Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00069: Permutations —complement⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Images
=>
Cc0010;cc-rep-0Cc0010;cc-rep-3
[.,.]=>[1]=>[1]=>[.,.]
[.,[.,.]]=>[2,1]=>[1,2]=>[.,[.,.]]
[[.,.],.]=>[1,2]=>[2,1]=>[[.,.],.]
[.,[.,[.,.]]]=>[3,2,1]=>[1,2,3]=>[.,[.,[.,.]]]
[.,[[.,.],.]]=>[2,3,1]=>[2,1,3]=>[[.,.],[.,.]]
[[.,.],[.,.]]=>[3,1,2]=>[1,3,2]=>[.,[[.,.],.]]
[[.,[.,.]],.]=>[2,1,3]=>[2,3,1]=>[[.,[.,.]],.]
[[[.,.],.],.]=>[1,2,3]=>[3,2,1]=>[[[.,.],.],.]
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[1,2,4,3]=>[.,[.,[[.,.],.]]]
[[.,.],[[.,.],.]]=>[3,4,1,2]=>[2,1,4,3]=>[[.,.],[[.,.],.]]
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[1,3,4,2]=>[.,[[.,[.,.]],.]]
[[[.,.],.],[.,.]]=>[4,1,2,3]=>[1,4,3,2]=>[.,[[[.,.],.],.]]
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,2,4,1]=>[[[.,.],[.,.]],.]
[[[.,.],[.,.]],.]=>[3,1,2,4]=>[2,4,3,1]=>[[.,[[.,.],.]],.]
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[3,4,2,1]=>[[[.,[.,.]],.],.]
[[[[.,.],.],.],.]=>[1,2,3,4]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[2,3,1,5,4]=>[[.,[.,.]],[[.,.],.]]
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[1,2,4,5,3]=>[.,[.,[[.,[.,.]],.]]]
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[2,1,4,5,3]=>[[.,.],[[.,[.,.]],.]]
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]]
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[2,1,5,4,3]=>[[.,.],[[[.,.],.],.]]
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[1,3,4,5,2]=>[.,[[.,[.,[.,.]]],.]]
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[1,4,3,5,2]=>[.,[[[.,.],[.,.]],.]]
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[1,3,5,4,2]=>[.,[[.,[[.,.],.]],.]]
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[1,4,5,3,2]=>[.,[[[.,[.,.]],.],.]]
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.]
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.]
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.]
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.]
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.]
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[3,5,4,2,1]=>[[[.,[[.,.],.]],.],.]
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[4,5,3,2,1]=>[[[[.,[.,.]],.],.],.]
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[1,3,2,4,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]]
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[2,1,4,3,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[1,3,4,2,5,6]=>[.,[[.,[.,.]],[.,[.,.]]]]
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[1,4,3,2,5,6]=>[.,[[[.,.],.],[.,[.,.]]]]
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[2,3,4,1,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[3,2,4,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[2,4,3,1,5,6]=>[[.,[[.,.],.]],[.,[.,.]]]
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[3,4,2,1,5,6]=>[[[.,[.,.]],.],[.,[.,.]]]
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]]
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]]
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[2,1,3,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>[.,[[.,.],[[.,.],[.,.]]]]
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[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[3,2,1,5,4,6]=>[[[.,.],.],[[.,.],[.,.]]]
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[1,2,4,5,3,6]=>[.,[.,[[.,[.,.]],[.,.]]]]
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[2,1,4,5,3,6]=>[[.,.],[[.,[.,.]],[.,.]]]
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[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[1,3,5,4,2,6]=>[.,[[.,[[.,.],.]],[.,.]]]
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[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[.,[[[[.,.],.],.],[.,.]]]
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[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]]
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[1,3,2,4,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[2,3,1,4,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[3,2,1,4,6,5]=>[[[.,.],.],[.,[[.,.],.]]]
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[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[1,4,3,2,6,5]=>[.,[[[.,.],.],[[.,.],.]]]
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[2,3,4,1,6,5]=>[[.,[.,[.,.]]],[[.,.],.]]
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[3,2,4,1,6,5]=>[[[.,.],[.,.]],[[.,.],.]]
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[2,4,3,1,6,5]=>[[.,[[.,.],.]],[[.,.],.]]
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[3,4,2,1,6,5]=>[[[.,[.,.]],.],[[.,.],.]]
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]]
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[1,2,3,5,6,4]=>[.,[.,[.,[[.,[.,.]],.]]]]
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[2,1,3,5,6,4]=>[[.,.],[.,[[.,[.,.]],.]]]
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[1,3,2,5,6,4]=>[.,[[.,.],[[.,[.,.]],.]]]
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[2,3,1,5,6,4]=>[[.,[.,.]],[[.,[.,.]],.]]
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[3,2,1,5,6,4]=>[[[.,.],.],[[.,[.,.]],.]]
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[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[2,1,3,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]]
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[1,3,2,6,5,4]=>[.,[[.,.],[[[.,.],.],.]]]
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[2,3,1,6,5,4]=>[[.,[.,.]],[[[.,.],.],.]]
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[1,2,4,5,6,3]=>[.,[.,[[.,[.,[.,.]]],.]]]
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[2,1,4,5,6,3]=>[[.,.],[[.,[.,[.,.]]],.]]
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[1,2,5,4,6,3]=>[.,[.,[[[.,.],[.,.]],.]]]
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[2,1,5,4,6,3]=>[[.,.],[[[.,.],[.,.]],.]]
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[1,2,4,6,5,3]=>[.,[.,[[.,[[.,.],.]],.]]]
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[2,1,4,6,5,3]=>[[.,.],[[.,[[.,.],.]],.]]
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[1,2,5,6,4,3]=>[.,[.,[[[.,[.,.]],.],.]]]
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[2,1,5,6,4,3]=>[[.,.],[[[.,[.,.]],.],.]]
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[1,2,6,5,4,3]=>[.,[.,[[[[.,.],.],.],.]]]
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[2,1,6,5,4,3]=>[[.,.],[[[[.,.],.],.],.]]
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[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[1,4,3,5,6,2]=>[.,[[[.,.],[.,[.,.]]],.]]
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[1,3,5,4,6,2]=>[.,[[.,[[.,.],[.,.]]],.]]
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[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[1,5,6,4,3,2,7]=>[.,[[[[.,[.,.]],.],.],[.,.]]]
