Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Images
=>
Cc0010;cc-rep-0Cc0010;cc-rep-3
[.,.]=>[1]=>[1]=>[.,.]
[.,[.,.]]=>[2,1]=>[2,1]=>[[.,.],.]
[[.,.],.]=>[1,2]=>[1,2]=>[.,[.,.]]
[.,[.,[.,.]]]=>[3,2,1]=>[3,1,2]=>[[.,.],[.,.]]
[.,[[.,.],.]]=>[2,3,1]=>[3,2,1]=>[[[.,.],.],.]
[[.,.],[.,.]]=>[3,1,2]=>[2,3,1]=>[[.,[.,.]],.]
[[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[4,3,1,2]=>[[[.,.],.],[.,.]]
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[[.,.],[[.,.],.]]=>[3,4,1,2]=>[2,4,3,1]=>[[.,[[.,.],.]],.]
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[[[.,.],.],[.,.]]=>[4,1,2,3]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[[[.,.],[.,.]],.]=>[3,1,2,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[5,1,4,2,3]=>[[.,.],[[.,.],[.,.]]]
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]]
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[5,1,3,4,2]=>[[.,.],[[.,[.,.]],.]]
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[5,3,1,2,4]=>[[[.,.],.],[.,[.,.]]]
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[5,3,1,4,2]=>[[[.,.],.],[[.,.],.]]
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[5,4,2,1,3]=>[[[[.,.],.],.],[.,.]]
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[5,3,4,1,2]=>[[[.,.],[.,.]],[.,.]]
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.]
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.]
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[2,5,1,4,3]=>[[.,[.,.]],[[.,.],.]]
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[2,5,4,1,3]=>[[.,[[.,.],.]],[.,.]]
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.]
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[3,1,5,4,2]=>[[.,.],[[[.,.],.],.]]
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[4,3,1,5,2]=>[[[.,.],.],[[.,.],.]]
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[2,4,1,5,3]=>[[.,[.,.]],[[.,.],.]]
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[3,1,4,5,2]=>[[.,.],[[.,[.,.]],.]]
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[6,1,2,3,4,5]=>[[.,.],[.,[.,[.,[.,.]]]]]
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[6,1,2,5,3,4]=>[[.,.],[.,[[.,.],[.,.]]]]
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[6,1,2,5,4,3]=>[[.,.],[.,[[[.,.],.],.]]]
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[6,1,4,2,3,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[6,1,4,2,5,3]=>[[.,.],[[.,.],[[.,.],.]]]
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[6,1,5,3,2,4]=>[[.,.],[[[.,.],.],[.,.]]]
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[6,1,4,5,2,3]=>[[.,.],[[.,[.,.]],[.,.]]]
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[6,1,5,3,4,2]=>[[.,.],[[[.,.],[.,.]],.]]
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[6,1,5,4,3,2]=>[[.,.],[[[[.,.],.],.],.]]
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[6,1,4,5,3,2]=>[[.,.],[[[.,[.,.]],.],.]]
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[6,1,4,3,5,2]=>[[.,.],[[[.,.],[.,.]],.]]
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[6,1,3,4,5,2]=>[[.,.],[[.,[.,[.,.]]],.]]
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[6,3,1,2,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[6,3,1,2,5,4]=>[[[.,.],.],[.,[[.,.],.]]]
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[6,3,1,5,2,4]=>[[[.,.],.],[[.,.],[.,.]]]
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[6,3,1,5,4,2]=>[[[.,.],.],[[[.,.],.],.]]
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[6,3,1,4,5,2]=>[[[.,.],.],[[.,[.,.]],.]]
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[6,4,2,1,3,5]=>[[[[.,.],.],.],[.,[.,.]]]
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[6,4,2,1,5,3]=>[[[[.,.],.],.],[[.,.],.]]
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[6,3,4,1,2,5]=>[[[.,.],[.,.]],[.,[.,.]]]
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[6,3,4,1,5,2]=>[[[.,.],[.,.]],[[.,.],.]]
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[6,5,2,3,1,4]=>[[[[.,.],.],[.,.]],[.,.]]
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[6,5,4,2,1,3]=>[[[[[.,.],.],.],.],[.,.]]
