Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00059: Permutations —Robinson-Schensted insertion tableau⟶ Standard tableaux
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00059: Permutations —Robinson-Schensted insertion tableau⟶ Standard tableaux
Images
=>
Cc0010;cc-rep-0Cc0007;cc-rep-3
[.,.]=>[1]=>[1]=>[[1]]
[.,[.,.]]=>[2,1]=>[2,1]=>[[1],[2]]
[[.,.],.]=>[1,2]=>[1,2]=>[[1,2]]
[.,[.,[.,.]]]=>[3,2,1]=>[2,3,1]=>[[1,3],[2]]
[.,[[.,.],.]]=>[2,3,1]=>[3,2,1]=>[[1],[2],[3]]
[[.,.],[.,.]]=>[3,1,2]=>[3,1,2]=>[[1,2],[3]]
[[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>[[1,3],[2]]
[[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>[[1,2,3]]
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[2,3,4,1]=>[[1,3,4],[2]]
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[2,4,3,1]=>[[1,3],[2],[4]]
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[3,4,2,1]=>[[1,4],[2],[3]]
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,3,2,1]=>[[1],[2],[3],[4]]
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,2,3,1]=>[[1,3],[2],[4]]
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[3,1,4,2]=>[[1,2],[3,4]]
[[.,.],[[.,.],.]]=>[3,4,1,2]=>[4,1,3,2]=>[[1,2],[3],[4]]
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[2,4,1,3]=>[[1,3],[2,4]]
[[[.,.],.],[.,.]]=>[4,1,2,3]=>[4,1,2,3]=>[[1,2,3],[4]]
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[2,3,1,4]=>[[1,3,4],[2]]
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,2,1,4]=>[[1,4],[2],[3]]
[[[.,.],[.,.]],.]=>[3,1,2,4]=>[3,1,2,4]=>[[1,2,4],[3]]
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>[[1,3,4],[2]]
[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>[[1,2,3,4]]
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[[1,3,4,5],[2]]
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[2,3,5,4,1]=>[[1,3,4],[2],[5]]
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[2,4,5,3,1]=>[[1,3,5],[2],[4]]
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[2,5,4,3,1]=>[[1,3],[2],[4],[5]]
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[2,5,3,4,1]=>[[1,3,4],[2],[5]]
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[3,4,2,5,1]=>[[1,4,5],[2],[3]]
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[3,5,2,4,1]=>[[1,4],[2,5],[3]]
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[4,3,5,2,1]=>[[1,5],[2],[3],[4]]
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[4,5,2,3,1]=>[[1,3],[2,5],[4]]
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,3,4,2,1]=>[[1,4],[2],[3],[5]]
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,4,3,2,1]=>[[1],[2],[3],[4],[5]]
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[5,4,2,3,1]=>[[1,3],[2],[4],[5]]
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,3,2,4,1]=>[[1,4],[2],[3],[5]]
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[[1,3,4],[2],[5]]
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[3,1,4,5,2]=>[[1,2,5],[3,4]]
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[3,1,5,4,2]=>[[1,2],[3,4],[5]]
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[[1,2],[3,5],[4]]
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[[1,2],[3],[4],[5]]
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[5,1,3,4,2]=>[[1,2,4],[3],[5]]
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[2,4,1,5,3]=>[[1,3,5],[2,4]]
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[2,5,1,4,3]=>[[1,3],[2,4],[5]]
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[[1,2,3],[4,5]]
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[1,2,3],[4],[5]]
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[2,3,5,1,4]=>[[1,3,4],[2,5]]
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[3,5,2,1,4]=>[[1,4],[2,5],[3]]
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[[1,2,4],[3,5]]
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[[1,3,4],[2,5]]
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[[1,2,3,4],[5]]
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[2,3,4,1,5]=>[[1,3,4,5],[2]]
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[2,4,3,1,5]=>[[1,3,5],[2],[4]]
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[3,4,2,1,5]=>[[1,4,5],[2],[3]]
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,3,2,1,5]=>[[1,5],[2],[3],[4]]
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[[1,3,5],[2],[4]]
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[[1,2,5],[3,4]]
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[1,2,5],[3],[4]]
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[[1,3,5],[2,4]]
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[[1,2,3,5],[4]]
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[[1,3,4,5],[2]]
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[[1,4,5],[2],[3]]
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[[1,2,4,5],[3]]
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[1,3,4,5],[2]]
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[[1,2,3,4,5]]
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[[1,3,4,5,6],[2]]
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[2,3,4,6,5,1]=>[[1,3,4,5],[2],[6]]
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[2,3,5,6,4,1]=>[[1,3,4,6],[2],[5]]
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[2,3,6,5,4,1]=>[[1,3,4],[2],[5],[6]]
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[2,3,6,4,5,1]=>[[1,3,4,5],[2],[6]]
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[[1,3,5,6],[2],[4]]
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[2,4,6,3,5,1]=>[[1,3,5],[2,6],[4]]
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[2,5,4,6,3,1]=>[[1,3,6],[2],[4],[5]]
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[2,5,6,3,4,1]=>[[1,3,4],[2,6],[5]]
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[2,6,4,5,3,1]=>[[1,3,5],[2],[4],[6]]
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[2,6,5,4,3,1]=>[[1,3],[2],[4],[5],[6]]
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[2,6,5,3,4,1]=>[[1,3,4],[2],[5],[6]]
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[2,6,4,3,5,1]=>[[1,3,5],[2],[4],[6]]
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[2,6,3,4,5,1]=>[[1,3,4,5],[2],[6]]
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[3,4,2,5,6,1]=>[[1,4,5,6],[2],[3]]
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[3,4,2,6,5,1]=>[[1,4,5],[2,6],[3]]
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[3,5,2,6,4,1]=>[[1,4,6],[2,5],[3]]
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[3,6,2,5,4,1]=>[[1,4],[2,5],[3],[6]]
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[3,6,2,4,5,1]=>[[1,4,5],[2,6],[3]]
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[4,3,5,2,6,1]=>[[1,5,6],[2],[3],[4]]
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[4,3,6,2,5,1]=>[[1,5],[2,6],[3],[4]]
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[4,5,2,3,6,1]=>[[1,3,6],[2,5],[4]]
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[4,6,2,3,5,1]=>[[1,3,5],[2,6],[4]]
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>[[1,4,6],[2],[3],[5]]
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[5,4,6,3,2,1]=>[[1,6],[2],[3],[4],[5]]
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[5,4,2,6,3,1]=>[[1,3],[2,6],[4],[5]]
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[5,3,6,2,4,1]=>[[1,4],[2,6],[3],[5]]
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[5,6,2,3,4,1]=>[[1,3,4],[2,6],[5]]
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,3,4,5,2,1]=>[[1,4,5],[2],[3],[6]]
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,3,5,4,2,1]=>[[1,4],[2],[3],[5],[6]]
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[6,4,5,3,2,1]=>[[1,5],[2],[3],[4],[6]]
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6]]
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>[[1,4],[2],[3],[5],[6]]
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[6,4,2,5,3,1]=>[[1,3],[2,5],[4],[6]]
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[6,5,2,4,3,1]=>[[1,3],[2],[4],[5],[6]]
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[6,3,5,2,4,1]=>[[1,4],[2,5],[3],[6]]
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[6,5,2,3,4,1]=>[[1,3,4],[2],[5],[6]]
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,3,4,2,5,1]=>[[1,4,5],[2],[3],[6]]
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>[[1,5],[2],[3],[4],[6]]
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[6,4,2,3,5,1]=>[[1,3,5],[2],[4],[6]]
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>[[1,4,5],[2],[3],[6]]
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[[1,3,4,5],[2],[6]]
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]=>[[1,2,5,6],[3,4]]
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[3,1,4,6,5,2]=>[[1,2,5],[3,4],[6]]
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[3,1,5,6,4,2]=>[[1,2,6],[3,4],[5]]
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[3,1,6,5,4,2]=>[[1,2],[3,4],[5],[6]]
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[3,1,6,4,5,2]=>[[1,2,5],[3,4],[6]]
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[4,1,5,3,6,2]=>[[1,2,6],[3,5],[4]]
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>[[1,2,5],[3,6],[4]]
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[5,1,4,6,3,2]=>[[1,2,6],[3],[4],[5]]
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[5,1,6,3,4,2]=>[[1,2,4],[3,6],[5]]
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[6,1,4,5,3,2]=>[[1,2,5],[3],[4],[6]]
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[6,1,5,4,3,2]=>[[1,2],[3],[4],[5],[6]]
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[6,1,5,3,4,2]=>[[1,2,4],[3],[5],[6]]
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[6,1,4,3,5,2]=>[[1,2,5],[3],[4],[6]]
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[6,1,3,4,5,2]=>[[1,2,4,5],[3],[6]]
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]=>[[1,3,5,6],[2,4]]
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[2,4,1,6,5,3]=>[[1,3,5],[2,4],[6]]
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[2,5,1,6,4,3]=>[[1,3,6],[2,4],[5]]
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[2,6,1,5,4,3]=>[[1,3],[2,4],[5],[6]]
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[2,6,1,4,5,3]=>[[1,3,5],[2,4],[6]]
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]=>[[1,2,3,6],[4,5]]
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[4,1,2,6,5,3]=>[[1,2,3],[4,5],[6]]
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>[[1,2,3],[4,6],[5]]
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>[[1,2,3],[4],[5],[6]]
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[1,2,3,5],[4],[6]]
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[2,3,5,1,6,4]=>[[1,3,4,6],[2,5]]
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[2,3,6,1,5,4]=>[[1,3,4],[2,5],[6]]
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[3,5,2,1,6,4]=>[[1,4,6],[2,5],[3]]
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[3,6,2,1,5,4]=>[[1,4],[2,5],[3,6]]
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]=>[[1,2,4],[3,5,6]]
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[3,1,6,2,5,4]=>[[1,2,4],[3,5],[6]]
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[2,5,1,3,6,4]=>[[1,3,4],[2,5,6]]
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[2,6,1,3,5,4]=>[[1,3,4],[2,5],[6]]
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>[[1,2,3,4],[5,6]]
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[[1,2,3,4],[5],[6]]
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[2,3,4,6,1,5]=>[[1,3,4,5],[2,6]]
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[2,4,6,3,1,5]=>[[1,3,5],[2,6],[4]]
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[3,4,2,6,1,5]=>[[1,4,5],[2,6],[3]]
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[4,3,6,2,1,5]=>[[1,5],[2,6],[3],[4]]
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[4,6,2,3,1,5]=>[[1,3,5],[2,6],[4]]
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]=>[[1,2,5],[3,4,6]]