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[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[1,3,2,4,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[2,3,1,4,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[3,2,1,4,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[1,2,4,3,5,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,1,4,3,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[1,3,4,2,5,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[1,4,3,2,5,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[2,3,4,1,5,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[3,2,4,1,5,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[2,4,3,1,5,7,6]=>[[.,[[.,.],.]],[.,[[.,.],.]]]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[3,4,2,1,5,7,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[4,3,2,1,5,7,6]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[1,2,3,5,4,7,6]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,3,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[1,3,2,5,4,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,3,1,5,4,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[3,2,1,5,4,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[1,2,4,5,3,7,6]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,4,5,3,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[1,2,5,4,3,7,6]=>[.,[.,[[[.,.],.],[[.,.],.]]]]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[1,3,4,5,2,7,6]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[1,4,3,5,2,7,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[1,3,5,4,2,7,6]=>[.,[[.,[[.,.],.]],[[.,.],.]]]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[1,4,5,3,2,7,6]=>[.,[[[.,[.,.]],.],[[.,.],.]]]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[1,5,4,3,2,7,6]=>[.,[[[[.,.],.],.],[[.,.],.]]]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[2,3,4,5,1,7,6]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[3,2,4,5,1,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
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[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[3,4,2,5,1,7,6]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[4,3,2,5,1,7,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[2,3,5,4,1,7,6]=>[[.,[.,[[.,.],.]]],[[.,.],.]]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[3,2,5,4,1,7,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[2,4,5,3,1,7,6]=>[[.,[[.,[.,.]],.]],[[.,.],.]]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[2,5,4,3,1,7,6]=>[[.,[[[.,.],.],.]],[[.,.],.]]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[3,4,5,2,1,7,6]=>[[[.,[.,[.,.]]],.],[[.,.],.]]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[4,3,5,2,1,7,6]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[3,5,4,2,1,7,6]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[4,5,3,2,1,7,6]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[1,2,3,4,6,7,5]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[2,1,3,4,6,7,5]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[1,3,2,4,6,7,5]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[2,3,1,4,6,7,5]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,2,1,4,6,7,5]=>[[[.,.],.],[.,[[.,[.,.]],.]]]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[1,2,4,3,6,7,5]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[2,1,4,3,6,7,5]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[1,3,4,2,6,7,5]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[1,4,3,2,6,7,5]=>[.,[[[.,.],.],[[.,[.,.]],.]]]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[2,3,4,1,6,7,5]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[3,2,4,1,6,7,5]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[2,4,3,1,6,7,5]=>[[.,[[.,.],.]],[[.,[.,.]],.]]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[3,4,2,1,6,7,5]=>[[[.,[.,.]],.],[[.,[.,.]],.]]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[4,3,2,1,6,7,5]=>[[[[.,.],.],.],[[.,[.,.]],.]]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[1,2,3,4,7,6,5]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]
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[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[1,3,2,4,7,6,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]]
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[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[3,5,4,2,6,7,1]=>[[[.,[[.,.],.]],[.,[.,.]]],.]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[4,5,3,2,6,7,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[5,4,3,2,6,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[2,3,4,6,5,7,1]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[3,2,4,6,5,7,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[2,4,3,6,5,7,1]=>[[.,[[.,.],[[.,.],[.,.]]]],.]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[3,4,2,6,5,7,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[4,3,2,6,5,7,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[2,3,5,6,4,7,1]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[3,2,5,6,4,7,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[2,3,6,5,4,7,1]=>[[.,[.,[[[.,.],.],[.,.]]]],.]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[3,2,6,5,4,7,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[2,4,5,6,3,7,1]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[2,5,4,6,3,7,1]=>[[.,[[[.,.],[.,.]],[.,.]]],.]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[2,4,6,5,3,7,1]=>[[.,[[.,[[.,.],.]],[.,.]]],.]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[2,5,6,4,3,7,1]=>[[.,[[[.,[.,.]],.],[.,.]]],.]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[2,6,5,4,3,7,1]=>[[.,[[[[.,.],.],.],[.,.]]],.]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[3,4,5,6,2,7,1]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[4,3,5,6,2,7,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[3,5,4,6,2,7,1]=>[[[.,[[.,.],[.,.]]],[.,.]],.]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[4,5,3,6,2,7,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[5,4,3,6,2,7,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[3,4,6,5,2,7,1]=>[[[.,[.,[[.,.],.]]],[.,.]],.]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[4,3,6,5,2,7,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[3,5,6,4,2,7,1]=>[[[.,[[.,[.,.]],.]],[.,.]],.]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[3,6,5,4,2,7,1]=>[[[.,[[[.,.],.],.]],[.,.]],.]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[4,5,6,3,2,7,1]=>[[[[.,[.,[.,.]]],.],[.,.]],.]
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[5,4,6,3,2,7,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[4,6,5,3,2,7,1]=>[[[[.,[[.,.],.]],.],[.,.]],.]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[5,6,4,3,2,7,1]=>[[[[[.,[.,.]],.],.],[.,.]],.]
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,7,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[2,3,4,5,7,6,1]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[3,2,4,5,7,6,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[2,4,3,5,7,6,1]=>[[.,[[.,.],[.,[[.,.],.]]]],.]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[3,4,2,5,7,6,1]=>[[[.,[.,.]],[.,[[.,.],.]]],.]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[4,3,2,5,7,6,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[2,3,5,4,7,6,1]=>[[.,[.,[[.,.],[[.,.],.]]]],.]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[3,2,5,4,7,6,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[2,4,5,3,7,6,1]=>[[.,[[.,[.,.]],[[.,.],.]]],.]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[2,5,4,3,7,6,1]=>[[.,[[[.,.],.],[[.,.],.]]],.]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[3,4,5,2,7,6,1]=>[[[.,[.,[.,.]]],[[.,.],.]],.]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[4,3,5,2,7,6,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[3,5,4,2,7,6,1]=>[[[.,[[.,.],.]],[[.,.],.]],.]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[4,5,3,2,7,6,1]=>[[[[.,[.,.]],.],[[.,.],.]],.]
[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[5,4,3,2,7,6,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[2,3,4,6,7,5,1]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[3,2,4,6,7,5,1]=>[[[.,.],[.,[[.,[.,.]],.]]],.]
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[2,4,3,6,7,5,1]=>[[.,[[.,.],[[.,[.,.]],.]]],.]