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[6,3,5,2,1,4]=>[[[[.,.],[.,.]],.],[.,.]]
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[6,4,2,5,1,3]=>[[[[.,.],.],[.,.]],[.,.]]
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[6,3,4,5,1,2]=>[[[.,.],[.,[.,.]]],[.,.]]
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,5,2,3,4,1]=>[[[[.,.],.],[.,[.,.]]],.]
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,5,2,4,3,1]=>[[[[.,.],.],[[.,.],.]],.]
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[6,5,4,2,3,1]=>[[[[[.,.],.],.],[.,.]],.]
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[6,3,5,2,4,1]=>[[[[.,.],[.,.]],[.,.]],.]
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[6,3,5,4,2,1]=>[[[[.,.],[[.,.],.]],.],.]
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[6,4,2,5,3,1]=>[[[[.,.],.],[[.,.],.]],.]
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[6,3,4,5,2,1]=>[[[[.,.],[.,[.,.]]],.],.]
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,4,2,3,5,1]=>[[[[.,.],.],[.,[.,.]]],.]
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[6,3,4,2,5,1]=>[[[[.,.],[.,.]],[.,.]],.]
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],.]
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[2,6,1,3,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[2,6,1,3,5,4]=>[[.,[.,.]],[.,[[.,.],.]]]
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[2,6,1,5,3,4]=>[[.,[.,.]],[[.,.],[.,.]]]
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[2,6,1,5,4,3]=>[[.,[.,.]],[[[.,.],.],.]]
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[2,6,1,4,5,3]=>[[.,[.,.]],[[.,[.,.]],.]]
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[2,6,4,1,3,5]=>[[.,[[.,.],.]],[.,[.,.]]]
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,6,4,1,5,3]=>[[.,[[.,.],.]],[[.,.],.]]
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[2,6,5,3,1,4]=>[[.,[[[.,.],.],.]],[.,.]]
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[2,6,4,5,1,3]=>[[.,[[.,.],[.,.]]],[.,.]]
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[2,6,5,3,4,1]=>[[.,[[[.,.],.],[.,.]]],.]
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[2,6,5,4,3,1]=>[[.,[[[[.,.],.],.],.]],.]
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[2,6,4,5,3,1]=>[[.,[[[.,.],[.,.]],.]],.]
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[2,6,4,3,5,1]=>[[.,[[[.,.],.],[.,.]]],.]
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[2,6,3,4,5,1]=>[[.,[[.,.],[.,[.,.]]]],.]
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[3,1,6,2,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[3,1,6,2,5,4]=>[[.,.],[[.,.],[[.,.],.]]]
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,6,5,2,4]=>[[.,.],[[[.,.],.],[.,.]]]
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[3,1,6,5,4,2]=>[[.,.],[[[[.,.],.],.],.]]
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[3,1,6,4,5,2]=>[[.,.],[[[.,.],[.,.]],.]]
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[2,3,6,1,4,5]=>[[.,[.,[.,.]]],[.,[.,.]]]
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[2,3,6,1,5,4]=>[[.,[.,[.,.]]],[[.,.],.]]
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[2,3,6,5,1,4]=>[[.,[.,[[.,.],.]]],[.,.]]
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[2,3,6,5,4,1]=>[[.,[.,[[[.,.],.],.]]],.]
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[2,3,6,4,5,1]=>[[.,[.,[[.,.],[.,.]]]],.]
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[4,1,2,6,3,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[4,1,2,6,5,3]=>[[.,.],[.,[[[.,.],.],.]]]
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[4,3,1,6,2,5]=>[[[.,.],.],[[.,.],[.,.]]]
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[4,3,1,6,5,2]=>[[[.,.],.],[[[.,.],.],.]]
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[2,4,1,6,3,5]=>[[.,[.,.]],[[.,.],[.,.]]]
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[2,4,1,6,5,3]=>[[.,[.,.]],[[[.,.],.],.]]
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[3,1,4,6,2,5]=>[[.,.],[[.,[.,.]],[.,.]]]
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[3,1,4,6,5,2]=>[[.,.],[[.,[[.,.],.]],.]]
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[2,3,4,6,1,5]=>[[.,[.,[.,[.,.]]]],[.,.]]