[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>[[1,2,5],[3,6],[4]]
[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[2,4,1,6,3,5]=>[[1,3,5],[2,4,6]]
[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>[[1,2,3,5],[4,6]]
[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[2,3,6,1,4,5]=>[[1,3,4,5],[2,6]]
[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[3,6,2,1,4,5]=>[[1,4,5],[2,6],[3]]
[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>[[1,2,4,5],[3,6]]
[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>[[1,3,4,5],[2,6]]
[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>[[1,2,3,4,5],[6]]
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[[1,3,4,5,6],[2]]
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[2,3,5,4,1,6]=>[[1,3,4,6],[2],[5]]
[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[2,4,5,3,1,6]=>[[1,3,5,6],[2],[4]]
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[2,5,4,3,1,6]=>[[1,3,6],[2],[4],[5]]
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[2,5,3,4,1,6]=>[[1,3,4,6],[2],[5]]
[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[3,4,2,5,1,6]=>[[1,4,5,6],[2],[3]]
[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[3,5,2,4,1,6]=>[[1,4,6],[2,5],[3]]
[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[4,3,5,2,1,6]=>[[1,5,6],[2],[3],[4]]
[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[4,5,2,3,1,6]=>[[1,3,6],[2,5],[4]]
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[5,3,4,2,1,6]=>[[1,4,6],[2],[3],[5]]
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>[[1,6],[2],[3],[4],[5]]
[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[5,4,2,3,1,6]=>[[1,3,6],[2],[4],[5]]
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[5,3,2,4,1,6]=>[[1,4,6],[2],[3],[5]]
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[[1,3,4,6],[2],[5]]
[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[3,1,4,5,2,6]=>[[1,2,5,6],[3,4]]
[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[3,1,5,4,2,6]=>[[1,2,6],[3,4],[5]]
[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>[[1,2,6],[3,5],[4]]
[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>[[1,2,6],[3],[4],[5]]
[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[5,1,3,4,2,6]=>[[1,2,4,6],[3],[5]]
[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[2,4,1,5,3,6]=>[[1,3,5,6],[2,4]]
[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[2,5,1,4,3,6]=>[[1,3,6],[2,4],[5]]
[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>[[1,2,3,6],[4,5]]
[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[[1,2,3,6],[4],[5]]
[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[2,3,5,1,4,6]=>[[1,3,4,6],[2,5]]
[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[3,5,2,1,4,6]=>[[1,4,6],[2,5],[3]]
[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>[[1,2,4,6],[3,5]]
[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>[[1,3,4,6],[2,5]]
[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>[[1,2,3,4,6],[5]]
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>[[1,3,4,5,6],[2]]
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[2,4,3,1,5,6]=>[[1,3,5,6],[2],[4]]
[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[3,4,2,1,5,6]=>[[1,4,5,6],[2],[3]]
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>[[1,5,6],[2],[3],[4]]
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[[1,3,5,6],[2],[4]]
[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>[[1,2,5,6],[3,4]]
[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[[1,2,5,6],[3],[4]]
[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>[[1,3,5,6],[2,4]]
[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>[[1,2,3,5,6],[4]]
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[[1,3,4,5,6],[2]]
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[[1,4,5,6],[2],[3]]
[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>[[1,2,4,5,6],[3]]
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[[1,3,4,5,6],[2]]
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[[1,2,3,4,5,6]]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[[1,3,4,5,6,7],[2]]
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[2,3,4,5,7,6,1]=>[[1,3,4,5,6],[2],[7]]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[2,3,4,6,7,5,1]=>[[1,3,4,5,7],[2],[6]]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[2,3,4,7,6,5,1]=>[[1,3,4,5],[2],[6],[7]]
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[2,3,4,7,5,6,1]=>[[1,3,4,5,6],[2],[7]]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[2,3,5,6,4,7,1]=>[[1,3,4,6,7],[2],[5]]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[2,3,5,7,4,6,1]=>[[1,3,4,6],[2,7],[5]]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[2,3,6,5,7,4,1]=>[[1,3,4,7],[2],[5],[6]]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[2,3,6,7,4,5,1]=>[[1,3,4,5],[2,7],[6]]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[2,3,7,5,6,4,1]=>[[1,3,4,6],[2],[5],[7]]
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[2,3,7,6,5,4,1]=>[[1,3,4],[2],[5],[6],[7]]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[2,3,7,6,4,5,1]=>[[1,3,4,5],[2],[6],[7]]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[2,3,7,5,4,6,1]=>[[1,3,4,6],[2],[5],[7]]
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[2,3,7,4,5,6,1]=>[[1,3,4,5,6],[2],[7]]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[2,4,5,3,6,7,1]=>[[1,3,5,6,7],[2],[4]]
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[2,4,5,3,7,6,1]=>[[1,3,5,6],[2,7],[4]]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[2,4,6,3,7,5,1]=>[[1,3,5,7],[2,6],[4]]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[2,4,7,3,6,5,1]=>[[1,3,5],[2,6],[4],[7]]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[2,4,7,3,5,6,1]=>[[1,3,5,6],[2,7],[4]]
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[[1,3,6,7],[2],[4],[5]]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[2,5,4,7,3,6,1]=>[[1,3,6],[2,7],[4],[5]]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>[[1,3,4,7],[2,6],[5]]
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[2,5,7,3,4,6,1]=>[[1,3,4,6],[2,7],[5]]
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[2,6,4,5,7,3,1]=>[[1,3,5,7],[2],[4],[6]]
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[2,6,5,7,4,3,1]=>[[1,3,7],[2],[4],[5],[6]]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[2,6,5,3,7,4,1]=>[[1,3,4],[2,7],[5],[6]]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[2,6,4,7,3,5,1]=>[[1,3,5],[2,7],[4],[6]]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[2,6,7,3,4,5,1]=>[[1,3,4,5],[2,7],[6]]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[2,7,4,5,6,3,1]=>[[1,3,5,6],[2],[4],[7]]
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[2,7,4,6,5,3,1]=>[[1,3,5],[2],[4],[6],[7]]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[2,7,5,6,4,3,1]=>[[1,3,6],[2],[4],[5],[7]]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[2,7,6,5,4,3,1]=>[[1,3],[2],[4],[5],[6],[7]]
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[2,7,6,4,5,3,1]=>[[1,3,5],[2],[4],[6],[7]]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[2,7,5,3,6,4,1]=>[[1,3,4],[2,6],[5],[7]]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[2,7,6,3,5,4,1]=>[[1,3,4],[2],[5],[6],[7]]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[2,7,4,6,3,5,1]=>[[1,3,5],[2,6],[4],[7]]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[2,7,6,3,4,5,1]=>[[1,3,4,5],[2],[6],[7]]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[2,7,4,5,3,6,1]=>[[1,3,5,6],[2],[4],[7]]
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[2,7,5,4,3,6,1]=>[[1,3,6],[2],[4],[5],[7]]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[2,7,5,3,4,6,1]=>[[1,3,4,6],[2],[5],[7]]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[2,7,4,3,5,6,1]=>[[1,3,5,6],[2],[4],[7]]
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[2,7,3,4,5,6,1]=>[[1,3,4,5,6],[2],[7]]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[3,4,2,5,6,7,1]=>[[1,4,5,6,7],[2],[3]]
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[3,4,2,5,7,6,1]=>[[1,4,5,6],[2,7],[3]]
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[3,4,2,6,7,5,1]=>[[1,4,5,7],[2,6],[3]]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[3,4,2,7,6,5,1]=>[[1,4,5],[2,6],[3],[7]]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[3,4,2,7,5,6,1]=>[[1,4,5,6],[2,7],[3]]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[3,5,2,6,4,7,1]=>[[1,4,6,7],[2,5],[3]]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[3,5,2,7,4,6,1]=>[[1,4,6],[2,5,7],[3]]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[3,6,2,5,7,4,1]=>[[1,4,7],[2,5],[3],[6]]
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[3,6,2,7,4,5,1]=>[[1,4,5],[2,6,7],[3]]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[3,7,2,5,6,4,1]=>[[1,4,6],[2,5],[3],[7]]
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[3,7,2,6,5,4,1]=>[[1,4],[2,5],[3],[6],[7]]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[3,7,2,6,4,5,1]=>[[1,4,5],[2,6],[3],[7]]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[3,7,2,5,4,6,1]=>[[1,4,6],[2,5],[3],[7]]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[3,7,2,4,5,6,1]=>[[1,4,5,6],[2,7],[3]]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[4,3,5,2,6,7,1]=>[[1,5,6,7],[2],[3],[4]]
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[4,3,5,2,7,6,1]=>[[1,5,6],[2,7],[3],[4]]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[4,3,6,2,7,5,1]=>[[1,5,7],[2,6],[3],[4]]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[4,3,7,2,6,5,1]=>[[1,5],[2,6],[3,7],[4]]
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[4,3,7,2,5,6,1]=>[[1,5,6],[2,7],[3],[4]]
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[4,5,2,3,6,7,1]=>[[1,3,6,7],[2,5],[4]]
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[4,5,2,3,7,6,1]=>[[1,3,6],[2,5,7],[4]]
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[4,6,2,3,7,5,1]=>[[1,3,5],[2,6,7],[4]]
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[4,7,2,3,6,5,1]=>[[1,3,5],[2,6],[4],[7]]
[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[4,7,2,3,5,6,1]=>[[1,3,5,6],[2,7],[4]]
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[5,3,4,6,2,7,1]=>[[1,4,6,7],[2],[3],[5]]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[5,3,4,7,2,6,1]=>[[1,4,6],[2,7],[3],[5]]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[5,4,6,3,2,7,1]=>[[1,6,7],[2],[3],[4],[5]]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[5,4,7,3,2,6,1]=>[[1,6],[2,7],[3],[4],[5]]
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[5,4,2,6,3,7,1]=>[[1,3,7],[2,6],[4],[5]]
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[5,4,2,7,3,6,1]=>[[1,3,6],[2,7],[4],[5]]
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[5,3,6,2,4,7,1]=>[[1,4,7],[2,6],[3],[5]]
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[5,3,7,2,4,6,1]=>[[1,4,6],[2,7],[3],[5]]
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[5,6,2,3,4,7,1]=>[[1,3,4,7],[2,6],[5]]
[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[5,7,2,3,4,6,1]=>[[1,3,4,6],[2,7],[5]]
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[[1,4,5,7],[2],[3],[6]]
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[6,3,5,7,4,2,1]=>[[1,4,7],[2],[3],[5],[6]]
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[6,4,5,3,7,2,1]=>[[1,5,7],[2],[3],[4],[6]]
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[6,5,4,7,3,2,1]=>[[1,7],[2],[3],[4],[5],[6]]
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[6,5,7,3,4,2,1]=>[[1,4],[2,7],[3],[5],[6]]
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[6,4,2,5,7,3,1]=>[[1,3,7],[2,5],[4],[6]]
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[6,5,2,7,4,3,1]=>[[1,3],[2,7],[4],[5],[6]]
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[6,3,5,2,7,4,1]=>[[1,4,7],[2,5],[3],[6]]
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[6,5,2,3,7,4,1]=>[[1,3,4],[2,7],[5],[6]]