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[3,4,2,6,7,5,1]=>[[[.,[.,.]],[[.,[.,.]],.]],.]
[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[4,3,2,6,7,5,1]=>[[[[.,.],.],[[.,[.,.]],.]],.]
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[2,3,4,7,6,5,1]=>[[.,[.,[.,[[[.,.],.],.]]]],.]
[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[3,2,4,7,6,5,1]=>[[[.,.],[.,[[[.,.],.],.]]],.]
[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[2,4,3,7,6,5,1]=>[[.,[[.,.],[[[.,.],.],.]]],.]
[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[3,4,2,7,6,5,1]=>[[[.,[.,.]],[[[.,.],.],.]],.]
[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[4,3,2,7,6,5,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[2,3,5,6,7,4,1]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[3,2,5,6,7,4,1]=>[[[.,.],[[.,[.,[.,.]]],.]],.]
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[2,3,6,5,7,4,1]=>[[.,[.,[[[.,.],[.,.]],.]]],.]
[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[3,2,6,5,7,4,1]=>[[[.,.],[[[.,.],[.,.]],.]],.]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[2,3,5,7,6,4,1]=>[[.,[.,[[.,[[.,.],.]],.]]],.]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[3,2,5,7,6,4,1]=>[[[.,.],[[.,[[.,.],.]],.]],.]
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[2,3,6,7,5,4,1]=>[[.,[.,[[[.,[.,.]],.],.]]],.]
[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[3,2,6,7,5,4,1]=>[[[.,.],[[[.,[.,.]],.],.]],.]
[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[2,3,7,6,5,4,1]=>[[.,[.,[[[[.,.],.],.],.]]],.]
[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[3,2,7,6,5,4,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[2,4,5,6,7,3,1]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[2,5,4,6,7,3,1]=>[[.,[[[.,.],[.,[.,.]]],.]],.]
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[2,4,6,5,7,3,1]=>[[.,[[.,[[.,.],[.,.]]],.]],.]
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[2,5,6,4,7,3,1]=>[[.,[[[.,[.,.]],[.,.]],.]],.]
[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[2,6,5,4,7,3,1]=>[[.,[[[[.,.],.],[.,.]],.]],.]
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[2,4,5,7,6,3,1]=>[[.,[[.,[.,[[.,.],.]]],.]],.]
[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[2,5,4,7,6,3,1]=>[[.,[[[.,.],[[.,.],.]],.]],.]
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[2,4,6,7,5,3,1]=>[[.,[[.,[[.,[.,.]],.]],.]],.]
[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[2,4,7,6,5,3,1]=>[[.,[[.,[[[.,.],.],.]],.]],.]
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[2,5,6,7,4,3,1]=>[[.,[[[.,[.,[.,.]]],.],.]],.]
[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[2,6,5,7,4,3,1]=>[[.,[[[[.,.],[.,.]],.],.]],.]
[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[2,5,7,6,4,3,1]=>[[.,[[[.,[[.,.],.]],.],.]],.]
[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[2,6,7,5,4,3,1]=>[[.,[[[[.,[.,.]],.],.],.]],.]
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[2,7,6,5,4,3,1]=>[[.,[[[[[.,.],.],.],.],.]],.]
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[3,4,5,6,7,2,1]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[4,3,5,6,7,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[3,5,4,6,7,2,1]=>[[[.,[[.,.],[.,[.,.]]]],.],.]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[4,5,3,6,7,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.]
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[5,4,3,6,7,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[3,4,6,5,7,2,1]=>[[[.,[.,[[.,.],[.,.]]]],.],.]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[4,3,6,5,7,2,1]=>[[[[.,.],[[.,.],[.,.]]],.],.]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[3,5,6,4,7,2,1]=>[[[.,[[.,[.,.]],[.,.]]],.],.]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[3,6,5,4,7,2,1]=>[[[.,[[[.,.],.],[.,.]]],.],.]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[4,5,6,3,7,2,1]=>[[[[.,[.,[.,.]]],[.,.]],.],.]
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,4,6,3,7,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[4,6,5,3,7,2,1]=>[[[[.,[[.,.],.]],[.,.]],.],.]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[5,6,4,3,7,2,1]=>[[[[[.,[.,.]],.],[.,.]],.],.]
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[6,5,4,3,7,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[3,4,5,7,6,2,1]=>[[[.,[.,[.,[[.,.],.]]]],.],.]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[4,3,5,7,6,2,1]=>[[[[.,.],[.,[[.,.],.]]],.],.]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[3,5,4,7,6,2,1]=>[[[.,[[.,.],[[.,.],.]]],.],.]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[4,5,3,7,6,2,1]=>[[[[.,[.,.]],[[.,.],.]],.],.]
[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[5,4,3,7,6,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[3,4,6,7,5,2,1]=>[[[.,[.,[[.,[.,.]],.]]],.],.]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[4,3,6,7,5,2,1]=>[[[[.,.],[[.,[.,.]],.]],.],.]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[3,4,7,6,5,2,1]=>[[[.,[.,[[[.,.],.],.]]],.],.]
[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[4,3,7,6,5,2,1]=>[[[[.,.],[[[.,.],.],.]],.],.]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[3,5,6,7,4,2,1]=>[[[.,[[.,[.,[.,.]]],.]],.],.]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[3,6,5,7,4,2,1]=>[[[.,[[[.,.],[.,.]],.]],.],.]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[3,5,7,6,4,2,1]=>[[[.,[[.,[[.,.],.]],.]],.],.]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[3,6,7,5,4,2,1]=>[[[.,[[[.,[.,.]],.],.]],.],.]
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[3,7,6,5,4,2,1]=>[[[.,[[[[.,.],.],.],.]],.],.]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,5,6,7,3,2,1]=>[[[[.,[.,[.,[.,.]]]],.],.],.]
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[5,4,6,7,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[4,6,5,7,3,2,1]=>[[[[.,[[.,.],[.,.]]],.],.],.]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[5,6,4,7,3,2,1]=>[[[[[.,[.,.]],[.,.]],.],.],.]
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[6,5,4,7,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[4,5,7,6,3,2,1]=>[[[[.,[.,[[.,.],.]]],.],.],.]
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[5,4,7,6,3,2,1]=>[[[[[.,.],[[.,.],.]],.],.],.]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[4,6,7,5,3,2,1]=>[[[[.,[[.,[.,.]],.]],.],.],.]
