Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00059: Permutations —Robinson-Schensted insertion tableau⟶ Standard tableaux
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Mp00059: Permutations —Robinson-Schensted insertion tableau⟶ Standard tableaux
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Images
=>
Cc0010;cc-rep-0Cc0007;cc-rep-2
[.,.]=>[1]=>[[1]]=>[1]
[.,[.,.]]=>[2,1]=>[[1],[2]]=>[1,1]
[[.,.],.]=>[1,2]=>[[1,2]]=>[2]
[.,[.,[.,.]]]=>[3,2,1]=>[[1],[2],[3]]=>[1,1,1]
[.,[[.,.],.]]=>[2,3,1]=>[[1,3],[2]]=>[1,2]
[[.,.],[.,.]]=>[3,1,2]=>[[1,2],[3]]=>[2,1]
[[.,[.,.]],.]=>[2,1,3]=>[[1,3],[2]]=>[1,2]
[[[.,.],.],.]=>[1,2,3]=>[[1,2,3]]=>[3]
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[[1],[2],[3],[4]]=>[1,1,1,1]
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[[1,4],[2],[3]]=>[1,1,2]
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[[1,3],[2],[4]]=>[1,2,1]
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[[1,4],[2],[3]]=>[1,1,2]
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[[1,3,4],[2]]=>[1,3]
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[[1,2],[3],[4]]=>[2,1,1]
[[.,.],[[.,.],.]]=>[3,4,1,2]=>[[1,2],[3,4]]=>[2,2]
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[[1,3],[2],[4]]=>[1,2,1]
[[[.,.],.],[.,.]]=>[4,1,2,3]=>[[1,2,3],[4]]=>[3,1]
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[[1,4],[2],[3]]=>[1,1,2]
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[[1,3,4],[2]]=>[1,3]
[[[.,.],[.,.]],.]=>[3,1,2,4]=>[[1,2,4],[3]]=>[2,2]
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[[1,3,4],[2]]=>[1,3]
[[[[.,.],.],.],.]=>[1,2,3,4]=>[[1,2,3,4]]=>[4]
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[[1],[2],[3],[4],[5]]=>[1,1,1,1,1]
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[[1,5],[2],[3],[4]]=>[1,1,1,2]
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[[1,4],[2],[3],[5]]=>[1,1,2,1]
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[[1,5],[2],[3],[4]]=>[1,1,1,2]
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[[1,4,5],[2],[3]]=>[1,1,3]
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[[1,3],[2],[4],[5]]=>[1,2,1,1]
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[[1,3],[2,5],[4]]=>[1,2,2]
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[[1,4],[2],[3],[5]]=>[1,1,2,1]
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[[1,3,4],[2],[5]]=>[1,3,1]
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[[1,5],[2],[3],[4]]=>[1,1,1,2]
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[[1,4,5],[2],[3]]=>[1,1,3]
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[[1,3,5],[2],[4]]=>[1,2,2]
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[[1,4,5],[2],[3]]=>[1,1,3]
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[[1,3,4,5],[2]]=>[1,4]
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[[1,2],[3],[4],[5]]=>[2,1,1,1]
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[[1,2],[3,5],[4]]=>[2,1,2]
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[[1,2],[3,4],[5]]=>[2,2,1]
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[[1,2],[3,5],[4]]=>[2,1,2]
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[[1,2,5],[3,4]]=>[2,3]
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[[1,3],[2],[4],[5]]=>[1,2,1,1]
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[[1,3],[2,5],[4]]=>[1,2,2]
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[[1,2,3],[4],[5]]=>[3,1,1]
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[[1,2,3],[4,5]]=>[3,2]
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[[1,4],[2],[3],[5]]=>[1,1,2,1]
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[[1,3,4],[2],[5]]=>[1,3,1]
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[[1,2,4],[3],[5]]=>[2,2,1]
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[[1,3,4],[2],[5]]=>[1,3,1]
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[[1,2,3,4],[5]]=>[4,1]
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[[1,5],[2],[3],[4]]=>[1,1,1,2]
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[[1,4,5],[2],[3]]=>[1,1,3]
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[[1,3,5],[2],[4]]=>[1,2,2]
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[[1,4,5],[2],[3]]=>[1,1,3]
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[[1,3,4,5],[2]]=>[1,4]
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[[1,2,5],[3],[4]]=>[2,1,2]
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[[1,2,5],[3,4]]=>[2,3]
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[[1,3,5],[2],[4]]=>[1,2,2]
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[[1,2,3,5],[4]]=>[3,2]
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[[1,4,5],[2],[3]]=>[1,1,3]
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[[1,3,4,5],[2]]=>[1,4]
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[[1,2,4,5],[3]]=>[2,3]
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[[1,3,4,5],[2]]=>[1,4]
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[[1,2,3,4,5]]=>[5]
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,1]
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[[1,6],[2],[3],[4],[5]]=>[1,1,1,1,2]
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[[1,5],[2],[3],[4],[6]]=>[1,1,1,2,1]
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[[1,6],[2],[3],[4],[5]]=>[1,1,1,1,2]
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[[1,4],[2],[3],[5],[6]]=>[1,1,2,1,1]
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[[1,5],[2],[3],[4],[6]]=>[1,1,1,2,1]
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[[1,4,5],[2],[3],[6]]=>[1,1,3,1]
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[[1,6],[2],[3],[4],[5]]=>[1,1,1,1,2]
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[[1,4,6],[2],[3],[5]]=>[1,1,2,2]
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[[1,3],[2],[4],[5],[6]]=>[1,2,1,1,1]
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[[1,3],[2,6],[4],[5]]=>[1,2,1,2]
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[[1,3],[2,5],[4],[6]]=>[1,2,2,1]
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[[1,3],[2,6],[4],[5]]=>[1,2,1,2]
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[[1,4],[2],[3],[5],[6]]=>[1,1,2,1,1]
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[[1,3,4],[2],[5],[6]]=>[1,3,1,1]
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[[1,3,4],[2,6],[5]]=>[1,3,2]
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[[1,5],[2],[3],[4],[6]]=>[1,1,1,2,1]
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[[1,4,5],[2],[3],[6]]=>[1,1,3,1]
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[[1,3,5],[2],[4],[6]]=>[1,2,2,1]
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[[1,4,5],[2],[3],[6]]=>[1,1,3,1]
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[[1,3,4,5],[2],[6]]=>[1,4,1]
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[[1,6],[2],[3],[4],[5]]=>[1,1,1,1,2]
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[[1,4,6],[2],[3],[5]]=>[1,1,2,2]
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[[1,3,6],[2],[4],[5]]=>[1,2,1,2]
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[[1,4,6],[2],[3],[5]]=>[1,1,2,2]
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[[1,3,4,6],[2],[5]]=>[1,3,2]
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[[1,3,5,6],[2],[4]]=>[1,2,3]
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[[1,3,4,5,6],[2]]=>[1,5]
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[[1,2],[3],[4],[5],[6]]=>[2,1,1,1,1]
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[[1,2],[3,6],[4],[5]]=>[2,1,1,2]
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[[1,2],[3,5],[4],[6]]=>[2,1,2,1]
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[[1,2],[3,6],[4],[5]]=>[2,1,1,2]
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[[1,2,6],[3,5],[4]]=>[2,1,3]
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[[1,2],[3,4],[5],[6]]=>[2,2,1,1]
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[[1,2],[3,4],[5,6]]=>[2,2,2]
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[[1,2],[3,5],[4],[6]]=>[2,1,2,1]
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[[1,2,5],[3,4],[6]]=>[2,3,1]
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[[1,2],[3,6],[4],[5]]=>[2,1,1,2]
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[[1,2,6],[3,5],[4]]=>[2,1,3]
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[[1,2,6],[3,4],[5]]=>[2,2,2]
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[[1,2,6],[3,5],[4]]=>[2,1,3]
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[[1,2,5,6],[3,4]]=>[2,4]
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[[1,3],[2],[4],[5],[6]]=>[1,2,1,1,1]
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[[1,3],[2,6],[4],[5]]=>[1,2,1,2]
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[[1,3],[2,5],[4],[6]]=>[1,2,2,1]
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[[1,3],[2,6],[4],[5]]=>[1,2,1,2]
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[[1,2,3],[4],[5],[6]]=>[3,1,1,1]
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[[1,2,3],[4,6],[5]]=>[3,1,2]
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[[1,2,3],[4,5],[6]]=>[3,2,1]
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[[1,2,3],[4,6],[5]]=>[3,1,2]
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[[1,2,3],[4,5,6]]=>[3,3]
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[[1,4],[2],[3],[5],[6]]=>[1,1,2,1,1]
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[[1,3,4],[2],[5],[6]]=>[1,3,1,1]
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[[1,3,4],[2,6],[5]]=>[1,3,2]
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[[1,2,4],[3],[5],[6]]=>[2,2,1,1]
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[[1,2,4],[3,6],[5]]=>[2,2,2]
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[[1,3,4],[2],[5],[6]]=>[1,3,1,1]
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[[1,3,4],[2,6],[5]]=>[1,3,2]
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[[1,2,3,4],[5],[6]]=>[4,1,1]
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[[1,2,3,4],[5,6]]=>[4,2]
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[[1,5],[2],[3],[4],[6]]=>[1,1,1,2,1]
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[[1,4,5],[2],[3],[6]]=>[1,1,3,1]
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[[1,3,5],[2],[4],[6]]=>[1,2,2,1]
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[[1,4,5],[2],[3],[6]]=>[1,1,3,1]
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[[1,3,4,5],[2],[6]]=>[1,4,1]
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[[1,2,5],[3],[4],[6]]=>[2,1,2,1]
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[[1,2,5],[3,4],[6]]=>[2,3,1]
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[[1,3,5],[2],[4],[6]]=>[1,2,2,1]
[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[[1,2,3,5],[4],[6]]=>[3,2,1]
[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[[1,4,5],[2],[3],[6]]=>[1,1,3,1]
[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[[1,3,4,5],[2],[6]]=>[1,4,1]
[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[[1,2,4,5],[3],[6]]=>[2,3,1]
[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[[1,3,4,5],[2],[6]]=>[1,4,1]
[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[[1,2,3,4,5],[6]]=>[5,1]
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[[1,6],[2],[3],[4],[5]]=>[1,1,1,1,2]
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[[1,4,6],[2],[3],[5]]=>[1,1,2,2]
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[[1,3,6],[2],[4],[5]]=>[1,2,1,2]
[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[[1,4,6],[2],[3],[5]]=>[1,1,2,2]
[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[[1,3,4,6],[2],[5]]=>[1,3,2]
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[[1,3,5,6],[2],[4]]=>[1,2,3]
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[[1,3,4,5,6],[2]]=>[1,5]
[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[[1,2,6],[3],[4],[5]]=>[2,1,1,2]
[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[[1,2,6],[3,5],[4]]=>[2,1,3]
[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[[1,2,6],[3,4],[5]]=>[2,2,2]
[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[[1,2,6],[3,5],[4]]=>[2,1,3]
[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[[1,2,5,6],[3,4]]=>[2,4]
[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[[1,3,6],[2],[4],[5]]=>[1,2,1,2]
[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[[1,2,3,6],[4],[5]]=>[3,1,2]
[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[[1,2,3,6],[4,5]]=>[3,3]
[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[[1,4,6],[2],[3],[5]]=>[1,1,2,2]
[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[[1,3,4,6],[2],[5]]=>[1,3,2]
[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[[1,2,4,6],[3],[5]]=>[2,2,2]
[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[[1,3,4,6],[2],[5]]=>[1,3,2]
[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[[1,2,3,4,6],[5]]=>[4,2]
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[[1,3,5,6],[2],[4]]=>[1,2,3]
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[[1,3,4,5,6],[2]]=>[1,5]
[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[[1,2,5,6],[3],[4]]=>[2,1,3]
[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[[1,2,5,6],[3,4]]=>[2,4]
[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[[1,3,5,6],[2],[4]]=>[1,2,3]
[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[[1,2,3,5,6],[4]]=>[3,3]
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[[1,3,4,5,6],[2]]=>[1,5]
[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[[1,2,4,5,6],[3]]=>[2,4]
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[[1,3,4,5,6],[2]]=>[1,5]
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[[1,2,3,4,5,6]]=>[6]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[[1,6],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,1]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[[1,5],[2],[3],[4],[6],[7]]=>[1,1,1,2,1,1]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[[1,6],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,1]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[[1,5,6],[2],[3],[4],[7]]=>[1,1,1,3,1]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[[1,5,7],[2],[3],[4],[6]]=>[1,1,1,2,2]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[[1,4],[2],[3],[5],[6],[7]]=>[1,1,2,1,1,1]
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[[1,4],[2,7],[3],[5],[6]]=>[1,1,2,1,2]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[[1,4],[2,6],[3],[5],[7]]=>[1,1,2,2,1]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[[1,4],[2,7],[3],[5],[6]]=>[1,1,2,1,2]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[[1,5],[2],[3],[4],[6],[7]]=>[1,1,1,2,1,1]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[[1,4,5],[2],[3],[6],[7]]=>[1,1,3,1,1]
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[[1,4,5],[2,7],[3],[6]]=>[1,1,3,2]
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[[1,6],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,1]
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[[1,5,6],[2],[3],[4],[7]]=>[1,1,1,3,1]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[[1,4,6],[2],[3],[5],[7]]=>[1,1,2,2,1]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[[1,5,6],[2],[3],[4],[7]]=>[1,1,1,3,1]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[[1,4,5,6],[2],[3],[7]]=>[1,1,4,1]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[[1,5,7],[2],[3],[4],[6]]=>[1,1,1,2,2]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[[1,4,7],[2],[3],[5],[6]]=>[1,1,2,1,2]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[[1,5,7],[2],[3],[4],[6]]=>[1,1,1,2,2]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[[1,4,5,7],[2],[3],[6]]=>[1,1,3,2]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[[1,4,6,7],[2],[3],[5]]=>[1,1,2,3]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[[1,3],[2],[4],[5],[6],[7]]=>[1,2,1,1,1,1]
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[[1,3],[2,7],[4],[5],[6]]=>[1,2,1,1,2]
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[[1,3],[2,6],[4],[5],[7]]=>[1,2,1,2,1]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[[1,3],[2,7],[4],[5],[6]]=>[1,2,1,1,2]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[[1,3,7],[2,6],[4],[5]]=>[1,2,1,3]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[[1,3],[2,5],[4],[6],[7]]=>[1,2,2,1,1]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[[1,3],[2,6],[4],[5],[7]]=>[1,2,1,2,1]
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[[1,3,6],[2,5],[4],[7]]=>[1,2,3,1]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[[1,3],[2,7],[4],[5],[6]]=>[1,2,1,1,2]
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[[1,3,7],[2,6],[4],[5]]=>[1,2,1,3]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[[1,3,7],[2,5],[4],[6]]=>[1,2,2,2]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[[1,3,7],[2,6],[4],[5]]=>[1,2,1,3]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[[1,4],[2],[3],[5],[6],[7]]=>[1,1,2,1,1,1]
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[[1,4],[2,7],[3],[5],[6]]=>[1,1,2,1,2]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[[1,4],[2,6],[3],[5],[7]]=>[1,1,2,2,1]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[[1,4],[2,7],[3],[5],[6]]=>[1,1,2,1,2]
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[[1,3,4],[2],[5],[6],[7]]=>[1,3,1,1,1]
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[[1,3,4],[2,7],[5],[6]]=>[1,3,1,2]
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[[1,3,4],[2,6],[5],[7]]=>[1,3,2,1]
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[[1,3,4],[2,7],[5],[6]]=>[1,3,1,2]
[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[[1,5],[2],[3],[4],[6],[7]]=>[1,1,1,2,1,1]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[[1,4,5],[2],[3],[6],[7]]=>[1,1,3,1,1]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[[1,4,5],[2,7],[3],[6]]=>[1,1,3,2]