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[6,3,4,7,2,5,1]=>[[1,4,5],[2,7],[3],[6]]
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[6,4,7,3,2,5,1]=>[[1,5],[2,7],[3],[4],[6]]
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[6,4,2,7,3,5,1]=>[[1,3,5],[2,7],[4],[6]]
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[6,3,7,2,4,5,1]=>[[1,4,5],[2,7],[3],[6]]
[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[6,7,2,3,4,5,1]=>[[1,3,4,5],[2,7],[6]]
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[7,3,4,5,6,2,1]=>[[1,4,5,6],[2],[3],[7]]
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[7,3,4,6,5,2,1]=>[[1,4,5],[2],[3],[6],[7]]
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[7,3,5,6,4,2,1]=>[[1,4,6],[2],[3],[5],[7]]
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[7,3,6,5,4,2,1]=>[[1,4],[2],[3],[5],[6],[7]]
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[7,3,6,4,5,2,1]=>[[1,4,5],[2],[3],[6],[7]]
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[7,4,5,3,6,2,1]=>[[1,5,6],[2],[3],[4],[7]]
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[7,4,6,3,5,2,1]=>[[1,5],[2,6],[3],[4],[7]]
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[7,5,4,6,3,2,1]=>[[1,6],[2],[3],[4],[5],[7]]
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[7,5,6,3,4,2,1]=>[[1,4],[2,6],[3],[5],[7]]
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[7,6,4,5,3,2,1]=>[[1,5],[2],[3],[4],[6],[7]]
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7]]
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[7,6,5,3,4,2,1]=>[[1,4],[2],[3],[5],[6],[7]]
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[7,6,4,3,5,2,1]=>[[1,5],[2],[3],[4],[6],[7]]
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[7,6,3,4,5,2,1]=>[[1,4,5],[2],[3],[6],[7]]
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[7,4,2,5,6,3,1]=>[[1,3,6],[2,5],[4],[7]]
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[7,4,2,6,5,3,1]=>[[1,3],[2,5],[4],[6],[7]]
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[7,5,2,6,4,3,1]=>[[1,3],[2,6],[4],[5],[7]]
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[7,6,2,5,4,3,1]=>[[1,3],[2],[4],[5],[6],[7]]
[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[7,6,2,4,5,3,1]=>[[1,3,5],[2],[4],[6],[7]]
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[7,3,5,2,6,4,1]=>[[1,4,6],[2,5],[3],[7]]
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[7,3,6,2,5,4,1]=>[[1,4],[2,5],[3],[6],[7]]
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[7,5,2,3,6,4,1]=>[[1,3,4],[2,6],[5],[7]]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[7,6,2,3,5,4,1]=>[[1,3,4],[2],[5],[6],[7]]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[7,3,4,6,2,5,1]=>[[1,4,5],[2,6],[3],[7]]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[7,4,6,3,2,5,1]=>[[1,5],[2,6],[3],[4],[7]]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[7,4,2,6,3,5,1]=>[[1,3,5],[2,6],[4],[7]]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[7,3,6,2,4,5,1]=>[[1,4,5],[2,6],[3],[7]]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[7,6,2,3,4,5,1]=>[[1,3,4,5],[2],[6],[7]]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[7,3,4,5,2,6,1]=>[[1,4,5,6],[2],[3],[7]]
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[7,3,5,4,2,6,1]=>[[1,4,6],[2],[3],[5],[7]]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[7,4,5,3,2,6,1]=>[[1,5,6],[2],[3],[4],[7]]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[7,5,4,3,2,6,1]=>[[1,6],[2],[3],[4],[5],[7]]
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[7,5,3,4,2,6,1]=>[[1,4,6],[2],[3],[5],[7]]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[7,4,2,5,3,6,1]=>[[1,3,6],[2,5],[4],[7]]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[7,5,2,4,3,6,1]=>[[1,3,6],[2],[4],[5],[7]]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[7,3,5,2,4,6,1]=>[[1,4,6],[2,5],[3],[7]]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[7,5,2,3,4,6,1]=>[[1,3,4,6],[2],[5],[7]]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[7,3,4,2,5,6,1]=>[[1,4,5,6],[2],[3],[7]]
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[7,4,3,2,5,6,1]=>[[1,5,6],[2],[3],[4],[7]]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[7,4,2,3,5,6,1]=>[[1,3,5,6],[2],[4],[7]]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[7,3,2,4,5,6,1]=>[[1,4,5,6],[2],[3],[7]]
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[[1,3,4,5,6],[2],[7]]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[3,1,4,5,6,7,2]=>[[1,2,5,6,7],[3,4]]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[3,1,4,5,7,6,2]=>[[1,2,5,6],[3,4],[7]]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[3,1,4,6,7,5,2]=>[[1,2,5,7],[3,4],[6]]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[3,1,4,7,6,5,2]=>[[1,2,5],[3,4],[6],[7]]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[3,1,4,7,5,6,2]=>[[1,2,5,6],[3,4],[7]]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[3,1,5,6,4,7,2]=>[[1,2,6,7],[3,4],[5]]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[3,1,5,7,4,6,2]=>[[1,2,6],[3,4,7],[5]]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[3,1,6,5,7,4,2]=>[[1,2,7],[3,4],[5],[6]]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[3,1,6,7,4,5,2]=>[[1,2,5],[3,4,7],[6]]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[3,1,7,5,6,4,2]=>[[1,2,6],[3,4],[5],[7]]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[3,1,7,6,5,4,2]=>[[1,2],[3,4],[5],[6],[7]]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[3,1,7,6,4,5,2]=>[[1,2,5],[3,4],[6],[7]]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[3,1,7,5,4,6,2]=>[[1,2,6],[3,4],[5],[7]]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[3,1,7,4,5,6,2]=>[[1,2,5,6],[3,4],[7]]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[4,1,5,3,6,7,2]=>[[1,2,6,7],[3,5],[4]]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[4,1,5,3,7,6,2]=>[[1,2,6],[3,5,7],[4]]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[4,1,6,3,7,5,2]=>[[1,2,5],[3,6,7],[4]]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[4,1,7,3,6,5,2]=>[[1,2,5],[3,6],[4],[7]]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[4,1,7,3,5,6,2]=>[[1,2,5,6],[3,7],[4]]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[5,1,4,6,3,7,2]=>[[1,2,6,7],[3],[4],[5]]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[5,1,4,7,3,6,2]=>[[1,2,6],[3,7],[4],[5]]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[5,1,6,3,4,7,2]=>[[1,2,4,7],[3,6],[5]]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[5,1,7,3,4,6,2]=>[[1,2,4,6],[3,7],[5]]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[6,1,4,5,7,3,2]=>[[1,2,5,7],[3],[4],[6]]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[6,1,5,7,4,3,2]=>[[1,2,7],[3],[4],[5],[6]]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[6,1,5,3,7,4,2]=>[[1,2,4],[3,7],[5],[6]]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[6,1,4,7,3,5,2]=>[[1,2,5],[3,7],[4],[6]]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[6,1,7,3,4,5,2]=>[[1,2,4,5],[3,7],[6]]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[7,1,4,5,6,3,2]=>[[1,2,5,6],[3],[4],[7]]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[7,1,4,6,5,3,2]=>[[1,2,5],[3],[4],[6],[7]]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[7,1,5,6,4,3,2]=>[[1,2,6],[3],[4],[5],[7]]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[7,1,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6],[7]]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[7,1,6,4,5,3,2]=>[[1,2,5],[3],[4],[6],[7]]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[7,1,5,3,6,4,2]=>[[1,2,4],[3,6],[5],[7]]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[7,1,6,3,5,4,2]=>[[1,2,4],[3],[5],[6],[7]]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[7,1,4,6,3,5,2]=>[[1,2,5],[3,6],[4],[7]]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[7,1,6,3,4,5,2]=>[[1,2,4,5],[3],[6],[7]]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[7,1,4,5,3,6,2]=>[[1,2,5,6],[3],[4],[7]]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[7,1,5,4,3,6,2]=>[[1,2,6],[3],[4],[5],[7]]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[7,1,5,3,4,6,2]=>[[1,2,4,6],[3],[5],[7]]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[7,1,4,3,5,6,2]=>[[1,2,5,6],[3],[4],[7]]
[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[7,1,3,4,5,6,2]=>[[1,2,4,5,6],[3],[7]]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]=>[[1,3,5,6,7],[2,4]]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[2,4,1,5,7,6,3]=>[[1,3,5,6],[2,4],[7]]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[2,4,1,6,7,5,3]=>[[1,3,5,7],[2,4],[6]]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[2,4,1,7,6,5,3]=>[[1,3,5],[2,4],[6],[7]]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[2,4,1,7,5,6,3]=>[[1,3,5,6],[2,4],[7]]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[2,5,1,6,4,7,3]=>[[1,3,6,7],[2,4],[5]]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[2,5,1,7,4,6,3]=>[[1,3,6],[2,4,7],[5]]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[2,6,1,5,7,4,3]=>[[1,3,7],[2,4],[5],[6]]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[2,6,1,7,4,5,3]=>[[1,3,5],[2,4,7],[6]]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[2,7,1,5,6,4,3]=>[[1,3,6],[2,4],[5],[7]]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[2,7,1,6,5,4,3]=>[[1,3],[2,4],[5],[6],[7]]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[2,7,1,6,4,5,3]=>[[1,3,5],[2,4],[6],[7]]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[2,7,1,5,4,6,3]=>[[1,3,6],[2,4],[5],[7]]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[2,7,1,4,5,6,3]=>[[1,3,5,6],[2,4],[7]]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[4,1,2,5,6,7,3]=>[[1,2,3,6,7],[4,5]]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[4,1,2,5,7,6,3]=>[[1,2,3,6],[4,5],[7]]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[4,1,2,6,7,5,3]=>[[1,2,3,7],[4,5],[6]]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[4,1,2,7,6,5,3]=>[[1,2,3],[4,5],[6],[7]]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[4,1,2,7,5,6,3]=>[[1,2,3,6],[4,5],[7]]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[5,1,2,6,4,7,3]=>[[1,2,3,7],[4,6],[5]]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[5,1,2,7,4,6,3]=>[[1,2,3,6],[4,7],[5]]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[6,1,2,5,7,4,3]=>[[1,2,3,7],[4],[5],[6]]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[6,1,2,7,4,5,3]=>[[1,2,3,5],[4,7],[6]]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[7,1,2,5,6,4,3]=>[[1,2,3,6],[4],[5],[7]]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[7,1,2,6,5,4,3]=>[[1,2,3],[4],[5],[6],[7]]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[7,1,2,6,4,5,3]=>[[1,2,3,5],[4],[6],[7]]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[7,1,2,5,4,6,3]=>[[1,2,3,6],[4],[5],[7]]
[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[7,1,2,4,5,6,3]=>[[1,2,3,5,6],[4],[7]]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]=>[[1,3,4,6,7],[2,5]]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[2,3,5,1,7,6,4]=>[[1,3,4,6],[2,5],[7]]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[2,3,6,1,7,5,4]=>[[1,3,4,7],[2,5],[6]]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[2,3,7,1,6,5,4]=>[[1,3,4],[2,5],[6],[7]]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[2,3,7,1,5,6,4]=>[[1,3,4,6],[2,5],[7]]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[3,5,2,1,6,7,4]=>[[1,4,6,7],[2,5],[3]]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[3,5,2,1,7,6,4]=>[[1,4,6],[2,5],[3,7]]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[3,6,2,1,7,5,4]=>[[1,4,7],[2,5],[3,6]]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[3,7,2,1,6,5,4]=>[[1,4],[2,5],[3,6],[7]]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[3,7,2,1,5,6,4]=>[[1,4,6],[2,5],[3,7]]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]=>[[1,2,4,7],[3,5,6]]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[3,1,5,2,7,6,4]=>[[1,2,4],[3,5,6],[7]]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[3,1,6,2,7,5,4]=>[[1,2,4],[3,5,7],[6]]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[3,1,7,2,6,5,4]=>[[1,2,4],[3,5],[6],[7]]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[3,1,7,2,5,6,4]=>[[1,2,4,6],[3,5],[7]]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[2,5,1,3,6,7,4]=>[[1,3,4,7],[2,5,6]]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[2,5,1,3,7,6,4]=>[[1,3,4],[2,5,6],[7]]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[2,6,1,3,7,5,4]=>[[1,3,4],[2,5,7],[6]]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[2,7,1,3,6,5,4]=>[[1,3,4],[2,5],[6],[7]]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[2,7,1,3,5,6,4]=>[[1,3,4,6],[2,5],[7]]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]=>[[1,2,3,4,7],[5,6]]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[5,1,2,3,7,6,4]=>[[1,2,3,4],[5,6],[7]]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[6,1,2,3,7,5,4]=>[[1,2,3,4],[5,7],[6]]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[7,1,2,3,6,5,4]=>[[1,2,3,4],[5],[6],[7]]