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[4,7,6,5,3,2,1]=>[[[[.,[[[.,.],.],.]],.],.],.]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[5,6,7,4,3,2,1]=>[[[[[.,[.,[.,.]]],.],.],.],.]
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[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>[1,2,4,3,5,7,6,8]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,2,3,1]=>[1,3,4,2,5,7,6,8]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,2,3,1]=>[1,4,3,2,5,7,6,8]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,2,3,1]=>[2,3,4,1,5,7,6,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,2,3,1]=>[3,2,4,1,5,7,6,8]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[4,3,2,1,5,7,6,8]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,2,3,5,4,7,6,8]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>[2,3,1,5,4,7,6,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,2,3,1]=>[3,2,1,5,4,7,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[1,2,4,5,3,7,6,8]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,2,3,1]=>[2,1,5,4,3,7,6,8]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[1,3,4,5,2,7,6,8]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,2,3,1]=>[1,4,3,5,2,7,6,8]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,2,3,1]=>[1,3,5,4,2,7,6,8]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]
[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]=>[8,5,4,6,7,2,3,1]=>[1,4,5,3,2,7,6,8]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[8,4,5,6,7,2,3,1]=>[1,5,4,3,2,7,6,8]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,2,3,1]=>[2,3,4,5,1,7,6,8]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,2,3,1]=>[2,4,3,5,1,7,6,8]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>[3,4,2,5,1,7,6,8]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,2,3,1]=>[3,2,5,4,1,7,6,8]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[7,5,4,6,8,2,3,1]=>[2,4,5,3,1,7,6,8]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]
[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[6,5,4,7,8,2,3,1]=>[3,4,5,2,1,7,6,8]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[6,4,5,7,8,2,3,1]=>[3,5,4,2,1,7,6,8]=>[[[.,[[.,.],.]],.],[[.,.],[.,.]]]
[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,2,3,1]=>[4,5,3,2,1,7,6,8]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[5,4,3,2,1,7,6,8]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[1,2,3,4,6,7,5,8]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[1,3,2,4,6,7,5,8]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,2,4,1]=>[2,3,1,4,6,7,5,8]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[1,2,4,3,6,7,5,8]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,2,4,1]=>[2,1,4,3,6,7,5,8]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[1,3,4,2,6,7,5,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,2,4,1]=>[1,4,3,2,6,7,5,8]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,2,4,1]=>[2,3,4,1,6,7,5,8]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,2,4,1]=>[3,2,4,1,6,7,5,8]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[4,3,2,1,6,7,5,8]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[1,2,3,4,7,6,5,8]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,2,3,4,1]=>[1,3,2,4,7,6,5,8]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[3,2,1,4,7,6,5,8]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,2,3,4,1]=>[2,3,4,1,7,6,5,8]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,2,3,4,1]=>[3,2,4,1,7,6,5,8]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[4,3,2,1,7,6,5,8]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[1,2,3,5,6,7,4,8]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>[1,3,2,5,6,7,4,8]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[7,6,8,4,3,2,5,1]=>[2,3,1,5,6,7,4,8]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[8,7,6,3,4,2,5,1]=>[1,2,3,6,5,7,4,8]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[1,3,2,6,5,7,4,8]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>[2,3,1,6,5,7,4,8]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[6,7,8,3,4,2,5,1]=>[3,2,1,6,5,7,4,8]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,2,3,5,1]=>[1,2,3,5,7,6,4,8]=>[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]
[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,2,3,5,1]=>[1,3,2,5,7,6,4,8]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[3,2,1,5,7,6,4,8]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[8,7,6,3,2,4,5,1]=>[1,2,3,6,7,5,4,8]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[7,8,6,3,2,4,5,1]=>[2,1,3,6,7,5,4,8]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
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[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[7,6,8,3,2,4,5,1]=>[2,3,1,6,7,5,4,8]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[8,7,6,2,3,4,5,1]=>[1,2,3,7,6,5,4,8]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]
[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[8,6,7,2,3,4,5,1]=>[1,3,2,7,6,5,4,8]=>[.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[6,7,8,2,3,4,5,1]=>[3,2,1,7,6,5,4,8]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[1,2,4,5,6,7,3,8]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1]=>[2,1,4,5,6,7,3,8]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
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[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]=>[7,8,4,5,3,2,6,1]=>[2,1,5,4,6,7,3,8]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[8,7,5,3,4,2,6,1]=>[1,2,4,6,5,7,3,8]=>[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]
[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[8,7,4,3,5,2,6,1]=>[1,2,5,6,4,7,3,8]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[8,7,5,3,2,4,6,1]=>[1,2,4,6,7,5,3,8]=>[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[8,7,4,3,2,5,6,1]=>[1,2,5,6,7,4,3,8]=>[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[7,8,4,3,2,5,6,1]=>[2,1,5,6,7,4,3,8]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]
[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[8,7,4,2,3,5,6,1]=>[1,2,5,7,6,4,3,8]=>[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]
[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]=>[8,7,3,2,4,5,6,1]=>[1,2,6,7,5,4,3,8]=>[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>[2,1,6,7,5,4,3,8]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[8,7,2,3,4,5,6,1]=>[1,2,7,6,5,4,3,8]=>[.,[.,[[[[[.,.],.],.],.],[.,.]]]]
