Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
Mp00085: Standard tableaux —Schützenberger involution⟶ Standard tableaux
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
Mp00085: Standard tableaux —Schützenberger involution⟶ Standard tableaux
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Images
=>
Cc0010;cc-rep-0Cc0007;cc-rep-2Cc0007;cc-rep-3
[.,.]=>[1]=>[[1]]=>[[1]]=>[1]
[.,[.,.]]=>[2,1]=>[[1],[2]]=>[[1],[2]]=>[1,1]
[[.,.],.]=>[1,2]=>[[1,2]]=>[[1,2]]=>[2]
[.,[.,[.,.]]]=>[3,2,1]=>[[1],[2],[3]]=>[[1],[2],[3]]=>[1,1,1]
[.,[[.,.],.]]=>[2,3,1]=>[[1,2],[3]]=>[[1,3],[2]]=>[1,2]
[[.,.],[.,.]]=>[3,1,2]=>[[1,3],[2]]=>[[1,2],[3]]=>[2,1]
[[.,[.,.]],.]=>[2,1,3]=>[[1,3],[2]]=>[[1,2],[3]]=>[2,1]
[[[.,.],.],.]=>[1,2,3]=>[[1,2,3]]=>[[1,2,3]]=>[3]
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[[1],[2],[3],[4]]=>[[1],[2],[3],[4]]=>[1,1,1,1]
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[[1,2],[3],[4]]=>[[1,4],[2],[3]]=>[1,1,2]
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[[1,3],[2],[4]]=>[[1,3],[2],[4]]=>[1,2,1]
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[[1,3],[2],[4]]=>[[1,3],[2],[4]]=>[1,2,1]
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[[1,2,3],[4]]=>[[1,3,4],[2]]=>[1,3]
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[[1,4],[2],[3]]=>[[1,2],[3],[4]]=>[2,1,1]
[[.,.],[[.,.],.]]=>[3,4,1,2]=>[[1,2],[3,4]]=>[[1,2],[3,4]]=>[2,2]
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[[1,4],[2],[3]]=>[[1,2],[3],[4]]=>[2,1,1]
[[[.,.],.],[.,.]]=>[4,1,2,3]=>[[1,3,4],[2]]=>[[1,2,3],[4]]=>[3,1]
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[[1,4],[2],[3]]=>[[1,2],[3],[4]]=>[2,1,1]
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[[1,2,4],[3]]=>[[1,2,4],[3]]=>[2,2]
[[[.,.],[.,.]],.]=>[3,1,2,4]=>[[1,3,4],[2]]=>[[1,2,3],[4]]=>[3,1]
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[[1,3,4],[2]]=>[[1,2,3],[4]]=>[3,1]
[[[[.,.],.],.],.]=>[1,2,3,4]=>[[1,2,3,4]]=>[[1,2,3,4]]=>[4]
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[[1],[2],[3],[4],[5]]=>[[1],[2],[3],[4],[5]]=>[1,1,1,1,1]
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[[1,2],[3],[4],[5]]=>[[1,5],[2],[3],[4]]=>[1,1,1,2]
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[[1,3],[2],[4],[5]]=>[[1,4],[2],[3],[5]]=>[1,1,2,1]
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[[1,3],[2],[4],[5]]=>[[1,4],[2],[3],[5]]=>[1,1,2,1]
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[[1,2,3],[4],[5]]=>[[1,4,5],[2],[3]]=>[1,1,3]
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[[1,4],[2],[3],[5]]=>[[1,3],[2],[4],[5]]=>[1,2,1,1]
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[[1,2],[3,4],[5]]=>[[1,3],[2,5],[4]]=>[1,2,2]
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[[1,4],[2],[3],[5]]=>[[1,3],[2],[4],[5]]=>[1,2,1,1]
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[[1,3,4],[2],[5]]=>[[1,3,4],[2],[5]]=>[1,3,1]
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[[1,4],[2],[3],[5]]=>[[1,3],[2],[4],[5]]=>[1,2,1,1]
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[[1,2,4],[3],[5]]=>[[1,3,5],[2],[4]]=>[1,2,2]
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[[1,3,4],[2],[5]]=>[[1,3,4],[2],[5]]=>[1,3,1]
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[[1,3,4],[2],[5]]=>[[1,3,4],[2],[5]]=>[1,3,1]
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[[1,2,3,4],[5]]=>[[1,3,4,5],[2]]=>[1,4]
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[[1,5],[2],[3],[4]]=>[[1,2],[3],[4],[5]]=>[2,1,1,1]
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[[1,2],[3,5],[4]]=>[[1,2],[3,5],[4]]=>[2,1,2]
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[[1,3],[2,5],[4]]=>[[1,2],[3,4],[5]]=>[2,2,1]
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[[1,3],[2,5],[4]]=>[[1,2],[3,4],[5]]=>[2,2,1]
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[[1,2,3],[4,5]]=>[[1,2,5],[3,4]]=>[2,3]
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[[1,5],[2],[3],[4]]=>[[1,2],[3],[4],[5]]=>[2,1,1,1]
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[[1,2],[3,5],[4]]=>[[1,2],[3,5],[4]]=>[2,1,2]
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[[1,4,5],[2],[3]]=>[[1,2,3],[4],[5]]=>[3,1,1]
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[[1,2,5],[3,4]]=>[[1,2,3],[4,5]]=>[3,2]
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[[1,5],[2],[3],[4]]=>[[1,2],[3],[4],[5]]=>[2,1,1,1]
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[[1,3,5],[2],[4]]=>[[1,2,4],[3],[5]]=>[2,2,1]
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[[1,4,5],[2],[3]]=>[[1,2,3],[4],[5]]=>[3,1,1]
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[[1,4,5],[2],[3]]=>[[1,2,3],[4],[5]]=>[3,1,1]
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[[1,3,4,5],[2]]=>[[1,2,3,4],[5]]=>[4,1]
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[[1,5],[2],[3],[4]]=>[[1,2],[3],[4],[5]]=>[2,1,1,1]
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[[1,2,5],[3],[4]]=>[[1,2,5],[3],[4]]=>[2,1,2]
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[[1,3,5],[2],[4]]=>[[1,2,4],[3],[5]]=>[2,2,1]
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[[1,3,5],[2],[4]]=>[[1,2,4],[3],[5]]=>[2,2,1]
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[[1,2,3,5],[4]]=>[[1,2,4,5],[3]]=>[2,3]
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[[1,4,5],[2],[3]]=>[[1,2,3],[4],[5]]=>[3,1,1]
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[[1,2,5],[3,4]]=>[[1,2,3],[4,5]]=>[3,2]
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[[1,4,5],[2],[3]]=>[[1,2,3],[4],[5]]=>[3,1,1]
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[[1,3,4,5],[2]]=>[[1,2,3,4],[5]]=>[4,1]
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[[1,4,5],[2],[3]]=>[[1,2,3],[4],[5]]=>[3,1,1]
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[[1,2,4,5],[3]]=>[[1,2,3,5],[4]]=>[3,2]
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[[1,3,4,5],[2]]=>[[1,2,3,4],[5]]=>[4,1]
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[[1,3,4,5],[2]]=>[[1,2,3,4],[5]]=>[4,1]
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[[1,2,3,4,5]]=>[[1,2,3,4,5]]=>[5]
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6]]=>[[1],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,1]
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[[1,2],[3],[4],[5],[6]]=>[[1,6],[2],[3],[4],[5]]=>[1,1,1,1,2]
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[[1,3],[2],[4],[5],[6]]=>[[1,5],[2],[3],[4],[6]]=>[1,1,1,2,1]
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[[1,3],[2],[4],[5],[6]]=>[[1,5],[2],[3],[4],[6]]=>[1,1,1,2,1]
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[[1,2,3],[4],[5],[6]]=>[[1,5,6],[2],[3],[4]]=>[1,1,1,3]
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[[1,4],[2],[3],[5],[6]]=>[[1,4],[2],[3],[5],[6]]=>[1,1,2,1,1]
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[[1,2],[3,4],[5],[6]]=>[[1,4],[2,6],[3],[5]]=>[1,1,2,2]
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[[1,4],[2],[3],[5],[6]]=>[[1,4],[2],[3],[5],[6]]=>[1,1,2,1,1]
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[[1,3,4],[2],[5],[6]]=>[[1,4,5],[2],[3],[6]]=>[1,1,3,1]
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[[1,4],[2],[3],[5],[6]]=>[[1,4],[2],[3],[5],[6]]=>[1,1,2,1,1]
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[[1,2,4],[3],[5],[6]]=>[[1,4,6],[2],[3],[5]]=>[1,1,2,2]
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[[1,3,4],[2],[5],[6]]=>[[1,4,5],[2],[3],[6]]=>[1,1,3,1]
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[[1,3,4],[2],[5],[6]]=>[[1,4,5],[2],[3],[6]]=>[1,1,3,1]
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[[1,2,3,4],[5],[6]]=>[[1,4,5,6],[2],[3]]=>[1,1,4]
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[[1,5],[2],[3],[4],[6]]=>[[1,3],[2],[4],[5],[6]]=>[1,2,1,1,1]
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[[1,2],[3,5],[4],[6]]=>[[1,3],[2,6],[4],[5]]=>[1,2,1,2]
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[[1,3],[2,5],[4],[6]]=>[[1,3],[2,5],[4],[6]]=>[1,2,2,1]
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[[1,3],[2,5],[4],[6]]=>[[1,3],[2,5],[4],[6]]=>[1,2,2,1]
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[[1,2,3],[4,5],[6]]=>[[1,3,6],[2,5],[4]]=>[1,2,3]
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[[1,5],[2],[3],[4],[6]]=>[[1,3],[2],[4],[5],[6]]=>[1,2,1,1,1]
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[[1,2],[3,5],[4],[6]]=>[[1,3],[2,6],[4],[5]]=>[1,2,1,2]
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[[1,4,5],[2],[3],[6]]=>[[1,3,4],[2],[5],[6]]=>[1,3,1,1]
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[[1,2,5],[3,4],[6]]=>[[1,3,4],[2,6],[5]]=>[1,3,2]
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[[1,5],[2],[3],[4],[6]]=>[[1,3],[2],[4],[5],[6]]=>[1,2,1,1,1]
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[[1,3,5],[2],[4],[6]]=>[[1,3,5],[2],[4],[6]]=>[1,2,2,1]
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[[1,4,5],[2],[3],[6]]=>[[1,3,4],[2],[5],[6]]=>[1,3,1,1]
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[[1,4,5],[2],[3],[6]]=>[[1,3,4],[2],[5],[6]]=>[1,3,1,1]
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[[1,3,4,5],[2],[6]]=>[[1,3,4,5],[2],[6]]=>[1,4,1]
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[[1,5],[2],[3],[4],[6]]=>[[1,3],[2],[4],[5],[6]]=>[1,2,1,1,1]
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[[1,2,5],[3],[4],[6]]=>[[1,3,6],[2],[4],[5]]=>[1,2,1,2]
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[[1,3,5],[2],[4],[6]]=>[[1,3,5],[2],[4],[6]]=>[1,2,2,1]
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[[1,3,5],[2],[4],[6]]=>[[1,3,5],[2],[4],[6]]=>[1,2,2,1]
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[[1,2,3,5],[4],[6]]=>[[1,3,5,6],[2],[4]]=>[1,2,3]
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[[1,4,5],[2],[3],[6]]=>[[1,3,4],[2],[5],[6]]=>[1,3,1,1]
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[[1,2,5],[3,4],[6]]=>[[1,3,4],[2,6],[5]]=>[1,3,2]
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[[1,4,5],[2],[3],[6]]=>[[1,3,4],[2],[5],[6]]=>[1,3,1,1]
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[[1,3,4,5],[2],[6]]=>[[1,3,4,5],[2],[6]]=>[1,4,1]
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[[1,4,5],[2],[3],[6]]=>[[1,3,4],[2],[5],[6]]=>[1,3,1,1]
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[[1,2,4,5],[3],[6]]=>[[1,3,4,6],[2],[5]]=>[1,3,2]
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[[1,3,4,5],[2],[6]]=>[[1,3,4,5],[2],[6]]=>[1,4,1]
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[[1,3,4,5],[2],[6]]=>[[1,3,4,5],[2],[6]]=>[1,4,1]
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[[1,2,3,4,5],[6]]=>[[1,3,4,5,6],[2]]=>[1,5]
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[[1,6],[2],[3],[4],[5]]=>[[1,2],[3],[4],[5],[6]]=>[2,1,1,1,1]
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[[1,2],[3,6],[4],[5]]=>[[1,2],[3,6],[4],[5]]=>[2,1,1,2]
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[[1,3],[2,6],[4],[5]]=>[[1,2],[3,5],[4],[6]]=>[2,1,2,1]
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[[1,3],[2,6],[4],[5]]=>[[1,2],[3,5],[4],[6]]=>[2,1,2,1]
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[[1,2,3],[4,6],[5]]=>[[1,2,6],[3,5],[4]]=>[2,1,3]
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[[1,4],[2,6],[3],[5]]=>[[1,2],[3,4],[5],[6]]=>[2,2,1,1]
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[[1,2],[3,4],[5,6]]=>[[1,2],[3,4],[5,6]]=>[2,2,2]
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[[1,4],[2,6],[3],[5]]=>[[1,2],[3,4],[5],[6]]=>[2,2,1,1]
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[[1,3,4],[2,6],[5]]=>[[1,2,5],[3,4],[6]]=>[2,3,1]
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[[1,4],[2,6],[3],[5]]=>[[1,2],[3,4],[5],[6]]=>[2,2,1,1]
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[[1,2,4],[3,6],[5]]=>[[1,2,6],[3,4],[5]]=>[2,2,2]
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[[1,3,4],[2,6],[5]]=>[[1,2,5],[3,4],[6]]=>[2,3,1]
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[[1,3,4],[2,6],[5]]=>[[1,2,5],[3,4],[6]]=>[2,3,1]
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[[1,2,3,4],[5,6]]=>[[1,2,5,6],[3,4]]=>[2,4]
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[[1,6],[2],[3],[4],[5]]=>[[1,2],[3],[4],[5],[6]]=>[2,1,1,1,1]
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[[1,2],[3,6],[4],[5]]=>[[1,2],[3,6],[4],[5]]=>[2,1,1,2]
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[[1,3],[2,6],[4],[5]]=>[[1,2],[3,5],[4],[6]]=>[2,1,2,1]
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[[1,3],[2,6],[4],[5]]=>[[1,2],[3,5],[4],[6]]=>[2,1,2,1]
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[[1,2,3],[4,6],[5]]=>[[1,2,6],[3,5],[4]]=>[2,1,3]
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[[1,5,6],[2],[3],[4]]=>[[1,2,3],[4],[5],[6]]=>[3,1,1,1]
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[[1,2,6],[3,5],[4]]=>[[1,2,3],[4,6],[5]]=>[3,1,2]
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[[1,3,6],[2,5],[4]]=>[[1,2,3],[4,5],[6]]=>[3,2,1]
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[[1,3,6],[2,5],[4]]=>[[1,2,3],[4,5],[6]]=>[3,2,1]
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[[1,2,3],[4,5,6]]=>[[1,2,3],[4,5,6]]=>[3,3]
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[[1,6],[2],[3],[4],[5]]=>[[1,2],[3],[4],[5],[6]]=>[2,1,1,1,1]
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[[1,2],[3,6],[4],[5]]=>[[1,2],[3,6],[4],[5]]=>[2,1,1,2]
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[[1,4,6],[2],[3],[5]]=>[[1,2,4],[3],[5],[6]]=>[2,2,1,1]
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[[1,2,6],[3,4],[5]]=>[[1,2,4],[3,6],[5]]=>[2,2,2]
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[[1,5,6],[2],[3],[4]]=>[[1,2,3],[4],[5],[6]]=>[3,1,1,1]
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[[1,2,6],[3,5],[4]]=>[[1,2,3],[4,6],[5]]=>[3,1,2]
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[[1,5,6],[2],[3],[4]]=>[[1,2,3],[4],[5],[6]]=>[3,1,1,1]
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[[1,2,6],[3,5],[4]]=>[[1,2,3],[4,6],[5]]=>[3,1,2]
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[[1,4,5,6],[2],[3]]=>[[1,2,3,4],[5],[6]]=>[4,1,1]
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[[1,2,5,6],[3,4]]=>[[1,2,3,4],[5,6]]=>[4,2]
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[[1,6],[2],[3],[4],[5]]=>[[1,2],[3],[4],[5],[6]]=>[2,1,1,1,1]
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[[1,3,6],[2],[4],[5]]=>[[1,2,5],[3],[4],[6]]=>[2,1,2,1]
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[[1,4,6],[2],[3],[5]]=>[[1,2,4],[3],[5],[6]]=>[2,2,1,1]
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[[1,4,6],[2],[3],[5]]=>[[1,2,4],[3],[5],[6]]=>[2,2,1,1]
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[[1,3,4,6],[2],[5]]=>[[1,2,4,5],[3],[6]]=>[2,3,1]
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[[1,5,6],[2],[3],[4]]=>[[1,2,3],[4],[5],[6]]=>[3,1,1,1]
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[[1,3,6],[2,5],[4]]=>[[1,2,3],[4,5],[6]]=>[3,2,1]
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[[1,5,6],[2],[3],[4]]=>[[1,2,3],[4],[5],[6]]=>[3,1,1,1]
[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[[1,4,5,6],[2],[3]]=>[[1,2,3,4],[5],[6]]=>[4,1,1]
[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[[1,5,6],[2],[3],[4]]=>[[1,2,3],[4],[5],[6]]=>[3,1,1,1]
[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[[1,3,5,6],[2],[4]]=>[[1,2,3,5],[4],[6]]=>[3,2,1]
[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[[1,4,5,6],[2],[3]]=>[[1,2,3,4],[5],[6]]=>[4,1,1]
[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[[1,4,5,6],[2],[3]]=>[[1,2,3,4],[5],[6]]=>[4,1,1]
[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[[1,3,4,5,6],[2]]=>[[1,2,3,4,5],[6]]=>[5,1]
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[[1,6],[2],[3],[4],[5]]=>[[1,2],[3],[4],[5],[6]]=>[2,1,1,1,1]
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[[1,2,6],[3],[4],[5]]=>[[1,2,6],[3],[4],[5]]=>[2,1,1,2]
[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[[1,3,6],[2],[4],[5]]=>[[1,2,5],[3],[4],[6]]=>[2,1,2,1]
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[[1,3,6],[2],[4],[5]]=>[[1,2,5],[3],[4],[6]]=>[2,1,2,1]
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[[1,2,3,6],[4],[5]]=>[[1,2,5,6],[3],[4]]=>[2,1,3]
[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[[1,4,6],[2],[3],[5]]=>[[1,2,4],[3],[5],[6]]=>[2,2,1,1]
[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[[1,2,6],[3,4],[5]]=>[[1,2,4],[3,6],[5]]=>[2,2,2]
[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[[1,4,6],[2],[3],[5]]=>[[1,2,4],[3],[5],[6]]=>[2,2,1,1]
[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[[1,3,4,6],[2],[5]]=>[[1,2,4,5],[3],[6]]=>[2,3,1]
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[[1,4,6],[2],[3],[5]]=>[[1,2,4],[3],[5],[6]]=>[2,2,1,1]
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[[1,2,4,6],[3],[5]]=>[[1,2,4,6],[3],[5]]=>[2,2,2]
[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[[1,3,4,6],[2],[5]]=>[[1,2,4,5],[3],[6]]=>[2,3,1]
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[[1,3,4,6],[2],[5]]=>[[1,2,4,5],[3],[6]]=>[2,3,1]
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[[1,2,3,4,6],[5]]=>[[1,2,4,5,6],[3]]=>[2,4]
[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[[1,5,6],[2],[3],[4]]=>[[1,2,3],[4],[5],[6]]=>[3,1,1,1]
[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[[1,2,6],[3,5],[4]]=>[[1,2,3],[4,6],[5]]=>[3,1,2]
[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[[1,3,6],[2,5],[4]]=>[[1,2,3],[4,5],[6]]=>[3,2,1]
[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[[1,3,6],[2,5],[4]]=>[[1,2,3],[4,5],[6]]=>[3,2,1]
[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[[1,2,3,6],[4,5]]=>[[1,2,3,6],[4,5]]=>[3,3]
[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[[1,5,6],[2],[3],[4]]=>[[1,2,3],[4],[5],[6]]=>[3,1,1,1]
[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[[1,2,6],[3,5],[4]]=>[[1,2,3],[4,6],[5]]=>[3,1,2]
[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[[1,4,5,6],[2],[3]]=>[[1,2,3,4],[5],[6]]=>[4,1,1]
[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[[1,2,5,6],[3,4]]=>[[1,2,3,4],[5,6]]=>[4,2]
[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[[1,5,6],[2],[3],[4]]=>[[1,2,3],[4],[5],[6]]=>[3,1,1,1]
[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[[1,3,5,6],[2],[4]]=>[[1,2,3,5],[4],[6]]=>[3,2,1]
[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[[1,4,5,6],[2],[3]]=>[[1,2,3,4],[5],[6]]=>[4,1,1]