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[[1,3,5],[2],[4],[6],[7]]=>[1,2,2,1,1]
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[[1,3,5],[2,7],[4],[6]]=>[1,2,2,2]
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[[1,4,5],[2],[3],[6],[7]]=>[1,1,3,1,1]
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[[1,4,5],[2,7],[3],[6]]=>[1,1,3,2]
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[[1,3,4,5],[2],[6],[7]]=>[1,4,1,1]
[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[[1,3,4,5],[2,7],[6]]=>[1,4,2]
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[[1,6],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,1]
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[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[[1,4,6],[2],[3],[5],[7]]=>[1,1,2,2,1]
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[[1,5,6],[2],[3],[4],[7]]=>[1,1,1,3,1]
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[[1,4,5,6],[2],[3],[7]]=>[1,1,4,1]
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[[1,3,6],[2],[4],[5],[7]]=>[1,2,1,2,1]
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[[1,3,6],[2,5],[4],[7]]=>[1,2,3,1]
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[[1,4,6],[2],[3],[5],[7]]=>[1,1,2,2,1]
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[[1,3,4,6],[2],[5],[7]]=>[1,3,2,1]
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[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[[1,4,5,6],[2],[3],[7]]=>[1,1,4,1]
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[[1,3,5,6],[2],[4],[7]]=>[1,2,3,1]
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[[1,4,5,6],[2],[3],[7]]=>[1,1,4,1]
[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[[1,3,4,5,6],[2],[7]]=>[1,5,1]
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[[1,5,7],[2],[3],[4],[6]]=>[1,1,1,2,2]
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[[1,4,7],[2],[3],[5],[6]]=>[1,1,2,1,2]
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[[1,5,7],[2],[3],[4],[6]]=>[1,1,1,2,2]
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[[1,4,5,7],[2],[3],[6]]=>[1,1,3,2]
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[[1,4,6,7],[2],[3],[5]]=>[1,1,2,3]
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[[1,3,7],[2],[4],[5],[6]]=>[1,2,1,1,2]
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[[1,3,7],[2,6],[4],[5]]=>[1,2,1,3]
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[[1,3,7],[2,5],[4],[6]]=>[1,2,2,2]
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[[1,3,7],[2,6],[4],[5]]=>[1,2,1,3]
[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[[1,4,7],[2],[3],[5],[6]]=>[1,1,2,1,2]
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[[1,3,4,7],[2],[5],[6]]=>[1,3,1,2]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[[1,3,4,7],[2,6],[5]]=>[1,3,3]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[[1,5,7],[2],[3],[4],[6]]=>[1,1,1,2,2]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[[1,4,5,7],[2],[3],[6]]=>[1,1,3,2]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[[1,3,5,7],[2],[4],[6]]=>[1,2,2,2]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[[1,4,5,7],[2],[3],[6]]=>[1,1,3,2]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[[1,3,4,5,7],[2],[6]]=>[1,4,2]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[[1,4,6,7],[2],[3],[5]]=>[1,1,2,3]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[[1,3,6,7],[2],[4],[5]]=>[1,2,1,3]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[[1,4,6,7],[2],[3],[5]]=>[1,1,2,3]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[[1,3,4,6,7],[2],[5]]=>[1,3,3]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[[1,3,5,6,7],[2],[4]]=>[1,2,4]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[[1,3,4,5,6,7],[2]]=>[1,6]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[[1,2],[3],[4],[5],[6],[7]]=>[2,1,1,1,1,1]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[[1,2],[3,7],[4],[5],[6]]=>[2,1,1,1,2]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[[1,2],[3,6],[4],[5],[7]]=>[2,1,1,2,1]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[[1,2],[3,7],[4],[5],[6]]=>[2,1,1,1,2]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[[1,2,7],[3,6],[4],[5]]=>[2,1,1,3]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[[1,2],[3,5],[4],[6],[7]]=>[2,1,2,1,1]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[[1,2],[3,5],[4,7],[6]]=>[2,1,2,2]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[[1,2],[3,6],[4],[5],[7]]=>[2,1,1,2,1]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[[1,2,6],[3,5],[4],[7]]=>[2,1,3,1]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[[1,2],[3,7],[4],[5],[6]]=>[2,1,1,1,2]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[[1,2,7],[3,6],[4],[5]]=>[2,1,1,3]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[[1,2,7],[3,5],[4],[6]]=>[2,1,2,2]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[[1,2,7],[3,6],[4],[5]]=>[2,1,1,3]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[[1,2,6,7],[3,5],[4]]=>[2,1,4]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[[1,2],[3,4],[5],[6],[7]]=>[2,2,1,1,1]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[[1,2],[3,4],[5,7],[6]]=>[2,2,1,2]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[[1,2],[3,4],[5,6],[7]]=>[2,2,2,1]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[[1,2],[3,4],[5,7],[6]]=>[2,2,1,2]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[[1,2],[3,5],[4],[6],[7]]=>[2,1,2,1,1]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[[1,2],[3,5],[4,7],[6]]=>[2,1,2,2]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,1,1]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[[1,2,5],[3,4],[6,7]]=>[2,3,2]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[[1,2],[3,6],[4],[5],[7]]=>[2,1,1,2,1]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[[1,2,6],[3,5],[4],[7]]=>[2,1,3,1]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[[1,2,6],[3,5],[4],[7]]=>[2,1,3,1]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[[1,2],[3,7],[4],[5],[6]]=>[2,1,1,1,2]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[[1,2,7],[3,6],[4],[5]]=>[2,1,1,3]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[[1,2,7],[3,5],[4],[6]]=>[2,1,2,2]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[[1,2,7],[3,6],[4],[5]]=>[2,1,1,3]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[[1,2,6,7],[3,5],[4]]=>[2,1,4]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,1,2]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[[1,2,7],[3,5],[4],[6]]=>[2,1,2,2]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[[1,2,7],[3,6],[4],[5]]=>[2,1,1,3]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[[1,2,6,7],[3,5],[4]]=>[2,1,4]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[[1,2,6,7],[3,5],[4]]=>[2,1,4]
[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[[1,2,5,6,7],[3,4]]=>[2,5]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[[1,3],[2],[4],[5],[6],[7]]=>[1,2,1,1,1,1]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[[1,3],[2,7],[4],[5],[6]]=>[1,2,1,1,2]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[[1,3],[2,6],[4],[5],[7]]=>[1,2,1,2,1]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[[1,3],[2,7],[4],[5],[6]]=>[1,2,1,1,2]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[[1,3,7],[2,6],[4],[5]]=>[1,2,1,3]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[[1,3],[2,5],[4],[6],[7]]=>[1,2,2,1,1]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[[1,3],[2,6],[4],[5],[7]]=>[1,2,1,2,1]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[[1,3,6],[2,5],[4],[7]]=>[1,2,3,1]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[[1,3],[2,7],[4],[5],[6]]=>[1,2,1,1,2]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[[1,3,7],[2,6],[4],[5]]=>[1,2,1,3]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[[1,3,7],[2,5],[4],[6]]=>[1,2,2,2]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[[1,3,7],[2,6],[4],[5]]=>[1,2,1,3]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[[1,2,3],[4],[5],[6],[7]]=>[3,1,1,1,1]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[[1,2,3],[4,7],[5],[6]]=>[3,1,1,2]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[[1,2,3],[4,6],[5],[7]]=>[3,1,2,1]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[[1,2,3],[4,7],[5],[6]]=>[3,1,1,2]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[[1,2,3],[4,6,7],[5]]=>[3,1,3]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,1,1]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[[1,2,3],[4,5],[6,7]]=>[3,2,2]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[[1,2,3],[4,6],[5],[7]]=>[3,1,2,1]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[[1,2,3],[4,5,6],[7]]=>[3,3,1]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[[1,2,3],[4,7],[5],[6]]=>[3,1,1,2]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[[1,2,3],[4,6,7],[5]]=>[3,1,3]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[[1,2,3],[4,5,7],[6]]=>[3,2,2]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[[1,2,3],[4,6,7],[5]]=>[3,1,3]
[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[[1,2,3,7],[4,5,6]]=>[3,4]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[[1,4],[2],[3],[5],[6],[7]]=>[1,1,2,1,1,1]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[[1,4],[2,7],[3],[5],[6]]=>[1,1,2,1,2]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[[1,4],[2,6],[3],[5],[7]]=>[1,1,2,2,1]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[[1,4],[2,7],[3],[5],[6]]=>[1,1,2,1,2]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[[1,3,4],[2],[5],[6],[7]]=>[1,3,1,1,1]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[[1,3,4],[2,7],[5],[6]]=>[1,3,1,2]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[[1,3,4],[2,6],[5],[7]]=>[1,3,2,1]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[[1,3,4],[2,7],[5],[6]]=>[1,3,1,2]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[[1,2,4],[3],[5],[6],[7]]=>[2,2,1,1,1]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,1,2]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,1,2]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[[1,2,4],[3,6,7],[5]]=>[2,2,3]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[[1,3,4],[2],[5],[6],[7]]=>[1,3,1,1,1]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[[1,3,4],[2,7],[5],[6]]=>[1,3,1,2]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[[1,3,4],[2,6],[5],[7]]=>[1,3,2,1]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[[1,3,4],[2,7],[5],[6]]=>[1,3,1,2]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[[1,2,3,4],[5],[6],[7]]=>[4,1,1,1]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[[1,2,3,4],[5,7],[6]]=>[4,1,2]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[[1,2,3,4],[5,7],[6]]=>[4,1,2]
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[[1,2,3,4],[5,6,7]]=>[4,3]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[[1,5],[2],[3],[4],[6],[7]]=>[1,1,1,2,1,1]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[[1,4,5],[2],[3],[6],[7]]=>[1,1,3,1,1]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[[1,4,5],[2,7],[3],[6]]=>[1,1,3,2]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[[1,3,5],[2],[4],[6],[7]]=>[1,2,2,1,1]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[[1,3,5],[2,7],[4],[6]]=>[1,2,2,2]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[[1,4,5],[2],[3],[6],[7]]=>[1,1,3,1,1]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[[1,4,5],[2,7],[3],[6]]=>[1,1,3,2]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[[1,3,4,5],[2],[6],[7]]=>[1,4,1,1]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[[1,3,4,5],[2,7],[6]]=>[1,4,2]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[[1,2,5],[3],[4],[6],[7]]=>[2,1,2,1,1]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[[1,2,5],[3,7],[4],[6]]=>[2,1,2,2]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,1,1]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[[1,2,5],[3,4],[6,7]]=>[2,3,2]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[[1,3,5],[2],[4],[6],[7]]=>[1,2,2,1,1]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[[1,3,5],[2,7],[4],[6]]=>[1,2,2,2]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,1,1]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[[1,4,5],[2],[3],[6],[7]]=>[1,1,3,1,1]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[[1,4,5],[2,7],[3],[6]]=>[1,1,3,2]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[[1,3,4,5],[2],[6],[7]]=>[1,4,1,1]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[[1,3,4,5],[2,7],[6]]=>[1,4,2]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,1,1]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[[1,3,4,5],[2],[6],[7]]=>[1,4,1,1]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[[1,3,4,5],[2,7],[6]]=>[1,4,2]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[[1,2,3,4,5],[6],[7]]=>[5,1,1]
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[[1,2,3,4,5],[6,7]]=>[5,2]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[[1,6],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,1]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[[1,5,6],[2],[3],[4],[7]]=>[1,1,1,3,1]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[[1,4,6],[2],[3],[5],[7]]=>[1,1,2,2,1]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[[1,5,6],[2],[3],[4],[7]]=>[1,1,1,3,1]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[[1,4,5,6],[2],[3],[7]]=>[1,1,4,1]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[[1,3,6],[2],[4],[5],[7]]=>[1,2,1,2,1]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[[1,3,6],[2,5],[4],[7]]=>[1,2,3,1]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[[1,4,6],[2],[3],[5],[7]]=>[1,1,2,2,1]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[[1,3,4,6],[2],[5],[7]]=>[1,3,2,1]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[[1,5,6],[2],[3],[4],[7]]=>[1,1,1,3,1]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[[1,4,5,6],[2],[3],[7]]=>[1,1,4,1]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[[1,3,5,6],[2],[4],[7]]=>[1,2,3,1]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[[1,4,5,6],[2],[3],[7]]=>[1,1,4,1]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[[1,3,4,5,6],[2],[7]]=>[1,5,1]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[[1,2,6],[3],[4],[5],[7]]=>[2,1,1,2,1]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[[1,2,6],[3,5],[4],[7]]=>[2,1,3,1]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[[1,2,6],[3,5],[4],[7]]=>[2,1,3,1]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[[1,3,6],[2],[4],[5],[7]]=>[1,2,1,2,1]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[[1,3,6],[2,5],[4],[7]]=>[1,2,3,1]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[[1,2,3,6],[4],[5],[7]]=>[3,1,2,1]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[[1,4,6],[2],[3],[5],[7]]=>[1,1,2,2,1]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[[1,3,4,6],[2],[5],[7]]=>[1,3,2,1]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[[1,2,4,6],[3],[5],[7]]=>[2,2,2,1]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[[1,3,4,6],[2],[5],[7]]=>[1,3,2,1]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[[1,2,3,4,6],[5],[7]]=>[4,2,1]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[[1,5,6],[2],[3],[4],[7]]=>[1,1,1,3,1]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[[1,4,5,6],[2],[3],[7]]=>[1,1,4,1]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[[1,3,5,6],[2],[4],[7]]=>[1,2,3,1]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[[1,4,5,6],[2],[3],[7]]=>[1,1,4,1]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[[1,3,4,5,6],[2],[7]]=>[1,5,1]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[[1,2,5,6],[3],[4],[7]]=>[2,1,3,1]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[[1,3,5,6],[2],[4],[7]]=>[1,2,3,1]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[[1,2,3,5,6],[4],[7]]=>[3,3,1]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[[1,4,5,6],[2],[3],[7]]=>[1,1,4,1]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[[1,3,4,5,6],[2],[7]]=>[1,5,1]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[[1,2,4,5,6],[3],[7]]=>[2,4,1]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[[1,3,4,5,6],[2],[7]]=>[1,5,1]
[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[[1,2,3,4,5,6],[7]]=>[6,1]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[[1,5,7],[2],[3],[4],[6]]=>[1,1,1,2,2]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[[1,4,7],[2],[3],[5],[6]]=>[1,1,2,1,2]
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[[1,5,7],[2],[3],[4],[6]]=>[1,1,1,2,2]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[[1,4,5,7],[2],[3],[6]]=>[1,1,3,2]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[[1,4,6,7],[2],[3],[5]]=>[1,1,2,3]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[[1,3,7],[2],[4],[5],[6]]=>[1,2,1,1,2]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[[1,3,7],[2,6],[4],[5]]=>[1,2,1,3]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[[1,3,7],[2,5],[4],[6]]=>[1,2,2,2]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[[1,3,7],[2,6],[4],[5]]=>[1,2,1,3]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[[1,4,7],[2],[3],[5],[6]]=>[1,1,2,1,2]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[[1,3,4,7],[2],[5],[6]]=>[1,3,1,2]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[[1,3,4,7],[2,6],[5]]=>[1,3,3]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[[1,5,7],[2],[3],[4],[6]]=>[1,1,1,2,2]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[[1,4,5,7],[2],[3],[6]]=>[1,1,3,2]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[[1,3,5,7],[2],[4],[6]]=>[1,2,2,2]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[[1,4,5,7],[2],[3],[6]]=>[1,1,3,2]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[[1,3,4,5,7],[2],[6]]=>[1,4,2]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[[1,4,6,7],[2],[3],[5]]=>[1,1,2,3]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[[1,3,6,7],[2],[4],[5]]=>[1,2,1,3]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[[1,4,6,7],[2],[3],[5]]=>[1,1,2,3]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[[1,3,4,6,7],[2],[5]]=>[1,3,3]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[[1,3,5,6,7],[2],[4]]=>[1,2,4]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[[1,3,4,5,6,7],[2]]=>[1,6]
