4,5]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,1,4,6,2,8,5]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,4,1,2,5,6,3,8]=>[7,6,3,4,5,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,4,1,3,6,8,7,2]=>[8,4,3,2,5,7,6,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[5,7,4,8,1,6,3,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,3,1,2,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,2,3,4,5,8,9,7,6]=>[1,2,3,4,5,9,8,7,6]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,8,9,6,7,5]=>[1,2,3,4,9,8,7,6,5]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,8,9,5,6,7,4]=>[1,2,3,9,8,7,6,5,4]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,4,7,8,5,6,3]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,8,9,4,5,6,7,3]=>[1,2,9,8,7,6,5,4,3]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[8,3,6,5,7,4,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,6,5,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,7,1,5,2,6,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,6,3,7,5,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,2,5,3,7,6,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,7,1,4,3,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,1,8,4,2,6,7]=>[6,5,3,8,2,1,7,4]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[4,5,3,6,8,7,1,2]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,1,6,5,8,7,3,4]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[6,1,5,4,7,3,8,2]=>[8,2,6,4,5,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,1,8,4,2,7,6,5]=>[5,2,8,4,1,7,6,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[2,8,7,4,1,3,6,5]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[8,2,3,1,7,6,4,5]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,7,2,3,1,6,4,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,2,5,8,3,1,4,6]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[6,8,2,3,1,7,4,5]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,2,5,7,3,1,4,6]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[8,2,7,3,1,4,5,6]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[5,3,2,8,7,1,6,4]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,6,7,4,1,3,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,1,3,6,5,2,8,7]=>[6,2,3,5,4,1,8,7]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,6,3,2,5,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[4,8,3,2,6,5,7,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,8,3,6,5,2,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,6,2,5,4,7,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,4,3,8,6,1,7,5]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[2,6,3,8,5,4,7,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,8,4,2,5,3,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,4,3,5,2,7,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,4,6,5,3,7,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,5,4,6,1,2,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,8,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[7,3,5,6,1,8,2,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,6,3,4,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,6,7,2,3,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,5,4,8,7,2,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,8,3,9,10,4,5,1,6]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[7,2,8,9,3,4,10,5,1,6]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[7,2,8,9,3,10,4,5,1,6]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,2,8,9,10,3,4,5,1,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,2,3,9,10,4,5,1,6]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[7,8,2,3,9,10,4,1,5,6]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[7,8,2,9,3,4,10,5,1,6]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[7,8,2,9,3,4,10,1,5,6]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[7,8,2,9,3,10,4,5,1,6]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,8,2,9,3,10,4,1,5,6]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,8,2,9,10,3,4,5,1,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,2,9,10,3,4,1,5,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,2,3,4,10,5,1,6]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[7,8,9,2,3,4,10,1,5,6]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[7,8,9,2,3,10,4,5,1,6]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,8,9,2,3,10,4,1,5,6]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,8,9,2,3,10,1,4,5,6]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,8,9,2,10,3,4,5,1,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,2,10,3,4,1,5,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,2,10,3,1,4,5,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,10,2,3,4,1,5,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,10,2,3,1,4,5,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,10,2,1,3,4,5,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,2,9,10,11,12,3,4,5,6,1,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,9,2,10,11,12,3,4,5,6,1,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,9,2,10,11,12,3,4,5,1,6,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,9,10,2,11,12,3,4,5,6,1,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,9,10,2,11,12,3,4,5,1,6,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,9,10,2,11,12,3,4,1,5,6,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,9,10,11,2,12,3,4,5,6,1,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,9,10,11,2,12,3,4,5,1,6,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,9,10,11,2,12,3,4,1,5,6,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,9,10,11,2,12,3,1,4,5,6,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,9,10,11,12,2,3,4,5,6,1,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,9,10,11,12,2,3,4,5,1,6,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,9,10,11,12,2,3,4,1,5,6,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,9,10,11,12,2,3,1,4,5,6,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,9,10,11,12,2,1,3,4,5,6,7]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[4,8,7,6,5,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[5,9,8,7,6,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[5,8,7,4,6,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[8,4,7,6,5,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[5,7,4,3,6,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,9,8,5,7,4,1,3,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,5,1,6,4,3,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,9,8,6,1,7,5,4,3,2]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[1,2,8,3,4,5,6,9,7]=>[1,2,9,4,5,6,7,8,3]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,9,3,4,5,6,7,10,8]=>[1,2,10,4,5,6,7,8,9,3]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,2,3,4,5,9,6,7,10,8]=>[1,2,3,4,5,10,7,8,9,6]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[9,8,1,2,3,5,6,4,7]=>[9,8,3,4,5,7,6,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[1,8,5,6,2,3,7,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,2,4,6,8,1,5,3]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[6,2,5,4,7,8,1,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[3,8,2,6,1,7,4,5]=>[5,8,3,7,1,6,4,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[8,5,6,1,3,2,7,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[5,3,7,8,2,6,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,8,3,6,1,7,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[4,5,8,7,2,3,1,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[8,2,6,4,3,7,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