[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[[1,4,5,6],[2],[3]]=>[[1,2,3,4],[5],[6]]=>[4,1,1]
[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[[1,3,4,5,6],[2]]=>[[1,2,3,4,5],[6]]=>[5,1]
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[[1,5,6],[2],[3],[4]]=>[[1,2,3],[4],[5],[6]]=>[3,1,1,1]
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[[1,2,5,6],[3],[4]]=>[[1,2,3,6],[4],[5]]=>[3,1,2]
[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[[1,3,5,6],[2],[4]]=>[[1,2,3,5],[4],[6]]=>[3,2,1]
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[[1,3,5,6],[2],[4]]=>[[1,2,3,5],[4],[6]]=>[3,2,1]
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[[1,2,3,5,6],[4]]=>[[1,2,3,5,6],[4]]=>[3,3]
[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[[1,4,5,6],[2],[3]]=>[[1,2,3,4],[5],[6]]=>[4,1,1]
[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[[1,2,5,6],[3,4]]=>[[1,2,3,4],[5,6]]=>[4,2]
[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[[1,4,5,6],[2],[3]]=>[[1,2,3,4],[5],[6]]=>[4,1,1]
[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[[1,3,4,5,6],[2]]=>[[1,2,3,4,5],[6]]=>[5,1]
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[[1,4,5,6],[2],[3]]=>[[1,2,3,4],[5],[6]]=>[4,1,1]
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[[1,2,4,5,6],[3]]=>[[1,2,3,4,6],[5]]=>[4,2]
[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[[1,3,4,5,6],[2]]=>[[1,2,3,4,5],[6]]=>[5,1]
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[[1,3,4,5,6],[2]]=>[[1,2,3,4,5],[6]]=>[5,1]
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[[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],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7]]=>[[1,7],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,2]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[[1,3],[2],[4],[5],[6],[7]]=>[[1,6],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,1]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[[1,3],[2],[4],[5],[6],[7]]=>[[1,6],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,1]
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[[1,2,3],[4],[5],[6],[7]]=>[[1,6,7],[2],[3],[4],[5]]=>[1,1,1,1,3]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[[1,4],[2],[3],[5],[6],[7]]=>[[1,5],[2],[3],[4],[6],[7]]=>[1,1,1,2,1,1]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[[1,2],[3,4],[5],[6],[7]]=>[[1,5],[2,7],[3],[4],[6]]=>[1,1,1,2,2]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[[1,4],[2],[3],[5],[6],[7]]=>[[1,5],[2],[3],[4],[6],[7]]=>[1,1,1,2,1,1]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[[1,3,4],[2],[5],[6],[7]]=>[[1,5,6],[2],[3],[4],[7]]=>[1,1,1,3,1]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[[1,4],[2],[3],[5],[6],[7]]=>[[1,5],[2],[3],[4],[6],[7]]=>[1,1,1,2,1,1]
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[[1,2,4],[3],[5],[6],[7]]=>[[1,5,7],[2],[3],[4],[6]]=>[1,1,1,2,2]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[[1,3,4],[2],[5],[6],[7]]=>[[1,5,6],[2],[3],[4],[7]]=>[1,1,1,3,1]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[[1,3,4],[2],[5],[6],[7]]=>[[1,5,6],[2],[3],[4],[7]]=>[1,1,1,3,1]
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[[1,2,3,4],[5],[6],[7]]=>[[1,5,6,7],[2],[3],[4]]=>[1,1,1,4]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[[1,5],[2],[3],[4],[6],[7]]=>[[1,4],[2],[3],[5],[6],[7]]=>[1,1,2,1,1,1]
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[[1,2],[3,5],[4],[6],[7]]=>[[1,4],[2,7],[3],[5],[6]]=>[1,1,2,1,2]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[[1,3],[2,5],[4],[6],[7]]=>[[1,4],[2,6],[3],[5],[7]]=>[1,1,2,2,1]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[[1,3],[2,5],[4],[6],[7]]=>[[1,4],[2,6],[3],[5],[7]]=>[1,1,2,2,1]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[[1,2,3],[4,5],[6],[7]]=>[[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]]=>[[1,4],[2],[3],[5],[6],[7]]=>[1,1,2,1,1,1]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[[1,2],[3,5],[4],[6],[7]]=>[[1,4],[2,7],[3],[5],[6]]=>[1,1,2,1,2]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[[1,4,5],[2],[3],[6],[7]]=>[[1,4,5],[2],[3],[6],[7]]=>[1,1,3,1,1]
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[[1,2,5],[3,4],[6],[7]]=>[[1,4,5],[2,7],[3],[6]]=>[1,1,3,2]
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[[1,5],[2],[3],[4],[6],[7]]=>[[1,4],[2],[3],[5],[6],[7]]=>[1,1,2,1,1,1]
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[[1,3,5],[2],[4],[6],[7]]=>[[1,4,6],[2],[3],[5],[7]]=>[1,1,2,2,1]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[[1,4,5],[2],[3],[6],[7]]=>[[1,4,5],[2],[3],[6],[7]]=>[1,1,3,1,1]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[[1,4,5],[2],[3],[6],[7]]=>[[1,4,5],[2],[3],[6],[7]]=>[1,1,3,1,1]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[[1,3,4,5],[2],[6],[7]]=>[[1,4,5,6],[2],[3],[7]]=>[1,1,4,1]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[[1,5],[2],[3],[4],[6],[7]]=>[[1,4],[2],[3],[5],[6],[7]]=>[1,1,2,1,1,1]
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[[1,2,5],[3],[4],[6],[7]]=>[[1,4,7],[2],[3],[5],[6]]=>[1,1,2,1,2]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[[1,3,5],[2],[4],[6],[7]]=>[[1,4,6],[2],[3],[5],[7]]=>[1,1,2,2,1]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[[1,3,5],[2],[4],[6],[7]]=>[[1,4,6],[2],[3],[5],[7]]=>[1,1,2,2,1]
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[[1,2,3,5],[4],[6],[7]]=>[[1,4,6,7],[2],[3],[5]]=>[1,1,2,3]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[[1,4,5],[2],[3],[6],[7]]=>[[1,4,5],[2],[3],[6],[7]]=>[1,1,3,1,1]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[[1,2,5],[3,4],[6],[7]]=>[[1,4,5],[2,7],[3],[6]]=>[1,1,3,2]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[[1,4,5],[2],[3],[6],[7]]=>[[1,4,5],[2],[3],[6],[7]]=>[1,1,3,1,1]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[[1,3,4,5],[2],[6],[7]]=>[[1,4,5,6],[2],[3],[7]]=>[1,1,4,1]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[[1,4,5],[2],[3],[6],[7]]=>[[1,4,5],[2],[3],[6],[7]]=>[1,1,3,1,1]
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[[1,2,4,5],[3],[6],[7]]=>[[1,4,5,7],[2],[3],[6]]=>[1,1,3,2]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[[1,3,4,5],[2],[6],[7]]=>[[1,4,5,6],[2],[3],[7]]=>[1,1,4,1]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[[1,3,4,5],[2],[6],[7]]=>[[1,4,5,6],[2],[3],[7]]=>[1,1,4,1]
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[[1,2,3,4,5],[6],[7]]=>[[1,4,5,6,7],[2],[3]]=>[1,1,5]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[[1,6],[2],[3],[4],[5],[7]]=>[[1,3],[2],[4],[5],[6],[7]]=>[1,2,1,1,1,1]
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[[1,2],[3,6],[4],[5],[7]]=>[[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]]=>[[1,3],[2,6],[4],[5],[7]]=>[1,2,1,2,1]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[[1,3],[2,6],[4],[5],[7]]=>[[1,3],[2,6],[4],[5],[7]]=>[1,2,1,2,1]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[[1,2,3],[4,6],[5],[7]]=>[[1,3,7],[2,6],[4],[5]]=>[1,2,1,3]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[[1,4],[2,6],[3],[5],[7]]=>[[1,3],[2,5],[4],[6],[7]]=>[1,2,2,1,1]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[[1,2],[3,4],[5,6],[7]]=>[[1,3],[2,5],[4,7],[6]]=>[1,2,2,2]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[[1,4],[2,6],[3],[5],[7]]=>[[1,3],[2,5],[4],[6],[7]]=>[1,2,2,1,1]
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[[1,3,4],[2,6],[5],[7]]=>[[1,3,6],[2,5],[4],[7]]=>[1,2,3,1]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[[1,4],[2,6],[3],[5],[7]]=>[[1,3],[2,5],[4],[6],[7]]=>[1,2,2,1,1]
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[[1,2,4],[3,6],[5],[7]]=>[[1,3,7],[2,5],[4],[6]]=>[1,2,2,2]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[[1,3,4],[2,6],[5],[7]]=>[[1,3,6],[2,5],[4],[7]]=>[1,2,3,1]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[[1,3,4],[2,6],[5],[7]]=>[[1,3,6],[2,5],[4],[7]]=>[1,2,3,1]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[[1,2,3,4],[5,6],[7]]=>[[1,3,6,7],[2,5],[4]]=>[1,2,4]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[[1,6],[2],[3],[4],[5],[7]]=>[[1,3],[2],[4],[5],[6],[7]]=>[1,2,1,1,1,1]
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[[1,2],[3,6],[4],[5],[7]]=>[[1,3],[2,7],[4],[5],[6]]=>[1,2,1,1,2]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[[1,3],[2,6],[4],[5],[7]]=>[[1,3],[2,6],[4],[5],[7]]=>[1,2,1,2,1]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[[1,3],[2,6],[4],[5],[7]]=>[[1,3],[2,6],[4],[5],[7]]=>[1,2,1,2,1]
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[[1,2,3],[4,6],[5],[7]]=>[[1,3,7],[2,6],[4],[5]]=>[1,2,1,3]
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[[1,5,6],[2],[3],[4],[7]]=>[[1,3,4],[2],[5],[6],[7]]=>[1,3,1,1,1]
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[[1,2,6],[3,5],[4],[7]]=>[[1,3,4],[2,7],[5],[6]]=>[1,3,1,2]
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[[1,3,6],[2,5],[4],[7]]=>[[1,3,4],[2,6],[5],[7]]=>[1,3,2,1]
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[[1,3,6],[2,5],[4],[7]]=>[[1,3,4],[2,6],[5],[7]]=>[1,3,2,1]
[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[[1,2,3],[4,5,6],[7]]=>[[1,3,4],[2,6,7],[5]]=>[1,3,3]
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[[1,6],[2],[3],[4],[5],[7]]=>[[1,3],[2],[4],[5],[6],[7]]=>[1,2,1,1,1,1]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[[1,2],[3,6],[4],[5],[7]]=>[[1,3],[2,7],[4],[5],[6]]=>[1,2,1,1,2]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[[1,4,6],[2],[3],[5],[7]]=>[[1,3,5],[2],[4],[6],[7]]=>[1,2,2,1,1]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[[1,2,6],[3,4],[5],[7]]=>[[1,3,5],[2,7],[4],[6]]=>[1,2,2,2]
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[[1,5,6],[2],[3],[4],[7]]=>[[1,3,4],[2],[5],[6],[7]]=>[1,3,1,1,1]
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[[1,2,6],[3,5],[4],[7]]=>[[1,3,4],[2,7],[5],[6]]=>[1,3,1,2]
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[[1,5,6],[2],[3],[4],[7]]=>[[1,3,4],[2],[5],[6],[7]]=>[1,3,1,1,1]
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[[1,2,6],[3,5],[4],[7]]=>[[1,3,4],[2,7],[5],[6]]=>[1,3,1,2]
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[[1,4,5,6],[2],[3],[7]]=>[[1,3,4,5],[2],[6],[7]]=>[1,4,1,1]
[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[[1,2,5,6],[3,4],[7]]=>[[1,3,4,5],[2,7],[6]]=>[1,4,2]
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[[1,6],[2],[3],[4],[5],[7]]=>[[1,3],[2],[4],[5],[6],[7]]=>[1,2,1,1,1,1]
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[[1,3,6],[2],[4],[5],[7]]=>[[1,3,6],[2],[4],[5],[7]]=>[1,2,1,2,1]
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[[1,4,6],[2],[3],[5],[7]]=>[[1,3,5],[2],[4],[6],[7]]=>[1,2,2,1,1]
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[[1,4,6],[2],[3],[5],[7]]=>[[1,3,5],[2],[4],[6],[7]]=>[1,2,2,1,1]
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[[1,3,4,6],[2],[5],[7]]=>[[1,3,5,6],[2],[4],[7]]=>[1,2,3,1]
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[[1,5,6],[2],[3],[4],[7]]=>[[1,3,4],[2],[5],[6],[7]]=>[1,3,1,1,1]
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[[1,3,6],[2,5],[4],[7]]=>[[1,3,4],[2,6],[5],[7]]=>[1,3,2,1]
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[[1,5,6],[2],[3],[4],[7]]=>[[1,3,4],[2],[5],[6],[7]]=>[1,3,1,1,1]
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[[1,4,5,6],[2],[3],[7]]=>[[1,3,4,5],[2],[6],[7]]=>[1,4,1,1]
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[[1,5,6],[2],[3],[4],[7]]=>[[1,3,4],[2],[5],[6],[7]]=>[1,3,1,1,1]
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[[1,3,5,6],[2],[4],[7]]=>[[1,3,4,6],[2],[5],[7]]=>[1,3,2,1]
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[[1,4,5,6],[2],[3],[7]]=>[[1,3,4,5],[2],[6],[7]]=>[1,4,1,1]
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[[1,4,5,6],[2],[3],[7]]=>[[1,3,4,5],[2],[6],[7]]=>[1,4,1,1]
[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[[1,3,4,5,6],[2],[7]]=>[[1,3,4,5,6],[2],[7]]=>[1,5,1]
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[[1,6],[2],[3],[4],[5],[7]]=>[[1,3],[2],[4],[5],[6],[7]]=>[1,2,1,1,1,1]
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[[1,2,6],[3],[4],[5],[7]]=>[[1,3,7],[2],[4],[5],[6]]=>[1,2,1,1,2]
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[[1,3,6],[2],[4],[5],[7]]=>[[1,3,6],[2],[4],[5],[7]]=>[1,2,1,2,1]
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[[1,3,6],[2],[4],[5],[7]]=>[[1,3,6],[2],[4],[5],[7]]=>[1,2,1,2,1]
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[[1,2,3,6],[4],[5],[7]]=>[[1,3,6,7],[2],[4],[5]]=>[1,2,1,3]
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[[1,4,6],[2],[3],[5],[7]]=>[[1,3,5],[2],[4],[6],[7]]=>[1,2,2,1,1]
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[[1,2,6],[3,4],[5],[7]]=>[[1,3,5],[2,7],[4],[6]]=>[1,2,2,2]
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[[1,4,6],[2],[3],[5],[7]]=>[[1,3,5],[2],[4],[6],[7]]=>[1,2,2,1,1]
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[[1,3,4,6],[2],[5],[7]]=>[[1,3,5,6],[2],[4],[7]]=>[1,2,3,1]
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[[1,4,6],[2],[3],[5],[7]]=>[[1,3,5],[2],[4],[6],[7]]=>[1,2,2,1,1]
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[[1,2,4,6],[3],[5],[7]]=>[[1,3,5,7],[2],[4],[6]]=>[1,2,2,2]
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[[1,3,4,6],[2],[5],[7]]=>[[1,3,5,6],[2],[4],[7]]=>[1,2,3,1]
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[[1,3,4,6],[2],[5],[7]]=>[[1,3,5,6],[2],[4],[7]]=>[1,2,3,1]
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[[1,2,3,4,6],[5],[7]]=>[[1,3,5,6,7],[2],[4]]=>[1,2,4]
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[[1,5,6],[2],[3],[4],[7]]=>[[1,3,4],[2],[5],[6],[7]]=>[1,3,1,1,1]
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[[1,2,6],[3,5],[4],[7]]=>[[1,3,4],[2,7],[5],[6]]=>[1,3,1,2]
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[[1,3,6],[2,5],[4],[7]]=>[[1,3,4],[2,6],[5],[7]]=>[1,3,2,1]
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[[1,3,6],[2,5],[4],[7]]=>[[1,3,4],[2,6],[5],[7]]=>[1,3,2,1]
[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[[1,2,3,6],[4,5],[7]]=>[[1,3,4,7],[2,6],[5]]=>[1,3,3]
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[[1,5,6],[2],[3],[4],[7]]=>[[1,3,4],[2],[5],[6],[7]]=>[1,3,1,1,1]
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[[1,2,6],[3,5],[4],[7]]=>[[1,3,4],[2,7],[5],[6]]=>[1,3,1,2]
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[[1,4,5,6],[2],[3],[7]]=>[[1,3,4,5],[2],[6],[7]]=>[1,4,1,1]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[[1,2,5,6],[3,4],[7]]=>[[1,3,4,5],[2,7],[6]]=>[1,4,2]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[[1,5,6],[2],[3],[4],[7]]=>[[1,3,4],[2],[5],[6],[7]]=>[1,3,1,1,1]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[[1,3,5,6],[2],[4],[7]]=>[[1,3,4,6],[2],[5],[7]]=>[1,3,2,1]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[[1,4,5,6],[2],[3],[7]]=>[[1,3,4,5],[2],[6],[7]]=>[1,4,1,1]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[[1,4,5,6],[2],[3],[7]]=>[[1,3,4,5],[2],[6],[7]]=>[1,4,1,1]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[[1,3,4,5,6],[2],[7]]=>[[1,3,4,5,6],[2],[7]]=>[1,5,1]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[[1,5,6],[2],[3],[4],[7]]=>[[1,3,4],[2],[5],[6],[7]]=>[1,3,1,1,1]
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[[1,2,5,6],[3],[4],[7]]=>[[1,3,4,7],[2],[5],[6]]=>[1,3,1,2]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[[1,3,5,6],[2],[4],[7]]=>[[1,3,4,6],[2],[5],[7]]=>[1,3,2,1]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[[1,3,5,6],[2],[4],[7]]=>[[1,3,4,6],[2],[5],[7]]=>[1,3,2,1]
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[[1,2,3,5,6],[4],[7]]=>[[1,3,4,6,7],[2],[5]]=>[1,3,3]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[[1,4,5,6],[2],[3],[7]]=>[[1,3,4,5],[2],[6],[7]]=>[1,4,1,1]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[[1,2,5,6],[3,4],[7]]=>[[1,3,4,5],[2,7],[6]]=>[1,4,2]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[[1,4,5,6],[2],[3],[7]]=>[[1,3,4,5],[2],[6],[7]]=>[1,4,1,1]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[[1,3,4,5,6],[2],[7]]=>[[1,3,4,5,6],[2],[7]]=>[1,5,1]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[[1,4,5,6],[2],[3],[7]]=>[[1,3,4,5],[2],[6],[7]]=>[1,4,1,1]
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[[1,2,4,5,6],[3],[7]]=>[[1,3,4,5,7],[2],[6]]=>[1,4,2]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[[1,3,4,5,6],[2],[7]]=>[[1,3,4,5,6],[2],[7]]=>[1,5,1]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[[1,3,4,5,6],[2],[7]]=>[[1,3,4,5,6],[2],[7]]=>[1,5,1]