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[[1,2,7],[3],[4],[5],[6]]=>[2,1,1,1,2]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[[1,2,7],[3,6],[4],[5]]=>[2,1,1,3]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[[1,2,7],[3,5],[4],[6]]=>[2,1,2,2]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[[1,2,7],[3,6],[4],[5]]=>[2,1,1,3]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[[1,2,6,7],[3,5],[4]]=>[2,1,4]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,1,2]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[[1,2,7],[3,5],[4],[6]]=>[2,1,2,2]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[[1,2,7],[3,6],[4],[5]]=>[2,1,1,3]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[[1,2,6,7],[3,5],[4]]=>[2,1,4]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[[1,2,6,7],[3,5],[4]]=>[2,1,4]
[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[[1,2,5,6,7],[3,4]]=>[2,5]
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[[1,3,7],[2],[4],[5],[6]]=>[1,2,1,1,2]
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[[1,3,7],[2,6],[4],[5]]=>[1,2,1,3]
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[[1,3,7],[2,5],[4],[6]]=>[1,2,2,2]
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[[1,3,7],[2,6],[4],[5]]=>[1,2,1,3]
[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[[1,2,3,7],[4],[5],[6]]=>[3,1,1,2]
[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[[1,2,3,7],[4,6],[5]]=>[3,1,3]
[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]
[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[[1,2,3,7],[4,6],[5]]=>[3,1,3]
[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[[1,2,3,7],[4,5,6]]=>[3,4]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[[1,4,7],[2],[3],[5],[6]]=>[1,1,2,1,2]
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[[1,4,7],[2,6],[3],[5]]=>[1,1,2,3]
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[[1,3,4,7],[2],[5],[6]]=>[1,3,1,2]
[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[[1,3,4,7],[2,6],[5]]=>[1,3,3]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[[1,2,4,7],[3],[5],[6]]=>[2,2,1,2]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[[1,3,4,7],[2],[5],[6]]=>[1,3,1,2]
[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[[1,3,4,7],[2,6],[5]]=>[1,3,3]
[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[[1,2,3,4,7],[5],[6]]=>[4,1,2]
[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[[1,2,3,4,7],[5,6]]=>[4,3]
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[[1,5,7],[2],[3],[4],[6]]=>[1,1,1,2,2]
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[[1,4,5,7],[2],[3],[6]]=>[1,1,3,2]
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[[1,3,5,7],[2],[4],[6]]=>[1,2,2,2]
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[[1,4,5,7],[2],[3],[6]]=>[1,1,3,2]
[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[[1,3,4,5,7],[2],[6]]=>[1,4,2]
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[[1,2,5,7],[3],[4],[6]]=>[2,1,2,2]
[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[[1,3,5,7],[2],[4],[6]]=>[1,2,2,2]
[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[[1,2,3,5,7],[4],[6]]=>[3,2,2]
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[[1,4,5,7],[2],[3],[6]]=>[1,1,3,2]
[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[[1,3,4,5,7],[2],[6]]=>[1,4,2]
[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[[1,2,4,5,7],[3],[6]]=>[2,3,2]
[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[[1,3,4,5,7],[2],[6]]=>[1,4,2]
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[[1,2,3,4,5,7],[6]]=>[5,2]
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[[1,4,6,7],[2],[3],[5]]=>[1,1,2,3]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[[1,3,6,7],[2],[4],[5]]=>[1,2,1,3]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[[1,4,6,7],[2],[3],[5]]=>[1,1,2,3]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[[1,3,4,6,7],[2],[5]]=>[1,3,3]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[[1,3,5,6,7],[2],[4]]=>[1,2,4]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[[1,3,4,5,6,7],[2]]=>[1,6]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[[1,2,6,7],[3],[4],[5]]=>[2,1,1,3]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[[1,2,6,7],[3,5],[4]]=>[2,1,4]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[[1,2,6,7],[3,5],[4]]=>[2,1,4]
[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[[1,2,5,6,7],[3,4]]=>[2,5]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[[1,3,6,7],[2],[4],[5]]=>[1,2,1,3]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[[1,2,3,6,7],[4],[5]]=>[3,1,3]
[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[[1,2,3,6,7],[4,5]]=>[3,4]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[[1,4,6,7],[2],[3],[5]]=>[1,1,2,3]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[[1,3,4,6,7],[2],[5]]=>[1,3,3]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[[1,2,4,6,7],[3],[5]]=>[2,2,3]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[[1,3,4,6,7],[2],[5]]=>[1,3,3]
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[[1,2,3,4,6,7],[5]]=>[4,3]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[[1,3,5,6,7],[2],[4]]=>[1,2,4]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[[1,3,4,5,6,7],[2]]=>[1,6]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[[1,2,5,6,7],[3],[4]]=>[2,1,4]
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[[1,2,5,6,7],[3,4]]=>[2,5]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[[1,3,5,6,7],[2],[4]]=>[1,2,4]
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[[1,2,3,5,6,7],[4]]=>[3,4]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[[1,3,4,5,6,7],[2]]=>[1,6]
[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[[1,2,4,5,6,7],[3]]=>[2,5]
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[[1,3,4,5,6,7],[2]]=>[1,6]
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7]]=>[7]
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[8,6,7,5,4,3,2,1]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,1]
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[8,7,5,6,4,3,2,1]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>[1,1,1,1,2,1,1]
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,1]
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[8,5,6,7,4,3,2,1]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[1,1,1,1,3,1]
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>[1,1,1,2,1,1,1]
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[7,8,6,4,5,3,2,1]=>[[1,5],[2,8],[3],[4],[6],[7]]=>[1,1,1,2,1,2]
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[1,1,1,2,2,1]
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[8,7,5,4,6,3,2,1]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>[1,1,1,1,2,1,1]
[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[8,7,4,5,6,3,2,1]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[1,1,1,3,1,1]
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[8,5,6,4,7,3,2,1]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[1,1,1,1,3,1]
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[8,6,4,5,7,3,2,1]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[1,1,1,2,2,1]
[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[8,4,5,6,7,3,2,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>[1,1,1,4,1]
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[7,5,6,4,8,3,2,1]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[7,6,4,5,8,3,2,1]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[1,1,1,2,1,2]
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[6,7,4,5,8,3,2,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[7,5,4,6,8,3,2,1]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[[1,5,6,8],[2],[3],[4],[7]]=>[1,1,1,3,2]
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[6,4,5,7,8,3,2,1]=>[[1,5,7,8],[2],[3],[4],[6]]=>[1,1,1,2,3]
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>[1,1,2,1,1,1,1]
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[1,1,2,1,1,2]
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,3,4,2,1]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[1,1,2,1,1,2]
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[[1,4],[2,6],[3],[5],[7],[8]]=>[1,1,2,2,1,1]
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[8,5,6,7,3,4,2,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>[1,1,2,3,1]
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,3,4,2,1]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[1,1,2,1,1,2]
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[6,7,5,8,3,4,2,1]=>[[1,4,8],[2,7],[3],[5],[6]]=>[1,1,2,1,3]
[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[6,5,7,8,3,4,2,1]=>[[1,4,8],[2,7],[3],[5],[6]]=>[1,1,2,1,3]
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>[1,1,1,2,1,1,1]
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[7,8,6,4,3,5,2,1]=>[[1,5],[2,8],[3],[4],[6],[7]]=>[1,1,1,2,1,2]
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[7,6,8,4,3,5,2,1]=>[[1,5],[2,8],[3],[4],[6],[7]]=>[1,1,1,2,1,2]
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[8,7,6,3,4,5,2,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[1,1,3,1,1,1]
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[7,8,6,3,4,5,2,1]=>[[1,4,5],[2,8],[3],[6],[7]]=>[1,1,3,1,2]
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[8,6,7,3,4,5,2,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>[1,1,3,2,1]
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[7,6,8,3,4,5,2,1]=>[[1,4,5],[2,8],[3],[6],[7]]=>[1,1,3,1,2]
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>[1,1,1,1,2,1,1]
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[7,8,5,4,3,6,2,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]=>[8,7,5,3,4,6,2,1]=>[[1,4,6],[2],[3],[5],[7],[8]]=>[1,1,2,2,1,1]
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[7,8,5,3,4,6,2,1]=>[[1,4,6],[2,8],[3],[5],[7]]=>[1,1,2,2,2]
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[8,7,4,3,5,6,2,1]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[1,1,1,3,1,1]
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[8,7,3,4,5,6,2,1]=>[[1,4,5,6],[2],[3],[7],[8]]=>[1,1,4,1,1]
[.,[.,[[[[.,.],.],.],[[.,.],.]]]]=>[7,8,3,4,5,6,2,1]=>[[1,4,5,6],[2,8],[3],[7]]=>[1,1,4,2]
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[8,6,5,4,3,7,2,1]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,1]
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[8,6,4,3,5,7,2,1]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[1,1,1,2,2,1]
[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]=>[8,5,3,4,6,7,2,1]=>[[1,4,6,7],[2],[3],[5],[8]]=>[1,1,2,3,1]
[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]=>[8,4,3,5,6,7,2,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>[1,1,1,4,1]
[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[8,3,4,5,6,7,2,1]=>[[1,4,5,6,7],[2],[3],[8]]=>[1,1,5,1]
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[6,7,5,4,3,8,2,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[7,5,6,4,3,8,2,1]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
[.,[.,[[.,[.,[[.,[.,.]],.]]],.]]]=>[6,5,7,4,3,8,2,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[5,6,7,4,3,8,2,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[6,7,4,5,3,8,2,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]=>[7,5,4,6,3,8,2,1]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[7,4,5,6,3,8,2,1]=>[[1,5,6,8],[2],[3],[4],[7]]=>[1,1,1,3,2]
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[6,4,5,7,3,8,2,1]=>[[1,5,7,8],[2],[3],[4],[6]]=>[1,1,1,2,3]
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[7,6,5,3,4,8,2,1]=>[[1,4,8],[2],[3],[5],[6],[7]]=>[1,1,2,1,1,2]
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]=>[7,6,4,3,5,8,2,1]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[1,1,1,2,1,2]
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[7,6,3,4,5,8,2,1]=>[[1,4,5,8],[2],[3],[6],[7]]=>[1,1,3,1,2]
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[7,5,4,3,6,8,2,1]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[7,5,3,4,6,8,2,1]=>[[1,4,6,8],[2],[3],[5],[7]]=>[1,1,2,2,2]
[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[7,3,4,5,6,8,2,1]=>[[1,4,5,6,8],[2],[3],[7]]=>[1,1,4,2]
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]=>[6,5,3,4,7,8,2,1]=>[[1,4,7,8],[2],[3],[5],[6]]=>[1,1,2,1,3]
[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[6,3,4,5,7,8,2,1]=>[[1,4,5,7,8],[2],[3],[6]]=>[1,1,3,3]
[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[5,4,3,6,7,8,2,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[5,3,4,6,7,8,2,1]=>[[1,4,6,7,8],[2],[3],[5]]=>[1,1,2,4]
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[[1,3],[2],[4],[5],[6],[7],[8]]=>[1,2,1,1,1,1,1]
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[1,2,1,1,1,2]
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[1,2,1,1,2,1]
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,2,3,1]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[1,2,1,1,1,2]
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>[[1,3],[2,6],[4],[5],[7],[8]]=>[1,2,1,2,1,1]
[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,2,3,1]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[1,2,1,1,2,1]
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,2,3,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[1,2,1,3,1]
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,2,3,1]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[1,2,1,1,1,2]
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,2,3,1]=>[[1,3,8],[2,7],[4],[5],[6]]=>[1,2,1,1,3]
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,2,3,1]=>[[1,3,8],[2,6],[4],[5],[7]]=>[1,2,1,2,2]
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[[1,3,7,8],[2,6],[4],[5]]=>[1,2,1,4]
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[[1,3],[2,5],[4],[6],[7],[8]]=>[1,2,2,1,1,1]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[[1,3],[2,5],[4,7],[6],[8]]=>[1,2,2,2,1]
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>[[1,3],[2,5],[4,8],[6],[7]]=>[1,2,2,1,2]
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[8,7,4,5,6,2,3,1]=>[[1,3,6],[2,5],[4],[7],[8]]=>[1,2,3,1,1]
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,2,3,1]=>[[1,3,6],[2,5],[4,8],[7]]=>[1,2,3,2]
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,2,3,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[1,2,1,3,1]
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,2,3,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[1,2,2,2,1]
[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[8,4,5,6,7,2,3,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[1,2,4,1]
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,2,3,1]=>[[1,3,8],[2,6],[4],[5],[7]]=>[1,2,1,2,2]
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>[[1,3,8],[2,7],[4],[5],[6]]=>[1,2,1,1,3]
[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,2,3,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>[1,1,2,1,1,1,1]
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[1,1,2,1,1,2]
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[1,1,2,1,2,1]
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,2,4,1]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[1,1,2,1,1,2]
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,2,4,1]=>[[1,4,8],[2,7],[3],[5],[6]]=>[1,1,2,1,3]
[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[[1,4],[2,6],[3],[5],[7],[8]]=>[1,1,2,2,1,1]
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[1,1,2,1,2,1]
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,2,4,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>[1,1,2,3,1]
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,2,4,1]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[1,1,2,1,1,2]
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,2,4,1]=>[[1,4,8],[2,7],[3],[5],[6]]=>[1,1,2,1,3]
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[1,3,1,1,1,1]
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,2,3,4,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>[1,3,1,2,1]
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,2,3,4,1]=>[[1,3,4],[2,8],[5],[6],[7]]=>[1,3,1,1,2]
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[[1,3,4],[2,7,8],[5],[6]]=>[1,3,1,3]
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,2,3,4,1]=>[[1,3,4],[2,6],[5],[7],[8]]=>[1,3,2,1,1]
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,2,3,4,1]=>[[1,3,4],[2,6],[5,8],[7]]=>[1,3,2,2]
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,2,3,4,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>[1,3,1,2,1]
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[[1,3,4],[2,6,7],[5],[8]]=>[1,3,3,1]
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,2,3,4,1]=>[[1,3,4],[2,8],[5],[6],[7]]=>[1,3,1,1,2]
[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,2,3,4,1]=>[[1,3,4],[2,7,8],[5],[6]]=>[1,3,1,3]
[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,2,3,4,1]=>[[1,3,4],[2,7,8],[5],[6]]=>[1,3,1,3]
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>[1,1,1,2,1,1,1]
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[8,7,6,3,4,2,5,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[1,1,3,1,1,1]
[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[7,8,6,3,4,2,5,1]=>[[1,4,5],[2,8],[3],[6],[7]]=>[1,1,3,1,2]
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>[1,1,3,2,1]
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>[[1,4,5],[2,8],[3],[6],[7]]=>[1,1,3,1,2]