,1,8,7,4,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,6,3,2,7,4,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,3,6,8,7,4,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,1,3,6,2,4,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,7,5,2,3,6,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,6,4,1,2,5,7,8]=>[5,6,4,3,1,2,7,8]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[4,7,1,3,2,5,8,6]=>[5,8,3,4,1,6,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[4,7,1,3,2,6,8,5]=>[5,8,3,4,1,6,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[5,7,1,3,6,2,8,4]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,8,2,5,7,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,5,2,3,6,1,7]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[5,8,6,3,4,7,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,5,4,2,8,1,6]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[4,6,5,1,7,8,2,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,7,1,3,2,8,5,6]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[3,6,5,1,8,2,4,7]=>[6,7,4,3,8,1,2,5]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[5,8,7,3,4,2,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,7,6,5,4,1,9,3,2]=>[9,8,6,5,4,3,7,2,1]=>[9,8,6,5,4,3,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[8,7,6,5,2,9,1,3,4]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[8,7,6,3,9,2,1,4,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,7,4,9,3,2,1,6,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,6,5,4,1,10,3,2]=>[10,9,7,6,5,4,3,8,2,1]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[10,9,8,7,6,5,4,2,1,3,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[8,7,6,5,2,1,4,3,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[9,8,7,6,5,2,10,1,3,4]=>[10,9,8,6,5,4,7,3,2,1]=>[10,9,8,6,5,4,7,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[10,9,8,7,6,5,3,2,1,4,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[8,7,6,3,2,5,1,4,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[8,7,6,5,1,9,4,3,2]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[9,8,7,6,3,10,2,1,4,5]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,7,4,3,6,2,1,9,5]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[8,7,6,2,9,5,1,3,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,4,10,3,2,1,6,5]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,5,4,3,2,1,6,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[8,5,4,7,3,2,1,6,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[8,7,3,9,6,2,1,4,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,5,10,4,3,2,1,6,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,6,5,4,3,2,1,7,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[10,8,7,6,5,4,3,2,1,9,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[8,5,2,3,7,4,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,3,1,5,4,8,2,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,7,6,3,5,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,7,5,3,4,8,6,2]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,2,3,4,7,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,7,3,2,6,4,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,1,4,7,5,2,6]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,3,1,6,4,8,7,2]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[3,4,8,5,7,2,6,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[8,5,1,2,7,6,4,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,2,6,3,1,5,4,7]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[3,7,8,5,6,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,3,6,2,5,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[4,3,8,7,1,6,2,5]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[8,2,3,1,6,5,7,4]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,4,2,7,1,3,6,5]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[8,4,2,3,1,6,7,5]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[4,7,2,3,6,5,8,1]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[3,8,2,6,4,7,1,5]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[1,7,5,8,6,2,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,5,1,7,4,8,3,2]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[10,9,8,6,7,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,6,3,5,1,4,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[6,5,4,1,7,2,3,8]=>[7,6,4,3,5,2,1,8]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[8,3,6,1,7,4,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,1,2,6,4,8,3,5]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,5,1,8,6,2,4,7]=>[6,7,3,8,5,1,2,4]=>[6,8,3,7,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[8,7,5,6,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[8,6,5,7,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[9,8,7,6,4,3,2,5,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,6,4,3,5,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,5,6,7,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[10,9,7,6,8,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,7,5,8,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[10,8,7,6,9,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,7,6,4,3,2,1,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,6,5,3,2,1,4,8,9]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[9,8,7,6,4,3,5,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,6,4,3,2,5,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[9,8,7,6,4,5,2,3,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,6,4,3,5,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[9,8,7,6,5,3,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[1,8,7,5,4,6,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,6,7,4,5,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,6,4,7,5,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,4,8,1,5,3,7,2]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,6,4,3,5,8,2,7]=>[1,7,5,4,3,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,1,4,3,7,8,6,2]=>[8,2,4,3,7,6,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,7,1,8,6,3,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,7,6,3,4,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[4,1,3,7,6,5,2,8]=>[7,2,3,6,5,4,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,7,6,5,4,2,3,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,10,9,8,6,5,7,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[2,9,8,6,5,7,4,3,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,2,6,1,3,5,8,4]=>[8,4,6,2,5,3,7,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,2,7,1,5,8,3,4]=>[8,4,7,2,5,6,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[5,8,3,6,7,2,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,6,2,5,7,4,3]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,7,1,5,3,6,8,4]=>[3,8,1,6,5,4,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[6,8,7,3,4,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,8,6,2,4,7,5,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,3,6,4,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,7,3,6,4,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,7,5,6,4,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,1,8,2,3,4,5,9,6]=>[9,2,7,4,5,6,3,8,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[9,6,7,4,5,2,3,1,8]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,9,6,7,4,5,2,1,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,8,9,6,7,4,5,2,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,8,6,5,4,3,7,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[2,8,5,7,3,4,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,