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[[1,2,3,4,5,6],[7]]=>[[1,3,4,5,6,7],[2]]=>[1,6]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[[1,7],[2],[3],[4],[5],[6]]=>[[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]]=>[[1,2],[3,7],[4],[5],[6]]=>[2,1,1,1,2]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[[1,3],[2,7],[4],[5],[6]]=>[[1,2],[3,6],[4],[5],[7]]=>[2,1,1,2,1]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[[1,3],[2,7],[4],[5],[6]]=>[[1,2],[3,6],[4],[5],[7]]=>[2,1,1,2,1]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[[1,2,3],[4,7],[5],[6]]=>[[1,2,7],[3,6],[4],[5]]=>[2,1,1,3]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[[1,4],[2,7],[3],[5],[6]]=>[[1,2],[3,5],[4],[6],[7]]=>[2,1,2,1,1]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[[1,2],[3,4],[5,7],[6]]=>[[1,2],[3,5],[4,7],[6]]=>[2,1,2,2]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[[1,4],[2,7],[3],[5],[6]]=>[[1,2],[3,5],[4],[6],[7]]=>[2,1,2,1,1]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[[1,3,4],[2,7],[5],[6]]=>[[1,2,6],[3,5],[4],[7]]=>[2,1,3,1]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[[1,4],[2,7],[3],[5],[6]]=>[[1,2],[3,5],[4],[6],[7]]=>[2,1,2,1,1]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[[1,2,4],[3,7],[5],[6]]=>[[1,2,7],[3,5],[4],[6]]=>[2,1,2,2]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[[1,3,4],[2,7],[5],[6]]=>[[1,2,6],[3,5],[4],[7]]=>[2,1,3,1]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[[1,3,4],[2,7],[5],[6]]=>[[1,2,6],[3,5],[4],[7]]=>[2,1,3,1]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[[1,2,3,4],[5,7],[6]]=>[[1,2,6,7],[3,5],[4]]=>[2,1,4]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[[1,5],[2,7],[3],[4],[6]]=>[[1,2],[3,4],[5],[6],[7]]=>[2,2,1,1,1]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[[1,2],[3,5],[4,7],[6]]=>[[1,2],[3,4],[5,7],[6]]=>[2,2,1,2]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[[1,3],[2,5],[4,7],[6]]=>[[1,2],[3,4],[5,6],[7]]=>[2,2,2,1]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[[1,3],[2,5],[4,7],[6]]=>[[1,2],[3,4],[5,6],[7]]=>[2,2,2,1]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[[1,2,3],[4,5],[6,7]]=>[[1,2,7],[3,4],[5,6]]=>[2,2,3]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[[1,5],[2,7],[3],[4],[6]]=>[[1,2],[3,4],[5],[6],[7]]=>[2,2,1,1,1]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[[1,2],[3,5],[4,7],[6]]=>[[1,2],[3,4],[5,7],[6]]=>[2,2,1,2]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[[1,4,5],[2,7],[3],[6]]=>[[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]]=>[[1,2,5],[3,4],[6,7]]=>[2,3,2]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[[1,5],[2,7],[3],[4],[6]]=>[[1,2],[3,4],[5],[6],[7]]=>[2,2,1,1,1]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[[1,3,5],[2,7],[4],[6]]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[[1,4,5],[2,7],[3],[6]]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,1,1]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[[1,4,5],[2,7],[3],[6]]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,1,1]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[[1,3,4,5],[2,7],[6]]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[[1,5],[2,7],[3],[4],[6]]=>[[1,2],[3,4],[5],[6],[7]]=>[2,2,1,1,1]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[[1,2,5],[3,7],[4],[6]]=>[[1,2,7],[3,4],[5],[6]]=>[2,2,1,2]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[[1,3,5],[2,7],[4],[6]]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[[1,3,5],[2,7],[4],[6]]=>[[1,2,6],[3,4],[5],[7]]=>[2,2,2,1]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[[1,2,3,5],[4,7],[6]]=>[[1,2,6,7],[3,4],[5]]=>[2,2,3]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[[1,4,5],[2,7],[3],[6]]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,1,1]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[[1,2,5],[3,4],[6,7]]=>[[1,2,5],[3,4],[6,7]]=>[2,3,2]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[[1,4,5],[2,7],[3],[6]]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,1,1]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[[1,3,4,5],[2,7],[6]]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[[1,4,5],[2,7],[3],[6]]=>[[1,2,5],[3,4],[6],[7]]=>[2,3,1,1]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[[1,2,4,5],[3,7],[6]]=>[[1,2,5,7],[3,4],[6]]=>[2,3,2]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[[1,3,4,5],[2,7],[6]]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[[1,3,4,5],[2,7],[6]]=>[[1,2,5,6],[3,4],[7]]=>[2,4,1]
[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[[1,2,3,4,5],[6,7]]=>[[1,2,5,6,7],[3,4]]=>[2,5]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[[1,7],[2],[3],[4],[5],[6]]=>[[1,2],[3],[4],[5],[6],[7]]=>[2,1,1,1,1,1]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[[1,2],[3,7],[4],[5],[6]]=>[[1,2],[3,7],[4],[5],[6]]=>[2,1,1,1,2]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[[1,3],[2,7],[4],[5],[6]]=>[[1,2],[3,6],[4],[5],[7]]=>[2,1,1,2,1]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[[1,3],[2,7],[4],[5],[6]]=>[[1,2],[3,6],[4],[5],[7]]=>[2,1,1,2,1]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[[1,2,3],[4,7],[5],[6]]=>[[1,2,7],[3,6],[4],[5]]=>[2,1,1,3]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[[1,4],[2,7],[3],[5],[6]]=>[[1,2],[3,5],[4],[6],[7]]=>[2,1,2,1,1]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[[1,2],[3,4],[5,7],[6]]=>[[1,2],[3,5],[4,7],[6]]=>[2,1,2,2]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[[1,4],[2,7],[3],[5],[6]]=>[[1,2],[3,5],[4],[6],[7]]=>[2,1,2,1,1]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[[1,3,4],[2,7],[5],[6]]=>[[1,2,6],[3,5],[4],[7]]=>[2,1,3,1]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[[1,4],[2,7],[3],[5],[6]]=>[[1,2],[3,5],[4],[6],[7]]=>[2,1,2,1,1]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[[1,2,4],[3,7],[5],[6]]=>[[1,2,7],[3,5],[4],[6]]=>[2,1,2,2]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[[1,3,4],[2,7],[5],[6]]=>[[1,2,6],[3,5],[4],[7]]=>[2,1,3,1]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[[1,3,4],[2,7],[5],[6]]=>[[1,2,6],[3,5],[4],[7]]=>[2,1,3,1]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[[1,2,3,4],[5,7],[6]]=>[[1,2,6,7],[3,5],[4]]=>[2,1,4]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[[1,6,7],[2],[3],[4],[5]]=>[[1,2,3],[4],[5],[6],[7]]=>[3,1,1,1,1]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[[1,2,7],[3,6],[4],[5]]=>[[1,2,3],[4,7],[5],[6]]=>[3,1,1,2]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[[1,3,7],[2,6],[4],[5]]=>[[1,2,3],[4,6],[5],[7]]=>[3,1,2,1]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[[1,3,7],[2,6],[4],[5]]=>[[1,2,3],[4,6],[5],[7]]=>[3,1,2,1]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[[1,2,3],[4,6,7],[5]]=>[[1,2,3],[4,6,7],[5]]=>[3,1,3]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[[1,4,7],[2,6],[3],[5]]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,1,1]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[[1,2,7],[3,4],[5,6]]=>[[1,2,3],[4,5],[6,7]]=>[3,2,2]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[[1,4,7],[2,6],[3],[5]]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,1,1]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[[1,3,4],[2,6,7],[5]]=>[[1,2,3],[4,5,6],[7]]=>[3,3,1]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[[1,4,7],[2,6],[3],[5]]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,1,1]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[[1,2,4],[3,6,7],[5]]=>[[1,2,3],[4,5,7],[6]]=>[3,2,2]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[[1,3,4],[2,6,7],[5]]=>[[1,2,3],[4,5,6],[7]]=>[3,3,1]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[[1,3,4],[2,6,7],[5]]=>[[1,2,3],[4,5,6],[7]]=>[3,3,1]
[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[[1,2,3,4],[5,6,7]]=>[[1,2,3,7],[4,5,6]]=>[3,4]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[[1,7],[2],[3],[4],[5],[6]]=>[[1,2],[3],[4],[5],[6],[7]]=>[2,1,1,1,1,1]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[[1,2],[3,7],[4],[5],[6]]=>[[1,2],[3,7],[4],[5],[6]]=>[2,1,1,1,2]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[[1,3],[2,7],[4],[5],[6]]=>[[1,2],[3,6],[4],[5],[7]]=>[2,1,1,2,1]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[[1,3],[2,7],[4],[5],[6]]=>[[1,2],[3,6],[4],[5],[7]]=>[2,1,1,2,1]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[[1,2,3],[4,7],[5],[6]]=>[[1,2,7],[3,6],[4],[5]]=>[2,1,1,3]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[[1,5,7],[2],[3],[4],[6]]=>[[1,2,4],[3],[5],[6],[7]]=>[2,2,1,1,1]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[[1,2,7],[3,5],[4],[6]]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,1,2]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[[1,3,7],[2,5],[4],[6]]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[[1,3,7],[2,5],[4],[6]]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[[1,2,3],[4,5,7],[6]]=>[[1,2,4],[3,6,7],[5]]=>[2,2,3]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[[1,6,7],[2],[3],[4],[5]]=>[[1,2,3],[4],[5],[6],[7]]=>[3,1,1,1,1]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[[1,2,7],[3,6],[4],[5]]=>[[1,2,3],[4,7],[5],[6]]=>[3,1,1,2]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[[1,3,7],[2,6],[4],[5]]=>[[1,2,3],[4,6],[5],[7]]=>[3,1,2,1]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[[1,3,7],[2,6],[4],[5]]=>[[1,2,3],[4,6],[5],[7]]=>[3,1,2,1]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[[1,2,3],[4,6,7],[5]]=>[[1,2,3],[4,6,7],[5]]=>[3,1,3]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[[1,6,7],[2],[3],[4],[5]]=>[[1,2,3],[4],[5],[6],[7]]=>[3,1,1,1,1]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[[1,2,7],[3,6],[4],[5]]=>[[1,2,3],[4,7],[5],[6]]=>[3,1,1,2]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[[1,3,7],[2,6],[4],[5]]=>[[1,2,3],[4,6],[5],[7]]=>[3,1,2,1]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[[1,3,7],[2,6],[4],[5]]=>[[1,2,3],[4,6],[5],[7]]=>[3,1,2,1]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[[1,2,3],[4,6,7],[5]]=>[[1,2,3],[4,6,7],[5]]=>[3,1,3]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[[1,5,6,7],[2],[3],[4]]=>[[1,2,3,4],[5],[6],[7]]=>[4,1,1,1]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[[1,2,6,7],[3,5],[4]]=>[[1,2,3,4],[5,7],[6]]=>[4,1,2]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[[1,3,6,7],[2,5],[4]]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[[1,3,6,7],[2,5],[4]]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[[1,2,3,7],[4,5,6]]=>[[1,2,3,4],[5,6,7]]=>[4,3]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[[1,7],[2],[3],[4],[5],[6]]=>[[1,2],[3],[4],[5],[6],[7]]=>[2,1,1,1,1,1]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[[1,2],[3,7],[4],[5],[6]]=>[[1,2],[3,7],[4],[5],[6]]=>[2,1,1,1,2]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[[1,4,7],[2],[3],[5],[6]]=>[[1,2,5],[3],[4],[6],[7]]=>[2,1,2,1,1]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[[1,2,7],[3,4],[5],[6]]=>[[1,2,5],[3,7],[4],[6]]=>[2,1,2,2]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[[1,5,7],[2],[3],[4],[6]]=>[[1,2,4],[3],[5],[6],[7]]=>[2,2,1,1,1]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[[1,2,7],[3,5],[4],[6]]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,1,2]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[[1,5,7],[2],[3],[4],[6]]=>[[1,2,4],[3],[5],[6],[7]]=>[2,2,1,1,1]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[[1,2,7],[3,5],[4],[6]]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,1,2]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[[1,4,5,7],[2],[3],[6]]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,1,1]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[[1,2,5,7],[3,4],[6]]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[[1,6,7],[2],[3],[4],[5]]=>[[1,2,3],[4],[5],[6],[7]]=>[3,1,1,1,1]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[[1,2,7],[3,6],[4],[5]]=>[[1,2,3],[4,7],[5],[6]]=>[3,1,1,2]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[[1,4,7],[2,6],[3],[5]]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,1,1]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[[1,2,7],[3,4],[5,6]]=>[[1,2,3],[4,5],[6,7]]=>[3,2,2]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[[1,6,7],[2],[3],[4],[5]]=>[[1,2,3],[4],[5],[6],[7]]=>[3,1,1,1,1]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[[1,2,7],[3,6],[4],[5]]=>[[1,2,3],[4,7],[5],[6]]=>[3,1,1,2]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[[1,5,6,7],[2],[3],[4]]=>[[1,2,3,4],[5],[6],[7]]=>[4,1,1,1]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[[1,2,6,7],[3,5],[4]]=>[[1,2,3,4],[5,7],[6]]=>[4,1,2]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[[1,6,7],[2],[3],[4],[5]]=>[[1,2,3],[4],[5],[6],[7]]=>[3,1,1,1,1]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[[1,2,7],[3,6],[4],[5]]=>[[1,2,3],[4,7],[5],[6]]=>[3,1,1,2]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[[1,4,6,7],[2],[3],[5]]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,1,1]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[[1,2,6,7],[3,4],[5]]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[[1,5,6,7],[2],[3],[4]]=>[[1,2,3,4],[5],[6],[7]]=>[4,1,1,1]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[[1,2,6,7],[3,5],[4]]=>[[1,2,3,4],[5,7],[6]]=>[4,1,2]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[[1,5,6,7],[2],[3],[4]]=>[[1,2,3,4],[5],[6],[7]]=>[4,1,1,1]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[[1,2,6,7],[3,5],[4]]=>[[1,2,3,4],[5,7],[6]]=>[4,1,2]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[[1,4,5,6,7],[2],[3]]=>[[1,2,3,4,5],[6],[7]]=>[5,1,1]
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[[1,2,5,6,7],[3,4]]=>[[1,2,3,4,5],[6,7]]=>[5,2]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[[1,7],[2],[3],[4],[5],[6]]=>[[1,2],[3],[4],[5],[6],[7]]=>[2,1,1,1,1,1]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[[1,3,7],[2],[4],[5],[6]]=>[[1,2,6],[3],[4],[5],[7]]=>[2,1,1,2,1]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[[1,4,7],[2],[3],[5],[6]]=>[[1,2,5],[3],[4],[6],[7]]=>[2,1,2,1,1]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[[1,4,7],[2],[3],[5],[6]]=>[[1,2,5],[3],[4],[6],[7]]=>[2,1,2,1,1]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[[1,3,4,7],[2],[5],[6]]=>[[1,2,5,6],[3],[4],[7]]=>[2,1,3,1]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[[1,5,7],[2],[3],[4],[6]]=>[[1,2,4],[3],[5],[6],[7]]=>[2,2,1,1,1]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[[1,3,7],[2,5],[4],[6]]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[[1,5,7],[2],[3],[4],[6]]=>[[1,2,4],[3],[5],[6],[7]]=>[2,2,1,1,1]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[[1,4,5,7],[2],[3],[6]]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,1,1]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[[1,5,7],[2],[3],[4],[6]]=>[[1,2,4],[3],[5],[6],[7]]=>[2,2,1,1,1]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[[1,3,5,7],[2],[4],[6]]=>[[1,2,4,6],[3],[5],[7]]=>[2,2,2,1]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[[1,4,5,7],[2],[3],[6]]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,1,1]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[[1,4,5,7],[2],[3],[6]]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,1,1]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[[1,3,4,5,7],[2],[6]]=>[[1,2,4,5,6],[3],[7]]=>[2,4,1]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[[1,6,7],[2],[3],[4],[5]]=>[[1,2,3],[4],[5],[6],[7]]=>[3,1,1,1,1]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[[1,3,7],[2,6],[4],[5]]=>[[1,2,3],[4,6],[5],[7]]=>[3,1,2,1]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[[1,4,7],[2,6],[3],[5]]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,1,1]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[[1,4,7],[2,6],[3],[5]]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,1,1]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[[1,3,4,7],[2,6],[5]]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[[1,6,7],[2],[3],[4],[5]]=>[[1,2,3],[4],[5],[6],[7]]=>[3,1,1,1,1]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[[1,3,7],[2,6],[4],[5]]=>[[1,2,3],[4,6],[5],[7]]=>[3,1,2,1]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[[1,5,6,7],[2],[3],[4]]=>[[1,2,3,4],[5],[6],[7]]=>[4,1,1,1]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[[1,3,6,7],[2,5],[4]]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[[1,6,7],[2],[3],[4],[5]]=>[[1,2,3],[4],[5],[6],[7]]=>[3,1,1,1,1]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[[1,4,6,7],[2],[3],[5]]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,1,1]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[[1,5,6,7],[2],[3],[4]]=>[[1,2,3,4],[5],[6],[7]]=>[4,1,1,1]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[[1,5,6,7],[2],[3],[4]]=>[[1,2,3,4],[5],[6],[7]]=>[4,1,1,1]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[[1,4,5,6,7],[2],[3]]=>[[1,2,3,4,5],[6],[7]]=>[5,1,1]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[[1,6,7],[2],[3],[4],[5]]=>[[1,2,3],[4],[5],[6],[7]]=>[3,1,1,1,1]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[[1,3,6,7],[2],[4],[5]]=>[[1,2,3,6],[4],[5],[7]]=>[3,1,2,1]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[[1,4,6,7],[2],[3],[5]]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,1,1]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[[1,4,6,7],[2],[3],[5]]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,1,1]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[[1,3,4,6,7],[2],[5]]=>[[1,2,3,5,6],[4],[7]]=>[3,3,1]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[[1,5,6,7],[2],[3],[4]]=>[[1,2,3,4],[5],[6],[7]]=>[4,1,1,1]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[[1,3,6,7],[2,5],[4]]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[[1,5,6,7],[2],[3],[4]]=>[[1,2,3,4],[5],[6],[7]]=>[4,1,1,1]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[[1,4,5,6,7],[2],[3]]=>[[1,2,3,4,5],[6],[7]]=>[5,1,1]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[[1,5,6,7],[2],[3],[4]]=>[[1,2,3,4],[5],[6],[7]]=>[4,1,1,1]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[[1,3,5,6,7],[2],[4]]=>[[1,2,3,4,6],[5],[7]]=>[4,2,1]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[[1,4,5,6,7],[2],[3]]=>[[1,2,3,4,5],[6],[7]]=>[5,1,1]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[[1,4,5,6,7],[2],[3]]=>[[1,2,3,4,5],[6],[7]]=>[5,1,1]
[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[[1,3,4,5,6,7],[2]]=>[[1,2,3,4,5,6],[7]]=>[6,1]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[[1,7],[2],[3],[4],[5],[6]]=>[[1,2],[3],[4],[5],[6],[7]]=>[2,1,1,1,1,1]
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[[1,2,7],[3],[4],[5],[6]]=>[[1,2,7],[3],[4],[5],[6]]=>[2,1,1,1,2]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[[1,3,7],[2],[4],[5],[6]]=>[[1,2,6],[3],[4],[5],[7]]=>[2,1,1,2,1]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[[1,3,7],[2],[4],[5],[6]]=>[[1,2,6],[3],[4],[5],[7]]=>[2,1,1,2,1]
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[[1,2,3,7],[4],[5],[6]]=>[[1,2,6,7],[3],[4],[5]]=>[2,1,1,3]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[[1,4,7],[2],[3],[5],[6]]=>[[1,2,5],[3],[4],[6],[7]]=>[2,1,2,1,1]
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[[1,2,7],[3,4],[5],[6]]=>[[1,2,5],[3,7],[4],[6]]=>[2,1,2,2]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[[1,4,7],[2],[3],[5],[6]]=>[[1,2,5],[3],[4],[6],[7]]=>[2,1,2,1,1]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[[1,3,4,7],[2],[5],[6]]=>[[1,2,5,6],[3],[4],[7]]=>[2,1,3,1]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[[1,4,7],[2],[3],[5],[6]]=>[[1,2,5],[3],[4],[6],[7]]=>[2,1,2,1,1]
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[[1,2,4,7],[3],[5],[6]]=>[[1,2,5,7],[3],[4],[6]]=>[2,1,2,2]
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[[1,3,4,7],[2],[5],[6]]=>[[1,2,5,6],[3],[4],[7]]=>[2,1,3,1]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[[1,3,4,7],[2],[5],[6]]=>[[1,2,5,6],[3],[4],[7]]=>[2,1,3,1]