[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[7,8,2,3,4,5,6,1]=>[2,1,7,6,5,4,3,8]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>[1,3,4,5,6,7,2,8]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]=>[8,5,6,4,3,2,7,1]=>[1,4,3,5,6,7,2,8]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[8,5,4,6,3,2,7,1]=>[1,4,5,3,6,7,2,8]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[8,4,5,6,3,2,7,1]=>[1,5,4,3,6,7,2,8]=>[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[8,6,5,3,4,2,7,1]=>[1,3,4,6,5,7,2,8]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[8,5,6,3,4,2,7,1]=>[1,4,3,6,5,7,2,8]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[8,6,4,3,5,2,7,1]=>[1,3,5,6,4,7,2,8]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[8,6,3,4,5,2,7,1]=>[1,3,6,5,4,7,2,8]=>[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[8,5,4,3,6,2,7,1]=>[1,4,5,6,3,7,2,8]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[1,5,4,6,3,7,2,8]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,2,3,7,1]=>[1,3,4,5,7,6,2,8]=>[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[8,5,6,4,2,3,7,1]=>[1,4,3,5,7,6,2,8]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[8,6,4,5,2,3,7,1]=>[1,3,5,4,7,6,2,8]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[8,6,5,3,2,4,7,1]=>[1,3,4,6,7,5,2,8]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]
[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[8,6,4,3,2,5,7,1]=>[1,3,5,6,7,4,2,8]=>[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]
[.,[[[.,[[.,.],.]],[.,.]],[.,.]]]=>[8,6,3,4,2,5,7,1]=>[1,3,6,5,7,4,2,8]=>[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[8,6,4,2,3,5,7,1]=>[1,3,5,7,6,4,2,8]=>[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[8,4,5,3,2,6,7,1]=>[1,5,4,6,7,3,2,8]=>[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]
[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]=>[8,4,3,5,2,6,7,1]=>[1,5,6,4,7,3,2,8]=>[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]
[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]=>[8,5,3,2,4,6,7,1]=>[1,4,6,7,5,3,2,8]=>[.,[[[.,[[.,[.,.]],.]],.],[.,.]]]
[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[8,5,2,3,4,6,7,1]=>[1,4,7,6,5,3,2,8]=>[.,[[[.,[[[.,.],.],.]],.],[.,.]]]
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[8,4,3,2,5,6,7,1]=>[1,5,6,7,4,3,2,8]=>[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]
[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[8,3,4,2,5,6,7,1]=>[1,6,5,7,4,3,2,8]=>[.,[[[[[.,.],[.,.]],.],.],[.,.]]]
[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[8,3,2,4,5,6,7,1]=>[1,6,7,5,4,3,2,8]=>[.,[[[[[.,[.,.]],.],.],.],[.,.]]]
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[8,2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2,8]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[2,3,4,5,6,7,1,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>[3,2,4,5,6,7,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[7,5,6,4,3,2,8,1]=>[2,4,3,5,6,7,1,8]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
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[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,3,1,2]=>[4,5,3,2,1,6,8,7]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[5,4,3,2,1,6,8,7]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[1,2,3,4,6,5,8,7]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[2,1,3,4,6,5,8,7]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,4,1,2]=>[1,3,2,4,6,5,8,7]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,4,1,2]=>[2,3,1,4,6,5,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[1,2,4,3,6,5,8,7]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,4,1,2]=>[1,3,4,2,6,5,8,7]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[2,3,4,1,6,5,8,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[3,2,4,1,6,5,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,4,3,1,6,5,8,7]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[3,4,2,1,6,5,8,7]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[4,3,2,1,6,5,8,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[1,2,3,5,6,4,8,7]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,3,5,1,2]=>[2,1,3,5,6,4,8,7]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,3,5,1,2]=>[1,3,2,5,6,4,8,7]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[1,2,3,6,5,4,8,7]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[7,8,6,3,4,5,1,2]=>[2,1,3,6,5,4,8,7]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[1,3,2,6,5,4,8,7]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[7,6,8,3,4,5,1,2]=>[2,3,1,6,5,4,8,7]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[8,7,5,4,3,6,1,2]=>[1,2,4,5,6,3,8,7]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[2,1,4,5,6,3,8,7]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[2,1,5,4,6,3,8,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,4,6,5,3,8,7]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[2,1,5,6,4,3,8,7]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[2,1,6,5,4,3,8,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,3,7,1,2]=>[1,3,4,5,6,2,8,7]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]
[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[8,6,3,4,5,7,1,2]=>[1,3,6,5,4,2,8,7]=>[.,[[.,[[[.,.],.],.]],[[.,.],.]]]
[[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>[8,4,5,3,6,7,1,2]=>[1,5,4,6,3,2,8,7]=>[.,[[[[.,.],[.,.]],.],[[.,.],.]]]
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[1,5,6,4,3,2,8,7]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>[1,6,5,4,3,2,8,7]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>[2,3,4,5,6,1,8,7]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[7,5,6,4,3,8,1,2]=>[2,4,3,5,6,1,8,7]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,3,8,1,2]=>[3,4,2,5,6,1,8,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,3,8,1,2]=>[4,3,2,5,6,1,8,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>[3,2,5,4,6,1,8,7]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,3,8,1,2]=>[2,4,5,3,6,1,8,7]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]
[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,3,8,1,2]=>[2,5,4,3,6,1,8,7]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,3,8,1,2]=>[3,4,5,2,6,1,8,7]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,3,8,1,2]=>[4,3,5,2,6,1,8,7]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[4,5,6,7,3,8,1,2]=>[5,4,3,2,6,1,8,7]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[2,4,3,6,5,1,8,7]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[6,5,7,3,4,8,1,2]=>[3,4,2,6,5,1,8,7]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[5,6,7,3,4,8,1,2]=>[4,3,2,6,5,1,8,7]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[7,6,4,3,5,8,1,2]=>[2,3,5,6,4,1,8,7]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]
[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[6,7,4,3,5,8,1,2]=>[3,2,5,6,4,1,8,7]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[7,6,3,4,5,8,1,2]=>[2,3,6,5,4,1,8,7]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]
[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[6,7,3,4,5,8,1,2]=>[3,2,6,5,4,1,8,7]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[2,4,6,5,3,1,8,7]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[7,3,4,5,6,8,1,2]=>[2,6,5,4,3,1,8,7]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[6,5,4,3,7,8,1,2]=>[3,4,5,6,2,1,8,7]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[5,6,4,3,7,8,1,2]=>[4,3,5,6,2,1,8,7]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[5,4,6,3,7,8,1,2]=>[4,5,3,6,2,1,8,7]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[4,5,6,3,7,8,1,2]=>[5,4,3,6,2,1,8,7]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[6,5,3,4,7,8,1,2]=>[3,4,6,5,2,1,8,7]=>[[[.,[.,[[.,.],.]]],.],[[.,.],.]]