7,6,1,4,2,8,9]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[4,6,7,8,3,1,5,2,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[5,7,8,3,9,4,1,6,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[2,4,3,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[3,4,5,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,10,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[3,5,7,6,1,4,2,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,10,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[4,6,7,8,3,1,5,2,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[4,6,8,7,3,9,10,5,2,1]=>[10,9,8,5,4,6,7,3,2,1]=>[10,9,8,5,4,7,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[5,7,8,3,9,4,1,6,2,10]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[6,8,9,3,4,10,5,1,7,2]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[6,7,2,3,5,8,1,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,4,5,8,2,3,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,1,3,8,5,4,6,7]=>[2,1,3,8,6,5,7,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[5,3,6,8,2,4,1,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,7,8,6,3,2,4,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,1,2,5,3,8,4,6]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[3,7,4,2,5,1,8,6]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[1,8,3,4,5,7,2,6]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,7,5,3,8,1,4]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[4,5,2,6,8,7,1,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,5,2,6,8,3,1,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,5,7,6,2,1,3,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,8,2,6,5,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,3,7,8,4,2,1,6]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[7,3,6,8,1,5,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[9,7,8,5,6,2,4,1,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,7,8,4,6,2,5,1,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,6,8,4,7,2,5,1,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,9,6,4,7,2,5,1,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,9,6,7,4,2,5,1,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,7,8,3,6,2,5,1,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,5,8,4,7,2,6,1,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,6,9,4,8,2,5,1,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,6,9,7,4,2,5,1,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,8,9,6,4,7,2,5,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,6,4,7,5,2,1,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,8,9,6,7,4,2,5,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,6,7,4,2,5,3,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,5,8,2,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,8,2,3,4,1,7]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[8,1,5,3,4,6,2,7]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[5,8,7,2,4,3,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,2,4,8,5,6,3]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,8,2,3,7,4,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,8,2,3,5,4,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,4,1,3,2,6,5,7]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[8,7,2,3,5,4,6,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,7,6,8,4,5,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,7,3,1,8,5,6,4]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[3,8,5,2,1,6,7,4]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,8,6,1,5,7,4,3]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[8,3,5,1,7,6,4,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,5,4,7,1,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,1,5,7,8,2,3]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,8,7,1,2,5,3,6]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[8,7,2,6,1,4,3,5]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,1,7,3,8,2,4,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,8,6,4,2,3,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,1,3,5,8,2,6,7]=>[6,2,3,4,8,1,7,5]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,8,5,7,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,7,6,8,3,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,2,8,6,5,3,4]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,1,6,4,2,3,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[4,8,2,7,5,1,6,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,4,6,7,1,5,3]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[3,8,5,1,4,2,6,7]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,7,6,2,5,3,8,4]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,5,2,4,3,8,6]=>[1,8,6,4,5,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,8,5,1,4,3,6,7]=>[4,8,6,1,5,3,7,2]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[9,7,6,5,4,3,2,8,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,6,3,5,4,8,2,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,9,8,5,6,7,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,10,9,8,5,6,7,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,9,8,5,4,6,7,3,2]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,10,9,5,6,7,8,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,9,5,4,6,7,8,3,2]=>[1,9,8,7,5,6,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,10,4,5,6,7,8,9,3,2]=>[1,10,9,8,5,6,7,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[3,1,2,5,7,6,8,4]=>[3,2,1,8,6,5,7,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[5,1,7,3,2,6,8,4]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,8,2,3,7,5,1,6]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[8,7,2,4,3,5,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,2,4,3,5,1,7]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,2,4,7,3,5,6]=>[8,2,3,6,7,4,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,2,8,4,5,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,8,1,5,7,3,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,1,7,5,6,8,2,3]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,8,7,2,5,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,8,7,6,3,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,1,8,4,5,2,7,6]=>[6,2,8,4,5,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[2,3,7,6,1,8,4,5]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[4,8,5,2,1,3,7,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[5,8,4,2,1,3,7,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[9,8,7,6,5,3,1,4,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,6,4,1,5,3,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,6,1,7,5,4,3,2]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[9,7,1,8,6,5,4,3,2]=>[9,8,3,7,6,5,4,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[4,6,7,5,2,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,2,5,3,1,8,7,4]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[6,2,5,3,8,7,1,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,4,5,3,8,7,1,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,6,4,5,8,7,3,2]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,4,7,5,2,3,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,7,4,5,3,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,4,7,5,3,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,2,6,7,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,6,7,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,4,5,8,7,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,8,7,5,3,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,6,5,3,8,7,1,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