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[[1,2,3,4,7],[5],[6]]=>[[1,2,5,6,7],[3],[4]]=>[2,1,4]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[[1,5,7],[2],[3],[4],[6]]=>[[1,2,4],[3],[5],[6],[7]]=>[2,2,1,1,1]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[[1,2,7],[3,5],[4],[6]]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,1,2]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[[1,3,7],[2,5],[4],[6]]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[[1,3,7],[2,5],[4],[6]]=>[[1,2,4],[3,6],[5],[7]]=>[2,2,2,1]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[[1,2,3,7],[4,5],[6]]=>[[1,2,4,7],[3,6],[5]]=>[2,2,3]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[[1,5,7],[2],[3],[4],[6]]=>[[1,2,4],[3],[5],[6],[7]]=>[2,2,1,1,1]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[[1,2,7],[3,5],[4],[6]]=>[[1,2,4],[3,7],[5],[6]]=>[2,2,1,2]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[[1,4,5,7],[2],[3],[6]]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,1,1]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[[1,2,5,7],[3,4],[6]]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[[1,5,7],[2],[3],[4],[6]]=>[[1,2,4],[3],[5],[6],[7]]=>[2,2,1,1,1]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[[1,3,5,7],[2],[4],[6]]=>[[1,2,4,6],[3],[5],[7]]=>[2,2,2,1]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[[1,4,5,7],[2],[3],[6]]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,1,1]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[[1,4,5,7],[2],[3],[6]]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,1,1]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[[1,3,4,5,7],[2],[6]]=>[[1,2,4,5,6],[3],[7]]=>[2,4,1]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[[1,5,7],[2],[3],[4],[6]]=>[[1,2,4],[3],[5],[6],[7]]=>[2,2,1,1,1]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[[1,2,5,7],[3],[4],[6]]=>[[1,2,4,7],[3],[5],[6]]=>[2,2,1,2]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[[1,3,5,7],[2],[4],[6]]=>[[1,2,4,6],[3],[5],[7]]=>[2,2,2,1]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[[1,3,5,7],[2],[4],[6]]=>[[1,2,4,6],[3],[5],[7]]=>[2,2,2,1]
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[[1,2,3,5,7],[4],[6]]=>[[1,2,4,6,7],[3],[5]]=>[2,2,3]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[[1,4,5,7],[2],[3],[6]]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,1,1]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[[1,2,5,7],[3,4],[6]]=>[[1,2,4,5],[3,7],[6]]=>[2,3,2]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[[1,4,5,7],[2],[3],[6]]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,1,1]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[[1,3,4,5,7],[2],[6]]=>[[1,2,4,5,6],[3],[7]]=>[2,4,1]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[[1,4,5,7],[2],[3],[6]]=>[[1,2,4,5],[3],[6],[7]]=>[2,3,1,1]
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[[1,2,4,5,7],[3],[6]]=>[[1,2,4,5,7],[3],[6]]=>[2,3,2]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[[1,3,4,5,7],[2],[6]]=>[[1,2,4,5,6],[3],[7]]=>[2,4,1]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[[1,3,4,5,7],[2],[6]]=>[[1,2,4,5,6],[3],[7]]=>[2,4,1]
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[[1,2,3,4,5,7],[6]]=>[[1,2,4,5,6,7],[3]]=>[2,5]
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[[1,6,7],[2],[3],[4],[5]]=>[[1,2,3],[4],[5],[6],[7]]=>[3,1,1,1,1]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[[1,2,7],[3,6],[4],[5]]=>[[1,2,3],[4,7],[5],[6]]=>[3,1,1,2]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[[1,3,7],[2,6],[4],[5]]=>[[1,2,3],[4,6],[5],[7]]=>[3,1,2,1]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[[1,3,7],[2,6],[4],[5]]=>[[1,2,3],[4,6],[5],[7]]=>[3,1,2,1]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[[1,2,3,7],[4,6],[5]]=>[[1,2,3,7],[4,6],[5]]=>[3,1,3]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[[1,4,7],[2,6],[3],[5]]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,1,1]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[[1,2,7],[3,4],[5,6]]=>[[1,2,3],[4,5],[6,7]]=>[3,2,2]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[[1,4,7],[2,6],[3],[5]]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,1,1]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[[1,3,4,7],[2,6],[5]]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[[1,4,7],[2,6],[3],[5]]=>[[1,2,3],[4,5],[6],[7]]=>[3,2,1,1]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[[1,2,4,7],[3,6],[5]]=>[[1,2,3,7],[4,5],[6]]=>[3,2,2]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[[1,3,4,7],[2,6],[5]]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[[1,3,4,7],[2,6],[5]]=>[[1,2,3,6],[4,5],[7]]=>[3,3,1]
[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[[1,2,3,4,7],[5,6]]=>[[1,2,3,6,7],[4,5]]=>[3,4]
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[[1,6,7],[2],[3],[4],[5]]=>[[1,2,3],[4],[5],[6],[7]]=>[3,1,1,1,1]
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[[1,2,7],[3,6],[4],[5]]=>[[1,2,3],[4,7],[5],[6]]=>[3,1,1,2]
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[[1,3,7],[2,6],[4],[5]]=>[[1,2,3],[4,6],[5],[7]]=>[3,1,2,1]
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[[1,3,7],[2,6],[4],[5]]=>[[1,2,3],[4,6],[5],[7]]=>[3,1,2,1]
[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[[1,2,3,7],[4,6],[5]]=>[[1,2,3,7],[4,6],[5]]=>[3,1,3]
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[[1,5,6,7],[2],[3],[4]]=>[[1,2,3,4],[5],[6],[7]]=>[4,1,1,1]
[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[[1,2,6,7],[3,5],[4]]=>[[1,2,3,4],[5,7],[6]]=>[4,1,2]
[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[[1,3,6,7],[2,5],[4]]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]
[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[[1,3,6,7],[2,5],[4]]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]
[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[[1,2,3,7],[4,5,6]]=>[[1,2,3,4],[5,6,7]]=>[4,3]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[[1,6,7],[2],[3],[4],[5]]=>[[1,2,3],[4],[5],[6],[7]]=>[3,1,1,1,1]
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[[1,2,7],[3,6],[4],[5]]=>[[1,2,3],[4,7],[5],[6]]=>[3,1,1,2]
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[[1,4,6,7],[2],[3],[5]]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,1,1]
[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[[1,2,6,7],[3,4],[5]]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[[1,5,6,7],[2],[3],[4]]=>[[1,2,3,4],[5],[6],[7]]=>[4,1,1,1]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[[1,2,6,7],[3,5],[4]]=>[[1,2,3,4],[5,7],[6]]=>[4,1,2]
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[[1,5,6,7],[2],[3],[4]]=>[[1,2,3,4],[5],[6],[7]]=>[4,1,1,1]
[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[[1,2,6,7],[3,5],[4]]=>[[1,2,3,4],[5,7],[6]]=>[4,1,2]
[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[[1,4,5,6,7],[2],[3]]=>[[1,2,3,4,5],[6],[7]]=>[5,1,1]
[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[[1,2,5,6,7],[3,4]]=>[[1,2,3,4,5],[6,7]]=>[5,2]
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[[1,6,7],[2],[3],[4],[5]]=>[[1,2,3],[4],[5],[6],[7]]=>[3,1,1,1,1]
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[[1,3,6,7],[2],[4],[5]]=>[[1,2,3,6],[4],[5],[7]]=>[3,1,2,1]
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[[1,4,6,7],[2],[3],[5]]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,1,1]
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[[1,4,6,7],[2],[3],[5]]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,1,1]
[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[[1,3,4,6,7],[2],[5]]=>[[1,2,3,5,6],[4],[7]]=>[3,3,1]
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[[1,5,6,7],[2],[3],[4]]=>[[1,2,3,4],[5],[6],[7]]=>[4,1,1,1]
[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[[1,3,6,7],[2,5],[4]]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[[1,5,6,7],[2],[3],[4]]=>[[1,2,3,4],[5],[6],[7]]=>[4,1,1,1]
[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[[1,4,5,6,7],[2],[3]]=>[[1,2,3,4,5],[6],[7]]=>[5,1,1]
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[[1,5,6,7],[2],[3],[4]]=>[[1,2,3,4],[5],[6],[7]]=>[4,1,1,1]
[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[[1,3,5,6,7],[2],[4]]=>[[1,2,3,4,6],[5],[7]]=>[4,2,1]
[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[[1,4,5,6,7],[2],[3]]=>[[1,2,3,4,5],[6],[7]]=>[5,1,1]
[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[[1,4,5,6,7],[2],[3]]=>[[1,2,3,4,5],[6],[7]]=>[5,1,1]
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[[1,3,4,5,6,7],[2]]=>[[1,2,3,4,5,6],[7]]=>[6,1]
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[[1,6,7],[2],[3],[4],[5]]=>[[1,2,3],[4],[5],[6],[7]]=>[3,1,1,1,1]
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[[1,2,6,7],[3],[4],[5]]=>[[1,2,3,7],[4],[5],[6]]=>[3,1,1,2]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[[1,3,6,7],[2],[4],[5]]=>[[1,2,3,6],[4],[5],[7]]=>[3,1,2,1]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[[1,3,6,7],[2],[4],[5]]=>[[1,2,3,6],[4],[5],[7]]=>[3,1,2,1]
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[[1,2,3,6,7],[4],[5]]=>[[1,2,3,6,7],[4],[5]]=>[3,1,3]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[[1,4,6,7],[2],[3],[5]]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,1,1]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[[1,2,6,7],[3,4],[5]]=>[[1,2,3,5],[4,7],[6]]=>[3,2,2]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[[1,4,6,7],[2],[3],[5]]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,1,1]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[[1,3,4,6,7],[2],[5]]=>[[1,2,3,5,6],[4],[7]]=>[3,3,1]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[[1,4,6,7],[2],[3],[5]]=>[[1,2,3,5],[4],[6],[7]]=>[3,2,1,1]
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[[1,2,4,6,7],[3],[5]]=>[[1,2,3,5,7],[4],[6]]=>[3,2,2]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[[1,3,4,6,7],[2],[5]]=>[[1,2,3,5,6],[4],[7]]=>[3,3,1]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[[1,3,4,6,7],[2],[5]]=>[[1,2,3,5,6],[4],[7]]=>[3,3,1]
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[[1,2,3,4,6,7],[5]]=>[[1,2,3,5,6,7],[4]]=>[3,4]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[[1,5,6,7],[2],[3],[4]]=>[[1,2,3,4],[5],[6],[7]]=>[4,1,1,1]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[[1,2,6,7],[3,5],[4]]=>[[1,2,3,4],[5,7],[6]]=>[4,1,2]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[[1,3,6,7],[2,5],[4]]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[[1,3,6,7],[2,5],[4]]=>[[1,2,3,4],[5,6],[7]]=>[4,2,1]
[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[[1,2,3,6,7],[4,5]]=>[[1,2,3,4,7],[5,6]]=>[4,3]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[[1,5,6,7],[2],[3],[4]]=>[[1,2,3,4],[5],[6],[7]]=>[4,1,1,1]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[[1,2,6,7],[3,5],[4]]=>[[1,2,3,4],[5,7],[6]]=>[4,1,2]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[[1,4,5,6,7],[2],[3]]=>[[1,2,3,4,5],[6],[7]]=>[5,1,1]
[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[[1,2,5,6,7],[3,4]]=>[[1,2,3,4,5],[6,7]]=>[5,2]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[[1,5,6,7],[2],[3],[4]]=>[[1,2,3,4],[5],[6],[7]]=>[4,1,1,1]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[[1,3,5,6,7],[2],[4]]=>[[1,2,3,4,6],[5],[7]]=>[4,2,1]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[[1,4,5,6,7],[2],[3]]=>[[1,2,3,4,5],[6],[7]]=>[5,1,1]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[[1,4,5,6,7],[2],[3]]=>[[1,2,3,4,5],[6],[7]]=>[5,1,1]
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[[1,3,4,5,6,7],[2]]=>[[1,2,3,4,5,6],[7]]=>[6,1]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[[1,5,6,7],[2],[3],[4]]=>[[1,2,3,4],[5],[6],[7]]=>[4,1,1,1]
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[[1,2,5,6,7],[3],[4]]=>[[1,2,3,4,7],[5],[6]]=>[4,1,2]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[[1,3,5,6,7],[2],[4]]=>[[1,2,3,4,6],[5],[7]]=>[4,2,1]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[[1,3,5,6,7],[2],[4]]=>[[1,2,3,4,6],[5],[7]]=>[4,2,1]
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[[1,2,3,5,6,7],[4]]=>[[1,2,3,4,6,7],[5]]=>[4,3]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[[1,4,5,6,7],[2],[3]]=>[[1,2,3,4,5],[6],[7]]=>[5,1,1]
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[[1,2,5,6,7],[3,4]]=>[[1,2,3,4,5],[6,7]]=>[5,2]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[[1,4,5,6,7],[2],[3]]=>[[1,2,3,4,5],[6],[7]]=>[5,1,1]
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[[1,3,4,5,6,7],[2]]=>[[1,2,3,4,5,6],[7]]=>[6,1]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[[1,4,5,6,7],[2],[3]]=>[[1,2,3,4,5],[6],[7]]=>[5,1,1]
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[[1,2,4,5,6,7],[3]]=>[[1,2,3,4,5,7],[6]]=>[5,2]
[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[[1,3,4,5,6,7],[2]]=>[[1,2,3,4,5,6],[7]]=>[6,1]
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[[1,3,4,5,6,7],[2]]=>[[1,2,3,4,5,6],[7]]=>[6,1]
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[[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],[2],[3],[4],[5],[6],[7],[8]]=>[1,1,1,1,1,1,1,1]
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[1,1,1,1,1,1,2]
[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[8,6,7,5,4,3,2,1]=>[[1,3],[2],[4],[5],[6],[7],[8]]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,1]
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[[1,3],[2],[4],[5],[6],[7],[8]]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>[1,1,1,1,1,2,1]
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[1,1,1,1,1,3]
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[8,7,5,6,4,3,2,1]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>[1,1,1,1,2,1,1]
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>[1,1,1,1,2,1,1]
[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[8,5,6,7,4,3,2,1]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[1,1,1,1,3,1]
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>[1,1,1,1,2,1,1]
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[1,1,1,1,2,2]
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[1,1,1,1,3,1]
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[1,1,1,1,3,1]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[[1,2,3,4],[5],[6],[7],[8]]=>[[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]]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>[1,1,1,2,1,1,1]
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[[1,3],[2,5],[4],[6],[7],[8]]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[1,1,1,2,2,1]
[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[7,6,8,4,5,3,2,1]=>[[1,3],[2,5],[4],[6],[7],[8]]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[1,1,1,2,2,1]
[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[8,7,5,4,6,3,2,1]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>[1,1,1,2,1,1,1]
[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[8,6,5,4,7,3,2,1]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>[1,1,1,2,1,1,1]
[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[8,5,6,4,7,3,2,1]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[1,1,1,2,2,1]
[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[8,6,4,5,7,3,2,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[1,1,1,3,1,1]
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>[1,1,1,2,1,1,1]
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[1,1,1,2,1,2]
[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[7,5,6,4,8,3,2,1]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[1,1,1,2,2,1]
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[1,1,1,2,2,1]
[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[[1,2,3,5],[4],[6],[7],[8]]=>[[1,5,7,8],[2],[3],[4],[6]]=>[1,1,1,2,3]
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[7,6,4,5,8,3,2,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[1,1,1,3,1,1]
[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[6,7,4,5,8,3,2,1]=>[[1,2,5],[3,4],[6],[7],[8]]=>[[1,5,6],[2,8],[3],[4],[7]]=>[1,1,1,3,2]
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[7,5,4,6,8,3,2,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[1,1,1,3,1,1]
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[[1,3,4,5],[2],[6],[7],[8]]=>[[1,5,6,7],[2],[3],[4],[8]]=>[1,1,1,4,1]
[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[1,1,1,3,1,1]
[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[[1,2,4,5],[3],[6],[7],[8]]=>[[1,5,6,8],[2],[3],[4],[7]]=>[1,1,1,3,2]
[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[6,4,5,7,8,3,2,1]=>[[1,3,4,5],[2],[6],[7],[8]]=>[[1,5,6,7],[2],[3],[4],[8]]=>[1,1,1,4,1]
[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[[1,3,4,5],[2],[6],[7],[8]]=>[[1,5,6,7],[2],[3],[4],[8]]=>[1,1,1,4,1]
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]=>[1,1,1,5]
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>[1,1,2,1,1,1,1]
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[1,1,2,1,1,2]
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,3,4,2,1]=>[[1,3],[2,6],[4],[5],[7],[8]]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[1,1,2,1,2,1]
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[[1,4],[2,6],[3],[5],[7],[8]]=>[[1,4],[2,6],[3],[5],[7],[8]]=>[1,1,2,2,1,1]
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[[1,2],[3,4],[5,6],[7],[8]]=>[[1,4],[2,6],[3,8],[5],[7]]=>[1,1,2,2,2]
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[8,5,6,7,3,4,2,1]=>[[1,3,4],[2,6],[5],[7],[8]]=>[[1,4,7],[2,6],[3],[5],[8]]=>[1,1,2,3,1]
[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,3,4,2,1]=>[[1,4],[2,6],[3],[5],[7],[8]]=>[[1,4],[2,6],[3],[5],[7],[8]]=>[1,1,2,2,1,1]
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[6,7,5,8,3,4,2,1]=>[[1,2,4],[3,6],[5],[7],[8]]=>[[1,4,8],[2,6],[3],[5],[7]]=>[1,1,2,2,2]
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[[1,2,3,4],[5,6],[7],[8]]=>[[1,4,7,8],[2,6],[3],[5]]=>[1,1,2,4]
[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>[1,1,2,1,1,1,1]
[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[7,8,6,4,3,5,2,1]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[1,1,2,1,1,2]
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[7,6,8,4,3,5,2,1]=>[[1,3],[2,6],[4],[5],[7],[8]]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[1,1,2,1,2,1]
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[[1,2,3],[4,6],[5],[7],[8]]=>[[1,4,8],[2,7],[3],[5],[6]]=>[1,1,2,1,3]
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[8,7,6,3,4,5,2,1]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[1,1,3,1,1,1]
[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[7,8,6,3,4,5,2,1]=>[[1,2,6],[3,5],[4],[7],[8]]=>[[1,4,5],[2,8],[3],[6],[7]]=>[1,1,3,1,2]
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[8,6,7,3,4,5,2,1]=>[[1,3,6],[2,5],[4],[7],[8]]=>[[1,4,5],[2,7],[3],[6],[8]]=>[1,1,3,2,1]
[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[7,6,8,3,4,5,2,1]=>[[1,3,6],[2,5],[4],[7],[8]]=>[[1,4,5],[2,7],[3],[6],[8]]=>[1,1,3,2,1]