[.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[6,7,8,3,4,2,5,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[[1,3,5],[2,7,8],[4],[6]]=>[1,2,2,3]
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[8,7,6,3,2,4,5,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[1,1,3,1,1,1]
[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[7,8,6,3,2,4,5,1]=>[[1,4,5],[2,8],[3],[6],[7]]=>[1,1,3,1,2]
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[8,6,7,3,2,4,5,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>[1,1,3,2,1]
[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[6,7,8,3,2,4,5,1]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[8,7,6,2,3,4,5,1]=>[[1,3,4,5],[2],[6],[7],[8]]=>[1,4,1,1,1]
[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[7,8,6,2,3,4,5,1]=>[[1,3,4,5],[2,8],[6],[7]]=>[1,4,1,2]
[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[8,6,7,2,3,4,5,1]=>[[1,3,4,5],[2,7],[6],[8]]=>[1,4,2,1]
[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[7,6,8,2,3,4,5,1]=>[[1,3,4,5],[2,8],[6],[7]]=>[1,4,1,2]
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[6,7,8,2,3,4,5,1]=>[[1,3,4,5],[2,7,8],[6]]=>[1,4,3]
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[8,7,5,3,4,2,6,1]=>[[1,4,6],[2],[3],[5],[7],[8]]=>[1,1,2,2,1,1]
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[7,8,5,3,4,2,6,1]=>[[1,4,6],[2,8],[3],[5],[7]]=>[1,1,2,2,2]
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[8,7,5,3,2,4,6,1]=>[[1,4,6],[2],[3],[5],[7],[8]]=>[1,1,2,2,1,1]
[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[8,7,4,3,2,5,6,1]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[1,1,1,3,1,1]
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[7,8,4,3,2,5,6,1]=>[[1,5,6],[2,8],[3],[4],[7]]=>[1,1,1,3,2]
[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[7,8,3,4,2,5,6,1]=>[[1,4,5,6],[2,8],[3],[7]]=>[1,1,4,2]
[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[7,8,4,2,3,5,6,1]=>[[1,3,5,6],[2,8],[4],[7]]=>[1,2,3,2]
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>[[1,4,5,6],[2,8],[3],[7]]=>[1,1,4,2]
[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[8,7,2,3,4,5,6,1]=>[[1,3,4,5,6],[2],[7],[8]]=>[1,5,1,1]
[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[7,8,2,3,4,5,6,1]=>[[1,3,4,5,6],[2,8],[7]]=>[1,5,2]
[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,1]
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[8,5,6,3,4,2,7,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>[1,1,2,3,1]
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[8,6,4,3,5,2,7,1]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[1,1,1,2,2,1]
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[8,6,3,4,5,2,7,1]=>[[1,4,5,7],[2],[3],[6],[8]]=>[1,1,3,2,1]
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>[1,1,1,4,1]
[.,[[.,[[[.,[.,.]],.],.]],[.,.]]]=>[8,4,3,5,6,2,7,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>[1,1,1,4,1]
[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,2,3,7,1]=>[[1,3,7],[2],[4],[5],[6],[8]]=>[1,2,1,1,2,1]
[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[8,5,6,4,2,3,7,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[1,2,1,3,1]
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[8,6,5,3,2,4,7,1]=>[[1,4,7],[2],[3],[5],[6],[8]]=>[1,1,2,1,2,1]
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[8,6,4,2,3,5,7,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>[1,2,2,2,1]
[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[8,6,2,3,4,5,7,1]=>[[1,3,4,5,7],[2],[6],[8]]=>[1,4,2,1]
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[8,5,4,3,2,6,7,1]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[1,1,1,1,3,1]
[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]=>[8,4,5,3,2,6,7,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>[1,1,1,4,1]
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[8,5,3,4,2,6,7,1]=>[[1,4,6,7],[2],[3],[5],[8]]=>[1,1,2,3,1]
[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[8,3,4,5,2,6,7,1]=>[[1,4,5,6,7],[2],[3],[8]]=>[1,1,5,1]
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[8,5,4,2,3,6,7,1]=>[[1,3,6,7],[2],[4],[5],[8]]=>[1,2,1,3,1]
[.,[[[[.,[.,[.,.]]],.],.],[.,.]]]=>[8,4,3,2,5,6,7,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>[1,1,1,4,1]
[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[8,3,4,2,5,6,7,1]=>[[1,4,5,6,7],[2],[3],[8]]=>[1,1,5,1]
[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[8,4,2,3,5,6,7,1]=>[[1,3,5,6,7],[2],[4],[8]]=>[1,2,4,1]
[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[8,3,2,4,5,6,7,1]=>[[1,4,5,6,7],[2],[3],[8]]=>[1,1,5,1]
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[8,2,3,4,5,6,7,1]=>[[1,3,4,5,6,7],[2],[8]]=>[1,6,1]
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[5,6,7,4,3,2,8,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[7,6,4,5,3,2,8,1]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[1,1,1,2,1,2]
[.,[[.,[.,[[.,.],[[.,.],.]]]],.]]=>[6,7,4,5,3,2,8,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[7,4,5,6,3,2,8,1]=>[[1,5,6,8],[2],[3],[4],[7]]=>[1,1,1,3,2]
[.,[[.,[.,[[.,[.,[.,.]]],.]]],.]]=>[6,5,4,7,3,2,8,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[6,4,5,7,3,2,8,1]=>[[1,5,7,8],[2],[3],[4],[6]]=>[1,1,1,2,3]
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[7,5,6,3,4,2,8,1]=>[[1,4,8],[2,6],[3],[5],[7]]=>[1,1,2,2,2]
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[6,5,7,3,4,2,8,1]=>[[1,4,8],[2,7],[3],[5],[6]]=>[1,1,2,1,3]
[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]=>[7,6,4,3,5,2,8,1]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[1,1,1,2,1,2]
[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]=>[7,6,3,4,5,2,8,1]=>[[1,4,5,8],[2],[3],[6],[7]]=>[1,1,3,1,2]
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[7,5,4,3,6,2,8,1]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[7,4,5,3,6,2,8,1]=>[[1,5,6,8],[2],[3],[4],[7]]=>[1,1,1,3,2]
[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[7,5,3,4,6,2,8,1]=>[[1,4,6,8],[2],[3],[5],[7]]=>[1,1,2,2,2]
[.,[[.,[[[[.,.],.],.],[.,.]]],.]]=>[7,3,4,5,6,2,8,1]=>[[1,4,5,6,8],[2],[3],[7]]=>[1,1,4,2]
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[6,4,5,3,7,2,8,1]=>[[1,5,7,8],[2],[3],[4],[6]]=>[1,1,1,2,3]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[[1,4,7,8],[2],[3],[5],[6]]=>[1,1,2,1,3]
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[5,6,3,4,7,2,8,1]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[6,4,3,5,7,2,8,1]=>[[1,5,7,8],[2],[3],[4],[6]]=>[1,1,1,2,3]
[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[6,3,4,5,7,2,8,1]=>[[1,4,5,7,8],[2],[3],[6]]=>[1,1,3,3]
[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[4,5,3,6,7,2,8,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[.,[[.,[[[[.,[.,.]],.],.],.]],.]]=>[4,3,5,6,7,2,8,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,2,3,8,1]=>[[1,3,8],[2],[4],[5],[6],[7]]=>[1,2,1,1,1,2]
[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]=>[6,7,5,4,2,3,8,1]=>[[1,3,8],[2,7],[4],[5],[6]]=>[1,2,1,1,3]
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[7,5,6,4,2,3,8,1]=>[[1,3,8],[2,6],[4],[5],[7]]=>[1,2,1,2,2]
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,2,3,8,1]=>[[1,3,8],[2,7],[4],[5],[6]]=>[1,2,1,1,3]
[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,2,3,8,1]=>[[1,3,7,8],[2,6],[4],[5]]=>[1,2,1,4]
[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[7,6,4,5,2,3,8,1]=>[[1,3,8],[2,5],[4],[6],[7]]=>[1,2,2,1,2]
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,2,3,8,1]=>[[1,3,6,8],[2,5],[4],[7]]=>[1,2,3,2]
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,2,3,8,1]=>[[1,3,8],[2,7],[4],[5],[6]]=>[1,2,1,1,3]
[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,2,3,8,1]=>[[1,3,7,8],[2,6],[4],[5]]=>[1,2,1,4]
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,2,3,8,1]=>[[1,3,7,8],[2,6],[4],[5]]=>[1,2,1,4]
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[7,6,5,3,2,4,8,1]=>[[1,4,8],[2],[3],[5],[6],[7]]=>[1,1,2,1,1,2]
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[6,7,5,3,2,4,8,1]=>[[1,4,8],[2,7],[3],[5],[6]]=>[1,1,2,1,3]
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[6,5,7,3,2,4,8,1]=>[[1,4,8],[2,7],[3],[5],[6]]=>[1,1,2,1,3]
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[[1,3,4,8],[2],[5],[6],[7]]=>[1,3,1,1,2]
[.,[[[[.,.],.],[[.,.],[.,.]]],.]]=>[7,5,6,2,3,4,8,1]=>[[1,3,4,8],[2,6],[5],[7]]=>[1,3,2,2]
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[5,6,7,2,3,4,8,1]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[6,7,4,3,2,5,8,1]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[[1,3,5,8],[2],[4],[6],[7]]=>[1,2,2,1,2]
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[7,6,3,2,4,5,8,1]=>[[1,4,5,8],[2],[3],[6],[7]]=>[1,1,3,1,2]
[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[6,7,3,2,4,5,8,1]=>[[1,4,5,8],[2,7],[3],[6]]=>[1,1,3,3]
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[7,6,2,3,4,5,8,1]=>[[1,3,4,5,8],[2],[6],[7]]=>[1,4,1,2]
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[6,7,2,3,4,5,8,1]=>[[1,3,4,5,8],[2,7],[6]]=>[1,4,3]
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[7,5,4,3,2,6,8,1]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[7,4,3,5,2,6,8,1]=>[[1,5,6,8],[2],[3],[4],[7]]=>[1,1,1,3,2]
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[7,5,4,2,3,6,8,1]=>[[1,3,6,8],[2],[4],[5],[7]]=>[1,2,1,2,2]
[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[7,4,5,2,3,6,8,1]=>[[1,3,6,8],[2,5],[4],[7]]=>[1,2,3,2]
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[7,5,3,2,4,6,8,1]=>[[1,4,6,8],[2],[3],[5],[7]]=>[1,1,2,2,2]
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[7,5,2,3,4,6,8,1]=>[[1,3,4,6,8],[2],[5],[7]]=>[1,3,2,2]
[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]=>[7,4,3,2,5,6,8,1]=>[[1,5,6,8],[2],[3],[4],[7]]=>[1,1,1,3,2]
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[7,3,2,4,5,6,8,1]=>[[1,4,5,6,8],[2],[3],[7]]=>[1,1,4,2]
[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[7,2,3,4,5,6,8,1]=>[[1,3,4,5,6,8],[2],[7]]=>[1,5,2]
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[4,5,6,3,2,7,8,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]=>[6,5,3,4,2,7,8,1]=>[[1,4,7,8],[2],[3],[5],[6]]=>[1,1,2,1,3]
[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[6,3,4,5,2,7,8,1]=>[[1,4,5,7,8],[2],[3],[6]]=>[1,1,3,3]
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[4,3,5,6,2,7,8,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[6,5,4,2,3,7,8,1]=>[[1,3,7,8],[2],[4],[5],[6]]=>[1,2,1,1,3]
[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[6,4,5,2,3,7,8,1]=>[[1,3,7,8],[2,5],[4],[6]]=>[1,2,2,3]
[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[4,5,6,2,3,7,8,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]=>[6,5,3,2,4,7,8,1]=>[[1,4,7,8],[2],[3],[5],[6]]=>[1,1,2,1,3]
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[6,5,2,3,4,7,8,1]=>[[1,3,4,7,8],[2],[5],[6]]=>[1,3,1,3]
[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[6,2,3,4,5,7,8,1]=>[[1,3,4,5,7,8],[2],[6]]=>[1,4,3]
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[4,5,3,2,6,7,8,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[5,3,4,2,6,7,8,1]=>[[1,4,6,7,8],[2],[3],[5]]=>[1,1,2,4]
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[5,4,2,3,6,7,8,1]=>[[1,3,6,7,8],[2],[4],[5]]=>[1,2,1,4]
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[4,5,2,3,6,7,8,1]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[5,3,2,4,6,7,8,1]=>[[1,4,6,7,8],[2],[3],[5]]=>[1,1,2,4]
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>[[1,3,4,6,7,8],[2],[5]]=>[1,3,4]
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[4,2,3,5,6,7,8,1]=>[[1,3,5,6,7,8],[2],[4]]=>[1,2,5]
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[[1,3,4,5,6,7,8],[2]]=>[1,7]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[2,1,1,1,1,1,1]
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,1,1,1,1,2]
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[2,1,1,1,2,1]
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,3,1,2]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,1,1,1,1,2]
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[6,7,8,5,4,3,1,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,1,1,1,3]
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,1,1,2,1,1]
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[[1,2],[3,6],[4,8],[5],[7]]=>[2,1,1,2,2]
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[2,1,1,1,2,1]
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,3,1,2]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,1,1,1,1,2]
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,3,1,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,1,1,1,3]
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,3,1,2]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,1,1,2,2]
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,3,1,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,1,1,1,3]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,1,1,4]
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[[1,2],[3,5],[4],[6],[7],[8]]=>[2,1,2,1,1,1]
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[[1,2],[3,5],[4,8],[6],[7]]=>[2,1,2,1,2]
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,3,1,2]=>[[1,2],[3,5],[4,7],[6],[8]]=>[2,1,2,2,1]
[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,3,1,2]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,1,2,3]
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,1,1,2,1,1]
[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,3,1,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,1,1,3,1]
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,3,1,2]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,1,2,2,1]
[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>[8,5,4,6,7,3,1,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,1,1,3,1]
[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,3,1,2]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,1,1,1,1,2]
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,3,1,2]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,1,1,2,2]
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,3,1,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,1,1,1,3]
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,3,1,2]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,1,2,1,2]
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,3,1,2]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,1,2,3]
[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[6,5,4,7,8,3,1,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,1,1,1,3]
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,3,1,2]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,1,1,4]
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,3,1,2]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,1,1,4]
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[[1,2,6,7,8],[3,5],[4]]=>[2,1,5]
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[2,2,1,1,1,1]
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[[1,2],[3,4],[5,8],[6],[7]]=>[2,2,1,1,2]
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,4,1,2]=>[[1,2],[3,4],[5,8],[6],[7]]=>[2,2,1,1,2]
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,4,1,2]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,1,3]
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[[1,2],[3,4],[5,6],[7],[8]]=>[2,2,2,1,1]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,4,1,2]=>[[1,2],[3,4],[5,7],[6],[8]]=>[2,2,1,2,1]
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,4,1,2]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[[1,2],[3,4],[5,8],[6],[7]]=>[2,2,1,1,2]
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,1,3]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,1,3]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,3,5,1,2]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,1,2,3]
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,1,1,1]
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[[1,2],[3,6],[4,8],[5],[7]]=>[2,1,1,2,2]
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[8,7,4,5,3,6,1,2]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,1,3,1,1]
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,1,3,2]
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[8,7,4,3,5,6,1,2]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,1,3,1,1]
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,1,3,2]
[[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>[8,7,3,4,5,6,1,2]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,1,1]
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[8,5,4,3,6,7,1,2]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,1,1,3,1]
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[8,5,3,4,6,7,1,2]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,1,4,1]
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,1,1,1,1,2]
[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>[7,5,6,4,3,8,1,2]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,1,1,2,2]
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,3,8,1,2]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,1,1,4]
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>[[1,2,8],[3,5],[4,7],[6]]=>[2,1,2,3]
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,3,8,1,2]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,1,1,4]
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[4,5,6,7,3,8,1,2]=>[[1,2,6,7,8],[3,5],[4]]=>[2,1,5]
[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>[7,6,5,3,4,8,1,2]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,1,1,2]
[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[7,6,4,3,5,8,1,2]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,1,2,1,2]
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[7,6,3,4,5,8,1,2]=>[[1,2,5,8],[3,4],[6],[7]]=>[2,3,1,2]