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[2,3,4,6,5,1]=>[[.,[.,[.,[[.,.],.]]]],.]
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[5,1,2,3,6,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[5,1,4,2,6,3]=>[[.,.],[[.,.],[[.,.],.]]]
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[5,3,1,2,6,4]=>[[[.,.],.],[.,[[.,.],.]]]
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[5,4,2,1,6,3]=>[[[[.,.],.],.],[[.,.],.]]
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[5,3,4,1,6,2]=>[[[.,.],[.,.]],[[.,.],.]]
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[2,5,1,3,6,4]=>[[.,[.,.]],[.,[[.,.],.]]]
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[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[2,3,7,1,5,6,4]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[2,3,7,5,1,4,6]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[2,3,7,5,1,6,4]=>[[.,[.,[[.,.],.]]],[[.,.],.]]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[2,3,7,6,4,1,5]=>[[.,[.,[[[.,.],.],.]]],[.,.]]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[2,3,7,5,6,1,4]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[2,3,7,6,4,5,1]=>[[.,[.,[[[.,.],.],[.,.]]]],.]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[2,3,7,6,5,4,1]=>[[.,[.,[[[[.,.],.],.],.]]],.]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[2,3,7,5,6,4,1]=>[[.,[.,[[[.,.],[.,.]],.]]],.]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[2,3,7,5,4,6,1]=>[[.,[.,[[[.,.],.],[.,.]]]],.]
[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[2,3,7,4,5,6,1]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,7,3,5,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,7,3,6,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,7,6,3,5]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,7,6,5,3]=>[[.,.],[.,[[[[.,.],.],.],.]]]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,7,5,6,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,3,1,7,2,5,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,3,1,7,2,6,5]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,3,1,7,6,2,5]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,3,1,7,6,5,2]=>[[[.,.],.],[[[[.,.],.],.],.]]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,3,1,7,5,6,2]=>[[[.,.],.],[[[.,.],[.,.]],.]]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[2,4,1,7,3,5,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[2,4,1,7,3,6,5]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[2,4,1,7,6,3,5]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[2,4,1,7,6,5,3]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[2,4,1,7,5,6,3]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[3,1,4,7,2,5,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[3,1,4,7,2,6,5]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[3,1,4,7,6,2,5]=>[[.,.],[[.,[[.,.],.]],[.,.]]]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[3,1,4,7,6,5,2]=>[[.,.],[[.,[[[.,.],.],.]],.]]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[3,1,4,7,5,6,2]=>[[.,.],[[.,[[.,.],[.,.]]],.]]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[2,3,4,7,1,5,6]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[2,3,4,7,1,6,5]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[2,3,4,7,6,1,5]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[2,3,4,7,6,5,1]=>[[.,[.,[.,[[[.,.],.],.]]]],.]
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[2,3,4,7,5,6,1]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,7,4,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[5,1,2,3,7,6,4]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[5,1,4,2,7,3,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[5,1,4,2,7,6,3]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,3,1,2,7,4,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,3,1,2,7,6,4]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[5,4,2,1,7,3,6]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[5,4,2,1,7,6,3]=>[[[[.,.],.],.],[[[.,.],.],.]]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[5,3,4,1,7,2,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[5,3,4,1,7,6,2]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[2,5,1,3,7,4,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[2,5,1,3,7,6,4]=>[[.,[.,.]],[.,[[[.,.],.],.]]]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[2,5,4,1,7,3,6]=>[[.,[[.,.],.]],[[.,.],[.,.]]]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[2,5,4,1,7,6,3]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[3,1,5,2,7,4,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[3,1,5,2,7,6,4]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[2,3,5,1,7,4,6]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[2,3,5,1,7,6,4]=>[[.,[.,[.,.]]],[[[.,.],.],.]]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[4,1,2,5,7,3,6]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[4,1,2,5,7,6,3]=>[[.,.],[.,[[.,[[.,.],.]],.]]]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[4,3,1,5,7,2,6]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[4,3,1,5,7,6,2]=>[[[.,.],.],[[.,[[.,.],.]],.]]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[2,4,1,5,7,3,6]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[2,4,1,5,7,6,3]=>[[.,[.,.]],[[.,[[.,.],.]],.]]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[3,1,4,5,7,2,6]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[3,1,4,5,7,6,2]=>[[.,.],[[.,[.,[[.,.],.]]],.]]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[2,3,4,5,7,1,6]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[2,3,4,5,7,6,1]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]
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[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[6,1,2,5,3,7,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[6,1,4,2,3,7,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[6,1,5,3,2,7,4]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[6,1,4,5,2,7,3]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,3,1,2,4,7,5]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
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[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[2,6,1,3,4,7,5]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[2,6,1,5,3,7,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[2,6,4,1,3,7,5]=>[[.,[[.,.],.]],[.,[[.,.],.]]]