,7,2,4,5,3,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,8,7,4,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,8,4,7,5,3,1,6]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,8,7,4,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,8,4,7,2,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,8,6,2,5,7,1,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,1,6,2,5,7,3,4]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,8,1,2,4,7,3,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[8,1,5,3,2,7,4,6]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,3,7,6,2,5,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,2,3,4,6,5,8,7,9]=>[1,2,3,4,6,5,8,7,9]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,2,3,4,8,9,5,6,7]=>[1,2,3,4,9,8,7,6,5]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[4,6,1,3,5,8,2,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[4,5,1,3,8,7,2,6]=>[7,4,3,2,8,6,1,5]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[6,2,7,1,8,3,4,5]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[6,4,5,8,1,7,2,3]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[6,2,8,5,1,4,7,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[2,4,7,6,1,8,3,5]=>[5,7,8,4,1,6,2,3]=>[5,8,7,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[2,1,7,8,9,3,4,5,6]=>[2,1,9,8,7,6,5,4,3]=>[2,1,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[9,7,5,3,8,6,4,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,8,9,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,4,5,8,6,3,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,9,7,4,3,2,1,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,6,4,9,7,5,2,1,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,8,6,4,9,7,5,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,5,3,8,6,4,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,8,6,4,2,1,9,7,5,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[11,9,10,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[9,6,7,8,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,8,9,6,5,4,3,2,1,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,8,11,9,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[8,5,6,9,7,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,7,10,8,5,4,3,2,1,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,8,4,3,2,1,5,6]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,8,6,11,9,7,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[8,6,3,4,9,7,5,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,6,9,7,3,2,1,4,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,7,5,10,8,6,3,2,1,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[11,9,7,5,10,8,6,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[9,7,5,2,3,8,6,4,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,8,6,4,9,7,5,2,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[11,9,7,5,3,2,1,10,8,6,4]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[8,6,4,9,7,5,1,2,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,8,6,4,1,2,9,7,5,3]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[11,9,7,5,3,10,8,6,4,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[10,8,6,4,2,11,9,7,5,3,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[7,9,8,5,4,3,2,1,6]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,6,9,8,4,3,2,1,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,6,5,9,8,3,2,1,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,6,5,4,9,8,2,1,3]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[1,6,2,3,8,5,7,4]=>[1,8,3,4,7,6,5,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,4,2,6,8,5,7,1]=>[8,3,2,6,7,4,5,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[9,8,7,6,5,2,3,4,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,1,7,8,9,2,3,4,5]=>[9,2,8,7,6,5,4,3,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[7,4,1,3,6,8,2,5]=>[8,7,3,4,5,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,8,1,2,7,3,4,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,6,2,8,7,3,4,5]=>[1,8,3,7,6,5,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,6,8,5,7,4,3,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,8,1,2,4,7,6,5]=>[4,8,3,1,5,7,6,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,3,8,1,4,6,5,7]=>[4,2,8,1,5,7,6,3]=>[4,2,8,1,7,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[3,6,2,4,7,5,8,1]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[3,1,8,4,6,2,5,7]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[4,2,7,3,5,8,1,6]=>[7,4,8,2,5,6,1,3]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[3,1,8,4,5,6,2,7]=>[7,2,8,4,5,6,1,3]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[4,2,7,8,6,3,1,5]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[7,1,4,2,8,6,3,5]=>[8,2,7,4,6,5,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,3,7,4,8,1,6,5]=>[6,2,8,4,7,1,5,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,6,3,5,8,7,4,2]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,4,6,3,5,1,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,3,2,6,8,4,5,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[2,4,5,7,1,6,8,3]=>[5,8,3,6,1,4,7,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[8,4,2,6,7,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,1,5,7,8,6,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[6,1,4,8,2,3,7,5]=>[8,2,6,7,5,3,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,6,2,3,5,8,4,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[2,8,5,7,6,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,5,7,8,6,4,1,3]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[7,4,1,6,2,5,8,3]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,7,4,6,2,5,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,7,5,4,6,2,3,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,2,7,5,3,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[6,1,7,4,8,5,2,3]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,2,4,6,3,1,7,5]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[5,6,2,4,8,7,3,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,5,6,2,3,7,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,8,1,4,5,6,2,3]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,6,7,8,9,1,3,4,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,7,8,9,1,3,4,5,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,7,8,9,1,4,5,2,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,7,8,9,1,4,5,3,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,7,8,9,1,5,4,3,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,8,9,1,4,5,6,2,3]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[7,8,9,1,4,5,6,3,2]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[7,8,9,1,5,6,3,4,2]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[7,8,9,1,5,6,4,3,2]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[7,8,9,1,6,5,4,3,2]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[8,9,1,5,6,7,3,4,2]=>[9,8,3,7,6,5,4,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[8,9,1,5,6,7,4,3,2]=>[9,8,3,7,6,5,4,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[8,9,1,6,7,4,5,2,3]=>[9,8,3,7,6,5,4,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[8,9,1,6,7,4,5,3,2]=>[9,8,3,7,6,5,4,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[8,9,1,6,7,5,4,3,2]=>[9,8,3,7,6,5,4,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[9,1,7,8,5,6,3,4,2]=>[9,2,8,7,6,5,4,3,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[9,1,7,8,5,6,4,3,2]=>[9,2,8,7,6,5,4,3,1]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[5,6,7,8,9,10,1,3,4,2]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