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>[[1,2,3],[4,5,6],[7],[8]]=>[[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]]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>[1,1,2,1,1,1,1]
[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[7,8,5,4,3,6,2,1]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[1,1,2,1,1,2]
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[7,8,5,3,4,6,2,1]=>[[1,2,6],[3,5],[4],[7],[8]]=>[[1,4,5],[2,8],[3],[6],[7]]=>[1,1,3,1,2]
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>[1,1,2,1,1,1,1]
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[7,5,6,4,3,8,2,1]=>[[1,3,6],[2],[4],[5],[7],[8]]=>[[1,4,7],[2],[3],[5],[6],[8]]=>[1,1,2,1,2,1]
[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[7,4,5,6,3,8,2,1]=>[[1,3,4,6],[2],[5],[7],[8]]=>[[1,4,6,7],[2],[3],[5],[8]]=>[1,1,2,3,1]
[.,[.,[[.,[[[.,.],[.,.]],.]],.]]]=>[6,4,5,7,3,8,2,1]=>[[1,3,4,6],[2],[5],[7],[8]]=>[[1,4,6,7],[2],[3],[5],[8]]=>[1,1,2,3,1]
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[[1,3,4,6],[2],[5],[7],[8]]=>[[1,4,6,7],[2],[3],[5],[8]]=>[1,1,2,3,1]
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[[1,2,3,4,6],[5],[7],[8]]=>[[1,4,6,7,8],[2],[3],[5]]=>[1,1,2,4]
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[7,6,3,4,5,8,2,1]=>[[1,4,5,6],[2],[3],[7],[8]]=>[[1,4,5,6],[2],[3],[7],[8]]=>[1,1,4,1,1]
[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[7,5,4,3,6,8,2,1]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[1,1,3,1,1,1]
[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[7,5,3,4,6,8,2,1]=>[[1,4,5,6],[2],[3],[7],[8]]=>[[1,4,5,6],[2],[3],[7],[8]]=>[1,1,4,1,1]
[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[[1,5,6],[2],[3],[4],[7],[8]]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[1,1,3,1,1,1]
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>[[1,3],[2],[4],[5],[6],[7],[8]]=>[1,2,1,1,1,1,1]
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[1,2,1,1,2,1]
[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,2,3,1]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[1,2,1,1,2,1]
[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,2,3,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>[[1,3,7],[2,6],[4],[5],[8]]=>[1,2,1,3,1]
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,2,3,1]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[[1,3],[2,6],[4],[5],[7],[8]]=>[1,2,1,2,1,1]
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,2,3,1]=>[[1,2,4],[3,7],[5],[6],[8]]=>[[1,3,8],[2,6],[4],[5],[7]]=>[1,2,1,2,2]
[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,2,3,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>[[1,3,7],[2,6],[4],[5],[8]]=>[1,2,1,3,1]
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[[1,2,3,4],[5,7],[6],[8]]=>[[1,3,7,8],[2,6],[4],[5]]=>[1,2,1,4]
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[[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]]=>[[1,3],[2,5],[4,7],[6],[8]]=>[1,2,2,2,1]
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>[[1,3],[2,5],[4,7],[6],[8]]=>[[1,3],[2,5],[4,7],[6],[8]]=>[1,2,2,2,1]
[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[[1,3],[2,5],[4],[6],[7],[8]]=>[1,2,2,1,1,1]
[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[8,7,4,5,6,2,3,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>[[1,3,6],[2,5],[4],[7],[8]]=>[1,2,3,1,1]
[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[[1,5],[2,7],[3],[4],[6],[8]]=>[[1,3],[2,5],[4],[6],[7],[8]]=>[1,2,2,1,1,1]
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,2,3,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[[1,3,7],[2,5],[4],[6],[8]]=>[1,2,2,2,1]
[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,2,3,1]=>[[1,4,5],[2,7],[3],[6],[8]]=>[[1,3,6],[2,5],[4],[7],[8]]=>[1,2,3,1,1]
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,2,3,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[[1,3,7],[2,5],[4],[6],[8]]=>[1,2,2,2,1]
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>[[1,3,5],[2,7],[4],[6],[8]]=>[[1,3,7],[2,5],[4],[6],[8]]=>[1,2,2,2,1]
[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[[1,2,3,4,5],[6,7],[8]]=>[[1,3,6,7,8],[2,5],[4]]=>[1,2,5]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>[[1,3],[2],[4],[5],[6],[7],[8]]=>[1,2,1,1,1,1,1]
[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[1,2,1,1,1,2]
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[1,2,1,1,2,1]
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,2,4,1]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[1,2,1,1,2,1]
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,2,4,1]=>[[1,2,3],[4,7],[5],[6],[8]]=>[[1,3,8],[2,7],[4],[5],[6]]=>[1,2,1,1,3]
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[[1,3],[2,6],[4],[5],[7],[8]]=>[1,2,1,2,1,1]
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,2,4,1]=>[[1,3,4],[2,7],[5],[6],[8]]=>[[1,3,7],[2,6],[4],[5],[8]]=>[1,2,1,3,1]
[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,2,4,1]=>[[1,4],[2,7],[3],[5],[6],[8]]=>[[1,3],[2,6],[4],[5],[7],[8]]=>[1,2,1,2,1,1]
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,2,4,1]=>[[1,2,4],[3,7],[5],[6],[8]]=>[[1,3,8],[2,6],[4],[5],[7]]=>[1,2,1,2,2]
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[[1,2,3,4],[5,7],[6],[8]]=>[[1,3,7,8],[2,6],[4],[5]]=>[1,2,1,4]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[1,3,1,1,1,1]
[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,2,3,4,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[[1,3,4],[2,7],[5],[6],[8]]=>[1,3,1,2,1]
[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,2,3,4,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[[1,3,4],[2,7],[5],[6],[8]]=>[1,3,1,2,1]
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[[1,2,3],[4,6,7],[5],[8]]=>[[1,3,4],[2,7,8],[5],[6]]=>[1,3,1,3]
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,2,3,4,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>[[1,3,4],[2,6],[5],[7],[8]]=>[1,3,2,1,1]
[.,[[[.,.],.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,2,3,4,1]=>[[1,2,7],[3,4],[5,6],[8]]=>[[1,3,4],[2,6],[5,8],[7]]=>[1,3,2,2]
[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,2,3,4,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>[[1,3,4],[2,6],[5],[7],[8]]=>[1,3,2,1,1]
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[[1,3,4],[2,6,7],[5],[8]]=>[[1,3,4],[2,6,7],[5],[8]]=>[1,3,3,1]
[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,2,3,4,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>[[1,3,4],[2,6],[5],[7],[8]]=>[1,3,2,1,1]
[.,[[[.,.],.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,2,3,4,1]=>[[1,2,4],[3,6,7],[5],[8]]=>[[1,3,4],[2,6,8],[5],[7]]=>[1,3,2,2]
[.,[[[.,.],.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,2,3,4,1]=>[[1,3,4],[2,6,7],[5],[8]]=>[[1,3,4],[2,6,7],[5],[8]]=>[1,3,3,1]
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[[1,2,3,4],[5,6,7],[8]]=>[[1,3,4,8],[2,6,7],[5]]=>[1,3,4]
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>[[1,3],[2],[4],[5],[6],[7],[8]]=>[1,2,1,1,1,1,1]
[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[7,8,6,4,3,2,5,1]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[1,2,1,1,1,2]
[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[1,2,1,1,2,1]
[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[7,6,8,4,3,2,5,1]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[[1,3],[2,7],[4],[5],[6],[8]]=>[1,2,1,1,2,1]
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[6,7,8,4,3,2,5,1]=>[[1,2,3],[4,7],[5],[6],[8]]=>[[1,3,8],[2,7],[4],[5],[6]]=>[1,2,1,1,3]
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[8,7,6,3,4,2,5,1]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[1,2,2,1,1,1]
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[[1,3,5],[2,7],[4],[6],[8]]=>[1,2,2,2,1]
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[[1,3,5],[2,7],[4],[6],[8]]=>[1,2,2,2,1]
[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[7,6,8,4,2,3,5,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[[1,3,4],[2,7],[5],[6],[8]]=>[1,3,1,2,1]
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[[1,2,3],[4,6,7],[5],[8]]=>[[1,3,4],[2,7,8],[5],[6]]=>[1,3,1,3]
[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[8,6,7,3,2,4,5,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[[1,3,4],[2,7],[5],[6],[8]]=>[1,3,1,2,1]
[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[6,7,8,3,2,4,5,1]=>[[1,2,3],[4,6,7],[5],[8]]=>[[1,3,4],[2,7,8],[5],[6]]=>[1,3,1,3]
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[8,7,6,2,3,4,5,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>[[1,3,4,5],[2],[6],[7],[8]]=>[1,4,1,1,1]
[.,[[[[.,.],.],.],[.,[[.,.],.]]]]=>[7,8,6,2,3,4,5,1]=>[[1,2,6,7],[3,5],[4],[8]]=>[[1,3,4,5],[2,8],[6],[7]]=>[1,4,1,2]
[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[8,6,7,2,3,4,5,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[[1,3,4,5],[2,7],[6],[8]]=>[1,4,2,1]
[.,[[[[.,.],.],.],[[.,[.,.]],.]]]=>[7,6,8,2,3,4,5,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[[1,3,4,5],[2,7],[6],[8]]=>[1,4,2,1]
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[6,7,8,2,3,4,5,1]=>[[1,2,3,7],[4,5,6],[8]]=>[[1,3,4,5],[2,7,8],[6]]=>[1,4,3]
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[8,7,5,3,4,2,6,1]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[1,2,2,1,1,1]
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[7,8,5,3,4,2,6,1]=>[[1,2,7],[3,5],[4],[6],[8]]=>[[1,3,5],[2,8],[4],[6],[7]]=>[1,2,2,1,2]
[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[8,7,5,3,2,4,6,1]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[1,3,1,1,1,1]
[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[7,8,4,3,2,5,6,1]=>[[1,2,7],[3,6],[4],[5],[8]]=>[[1,3,4],[2,8],[5],[6],[7]]=>[1,3,1,1,2]
[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[7,8,3,4,2,5,6,1]=>[[1,2,6,7],[3,4],[5],[8]]=>[[1,3,4,6],[2,8],[5],[7]]=>[1,3,2,2]
[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>[[1,2,6,7],[3,5],[4],[8]]=>[[1,3,4,5],[2,8],[6],[7]]=>[1,4,1,2]
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[8,5,6,3,4,2,7,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[[1,3,5],[2,7],[4],[6],[8]]=>[1,2,2,2,1]
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>[[1,3,5,7],[2],[4],[6],[8]]=>[1,2,2,2,1]
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[8,6,4,2,3,5,7,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>[[1,3,4,5],[2],[6],[7],[8]]=>[1,4,1,1,1]
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[8,5,3,4,2,6,7,1]=>[[1,4,6,7],[2],[3],[5],[8]]=>[[1,3,4,6],[2],[5],[7],[8]]=>[1,3,2,1,1]
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[8,5,4,2,3,6,7,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>[[1,3,4,5],[2],[6],[7],[8]]=>[1,4,1,1,1]
[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]=>[7,4,5,6,3,2,8,1]=>[[1,3,4,7],[2],[5],[6],[8]]=>[[1,3,6,7],[2],[4],[5],[8]]=>[1,2,1,3,1]
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[[1,2,3,4,7],[5],[6],[8]]=>[[1,3,6,7,8],[2],[4],[5]]=>[1,2,1,4]
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[7,5,6,3,4,2,8,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[[1,3,5],[2,7],[4],[6],[8]]=>[1,2,2,2,1]
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[6,5,7,3,4,2,8,1]=>[[1,3,7],[2,5],[4],[6],[8]]=>[[1,3,5],[2,7],[4],[6],[8]]=>[1,2,2,2,1]
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[7,4,5,3,6,2,8,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>[[1,3,5,7],[2],[4],[6],[8]]=>[1,2,2,2,1]
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[1,2,2,1,1,1]
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[6,4,5,3,7,2,8,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>[[1,3,5,7],[2],[4],[6],[8]]=>[1,2,2,2,1]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[[1,3,5,7],[2],[4],[6],[8]]=>[[1,3,5,7],[2],[4],[6],[8]]=>[1,2,2,2,1]
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[[1,2,3,5,7],[4],[6],[8]]=>[[1,3,5,7,8],[2],[4],[6]]=>[1,2,2,3]
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[[1,4,5,7],[2],[3],[6],[8]]=>[[1,3,5,6],[2],[4],[7],[8]]=>[1,2,3,1,1]
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[5,6,3,4,7,2,8,1]=>[[1,2,5,7],[3,4],[6],[8]]=>[[1,3,5,6],[2,8],[4],[7]]=>[1,2,3,2]
[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[[1,4,5,7],[2],[3],[6],[8]]=>[[1,3,5,6],[2],[4],[7],[8]]=>[1,2,3,1,1]
[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]=>[6,7,5,4,2,3,8,1]=>[[1,2,7],[3,6],[4],[5],[8]]=>[[1,3,4],[2,8],[5],[6],[7]]=>[1,3,1,1,2]
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[7,5,6,4,2,3,8,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[[1,3,4],[2,7],[5],[6],[8]]=>[1,3,1,2,1]
[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,2,3,8,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[[1,3,4],[2,7],[5],[6],[8]]=>[1,3,1,2,1]
[.,[[[.,.],[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,2,3,8,1]=>[[1,2,3,7],[4,6],[5],[8]]=>[[1,3,4,8],[2,7],[5],[6]]=>[1,3,1,3]
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[[1,2,7],[3,4],[5,6],[8]]=>[[1,3,4],[2,6],[5,8],[7]]=>[1,3,2,2]
[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,2,3,8,1]=>[[1,3,4,7],[2,6],[5],[8]]=>[[1,3,4,7],[2,6],[5],[8]]=>[1,3,3,1]
[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,2,3,8,1]=>[[1,4,7],[2,6],[3],[5],[8]]=>[[1,3,4],[2,6],[5],[7],[8]]=>[1,3,2,1,1]
[.,[[[.,.],[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,2,3,8,1]=>[[1,2,4,7],[3,6],[5],[8]]=>[[1,3,4,8],[2,6],[5],[7]]=>[1,3,2,2]
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,2,3,8,1]=>[[1,3,4,7],[2,6],[5],[8]]=>[[1,3,4,7],[2,6],[5],[8]]=>[1,3,3,1]
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[[1,2,3,4,7],[5,6],[8]]=>[[1,3,4,7,8],[2,6],[5]]=>[1,3,4]
[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[6,7,5,3,2,4,8,1]=>[[1,2,7],[3,6],[4],[5],[8]]=>[[1,3,4],[2,8],[5],[6],[7]]=>[1,3,1,1,2]
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[6,5,7,3,2,4,8,1]=>[[1,3,7],[2,6],[4],[5],[8]]=>[[1,3,4],[2,7],[5],[6],[8]]=>[1,3,1,2,1]
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>[[1,3,4,5],[2],[6],[7],[8]]=>[1,4,1,1,1]
[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[5,6,7,2,3,4,8,1]=>[[1,2,3,7],[4,5,6],[8]]=>[[1,3,4,5],[2,7,8],[6]]=>[1,4,3]
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[6,7,4,3,2,5,8,1]=>[[1,2,7],[3,6],[4],[5],[8]]=>[[1,3,4],[2,8],[5],[6],[7]]=>[1,3,1,1,2]
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>[[1,3,4,5],[2],[6],[7],[8]]=>[1,4,1,1,1]
[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[6,7,3,2,4,5,8,1]=>[[1,2,6,7],[3,5],[4],[8]]=>[[1,3,4,5],[2,8],[6],[7]]=>[1,4,1,2]
[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[6,7,2,3,4,5,8,1]=>[[1,2,5,6,7],[3,4],[8]]=>[[1,3,4,5,6],[2,8],[7]]=>[1,5,2]
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[7,5,2,3,4,6,8,1]=>[[1,4,5,6,7],[2],[3],[8]]=>[[1,3,4,5,6],[2],[7],[8]]=>[1,5,1,1]
[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[[1,6,7],[2],[3],[4],[5],[8]]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[1,3,1,1,1,1]
[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]=>[5,4,6,3,2,7,8,1]=>[[1,3,6,7],[2],[4],[5],[8]]=>[[1,3,4,7],[2],[5],[6],[8]]=>[1,3,1,2,1]
[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[[1,4,6,7],[2],[3],[5],[8]]=>[[1,3,4,6],[2],[5],[7],[8]]=>[1,3,2,1,1]
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[[1,2,3,4,6,7],[5],[8]]=>[[1,3,4,6,7,8],[2],[5]]=>[1,3,4]
[.,[[[[.,.],[.,[[.,.],.]]],.],.]]=>[5,6,4,2,3,7,8,1]=>[[1,2,6,7],[3,5],[4],[8]]=>[[1,3,4,5],[2,8],[6],[7]]=>[1,4,1,2]
[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[6,4,5,2,3,7,8,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[[1,3,4,5],[2,7],[6],[8]]=>[1,4,2,1]
[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[5,4,6,2,3,7,8,1]=>[[1,3,6,7],[2,5],[4],[8]]=>[[1,3,4,5],[2,7],[6],[8]]=>[1,4,2,1]
[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[6,5,2,3,4,7,8,1]=>[[1,4,5,6,7],[2],[3],[8]]=>[[1,3,4,5,6],[2],[7],[8]]=>[1,5,1,1]
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[[1,5,6,7],[2],[3],[4],[8]]=>[[1,3,4,5],[2],[6],[7],[8]]=>[1,4,1,1,1]
[.,[[[[.,[[.,[.,.]],.]],.],.],.]]=>[4,3,5,2,6,7,8,1]=>[[1,3,5,6,7],[2],[4],[8]]=>[[1,3,4,5,7],[2],[6],[8]]=>[1,4,2,1]
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[5,4,2,3,6,7,8,1]=>[[1,4,5,6,7],[2],[3],[8]]=>[[1,3,4,5,6],[2],[7],[8]]=>[1,5,1,1]
[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[4,5,2,3,6,7,8,1]=>[[1,2,5,6,7],[3,4],[8]]=>[[1,3,4,5,6],[2,8],[7]]=>[1,5,2]
[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>[[1,3,4,5,6,7],[2],[8]]=>[[1,3,4,5,6,7],[2],[8]]=>[1,6,1]
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[[1,4,5,6,7],[2],[3],[8]]=>[[1,3,4,5,6],[2],[7],[8]]=>[1,5,1,1]
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[[1,2,4,5,6,7],[3],[8]]=>[[1,3,4,5,6,8],[2],[7]]=>[1,5,2]
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[[1,3,4,5,6,7],[2],[8]]=>[[1,3,4,5,6,7],[2],[8]]=>[1,6,1]
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[[1,2,3,4,5,6,7],[8]]=>[[1,3,4,5,6,7,8],[2]]=>[1,7]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[[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]]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,1,1,1,1,2]
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,1,1,2,1,1]
[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[[1,2],[3,4],[5,8],[6],[7]]=>[[1,2],[3,6],[4,8],[5],[7]]=>[2,1,1,2,2]
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,3,1,2]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,1,1,2,1,1]
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,3,1,2]=>[[1,2,4],[3,8],[5],[6],[7]]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,1,1,2,2]
[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,3,1,2]=>[[1,3,4],[2,8],[5],[6],[7]]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,1,1,3,1]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[[1,2,3,4],[5,8],[6],[7]]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,1,1,4]
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[[1,2],[3,5],[4,8],[6],[7]]=>[[1,2],[3,5],[4,8],[6],[7]]=>[2,1,2,1,2]
[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,3,1,2]=>[[1,3],[2,5],[4,8],[6],[7]]=>[[1,2],[3,5],[4,7],[6],[8]]=>[2,1,2,2,1]
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[[1,5],[2,8],[3],[4],[6],[7]]=>[[1,2],[3,5],[4],[6],[7],[8]]=>[2,1,2,1,1,1]
[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,3,1,2]=>[[1,3,5],[2,8],[4],[6],[7]]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,1,2,2,1]
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,3,1,2]=>[[1,3,5],[2,8],[4],[6],[7]]=>[[1,2,7],[3,5],[4],[6],[8]]=>[2,1,2,2,1]