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[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[2,6,4,5,1,7,3]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
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[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[8,5,3,4,6,7,1,2]=>[2,8,4,6,3,7,1,5]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]
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[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[5,3,4,6,7,8,1,2]=>[2,8,4,5,3,6,7,1]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[2,8,4,3,5,6,7,1]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[2,8,3,4,5,6,7,1]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[3,1,8,2,4,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,2,1,3]=>[3,1,8,2,4,5,7,6]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[3,1,8,2,4,7,5,6]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[3,1,8,2,4,7,6,5]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[8,7,5,6,4,2,1,3]=>[3,1,8,2,6,4,5,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[3,1,8,2,6,4,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,8,2,7,5,4,6]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,2,1,3]=>[3,1,8,2,6,7,4,5]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[3,1,8,2,7,5,6,4]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,2,1,3]=>[3,1,8,2,7,6,5,4]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>[3,1,8,2,6,7,5,4]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,2,1,3]=>[3,1,8,2,6,5,7,4]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[3,1,8,2,5,6,7,4]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,2,1,3]=>[3,1,8,5,2,4,6,7]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,8,5,2,7,4,6]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[7,6,8,4,5,2,1,3]=>[3,1,8,5,2,7,6,4]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]
[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[3,1,8,6,4,2,7,5]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,2,1,3]=>[3,1,8,5,6,2,4,7]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,2,1,3]=>[3,1,8,5,6,2,7,4]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[3,1,8,5,7,4,2,6]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]
[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,2,1,3]=>[3,1,8,6,4,7,2,5]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,2,1,3]=>[3,1,8,5,6,7,2,4]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,2,1,3]=>[3,1,8,7,6,4,5,2]=>[[.,.],[[[[[.,.],.],.],[.,.]],.]]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,2,1,3]=>[3,1,8,7,6,5,4,2]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,2,1,3]=>[3,1,8,7,5,6,4,2]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,2,1,3]=>[3,1,8,5,7,4,6,2]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,2,1,3]=>[3,1,8,6,4,7,5,2]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,2,1,3]=>[3,1,8,5,4,6,7,2]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[3,1,8,4,5,6,7,2]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[2,3,8,1,4,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,1,2,3]=>[2,3,8,1,4,5,7,6]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[2,3,8,1,4,6,7,5]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,1,2,3]=>[2,3,8,1,6,4,7,5]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[2,3,8,1,6,7,4,5]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,1,2,3]=>[2,3,8,1,7,6,5,4]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[2,3,8,1,6,7,5,4]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[2,3,8,1,5,6,7,4]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[2,3,8,5,1,4,6,7]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,1,2,3]=>[2,3,8,5,1,4,7,6]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[2,3,8,5,1,7,4,6]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[6,7,8,4,5,1,2,3]=>[2,3,8,5,1,6,7,4]=>[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[2,3,8,6,4,1,5,7]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,1,2,3]=>[2,3,8,6,4,1,7,5]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[2,3,8,5,6,1,4,7]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>[2,3,8,5,6,1,7,4]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,1,2,3]=>[2,3,8,7,4,5,1,6]=>[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,1,2,3]=>[2,3,8,5,6,7,1,4]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[2,3,8,7,4,5,6,1]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>[2,3,8,7,6,5,4,1]=>[[.,[.,[[[[[.,.],.],.],.],.]]],.]
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[2,3,8,5,7,6,4,1]=>[[.,[.,[[[.,.],[[.,.],.]],.]]],.]