[5,6,7,8,9,10,1,4,3,2]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,8,9,10,1,4,5,6,2,3]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,8,9,10,1,4,5,6,3,2]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,8,9,10,1,5,6,4,3,2]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,8,9,10,1,6,5,4,3,2]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[8,9,10,1,4,5,6,7,2,3]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[8,9,10,1,4,5,6,7,3,2]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[8,9,10,1,5,6,7,2,3,4]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[8,9,10,1,5,6,7,4,3,2]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[8,9,10,1,6,7,4,5,2,3]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[8,9,10,1,6,7,4,5,3,2]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[8,9,10,1,6,7,5,4,3,2]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[8,9,10,1,7,6,5,4,3,2]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[9,10,1,6,7,8,3,4,5,2]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[9,10,1,6,7,8,4,5,2,3]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[9,10,1,6,7,8,4,5,3,2]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[9,10,1,6,7,8,5,4,3,2]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[9,10,1,7,8,5,6,3,4,2]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[9,10,1,7,8,5,6,4,3,2]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[9,10,1,7,8,6,5,4,3,2]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[10,1,8,9,6,7,4,5,3,2]=>[10,2,9,8,7,6,5,4,3,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[10,1,8,9,6,7,5,4,3,2]=>[10,2,9,8,7,6,5,4,3,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[10,1,8,9,7,6,5,4,3,2]=>[10,2,9,8,7,6,5,4,3,1]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[8,3,1,2,5,4,7,6]=>[8,4,3,2,6,5,7,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[8,1,5,3,7,4,2,6]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,2,6,7,8,3,5,4]=>[1,2,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,4,8,6,7,3,5]=>[1,2,7,8,6,5,3,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[8,1,2,6,5,7,3,4]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,2,6,5,8,3,4]=>[8,2,3,7,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,4,8,3,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,6,1,4,7,5,8,3]=>[3,8,1,6,5,4,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[5,2,7,3,1,6,8,4]=>[8,5,6,4,2,3,7,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[6,7,2,1,3,4,8,5]=>[8,6,4,3,5,2,7,1]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[4,6,3,1,2,7,8,5]=>[5,8,4,3,1,6,7,2]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[2,3,5,6,8,4,7,1]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[2,4,5,8,3,6,7,1]=>[8,5,3,7,2,6,4,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,9,8,7,6,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[5,4,8,7,6,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[4,5,8,7,6,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,9,8,7,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,7,4,6,5,3,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[9,5,8,7,6,4,3,1,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,10,9,8,7,5,4,3,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,1,4,3,6,2,5,7]=>[8,2,6,4,7,3,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,1,5,7,6,4,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,6,3,7,8,4,2,5]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,3,8,4,6,7,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,3,5,8,6,7,2,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[3,2,7,8,5,6,4,1]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,7,3,8,5,6,2,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,4,8,5,6,3,2]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,3,8,7,2,5,6,1]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,7,3,8,6,4,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,2,8,5,6,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,4,8,2,6,7,5,1]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[1,6,3,8,7,4,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,5,8,7,6,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,3,5,8,2,6,7]=>[1,6,3,4,8,2,7,5]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,1,3,8,6,4,5,7]=>[2,1,3,8,7,6,5,4]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,3,6,4,5,8,2,7]=>[1,7,5,4,3,8,2,6]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,1,4,3,5,8,2,7]=>[7,2,5,4,3,8,1,6]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,5,1,3,8,2,4,7]=>[7,6,3,4,8,2,1,5]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,4,3,8,6,2,5,7]=>[1,6,3,8,7,2,5,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,1,3,8,6,2,5,7]=>[6,2,3,8,7,1,5,4]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[7,1,5,4,6,3,8,2]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,9,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[7,6,8,5,4,3,2,9,1]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[6,8,7,5,4,3,2,9,1]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[6,4,7,8,3,5,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,5,6,7,1,8,4,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,5,2,4,8,6,7,1]=>[8,4,3,2,7,6,5,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[3,7,6,1,4,8,5,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[8,4,7,1,5,6,2,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[2,7,8,3,6,1,5,4]=>[6,8,7,4,5,1,3,2]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[1,7,8,3,6,2,5,4]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,4,3,5,8,1,6,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,3,6,4,1,8,5,2]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,8,4,3,6,1,5,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,1,6,4,3,8,5,2]=>[8,2,7,5,4,6,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[8,7,3,4,1,5,2,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,2,6,4,3,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,7,5,4,3,8,2,6]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,5,8,1,7,3,2,6]=>[7,6,8,4,5,2,1,3]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[4,6,7,1,3,8,2,5]=>[7,8,5,4,3,6,1,2]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[2,6,3,1,4,7,8,5]=>[4,8,3,1,5,6,7,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[2,7,3,4,1,8,5,6]=>[5,8,3,4,1,7,6,2]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[8,6,4,5,1,3,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,4,8,5,3,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,4,6,5,1,3,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,3,8,7,1,2,6]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,5,4,7,6,1,2,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[7,5,8,2,4,3,1,6]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[2,3,7,8,1,4,6,5]=>[5,2,8,7,1,6,4,3]=>[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[8,2,3,5,4,1,7,6]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[7,1,3,8,2,4,6,5]=>[8,2,5,7,3,6,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,2,3,6,4,1,8,5]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[6,5,2,4,1,8,3,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,7,2,4,1,3,8,6]=>[6,8,5,4,3,1,7,2]=>[6,8,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[6,2,5,4,1,8,3,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[4,2,6,3,5,8,1,7]=>[7,4,5,2,3,8,1,6]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[4,2,3,6,5,8,7,10,9,1]=>[10,3,2,5,4,7,6,9,8,1]=>[10,3,2,9,8,7,6,5,4,1]=>[[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.]