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,3,1,2]=>[[1,4,5],[2,8],[3],[6],[7]]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,1,3,1,1]
[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,3,1,2]=>[[1,2,5],[3,4],[6,8],[7]]=>[[1,2,6],[3,5],[4,8],[7]]=>[2,1,3,2]
[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,3,1,2]=>[[1,2,4,5],[3,8],[6],[7]]=>[[1,2,6,8],[3,5],[4],[7]]=>[2,1,3,2]
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[[1,2,3,4,5],[6,8],[7]]=>[[1,2,6,7,8],[3,5],[4]]=>[2,1,5]
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[2,2,1,1,1,1]
[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[[1,2],[3,6],[4,8],[5],[7]]=>[[1,2],[3,4],[5,8],[6],[7]]=>[2,2,1,1,2]
[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,4,1,2]=>[[1,2,3],[4,6],[5,8],[7]]=>[[1,2,8],[3,4],[5,7],[6]]=>[2,2,1,3]
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[[1,4],[2,6],[3,8],[5],[7]]=>[[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]]=>[[1,2],[3,4],[5,6],[7,8]]=>[2,2,2,2]
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,4,1,2]=>[[1,3,4],[2,6],[5,8],[7]]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[[1,4],[2,6],[3,8],[5],[7]]=>[[1,2],[3,4],[5,6],[7],[8]]=>[2,2,2,1,1]
[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[[1,2,4],[3,6],[5,8],[7]]=>[[1,2,8],[3,4],[5,6],[7]]=>[2,2,2,2]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[[1,3,4],[2,6],[5,8],[7]]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[[1,3,4],[2,6],[5,8],[7]]=>[[1,2,7],[3,4],[5,6],[8]]=>[2,2,3,1]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[[1,2,3,4],[5,6],[7,8]]=>[[1,2,7,8],[3,4],[5,6]]=>[2,2,4]
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[[1,5,6],[2,8],[3],[4],[7]]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,1,1,1]
[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>[8,7,4,5,3,6,1,2]=>[[1,4,6],[2,8],[3],[5],[7]]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,1,1]
[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[[1,2,6],[3,4],[5,8],[7]]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]
[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[[1,2,6],[3,5],[4,8],[7]]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,1,2]
[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>[8,7,4,3,5,6,1,2]=>[[1,5,6],[2,8],[3],[4],[7]]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,1,1,1]
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[[1,2,6],[3,5],[4,8],[7]]=>[[1,2,5],[3,4],[6,8],[7]]=>[2,3,1,2]
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[[1,2,5,6],[3,4],[7,8]]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]
[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[8,5,4,6,3,7,1,2]=>[[1,4,6],[2,8],[3],[5],[7]]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,1,1]
[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[8,5,4,3,6,7,1,2]=>[[1,5,6],[2,8],[3],[4],[7]]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,1,1,1]
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[8,5,3,4,6,7,1,2]=>[[1,4,5,6],[2,8],[3],[7]]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,1,1]
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[[1,4,5,6],[2,8],[3],[7]]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,1,1]
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[2,2,1,1,1,1]
[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,3,8,1,2]=>[[1,2,3,6],[4,8],[5],[7]]=>[[1,2,7,8],[3,4],[5],[6]]=>[2,2,1,3]
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>[[1,2,6],[3,4],[5,8],[7]]=>[[1,2,6],[3,4],[5,8],[7]]=>[2,2,2,2]
[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,3,8,1,2]=>[[1,4,6],[2,8],[3],[5],[7]]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,1,1]
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,3,8,1,2]=>[[1,4,6],[2,8],[3],[5],[7]]=>[[1,2,6],[3,4],[5],[7],[8]]=>[2,2,2,1,1]
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,3,8,1,2]=>[[1,2,4,6],[3,8],[5],[7]]=>[[1,2,6,8],[3,4],[5],[7]]=>[2,2,2,2]
[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[4,5,6,7,3,8,1,2]=>[[1,2,3,4,6],[5,8],[7]]=>[[1,2,6,7,8],[3,4],[5]]=>[2,2,4]
[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[7,6,3,4,5,8,1,2]=>[[1,4,5,6],[2,8],[3],[7]]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,1,1]
[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[7,5,4,3,6,8,1,2]=>[[1,5,6],[2,8],[3],[4],[7]]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,1,1,1]
[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[7,4,5,3,6,8,1,2]=>[[1,3,5,6],[2,8],[4],[7]]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[[1,4,5,6],[2,8],[3],[7]]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,1,1]
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[6,5,4,3,7,8,1,2]=>[[1,5,6],[2,8],[3],[4],[7]]=>[[1,2,5],[3,4],[6],[7],[8]]=>[2,3,1,1,1]
[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[5,4,6,3,7,8,1,2]=>[[1,3,5,6],[2,8],[4],[7]]=>[[1,2,5,7],[3,4],[6],[8]]=>[2,3,2,1]
[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[4,5,6,3,7,8,1,2]=>[[1,2,3,5,6],[4,8],[7]]=>[[1,2,5,7,8],[3,4],[6]]=>[2,3,3]
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[[1,2,5,6],[3,4],[7,8]]=>[[1,2,5,6],[3,4],[7,8]]=>[2,4,2]
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[[1,4,5,6],[2,8],[3],[7]]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,1,1]
[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[[1,3,4,5,6],[2,8],[7]]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[[1,4,5,6],[2,8],[3],[7]]=>[[1,2,5,6],[3,4],[7],[8]]=>[2,4,1,1]
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[[1,2,4,5,6],[3,8],[7]]=>[[1,2,5,6,8],[3,4],[7]]=>[2,4,2]
[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[5,3,4,6,7,8,1,2]=>[[1,3,4,5,6],[2,8],[7]]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[[1,3,4,5,6],[2,8],[7]]=>[[1,2,5,6,7],[3,4],[8]]=>[2,5,1]
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[[1,2,3,4,5,6],[7,8]]=>[[1,2,5,6,7,8],[3,4]]=>[2,6]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[2,1,1,1,1,1,1]
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[2,1,1,1,2,1]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,2,1,3]=>[[1,2,3],[4,8],[5],[6],[7]]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,1,1,1,3]
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[8,7,5,6,4,2,1,3]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,1,1,2,1,1]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[[1,2],[3,4],[5,8],[6],[7]]=>[[1,2],[3,6],[4,8],[5],[7]]=>[2,1,1,2,2]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,1,1,2,1,1]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,2,1,3]=>[[1,2,4],[3,8],[5],[6],[7]]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,1,1,2,2]
[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>[[1,3,4],[2,8],[5],[6],[7]]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,1,1,3,1]
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,2,1,3]=>[[1,3,4],[2,8],[5],[6],[7]]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,1,1,3,1]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[[1,2,3,4],[5,8],[6],[7]]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,1,1,4]
[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,2,1,3]=>[[1,2,5],[3,8],[4],[6],[7]]=>[[1,2,8],[3,5],[4],[6],[7]]=>[2,1,2,1,2]
[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,2,1,3]=>[[1,4,5],[2,8],[3],[6],[7]]=>[[1,2,6],[3,5],[4],[7],[8]]=>[2,1,3,1,1]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[[1,2,3,4,5],[6,8],[7]]=>[[1,2,6,7,8],[3,5],[4]]=>[2,1,5]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,1,1,1,1,1]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[[1,2,3],[4,7,8],[5],[6]]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,1,1,3]
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,1,2,3]=>[[1,2,8],[3,4],[5,7],[6]]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,1,2,2]
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[[1,3,4],[2,7,8],[5],[6]]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,1,3,1]
[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,1,2,3]=>[[1,4,8],[2,7],[3],[5],[6]]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,1,2,1,1]
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,1,2,3]=>[[1,2,4],[3,7,8],[5],[6]]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,1,2,2]
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[[1,3,4],[2,7,8],[5],[6]]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,1,3,1]
[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,1,2,3]=>[[1,3,4],[2,7,8],[5],[6]]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,1,3,1]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[[1,2,3,4],[5,7,8],[6]]=>[[1,2,3,8],[4,6,7],[5]]=>[3,1,4]
[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[[1,5,8],[2,7],[3],[4],[6]]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,1,1,1]
[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,1,2,3]=>[[1,5,8],[2,7],[3],[4],[6]]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,1,1,1]
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[[1,3,5],[2,7,8],[4],[6]]=>[[1,2,3],[4,5,7],[6],[8]]=>[3,2,2,1]
[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,1,2,3]=>[[1,4,5],[2,7,8],[3],[6]]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,1,1]
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[[1,5,8],[2,7],[3],[4],[6]]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,1,1,1]
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[[1,2,5],[3,4,8],[6,7]]=>[[1,2,3],[4,5,6],[7,8]]=>[3,3,2]
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>[[1,4,5],[2,7,8],[3],[6]]=>[[1,2,3],[4,5,6],[7],[8]]=>[3,3,1,1]
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,1,2,3]=>[[1,3,4,5],[2,7,8],[6]]=>[[1,2,3,7],[4,5,6],[8]]=>[3,4,1]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[[1,2,3,4,5],[6,7,8]]=>[[1,2,3,7,8],[4,5,6]]=>[3,5]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[2,1,1,1,1,1,1]
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,1,1,1,1,2]
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[2,1,1,1,2,1]
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[2,1,1,1,2,1]
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[[1,2,3],[4,8],[5],[6],[7]]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,1,1,1,3]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,1,1,2,1,1]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[[1,2],[3,4],[5,8],[6],[7]]=>[[1,2],[3,6],[4,8],[5],[7]]=>[2,1,1,2,2]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,1,1,2,1,1]
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,1,1,3,1]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[[1,4],[2,8],[3],[5],[6],[7]]=>[[1,2],[3,6],[4],[5],[7],[8]]=>[2,1,1,2,1,1]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[[1,2,4],[3,8],[5],[6],[7]]=>[[1,2,8],[3,6],[4],[5],[7]]=>[2,1,1,2,2]
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,2,1,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,1,1,3,1]
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,2,1,4]=>[[1,3,4],[2,8],[5],[6],[7]]=>[[1,2,7],[3,6],[4],[5],[8]]=>[2,1,1,3,1]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[[1,2,3,4],[5,8],[6],[7]]=>[[1,2,7,8],[3,6],[4],[5]]=>[2,1,1,4]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,1,1,1,1]
[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,3,1,4]=>[[1,2,8],[3,6],[4],[5],[7]]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,1,1,2]
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[[1,3,8],[2,6],[4],[5],[7]]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,1,2,1]
[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,3,1,4]=>[[1,3,8],[2,6],[4],[5],[7]]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,1,2,1]
[[.,[[.,.],.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,3,1,4]=>[[1,2,3],[4,6,8],[5],[7]]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,1,3]
[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,3,1,4]=>[[1,4,8],[2,6],[3],[5],[7]]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,1,1]
[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[[1,2,8],[3,4],[5,6],[7]]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]
[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,3,1,4]=>[[1,4,8],[2,6],[3],[5],[7]]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,1,1]
[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,3,1,4]=>[[1,3,4],[2,6,8],[5],[7]]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]
[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,3,1,4]=>[[1,4,8],[2,6],[3],[5],[7]]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,1,1]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[[1,2,4],[3,6,8],[5],[7]]=>[[1,2,4],[3,6,8],[5],[7]]=>[2,2,2,2]
[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[[1,3,4],[2,6,8],[5],[7]]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]
[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,3,1,4]=>[[1,3,4],[2,6,8],[5],[7]]=>[[1,2,4],[3,6,7],[5],[8]]=>[2,2,3,1]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[[1,2,3,4],[5,6,8],[7]]=>[[1,2,4,8],[3,6,7],[5]]=>[2,2,4]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,1,1,1,1,1]
[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[[1,2,8],[3,7],[4],[5],[6]]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,1,1,1,2]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[[1,2,8],[3,4],[5,7],[6]]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,1,2,2]
[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[[1,4,8],[2,7],[3],[5],[6]]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,1,2,1,1]
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[[1,2,4],[3,7,8],[5],[6]]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,1,2,2]
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[[1,3,4],[2,7,8],[5],[6]]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,1,3,1]
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[[1,3,4],[2,7,8],[5],[6]]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,1,3,1]
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[[1,2,3,4],[5,7,8],[6]]=>[[1,2,3,8],[4,6,7],[5]]=>[3,1,4]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,1,1,1,1,1]
[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,2,1,3,4]=>[[1,3,8],[2,7],[4],[5],[6]]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,1,1,2,1]
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[[1,2,3],[4,7,8],[5],[6]]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,1,1,3]
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[[1,2,8],[3,4],[5,7],[6]]=>[[1,2,3],[4,6],[5,8],[7]]=>[3,1,2,2]
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,1,3,4]=>[[1,4,8],[2,7],[3],[5],[6]]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,1,2,1,1]
[[[.,[.,.]],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,2,1,3,4]=>[[1,3,4],[2,7,8],[5],[6]]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,1,3,1]
[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,1,3,4]=>[[1,4,8],[2,7],[3],[5],[6]]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,1,2,1,1]
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[[1,2,4],[3,7,8],[5],[6]]=>[[1,2,3],[4,6,8],[5],[7]]=>[3,1,2,2]
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[[1,3,4],[2,7,8],[5],[6]]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,1,3,1]
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[[1,3,4],[2,7,8],[5],[6]]=>[[1,2,3],[4,6,7],[5],[8]]=>[3,1,3,1]
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[[1,2,3,4],[5,7,8],[6]]=>[[1,2,3,8],[4,6,7],[5]]=>[3,1,4]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[[1,6,7,8],[2],[3],[4],[5]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,1,1,1,1]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[[1,2,7,8],[3,6],[4],[5]]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,1,1,2]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[[1,3,7,8],[2,6],[4],[5]]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,1,2,1]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[[1,3,7,8],[2,6],[4],[5]]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,1,2,1]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[[1,2,3,8],[4,6,7],[5]]=>[[1,2,3,4],[5,7,8],[6]]=>[4,1,3]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[[1,4,7,8],[2,6],[3],[5]]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,1,1]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[[1,2,7,8],[3,4],[5,6]]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[[1,4,7,8],[2,6],[3],[5]]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,1,1]
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[[1,3,4,8],[2,6,7],[5]]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[[1,4,7,8],[2,6],[3],[5]]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,1,1]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[[1,2,4,8],[3,6,7],[5]]=>[[1,2,3,4],[5,6,8],[7]]=>[4,2,2]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[[1,3,4,8],[2,6,7],[5]]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[[1,3,4,8],[2,6,7],[5]]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[[1,2,3,4],[5,6,7,8]]=>[[1,2,3,4],[5,6,7,8]]=>[4,4]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[2,1,1,1,1,1,1]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,1,1,1,1,2]
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[8,6,7,4,3,2,1,5]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[2,1,1,1,2,1]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[[1,3],[2,8],[4],[5],[6],[7]]=>[[1,2],[3,7],[4],[5],[6],[8]]=>[2,1,1,1,2,1]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[[1,2,3],[4,8],[5],[6],[7]]=>[[1,2,8],[3,7],[4],[5],[6]]=>[2,1,1,1,3]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[2,1,2,1,1,1]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[7,8,6,3,4,2,1,5]=>[[1,2,8],[3,5],[4],[6],[7]]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,1,2,1,2]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>[[1,2,3],[4,5,8],[6],[7]]=>[[1,2,5],[3,7,8],[4],[6]]=>[2,1,2,3]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,1,1,1,1]
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,2,3,1,5]=>[[1,3,8],[2,6],[4],[5],[7]]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,1,2,1]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[[1,2,3],[4,6,8],[5],[7]]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,1,3]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,1,1,1,1]