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[2,3,8,5,6,7,4,1]=>[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>[2,3,8,6,4,5,7,1]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,1,2,3]=>[2,3,8,6,5,4,7,1]=>[[.,[.,[[[[.,.],.],.],[.,.]]]],.]
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,1,2,3]=>[2,3,8,5,6,4,7,1]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,1,2,3]=>[2,3,8,5,4,6,7,1]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[2,3,8,4,5,6,7,1]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,8,3,5,6,7]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,8,3,7,5,6]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[4,1,2,8,3,6,7,5]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,8,6,3,5,7]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,8,6,3,7,5]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,8,7,5,3,6]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[4,1,2,8,6,7,3,5]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[4,1,2,8,7,5,6,3]=>[[.,.],[.,[[[[.,.],.],[.,.]],.]]]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[4,1,2,8,7,6,5,3]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[4,1,2,8,5,6,7,3]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[4,3,1,8,2,5,6,7]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[4,3,1,8,2,7,5,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,3,1,4]=>[4,3,1,8,2,6,7,5]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]]
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,3,1,4]=>[4,3,1,8,6,2,5,7]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[4,3,1,8,6,2,7,5]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,3,1,4]=>[4,3,1,8,7,5,2,6]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,3,1,4]=>[4,3,1,8,6,7,2,5]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,3,1,4]=>[4,3,1,8,7,5,6,2]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[4,3,1,8,7,6,5,2]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[4,3,1,8,6,7,5,2]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,3,1,4]=>[4,3,1,8,6,5,7,2]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[4,3,1,8,5,6,7,2]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[2,4,1,8,3,5,6,7]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[2,4,1,8,3,5,7,6]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[2,4,1,8,3,7,5,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[2,4,1,8,6,3,5,7]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[2,4,1,8,6,3,7,5]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[2,4,1,8,6,7,3,5]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[2,4,1,8,7,6,5,3]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[2,4,1,8,6,7,5,3]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[2,4,1,8,5,6,7,3]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[3,1,4,8,2,5,6,7]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[3,1,4,8,2,5,7,6]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,1,3,4]=>[3,1,4,8,2,7,5,6]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[3,1,4,8,2,6,7,5]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>[3,1,4,8,6,2,5,7]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[3,1,4,8,6,2,7,5]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,1,3,4]=>[3,1,4,8,7,5,2,6]=>[[.,.],[[.,[[[.,.],.],.]],[.,.]]]
[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,1,3,4]=>[3,1,4,8,6,7,2,5]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[3,1,4,8,7,6,5,2]=>[[.,.],[[.,[[[[.,.],.],.],.]],.]]
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[3,1,4,8,6,5,7,2]=>[[.,.],[[.,[[[.,.],.],[.,.]]],.]]
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[3,1,4,8,5,6,7,2]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[2,3,4,8,1,5,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[2,3,4,8,1,5,7,6]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[2,3,4,8,1,7,5,6]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[2,3,4,8,1,7,6,5]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[2,3,4,8,1,6,7,5]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[2,3,4,8,6,1,5,7]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[2,3,4,8,6,1,7,5]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[2,3,4,8,7,5,1,6]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[2,3,4,8,6,7,1,5]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[2,3,4,8,7,5,6,1]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[2,3,4,8,7,6,5,1]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[2,3,4,8,6,7,5,1]=>[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[2,3,4,8,6,5,7,1]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[2,3,4,8,5,6,7,1]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,8,4,6,7]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[5,1,2,3,8,4,7,6]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[8,6,7,4,3,2,1,5]=>[5,1,2,3,8,7,4,6]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[5,1,2,3,8,7,6,4]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[5,1,2,3,8,6,7,4]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[5,1,4,2,8,3,6,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[7,8,6,3,4,2,1,5]=>[5,1,4,2,8,3,7,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>[5,1,4,2,8,6,7,3]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[5,3,