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>[[1,2,3,4,6],[5],[7]]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[2,3,4,6,1,7,5]=>[[1,3,4,5,7],[2,6]]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[2,3,4,7,1,6,5]=>[[1,3,4,5],[2,6],[7]]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[2,4,6,3,1,7,5]=>[[1,3,5,7],[2,6],[4]]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[2,4,7,3,1,6,5]=>[[1,3,5],[2,6],[4,7]]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[3,4,2,6,1,7,5]=>[[1,4,5,7],[2,6],[3]]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[3,4,2,7,1,6,5]=>[[1,4,5],[2,6],[3,7]]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[4,3,6,2,1,7,5]=>[[1,5,7],[2,6],[3],[4]]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[4,3,7,2,1,6,5]=>[[1,5],[2,6],[3,7],[4]]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[4,6,2,3,1,7,5]=>[[1,3,5],[2,6,7],[4]]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[4,7,2,3,1,6,5]=>[[1,3,5],[2,6],[4,7]]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]=>[[1,2,5,7],[3,4,6]]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[3,1,4,7,2,6,5]=>[[1,2,5],[3,4,6],[7]]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[4,1,6,3,2,7,5]=>[[1,2,5],[3,6,7],[4]]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[4,1,7,3,2,6,5]=>[[1,2,5],[3,6],[4,7]]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]=>[[1,3,5,7],[2,4,6]]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[2,4,1,7,3,6,5]=>[[1,3,5],[2,4,6],[7]]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]=>[[1,2,3,5],[4,6,7]]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[4,1,2,7,3,6,5]=>[[1,2,3,5],[4,6],[7]]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[2,3,6,1,4,7,5]=>[[1,3,4,5],[2,6,7]]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[2,3,7,1,4,6,5]=>[[1,3,4,5],[2,6],[7]]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[3,6,2,1,4,7,5]=>[[1,4,5],[2,6,7],[3]]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[3,7,2,1,4,6,5]=>[[1,4,5],[2,6],[3,7]]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[3,1,6,2,4,7,5]=>[[1,2,4,5],[3,6,7]]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[3,1,7,2,4,6,5]=>[[1,2,4,5],[3,6],[7]]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[2,6,1,3,4,7,5]=>[[1,3,4,5],[2,6,7]]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[2,7,1,3,4,6,5]=>[[1,3,4,5],[2,6],[7]]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]=>[[1,2,3,4,5],[6,7]]
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>[[1,2,3,4,5],[6],[7]]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[2,3,4,5,7,1,6]=>[[1,3,4,5,6],[2,7]]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[2,3,5,7,4,1,6]=>[[1,3,4,6],[2,7],[5]]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[2,4,5,3,7,1,6]=>[[1,3,5,6],[2,7],[4]]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[2,5,4,7,3,1,6]=>[[1,3,6],[2,7],[4],[5]]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[2,5,7,3,4,1,6]=>[[1,3,4,6],[2,7],[5]]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[3,4,2,5,7,1,6]=>[[1,4,5,6],[2,7],[3]]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[3,5,2,7,4,1,6]=>[[1,4,6],[2,5,7],[3]]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[4,3,5,2,7,1,6]=>[[1,5,6],[2,7],[3],[4]]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[4,5,2,3,7,1,6]=>[[1,3,6],[2,5,7],[4]]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[5,3,4,7,2,1,6]=>[[1,4,6],[2,7],[3],[5]]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[5,4,7,3,2,1,6]=>[[1,6],[2,7],[3],[4],[5]]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[5,4,2,7,3,1,6]=>[[1,3,6],[2,7],[4],[5]]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[5,3,7,2,4,1,6]=>[[1,4,6],[2,7],[3],[5]]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[5,7,2,3,4,1,6]=>[[1,3,4,6],[2,7],[5]]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[3,1,4,5,7,2,6]=>[[1,2,5,6],[3,4,7]]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[3,1,5,7,4,2,6]=>[[1,2,6],[3,4,7],[5]]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[4,1,5,3,7,2,6]=>[[1,2,6],[3,5,7],[4]]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[5,1,4,7,3,2,6]=>[[1,2,6],[3,7],[4],[5]]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[5,1,7,3,4,2,6]=>[[1,2,4,6],[3,7],[5]]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[2,4,1,5,7,3,6]=>[[1,3,5,6],[2,4,7]]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[2,5,1,7,4,3,6]=>[[1,3,6],[2,4,7],[5]]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[4,1,2,5,7,3,6]=>[[1,2,3,6],[4,5,7]]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[5,1,2,7,4,3,6]=>[[1,2,3,6],[4,7],[5]]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[2,3,5,1,7,4,6]=>[[1,3,4,6],[2,5,7]]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[3,5,2,1,7,4,6]=>[[1,4,6],[2,5,7],[3]]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]=>[[1,2,4,6],[3,5,7]]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[2,5,1,3,7,4,6]=>[[1,3,4,6],[2,5,7]]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[5,1,2,3,7,4,6]=>[[1,2,3,4,6],[5,7]]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[2,3,4,7,1,5,6]=>[[1,3,4,5,6],[2,7]]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[2,4,7,3,1,5,6]=>[[1,3,5,6],[2,7],[4]]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[3,4,2,7,1,5,6]=>[[1,4,5,6],[2,7],[3]]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[4,3,7,2,1,5,6]=>[[1,5,6],[2,7],[3],[4]]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[4,7,2,3,1,5,6]=>[[1,3,5,6],[2,7],[4]]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[3,1,4,7,2,5,6]=>[[1,2,5,6],[3,4,7]]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[4,1,7,3,2,5,6]=>[[1,2,5,6],[3,7],[4]]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[2,4,1,7,3,5,6]=>[[1,3,5,6],[2,4,7]]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[4,1,2,7,3,5,6]=>[[1,2,3,5,6],[4,7]]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[2,3,7,1,4,5,6]=>[[1,3,4,5,6],[2,7]]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[3,7,2,1,4,5,6]=>[[1,4,5,6],[2,7],[3]]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]=>[[1,2,4,5,6],[3,7]]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>[[1,3,4,5,6],[2,7]]
[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>[[1,2,3,4,5,6],[7]]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[[1,3,4,5,6,7],[2]]
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[2,3,4,6,5,1,7]=>[[1,3,4,5,7],[2],[6]]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[2,3,5,6,4,1,7]=>[[1,3,4,6,7],[2],[5]]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[2,3,6,5,4,1,7]=>[[1,3,4,7],[2],[5],[6]]
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[2,3,6,4,5,1,7]=>[[1,3,4,5,7],[2],[6]]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>[[1,3,5,6,7],[2],[4]]
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[2,4,6,3,5,1,7]=>[[1,3,5,7],[2,6],[4]]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[2,5,4,6,3,1,7]=>[[1,3,6,7],[2],[4],[5]]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[2,5,6,3,4,1,7]=>[[1,3,4,7],[2,6],[5]]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[2,6,4,5,3,1,7]=>[[1,3,5,7],[2],[4],[6]]
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[2,6,5,4,3,1,7]=>[[1,3,7],[2],[4],[5],[6]]
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[2,6,5,3,4,1,7]=>[[1,3,4,7],[2],[5],[6]]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[2,6,4,3,5,1,7]=>[[1,3,5,7],[2],[4],[6]]
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[2,6,3,4,5,1,7]=>[[1,3,4,5,7],[2],[6]]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[3,4,2,5,6,1,7]=>[[1,4,5,6,7],[2],[3]]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[3,4,2,6,5,1,7]=>[[1,4,5,7],[2,6],[3]]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[3,5,2,6,4,1,7]=>[[1,4,6,7],[2,5],[3]]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[3,6,2,5,4,1,7]=>[[1,4,7],[2,5],[3],[6]]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[3,6,2,4,5,1,7]=>[[1,4,5,7],[2,6],[3]]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[4,3,5,2,6,1,7]=>[[1,5,6,7],[2],[3],[4]]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[4,3,6,2,5,1,7]=>[[1,5,7],[2,6],[3],[4]]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[4,5,2,3,6,1,7]=>[[1,3,6,7],[2,5],[4]]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[4,6,2,3,5,1,7]=>[[1,3,5,7],[2,6],[4]]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[5,3,4,6,2,1,7]=>[[1,4,6,7],[2],[3],[5]]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[5,4,6,3,2,1,7]=>[[1,6,7],[2],[3],[4],[5]]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[5,4,2,6,3,1,7]=>[[1,3,7],[2,6],[4],[5]]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[5,3,6,2,4,1,7]=>[[1,4,7],[2,6],[3],[5]]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[5,6,2,3,4,1,7]=>[[1,3,4,7],[2,6],[5]]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[6,3,4,5,2,1,7]=>[[1,4,5,7],[2],[3],[6]]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[6,3,5,4,2,1,7]=>[[1,4,7],[2],[3],[5],[6]]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[6,4,5,3,2,1,7]=>[[1,5,7],[2],[3],[4],[6]]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[6,5,4,3,2,1,7]=>[[1,7],[2],[3],[4],[5],[6]]
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[6,5,3,4,2,1,7]=>[[1,4,7],[2],[3],[5],[6]]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[6,4,2,5,3,1,7]=>[[1,3,7],[2,5],[4],[6]]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[6,5,2,4,3,1,7]=>[[1,3,7],[2],[4],[5],[6]]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[6,3,5,2,4,1,7]=>[[1,4,7],[2,5],[3],[6]]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[6,5,2,3,4,1,7]=>[[1,3,4,7],[2],[5],[6]]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[6,3,4,2,5,1,7]=>[[1,4,5,7],[2],[3],[6]]
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[6,4,3,2,5,1,7]=>[[1,5,7],[2],[3],[4],[6]]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[6,4,2,3,5,1,7]=>[[1,3,5,7],[2],[4],[6]]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[6,3,2,4,5,1,7]=>[[1,4,5,7],[2],[3],[6]]
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[[1,3,4,5,7],[2],[6]]
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[3,1,4,5,6,2,7]=>[[1,2,5,6,7],[3,4]]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[3,1,4,6,5,2,7]=>[[1,2,5,7],[3,4],[6]]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[3,1,5,6,4,2,7]=>[[1,2,6,7],[3,4],[5]]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[3,1,6,5,4,2,7]=>[[1,2,7],[3,4],[5],[6]]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[3,1,6,4,5,2,7]=>[[1,2,5,7],[3,4],[6]]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[4,1,5,3,6,2,7]=>[[1,2,6,7],[3,5],[4]]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[4,1,6,3,5,2,7]=>[[1,2,5,7],[3,6],[4]]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[5,1,4,6,3,2,7]=>[[1,2,6,7],[3],[4],[5]]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[5,1,6,3,4,2,7]=>[[1,2,4,7],[3,6],[5]]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[6,1,4,5,3,2,7]=>[[1,2,5,7],[3],[4],[6]]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[6,1,5,4,3,2,7]=>[[1,2,7],[3],[4],[5],[6]]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[6,1,5,3,4,2,7]=>[[1,2,4,7],[3],[5],[6]]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[6,1,4,3,5,2,7]=>[[1,2,5,7],[3],[4],[6]]