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[8,6,7,3,2,4,1,5]=>[[1,3,8],[2,6],[4],[5],[7]]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,1,2,1]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[[1,2,3],[4,6,8],[5],[7]]=>[[1,2,4],[3,7,8],[5],[6]]=>[2,2,1,3]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[[1,5,6,8],[2],[3],[4],[7]]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,1,1,1]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[6,7,8,2,3,4,1,5]=>[[1,2,3,8],[4,5,6],[7]]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,1,1,1,1,1]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[[1,2,3],[4,7,8],[5],[6]]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,1,1,3]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[[1,5,8],[2,7],[3],[4],[6]]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,1,1,1]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[[1,2,3],[4,5,8],[6,7]]=>[[1,2,3],[4,5,8],[6,7]]=>[3,2,3]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,1,1,1,1,1]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[[1,2,8],[3,7],[4],[5],[6]]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,1,1,1,2]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[[1,3,8],[2,7],[4],[5],[6]]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,1,1,2,1]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[[1,2,3],[4,7,8],[5],[6]]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,1,1,3]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[[1,6,7,8],[2],[3],[4],[5]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,1,1,1,1]
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[[1,2,7,8],[3,6],[4],[5]]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,1,1,2]
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,1,2,3,5]=>[[1,3,7,8],[2,6],[4],[5]]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,1,2,1]
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[[1,2,3,8],[4,6,7],[5]]=>[[1,2,3,4],[5,7,8],[6]]=>[4,1,3]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,1,1,1,1,1]
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[7,6,8,3,2,1,4,5]=>[[1,3,8],[2,7],[4],[5],[6]]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,1,1,2,1]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[[1,2,3],[4,7,8],[5],[6]]=>[[1,2,3],[4,7,8],[5],[6]]=>[3,1,1,3]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[[1,5,7,8],[2],[3],[4],[6]]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,1,1,1]
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[7,6,8,2,3,1,4,5]=>[[1,3,7,8],[2,5],[4],[6]]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[[1,2,3,8],[4,5,7],[6]]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[[1,6,7,8],[2],[3],[4],[5]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,1,1,1,1]
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[7,8,6,3,1,2,4,5]=>[[1,2,7,8],[3,6],[4],[5]]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,1,1,2]
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[[1,2,3,8],[4,6,7],[5]]=>[[1,2,3,4],[5,7,8],[6]]=>[4,1,3]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[[1,6,7,8],[2],[3],[4],[5]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,1,1,1,1]
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[7,8,6,2,1,3,4,5]=>[[1,2,7,8],[3,6],[4],[5]]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,1,1,2]
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[[1,2,3,8],[4,6,7],[5]]=>[[1,2,3,4],[5,7,8],[6]]=>[4,1,3]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[[1,5,6,7,8],[2],[3],[4]]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,1,1,1]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[[1,2,6,7,8],[3,5],[4]]=>[[1,2,3,4,5],[6,8],[7]]=>[5,1,2]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[[1,3,6,7,8],[2,5],[4]]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[[1,3,6,7,8],[2,5],[4]]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[[1,2,3,7,8],[4,5,6]]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[2,1,1,1,1,1,1]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[2,1,1,1,1,2]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[2,1,2,1,1,1]
[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[7,8,3,4,5,2,1,6]=>[[1,2,5,8],[3,4],[6],[7]]=>[[1,2,5,6],[3,8],[4],[7]]=>[2,1,3,2]
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[8,7,4,5,2,3,1,6]=>[[1,4,8],[2,6],[3],[5],[7]]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,1,1]
[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,2,3,1,6]=>[[1,2,8],[3,4],[5,6],[7]]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[8,7,5,3,2,4,1,6]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,1,1,1,1]
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[8,7,4,3,2,5,1,6]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,1,1,1,1]
[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[7,8,4,3,2,5,1,6]=>[[1,2,8],[3,6],[4],[5],[7]]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,1,1,2]
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>[[1,2,6,8],[3,4],[5],[7]]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]
[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,1,1,1,1,1]
[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]=>[7,8,5,4,3,1,2,6]=>[[1,2,8],[3,7],[4],[5],[6]]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,1,1,1,2]
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[[1,5,8],[2,7],[3],[4],[6]]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,1,1,1]
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[[1,2,8],[3,7],[4],[5],[6]]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,1,1,1,2]
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[[1,2,7,8],[3,6],[4],[5]]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,1,1,2]
[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[[1,4,7,8],[2,6],[3],[5]]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,1,1]
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,1,1,1,1,1]
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[7,8,5,3,2,1,4,6]=>[[1,2,8],[3,7],[4],[5],[6]]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,1,1,1,2]
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[[1,6,7,8],[2],[3],[4],[5]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,1,1,1,1]
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[[1,2,7,8],[3,6],[4],[5]]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,1,1,2]
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[[1,6,7,8],[2],[3],[4],[5]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,1,1,1,1]
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[[1,2,7,8],[3,6],[4],[5]]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,1,1,2]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[[1,5,6,7,8],[2],[3],[4]]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,1,1,1]
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[[1,2,6,7,8],[3,5],[4]]=>[[1,2,3,4,5],[6,8],[7]]=>[5,1,2]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,1,1,1,1,1]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[[1,2,8],[3,7],[4],[5],[6]]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,1,1,1,2]
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[8,7,3,4,2,1,5,6]=>[[1,4,7,8],[2],[3],[5],[6]]=>[[1,2,3,6],[4],[5],[7],[8]]=>[3,1,2,1,1]
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[7,8,3,4,2,1,5,6]=>[[1,2,7,8],[3,4],[5],[6]]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,1,2,2]
[[[.,[[.,.],[.,.]]],.],[[.,.],.]]=>[7,8,4,2,3,1,5,6]=>[[1,2,7,8],[3,5],[4],[6]]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,1,2]
[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[8,7,3,2,4,1,5,6]=>[[1,5,7,8],[2],[3],[4],[6]]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,1,1,1]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[[1,2,7,8],[3,5],[4],[6]]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,1,2]
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>[[1,2,5,7,8],[3,4],[6]]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]
[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[[1,2,7,8],[3,6],[4],[5]]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,1,1,2]
[[[[.,.],[[.,.],.]],.],[.,[.,.]]]=>[8,7,3,4,1,2,5,6]=>[[1,4,7,8],[2,6],[3],[5]]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,1,1]
[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[[1,2,7,8],[3,4],[5,6]]=>[[1,2,3,4],[5,6],[7,8]]=>[4,2,2]
[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[[1,2,7,8],[3,6],[4],[5]]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,1,1,2]
[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>[[1,2,6,7,8],[3,5],[4]]=>[[1,2,3,4,5],[6,8],[7]]=>[5,1,2]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[[1,6,7,8],[2],[3],[4],[5]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,1,1,1,1]
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[[1,2,7,8],[3,6],[4],[5]]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,1,1,2]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[7,8,2,3,1,4,5,6]=>[[1,2,6,7,8],[3,4],[5]]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]
[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[7,8,3,1,2,4,5,6]=>[[1,2,6,7,8],[3,5],[4]]=>[[1,2,3,4,5],[6,8],[7]]=>[5,1,2]
[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[[1,5,6,7,8],[2],[3],[4]]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,1,1,1]
[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[[1,2,6,7,8],[3,5],[4]]=>[[1,2,3,4,5],[6,8],[7]]=>[5,1,2]
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[[1,2,5,6,7,8],[3,4]]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[2,1,1,1,1,1,1]
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[8,5,6,4,3,2,1,7]=>[[1,3,8],[2],[4],[5],[6],[7]]=>[[1,2,7],[3],[4],[5],[6],[8]]=>[2,1,1,1,2,1]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[[1,3,4,8],[2],[5],[6],[7]]=>[[1,2,6,7],[3],[4],[5],[8]]=>[2,1,1,3,1]
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[8,6,5,3,4,2,1,7]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[2,1,2,1,1,1]
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[8,5,6,3,4,2,1,7]=>[[1,3,8],[2,5],[4],[6],[7]]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,1,2,2,1]
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[8,4,5,3,6,2,1,7]=>[[1,3,5,8],[2],[4],[6],[7]]=>[[1,2,5,7],[3],[4],[6],[8]]=>[2,1,2,2,1]
[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,2,3,1,7]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,1,1,1,1]
[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]=>[8,5,6,4,2,3,1,7]=>[[1,3,8],[2,6],[4],[5],[7]]=>[[1,2,4],[3,7],[5],[6],[8]]=>[2,2,1,2,1]
[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[8,6,5,3,2,4,1,7]=>[[1,6,8],[2],[3],[4],[5],[7]]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[2,2,1,1,1,1]
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[8,6,5,2,3,4,1,7]=>[[1,5,6,8],[2],[3],[4],[7]]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,1,1,1]
[[.,[[[.,.],.],[[.,.],.]]],[.,.]]=>[8,5,6,2,3,4,1,7]=>[[1,3,6,8],[2,5],[4],[7]]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[8,6,4,2,3,5,1,7]=>[[1,5,6,8],[2],[3],[4],[7]]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,1,1,1]
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[8,6,3,2,4,5,1,7]=>[[1,5,6,8],[2],[3],[4],[7]]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,1,1,1]
[[.,[[[[.,.],.],[.,.]],.]],[.,.]]=>[8,5,2,3,4,6,1,7]=>[[1,4,5,6,8],[2],[3],[7]]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,1,1]
[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,3,1,2,7]=>[[1,4,8],[2,7],[3],[5],[6]]=>[[1,2,3],[4,6],[5],[7],[8]]=>[3,1,2,1,1]
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[[1,3,8],[2,5],[4,7],[6]]=>[[1,2,3],[4,5],[6,7],[8]]=>[3,2,2,1]
[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[8,6,3,4,5,1,2,7]=>[[1,4,5,8],[2,7],[3],[6]]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,1,1]
[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[8,4,5,3,6,1,2,7]=>[[1,3,5,8],[2,7],[4],[6]]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]
[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[8,4,3,5,6,1,2,7]=>[[1,4,5,8],[2,7],[3],[6]]=>[[1,2,3,6],[4,5],[7],[8]]=>[3,3,1,1]
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,1,1,1,1,1]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,2,1,3,7]=>[[1,3,8],[2,7],[4],[5],[6]]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,1,1,2,1]
[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[[1,3,7,8],[2,6],[4],[5]]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,1,2,1]
[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[8,4,5,6,1,2,3,7]=>[[1,3,4,8],[2,6,7],[5]]=>[[1,2,3,4],[5,6,7],[8]]=>[4,3,1]
[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,1,1,1,1,1]
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[8,5,6,3,2,1,4,7]=>[[1,3,8],[2,7],[4],[5],[6]]=>[[1,2,3],[4,7],[5],[6],[8]]=>[3,1,1,2,1]
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[[1,5,7,8],[2],[3],[4],[6]]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,1,1,1]
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[[1,3,7,8],[2,5],[4],[6]]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]
[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[8,5,6,3,1,2,4,7]=>[[1,3,7,8],[2,6],[4],[5]]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,1,2,1]
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[[1,6,7,8],[2],[3],[4],[5]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,1,1,1,1]
[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[[1,3,7,8],[2,6],[4],[5]]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,1,2,1]
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[[1,5,6,7,8],[2],[3],[4]]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,1,1,1]
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[[1,3,6,7,8],[2,5],[4]]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,1,1,1,1,1]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[[1,4,7,8],[2],[3],[5],[6]]=>[[1,2,3,6],[4],[5],[7],[8]]=>[3,1,2,1,1]
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[8,6,4,2,3,1,5,7]=>[[1,5,7,8],[2],[3],[4],[6]]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,1,1,1]
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[8,6,3,2,4,1,5,7]=>[[1,5,7,8],[2],[3],[4],[6]]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,1,1,1]
[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[8,6,3,4,1,2,5,7]=>[[1,4,7,8],[2,6],[3],[5]]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,1,1]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[[1,6,7,8],[2],[3],[4],[5]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,1,1,1,1]
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[[1,5,6,7,8],[2],[3],[4]]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,1,1,1]
[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[8,6,3,2,1,4,5,7]=>[[1,6,7,8],[2],[3],[4],[5]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,1,1,1,1]
[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]=>[8,4,5,3,2,1,6,7]=>[[1,3,7,8],[2],[4],[5],[6]]=>[[1,2,3,7],[4],[5],[6],[8]]=>[3,1,1,2,1]
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[8,4,3,5,2,1,6,7]=>[[1,4,7,8],[2],[3],[5],[6]]=>[[1,2,3,6],[4],[5],[7],[8]]=>[3,1,2,1,1]
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[8,3,4,5,2,1,6,7]=>[[1,3,4,7,8],[2],[5],[6]]=>[[1,2,3,6,7],[4],[5],[8]]=>[3,1,3,1]
[[[.,[[.,.],[[.,.],.]]],.],[.,.]]=>[8,4,5,2,3,1,6,7]=>[[1,3,7,8],[2,5],[4],[6]]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[8,5,2,3,4,1,6,7]=>[[1,4,5,7,8],[2],[3],[6]]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,1,1]
[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[8,4,2,3,5,1,6,7]=>[[1,4,5,7,8],[2],[3],[6]]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,1,1]
[[[[.,.],[[.,.],[.,.]]],.],[.,.]]=>[8,5,3,4,1,2,6,7]=>[[1,4,7,8],[2,6],[3],[5]]=>[[1,2,3,4],[5,6],[7],[8]]=>[4,2,1,1]
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[8,5,4,2,1,3,6,7]=>[[1,6,7,8],[2],[3],[4],[5]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,1,1,1,1]
[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[8,5,3,2,1,4,6,7]=>[[1,6,7,8],[2],[3],[4],[5]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,1,1,1,1]
[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[[1,5,6,7,8],[2],[3],[4]]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,1,1,1]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[[1,6,7,8],[2],[3],[4],[5]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,1,1,1,1]
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[8,3,4,1,2,5,6,7]=>[[1,3,6,7,8],[2,5],[4]]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[8,4,2,1,3,5,6,7]=>[[1,5,6,7,8],[2],[3],[4]]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,1,1,1]
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[[1,5,6,7,8],[2],[3],[4]]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,1,1,1]
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>[[1,3,5,6,7,8],[2],[4]]=>[[1,2,3,4,5,7],[6],[8]]=>[5,2,1]
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[[1,4,5,6,7,8],[2],[3]]=>[[1,2,3,4,5,6],[7],[8]]=>[6,1,1]
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[[1,3,4,5,6,7,8],[2]]=>[[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]]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[2,1,1,1,1,1,1]
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[[1,2,8],[3],[4],[5],[6],[7]]=>[2,1,1,1,1,2]
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[7,5,6,4,3,2,1,8]=>[[1,3,8],[2],[4],[5],[6],[7]]=>[[1,2,7],[3],[4],[5],[6],[8]]=>[2,1,1,1,2,1]
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[[1,3,8],[2],[4],[5],[6],[7]]=>[[1,2,7],[3],[4],[5],[6],[8]]=>[2,1,1,1,2,1]
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[[1,2,3,8],[4],[5],[6],[7]]=>[[1,2,7,8],[3],[4],[5],[6]]=>[2,1,1,1,3]
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>[[1,4,8],[2],[3],[5],[6],[7]]=>[[1,2,6],[3],[4],[5],[7],[8]]=>[2,1,1,2,1,1]
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[[1,4,8],[2],[3],[5],[6],[7]]=>[[1,2,6],[3],[4],[5],[7],[8]]=>[2,1,1,2,1,1]
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>[[1,2,4,8],[3],[5],[6],[7]]=>[[1,2,6,8],[3],[4],[5],[7]]=>[2,1,1,2,2]
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[[1,2,3,4,8],[5],[6],[7]]=>[[1,2,6,7,8],[3],[4],[5]]=>[2,1,1,4]
[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[7,6,5,3,4,2,1,8]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[2,1,2,1,1,1]
[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>[6,7,5,3,4,2,1,8]=>[[1,2,8],[3,5],[4],[6],[7]]=>[[1,2,5],[3,8],[4],[6],[7]]=>[2,1,2,1,2]
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[[1,3,8],[2,5],[4],[6],[7]]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,1,2,2,1]