1,2,8,4,6,7]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,2,3,1,5]=>[5,3,1,2,8,4,7,6]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,2,3,1,5]=>[5,3,1,2,8,7,4,6]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[5,3,1,2,8,6,7,4]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[5,4,2,1,8,3,6,7]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[8,6,7,3,2,4,1,5]=>[5,4,2,1,8,7,3,6]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[7,6,8,3,2,4,1,5]=>[5,4,2,1,8,7,6,3]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[5,3,4,1,8,2,6,7]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[7,8,6,2,3,4,1,5]=>[5,3,4,1,8,2,7,6]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[2,5,1,3,8,4,6,7]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,3,1,2,5]=>[2,5,1,3,8,4,7,6]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,3,1,2,5]=>[2,5,1,3,8,7,4,6]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[2,5,1,3,8,6,7,4]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[2,5,4,1,8,3,6,7]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[7,8,6,3,4,1,2,5]=>[2,5,4,1,8,3,7,6]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[8,6,7,3,4,1,2,5]=>[2,5,4,1,8,7,3,6]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[7,6,8,3,4,1,2,5]=>[2,5,4,1,8,7,6,3]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[2,5,4,1,8,6,7,3]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[3,1,5,2,8,4,6,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[3,1,5,2,8,4,7,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[3,1,5,2,8,7,4,6]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,2,1,3,5]=>[3,1,5,2,8,7,6,4]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[3,1,5,2,8,6,7,4]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[2,3,5,1,8,4,6,7]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[2,3,5,1,8,4,7,6]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[2,3,5,1,8,7,4,6]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[4,1,2,5,8,3,6,7]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[7,8,6,3,2,1,4,5]=>[4,1,2,5,8,3,7,6]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[8,6,7,3,2,1,4,5]=>[4,1,2,5,8,7,3,6]=>[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[4,1,2,5,8,6,7,3]=>[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[4,3,1,5,8,2,6,7]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[7,8,6,2,3,1,4,5]=>[4,3,1,5,8,2,7,6]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[7,6,8,2,3,1,4,5]=>[4,3,1,5,8,7,6,2]=>[[[.,.],.],[[.,[[[.,.],.],.]],.]]
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[4,3,1,5,8,6,7,2]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[2,4,1,5,8,3,6,7]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[7,8,6,3,1,2,4,5]=>[2,4,1,5,8,3,7,6]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[8,6,7,3,1,2,4,5]=>[2,4,1,5,8,7,3,6]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[7,6,8,3,1,2,4,5]=>[2,4,1,5,8,7,6,3]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[3,1,4,5,8,2,6,7]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>[3,1,4,5,8,7,2,6]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[3,1,4,5,8,6,7,2]=>[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[2,3,4,5,8,1,6,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[2,3,4,5,8,1,7,6]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[2,3,4,5,8,7,1,6]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[2,3,4,5,8,7,6,1]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[2,3,4,5,8,6,7,1]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,8,5,7]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[6,1,2,3,4,8,7,5]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[8,7,4,5,3,2,1,6]=>[6,1,2,5,3,8,4,7]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[6,1,4,2,3,8,5,7]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[8,7,4,3,5,2,1,6]=>[6,1,5,3,2,8,4,7]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[8,7,3,4,5,2,1,6]=>[6,1,4,5,2,8,3,7]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[7,8,3,4,5,2,1,6]=>[6,1,4,5,2,8,7,3]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,2,3,1,6]=>[6,3,1,2,4,8,5,7]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[8,7,4,5,2,3,1,6]=>[6,3,1,5,2,8,4,7]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[8,7,5,3,2,4,1,6]=>[6,4,2,1,3,8,5,7]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[7,8,5,3,2,4,1,6]=>[6,4,2,1,3,8,7,5]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[8,7,5,2,3,4,1,6]=>[6,3,4,1,2,8,5,7]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
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[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[7,8,4,3,2,5,1,6]=>[6,5,2,3,1,8,7,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[7,8,4,2,3,5,1,6]=>[6,3,5,2,1,8,7,4]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[8,7,3,2,4,5,1,6]=>[6,4,2,5,1,8,3,7]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[8,7,2,3,4,5,1,6]=>[6,3,4,5,1,8,2,7]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[2,6,1,3,4,8,5,7]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[2,6,4,1,3,8,5,7]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[2,6,4,1,3,8,7,5]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]