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[4,3,6,5,2,1,8,7]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[3,5,6,4,2,1,8,7]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[3,6,5,4,2,1,8,7]=>[[[.,[[[.,.],.],.]],.],[[.,.],.]]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[4,5,6,3,2,1,8,7]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[5,4,6,3,2,1,8,7]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[5,3,4,6,7,8,1,2]=>[4,6,5,3,2,1,8,7]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[5,6,4,3,2,1,8,7]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[1,2,3,4,5,7,8,6]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,2,1,3]=>[2,1,3,4,5,7,8,6]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[1,3,2,4,5,7,8,6]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[2,3,1,4,5,7,8,6]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,2,1,3]=>[3,2,1,4,5,7,8,6]=>[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[8,7,5,6,4,2,1,3]=>[1,2,4,3,5,7,8,6]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[2,1,4,3,5,7,8,6]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[1,3,4,2,5,7,8,6]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,2,1,3]=>[1,4,3,2,5,7,8,6]=>[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[2,3,4,1,5,7,8,6]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,2,1,3]=>[3,2,4,1,5,7,8,6]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[4,3,2,1,5,7,8,6]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,2,1,3]=>[1,2,3,5,4,7,8,6]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[2,1,3,5,4,7,8,6]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[1,3,2,5,4,7,8,6]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,2,1,3]=>[1,2,4,5,3,7,8,6]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,2,1,3]=>[1,2,5,4,3,7,8,6]=>[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]
[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[1,3,4,5,2,7,8,6]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[1,3,5,4,2,7,8,6]=>[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,2,1,3]=>[1,4,5,3,2,7,8,6]=>[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,2,1,3]=>[1,5,4,3,2,7,8,6]=>[.,[[[[.,.],.],.],[[.,[.,.]],.]]]
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,2,1,3]=>[2,3,4,5,1,7,8,6]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,2,1,3]=>[2,4,3,5,1,7,8,6]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,2,1,3]=>[3,4,2,5,1,7,8,6]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,2,1,3]=>[4,3,2,5,1,7,8,6]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,2,1,3]=>[3,2,5,4,1,7,8,6]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,2,1,3]=>[2,4,5,3,1,7,8,6]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]
[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,2,1,3]=>[3,5,4,2,1,7,8,6]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[5,4,3,2,1,7,8,6]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[1,2,3,4,5,8,7,6]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,1,2,3]=>[2,1,3,4,5,8,7,6]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,1,2,3]=>[1,3,2,4,5,8,7,6]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[3,2,1,4,5,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]=>[8,7,5,6,4,1,2,3]=>[1,2,4,3,5,8,7,6]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,1,2,3]=>[2,1,4,3,5,8,7,6]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[1,4,3,2,5,8,7,6]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,1,2,3]=>[2,3,4,1,5,8,7,6]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,1,2,3]=>[3,2,4,1,5,8,7,6]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[2,4,3,1,5,8,7,6]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[4,3,2,1,5,8,7,6]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[1,2,3,5,4,8,7,6]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,1,2,3]=>[2,1,3,5,4,8,7,6]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[1,3,2,5,4,8,7,6]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[1,2,4,5,3,8,7,6]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,1,2,3]=>[2,1,4,5,3,8,7,6]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[1,2,5,4,3,8,7,6]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>[2,1,5,4,3,8,7,6]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,1,2,3]=>[1,3,4,5,2,8,7,6]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]
[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,1,2,3]=>[1,4,5,3,2,8,7,6]=>[.,[[[.,[.,.]],.],[[[.,.],.],.]]]
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[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,1,2,3]=>[4,3,5,2,1,8,7,6]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
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[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,1,2,3]=>[4,5,3,2,1,8,7,6]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
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[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[1,3,2,4,6,7,8,5]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[2,3,1,4,6,7,8,5]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[3,2,1,4,6,7,8,5]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[1,2,4,3,6,7,8,5]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[2,1,4,3,6,7,8,5]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[1,3,4,2,6,7,8,5]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[1,4,3,2,6,7,8,5]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[2,3,4,1,6,7,8,5]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[3,2,4,1,6,7,8,5]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,2,1,4]=>[2,4,3,1,6,7,8,5]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,2,1,4]=>[3,4,2,1,6,7,8,5]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[4,3,2,1,6,7,8,5]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[1,2,3,4,7,6,8,5]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,3,1,4]=>[2,1,3,4,7,6,8,5]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[1,3,2,4,7,6,8,5]=>[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,3,1,4]=>[2,3,1,4,7,6,8,5]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,3,1,4]=>[1,2,4,3,7,6,8,5]=>[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[2,1,4,3,7,6,8,5]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,3,1,4]=>[1,3,4,2,7,6,8,5]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]
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[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[1,2,3,4,6,8,7,5]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[1,3,2,4,6,8,7,5]=>[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]
[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,1,2,4]=>[3,2,1,4,6,8,7,5]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[2,1,4,3,6,8,7,5]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]
[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[1,3,4,2,6,8,7,5]=>[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[1,4,3,2,6,8,7,5]=>[.,[[[.,.],.],[[.,[[.,.],.]],.]]]