[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[6,1,3,4,5,2,7]=>[[1,2,4,5,7],[3],[6]]
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[2,4,1,5,6,3,7]=>[[1,3,5,6,7],[2,4]]
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[2,4,1,6,5,3,7]=>[[1,3,5,7],[2,4],[6]]
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[2,5,1,6,4,3,7]=>[[1,3,6,7],[2,4],[5]]
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[2,6,1,5,4,3,7]=>[[1,3,7],[2,4],[5],[6]]
[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[2,6,1,4,5,3,7]=>[[1,3,5,7],[2,4],[6]]
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[4,1,2,5,6,3,7]=>[[1,2,3,6,7],[4,5]]
[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[4,1,2,6,5,3,7]=>[[1,2,3,7],[4,5],[6]]
[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[5,1,2,6,4,3,7]=>[[1,2,3,7],[4,6],[5]]
[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[6,1,2,5,4,3,7]=>[[1,2,3,7],[4],[5],[6]]
[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>[[1,2,3,5,7],[4],[6]]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[2,3,5,1,6,4,7]=>[[1,3,4,6,7],[2,5]]
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[2,3,6,1,5,4,7]=>[[1,3,4,7],[2,5],[6]]
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[3,5,2,1,6,4,7]=>[[1,4,6,7],[2,5],[3]]
[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[3,6,2,1,5,4,7]=>[[1,4,7],[2,5],[3,6]]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[3,1,5,2,6,4,7]=>[[1,2,4,7],[3,5,6]]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[3,1,6,2,5,4,7]=>[[1,2,4,7],[3,5],[6]]
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[2,5,1,3,6,4,7]=>[[1,3,4,7],[2,5,6]]
[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[2,6,1,3,5,4,7]=>[[1,3,4,7],[2,5],[6]]
[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[5,1,2,3,6,4,7]=>[[1,2,3,4,7],[5,6]]
[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>[[1,2,3,4,7],[5],[6]]
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[2,3,4,6,1,5,7]=>[[1,3,4,5,7],[2,6]]
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[2,4,6,3,1,5,7]=>[[1,3,5,7],[2,6],[4]]
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[3,4,2,6,1,5,7]=>[[1,4,5,7],[2,6],[3]]
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[4,3,6,2,1,5,7]=>[[1,5,7],[2,6],[3],[4]]
[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[4,6,2,3,1,5,7]=>[[1,3,5,7],[2,6],[4]]
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[3,1,4,6,2,5,7]=>[[1,2,5,7],[3,4,6]]
[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[4,1,6,3,2,5,7]=>[[1,2,5,7],[3,6],[4]]
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[2,4,1,6,3,5,7]=>[[1,3,5,7],[2,4,6]]
[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[4,1,2,6,3,5,7]=>[[1,2,3,5,7],[4,6]]
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[2,3,6,1,4,5,7]=>[[1,3,4,5,7],[2,6]]
[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[3,6,2,1,4,5,7]=>[[1,4,5,7],[2,6],[3]]
[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[3,1,6,2,4,5,7]=>[[1,2,4,5,7],[3,6]]
[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[2,6,1,3,4,5,7]=>[[1,3,4,5,7],[2,6]]
[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>[[1,2,3,4,5,7],[6]]
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[[1,3,4,5,6,7],[2]]
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[2,3,5,4,1,6,7]=>[[1,3,4,6,7],[2],[5]]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[2,4,5,3,1,6,7]=>[[1,3,5,6,7],[2],[4]]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[2,5,4,3,1,6,7]=>[[1,3,6,7],[2],[4],[5]]
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[2,5,3,4,1,6,7]=>[[1,3,4,6,7],[2],[5]]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[3,4,2,5,1,6,7]=>[[1,4,5,6,7],[2],[3]]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[3,5,2,4,1,6,7]=>[[1,4,6,7],[2,5],[3]]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[4,3,5,2,1,6,7]=>[[1,5,6,7],[2],[3],[4]]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[4,5,2,3,1,6,7]=>[[1,3,6,7],[2,5],[4]]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[5,3,4,2,1,6,7]=>[[1,4,6,7],[2],[3],[5]]
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]=>[[1,6,7],[2],[3],[4],[5]]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[5,4,2,3,1,6,7]=>[[1,3,6,7],[2],[4],[5]]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[5,3,2,4,1,6,7]=>[[1,4,6,7],[2],[3],[5]]
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[[1,3,4,6,7],[2],[5]]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[3,1,4,5,2,6,7]=>[[1,2,5,6,7],[3,4]]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[3,1,5,4,2,6,7]=>[[1,2,6,7],[3,4],[5]]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[4,1,5,3,2,6,7]=>[[1,2,6,7],[3,5],[4]]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[5,1,4,3,2,6,7]=>[[1,2,6,7],[3],[4],[5]]
[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[5,1,3,4,2,6,7]=>[[1,2,4,6,7],[3],[5]]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[2,4,1,5,3,6,7]=>[[1,3,5,6,7],[2,4]]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[2,5,1,4,3,6,7]=>[[1,3,6,7],[2,4],[5]]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[4,1,2,5,3,6,7]=>[[1,2,3,6,7],[4,5]]
[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>[[1,2,3,6,7],[4],[5]]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[2,3,5,1,4,6,7]=>[[1,3,4,6,7],[2,5]]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[3,5,2,1,4,6,7]=>[[1,4,6,7],[2,5],[3]]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[3,1,5,2,4,6,7]=>[[1,2,4,6,7],[3,5]]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[2,5,1,3,4,6,7]=>[[1,3,4,6,7],[2,5]]
[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>[[1,2,3,4,6,7],[5]]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]=>[[1,3,4,5,6,7],[2]]
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[2,4,3,1,5,6,7]=>[[1,3,5,6,7],[2],[4]]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[3,4,2,1,5,6,7]=>[[1,4,5,6,7],[2],[3]]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]=>[[1,5,6,7],[2],[3],[4]]
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[[1,3,5,6,7],[2],[4]]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[3,1,4,2,5,6,7]=>[[1,2,5,6,7],[3,4]]
[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>[[1,2,5,6,7],[3],[4]]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[2,4,1,3,5,6,7]=>[[1,3,5,6,7],[2,4]]
[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>[[1,2,3,5,6,7],[4]]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>[[1,3,4,5,6,7],[2]]
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[[1,4,5,6,7],[2],[3]]
[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>[[1,2,4,5,6,7],[3]]
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[[1,3,4,5,6,7],[2]]
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7]]
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[[1,3,4,5,6,7,8],[2]]
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[2,3,4,5,6,8,7,1]=>[[1,3,4,5,6,7],[2],[8]]
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[2,3,4,5,8,7,6,1]=>[[1,3,4,5,6],[2],[7],[8]]
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[2,3,4,5,8,6,7,1]=>[[1,3,4,5,6,7],[2],[8]]
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[2,3,4,6,8,5,7,1]=>[[1,3,4,5,7],[2,8],[6]]
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[2,3,4,8,6,7,5,1]=>[[1,3,4,5,7],[2],[6],[8]]
[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[2,3,4,8,7,6,5,1]=>[[1,3,4,5],[2],[6],[7],[8]]
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[2,3,4,8,7,5,6,1]=>[[1,3,4,5,6],[2],[7],[8]]
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[2,3,4,8,6,5,7,1]=>[[1,3,4,5,7],[2],[6],[8]]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[2,3,4,8,5,6,7,1]=>[[1,3,4,5,6,7],[2],[8]]
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[[1,3,4,6,7,8],[2],[5]]
[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[6,7,8,4,5,3,2,1]=>[2,3,5,8,4,6,7,1]=>[[1,3,4,6,7],[2,8],[5]]
[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[7,8,4,5,6,3,2,1]=>[2,3,6,8,4,5,7,1]=>[[1,3,4,5,7],[2,8],[6]]
[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[8,5,4,6,7,3,2,1]=>[2,3,7,5,8,4,6,1]=>[[1,3,4,6],[2,8],[5],[7]]
[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[2,3,8,5,7,6,4,1]=>[[1,3,4,6],[2],[5],[7],[8]]
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[2,3,8,7,6,5,4,1]=>[[1,3,4],[2],[5],[6],[7],[8]]
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[2,3,8,7,4,5,6,1]=>[[1,3,4,5,6],[2],[7],[8]]
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[2,3,8,4,5,6,7,1]=>[[1,3,4,5,6,7],[2],[8]]
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[2,4,5,3,6,7,8,1]=>[[1,3,5,6,7,8],[2],[4]]
[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[6,7,8,5,3,4,2,1]=>[2,4,5,3,8,6,7,1]=>[[1,3,5,6,7],[2,8],[4]]
[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[2,4,6,3,8,5,7,1]=>[[1,3,5,7],[2,6,8],[4]]
[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]=>[6,7,5,8,3,4,2,1]=>[2,4,8,3,7,6,5,1]=>[[1,3,5],[2,6],[4],[7],[8]]
[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[7,5,6,8,3,4,2,1]=>[2,4,8,3,7,5,6,1]=>[[1,3,5,6],[2,7],[4],[8]]
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[2,4,8,3,5,6,7,1]=>[[1,3,5,6,7],[2,8],[4]]
[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[7,6,8,4,3,5,2,1]=>[2,5,4,8,3,7,6,1]=>[[1,3,6],[2,7],[4,8],[5]]
[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[2,5,4,8,3,6,7,1]=>[[1,3,6,7],[2,8],[4],[5]]
[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]=>[8,6,7,3,4,5,2,1]=>[2,5,7,3,4,8,6,1]=>[[1,3,4,6],[2,7,8],[5]]
[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>[2,5,8,3,4,6,7,1]=>[[1,3,4,6,7],[2,8],[5]]
[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]=>[7,8,5,3,4,6,2,1]=>[2,6,5,3,8,4,7,1]=>[[1,3,4,7],[2,8],[5],[6]]
[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[8,7,4,3,5,6,2,1]=>[2,6,4,7,3,5,8,1]=>[[1,3,5,8],[2,7],[4],[6]]
[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[8,6,5,4,3,7,2,1]=>[2,7,4,5,6,8,3,1]=>[[1,3,5,6,8],[2],[4],[7]]
[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[2,8,7,5,6,4,3,1]=>[[1,3,6],[2],[4],[5],[7],[8]]
[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[5,6,4,7,3,8,2,1]=>[2,8,7,6,5,4,3,1]=>[[1,3],[2],[4],[5],[6],[7],[8]]
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[2,8,7,5,4,6,3,1]=>[[1,3,6],[2],[4],[5],[7],[8]]
[.,[.,[[[[.,[[.,.],.]],.],.],.]]]=>[4,5,3,6,7,8,2,1]=>[2,8,5,4,3,6,7,1]=>[[1,3,6,7],[2],[4],[5],[8]]
[.,[.,[[[[[.,.],[.,.]],.],.],.]]]=>[5,3,4,6,7,8,2,1]=>[2,8,5,3,4,6,7,1]=>[[1,3,4,6,7],[2],[5],[8]]
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[3,4,2,5,6,7,8,1]=>[[1,4,5,6,7,8],[2],[3]]
[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,2,3,1]=>[3,4,2,8,6,7,5,1]=>[[1,4,5,7],[2,6],[3],[8]]
[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,2,3,1]=>[3,4,2,8,7,6,5,1]=>[[1,4,5],[2,6],[3],[7],[8]]
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[3,4,2,8,5,6,7,1]=>[[1,4,5,6,7],[2,8],[3]]
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[3,5,2,6,4,7,8,1]=>[[1,4,6,7,8],[2,5],[3]]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[3,5,2,7,4,8,6,1]=>[[1,4,6,8],[2,5,7],[3]]
[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>[3,5,2,8,4,7,6,1]=>[[1,4,6],[2,5,7],[3],[8]]
[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,2,3,1]=>[3,5,2,8,4,6,7,1]=>[[1,4,6,7],[2,5,8],[3]]
[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,2,3,1]=>[3,6,2,8,4,5,7,1]=>[[1,4,5,7],[2,6,8],[3]]