[7,4,2,6,8,5,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,5,2,4,6,3,1,7]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,4,1,2,8,5,6,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[6,4,1,8,5,2,3,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[8,4,1,6,3,5,2,7]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,3,4,1,6,8,5,2]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,6,2,3,5,7,4,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,6,2,5,7,3,4,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,3,4,8,5,1,2,7]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[8,5,1,2,7,4,6,3]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,2,6,8,3,4,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,6,7,5,4,8,2,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,5,4,2,6,3,7]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,6,7,4,8,9,1,5,2]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[5,6,3,7,8,9,1,4,2]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[8,9,7,6,5,4,1,3,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,7,9,6,5,4,1,3,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,7,8,6,5,4,1,3,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,10,8,7,6,5,4,1,3,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,8,7,6,5,4,3,2,9,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[5,7,3,6,2,1,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,3,2,4,5,6,9,7,8]=>[1,3,2,4,5,6,9,8,7]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[5,8,6,1,2,4,3,7]=>[7,8,6,4,5,3,1,2]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,4,5,7,6,8,2,3]=>[1,8,7,5,4,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,2,1,6,8,4,3]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[2,6,3,1,7,8,5,4]=>[4,8,3,1,7,6,5,2]=>[4,8,3,1,7,6,5,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[6,2,5,7,4,1,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,6,1,8,7,4,5,2]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[4,3,9,5,6,7,8,2,1]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[7,8,4,5,6,1,3,9,2]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[4,8,9,5,6,7,2,1,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,9,4,5,6,7,1,3,10,2]=>[10,8,7,6,5,4,3,2,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[6,8,4,5,1,3,7,9,2]=>[9,7,6,5,4,3,2,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[4,7,1,3,5,6,8,2]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,3,5,7,8,2,6,1]=>[8,6,3,7,5,2,4,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,3,4,9,6,7,2,5,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[4,9,10,5,6,7,8,2,1,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[5,3,2,7,6,4,1,8]=>[7,6,3,5,4,2,1,8]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[5,3,7,4,6,2,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[5,7,3,2,1,8,6,4]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,7,6,3,2,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,2,7,5,4,1,8,6]=>[6,2,8,5,4,1,7,3]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,7,3,5,4,2,6,8]=>[1,7,6,5,4,3,2,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,3,7,4,1,8,6,2]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[7,3,5,4,1,6,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,5,1,6,8,3,2,4]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[5,3,1,7,6,8,2,4]=>[8,7,3,5,4,6,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,1,5,3,2,4,8,6]=>[8,2,6,5,4,3,7,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[7,1,5,2,4,3,6,8]=>[7,2,6,4,5,3,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[6,8,7,3,2,1,5,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,6,8,7,2,4,1,5]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[5,7,3,6,2,1,8,4]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[3,6,5,2,4,8,1,7]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[5,6,7,8,9,3,2,1,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,7,8,9,3,4,1,2,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,7,8,9,3,4,2,1,5]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,8,9,3,4,5,1,2,6]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,8,9,3,4,5,2,1,6]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,8,9,4,5,2,3,1,6]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[7,8,9,4,5,3,2,1,6]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,9,4,5,6,2,3,1,7]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,9,4,5,6,3,2,1,7]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,9,5,6,3,4,1,2,7]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,9,5,6,3,4,2,1,7]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,9,5,6,4,3,2,1,7]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,6,7,4,5,3,2,1,8]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[5,6,7,8,9,10,3,2,1,4]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[7,8,9,10,3,4,5,1,2,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,10,3,4,5,2,1,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,10,4,5,2,3,1,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,10,4,5,3,2,1,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[7,8,9,10,5,4,3,2,1,6]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,3,4,5,6,1,2,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,3,4,5,6,2,1,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,4,5,6,1,2,3,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,4,5,6,3,2,1,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,5,6,3,4,1,2,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,5,6,3,4,2,1,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,5,6,4,3,2,1,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[8,9,10,6,5,4,3,2,1,7]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,5,6,7,2,3,4,1,8]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,5,6,7,3,4,1,2,8]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,5,6,7,3,4,2,1,8]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,5,6,7,4,3,2,1,8]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,6,7,4,5,3,2,1,8]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,6,7,5,4,3,2,1,8]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,7,6,5,4,3,2,1,8]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,7,8,5,6,3,4,2,1,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,7,8,5,6,4,3,2,1,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,7,8,6,5,4,3,2,1,9]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,8,3,6,2,4,7,5]=>[1,8,5,7,3,6,4,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,8,7,5,6,4,2,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[6,8,2,1,5,4,3,7]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[9,8,1,10,7,2,3,4,5,6]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[2,9,1,10,8,7,3,4,5,6]=>[3,10,1,9,8,7,6,5,4,2]=>[3,10,1,9,8,7,6,5,4,2]=>[[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]]
[6,3,2,1,5,8,4,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[4,3,5,6,2,8,1,7]=>[7,5,3,4,2,8,1,6]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[6,3,5,2,7,8,4,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[4,5,3,1,6,8,2,7]=>[7,4,3,2,5,8,1,6]=>[7,4,3,2,8,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[3,4,6,7,5,1,8,2]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[7,4,1,2,5,6,8,3]=>[8,6,3,4,5,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[4,8,2,6,7,1,5,3]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,5,8,3,7,1,4,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[8,6,1,9,7,2,3,4,5]=>[9,8,3,7,6,5,4,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[9,8,6,1,7,2,3,4,5]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[8,5,1,9,6,2,7,3,4]=>[9,8,3,7,6,5,4,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[9,8,5,1,6,2,7,3,4]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[9,7,5,1,8,6,2,3,4]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[9,8,7,5,1,6,2,3,4]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,7,4,1,8,5,2,6,3]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[9,8,7,4,1,5,2,6,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[8,6,4,1,9,7,5,2,3]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[9,8,6,4,1,7,5,2,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,6,4,1,5,2,3]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,7,5,3,1,6,4,2]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,7,1,10,8,2,3,4,5,6]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[10,9,7,1,8,2,3,4,5,6]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