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[7,5,4,3,6,8,1,2]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,1,1,2,2]
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[7,3,4,5,6,8,1,2]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[6,5,4,3,7,8,1,2]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,1,1,1,3]
[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[5,6,4,3,7,8,1,2]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,1,1,4]
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[5,4,6,3,7,8,1,2]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,1,1,4]
[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[4,5,6,3,7,8,1,2]=>[[1,2,6,7,8],[3,5],[4]]=>[2,1,5]
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[[1,2,7,8],[3,5],[4],[6]]=>[2,1,2,3]
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,1,1,4]
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[[1,2,6,7,8],[3,5],[4]]=>[2,1,5]
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[5,3,4,6,7,8,1,2]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[[1,2,6,7,8],[3,5],[4]]=>[2,1,5]
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[[1,3],[2],[4],[5],[6],[7],[8]]=>[1,2,1,1,1,1,1]
[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,2,1,3]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[1,2,1,1,1,2]
[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[1,2,1,1,2,1]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[1,2,1,1,1,2]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,2,1,3]=>[[1,3,8],[2,7],[4],[5],[6]]=>[1,2,1,1,3]
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[8,7,5,6,4,2,1,3]=>[[1,3],[2,6],[4],[5],[7],[8]]=>[1,2,1,2,1,1]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[[1,3],[2,6],[4,8],[5],[7]]=>[1,2,1,2,2]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[1,2,1,1,1,2]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,2,1,3]=>[[1,3,8],[2,7],[4],[5],[6]]=>[1,2,1,1,3]
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>[[1,3,8],[2,6],[4],[5],[7]]=>[1,2,1,2,2]
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,2,1,3]=>[[1,3,8],[2,7],[4],[5],[6]]=>[1,2,1,1,3]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[[1,3,7,8],[2,6],[4],[5]]=>[1,2,1,4]
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,2,1,3]=>[[1,3],[2,5],[4],[6],[7],[8]]=>[1,2,2,1,1,1]
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[7,6,8,4,5,2,1,3]=>[[1,3],[2,5],[4,8],[6],[7]]=>[1,2,2,1,2]
[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,2,1,3]=>[[1,3,6,7],[2,5],[4],[8]]=>[1,2,4,1]
[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,2,1,3]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[1,2,1,1,1,2]
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,2,1,3]=>[[1,3,8],[2,7],[4],[5],[6]]=>[1,2,1,1,3]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,2,1,3]=>[[1,3,8],[2,7],[4],[5],[6]]=>[1,2,1,1,3]
[[.,[.,.]],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,2,1,3]=>[[1,3,7,8],[2,6],[4],[5]]=>[1,2,1,4]
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,2,1,3]=>[[1,3,8],[2,5],[4],[6],[7]]=>[1,2,2,1,2]
[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,2,1,3]=>[[1,3,6,8],[2,5],[4],[7]]=>[1,2,3,2]
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,2,1,3]=>[[1,3,7,8],[2,6],[4],[5]]=>[1,2,1,4]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,1,1,1,1,1]
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,1,2,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,1,1,1,2]
[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,1,2,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,1,1,1,2]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,1,1,3]
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,1,2,3]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,1,2,2]
[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,1,2,3]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,1,1,2,1]
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,1,3,1]
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,1,2,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,1,1,1,2]
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,1,2,3]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,1,1,3]
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,1,2,2]
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,1,2,3]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,1,1,3]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[[1,2,3,8],[4,6,7],[5]]=>[3,1,4]
[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[6,7,8,4,5,1,2,3]=>[[1,2,3],[4,5,8],[6,7]]=>[3,2,3]
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,1,2,1,1]
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,1,2,3]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,1,2,2]
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,1,1]
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,1,3,1]
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,1,2,3]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]
[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,1,2,3]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,1,1,1,2]
[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,1,2,3]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,1,1,3]
[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,1,2,3]=>[[1,2,3,8],[4,6,7],[5]]=>[3,1,4]
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[[1,2,3],[4,5,8],[6,7]]=>[3,2,3]
[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,1,2,3]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,1,2,2]
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,1,1,3]
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,1,2,3]=>[[1,2,3,8],[4,6,7],[5]]=>[3,1,4]
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,1,2,3]=>[[1,2,3,8],[4,6,7],[5]]=>[3,1,4]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>[1,1,2,1,1,1,1]
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[1,1,2,1,1,2]
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[1,1,2,1,2,1]
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[1,1,2,1,1,2]
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[[1,4,8],[2,7],[3],[5],[6]]=>[1,1,2,1,3]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[[1,4],[2,6],[3],[5],[7],[8]]=>[1,1,2,2,1,1]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[1,1,2,1,2,1]
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[[1,4,7],[2,6],[3],[5],[8]]=>[1,1,2,3,1]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[1,1,2,1,1,2]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[[1,4,8],[2,7],[3],[5],[6]]=>[1,1,2,1,3]
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,2,1,4]=>[[1,4,8],[2,6],[3],[5],[7]]=>[1,1,2,2,2]
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,2,1,4]=>[[1,4,8],[2,7],[3],[5],[6]]=>[1,1,2,1,3]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[1,3,1,1,1,1]
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,3,1,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>[1,3,1,1,2]
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[[1,3,4],[2,7],[5],[6],[8]]=>[1,3,1,2,1]
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,3,1,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>[1,3,1,1,2]
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,3,1,4]=>[[1,3,4],[2,7,8],[5],[6]]=>[1,3,1,3]
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,3,1,4]=>[[1,3,4],[2,6],[5],[7],[8]]=>[1,3,2,1,1]
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[[1,3,4],[2,6],[5,8],[7]]=>[1,3,2,2]
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,3,1,4]=>[[1,3,4],[2,7],[5],[6],[8]]=>[1,3,1,2,1]
[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,3,1,4]=>[[1,3,4],[2,6,7],[5],[8]]=>[1,3,3,1]
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,3,1,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>[1,3,1,1,2]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[[1,3,4],[2,7,8],[5],[6]]=>[1,3,1,3]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[[1,3,4],[2,6,8],[5],[7]]=>[1,3,2,2]
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,3,1,4]=>[[1,3,4],[2,7,8],[5],[6]]=>[1,3,1,3]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,1,1,1,1]
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,1,1,2]
[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,1,2,1]
[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,1,2,4]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,1,1,2]
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,1,1]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,1,1,2]
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,1,3]
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,1,3]
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[1,3,1,1,1,1]
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>[1,3,1,1,2]
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,1,3,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>[1,3,1,1,2]
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[[1,3,4],[2,7,8],[5],[6]]=>[1,3,1,3]
[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>[[1,3,4],[2,6],[5],[7],[8]]=>[1,3,2,1,1]
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[[1,3,4],[2,6],[5,8],[7]]=>[1,3,2,2]
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,1,3,4]=>[[1,3,4],[2,7],[5],[6],[8]]=>[1,3,1,2,1]
[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,1,3,4]=>[[1,3,4],[2,6,7],[5],[8]]=>[1,3,3,1]
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,1,3,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>[1,3,1,1,2]
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[[1,3,4],[2,7,8],[5],[6]]=>[1,3,1,3]
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[[1,3,4],[2,6,8],[5],[7]]=>[1,3,2,2]
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[[1,3,4],[2,7,8],[5],[6]]=>[1,3,1,3]
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,1,1,1,1]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,1,1,2]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,1,2,1]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,1,1,2]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[[1,2,3,4],[5,7,8],[6]]=>[4,1,3]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,1,1]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,1,2,1]
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,1,1,2]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[[1,2,3,4],[5,7,8],[6]]=>[4,1,3]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[[1,2,3,4],[5,7,8],[6]]=>[4,1,3]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>[1,1,1,2,1,1,1]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[[1,5],[2,8],[3],[4],[6],[7]]=>[1,1,1,2,1,2]
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[8,6,7,4,3,2,1,5]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[1,1,1,2,2,1]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[[1,5],[2,8],[3],[4],[6],[7]]=>[1,1,1,2,1,2]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[1,1,3,1,1,1]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[7,8,6,3,4,2,1,5]=>[[1,4,5],[2,8],[3],[6],[7]]=>[1,1,3,1,2]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[1,2,2,1,1,1]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[[1,3,5],[2,7,8],[4],[6]]=>[1,2,2,3]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[1,1,3,1,1,1]
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[8,6,7,3,2,4,1,5]=>[[1,4,5],[2,7],[3],[6],[8]]=>[1,1,3,2,1]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[[1,3,4,5],[2],[6],[7],[8]]=>[1,4,1,1,1]
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[8,6,7,2,3,4,1,5]=>[[1,3,4,5],[2,7],[6],[8]]=>[1,4,2,1]
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[7,6,8,2,3,4,1,5]=>[[1,3,4,5],[2,8],[6],[7]]=>[1,4,1,2]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[6,7,8,2,3,4,1,5]=>[[1,3,4,5],[2,7,8],[6]]=>[1,4,3]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[2,1,2,1,1,1]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,1,2,3]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,1,1,1]
[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[7,8,6,3,4,1,2,5]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,1,2]
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[8,6,7,3,4,1,2,5]=>[[1,2,5],[3,4],[6,7],[8]]=>[2,3,2,1]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[[1,2,5],[3,4,8],[6,7]]=>[2,3,3]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[1,2,2,1,1,1]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[[1,3,5],[2,8],[4],[6],[7]]=>[1,2,2,1,2]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[[1,3,5],[2,7],[4],[6],[8]]=>[1,2,2,2,1]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[[1,3,5],[2,7,8],[4],[6]]=>[1,2,2,3]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,1,1,1]
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,1,2]
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,1,2,3,5]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,1,2]
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[1,1,3,1,1,1]
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[7,8,6,3,2,1,4,5]=>[[1,4,5],[2,8],[3],[6],[7]]=>[1,1,3,1,2]
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[8,6,7,3,2,1,4,5]=>[[1,4,5],[2,7],[3],[6],[8]]=>[1,1,3,2,1]
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[7,6,8,3,2,1,4,5]=>[[1,4,5],[2,8],[3],[6],[7]]=>[1,1,3,1,2]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[[1,4,5],[2,7,8],[3],[6]]=>[1,1,3,3]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[[1,3,4,5],[2],[6],[7],[8]]=>[1,4,1,1,1]
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[7,8,6,2,3,1,4,5]=>[[1,3,4,5],[2,8],[6],[7]]=>[1,4,1,2]
[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[8,6,7,2,3,1,4,5]=>[[1,3,4,5],[2,7],[6],[8]]=>[1,4,2,1]
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[7,6,8,2,3,1,4,5]=>[[1,3,4,5],[2,8],[6],[7]]=>[1,4,1,2]
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[[1,3,4,5],[2,7,8],[6]]=>[1,4,3]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,1,1,1]
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[7,8,6,3,1,2,4,5]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,1,2]
[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[8,6,7,3,1,2,4,5]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[7,6,8,3,1,2,4,5]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,1,2]
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[[1,3,4,5],[2],[6],[7],[8]]=>[1,4,1,1,1]
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[7,8,6,2,1,3,4,5]=>[[1,3,4,5],[2,8],[6],[7]]=>[1,4,1,2]
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>[[1,3,4,5],[2,7],[6],[8]]=>[1,4,2,1]
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[[1,3,4,5],[2,7,8],[6]]=>[1,4,3]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,1,1,1]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[[1,2,3,4,5],[6,8],[7]]=>[5,1,2]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[[1,2,3,4,5],[6,8],[7]]=>[5,1,2]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>[1,1,1,1,2,1,1]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[8,7,4,5,3,2,1,6]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[1,1,1,3,1,1]
[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[7,8,4,5,3,2,1,6]=>[[1,5,6],[2,8],[3],[4],[7]]=>[1,1,1,3,2]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[[1,4,6],[2],[3],[5],[7],[8]]=>[1,1,2,2,1,1]
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[8,7,3,4,5,2,1,6]=>[[1,4,5,6],[2],[3],[7],[8]]=>[1,1,4,1,1]
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[7,8,3,4,5,2,1,6]=>[[1,4,5,6],[2,8],[3],[7]]=>[1,1,4,2]
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[8,7,4,5,2,3,1,6]=>[[1,3,6],[2,5],[4],[7],[8]]=>[1,2,3,1,1]
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,2,3,1,6]=>[[1,3,6],[2,5],[4,8],[7]]=>[1,2,3,2]
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[8,7,5,3,2,4,1,6]=>[[1,4,6],[2],[3],[5],[7],[8]]=>[1,1,2,2,1,1]
[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[7,8,5,2,3,4,1,6]=>[[1,3,4,6],[2,8],[5],[7]]=>[1,3,2,2]
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[8,7,4,3,2,5,1,6]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[1,1,1,3,1,1]
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[7,8,4,3,2,5,1,6]=>[[1,5,6],[2,8],[3],[4],[7]]=>[1,1,1,3,2]
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[8,7,3,4,2,5,1,6]=>[[1,4,5,6],[2],[3],[7],[8]]=>[1,1,4,1,1]
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>[[1,4,5,6],[2,8],[3],[7]]=>[1,1,4,2]
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[8,7,2,3,4,5,1,6]=>[[1,3,4,5,6],[2],[7],[8]]=>[1,5,1,1]
[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[7,8,2,3,4,5,1,6]=>[[1,3,4,5,6],[2,8],[7]]=>[1,5,2]
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[[1,2,6],[3],[4],[5],[7],[8]]=>[2,1,1,2,1,1]
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[7,8,5,4,3,1,2,6]=>[[1,2,6],[3,8],[4],[5],[7]]=>[2,1,1,2,2]
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,1,1]
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[8,7,3,4,5,1,2,6]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,1,1]
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[7,8,3,4,5,1,2,6]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[[1,3,6],[2,8],[4],[5],[7]]=>[1,2,1,2,2]
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[[1,2,3,6],[4],[5],[7],[8]]=>[3,1,2,1,1]
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,1,2,2]
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[[1,2,3,6],[4,5],[7,8]]=>[3,3,2]
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[[1,4,6],[2],[3],[5],[7],[8]]=>[1,1,2,2,1,1]
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[7,8,5,3,2,1,4,6]=>[[1,4,6],[2,8],[3],[5],[7]]=>[1,1,2,2,2]
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[[1,2,4,6],[3],[5],[7],[8]]=>[2,2,2,1,1]
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[[1,3,4,6],[2],[5],[7],[8]]=>[1,3,2,1,1]