[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,2,3,1]=>[3,7,2,6,8,5,4,1]=>[[1,4,8],[2,5],[3],[6],[7]]
[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,2,3,1]=>[3,8,2,6,7,5,4,1]=>[[1,4,7],[2,5],[3],[6],[8]]
[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>[3,8,2,7,6,5,4,1]=>[[1,4],[2,5],[3],[6],[7],[8]]
[.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,2,3,1]=>[3,8,2,5,4,6,7,1]=>[[1,4,6,7],[2,5],[3],[8]]
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[4,3,5,2,6,7,8,1]=>[[1,5,6,7,8],[2],[3],[4]]
[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,2,4,1]=>[4,3,5,2,8,6,7,1]=>[[1,5,6,7],[2,8],[3],[4]]
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[4,3,7,2,6,8,5,1]=>[[1,5,8],[2,6],[3,7],[4]]
[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,2,4,1]=>[4,3,7,2,8,5,6,1]=>[[1,5,6],[2,7,8],[3],[4]]
[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,2,4,1]=>[4,3,8,2,7,6,5,1]=>[[1,5],[2,6],[3,7],[4],[8]]
[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,2,4,1]=>[4,3,8,2,7,5,6,1]=>[[1,5,6],[2,7],[3,8],[4]]
[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[4,3,8,2,5,6,7,1]=>[[1,5,6,7],[2,8],[3],[4]]
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[4,5,2,3,6,7,8,1]=>[[1,3,6,7,8],[2,5],[4]]
[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[4,5,2,3,8,6,7,1]=>[[1,3,6,7],[2,5,8],[4]]
[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,2,3,4,1]=>[4,6,2,3,7,5,8,1]=>[[1,3,5,8],[2,6,7],[4]]
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[4,8,2,3,5,6,7,1]=>[[1,3,5,6,7],[2,8],[4]]
[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[6,7,8,4,3,2,5,1]=>[5,3,4,8,2,6,7,1]=>[[1,4,6,7],[2,8],[3],[5]]
[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[5,4,7,3,2,8,6,1]=>[[1,6,8],[2,7],[3],[4],[5]]
[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>[5,4,8,3,2,7,6,1]=>[[1,6],[2,7],[3,8],[4],[5]]
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,2,3,5,1]=>[5,4,2,6,3,7,8,1]=>[[1,3,7,8],[2,6],[4],[5]]
[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[5,4,2,8,3,6,7,1]=>[[1,3,6,7],[2,8],[4],[5]]
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[8,7,6,3,2,4,5,1]=>[5,3,6,2,4,7,8,1]=>[[1,4,7,8],[2,6],[3],[5]]
[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[6,7,8,3,2,4,5,1]=>[5,3,8,2,4,6,7,1]=>[[1,4,6,7],[2,8],[3],[5]]
[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[6,7,8,2,3,4,5,1]=>[5,8,2,3,4,6,7,1]=>[[1,3,4,6,7],[2,8],[5]]
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1]=>[6,3,4,5,8,2,7,1]=>[[1,4,5,7],[2,8],[3],[6]]
[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[8,7,5,3,4,2,6,1]=>[6,4,5,3,7,2,8,1]=>[[1,5,7,8],[2],[3],[4],[6]]
[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[7,8,5,3,4,2,6,1]=>[6,4,5,3,8,2,7,1]=>[[1,5,7],[2,8],[3],[4],[6]]
[.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[7,8,5,2,3,4,6,1]=>[6,5,2,3,8,4,7,1]=>[[1,3,4,7],[2,8],[5],[6]]
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[8,5,6,3,4,2,7,1]=>[7,4,6,3,8,5,2,1]=>[[1,5,8],[2,6],[3],[4],[7]]
[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[8,5,4,3,6,2,7,1]=>[7,6,4,5,8,3,2,1]=>[[1,5,8],[2],[3],[4],[6],[7]]
[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[7,6,5,8,4,3,2,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[8,5,4,3,2,6,7,1]=>[7,3,4,5,8,2,6,1]=>[[1,4,5,6],[2,8],[3],[7]]
[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[8,5,3,4,2,6,7,1]=>[7,4,5,3,8,2,6,1]=>[[1,5,6],[2,8],[3],[4],[7]]
[.,[[[.,[[[.,.],.],.]],.],[.,.]]]=>[8,3,4,5,2,6,7,1]=>[7,5,8,3,4,2,6,1]=>[[1,4,6],[2,8],[3],[5],[7]]
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[8,5,4,2,3,6,7,1]=>[7,4,2,5,8,3,6,1]=>[[1,3,6],[2,5,8],[4],[7]]
[.,[[[[[.,.],.],[.,.]],.],[.,.]]]=>[8,5,2,3,4,6,7,1]=>[7,5,2,3,8,4,6,1]=>[[1,3,4,6],[2,8],[5],[7]]
[.,[[[[.,[[.,.],.]],.],.],[.,.]]]=>[8,3,4,2,5,6,7,1]=>[7,4,8,3,2,5,6,1]=>[[1,5,6],[2,8],[3],[4],[7]]
[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[7,5,4,6,3,2,8,1]=>[8,3,6,5,7,4,2,1]=>[[1,4,7],[2],[3],[5],[6],[8]]
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[8,3,7,4,5,6,2,1]=>[[1,4,5,6],[2],[3],[7],[8]]
[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[7,5,6,3,4,2,8,1]=>[8,4,6,3,7,5,2,1]=>[[1,5,7],[2,6],[3],[4],[8]]
[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[6,5,7,3,4,2,8,1]=>[8,4,7,3,6,5,2,1]=>[[1,5],[2,6],[3],[4],[7],[8]]
[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[7,5,4,3,6,2,8,1]=>[8,6,4,5,7,3,2,1]=>[[1,5,7],[2],[3],[4],[6],[8]]
[.,[[.,[[.,[[.,.],.]],[.,.]]],.]]=>[7,4,5,3,6,2,8,1]=>[8,6,5,7,4,3,2,1]=>[[1,7],[2],[3],[4],[5],[6],[8]]
[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]=>[6,4,5,3,7,2,8,1]=>[8,7,5,6,4,3,2,1]=>[[1,6],[2],[3],[4],[5],[7],[8]]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[8,7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7],[8]]
[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[8,7,6,4,5,3,2,1]=>[[1,5],[2],[3],[4],[6],[7],[8]]
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[8,7,5,3,6,4,2,1]=>[[1,4],[2,6],[3],[5],[7],[8]]
[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[5,6,3,4,7,2,8,1]=>[8,7,6,3,5,4,2,1]=>[[1,4],[2],[3],[5],[6],[7],[8]]
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[6,4,3,5,7,2,8,1]=>[8,7,4,6,3,5,2,1]=>[[1,5],[2,6],[3],[4],[7],[8]]
[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]=>[6,7,5,4,2,3,8,1]=>[8,4,2,5,7,6,3,1]=>[[1,3,6],[2,5],[4],[7],[8]]
[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]=>[7,5,6,4,2,3,8,1]=>[8,4,2,6,7,5,3,1]=>[[1,3,7],[2,5],[4],[6],[8]]
[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[8,5,2,7,4,6,3,1]=>[[1,3,6],[2,7],[4],[5],[8]]
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,2,3,8,1]=>[8,6,2,5,7,4,3,1]=>[[1,3,7],[2],[4],[5],[6],[8]]
[.,[[[.,.],[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,2,3,8,1]=>[8,6,2,7,4,5,3,1]=>[[1,3,5],[2,7],[4],[6],[8]]
[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,2,3,8,1]=>[8,7,2,6,4,5,3,1]=>[[1,3,5],[2],[4],[6],[7],[8]]
[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[8,7,2,4,5,6,3,1]=>[[1,3,5,6],[2],[4],[7],[8]]
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[6,5,7,3,2,4,8,1]=>[8,3,7,2,6,5,4,1]=>[[1,4],[2,5],[3],[6],[7],[8]]
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[8,5,2,3,6,7,4,1]=>[[1,3,4,7],[2,6],[5],[8]]
[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[6,7,4,3,2,5,8,1]=>[8,3,4,7,2,6,5,1]=>[[1,4,5],[2,6],[3],[7],[8]]
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[8,4,2,6,3,7,5,1]=>[[1,3,5],[2,6,7],[4],[8]]
[.,[[[.,[[[.,.],.],.]],[.,.]],.]]=>[7,3,4,5,2,6,8,1]=>[8,5,7,3,4,2,6,1]=>[[1,4,6],[2,7],[3],[5],[8]]
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[7,5,3,2,4,6,8,1]=>[8,3,5,2,7,4,6,1]=>[[1,4,6],[2,5,7],[3],[8]]
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[7,5,2,3,4,6,8,1]=>[8,5,2,3,7,4,6,1]=>[[1,3,4,6],[2,7],[5],[8]]
[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[6,3,4,5,2,7,8,1]=>[8,5,6,3,4,2,7,1]=>[[1,4,7],[2,6],[3],[5],[8]]
[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[8,6,3,4,5,2,7,1]=>[[1,4,5,7],[2],[3],[6],[8]]
[.,[[[[.,.],[[[.,.],.],.]],.],.]]=>[4,5,6,2,3,7,8,1]=>[8,6,2,4,5,3,7,1]=>[[1,3,5,7],[2],[4],[6],[8]]
[.,[[[[.,[.,[[.,.],.]]],.],.],.]]=>[4,5,3,2,6,7,8,1]=>[8,3,5,4,2,6,7,1]=>[[1,4,6,7],[2],[3],[5],[8]]
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[8,5,3,4,2,6,7,1]=>[[1,4,6,7],[2],[3],[5],[8]]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,2]=>[[1,2,5,6,7,8],[3,4]]
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[3,1,4,5,6,8,7,2]=>[[1,2,5,6,7],[3,4],[8]]
[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>[3,1,4,7,6,8,5,2]=>[[1,2,5,8],[3,4],[6],[7]]
[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,3,1,2]=>[3,1,4,8,7,6,5,2]=>[[1,2,5],[3,4],[6],[7],[8]]
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,3,1,2]=>[3,1,4,8,6,5,7,2]=>[[1,2,5,7],[3,4],[6],[8]]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[3,1,4,8,5,6,7,2]=>[[1,2,5,6,7],[3,4],[8]]
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[3,1,5,6,4,8,7,2]=>[[1,2,6,7],[3,4,8],[5]]
[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[3,1,6,5,7,4,8,2]=>[[1,2,7,8],[3,4],[5],[6]]
[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,3,1,2]=>[3,1,6,8,4,5,7,2]=>[[1,2,5,7],[3,4,8],[6]]
[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,3,1,2]=>[3,1,7,6,4,8,5,2]=>[[1,2,5],[3,4,8],[6],[7]]
[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,3,1,2]=>[3,1,8,6,7,5,4,2]=>[[1,2,7],[3,4],[5],[6],[8]]
[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,3,1,2]=>[3,1,8,7,6,5,4,2]=>[[1,2],[3,4],[5],[6],[7],[8]]
[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,3,1,2]=>[3,1,8,6,4,7,5,2]=>[[1,2,5],[3,4,7],[6],[8]]
[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[7,5,4,6,8,3,1,2]=>[3,1,8,5,7,4,6,2]=>[[1,2,6],[3,4,7],[5],[8]]
[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,3,1,2]=>[3,1,8,5,4,6,7,2]=>[[1,2,6,7],[3,4],[5],[8]]
[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[3,1,8,4,5,6,7,2]=>[[1,2,5,6,7],[3,4],[8]]
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[4,1,5,3,6,7,8,2]=>[[1,2,6,7,8],[3,5],[4]]
[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,4,1,2]=>[4,1,5,3,8,7,6,2]=>[[1,2,6],[3,5,7],[4],[8]]
[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[4,1,6,3,7,5,8,2]=>[[1,2,5,8],[3,6,7],[4]]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[4,1,6,3,8,5,7,2]=>[[1,2,5,7],[3,6,8],[4]]
[[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,3,4,1,2]=>[4,1,7,3,8,5,6,2]=>[[1,2,5,6],[3,7,8],[4]]
[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[4,1,8,3,7,5,6,2]=>[[1,2,5,6],[3,7],[4],[8]]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[4,1,8,3,6,5,7,2]=>[[1,2,5,7],[3,6],[4],[8]]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[4,1,8,3,5,6,7,2]=>[[1,2,5,6,7],[3,8],[4]]
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[7,6,8,4,3,5,1,2]=>[5,1,4,8,3,7,6,2]=>[[1,2,6],[3,7],[4,8],[5]]
[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[5,1,7,3,4,8,6,2]=>[[1,2,4,6],[3,7,8],[5]]
[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[6,1,4,8,3,5,7,2]=>[[1,2,5,7],[3,8],[4],[6]]
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[6,1,8,3,4,5,7,2]=>[[1,2,4,5,7],[3,8],[6]]
[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[8,5,3,4,6,7,1,2]=>[7,1,5,3,8,4,6,2]=>[[1,2,4,6],[3,8],[5],[7]]
[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[7,1,4,8,3,5,6,2]=>[[1,2,5,6],[3,8],[4],[7]]
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>[7,1,8,3,4,5,6,2]=>[[1,2,4,5,6],[3,8],[7]]
[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>[8,1,5,7,4,6,3,2]=>[[1,2,6],[3,7],[4],[5],[8]]
[[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>[7,4,5,6,3,8,1,2]=>[8,1,6,7,4,5,3,2]=>[[1,2,5],[3,7],[4],[6],[8]]
[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,3,8,1,2]=>[8,1,7,5,6,4,3,2]=>[[1,2,6],[3],[4],[5],[7],[8]]
[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,3,8,1,2]=>[8,1,7,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6],[7],[8]]
[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,3,8,1,2]=>[8,1,7,6,4,5,3,2]=>[[1,2,5],[3],[4],[6],[7],[8]]
[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[8,1,6,3,7,5,4,2]=>[[1,2,4],[3,7],[5],[6],[8]]
[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[6,7,4,3,5,8,1,2]=>[8,1,4,7,3,6,5,2]=>[[1,2,5],[3,6],[4],[7],[8]]
[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[8,1,5,3,7,4,6,2]=>[[1,2,4,6],[3,7],[5],[8]]
[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[7,3,4,5,6,8,1,2]=>[8,1,7,3,4,5,6,2]=>[[1,2,4,5,6],[3],[7],[8]]
[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[6,5,4,3,7,8,1,2]=>[8,1,4,5,6,3,7,2]=>[[1,2,5,6,7],[3],[4],[8]]
[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[8,1,6,3,5,4,7,2]=>[[1,2,4,7],[3],[5],[6],[8]]
[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[8,1,4,6,3,5,7,2]=>[[1,2,5,7],[3,6],[4],[8]]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[8,1,4,5,3,6,7,2]=>[[1,2,5,6,7],[3],[4],[8]]