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[2,3,4,1,6,8,7,5]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[3,2,4,1,6,8,7,5]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]
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[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[3,4,2,1,6,8,7,5]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[4,3,2,1,6,8,7,5]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[1,2,3,4,7,8,6,5]=>[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[2,1,3,4,7,8,6,5]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,1,3,4]=>[2,3,1,4,7,8,6,5]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[3,2,1,4,7,8,6,5]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>[1,2,4,3,7,8,6,5]=>[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[2,1,4,3,7,8,6,5]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,1,3,4]=>[1,3,4,2,7,8,6,5]=>[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]
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[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[3,2,4,1,7,8,6,5]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[2,4,3,1,7,8,6,5]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]
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[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[4,3,2,1,7,8,6,5]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]
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[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[2,1,3,4,8,7,6,5]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[1,3,2,4,8,7,6,5]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[2,3,1,4,8,7,6,5]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[3,2,1,4,8,7,6,5]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[1,2,4,3,8,7,6,5]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[2,1,4,3,8,7,6,5]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[1,3,4,2,8,7,6,5]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[1,4,3,2,8,7,6,5]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[2,3,4,1,8,7,6,5]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[3,2,4,1,8,7,6,5]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[2,4,3,1,8,7,6,5]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[3,4,2,1,8,7,6,5]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[1,2,3,5,6,7,8,4]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[2,1,3,5,6,7,8,4]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[8,6,7,4,3,2,1,5]=>[1,3,2,5,6,7,8,4]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[2,3,1,5,6,7,8,4]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[3,2,1,5,6,7,8,4]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[1,2,3,6,5,7,8,4]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
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[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>[3,2,1,6,5,7,8,4]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[1,2,3,5,7,6,8,4]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,2,3,1,5]=>[2,3,1,5,7,6,8,4]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[3,2,1,5,7,6,8,4]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[1,2,3,6,7,5,8,4]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[8,6,7,3,2,4,1,5]=>[1,3,2,6,7,5,8,4]=>[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[7,6,8,3,2,4,1,5]=>[2,3,1,6,7,5,8,4]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]
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[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[5,6,4,3,7,2,1,8]=>[4,3,5,6,2,7,8,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[6,4,5,3,7,2,1,8]=>[3,5,4,6,2,7,8,1]=>[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]
[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[4,5,6,3,7,2,1,8]=>[5,4,3,6,2,7,8,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]=>[6,5,3,4,7,2,1,8]=>[3,4,6,5,2,7,8,1]=>[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]
[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]=>[6,4,3,5,7,2,1,8]=>[3,5,6,4,2,7,8,1]=>[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[4,5,6,3,2,7,8,1]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[3,4,5,6,7,2,1,8]=>[6,5,4,3,2,7,8,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,2,3,1,8]=>[2,3,4,5,7,6,8,1]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>[3,2,4,5,7,6,8,1]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
[[.,[[.,.],[.,[[.,[.,.]],.]]]],.]=>[6,5,7,4,2,3,1,8]=>[3,4,2,5,7,6,8,1]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>[4,3,2,5,7,6,8,1]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[2,3,5,4,7,6,8,1]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[3,2,5,4,7,6,8,1]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[6,5,4,7,2,3,1,8]=>[3,4,5,2,7,6,8,1]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[4,3,5,2,7,6,8,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>[6,4,5,7,2,3,1,8]=>[3,5,4,2,7,6,8,1]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],.]
[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[4,5,6,7,2,3,1,8]=>[5,4,3,2,7,6,8,1]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[7,6,5,3,2,4,1,8]=>[2,3,4,6,7,5,8,1]=>[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]
[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[7,5,6,3,2,4,1,8]=>[2,4,3,6,7,5,8,1]=>[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>[3,4,2,6,7,5,8,1]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[4,3,2,6,7,5,8,1]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[2,3,4,7,6,5,8,1]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[3,2,4,7,6,5,8,1]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],.]
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[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[3,4,2,7,6,5,8,1]=>[[[.,[.,.]],[[[.,.],.],[.,.]]],.]
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[4,3,2,7,6,5,8,1]=>[[[[.,.],.],[[[.,.],.],[.,.]]],.]
[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[7,6,4,3,2,5,1,8]=>[2,3,5,6,7,4,8,1]=>[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[6,7,4,3,2,5,1,8]=>[3,2,5,6,7,4,8,1]=>[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]
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[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[6,7,4,2,3,5,1,8]=>[3,2,5,7,6,4,8,1]=>[[[.,.],[[.,[[.,.],.]],[.,.]]],.]
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[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[7,5,4,3,2,6,1,8]=>[2,4,5,6,7,3,8,1]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]
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[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[7,4,5,2,3,6,1,8]=>[2,5,4,7,6,3,8,1]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[7,5,3,2,4,6,1,8]=>[2,4,6,7,5,3,8,1]=>[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]
[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[7,4,3,2,5,6,1,8]=>[2,5,6,7,4,3,8,1]=>[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]
[[.,[[[.,[[.,.],.]],.],[.,.]]],.]=>[7,3,4,2,5,6,1,8]=>[2,6,5,7,4,3,8,1]=>[[.,[[[[.,.],[.,.]],.],[.,.]]],.]
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[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[6,5,4,3,2,7,1,8]=>[3,4,5,6,7,2,8,1]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]
[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]=>[6,4,5,3,2,7,1,8]=>[3,5,4,6,7,2,8,1]=>[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[4,5,3,6,7,2,8,1]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]
[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[6,5,3,4,2,7,1,8]=>[3,4,6,5,7,2,8,1]=>[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[5,6,3,4,2,7,1,8]=>[4,3,6,5,7,2,8,1]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]
[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[6,4,3,5,2,7,1,8]=>[3,5,6,4,7,2,8,1]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[6,3,4,5,2,7,1,8]=>[3,6,5,4,7,2,8,1]=>[[[.,[[[.,.],.],[.,.]]],[.,.]],.]
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[4,5,6,3,7,2,8,1]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[5,4,6,3,7,2,8,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[5,3,4,6,2,7,1,8]=>[4,6,5,3,7,2,8,1]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[6,5,4,3,7,2,8,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[6,5,4,2,3,7,1,8]=>[3,4,5,7,6,2,8,1]=>[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]
[[.,[[[.,.],[[.,.],[.,.]]],.]],.]=>[6,4,5,2,3,7,1,8]=>[3,5,4,7,6,2,8,1]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],.]
[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[4,5,6,2,3,7,1,8]=>[5,4,3,7,6,2,8,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[6,5,3,2,4,7,1,8]=>[3,4,6,7,5,2,8,1]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]
[[.,[[[[.,.],.],[.,[.,.]]],.]],.]=>[6,5,2,3,4,7,1,8]=>[3,4,7,6,5,2,8,1]=>[[[.,[.,[[[.,.],.],.]]],[.,.]],.]
[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[5,6,2,3,4,7,1,8]=>[4,3,7,6,5,2,8,1]=>[[[[.,.],[[[.,.],.],.]],[.,.]],.]
[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]=>[6,4,3,2,5,7,1,8]=>[3,5,6,7,4,2,8,1]=>[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]
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[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[4,5,6,7,3,2,8,1]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]
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[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[7,6,5,3,4,1,2,8]=>[2,3,4,6,5,8,7,1]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]
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[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[6,5,7,3,4,1,2,8]=>[3,4,2,6,5,8,7,1]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]
[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[5,6,7,3,4,1,2,8]=>[4,3,2,6,5,8,7,1]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]
[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]=>[7,6,4,3,5,1,2,8]=>[2,3,5,6,4,8,7,1]=>[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[6,7,3,4,5,1,2,8]=>[3,2,6,5,4,8,7,1]=>[[[.,.],[[[.,.],.],[[.,.],.]]],.]
[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[7,5,4,3,6,1,2,8]=>[2,4,5,6,3,8,7,1]=>[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]
[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[7,5,3,4,6,1,2,8]=>[2,4,6,5,3,8,7,1]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],.]