[9,6,1,10,7,2,8,3,4,5]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[10,9,6,1,7,2,8,3,4,5]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[10,8,6,1,9,7,2,3,4,5]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[10,9,8,6,1,7,2,3,4,5]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[9,5,1,10,6,2,7,3,8,4]=>[10,9,3,8,7,6,5,4,2,1]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[10,9,5,1,6,2,7,3,8,4]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[10,8,5,1,9,6,2,7,3,4]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[10,9,8,5,1,6,2,7,3,4]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[9,7,5,1,10,8,6,2,3,4]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[10,9,7,5,1,8,6,2,3,4]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[10,9,8,7,5,1,6,2,3,4]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,4,1,10,8,5,2,6,3]=>[10,9,8,4,7,6,5,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[10,9,7,4,1,8,5,2,6,3]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[10,9,8,7,4,1,5,2,6,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,8,6,4,1,9,7,5,2,3]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[10,9,8,6,4,1,7,5,2,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,6,4,1,5,2,3]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,7,5,3,1,8,6,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,5,3,1,6,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,8,7,6,5,3,1,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[2,5,4,7,1,8,3,6]=>[5,7,3,8,1,6,2,4]=>[5,8,3,7,1,6,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,2,6,7,3,5,4,8]=>[1,2,7,6,5,4,3,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[9,10,7,8,5,3,6,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,7,8,5,3,1,6,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,7,5,8,6,3,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,7,5,8,6,3,1,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,7,5,8,3,6,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,7,5,8,3,1,6,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,7,5,3,8,6,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,7,5,3,8,6,1,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,7,5,3,8,1,6,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,10,7,5,3,1,8,6,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,10,8,5,6,3,1,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,10,8,5,3,6,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,10,8,5,3,6,1,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,10,8,5,3,1,6,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,10,5,8,6,3,1,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,10,5,8,3,1,6,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,10,5,3,8,6,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,10,5,3,8,6,1,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,10,5,3,8,1,6,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,10,5,3,1,8,6,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,5,10,8,6,3,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,5,10,8,6,3,1,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,5,10,8,3,6,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,5,10,8,3,6,1,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,5,10,8,3,1,6,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,5,10,3,8,6,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,5,10,3,8,6,1,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,5,10,3,8,1,6,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,5,10,3,1,8,6,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,5,3,10,8,6,4,1,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,5,3,10,8,6,1,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,5,3,10,8,1,6,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[9,7,5,3,10,1,8,6,4,2]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,7,8,5,6,3,1,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,7,8,5,3,6,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,7,8,5,3,6,1,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,7,8,5,3,1,6,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,7,5,8,6,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,7,5,8,6,3,1,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,7,5,8,3,6,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,7,5,8,3,6,1,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,7,5,8,3,1,6,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,7,5,3,8,6,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,7,5,3,8,6,1,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,7,5,3,8,1,6,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,10,7,5,3,1,8,6,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,7,10,8,5,6,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,7,10,8,5,6,3,1,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,12,9,7,10,8,5,3,6,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
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[11,9,7,12,10,5,8,3,6,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,12,10,5,8,3,6,1,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,12,10,5,8,3,1,6,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,12,10,5,3,8,6,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,12,10,5,3,8,6,1,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,12,10,5,3,8,1,6,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,12,10,5,3,1,8,6,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,12,5,10,8,6,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,12,5,10,8,6,3,1,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,12,5,10,8,3,6,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,12,5,10,8,3,6,1,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,12,5,10,8,3,1,6,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,12,5,10,3,8,6,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,12,5,10,3,8,6,1,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,12,5,10,3,8,1,6,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,12,5,10,3,1,8,6,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,12,5,3,10,8,6,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,12,5,3,10,8,6,1,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,12,5,3,10,8,1,6,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,12,5,3,10,1,8,6,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,12,5,3,1,10,8,6,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,5,12,10,8,6,3,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,5,12,10,8,6,3,1,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,5,12,10,8,3,6,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,5,12,10,8,3,6,1,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,5,12,10,8,3,1,6,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,5,12,10,3,8,6,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,5,12,10,3,8,6,1,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,5,12,10,3,8,1,6,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,5,12,10,3,1,8,6,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,5,12,3,10,8,6,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,5,12,3,10,8,6,1,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,5,12,3,10,8,1,6,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,5,12,3,10,1,8,6,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,5,12,3,1,10,8,6,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,5,3,12,10,8,6,4,1,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,5,3,12,10,8,6,1,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,5,3,12,10,8,1,6,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,5,3,12,10,1,8,6,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[11,9,7,5,3,12,1,10,8,6,4,2]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[8,1,2,4,6,3,5,7]=>[8,2,3,6,7,4,5,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[4,5,6,7,9,8,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[5,4,6,7,8,9,3,2,1]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[5,6,7,8,10,9,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[6,5,7,8,9,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[6,5,7,8,9,10,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[5,6,7,8,9,11,10,4,3,2,1]=>[11,10,9,8,5,7,6,4,3,2,1]=>[11,10,9,8,5,7,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.],.]
[4,5,6,7,8,10,9,3,2,1]=>[10,9,8,4,5,7,6,3,2,1]=>[10,9,8,4,7,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[[.,.],.],.]],.],.],.]