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[8,1,5,4,3,6,7,2]=>[[1,2,6,7],[3],[4],[5],[8]]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,3]=>[[1,3,5,6,7,8],[2,4]]
[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>[8,7,5,6,4,2,1,3]=>[2,4,1,6,7,5,8,3]=>[[1,3,5,7,8],[2,4],[6]]
[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[2,4,1,6,8,5,7,3]=>[[1,3,5,7],[2,4,8],[6]]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,2,1,3]=>[2,4,1,8,7,6,5,3]=>[[1,3,5],[2,4],[6],[7],[8]]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[2,4,1,8,5,6,7,3]=>[[1,3,5,6,7],[2,4],[8]]
[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]=>[7,6,8,4,5,2,1,3]=>[2,5,1,8,4,7,6,3]=>[[1,3,6],[2,4,7],[5],[8]]
[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,2,1,3]=>[2,6,1,5,7,4,8,3]=>[[1,3,7,8],[2,4],[5],[6]]
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,2,1,3]=>[2,6,1,8,4,5,7,3]=>[[1,3,5,7],[2,4,8],[6]]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,2,1,3]=>[2,8,1,7,6,5,4,3]=>[[1,3],[2,4],[5],[6],[7],[8]]
[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,2,1,3]=>[2,8,1,5,4,6,7,3]=>[[1,3,6,7],[2,4],[5],[8]]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[2,8,1,4,5,6,7,3]=>[[1,3,5,6,7],[2,4],[8]]
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,3]=>[[1,2,3,6,7,8],[4,5]]
[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,1,2,3]=>[4,1,2,5,6,8,7,3]=>[[1,2,3,6,7],[4,5],[8]]
[[[.,.],.],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,1,2,3]=>[4,1,2,6,8,5,7,3]=>[[1,2,3,7],[4,5,8],[6]]
[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[4,1,2,7,8,5,6,3]=>[[1,2,3,6],[4,5,8],[7]]
[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,1,2,3]=>[4,1,2,8,7,6,5,3]=>[[1,2,3],[4,5],[6],[7],[8]]
[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[4,1,2,8,7,5,6,3]=>[[1,2,3,6],[4,5],[7],[8]]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[4,1,2,8,5,6,7,3]=>[[1,2,3,6,7],[4,5],[8]]
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,1,2,3]=>[5,1,2,6,4,8,7,3]=>[[1,2,3,7],[4,6,8],[5]]
[[[.,.],.],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,1,2,3]=>[6,1,2,5,8,4,7,3]=>[[1,2,3,7],[4,8],[5],[6]]
[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[6,1,2,7,4,5,8,3]=>[[1,2,3,5,8],[4,7],[6]]
[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>[6,1,2,8,4,5,7,3]=>[[1,2,3,5,7],[4,8],[6]]
[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[7,1,2,6,8,5,4,3]=>[[1,2,3,8],[4],[5],[6],[7]]
[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[8,1,2,5,6,7,4,3]=>[[1,2,3,6,7],[4],[5],[8]]
[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,1,2,3]=>[8,1,2,6,7,5,4,3]=>[[1,2,3,7],[4],[5],[6],[8]]
[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>[8,1,2,7,6,5,4,3]=>[[1,2,3],[4],[5],[6],[7],[8]]
[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[8,1,2,7,4,6,5,3]=>[[1,2,3,5],[4],[6],[7],[8]]
[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[8,1,2,7,4,5,6,3]=>[[1,2,3,5,6],[4],[7],[8]]
[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,1,2,3]=>[8,1,2,6,4,5,7,3]=>[[1,2,3,5,7],[4],[6],[8]]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[8,1,2,4,5,6,7,3]=>[[1,2,3,5,6,7],[4],[8]]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]=>[[1,3,4,6,7,8],[2,5]]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[2,3,6,1,7,5,8,4]=>[[1,3,4,7,8],[2,5],[6]]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[2,3,6,1,8,5,7,4]=>[[1,3,4,7],[2,5,8],[6]]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[2,3,7,1,6,8,5,4]=>[[1,3,4,8],[2,5],[6],[7]]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[2,3,8,1,7,6,5,4]=>[[1,3,4],[2,5],[6],[7],[8]]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[2,3,8,1,5,6,7,4]=>[[1,3,4,6,7],[2,5],[8]]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[3,5,2,1,6,7,8,4]=>[[1,4,6,7,8],[2,5],[3]]
[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[3,5,2,1,7,8,6,4]=>[[1,4,6,8],[2,5],[3,7]]
[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[3,8,2,1,7,6,5,4]=>[[1,4],[2,5],[3,6],[7],[8]]
[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[3,8,2,1,5,6,7,4]=>[[1,4,6,7],[2,5],[3,8]]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]=>[[1,2,4,7,8],[3,5,6]]
[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[3,1,6,2,7,5,8,4]=>[[1,2,4,8],[3,5,7],[6]]
[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[3,1,6,2,8,5,7,4]=>[[1,2,4,7],[3,5,8],[6]]
[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[3,1,7,2,8,5,6,4]=>[[1,2,4,6],[3,5,8],[7]]
[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[3,1,8,2,7,6,5,4]=>[[1,2,4],[3,5],[6],[7],[8]]
[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[3,1,8,2,7,5,6,4]=>[[1,2,4,6],[3,5],[7],[8]]
[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[3,1,8,2,6,5,7,4]=>[[1,2,4,7],[3,5],[6],[8]]
[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[3,1,8,2,5,6,7,4]=>[[1,2,4,6,7],[3,5],[8]]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[2,5,1,3,6,7,8,4]=>[[1,3,4,7,8],[2,5,6]]
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[2,5,1,3,6,8,7,4]=>[[1,3,4,7],[2,5,6],[8]]
[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[2,5,1,3,8,6,7,4]=>[[1,3,4,7],[2,5,6],[8]]
[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[2,6,1,3,8,5,7,4]=>[[1,3,4,7],[2,5,8],[6]]
[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,2,1,3,4]=>[2,7,1,3,6,8,5,4]=>[[1,3,4,8],[2,5],[6],[7]]
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[2,8,1,3,7,6,5,4]=>[[1,3,4],[2,5],[6],[7],[8]]
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[2,8,1,3,6,5,7,4]=>[[1,3,4,7],[2,5],[6],[8]]
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[2,8,1,3,5,6,7,4]=>[[1,3,4,6,7],[2,5],[8]]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,4]=>[[1,2,3,4,7,8],[5,6]]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[5,1,2,3,6,8,7,4]=>[[1,2,3,4,7],[5,6],[8]]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[5,1,2,3,7,8,6,4]=>[[1,2,3,4,8],[5,6],[7]]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[5,1,2,3,8,7,6,4]=>[[1,2,3,4],[5,6],[7],[8]]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[5,1,2,3,8,6,7,4]=>[[1,2,3,4,7],[5,6],[8]]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[6,1,2,3,7,5,8,4]=>[[1,2,3,4,8],[5,7],[6]]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[6,1,2,3,8,5,7,4]=>[[1,2,3,4,7],[5,8],[6]]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[7,1,2,3,6,8,5,4]=>[[1,2,3,4,8],[5],[6],[7]]
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[7,1,2,3,8,5,6,4]=>[[1,2,3,4,6],[5,8],[7]]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[8,1,2,3,6,7,5,4]=>[[1,2,3,4,7],[5],[6],[8]]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[8,1,2,3,7,6,5,4]=>[[1,2,3,4],[5],[6],[7],[8]]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[8,1,2,3,7,5,6,4]=>[[1,2,3,4,6],[5],[7],[8]]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[8,1,2,3,6,5,7,4]=>[[1,2,3,4,7],[5],[6],[8]]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[8,1,2,3,5,6,7,4]=>[[1,2,3,4,6,7],[5],[8]]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[2,3,4,6,1,8,7,5]=>[[1,3,4,5,7],[2,6],[8]]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[2,3,4,8,1,7,6,5]=>[[1,3,4,5],[2,6],[7],[8]]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[2,3,4,8,1,6,7,5]=>[[1,3,4,5,7],[2,6],[8]]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[4,3,8,2,1,6,7,5]=>[[1,5,7],[2,6],[3,8],[4]]
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,3,1,2,5]=>[3,1,4,6,2,8,7,5]=>[[1,2,5,7],[3,4,6],[8]]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[3,1,4,8,2,6,7,5]=>[[1,2,5,7],[3,4,6],[8]]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]=>[[1,3,5,7,8],[2,4,6]]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[2,4,1,7,3,8,6,5]=>[[1,3,5,8],[2,4,6],[7]]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[4,1,2,6,3,7,8,5]=>[[1,2,3,5,8],[4,6,7]]
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[4,1,2,6,3,8,7,5]=>[[1,2,3,5],[4,6,7],[8]]
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[4,1,2,7,3,8,6,5]=>[[1,2,3,5],[4,6,8],[7]]
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[7,8,6,3,2,1,4,5]=>[2,3,6,1,4,8,7,5]=>[[1,3,4,5],[2,6,7],[8]]
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[8,6,7,3,2,1,4,5]=>[2,3,7,1,4,8,6,5]=>[[1,3,4,5],[2,6,8],[7]]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[3,6,2,1,4,7,8,5]=>[[1,4,5,8],[2,6,7],[3]]
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[7,8,6,2,3,1,4,5]=>[3,6,2,1,4,8,7,5]=>[[1,4,5],[2,6,7],[3,8]]
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[7,8,6,3,1,2,4,5]=>[3,1,6,2,4,8,7,5]=>[[1,2,4,5],[3,6,7],[8]]
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>[2,7,1,3,4,8,6,5]=>[[1,3,4,5],[2,6,8],[7]]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[6,1,2,3,4,7,8,5]=>[[1,2,3,4,5,8],[6,7]]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[6,1,2,3,4,8,7,5]=>[[1,2,3,4,5],[6,7],[8]]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[7,1,2,3,4,8,6,5]=>[[1,2,3,4,5],[6,8],[7]]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[8,1,2,3,4,7,6,5]=>[[1,2,3,4,5],[6],[7],[8]]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[8,1,2,3,4,6,7,5]=>[[1,2,3,4,5,7],[6],[8]]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[2,3,4,5,8,1,7,6]=>[[1,3,4,5,6],[2,7],[8]]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[2,4,5,3,7,1,8,6]=>[[1,3,5,6,8],[2,7],[4]]
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[7,8,4,3,5,2,1,6]=>[2,5,4,8,3,1,7,6]=>[[1,3,6],[2,7],[4,8],[5]]
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[8,7,4,5,2,3,1,6]=>[3,5,2,7,4,1,8,6]=>[[1,4,6,8],[2,5,7],[3]]
[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[7,8,5,2,3,4,1,6]=>[4,5,2,3,8,1,7,6]=>[[1,3,6],[2,5,7],[4,8]]
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>[5,4,8,3,2,1,7,6]=>[[1,6],[2,7],[3,8],[4],[5]]
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[4,1,5,3,7,2,8,6]=>[[1,2,6,8],[3,5,7],[4]]
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[4,1,5,3,8,2,7,6]=>[[1,2,6],[3,5,7],[4,8]]
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]=>[[1,3,5,6,8],[2,4,7]]
[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6]=>[2,5,1,8,4,3,7,6]=>[[1,3,6],[2,4,7],[5,8]]
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[4,1,2,5,7,3,8,6]=>[[1,2,3,6,8],[4,5,7]]
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[4,1,2,5,8,3,7,6]=>[[1,2,3,6],[4,5,7],[8]]
[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[7,8,5,3,2,1,4,6]=>[2,3,5,1,8,4,7,6]=>[[1,3,4,6],[2,5,7],[8]]
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]=>[[1,2,4,6],[3,5,7,8]]
[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[3,1,5,2,8,4,7,6]=>[[1,2,4,6],[3,5,7],[8]]
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[2,5,1,3,7,4,8,6]=>[[1,3,4,6],[2,5,7,8]]
[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[2,5,1,3,8,4,7,6]=>[[1,3,4,6],[2,5,7],[8]]
[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[5,1,2,3,7,4,8,6]=>[[1,2,3,4,6],[5,7,8]]
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[5,1,2,3,8,4,7,6]=>[[1,2,3,4,6],[5,7],[8]]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6]=>[2,3,4,7,1,5,8,6]=>[[1,3,4,5,6],[2,7,8]]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[2,3,4,8,1,5,7,6]=>[[1,3,4,5,6],[2,7],[8]]
[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[8,7,3,4,2,1,5,6]=>[2,4,7,3,1,5,8,6]=>[[1,3,5,6],[2,7,8],[4]]
[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[7,8,3,4,2,1,5,6]=>[2,4,8,3,1,5,7,6]=>[[1,3,5,6],[2,7],[4,8]]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[4,3,8,2,1,5,7,6]=>[[1,5,6],[2,7],[3,8],[4]]
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>[4,8,2,3,1,5,7,6]=>[[1,3,5,6],[2,7],[4,8]]
[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[4,1,2,7,3,5,8,6]=>[[1,2,3,5,6],[4,7,8]]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[2,3,7,1,4,5,8,6]=>[[1,3,4,5,6],[2,7,8]]