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[[[.,.],[[.,[[.,[.,.]],.]],.]],.]=>[5,4,6,3,7,1,2,8]=>[4,5,3,6,2,8,7,1]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]
[[[.,.],[[.,[[[.,.],.],.]],.]],.]=>[4,5,6,3,7,1,2,8]=>[5,4,3,6,2,8,7,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[5,6,3,4,7,1,2,8]=>[4,3,6,5,2,8,7,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[6,4,3,5,7,1,2,8]=>[3,5,6,4,2,8,7,1]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],.]
[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[4,5,3,6,7,1,2,8]=>[5,4,6,3,2,8,7,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
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[.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]]=>[6,2,3,4,5,7,8,9,10,1]=>[5,9,8,7,6,4,3,2,1,10]=>[[[[[.,[[[[.,.],.],.],.]],.],.],.],[.,.]]
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]=>[10,8,7,6,5,4,3,2,9,1]=>[1,3,4,5,6,7,8,9,2,10]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]
[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]=>[4,5,6,7,8,9,2,1,3]=>[6,5,4,3,2,1,8,9,7]=>[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]
[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]=>[8,9,7,6,5,4,2,1,3]=>[2,1,3,4,5,6,8,9,7]=>[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>[1,2,10,9,8,7,6,5,4,3]=>[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]=>[6,7,8,5,4,3,2,1,9]=>[4,3,2,5,6,7,8,9,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]=>[7,8,9,6,5,4,3,2,1,10]=>[4,3,2,5,6,7,8,9,10,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]=>[10,9,8,7,6,5,4,3,2,11,1]=>[2,3,4,5,6,7,8,9,10,1,11]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[9,8,7,1,2,3,4,5,6]=>[1,2,3,9,8,7,6,5,4]=>[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,1,2,3,4,5]=>[1,2,3,4,9,8,7,6,5]=>[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>[1,2,3,4,5,9,8,7,6]=>[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[9,7,1,2,3,4,5,6,8]=>[1,3,9,8,7,6,5,4,2]=>[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[10,9,8,1,2,3,4,5,6,7]=>[1,2,3,10,9,8,7,6,5,4]=>[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]
[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]=>[9,8,6,1,2,3,4,5,7]=>[1,2,4,9,8,7,6,5,3]=>[.,[.,[[.,[[[[[.,.],.],.],.],.]],.]]]
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,1,2,3,4,5,6]=>[1,2,3,4,10,9,8,7,6,5]=>[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]
[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]=>[9,8,7,5,1,2,3,4,6]=>[1,2,3,5,9,8,7,6,4]=>[.,[.,[.,[[.,[[[[.,.],.],.],.]],.]]]]
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,1,2,3,4,5]=>[1,2,3,4,5,10,9,8,7,6]=>[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]
[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,4,1,2,3,5]=>[1,2,3,4,6,9,8,7,5]=>[.,[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]]
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,1,2,3,4]=>[1,2,3,4,5,6,10,9,8,7]=>[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]
[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]=>[10,8,1,2,3,4,5,6,7,9]=>[1,3,10,9,8,7,6,5,4,2]=>[.,[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]]
[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]=>[10,9,11,8,7,6,5,4,3,2,1]=>[2,3,1,4,5,6,7,8,9,10,11]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]=>[8,9,7,6,5,4,2,3,1]=>[2,1,3,4,5,6,8,7,9]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[10,11,9,8,7,6,5,4,3,2,1]=>[2,1,3,4,5,6,7,8,9,10,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]=>[7,8,6,5,4,3,2,9,1]=>[3,2,4,5,6,7,8,1,9]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]=>[5,4,6,7,8,9,3,2,1]=>[5,6,4,3,2,1,7,8,9]=>[[[[[.,[.,.]],.],.],.],[.,[.,[.,.]]]]
[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]=>[6,5,7,8,9,4,3,2,1]=>[4,5,3,2,1,6,7,8,9]=>[[[[.,[.,.]],.],.],[.,[.,[.,[.,.]]]]]
[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]=>[7,6,5,4,3,2,8,1,9]=>[3,4,5,6,7,8,2,9,1]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]
[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]=>[8,7,1,2,3,4,5,6,9]=>[2,3,9,8,7,6,5,4,1]=>[[.,[.,[[[[[[.,.],.],.],.],.],.]]],.]
[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]=>[9,6,7,8,5,4,3,2,1]=>[1,4,3,2,5,6,7,8,9]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[8,7,6,5,4,3,9,1,2]=>[2,3,4,5,6,7,1,9,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]=>[8,7,6,5,4,2,3,1,9]=>[2,3,4,5,6,8,7,9,1]=>[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[3,4,1,2,5,6,7,8,9]=>[7,6,9,8,5,4,3,2,1]=>[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]
[.,[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]]=>[3,4,5,6,7,8,9,2,10,1]=>[8,7,6,5,4,3,2,9,1,10]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]
[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]=>[10,11,1,2,3,4,5,6,7,8,9]=>[2,1,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[8,7,6,5,4,1,2,3,9]=>[2,3,4,5,6,9,8,7,1]=>[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]
[[.,[.,[[[[[[.,.],.],.],.],.],.]]],.]=>[3,4,5,6,7,8,2,1,9]=>[7,6,5,4,3,2,8,9,1]=>[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,1,2,9]=>[1,3,4,5,6,7,8,10,9,2]=>[.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]]
[[[.,.],.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[8,7,6,5,4,9,1,2,3]=>[2,3,4,5,6,1,9,8,7]=>[[.,[.,[.,[.,[.,.]]]]],[[[.,.],.],.]]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]=>[9,10,7,6,5,4,3,2,1,8]=>[2,1,4,5,6,7,8,9,10,3]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]=>[7,6,8,9,5,4,3,2,1]=>[3,4,2,1,5,6,7,8,9]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]
[.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]=>[9,7,8,5,6,4,3,2,1]=>[1,3,2,5,4,6,7,8,9]=>[.,[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]
[.,[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]]=>[7,6,8,5,9,4,3,2,1]=>[3,4,2,5,1,6,7,8,9]=>[[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]
[.,[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]]=>[8,9,6,5,7,4,3,2,1]=>[2,1,4,5,3,6,7,8,9]=>[[.,.],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
Map
to 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
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 $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ 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 $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
searching the database
Sorry, this map was not found in the database.