[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[7,8,4,3,5,1,2,6]=>[2,6,5,3,1,8,7,4]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[7,8,3,4,5,1,2,6]=>[2,6,4,5,1,8,7,3]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[3,1,6,2,4,8,5,7]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[3,1,6,2,4,8,7,5]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6]=>[3,1,6,5,2,8,7,4]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[2,3,6,1,4,8,5,7]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[2,3,6,1,4,8,7,5]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[2,3,6,5,1,8,4,7]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[2,3,6,5,1,8,7,4]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[4,1,2,6,3,8,5,7]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[7,8,5,3,2,1,4,6]=>[4,1,2,6,3,8,7,5]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]
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[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[2,4,1,6,3,8,5,7]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[3,1,4,6,2,8,5,7]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[3,1,4,6,2,8,7,5]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[2,3,4,6,1,8,5,7]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[2,3,4,6,1,8,7,5]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6]=>[5,1,2,3,6,8,4,7]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[5,1,2,3,6,8,7,4]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[8,7,3,4,2,1,5,6]=>[5,1,4,2,6,8,3,7]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[7,8,3,4,2,1,5,6]=>[5,1,4,2,6,8,7,3]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[8,7,3,2,4,1,5,6]=>[5,4,2,1,6,8,3,7]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[5,4,2,1,6,8,7,3]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[8,7,2,3,4,1,5,6]=>[5,3,4,1,6,8,2,7]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[8,7,4,3,1,2,5,6]=>[2,5,1,3,6,8,4,7]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[2,5,1,3,6,8,7,4]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[8,7,3,4,1,2,5,6]=>[2,5,4,1,6,8,3,7]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[8,7,4,2,1,3,5,6]=>[3,1,5,2,6,8,4,7]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[2,3,5,1,6,8,4,7]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[4,1,2,5,6,8,3,7]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[4,1,2,5,6,8,7,3]=>[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[7,8,2,3,1,4,5,6]=>[4,3,1,5,6,8,7,2]=>[[[.,.],.],[[.,[.,[[.,.],.]]],.]]
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[3,1,4,5,6,8,2,7]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[3,1,4,5,6,8,7,2]=>[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[2,3,4,5,6,8,1,7]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[2,3,4,5,6,8,7,1]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]
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[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[8,4,3,5,6,2,1,7]=>[7,1,5,3,6,2,8,4]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
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[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]=>[8,6,4,3,2,5,1,7]=>[7,5,2,3,1,4,8,6]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]
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[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,3,1,2,7]=>[2,7,1,5,3,4,8,6]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
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[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.]=>[7,5,4,3,2,1,6,8,9]=>[6,1,2,3,4,7,5,8,9]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[8,6,5,4,3,2,1,7,9]=>[7,1,2,3,4,5,8,6,9]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>[8,2,3,4,5,6,7,1,9]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]=>[2,3,4,5,1,6,7,8,9]=>[5,2,3,4,1,6,7,8,9]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>[7,2,3,4,5,6,1,8,9]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.]=>[4,2,3,1,5,6,7,8,9]=>[4,3,1,2,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>[9,2,3,4,5,6,7,8,1,10]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]=>[4,1,2,3,5,6,7,8,9]=>[2,3,4,1,5,6,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[5,1,2,3,4,6,7,8,9]=>[2,3,4,5,1,6,7,8,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[6,1,2,3,4,5,7,8,9]=>[2,3,4,5,6,1,7,8,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[7,1,2,3,4,5,6,8,9]=>[2,3,4,5,6,7,1,8,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[8,1,2,3,4,5,6,7,9]=>[2,3,4,5,6,7,8,1,9]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[3,1,2,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]=>[4,1,2,3,5,6,7,8,9,10]=>[2,3,4,1,5,6,7,8,9,10]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[5,1,2,3,4,6,7,8,9,10]=>[2,3,4,5,1,6,7,8,9,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[6,1,2,3,4,5,7,8,9,10]=>[2,3,4,5,6,1,7,8,9,10]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[7,1,2,3,4,5,6,8,9,10]=>[2,3,4,5,6,7,1,8,9,10]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[8,1,2,3,4,5,6,7,9,10]=>[2,3,4,5,6,7,8,1,9,10]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[9,1,2,3,4,5,6,7,8,10]=>[2,3,4,5,6,7,8,9,1,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]=>[9,3,4,5,6,7,8,1,2]=>[2,9,4,5,6,7,8,1,3]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],[.,.]]