[3,5,6,7,9,8,4,2,1]=>[9,8,7,4,6,5,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[4,3,6,7,8,9,5,2,1]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[3,5,6,7,8,9,4,1,2]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[4,5,6,7,8,9,3,1,2]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[1,5,6,7,8,9,3,2,4]=>[1,9,8,7,5,6,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[3,4,5,8,9,6,7,1,2]=>[9,8,3,7,6,5,4,2,1]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[3,4,7,8,5,9,6,1,2]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[5,6,3,7,8,9,4,1,2]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[3,7,8,4,5,6,1,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,2,6,7,8,9,3,1,4]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[1,2,6,7,8,9,4,3,5]=>[1,2,9,8,7,6,5,4,3]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,3,8,6,7,4,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[2,6,5,3,7,1,8,4]=>[6,8,4,3,5,1,7,2]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[5,7,1,3,6,4,8,2]=>[8,6,3,5,4,2,7,1]=>[8,6,3,7,5,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[8,2,5,4,1,7,3,6]=>[8,5,7,4,2,6,3,1]=>[8,5,7,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[8,1,7,6,4,2,3,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,6,3,7,4,5,2]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[5,7,3,4,2,8,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[5,8,3,4,2,7,6,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,6,4,2,3,8,5,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[3,5,6,8,2,4,7,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[4,8,7,3,2,5,6,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[3,7,4,2,6,8,5,1]=>[8,7,4,3,5,6,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[6,4,8,7,3,2,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,6,2,8,7,4,3,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[6,2,8,3,7,4,5,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[3,7,5,6,4,2,8,1]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[5,2,3,8,6,1,4,7]=>[7,6,3,8,5,2,1,4]=>[7,6,3,8,5,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,4,3,8,5,6,2,7]=>[1,7,3,8,5,6,2,4]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[7,8,2,6,4,3,5,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,5,8,7,2,3,6,1]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[7,8,6,1,4,2,5,3]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[8,3,6,5,2,7,1,4]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[5,1,3,6,4,2,7,8]=>[6,2,5,4,3,1,7,8]=>[6,2,8,7,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[6,1,2,4,7,5,3,8]=>[7,2,3,6,5,4,1,8]=>[7,2,8,6,5,4,1,3]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[8,3,1,4,6,7,2,5]=>[8,7,3,4,6,5,2,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[7,8,5,1,2,6,3,4]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[6,4,5,1,8,7,3,2]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[8,6,2,1,7,3,5,4]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[9,3,4,5,6,8,7,2,1]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[9,4,3,5,6,7,8,2,1]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[10,9,3,4,5,6,8,7,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[9,8,3,4,5,7,6,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,4,3,5,6,7,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[10,9,4,3,5,6,7,8,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[9,2,4,5,6,8,7,3,1]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[9,4,3,5,6,7,2,8,1]=>[9,8,7,4,5,6,3,2,1]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[7,8,6,1,4,3,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,3,6,2,5,7,1,8]=>[7,4,5,2,3,6,1,8]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,6,5,7,3,4,8,2]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,2,3,4,9,7,5,6,8]=>[1,2,3,4,9,8,7,6,5]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[8,2,6,5,1,7,4,3]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[7,6,4,1,2,5,8,3]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[2,6,5,4,8,7,1,3]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[5,6,7,1,3,2,4,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[7,1,8,4,3,2,6,5]=>[8,2,7,6,5,4,3,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,8,5,2,7,6,4,3]=>[1,8,7,4,6,5,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,6,8,2,5,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,7,8,6,2,5,4,3]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[4,6,5,7,1,8,2,3]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,5,3,6,8,4,2,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[7,2,5,6,4,8,3,1]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[7,4,6,2,8,5,3,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[9,7,6,5,4,3,8,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[9,8,6,5,4,7,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[5,4,3,2,1,9,7,8,6]=>[5,4,3,2,1,9,8,7,6]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[10,8,7,6,5,4,3,9,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[10,9,7,6,5,4,8,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,6,3,4,2,5,8,7]=>[1,6,5,4,3,2,8,7]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,5,7,6,2,3,8,4]=>[1,8,6,5,4,3,7,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,4,3,7,6,2,5,8]=>[1,6,3,7,5,2,4,8]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,3,7,4,6,8,5,2]=>[1,8,7,4,5,6,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[3,7,4,6,8,1,5,2]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[4,8,3,1,7,6,2,5]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[2,6,7,5,3,4,1,8]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[2,4,1,7,5,6,8,3]=>[3,8,1,6,5,4,7,2]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[7,2,4,8,3,5,1,6]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[5,6,1,4,3,8,7,2]=>[8,5,3,4,2,7,6,1]=>[8,5,3,7,2,6,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[5,8,6,4,3,1,7,2]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[4,1,3,7,8,6,5,2]=>[8,2,3,7,6,5,4,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
Map
Demazure product with inverse
Description
This map sends a permutation π to π−1⋆π where ⋆ denotes the Demazure product on permutations.
This map is a surjection onto the set of involutions, i.e., the set of permutations π for which π=π−1.
This map is a surjection onto the set of involutions, i.e., the set of permutations π for which π=π−1.
Map
Simion-Schmidt map
Description
The Simion-Schmidt map sends any permutation to a 123-avoiding permutation.
Details can be found in [1].
In particular, this is a bijection between 132-avoiding permutations and 123-avoiding permutations, see [1, Proposition 19].
Details can be found in [1].
In particular, this is a bijection between 132-avoiding permutations and 123-avoiding permutations, see [1, Proposition 19].
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length 0 to the empty tree, and sending a permutation σ of length n≥1 to a root node with two subtrees L and R by splitting σ at the index σ−1(1), normalizing both sides again to permutations and sending the permutations on the left and on the right of σ−1(1) to the trees L and R, respectively.
This tree is recursively obtained by sending the unique permutation of length 0 to the empty tree, and sending a permutation σ of length n≥1 to a root node with two subtrees L and R by splitting σ at the index σ−1(1), normalizing both sides again to permutations and sending the permutations on the left and on the right of σ−1(1) to the trees L and R, respectively.
searching the database
Sorry, this map was not found in the database.