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[[1,3,4,6],[2,8],[5],[7]]=>[1,3,2,2]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[[1,2,3,4,6],[5],[7],[8]]=>[4,2,1,1]
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[1,1,1,3,1,1]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[[1,5,6],[2,8],[3],[4],[7]]=>[1,1,1,3,2]
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[8,7,3,4,2,1,5,6]=>[[1,4,5,6],[2],[3],[7],[8]]=>[1,1,4,1,1]
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[7,8,3,4,2,1,5,6]=>[[1,4,5,6],[2,8],[3],[7]]=>[1,1,4,2]
[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[7,8,4,2,3,1,5,6]=>[[1,3,5,6],[2,8],[4],[7]]=>[1,2,3,2]
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[8,7,3,2,4,1,5,6]=>[[1,4,5,6],[2],[3],[7],[8]]=>[1,1,4,1,1]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[[1,4,5,6],[2,8],[3],[7]]=>[1,1,4,2]
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[8,7,2,3,4,1,5,6]=>[[1,3,4,5,6],[2],[7],[8]]=>[1,5,1,1]
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>[[1,3,4,5,6],[2,8],[7]]=>[1,5,2]
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,1,3,2]
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[8,7,3,4,1,2,5,6]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,1,1]
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]
[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[8,7,4,2,1,3,5,6]=>[[1,3,5,6],[2],[4],[7],[8]]=>[1,2,3,1,1]
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[[1,3,5,6],[2,8],[4],[7]]=>[1,2,3,2]
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,1,1]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[[1,4,5,6],[2],[3],[7],[8]]=>[1,1,4,1,1]
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[[1,4,5,6],[2,8],[3],[7]]=>[1,1,4,2]
[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[8,7,2,3,1,4,5,6]=>[[1,3,4,5,6],[2],[7],[8]]=>[1,5,1,1]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[7,8,2,3,1,4,5,6]=>[[1,3,4,5,6],[2,8],[7]]=>[1,5,2]
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[7,8,3,1,2,4,5,6]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[[1,3,4,5,6],[2],[7],[8]]=>[1,5,1,1]
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[[1,3,4,5,6],[2,8],[7]]=>[1,5,2]
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[[1,2,3,4,5,6],[7],[8]]=>[6,1,1]
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,1]
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[8,5,6,4,3,2,1,7]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[1,1,1,1,3,1]
[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[8,6,4,5,3,2,1,7]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[1,1,1,2,2,1]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[[1,5,6,7],[2],[3],[4],[8]]=>[1,1,1,4,1]
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[8,6,5,3,4,2,1,7]=>[[1,4,7],[2],[3],[5],[6],[8]]=>[1,1,2,1,2,1]
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[8,5,6,3,4,2,1,7]=>[[1,4,7],[2,6],[3],[5],[8]]=>[1,1,2,3,1]
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[8,4,5,3,6,2,1,7]=>[[1,5,6,7],[2],[3],[4],[8]]=>[1,1,1,4,1]
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[8,4,3,5,6,2,1,7]=>[[1,5,6,7],[2],[3],[4],[8]]=>[1,1,1,4,1]
[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[8,3,4,5,6,2,1,7]=>[[1,4,5,6,7],[2],[3],[8]]=>[1,1,5,1]
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,2,3,1,7]=>[[1,3,7],[2],[4],[5],[6],[8]]=>[1,2,1,1,2,1]
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[8,5,6,4,2,3,1,7]=>[[1,3,7],[2,6],[4],[5],[8]]=>[1,2,1,3,1]
[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[8,4,5,6,2,3,1,7]=>[[1,3,6,7],[2,5],[4],[8]]=>[1,2,4,1]
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[8,6,5,3,2,4,1,7]=>[[1,4,7],[2],[3],[5],[6],[8]]=>[1,1,2,1,2,1]
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[8,6,5,2,3,4,1,7]=>[[1,3,4,7],[2],[5],[6],[8]]=>[1,3,1,2,1]
[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[8,5,6,2,3,4,1,7]=>[[1,3,4,7],[2,6],[5],[8]]=>[1,3,3,1]
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[8,6,4,2,3,5,1,7]=>[[1,3,5,7],[2],[4],[6],[8]]=>[1,2,2,2,1]
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[8,6,3,2,4,5,1,7]=>[[1,4,5,7],[2],[3],[6],[8]]=>[1,1,3,2,1]
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[8,5,4,3,2,6,1,7]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[1,1,1,1,3,1]
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[8,4,3,5,2,6,1,7]=>[[1,5,6,7],[2],[3],[4],[8]]=>[1,1,1,4,1]
[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]=>[8,5,4,2,3,6,1,7]=>[[1,3,6,7],[2],[4],[5],[8]]=>[1,2,1,3,1]
[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[8,4,5,2,3,6,1,7]=>[[1,3,6,7],[2,5],[4],[8]]=>[1,2,4,1]
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[8,5,3,2,4,6,1,7]=>[[1,4,6,7],[2],[3],[5],[8]]=>[1,1,2,3,1]
[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[8,5,2,3,4,6,1,7]=>[[1,3,4,6,7],[2],[5],[8]]=>[1,3,3,1]
[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[8,3,2,4,5,6,1,7]=>[[1,4,5,6,7],[2],[3],[8]]=>[1,1,5,1]
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[8,2,3,4,5,6,1,7]=>[[1,3,4,5,6,7],[2],[8]]=>[1,6,1]
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[[1,2,7],[3],[4],[5],[6],[8]]=>[2,1,1,1,2,1]
[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,3,1,2,7]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,1,2,2,1]
[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[8,6,5,3,4,1,2,7]=>[[1,2,7],[3,4],[5],[6],[8]]=>[2,2,1,2,1]
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]
[[[.,.],[[.,[.,[.,.]]],.]],[.,.]]=>[8,5,4,3,6,1,2,7]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,1,1,3,1]
[[[.,.],[[[.,.],[.,.]],.]],[.,.]]=>[8,5,3,4,6,1,2,7]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]
[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[8,4,3,5,6,1,2,7]=>[[1,2,6,7],[3,5],[4],[8]]=>[2,1,4,1]
[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[8,3,4,5,6,1,2,7]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[[1,3,7],[2],[4],[5],[6],[8]]=>[1,2,1,1,2,1]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,2,1,3,7]=>[[1,3,7],[2,6],[4],[5],[8]]=>[1,2,1,3,1]
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[8,4,5,6,2,1,3,7]=>[[1,3,6,7],[2,5],[4],[8]]=>[1,2,4,1]
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[[1,2,3,7],[4],[5],[6],[8]]=>[3,1,1,2,1]
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,1,3,1]
[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]
[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[8,4,5,6,1,2,3,7]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[[1,4,7],[2],[3],[5],[6],[8]]=>[1,1,2,1,2,1]
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[8,5,6,3,2,1,4,7]=>[[1,4,7],[2,6],[3],[5],[8]]=>[1,1,2,3,1]
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[[1,3,4,7],[2],[5],[6],[8]]=>[1,3,1,2,1]
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[[1,3,4,7],[2,6],[5],[8]]=>[1,3,3,1]
[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[8,5,6,3,1,2,4,7]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[[1,3,4,7],[2],[5],[6],[8]]=>[1,3,1,2,1]
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[[1,3,4,7],[2,6],[5],[8]]=>[1,3,3,1]
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[[1,2,3,4,7],[5],[6],[8]]=>[4,1,2,1]
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[[1,2,3,4,7],[5,6],[8]]=>[4,3,1]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[1,1,1,2,2,1]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[[1,4,5,7],[2],[3],[6],[8]]=>[1,1,3,2,1]
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[8,6,4,2,3,1,5,7]=>[[1,3,5,7],[2],[4],[6],[8]]=>[1,2,2,2,1]
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[8,6,3,2,4,1,5,7]=>[[1,4,5,7],[2],[3],[6],[8]]=>[1,1,3,2,1]
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[8,6,2,3,4,1,5,7]=>[[1,3,4,5,7],[2],[6],[8]]=>[1,4,2,1]
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[8,6,4,3,1,2,5,7]=>[[1,2,5,7],[3],[4],[6],[8]]=>[2,1,2,2,1]
[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[8,6,3,4,1,2,5,7]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[[1,3,5,7],[2],[4],[6],[8]]=>[1,2,2,2,1]
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[[1,2,3,5,7],[4],[6],[8]]=>[3,2,2,1]
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[8,6,3,2,1,4,5,7]=>[[1,4,5,7],[2],[3],[6],[8]]=>[1,1,3,2,1]
[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[[1,2,3,4,5,7],[6],[8]]=>[5,2,1]
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[8,5,4,3,2,1,6,7]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[1,1,1,1,3,1]
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[8,4,5,3,2,1,6,7]=>[[1,5,6,7],[2],[3],[4],[8]]=>[1,1,1,4,1]
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[8,4,3,5,2,1,6,7]=>[[1,5,6,7],[2],[3],[4],[8]]=>[1,1,1,4,1]
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[8,3,4,5,2,1,6,7]=>[[1,4,5,6,7],[2],[3],[8]]=>[1,1,5,1]
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[8,4,5,2,3,1,6,7]=>[[1,3,6,7],[2,5],[4],[8]]=>[1,2,4,1]
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[8,5,2,3,4,1,6,7]=>[[1,3,4,6,7],[2],[5],[8]]=>[1,3,3,1]
[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[8,4,2,3,5,1,6,7]=>[[1,3,5,6,7],[2],[4],[8]]=>[1,2,4,1]
[[[.,[[[[.,.],.],.],.]],.],[.,.]]=>[8,2,3,4,5,1,6,7]=>[[1,3,4,5,6,7],[2],[8]]=>[1,6,1]
[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[8,5,3,4,1,2,6,7]=>[[1,2,6,7],[3,4],[5],[8]]=>[2,2,3,1]
[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[8,3,4,5,1,2,6,7]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[8,5,4,2,1,3,6,7]=>[[1,3,6,7],[2],[4],[5],[8]]=>[1,2,1,3,1]
[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[8,5,4,1,2,3,6,7]=>[[1,2,3,6,7],[4],[5],[8]]=>[3,1,3,1]
[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[8,4,5,1,2,3,6,7]=>[[1,2,3,6,7],[4,5],[8]]=>[3,4,1]
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[8,5,3,2,1,4,6,7]=>[[1,4,6,7],[2],[3],[5],[8]]=>[1,1,2,3,1]
[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[[1,2,4,6,7],[3],[5],[8]]=>[2,2,3,1]
[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[[1,2,3,4,6,7],[5],[8]]=>[4,3,1]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[[1,5,6,7],[2],[3],[4],[8]]=>[1,1,1,4,1]
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[8,3,4,2,1,5,6,7]=>[[1,4,5,6,7],[2],[3],[8]]=>[1,1,5,1]
[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[8,4,2,3,1,5,6,7]=>[[1,3,5,6,7],[2],[4],[8]]=>[1,2,4,1]
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>[[1,3,4,5,6,7],[2],[8]]=>[1,6,1]
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[8,3,4,1,2,5,6,7]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[8,4,2,1,3,5,6,7]=>[[1,3,5,6,7],[2],[4],[8]]=>[1,2,4,1]
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[[1,2,3,5,6,7],[4],[8]]=>[3,4,1]
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[[1,4,5,6,7],[2],[3],[8]]=>[1,1,5,1]
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>[[1,3,4,5,6,7],[2],[8]]=>[1,6,1]
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[[1,2,4,5,6,7],[3],[8]]=>[2,5,1]
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>[[1,3,4,5,6,7],[2],[8]]=>[1,6,1]
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8]]=>[7,1]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[7,5,6,4,3,2,1,8]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[1,1,1,2,1,2]
[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[6,7,4,5,3,2,1,8]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[7,5,4,6,3,2,1,8]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[7,4,5,6,3,2,1,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>[1,1,1,3,2]
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[5,4,6,7,3,2,1,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[7,6,5,3,4,2,1,8]=>[[1,4,8],[2],[3],[5],[6],[7]]=>[1,1,2,1,1,2]
[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>[6,7,5,3,4,2,1,8]=>[[1,4,8],[2,7],[3],[5],[6]]=>[1,1,2,1,3]
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[[1,4,8],[2,6],[3],[5],[7]]=>[1,1,2,2,2]
[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]=>[6,5,7,3,4,2,1,8]=>[[1,4,8],[2,7],[3],[5],[6]]=>[1,1,2,1,3]
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[5,6,7,3,4,2,1,8]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[1,1,1,2,1,2]
[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]=>[6,7,4,3,5,2,1,8]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>[[1,4,5,8],[2],[3],[6],[7]]=>[1,1,3,1,2]
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[7,5,4,3,6,2,1,8]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[5,6,4,3,7,2,1,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[3,4,5,6,7,2,1,8]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,2,3,1,8]=>[[1,3,8],[2],[4],[5],[6],[7]]=>[1,2,1,1,1,2]
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>[[1,3,8],[2,7],[4],[5],[6]]=>[1,2,1,1,3]
[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,2,3,1,8]=>[[1,3,8],[2,6],[4],[5],[7]]=>[1,2,1,2,2]
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>[[1,3,7,8],[2,6],[4],[5]]=>[1,2,1,4]
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[[1,3,8],[2,5],[4],[6],[7]]=>[1,2,2,1,2]
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[[1,3,8],[2,5],[4,7],[6]]=>[1,2,2,3]
[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]=>[7,5,4,6,2,3,1,8]=>[[1,3,8],[2,6],[4],[5],[7]]=>[1,2,1,2,2]
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[6,5,4,7,2,3,1,8]=>[[1,3,8],[2,7],[4],[5],[6]]=>[1,2,1,1,3]
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[[1,3,7,8],[2,6],[4],[5]]=>[1,2,1,4]
[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,2,3,1,8]=>[[1,3,7,8],[2,6],[4],[5]]=>[1,2,1,4]
[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[4,5,6,7,2,3,1,8]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[7,6,5,3,2,4,1,8]=>[[1,4,8],[2],[3],[5],[6],[7]]=>[1,1,2,1,1,2]
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>[[1,4,8],[2,7],[3],[5],[6]]=>[1,1,2,1,3]
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[[1,3,4,8],[2],[5],[6],[7]]=>[1,3,1,1,2]
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[[1,3,4,8],[2,7],[5],[6]]=>[1,3,1,3]
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[[1,3,4,8],[2,6],[5],[7]]=>[1,3,2,2]
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[[1,3,4,8],[2,7],[5],[6]]=>[1,3,1,3]
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[6,7,4,3,2,5,1,8]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[6,7,3,4,2,5,1,8]=>[[1,4,5,8],[2,7],[3],[6]]=>[1,1,3,3]
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[7,6,4,2,3,5,1,8]=>[[1,3,5,8],[2],[4],[6],[7]]=>[1,2,2,1,2]
[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[6,7,4,2,3,5,1,8]=>[[1,3,5,8],[2,7],[4],[6]]=>[1,2,2,3]
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[7,6,3,2,4,5,1,8]=>[[1,4,5,8],[2],[3],[6],[7]]=>[1,1,3,1,2]
[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[6,7,3,2,4,5,1,8]=>[[1,4,5,8],[2,7],[3],[6]]=>[1,1,3,3]
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[7,6,2,3,4,5,1,8]=>[[1,3,4,5,8],[2],[6],[7]]=>[1,4,1,2]
[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[6,7,2,3,4,5,1,8]=>[[1,3,4,5,8],[2,7],[6]]=>[1,4,3]
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[7,5,4,3,2,6,1,8]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[7,4,5,3,2,6,1,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>[1,1,1,3,2]
[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[7,5,3,4,2,6,1,8]=>[[1,4,6,8],[2],[3],[5],[7]]=>[1,1,2,2,2]
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[7,4,3,5,2,6,1,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>[1,1,1,3,2]
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[7,5,3,2,4,6,1,8]=>[[1,4,6,8],[2],[3],[5],[7]]=>[1,1,2,2,2]
[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[7,4,2,3,5,6,1,8]=>[[1,3,5,6,8],[2],[4],[7]]=>[1,2,3,2]
[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[7,2,3,4,5,6,1,8]=>[[1,3,4,5,6,8],[2],[7]]=>[1,5,2]
[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[6,5,4,3,2,7,1,8]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[[.,[[.,[.,[.,[[.,.],.]]]],.]],.]=>[5,6,4,3,2,7,1,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[5,6,3,4,2,7,1,8]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[6,3,4,5,2,7,1,8]=>[[1,4,5,7,8],[2],[3],[6]]=>[1,1,3,3]
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[[.,[[.,[[[.,.],[.,.]],.]],.]],.]=>[5,3,4,6,2,7,1,8]=>[[1,4,6,7,8],[2],[3],[5]]=>[1,1,2,4]
[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[4,3,5,6,2,7,1,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[5,4,6,2,3,7,1,8]=>[[1,3,7,8],[2,6],[4],[5]]=>[1,2,1,4]
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[6,5,3,2,4,7,1,8]=>[[1,4,7,8],[2],[3],[5],[6]]=>[1,1,2,1,3]
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[6,4,2,3,5,7,1,8]=>[[1,3,5,7,8],[2],[4],[6]]=>[1,2,2,3]
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[4,5,2,3,6,7,1,8]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[5,2,3,4,6,7,1,8]=>[[1,3,4,6,7,8],[2],[5]]=>[1,3,4]
[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[4,3,2,5,6,7,1,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[3,4,2,5,6,7,1,8]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[4,2,3,5,6,7,1,8]=>[[1,3,5,6,7,8],[2],[4]]=>[1,2,5]
[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[3,2,4,5,6,7,1,8]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[[1,3,4,5,6,7,8],[2]]=>[1,7]
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,3,1,2,8]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[2,1,1,1,1,2]
[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,3,1,2,8]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,1,1,1,3]
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,3,1,2,8]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,1,1,2,2]
[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,3,1,2,8]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,1,2,1,2]