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[9,7,6,5,4,3,2,8,1]=>[9,8,2,3,4,5,6,1,7]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],[.,.]]
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[9,7,6,5,4,3,1,2,8]=>[2,8,1,3,4,5,6,9,7]=>[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]
[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,1,2,3]=>[2,3,10,1,4,5,6,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[.,[[[[[[.,.],.],.],.],[[.,.],.]],.]]=>[7,8,2,3,4,5,6,9,1]=>[9,3,4,5,6,8,7,2,1]=>[[[[.,.],[.,[.,[.,[[.,.],.]]]]],.],.]
[[[[[[[.,.],.],[[.,.],.]],.],.],.],.]=>[4,5,1,2,3,6,7,8,9]=>[2,3,5,4,1,6,7,8,9]=>[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]
[[[[.,[[[[.,.],.],.],.]],.],.],[.,.]]=>[9,2,3,4,5,1,6,7,8]=>[6,3,4,5,1,7,8,9,2]=>[[[.,.],[.,[.,.]]],[[.,[.,[.,.]]],.]]
[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.]=>[5,3,1,2,4,6,7,8,9]=>[2,4,1,5,3,6,7,8,9]=>[[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]]
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]=>[10,8,7,6,5,4,3,2,9,1]=>[10,9,2,3,4,5,6,7,1,8]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]=>[3,4,5,6,7,8,1,2,9]=>[2,8,3,4,5,6,7,1,9]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],[.,.]]
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>[2,3,4,5,6,7,8,10,1,9]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]=>[10,9,8,7,6,5,4,3,2,11,1]=>[11,10,2,3,4,5,6,7,8,9,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[9,8,7,1,2,3,4,5,6]=>[2,3,4,5,6,9,1,7,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,1,2,3,4,5]=>[2,3,4,5,9,1,6,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>[2,3,4,9,1,5,6,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[9,7,1,2,3,4,5,6,8]=>[2,3,4,5,6,8,1,9,7]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[10,9,8,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,10,1,8,9]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,1,2,3,4,5,6]=>[2,3,4,5,6,10,1,7,8,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,1,2,3,4,5]=>[2,3,4,5,10,1,6,7,8,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,1,2,3,4]=>[2,3,4,10,1,5,6,7,8,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[[[[[[.,[[.,[.,.]],.]],.],.],.],.],.]=>[3,2,4,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]]=>[9,4,3,2,1,5,6,7,8]=>[5,1,2,3,6,7,8,9,4]=>[[.,.],[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]=>[8,7,1,2,3,4,5,6,9]=>[2,3,4,5,6,8,1,7,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]=>[8,7,6,5,4,2,3,1,9]=>[8,3,1,2,4,5,6,7,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[9,2,3,4,5,6,7,1,8]=>[8,3,4,5,6,7,1,9,2]=>[[[.,.],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[3,4,1,2,5,6,7,8,9]=>[2,4,3,1,5,6,7,8,9]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]
[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]=>[10,11,1,2,3,4,5,6,7,8,9]=>[2,3,4,5,6,7,8,9,11,10,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]],.]
[.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]=>[9,8,2,3,4,5,6,7,1]=>[9,3,4,5,6,7,1,2,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]]=>[10,9,2,3,4,5,6,7,8,1]=>[10,3,4,5,6,7,8,1,2,9]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]=>[10,3,1,2,4,5,6,7,8,9]=>[2,4,1,5,6,7,8,9,10,3]=>[[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[[[.,[[[[[.,.],.],.],.],.]],.],[.,.]]=>[9,2,3,4,5,6,1,7,8]=>[7,3,4,5,6,1,8,9,2]=>[[[.,.],[.,[.,[.,.]]]],[[.,[.,.]],.]]
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,1,2,9]=>[2,9,1,3,4,5,6,7,10,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[[.,[[[[[.,.],.],.],.],.]],[.,[.,.]]]=>[9,8,2,3,4,5,6,1,7]=>[7,3,4,5,6,1,9,2,8]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],[.,.]]]
[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]=>[9,3,4,5,6,7,8,2,1]=>[9,1,4,5,6,7,8,2,3]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
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
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
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.