[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]=>[6,5,7,3,4,2,1,8]=>[[1,3,8],[2,5],[4],[6],[7]]=>[[1,2,5],[3,7],[4],[6],[8]]=>[2,1,2,2,1]
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[5,6,7,3,4,2,1,8]=>[[1,2,3,8],[4,5],[6],[7]]=>[[1,2,5,8],[3,7],[4],[6]]=>[2,1,2,3]
[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[7,3,4,5,6,2,1,8]=>[[1,3,4,5,8],[2],[6],[7]]=>[[1,2,5,6,7],[3],[4],[8]]=>[2,1,4,1]
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[[1,5,8],[2],[3],[4],[6],[7]]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[2,1,2,1,1,1]
[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[[1,3,5,8],[2],[4],[6],[7]]=>[[1,2,5,7],[3],[4],[6],[8]]=>[2,1,2,2,1]
[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[[1,4,5,8],[2],[3],[6],[7]]=>[[1,2,5,6],[3],[4],[7],[8]]=>[2,1,3,1,1]
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>[[1,2,3,8],[4,6],[5],[7]]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,1,3]
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[[1,4,8],[2,6],[3],[5],[7]]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,1,1]
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[[1,2,8],[3,4],[5,6],[7]]=>[[1,2,4],[3,6],[5,8],[7]]=>[2,2,2,2]
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[6,5,4,7,2,3,1,8]=>[[1,4,8],[2,6],[3],[5],[7]]=>[[1,2,4],[3,6],[5],[7],[8]]=>[2,2,2,1,1]
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[[1,2,4,8],[3,6],[5],[7]]=>[[1,2,4,8],[3,6],[5],[7]]=>[2,2,2,2]
[[.,[[.,.],[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,2,3,1,8]=>[[1,3,4,8],[2,6],[5],[7]]=>[[1,2,4,7],[3,6],[5],[8]]=>[2,2,3,1]
[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[4,5,6,7,2,3,1,8]=>[[1,2,3,4,8],[5,6],[7]]=>[[1,2,4,7,8],[3,6],[5]]=>[2,2,4]
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[[1,2,3,8],[4,6],[5],[7]]=>[[1,2,4,8],[3,7],[5],[6]]=>[2,2,1,3]
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,1,1,1]
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[[1,2,6,8],[3,5],[4],[7]]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,1,2]
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[[1,3,6,8],[2,5],[4],[7]]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[[1,3,6,8],[2,5],[4],[7]]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[[1,2,3,8],[4,5,6],[7]]=>[[1,2,4,5],[3,7,8],[6]]=>[2,3,3]
[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[6,7,4,3,2,5,1,8]=>[[1,2,8],[3,6],[4],[5],[7]]=>[[1,2,4],[3,8],[5],[6],[7]]=>[2,2,1,1,2]
[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[6,7,3,4,2,5,1,8]=>[[1,2,6,8],[3,4],[5],[7]]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]
[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[7,6,4,2,3,5,1,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,1,1,1]
[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[7,6,3,2,4,5,1,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,1,1,1]
[[.,[[[.,[.,.]],.],[[.,.],.]]],.]=>[6,7,3,2,4,5,1,8]=>[[1,2,6,8],[3,5],[4],[7]]=>[[1,2,4,5],[3,8],[6],[7]]=>[2,3,1,2]
[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[7,6,2,3,4,5,1,8]=>[[1,4,5,6,8],[2],[3],[7]]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,1,1]
[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[6,7,2,3,4,5,1,8]=>[[1,2,5,6,8],[3,4],[7]]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]
[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[7,4,5,3,2,6,1,8]=>[[1,3,6,8],[2],[4],[5],[7]]=>[[1,2,4,7],[3],[5],[6],[8]]=>[2,2,1,2,1]
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[7,4,3,5,2,6,1,8]=>[[1,4,6,8],[2],[3],[5],[7]]=>[[1,2,4,6],[3],[5],[7],[8]]=>[2,2,2,1,1]
[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[7,4,5,2,3,6,1,8]=>[[1,3,6,8],[2,5],[4],[7]]=>[[1,2,4,5],[3,7],[6],[8]]=>[2,3,2,1]
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[7,5,3,2,4,6,1,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,1,1,1]
[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[7,4,2,3,5,6,1,8]=>[[1,4,5,6,8],[2],[3],[7]]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,1,1]
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[[1,3,6,8],[2],[4],[5],[7]]=>[[1,2,4,7],[3],[5],[6],[8]]=>[2,2,1,2,1]
[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[5,6,3,4,2,7,1,8]=>[[1,2,6,8],[3,4],[5],[7]]=>[[1,2,4,6],[3,8],[5],[7]]=>[2,2,2,2]
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[6,3,4,5,2,7,1,8]=>[[1,3,4,6,8],[2],[5],[7]]=>[[1,2,4,6,7],[3],[5],[8]]=>[2,2,3,1]
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[[1,4,6,8],[2],[3],[5],[7]]=>[[1,2,4,6],[3],[5],[7],[8]]=>[2,2,2,1,1]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[[1,2,4,6,8],[3],[5],[7]]=>[[1,2,4,6,8],[3],[5],[7]]=>[2,2,2,2]
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[[1,2,3,4,6,8],[5],[7]]=>[[1,2,4,6,7,8],[3],[5]]=>[2,2,4]
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[6,5,3,2,4,7,1,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,1,1,1]
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[6,4,2,3,5,7,1,8]=>[[1,4,5,6,8],[2],[3],[7]]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,1,1]
[[.,[[[[.,[.,.]],.],[.,.]],.]],.]=>[6,3,2,4,5,7,1,8]=>[[1,4,5,6,8],[2],[3],[7]]=>[[1,2,4,5,6],[3],[7],[8]]=>[2,4,1,1]
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[6,2,3,4,5,7,1,8]=>[[1,3,4,5,6,8],[2],[7]]=>[[1,2,4,5,6,7],[3],[8]]=>[2,5,1]
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[[1,5,6,8],[2],[3],[4],[7]]=>[[1,2,4,5],[3],[6],[7],[8]]=>[2,3,1,1,1]
[[.,[[[[.,.],[[.,.],.]],.],.]],.]=>[4,5,2,3,6,7,1,8]=>[[1,2,5,6,8],[3,4],[7]]=>[[1,2,4,5,6],[3,8],[7]]=>[2,4,2]
[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,3,1,2,8]=>[[1,3,4,8],[2,7],[5],[6]]=>[[1,2,3,7],[4,6],[5],[8]]=>[3,1,3,1]
[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[4,5,6,7,3,1,2,8]=>[[1,2,3,4,8],[5,7],[6]]=>[[1,2,3,7,8],[4,6],[5]]=>[3,1,4]
[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[6,5,4,3,7,1,2,8]=>[[1,5,8],[2,7],[3],[4],[6]]=>[[1,2,3],[4,5],[6],[7],[8]]=>[3,2,1,1,1]
[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[6,4,5,3,7,1,2,8]=>[[1,3,5,8],[2,7],[4],[6]]=>[[1,2,3,7],[4,5],[6],[8]]=>[3,2,2,1]
[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[3,4,5,6,7,1,2,8]=>[[1,2,3,4,5,8],[6,7]]=>[[1,2,3,6,7,8],[4,5]]=>[3,5]
[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[4,5,6,7,2,1,3,8]=>[[1,2,3,4,8],[5,7],[6]]=>[[1,2,3,7,8],[4,6],[5]]=>[3,1,4]
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,1,1,1,1]
[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[4,5,6,7,1,2,3,8]=>[[1,2,3,4,8],[5,6,7]]=>[[1,2,3,4,8],[5,6,7]]=>[4,4]
[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[7,6,5,2,3,1,4,8]=>[[1,5,7,8],[2],[3],[4],[6]]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,1,1,1]
[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[6,7,5,2,3,1,4,8]=>[[1,2,7,8],[3,5],[4],[6]]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,1,2]
[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[7,5,6,2,3,1,4,8]=>[[1,3,7,8],[2,5],[4],[6]]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]
[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[6,5,7,2,3,1,4,8]=>[[1,3,7,8],[2,5],[4],[6]]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[5,6,7,2,3,1,4,8]=>[[1,2,3,8],[4,5,7],[6]]=>[[1,2,3,5],[4,7,8],[6]]=>[3,2,3]
[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[7,6,5,2,1,3,4,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,1,1,1,1]
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,1,1,1]
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[[1,2,6,7,8],[3,5],[4]]=>[[1,2,3,4,5],[6,8],[7]]=>[5,1,2]
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[[1,3,6,7,8],[2,5],[4]]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[[1,3,6,7,8],[2,5],[4]]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[[1,2,3,7,8],[4,5,6]]=>[[1,2,3,4,5],[6,7,8]]=>[5,3]
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[7,6,4,3,2,1,5,8]=>[[1,7,8],[2],[3],[4],[5],[6]]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[3,1,1,1,1,1]
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[6,7,4,3,2,1,5,8]=>[[1,2,8],[3,7],[4],[5],[6]]=>[[1,2,3],[4,8],[5],[6],[7]]=>[3,1,1,1,2]
[[[.,[.,[[.,.],.]]],[[.,.],.]],.]=>[6,7,3,4,2,1,5,8]=>[[1,2,7,8],[3,4],[5],[6]]=>[[1,2,3,6],[4,8],[5],[7]]=>[3,1,2,2]
[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[7,6,4,2,3,1,5,8]=>[[1,5,7,8],[2],[3],[4],[6]]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,1,1,1]
[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[7,6,3,2,4,1,5,8]=>[[1,5,7,8],[2],[3],[4],[6]]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,1,1,1]
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[7,6,2,3,4,1,5,8]=>[[1,4,5,7,8],[2],[3],[6]]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,1,1]
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[6,7,2,3,4,1,5,8]=>[[1,2,5,7,8],[3,4],[6]]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,1,1,1,1]
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[7,6,3,2,1,4,5,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,1,1,1,1]
[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[6,7,3,2,1,4,5,8]=>[[1,2,7,8],[3,6],[4],[5]]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,1,1,2]
[[[[.,[[.,.],.]],.],[.,[.,.]]],.]=>[7,6,2,3,1,4,5,8]=>[[1,4,6,7,8],[2],[3],[5]]=>[[1,2,3,4,6],[5],[7],[8]]=>[4,2,1,1]
[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[6,7,3,1,2,4,5,8]=>[[1,2,6,7,8],[3,5],[4]]=>[[1,2,3,4,5],[6,8],[7]]=>[5,1,2]
[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>[[1,2,5,6,7,8],[3,4]]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]
[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[7,5,2,3,4,1,6,8]=>[[1,4,5,7,8],[2],[3],[6]]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,1,1]
[[[.,[[[.,.],[.,.]],.]],[.,.]],.]=>[7,4,2,3,5,1,6,8]=>[[1,4,5,7,8],[2],[3],[6]]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,1,1]
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[7,2,3,4,5,1,6,8]=>[[1,3,4,5,7,8],[2],[6]]=>[[1,2,3,5,6,7],[4],[8]]=>[3,4,1]
[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[7,4,5,1,2,3,6,8]=>[[1,3,6,7,8],[2,5],[4]]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[7,5,3,2,1,4,6,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,1,1,1,1]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,1,1,1]
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[[1,4,5,6,7,8],[2],[3]]=>[[1,2,3,4,5,6],[7],[8]]=>[6,1,1]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,1,1,1,1]
[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[7,4,3,1,2,5,6,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,1,1,1]
[[[[[.,.],[[.,.],.]],.],[.,.]],.]=>[7,3,4,1,2,5,6,8]=>[[1,3,6,7,8],[2,5],[4]]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[7,3,1,2,4,5,6,8]=>[[1,4,5,6,7,8],[2],[3]]=>[[1,2,3,4,5,6],[7],[8]]=>[6,1,1]
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[[1,3,4,5,6,7,8],[2]]=>[[1,2,3,4,5,6,7],[8]]=>[7,1]
[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[[1,2,7,8],[3],[4],[5],[6]]=>[[1,2,3,8],[4],[5],[6],[7]]=>[3,1,1,1,2]
[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>[[1,3,7,8],[2],[4],[5],[6]]=>[[1,2,3,7],[4],[5],[6],[8]]=>[3,1,1,2,1]
[[[.,[.,[.,[[[.,.],.],.]]]],.],.]=>[4,5,6,3,2,1,7,8]=>[[1,2,3,7,8],[4],[5],[6]]=>[[1,2,3,7,8],[4],[5],[6]]=>[3,1,1,3]
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>[[1,4,7,8],[2],[3],[5],[6]]=>[[1,2,3,6],[4],[5],[7],[8]]=>[3,1,2,1,1]
[[[.,[.,[[[[.,.],.],.],.]]],.],.]=>[3,4,5,6,2,1,7,8]=>[[1,2,3,4,7,8],[5],[6]]=>[[1,2,3,6,7,8],[4],[5]]=>[3,1,4]
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[5,4,6,2,3,1,7,8]=>[[1,3,7,8],[2,5],[4],[6]]=>[[1,2,3,5],[4,7],[6],[8]]=>[3,2,2,1]
[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[5,6,3,2,4,1,7,8]=>[[1,2,7,8],[3,5],[4],[6]]=>[[1,2,3,5],[4,8],[6],[7]]=>[3,2,1,2]
[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[6,5,2,3,4,1,7,8]=>[[1,4,5,7,8],[2],[3],[6]]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,1,1]
[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[5,6,2,3,4,1,7,8]=>[[1,2,5,7,8],[3,4],[6]]=>[[1,2,3,5,6],[4,8],[7]]=>[3,3,2]
[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[6,4,3,2,5,1,7,8]=>[[1,5,7,8],[2],[3],[4],[6]]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,1,1,1]
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[[1,5,7,8],[2],[3],[4],[6]]=>[[1,2,3,5],[4],[6],[7],[8]]=>[3,2,1,1,1]
[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[[1,2,5,7,8],[3],[4],[6]]=>[[1,2,3,5,8],[4],[6],[7]]=>[3,2,1,2]
[[[.,[[[.,[.,.]],[.,.]],.]],.],.]=>[5,3,2,4,6,1,7,8]=>[[1,4,5,7,8],[2],[3],[6]]=>[[1,2,3,5,6],[4],[7],[8]]=>[3,3,1,1]
[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[6,5,4,3,1,2,7,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,1,1,1,1]
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[5,6,4,2,1,3,7,8]=>[[1,2,7,8],[3,6],[4],[5]]=>[[1,2,3,4],[5,8],[6],[7]]=>[4,1,1,2]
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[6,4,5,2,1,3,7,8]=>[[1,3,7,8],[2,6],[4],[5]]=>[[1,2,3,4],[5,7],[6],[8]]=>[4,1,2,1]
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[6,4,3,2,1,5,7,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,1,1,1,1]
[[[[.,[.,[[.,.],.]]],[.,.]],.],.]=>[6,3,4,2,1,5,7,8]=>[[1,3,6,7,8],[2],[4],[5]]=>[[1,2,3,4,7],[5],[6],[8]]=>[4,1,2,1]
[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[6,4,3,1,2,5,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,1,1,1]
[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[6,4,2,1,3,5,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,1,1,1]
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[[1,6,7,8],[2],[3],[4],[5]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[4,1,1,1,1]
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[[1,2,6,7,8],[3],[4],[5]]=>[[1,2,3,4,8],[5],[6],[7]]=>[4,1,1,2]
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[5,3,4,2,1,6,7,8]=>[[1,3,6,7,8],[2],[4],[5]]=>[[1,2,3,4,7],[5],[6],[8]]=>[4,1,2,1]
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[[1,3,6,7,8],[2],[4],[5]]=>[[1,2,3,4,7],[5],[6],[8]]=>[4,1,2,1]
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[[1,2,3,6,7,8],[4],[5]]=>[[1,2,3,4,7,8],[5],[6]]=>[4,1,3]
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[5,4,2,3,1,6,7,8]=>[[1,4,6,7,8],[2],[3],[5]]=>[[1,2,3,4,6],[5],[7],[8]]=>[4,2,1,1]
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>[[1,2,6,7,8],[3,4],[5]]=>[[1,2,3,4,6],[5,8],[7]]=>[4,2,2]
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[5,3,2,4,1,6,7,8]=>[[1,4,6,7,8],[2],[3],[5]]=>[[1,2,3,4,6],[5],[7],[8]]=>[4,2,1,1]
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[[1,3,4,6,7,8],[2],[5]]=>[[1,2,3,4,6,7],[5],[8]]=>[4,3,1]
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[[1,4,6,7,8],[2],[3],[5]]=>[[1,2,3,4,6],[5],[7],[8]]=>[4,2,1,1]
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[[1,2,4,6,7,8],[3],[5]]=>[[1,2,3,4,6,8],[5],[7]]=>[4,2,2]
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[4,2,3,5,1,6,7,8]=>[[1,3,4,6,7,8],[2],[5]]=>[[1,2,3,4,6,7],[5],[8]]=>[4,3,1]
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[[1,3,4,6,7,8],[2],[5]]=>[[1,2,3,4,6,7],[5],[8]]=>[4,3,1]
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[[1,2,3,4,6,7,8],[5]]=>[[1,2,3,4,6,7,8],[5]]=>[4,4]
[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[5,4,3,1,2,6,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,1,1,1]
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[5,3,4,1,2,6,7,8]=>[[1,3,6,7,8],[2,5],[4]]=>[[1,2,3,4,5],[6,7],[8]]=>[5,2,1]
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[5,4,2,1,3,6,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,1,1,1]
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[5,4,1,2,3,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>[[1,2,3,4,5,6],[7],[8]]=>[6,1,1]
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[4,5,1,2,3,6,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[5,3,2,1,4,6,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,1,1,1]
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[5,2,3,1,4,6,7,8]=>[[1,3,5,6,7,8],[2],[4]]=>[[1,2,3,4,5,7],[6],[8]]=>[5,2,1]
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[5,3,1,2,4,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>[[1,2,3,4,5,6],[7],[8]]=>[6,1,1]
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[5,2,1,3,4,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>[[1,2,3,4,5,6],[7],[8]]=>[6,1,1]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[[1,3,4,5,6,7,8],[2]]=>[[1,2,3,4,5,6,7],[8]]=>[7,1]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[[1,5,6,7,8],[2],[3],[4]]=>[[1,2,3,4,5],[6],[7],[8]]=>[5,1,1,1]
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[[1,2,5,6,7,8],[3],[4]]=>[[1,2,3,4,5,8],[6],[7]]=>[5,1,2]
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[4,2,3,1,5,6,7,8]=>[[1,3,5,6,7,8],[2],[4]]=>[[1,2,3,4,5,7],[6],[8]]=>[5,2,1]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[[1,3,5,6,7,8],[2],[4]]=>[[1,2,3,4,5,7],[6],[8]]=>[5,2,1]
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[[1,2,3,5,6,7,8],[4]]=>[[1,2,3,4,5,7,8],[6]]=>[5,3]
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[4,3,1,2,5,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>[[1,2,3,4,5,6],[7],[8]]=>[6,1,1]
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>[[1,2,5,6,7,8],[3,4]]=>[[1,2,3,4,5,6],[7,8]]=>[6,2]
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[4,2,1,3,5,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>[[1,2,3,4,5,6],[7],[8]]=>[6,1,1]
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[[1,3,4,5,6,7,8],[2]]=>[[1,2,3,4,5,6,7],[8]]=>[7,1]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]=>[[1,2,3,4,5,6],[7],[8]]=>[6,1,1]
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[[1,2,4,5,6,7,8],[3]]=>[[1,2,3,4,5,6,8],[7]]=>[6,2]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[2]]=>[[1,2,3,4,5,6,7],[8]]=>[7,1]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[[1,3,4,5,6,7,8],[2]]=>[[1,2,3,4,5,6,7],[8]]=>[7,1]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8]]=>[[1,2,3,4,5,6,7,8]]=>[8]
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 recording tableau
Description
Sends a permutation to its Robinson-Schensted recording 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 recording 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 recording tableau.
Map
Schützenberger involution
Description
Sends a standard tableau to the standard tableau obtained via the Schützenberger involution.
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 $i$.
searching the database
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