[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,3,1,2,8]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,1,1,4]
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[4,5,6,7,3,1,2,8]=>[[1,2,6,7,8],[3,5],[4]]=>[2,1,5]
[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]=>[7,6,5,3,4,1,2,8]=>[[1,2,8],[3,4],[5],[6],[7]]=>[2,2,1,1,2]
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[6,7,3,4,5,1,2,8]=>[[1,2,5,8],[3,4],[6,7]]=>[2,3,3]
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[6,5,4,3,7,1,2,8]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,1,1,1,3]
[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[5,6,3,4,7,1,2,8]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[6,3,4,5,7,1,2,8]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]
[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[4,3,5,6,7,1,2,8]=>[[1,2,6,7,8],[3,5],[4]]=>[2,1,5]
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[3,4,5,6,7,1,2,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,2,1,3,8]=>[[1,3,8],[2],[4],[5],[6],[7]]=>[1,2,1,1,1,2]
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[6,5,7,4,2,1,3,8]=>[[1,3,8],[2,7],[4],[5],[6]]=>[1,2,1,1,3]
[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,2,1,3,8]=>[[1,3,8],[2,5],[4],[6],[7]]=>[1,2,2,1,2]
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,2,1,3,8]=>[[1,3,8],[2,6],[4],[5],[7]]=>[1,2,1,2,2]
[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,2,1,3,8]=>[[1,3,7,8],[2,6],[4],[5]]=>[1,2,1,4]
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[4,5,6,7,2,1,3,8]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>[3,1,1,1,2]
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,1,2,3,8]=>[[1,2,3,8],[4,6,7],[5]]=>[3,1,4]
[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,1,2,3,8]=>[[1,2,3,8],[4,5,6],[7]]=>[3,3,2]
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,1,2,3,8]=>[[1,2,3,8],[4,6,7],[5]]=>[3,1,4]
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[4,5,6,7,1,2,3,8]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[7,6,5,3,2,1,4,8]=>[[1,4,8],[2],[3],[5],[6],[7]]=>[1,1,2,1,1,2]
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[7,6,5,2,3,1,4,8]=>[[1,3,4,8],[2],[5],[6],[7]]=>[1,3,1,1,2]
[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[6,7,5,2,3,1,4,8]=>[[1,3,4,8],[2,7],[5],[6]]=>[1,3,1,3]
[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[7,5,6,2,3,1,4,8]=>[[1,3,4,8],[2,6],[5],[7]]=>[1,3,2,2]
[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[6,5,7,2,3,1,4,8]=>[[1,3,4,8],[2,7],[5],[6]]=>[1,3,1,3]
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[5,6,7,2,3,1,4,8]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[7,6,5,2,1,3,4,8]=>[[1,3,4,8],[2],[5],[6],[7]]=>[1,3,1,1,2]
[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[7,5,6,2,1,3,4,8]=>[[1,3,4,8],[2,6],[5],[7]]=>[1,3,2,2]
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[5,6,7,2,1,3,4,8]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,1,1,2]
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[[1,2,3,4,8],[5,7],[6]]=>[4,1,3]
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[[1,2,3,4,8],[5,6],[7]]=>[4,2,2]
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[[1,2,3,4,8],[5,7],[6]]=>[4,1,3]
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[7,6,4,3,2,1,5,8]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[1,1,1,2,1,2]
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[6,7,4,3,2,1,5,8]=>[[1,5,8],[2,7],[3],[4],[6]]=>[1,1,1,2,3]
[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]=>[7,6,3,4,2,1,5,8]=>[[1,4,5,8],[2],[3],[6],[7]]=>[1,1,3,1,2]
[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[6,7,3,4,2,1,5,8]=>[[1,4,5,8],[2,7],[3],[6]]=>[1,1,3,3]
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[7,6,4,2,3,1,5,8]=>[[1,3,5,8],[2],[4],[6],[7]]=>[1,2,2,1,2]
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[7,6,3,2,4,1,5,8]=>[[1,4,5,8],[2],[3],[6],[7]]=>[1,1,3,1,2]
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[7,6,2,3,4,1,5,8]=>[[1,3,4,5,8],[2],[6],[7]]=>[1,4,1,2]
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[6,7,2,3,4,1,5,8]=>[[1,3,4,5,8],[2,7],[6]]=>[1,4,3]
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[7,6,4,3,1,2,5,8]=>[[1,2,5,8],[3],[4],[6],[7]]=>[2,1,2,1,2]
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[[1,3,5,8],[2],[4],[6],[7]]=>[1,2,2,1,2]
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[7,6,3,2,1,4,5,8]=>[[1,4,5,8],[2],[3],[6],[7]]=>[1,1,3,1,2]
[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[6,7,3,2,1,4,5,8]=>[[1,4,5,8],[2,7],[3],[6]]=>[1,1,3,3]
[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[7,6,2,3,1,4,5,8]=>[[1,3,4,5,8],[2],[6],[7]]=>[1,4,1,2]
[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[6,7,2,3,1,4,5,8]=>[[1,3,4,5,8],[2,7],[6]]=>[1,4,3]
[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[6,7,3,1,2,4,5,8]=>[[1,2,4,5,8],[3,7],[6]]=>[2,3,3]
[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[7,6,1,2,3,4,5,8]=>[[1,2,3,4,5,8],[6],[7]]=>[5,1,2]
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>[[1,2,3,4,5,8],[6,7]]=>[5,3]
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[7,5,4,3,2,1,6,8]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[7,4,5,3,2,1,6,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>[1,1,1,3,2]
[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[7,4,3,5,2,1,6,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>[1,1,1,3,2]
[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[7,3,4,5,2,1,6,8]=>[[1,4,5,6,8],[2],[3],[7]]=>[1,1,4,2]
[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[7,5,4,2,3,1,6,8]=>[[1,3,6,8],[2],[4],[5],[7]]=>[1,2,1,2,2]
[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[7,5,3,2,4,1,6,8]=>[[1,4,6,8],[2],[3],[5],[7]]=>[1,1,2,2,2]
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[7,5,2,3,4,1,6,8]=>[[1,3,4,6,8],[2],[5],[7]]=>[1,3,2,2]
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[7,4,2,3,5,1,6,8]=>[[1,3,5,6,8],[2],[4],[7]]=>[1,2,3,2]
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[7,2,3,4,5,1,6,8]=>[[1,3,4,5,6,8],[2],[7]]=>[1,5,2]
[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[7,5,4,3,1,2,6,8]=>[[1,2,6,8],[3],[4],[5],[7]]=>[2,1,1,2,2]
[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[7,4,5,1,2,3,6,8]=>[[1,2,3,6,8],[4,5],[7]]=>[3,3,2]
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[7,5,3,2,1,4,6,8]=>[[1,4,6,8],[2],[3],[5],[7]]=>[1,1,2,2,2]
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[7,5,2,3,1,4,6,8]=>[[1,3,4,6,8],[2],[5],[7]]=>[1,3,2,2]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[[1,2,4,6,8],[3],[5],[7]]=>[2,2,2,2]
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[[1,2,3,4,6,8],[5],[7]]=>[4,2,2]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>[1,1,1,3,2]
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[7,2,3,4,1,5,6,8]=>[[1,3,4,5,6,8],[2],[7]]=>[1,5,2]
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[7,4,3,1,2,5,6,8]=>[[1,2,5,6,8],[3],[4],[7]]=>[2,1,3,2]
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[7,3,4,1,2,5,6,8]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]
[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[7,4,1,2,3,5,6,8]=>[[1,2,3,5,6,8],[4],[7]]=>[3,3,2]
[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[7,3,2,1,4,5,6,8]=>[[1,4,5,6,8],[2],[3],[7]]=>[1,1,4,2]
[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[7,2,3,1,4,5,6,8]=>[[1,3,4,5,6,8],[2],[7]]=>[1,5,2]
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[7,3,1,2,4,5,6,8]=>[[1,2,4,5,6,8],[3],[7]]=>[2,4,2]
[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[7,2,1,3,4,5,6,8]=>[[1,3,4,5,6,8],[2],[7]]=>[1,5,2]
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[[1,2,3,4,5,6,8],[7]]=>[6,2]
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[6,5,3,4,2,1,7,8]=>[[1,4,7,8],[2],[3],[5],[6]]=>[1,1,2,1,3]
[[[.,[.,[[.,.],[[.,.],.]]]],.],.]=>[5,6,3,4,2,1,7,8]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
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[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[5,4,6,2,3,1,7,8]=>[[1,3,7,8],[2,6],[4],[5]]=>[1,2,1,4]
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[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[6,2,3,4,5,1,7,8]=>[[1,3,4,5,7,8],[2],[6]]=>[1,4,3]
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[1,1,1,1,4]
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
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[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[5,2,3,4,6,1,7,8]=>[[1,3,4,6,7,8],[2],[5]]=>[1,3,4]
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[[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[4,2,3,5,6,1,7,8]=>[[1,3,5,6,7,8],[2],[4]]=>[1,2,5]
[[[.,[[[[.,[.,.]],.],.],.]],.],.]=>[3,2,4,5,6,1,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[[1,3,4,5,6,7,8],[2]]=>[1,7]
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[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[5,4,3,6,1,2,7,8]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,1,1,4]
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[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[3,4,5,6,1,2,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
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[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
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[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>[[1,2,3,4,5,7,8],[6]]=>[5,3]
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[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[5,4,2,3,1,6,7,8]=>[[1,3,6,7,8],[2],[4],[5]]=>[1,2,1,4]
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[5,3,2,4,1,6,7,8]=>[[1,4,6,7,8],[2],[3],[5]]=>[1,1,2,4]
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[[1,3,4,6,7,8],[2],[5]]=>[1,3,4]
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[4,2,3,5,1,6,7,8]=>[[1,3,5,6,7,8],[2],[4]]=>[1,2,5]
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[[1,3,4,5,6,7,8],[2]]=>[1,7]
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[5,4,3,1,2,6,7,8]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,1,1,4]
[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[4,3,5,1,2,6,7,8]=>[[1,2,6,7,8],[3,5],[4]]=>[2,1,5]
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[3,4,5,1,2,6,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[5,4,2,1,3,6,7,8]=>[[1,3,6,7,8],[2],[4],[5]]=>[1,2,1,4]
[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[4,5,2,1,3,6,7,8]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[4,5,1,2,3,6,7,8]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[5,3,2,1,4,6,7,8]=>[[1,4,6,7,8],[2],[3],[5]]=>[1,1,2,4]
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[5,2,3,1,4,6,7,8]=>[[1,3,4,6,7,8],[2],[5]]=>[1,3,4]
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[5,3,1,2,4,6,7,8]=>[[1,2,4,6,7,8],[3],[5]]=>[2,2,4]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[[1,2,3,4,6,7,8],[5]]=>[4,4]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[4,2,3,1,5,6,7,8]=>[[1,3,5,6,7,8],[2],[4]]=>[1,2,5]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[[1,3,4,5,6,7,8],[2]]=>[1,7]
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[4,3,1,2,5,6,7,8]=>[[1,2,5,6,7,8],[3],[4]]=>[2,1,5]
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[4,2,1,3,5,6,7,8]=>[[1,3,5,6,7,8],[2],[4]]=>[1,2,5]
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[[1,2,3,5,6,7,8],[4]]=>[3,5]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>[1,1,6]
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[2]]=>[1,7]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[[1,2,4,5,6,7,8],[3]]=>[2,6]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[2]]=>[1,7]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8]]=>[8]
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[8,9,7,6,5,4,3,2,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,2]
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[7,8,9,6,5,4,3,2,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,3]
[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,3,2,1]=>[[1,5,6,7,8,9],[2],[3],[4]]=>[1,1,1,6]
[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,2,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>[1,1,7]
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>[[1,3,4,5,6,7,8,9],[2]]=>[1,8]
[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]=>[[1,2,3,4,5,6,7,8,9]]=>[9]
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[1,1,1,1,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[9,10,8,7,6,5,4,3,2,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]=>[9,7,8,6,5,4,3,2,1]=>[[1,8],[2],[3],[4],[5],[6],[7],[9]]=>[1,1,1,1,1,1,2,1]
[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]=>[8,9,6,7,5,4,3,2,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[6,7,8,9,10,5,4,3,2,1]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,5]
[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]=>[4,5,6,7,8,9,10,3,2,1]=>[[1,5,6,7,8,9,10],[2],[3],[4]]=>[1,1,1,7]
[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]=>[4,5,6,7,8,9,2,3,1]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]=>[3,4,5,6,7,8,9,10,2,1]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>[1,1,8]
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,1,2]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[1,9]
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>[[1,2,3,4,5,6,7,8,9,10]]=>[10]
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[8,7,9,6,5,4,3,2,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,2]
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]=>[8,7,6,9,5,4,3,2,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,2]
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]=>[8,7,6,5,9,4,3,2,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,2]
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]=>[8,7,6,5,4,9,3,2,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,2]
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[8,7,6,5,4,3,9,2,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,2]
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[8,7,6,5,4,3,2,9,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,2]
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,2]
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]=>[9,8,10,7,6,5,4,3,2,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]=>[8,6,7,9,5,4,3,2,1]=>[[1,7,9],[2],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]=>[9,8,7,10,6,5,4,3,2,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]=>[9,8,7,6,10,5,4,3,2,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]=>[9,8,7,6,5,10,4,3,2,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]=>[9,8,7,6,5,4,10,3,2,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[9,8,7,6,5,4,3,10,2,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[8,7,6,5,4,3,1,2,9]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]=>[2,1,1,1,1,1,2]
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[9,8,7,6,5,4,3,2,10,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[1,1,1,1,1,1,1,1,2]
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[9,10,7,8,5,6,3,4,1,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10]]=>[2,2,2,2,2]
[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]=>[9,10,6,7,4,5,2,3,1,8]=>[[1,3,8],[2,5],[4,7],[6,10],[9]]=>[1,2,2,3,2]
[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]=>[5,6,4,7,3,8,2,9,1,10]=>[[1,6,7,8,9,10],[2],[3],[4],[5]]=>[1,1,1,1,6]
[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]]=>[2,2,2,2,2,2]
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[9,1,2,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8],[9]]=>[8,1]
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[10,1,2,3,4,5,6,7,8,9]=>[[1,2,3,4,5,6,7,8,9],[10]]=>[9,1]
[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[9,2,1,3,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[2],[9]]=>[1,7,1]
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>[1,1,7]
[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[10,2,1,3,4,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2],[10]]=>[1,8,1]
[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>[9,2,3,1,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[2],[9]]=>[1,7,1]
[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>[4,2,3,5,6,7,8,9,1]=>[[1,3,5,6,7,8,9],[2],[4]]=>[1,2,6]
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[3,4,2,5,6,7,8,9,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>[1,1,7]
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,10,1]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>[1,1,8]
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[8,9,1,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8,9]]=>[7,2]
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[7,8,9,1,2,3,4,5,6]=>[[1,2,3,4,5,6],[7,8,9]]=>[6,3]
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[6,7,8,9,1,2,3,4,5]=>[[1,2,3,4,5],[6,7,8,9]]=>[5,4]
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]=>[5,6,7,8,9,1,2,3,4]=>[[1,2,3,4,9],[5,6,7,8]]=>[4,5]
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]=>[4,5,6,7,8,9,1,2,3]=>[[1,2,3,7,8,9],[4,5,6]]=>[3,6]
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8],[9]]=>[7,1,1]
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[9,10,1,2,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8],[9,10]]=>[8,2]
[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]=>[8,7,9,1,2,3,4,5,6]=>[[1,2,3,4,5,6],[7,9],[8]]=>[6,1,2]
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[8,9,10,1,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8,9,10]]=>[7,3]
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[7,8,9,10,1,2,3,4,5,6]=>[[1,2,3,4,5,6],[7,8,9,10]]=>[6,4]
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[6,7,8,9,10,1,2,3,4,5]=>[[1,2,3,4,5],[6,7,8,9,10]]=>[5,5]
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]=>[5,6,7,8,9,10,1,2,3,4]=>[[1,2,3,4,9,10],[5,6,7,8]]=>[4,6]
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]=>[4,5,6,7,8,9,10,1,2,3]=>[[1,2,3,7,8,9,10],[4,5,6]]=>[3,7]
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,10,1,2]=>[[1,2,5,6,7,8,9,10],[3,4]]=>[2,8]
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,3,1,2]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[2,1,1,1,1,1,1,1]
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,3]
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[8,9,7,6,5,4,3,1,2]=>[[1,2],[3,9],[4],[5],[6],[7],[8]]=>[2,1,1,1,1,1,2]
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,3,1,2]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[2,1,1,1,1,1,1,1,1]
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,3]
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>[7,6,8,5,4,3,2,1,9]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,3]
[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]=>[8,6,7,5,4,3,2,1,9]=>[[1,7,9],[2],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[8,7,9,6,5,4,3,1,2]=>[[1,2],[3,9],[4],[5],[6],[7],[8]]=>[2,1,1,1,1,1,2]
[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[9,7,8,6,5,4,3,1,2]=>[[1,2],[3,8],[4],[5],[6],[7],[9]]=>[2,1,1,1,1,2,1]
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[9,10,8,7,6,5,4,3,1,2]=>[[1,2],[3,10],[4],[5],[6],[7],[8],[9]]=>[2,1,1,1,1,1,1,2]
[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[6,5,7,4,8,3,9,2,10,1]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,5]
[.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]=>[9,8,10,6,7,4,5,2,3,1]=>[[1,3],[2,5],[4,7],[6,10],[8],[9]]=>[1,2,2,2,1,2]
[[.,[[.,[[.,[[[.,.],[.,.]],.]],.]],.]],.]=>[6,4,5,7,3,8,2,9,1,10]=>[[1,5,7,8,9,10],[2],[3],[4],[6]]=>[1,1,1,2,5]
[.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]]=>[8,9,6,7,4,5,2,3,10,1]=>[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[1,2,2,2,3]
[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,2,1,3]=>[[1,3],[2],[4],[5],[6],[7],[8],[9]]=>[1,2,1,1,1,1,1,1]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[9,7,6,5,4,3,2,1,8]=>[[1,8],[2],[3],[4],[5],[6],[7],[9]]=>[1,1,1,1,1,1,2,1]
[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[3,1,1,1,1,1,1]
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,2,1,3]=>[[1,3],[2],[4],[5],[6],[7],[8],[9],[10]]=>[1,2,1,1,1,1,1,1,1]
[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,2,3,1,4]=>[[1,3,4],[2],[5],[6],[7],[8],[9]]=>[1,3,1,1,1,1,1]
[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,3,2,1,4]=>[[1,4],[2],[3],[5],[6],[7],[8],[9],[10]]=>[1,1,2,1,1,1,1,1,1]
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,4,3,2,1,5]=>[[1,5],[2],[3],[4],[6],[7],[8],[9],[10]]=>[1,1,1,2,1,1,1,1,1]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,5,4,3,2,1,6]=>[[1,6],[2],[3],[4],[5],[7],[8],[9],[10]]=>[1,1,1,1,2,1,1,1,1]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[10,9,8,6,5,4,3,2,1,7]=>[[1,7],[2],[3],[4],[5],[6],[8],[9],[10]]=>[1,1,1,1,1,2,1,1,1]
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]=>[9,6,7,5,4,3,2,1,8]=>[[1,7,8],[2],[3],[4],[5],[6],[9]]=>[1,1,1,1,1,3,1]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[10,9,7,6,5,4,3,2,1,8]=>[[1,8],[2],[3],[4],[5],[6],[7],[9],[10]]=>[1,1,1,1,1,1,2,1,1]
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,2,1,9]=>[[1,9],[2],[3],[4],[5],[6],[7],[8],[10]]=>[1,1,1,1,1,1,1,2,1]
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,3]
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>[[1,7,8,9],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,4]
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>[[1,6,7,8,9],[2],[3],[4],[5]]=>[1,1,1,1,5]
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>[[1,5,6,7,8,9],[2],[3],[4]]=>[1,1,1,6]
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>[[1,4,5,6,7,8,9],[2],[3]]=>[1,1,7]
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2]]=>[1,8]
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,3]
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,4]
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,5]
[[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.]=>[6,5,4,3,1,2,7,8,9]=>[[1,2,7,8,9],[3],[4],[5],[6]]=>[2,1,1,1,4]
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>[[1,6,7,8,9,10],[2],[3],[4],[5]]=>[1,1,1,1,6]
[[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.]=>[5,4,3,1,2,6,7,8,9]=>[[1,2,6,7,8,9],[3],[4],[5]]=>[2,1,1,5]
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>[[1,5,6,7,8,9,10],[2],[3],[4]]=>[1,1,1,7]
[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[4,3,1,2,5,6,7,8,9]=>[[1,2,5,6,7,8,9],[3],[4]]=>[2,1,6]
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>[1,1,8]
[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[3,1,2,4,5,6,7,8,9]=>[[1,2,4,5,6,7,8,9],[3]]=>[2,7]
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[1,9]
[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,2,3,1]=>[[1,3],[2],[4],[5],[6],[7],[8],[9]]=>[1,2,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]=>[10,8,9,7,6,5,4,3,2,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8],[10]]=>[1,1,1,1,1,1,1,2,1]
[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]=>[10,9,8,6,7,5,4,3,2,1]=>[[1,7],[2],[3],[4],[5],[6],[8],[9],[10]]=>[1,1,1,1,1,2,1,1,1]
[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,5,6,4,3,2,1]=>[[1,6],[2],[3],[4],[5],[7],[8],[9],[10]]=>[1,1,1,1,2,1,1,1,1]
[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,2,3,1]=>[[1,3],[2],[4],[5],[6],[7],[8],[9],[10]]=>[1,2,1,1,1,1,1,1,1]
[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]=>[10,8,9,6,7,4,5,2,3,1]=>[[1,3],[2,5],[4,7],[6,9],[8],[10]]=>[1,2,2,2,2,1]
[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[9,2,3,4,5,6,7,8,1]=>[[1,3,4,5,6,7,8],[2],[9]]=>[1,7,1]
[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]]=>[8,9,2,1,3,4,5,6,7]=>[[1,3,4,5,6,7],[2,9],[8]]=>[1,6,2]
[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]=>[8,9,2,3,4,5,6,7,1]=>[[1,3,4,5,6,7],[2,9],[8]]=>[1,6,2]
[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]=>[10,2,3,4,5,6,7,8,9,1]=>[[1,3,4,5,6,7,8,9],[2],[10]]=>[1,8,1]
[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[8,6,5,4,3,2,1,7,9]=>[[1,7,9],[2],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]=>[3,4,5,6,7,8,2,9,1]=>[[1,4,5,6,7,8,9],[2],[3]]=>[1,1,7]
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>[[1,3,4,5,6,7,8,9],[2]]=>[1,8]
[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2]]=>[1,8]
[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]=>[2,3,4,5,1,6,7,8,9]=>[[1,3,4,5,6,7,8,9],[2]]=>[1,8]
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>[[1,3,4,5,6,7,8,9],[2]]=>[1,8]
[[[[[[.,[[.,.],[.,.]]],.],.],.],.],.]=>[4,2,3,1,5,6,7,8,9]=>[[1,3,5,6,7,8,9],[2],[4]]=>[1,2,6]
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>[[1,3,4,5,6,7,8,9,10],[2]]=>[1,9]
[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[8,1,2,3,4,5,6,7,9]=>[[1,2,3,4,5,6,7,9],[8]]=>[7,2]
[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[3,1,2,4,5,6,7,8,9,10]=>[[1,2,4,5,6,7,8,9,10],[3]]=>[2,8]
[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]=>[4,1,2,3,5,6,7,8,9,10]=>[[1,2,3,5,6,7,8,9,10],[4]]=>[3,7]
[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[5,1,2,3,4,6,7,8,9,10]=>[[1,2,3,4,6,7,8,9,10],[5]]=>[4,6]
[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[6,1,2,3,4,5,7,8,9,10]=>[[1,2,3,4,5,7,8,9,10],[6]]=>[5,5]
[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[7,1,2,3,4,5,6,8,9,10]=>[[1,2,3,4,5,6,8,9,10],[7]]=>[6,4]
[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[8,1,2,3,4,5,6,7,9,10]=>[[1,2,3,4,5,6,7,9,10],[8]]=>[7,3]
[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[9,1,2,3,4,5,6,7,8,10]=>[[1,2,3,4,5,6,7,8,10],[9]]=>[8,2]
[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]=>[9,3,4,5,6,7,8,1,2]=>[[1,2,5,6,7,8],[3,4],[9]]=>[2,6,1]
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[9,7,6,5,4,3,2,8,1]=>[[1,8],[2],[3],[4],[5],[6],[7],[9]]=>[1,1,1,1,1,1,2,1]
[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]]=>[6,5,4,3,2,7,8,9,1]=>[[1,7,8,9],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,4]
[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]=>[8,9,6,5,4,3,2,1,7]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,2]
[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,1,2,3]=>[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>[3,1,1,1,1,1,1,1]
[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,3,1,2,4]=>[[1,2,4],[3],[5],[6],[7],[8],[9]]=>[2,2,1,1,1,1,1]
[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[9,8,7,6,5,4,3,1,2,10]=>[[1,2,10],[3],[4],[5],[6],[7],[8],[9]]=>[2,1,1,1,1,1,1,2]
[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]]=>[8,7,9,6,5,4,2,3,1]=>[[1,3],[2,9],[4],[5],[6],[7],[8]]=>[1,2,1,1,1,1,2]
[[[[[[.,.],[[[.,.],.],.]],.],.],.],.]=>[3,4,5,1,2,6,7,8,9]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]
[[[[.,[[[[.,.],.],.],.]],.],.],[.,.]]=>[9,2,3,4,5,1,6,7,8]=>[[1,3,4,5,6,7,8],[2],[9]]=>[1,7,1]
[.,[.,[[[[.,[[[.,.],.],.]],.],.],.]]]=>[4,5,6,3,7,8,9,2,1]=>[[1,5,6,7,8,9],[2],[3],[4]]=>[1,1,1,6]
[.,[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]]=>[3,4,5,6,2,7,8,9,10,1]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>[1,1,8]
[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.]=>[4,5,2,1,3,6,7,8,9]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]=>[10,8,7,6,5,4,3,2,9,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8],[10]]=>[1,1,1,1,1,1,1,2,1]
[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]=>[4,5,6,7,8,9,2,1,3]=>[[1,3,6,7,8,9],[2,5],[4]]=>[1,2,6]
[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]=>[3,4,5,6,7,8,1,2,9]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]
[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]=>[8,9,7,6,5,4,2,1,3]=>[[1,3],[2,9],[4],[5],[6],[7],[8]]=>[1,2,1,1,1,1,2]
[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8],[9],[10]]=>[8,1,1]
[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]=>[6,7,8,5,4,3,2,1,9]=>[[1,7,8,9],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,4]
[[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]],.]=>[6,5,4,3,2,7,8,1,9]=>[[1,7,8,9],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,4]
[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]=>[7,8,9,6,5,4,3,2,1,10]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,4]
[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[9,8,7,1,2,3,4,5,6]=>[[1,2,3,4,5,6],[7],[8],[9]]=>[6,1,1,1]
[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,1,2,3,4,5]=>[[1,2,3,4,5],[6],[7],[8],[9]]=>[5,1,1,1,1]
[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>[[1,2,3,4],[5],[6],[7],[8],[9]]=>[4,1,1,1,1,1]
[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[9,7,1,2,3,4,5,6,8]=>[[1,2,3,4,5,6,8],[7],[9]]=>[6,2,1]
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[10,9,8,1,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8],[9],[10]]=>[7,1,1,1]
[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]=>[9,8,6,1,2,3,4,5,7]=>[[1,2,3,4,5,7],[6],[8],[9]]=>[5,2,1,1]
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,1,2,3,4,5,6]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[6,1,1,1,1]
[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]=>[9,8,7,5,1,2,3,4,6]=>[[1,2,3,4,6],[5],[7],[8],[9]]=>[4,2,1,1,1]
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,1,2,3,4,5]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[5,1,1,1,1,1]
[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,4,1,2,3,5]=>[[1,2,3,5],[4],[6],[7],[8],[9]]=>[3,2,1,1,1,1]
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,1,2,3,4]=>[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>[4,1,1,1,1,1,1]
[[[[[[.,[[.,[.,.]],.]],.],.],.],.],.]=>[3,2,4,1,5,6,7,8,9]=>[[1,4,5,6,7,8,9],[2],[3]]=>[1,1,7]
[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[9,8,10,7,6,5,4,3,1,2]=>[[1,2],[3,10],[4],[5],[6],[7],[8],[9]]=>[2,1,1,1,1,1,1,2]
[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]=>[8,9,7,6,5,4,2,3,1]=>[[1,3],[2,9],[4],[5],[6],[7],[8]]=>[1,2,1,1,1,1,2]
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]=>[7,8,6,5,4,3,2,9,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,3]
[.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]]=>[8,9,7,6,5,4,3,2,10,1]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,3]
[.,[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]]=>[7,6,8,5,4,3,2,9,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,3]
[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]=>[3,4,2,1,5,6,7,8,9]=>[[1,4,5,6,7,8,9],[2],[3]]=>[1,1,7]
[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]=>[5,4,6,7,8,9,3,2,1]=>[[1,6,7,8,9],[2],[3],[4],[5]]=>[1,1,1,1,5]
[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]=>[6,5,7,8,9,4,3,2,1]=>[[1,7,8,9],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,4]
[.,[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]]=>[6,5,7,8,9,10,4,3,2,1]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,5]
[.,[.,[[.,[[[[.,[.,.]],.],.],.]],.]]]=>[5,4,6,7,8,3,9,2,1]=>[[1,6,7,8,9],[2],[3],[4],[5]]=>[1,1,1,1,5]
[.,[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]]=>[5,4,6,7,8,9,10,3,2,1]=>[[1,6,7,8,9,10],[2],[3],[4],[5]]=>[1,1,1,1,6]
[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]=>[7,6,5,4,3,2,8,1,9]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,3]
[[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.]=>[6,5,4,3,2,7,1,8,9]=>[[1,7,8,9],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,4]
[[[[.,[[.,[.,[.,[.,.]]]],.]],.],.],.]=>[5,4,3,2,6,1,7,8,9]=>[[1,6,7,8,9],[2],[3],[4],[5]]=>[1,1,1,1,5]
[[[[[.,[[.,[.,[.,.]]],.]],.],.],.],.]=>[4,3,2,5,1,6,7,8,9]=>[[1,5,6,7,8,9],[2],[3],[4]]=>[1,1,1,6]
[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.]=>[4,5,3,2,1,6,7,8,9]=>[[1,5,6,7,8,9],[2],[3],[4]]=>[1,1,1,6]
[[.,[.,[.,[.,.]]]],[[[[[.,.],.],.],.],.]]=>[6,7,8,9,10,4,3,2,1,5]=>[[1,5,8,9,10],[2,7],[3],[4],[6]]=>[1,1,1,2,5]
[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]=>[3,2,4,5,6,7,8,1,9]=>[[1,4,5,6,7,8,9],[2],[3]]=>[1,1,7]
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]=>[9,7,6,5,4,3,2,1,8,10]=>[[1,8,10],[2],[3],[4],[5],[6],[7],[9]]=>[1,1,1,1,1,1,2,2]
[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]=>[9,6,7,8,5,4,3,2,1]=>[[1,7,8],[2],[3],[4],[5],[6],[9]]=>[1,1,1,1,1,3,1]
[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[8,7,6,5,4,3,9,1,2]=>[[1,2],[3,9],[4],[5],[6],[7],[8]]=>[2,1,1,1,1,1,2]
[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[9,2,3,4,5,6,7,1,8]=>[[1,3,4,5,6,7,8],[2],[9]]=>[1,7,1]
[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[3,4,1,2,5,6,7,8,9]=>[[1,2,5,6,7,8,9],[3,4]]=>[2,7]
[.,[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]]=>[3,4,5,6,7,8,9,2,10,1]=>[[1,4,5,6,7,8,9,10],[2],[3]]=>[1,1,8]
[[.,[.,[[[[[.,.],.],.],.],.]]],[.,.]]=>[9,3,4,5,6,7,2,1,8]=>[[1,4,5,6,7,8],[2],[3],[9]]=>[1,1,6,1]
[.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]]=>[4,5,6,7,8,9,10,2,3,1]=>[[1,3,6,7,8,9,10],[2,5],[4]]=>[1,2,7]
[[[[.,[.,[[[[.,.],.],.],.]]],.],.],.]=>[3,4,5,6,2,1,7,8,9]=>[[1,4,5,6,7,8,9],[2],[3]]=>[1,1,7]
[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[8,7,6,5,4,1,2,3,9]=>[[1,2,3,9],[4],[5],[6],[7],[8]]=>[3,1,1,1,1,2]
[.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]=>[9,8,2,3,4,5,6,7,1]=>[[1,3,4,5,6,7],[2],[8],[9]]=>[1,6,1,1]
[.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]]=>[10,9,2,3,4,5,6,7,8,1]=>[[1,3,4,5,6,7,8],[2],[9],[10]]=>[1,7,1,1]
[[.,[.,[[[[[[.,.],.],.],.],.],.]]],.]=>[3,4,5,6,7,8,2,1,9]=>[[1,4,5,6,7,8,9],[2],[3]]=>[1,1,7]
[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]=>[10,3,1,2,4,5,6,7,8,9]=>[[1,2,4,5,6,7,8,9],[3],[10]]=>[2,7,1]
[[[.,[[[[[.,.],.],.],.],.]],.],[.,.]]=>[9,2,3,4,5,6,1,7,8]=>[[1,3,4,5,6,7,8],[2],[9]]=>[1,7,1]
[[[.,[.,[[[[[.,.],.],.],.],.]]],.],.]=>[3,4,5,6,7,2,1,8,9]=>[[1,4,5,6,7,8,9],[2],[3]]=>[1,1,7]
[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.]=>[6,7,5,4,3,2,1,8,9]=>[[1,7,8,9],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,4]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]=>[9,10,7,6,5,4,3,2,1,8]=>[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>[1,1,1,1,1,1,2,2]
[[.,[[[[[.,.],.],.],.],.]],[.,[.,.]]]=>[9,8,2,3,4,5,6,1,7]=>[[1,3,4,5,6,7],[2],[8],[9]]=>[1,6,1,1]
[[[[[.,[.,[[[.,.],.],.]]],.],.],.],.]=>[3,4,5,2,1,6,7,8,9]=>[[1,4,5,6,7,8,9],[2],[3]]=>[1,1,7]
[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]=>[9,3,4,5,6,7,8,2,1]=>[[1,4,5,6,7,8],[2],[3],[9]]=>[1,1,6,1]
[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]=>[7,6,8,9,5,4,3,2,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,3]
[.,[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]]=>[7,6,8,5,9,4,3,2,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,3]
[.,[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]]=>[8,7,9,10,6,5,4,3,2,1]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,3]
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
Robinson-Schensted insertion tableau
Description
Sends a permutation to its Robinson-Schensted insertion tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding insertion tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding insertion tableau.
Map
horizontal strip sizes
Description
The composition of horizontal strip sizes.
We associate to a standard Young tableau $T$ the composition $(c_1,\dots,c_k)$, such that $k$ is minimal and the numbers $c_1+\dots+c_i + 1,\dots,c_1+\dots+c_{i+1}$ form a horizontal strip in $T$ for all $i$.
We associate to a standard Young tableau $T$ the composition $(c_1,\dots,c_k)$, such that $k$ is minimal and the numbers $c_1+\dots+c_i + 1,\dots,c_1+\dots+c_{i+1}$ form a horizontal strip in $T$ for all $i$.
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