[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[2,3,8,1,4,5,7,6]=>[[1,3,4,5,6],[2,7],[8]]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[7,8,2,3,1,4,5,6]=>[3,8,2,1,4,5,7,6]=>[[1,4,5,6],[2,7],[3,8]]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[2,3,6,8,4,5,1,7]=>[[1,3,4,5,7],[2,8],[6]]
[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]=>[8,5,6,3,4,2,1,7]=>[2,4,6,3,8,5,1,7]=>[[1,3,5,7],[2,6,8],[4]]
[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,2,3,1,7]=>[3,5,2,6,4,8,1,7]=>[[1,4,6,7],[2,5,8],[3]]
[[.,[[.,.],[[[.,.],.],.]]],[.,.]]=>[8,4,5,6,2,3,1,7]=>[3,6,2,8,4,5,1,7]=>[[1,4,5,7],[2,6,8],[3]]
[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[8,6,3,2,4,5,1,7]=>[5,3,6,2,4,8,1,7]=>[[1,4,7],[2,6,8],[3],[5]]
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[8,5,4,3,2,6,1,7]=>[6,3,4,5,8,2,1,7]=>[[1,4,5,7],[2,8],[3],[6]]
[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[8,4,5,3,2,6,1,7]=>[6,3,5,8,4,2,1,7]=>[[1,4,7],[2,8],[3],[5],[6]]
[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[8,3,4,5,2,6,1,7]=>[6,5,8,3,4,2,1,7]=>[[1,4,7],[2,8],[3],[5],[6]]
[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[4,1,6,3,8,5,2,7]=>[[1,2,5,7],[3,6,8],[4]]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,2,1,3,7]=>[2,4,1,6,8,5,3,7]=>[[1,3,5,7],[2,4,8],[6]]
[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[4,1,2,5,6,8,3,7]=>[[1,2,3,6,7],[4,5,8]]
[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[8,5,6,3,2,1,4,7]=>[2,3,6,1,8,5,4,7]=>[[1,3,4,7],[2,5,8],[6]]
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[3,5,2,1,6,8,4,7]=>[[1,4,6,7],[2,5,8],[3]]
[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[3,6,2,1,8,5,4,7]=>[[1,4,7],[2,5,8],[3,6]]
[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[2,5,1,3,6,8,4,7]=>[[1,3,4,7],[2,5,6,8]]
[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[5,1,2,3,6,8,4,7]=>[[1,2,3,4,7],[5,6,8]]
[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[6,1,2,3,8,5,4,7]=>[[1,2,3,4,7],[5,8],[6]]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[2,3,4,6,1,8,5,7]=>[[1,3,4,5,7],[2,6,8]]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[2,4,6,3,1,8,5,7]=>[[1,3,5,7],[2,6,8],[4]]
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[8,6,3,2,4,1,5,7]=>[4,3,6,2,1,8,5,7]=>[[1,5,7],[2,6,8],[3],[4]]
[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[8,6,4,3,1,2,5,7]=>[3,1,4,6,2,8,5,7]=>[[1,2,5,7],[3,4,6,8]]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[2,4,1,6,3,8,5,7]=>[[1,3,5,7],[2,4,6,8]]
[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[4,1,2,6,3,8,5,7]=>[[1,2,3,5,7],[4,6,8]]
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[8,5,4,3,2,1,6,7]=>[2,3,4,5,8,1,6,7]=>[[1,3,4,5,6,7],[2,8]]
[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[8,4,3,5,2,1,6,7]=>[2,5,4,8,3,1,6,7]=>[[1,3,6,7],[2,8],[4],[5]]
[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[8,3,4,5,2,1,6,7]=>[2,5,8,3,4,1,6,7]=>[[1,3,4,6,7],[2,8],[5]]
[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[8,5,2,3,4,1,6,7]=>[4,5,2,3,8,1,6,7]=>[[1,3,6,7],[2,5,8],[4]]
[[[.,[[[.,.],[.,.]],.]],.],[.,.]]=>[8,4,2,3,5,1,6,7]=>[5,4,2,8,3,1,6,7]=>[[1,3,6,7],[2,8],[4],[5]]
[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[3,1,5,2,8,4,6,7]=>[[1,2,4,6,7],[3,5,8]]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[2,3,4,8,1,5,6,7]=>[[1,3,4,5,6,7],[2,8]]
[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[8,3,4,2,1,5,6,7]=>[2,4,8,3,1,5,6,7]=>[[1,3,5,6,7],[2,8],[4]]
[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[8,4,2,3,1,5,6,7]=>[3,4,2,8,1,5,6,7]=>[[1,4,5,6,7],[2,8],[3]]
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[8,3,2,4,1,5,6,7]=>[4,3,8,2,1,5,6,7]=>[[1,5,6,7],[2,8],[3],[4]]
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>[4,8,2,3,1,5,6,7]=>[[1,3,5,6,7],[2,8],[4]]
[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[8,4,3,1,2,5,6,7]=>[3,1,4,8,2,5,6,7]=>[[1,2,5,6,7],[3,4,8]]
[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[8,3,4,1,2,5,6,7]=>[4,1,8,3,2,5,6,7]=>[[1,2,5,6,7],[3,8],[4]]
[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[8,4,2,1,3,5,6,7]=>[2,4,1,8,3,5,6,7]=>[[1,3,5,6,7],[2,4,8]]
[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[4,1,2,8,3,5,6,7]=>[[1,2,3,5,6,7],[4,8]]
[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[2,3,8,1,4,5,6,7]=>[[1,3,4,5,6,7],[2,8]]
[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>[3,8,2,1,4,5,6,7]=>[[1,4,5,6,7],[2,8],[3]]
[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[3,1,8,2,4,5,6,7]=>[[1,2,4,5,6,7],[3,8]]
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7],[8]]
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[2,3,4,7,6,5,1,8]=>[[1,3,4,5,8],[2],[6],[7]]
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[2,3,4,7,5,6,1,8]=>[[1,3,4,5,6,8],[2],[7]]
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[2,3,7,5,6,4,1,8]=>[[1,3,4,6,8],[2],[5],[7]]
[[.,[.,[.,[[.,[[.,.],.]],.]]]],.]=>[5,6,4,7,3,2,1,8]=>[2,3,7,6,5,4,1,8]=>[[1,3,4,8],[2],[5],[6],[7]]
[[.,[.,[.,[[[.,[.,.]],.],.]]]],.]=>[5,4,6,7,3,2,1,8]=>[2,3,7,5,4,6,1,8]=>[[1,3,4,6,8],[2],[5],[7]]
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[2,4,6,3,7,5,1,8]=>[[1,3,5,7,8],[2,6],[4]]
[[.,[.,[[.,.],[[[.,.],.],.]]]],.]=>[5,6,7,3,4,2,1,8]=>[2,4,7,3,5,6,1,8]=>[[1,3,5,6,8],[2,7],[4]]
[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[2,7,4,5,6,3,1,8]=>[[1,3,5,6,8],[2],[4],[7]]
[[.,[[.,.],[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,2,3,1,8]=>[3,4,2,7,5,6,1,8]=>[[1,4,5,6,8],[2,7],[3]]
[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[3,5,2,7,4,6,1,8]=>[[1,4,6,8],[2,5,7],[3]]
[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]=>[6,5,4,7,2,3,1,8]=>[3,7,2,5,6,4,1,8]=>[[1,4,6,8],[2,5],[3],[7]]
[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[3,7,2,6,5,4,1,8]=>[[1,4,8],[2,5],[3],[6],[7]]
[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[4,3,7,2,5,6,1,8]=>[[1,5,6,8],[2,7],[3],[4]]
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[4,5,2,3,6,7,1,8]=>[[1,3,6,7,8],[2,5],[4]]
[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[4,5,2,3,7,6,1,8]=>[[1,3,6,8],[2,5,7],[4]]
[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[4,6,2,3,7,5,1,8]=>[[1,3,5,8],[2,6,7],[4]]
[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[4,7,2,3,6,5,1,8]=>[[1,3,5,8],[2,6],[4],[7]]
[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[4,7,2,3,5,6,1,8]=>[[1,3,5,6,8],[2,7],[4]]
[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[7,4,3,5,2,6,1,8]=>[6,5,4,7,3,2,1,8]=>[[1,7,8],[2],[3],[4],[5],[6]]
[[.,[[.,[[[.,.],.],.]],[.,.]]],.]=>[7,3,4,5,2,6,1,8]=>[6,5,7,3,4,2,1,8]=>[[1,4,8],[2,7],[3],[5],[6]]
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[7,5,3,2,4,6,1,8]=>[6,3,5,2,7,4,1,8]=>[[1,4,7,8],[2,5],[3],[6]]
[[.,[[[[.,.],[.,.]],.],[.,.]]],.]=>[7,4,2,3,5,6,1,8]=>[6,4,2,7,3,5,1,8]=>[[1,3,5,8],[2,7],[4],[6]]
[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[7,3,6,5,4,2,1,8]=>[[1,4,8],[2],[3],[5],[6],[7]]
[[.,[[.,[[[.,.],.],[.,.]]],.]],.]=>[6,3,4,5,2,7,1,8]=>[7,5,6,3,4,2,1,8]=>[[1,4,8],[2,6],[3],[5],[7]]
[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[7,6,4,5,3,2,1,8]=>[[1,5,8],[2],[3],[4],[6],[7]]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[7,6,5,4,3,2,1,8]=>[[1,8],[2],[3],[4],[5],[6],[7]]
[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[7,6,3,4,5,2,1,8]=>[[1,4,5,8],[2],[3],[6],[7]]
[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[5,4,6,2,3,7,1,8]=>[7,6,2,5,4,3,1,8]=>[[1,3,8],[2],[4],[5],[6],[7]]
[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[4,5,6,2,3,7,1,8]=>[7,6,2,4,5,3,1,8]=>[[1,3,5,8],[2],[4],[6],[7]]
[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[6,5,3,2,4,7,1,8]=>[7,3,5,2,6,4,1,8]=>[[1,4,6,8],[2,5],[3],[7]]
[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[5,6,2,3,4,7,1,8]=>[7,6,2,3,5,4,1,8]=>[[1,3,4,8],[2],[5],[6],[7]]
[[.,[[[[.,.],[.,.]],[.,.]],.]],.]=>[6,4,2,3,5,7,1,8]=>[7,4,2,6,3,5,1,8]=>[[1,3,5,8],[2,6],[4],[7]]
[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[6,2,3,4,5,7,1,8]=>[7,6,2,3,4,5,1,8]=>[[1,3,4,5,8],[2],[6],[7]]
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[5,3,4,2,6,7,1,8]=>[7,4,5,3,2,6,1,8]=>[[1,5,6,8],[2],[3],[4],[7]]
[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[7,5,3,4,2,6,1,8]=>[[1,4,6,8],[2],[3],[5],[7]]
[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[4,2,3,5,6,7,1,8]=>[7,4,2,3,5,6,1,8]=>[[1,3,5,6,8],[2],[4],[7]]
[[[.,.],[.,[.,[[[.,.],.],.]]]],.]=>[5,6,7,4,3,1,2,8]=>[3,1,4,7,5,6,2,8]=>[[1,2,5,6,8],[3,4],[7]]
[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[4,1,6,3,7,5,2,8]=>[[1,2,5,8],[3,6,7],[4]]
[[[.,.],[[.,[[.,.],.]],[.,.]]],.]=>[7,4,5,3,6,1,2,8]=>[6,1,5,7,4,3,2,8]=>[[1,2,7,8],[3],[4],[5],[6]]
[[[.,.],[[.,[.,[[.,.],.]]],.]],.]=>[5,6,4,3,7,1,2,8]=>[7,1,4,6,5,3,2,8]=>[[1,2,5,8],[3],[4],[6],[7]]
[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[6,5,3,4,7,1,2,8]=>[7,1,5,3,6,4,2,8]=>[[1,2,4,8],[3,6],[5],[7]]
[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,2,1,3,8]=>[2,4,1,7,5,6,3,8]=>[[1,3,5,6,8],[2,4],[7]]
[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[6,5,4,7,2,1,3,8]=>[2,7,1,5,6,4,3,8]=>[[1,3,6,8],[2,4],[5],[7]]
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[4,1,2,5,6,7,3,8]=>[[1,2,3,6,7,8],[4,5]]
[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[6,7,5,4,1,2,3,8]=>[4,1,2,5,7,6,3,8]=>[[1,2,3,6,8],[4,5],[7]]
[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,1,2,3,8]=>[4,1,2,7,5,6,3,8]=>[[1,2,3,6,8],[4,5],[7]]
[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[5,6,4,7,1,2,3,8]=>[7,1,2,6,5,4,3,8]=>[[1,2,3,8],[4],[5],[6],[7]]
[[[[.,.],.],[[[.,.],[.,.]],.]],.]=>[6,4,5,7,1,2,3,8]=>[7,1,2,6,4,5,3,8]=>[[1,2,3,5,8],[4],[6],[7]]
[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,1,2,3,8]=>[7,1,2,5,4,6,3,8]=>[[1,2,3,6,8],[4],[5],[7]]
[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[5,6,7,3,2,1,4,8]=>[2,3,7,1,5,6,4,8]=>[[1,3,4,6,8],[2,5],[7]]
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[5,6,7,2,3,1,4,8]=>[3,7,2,1,5,6,4,8]=>[[1,4,6,8],[2,5],[3,7]]
[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[5,6,7,3,1,2,4,8]=>[3,1,7,2,5,6,4,8]=>[[1,2,4,6,8],[3,5],[7]]
[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[5,6,7,2,1,3,4,8]=>[2,7,1,3,5,6,4,8]=>[[1,3,4,6,8],[2,5],[7]]
[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[5,1,2,3,6,7,4,8]=>[[1,2,3,4,7,8],[5,6]]
[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[5,1,2,3,7,6,4,8]=>[[1,2,3,4,8],[5,6],[7]]
[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[6,1,2,3,7,5,4,8]=>[[1,2,3,4,8],[5,7],[6]]
[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[7,1,2,3,6,5,4,8]=>[[1,2,3,4,8],[5],[6],[7]]
[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[7,1,2,3,5,6,4,8]=>[[1,2,3,4,6,8],[5],[7]]
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[6,7,4,3,2,1,5,8]=>[2,3,4,7,1,6,5,8]=>[[1,3,4,5,8],[2,6],[7]]
[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[7,6,3,4,1,2,5,8]=>[4,1,6,3,2,7,5,8]=>[[1,2,5,8],[3,6,7],[4]]
[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[2,4,1,6,3,7,5,8]=>[[1,3,5,7,8],[2,4,6]]
[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[7,6,4,1,2,3,5,8]=>[4,1,2,6,3,7,5,8]=>[[1,2,3,5,8],[4,6,7]]
[[[.,[[[[.,.],.],.],.]],[.,.]],.]=>[7,2,3,4,5,1,6,8]=>[5,7,2,3,4,1,6,8]=>[[1,3,4,6,8],[2,7],[5]]
[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[7,5,4,1,2,3,6,8]=>[4,1,2,5,7,3,6,8]=>[[1,2,3,6,8],[4,5,7]]
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[7,5,2,3,1,4,6,8]=>[3,5,2,1,7,4,6,8]=>[[1,4,6,8],[2,5,7],[3]]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[3,1,5,2,7,4,6,8]=>[[1,2,4,6,8],[3,5,7]]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[2,3,4,7,1,5,6,8]=>[[1,3,4,5,6,8],[2,7]]
[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[7,4,2,3,1,5,6,8]=>[3,4,2,7,1,5,6,8]=>[[1,4,5,6,8],[2,7],[3]]
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[7,3,2,4,1,5,6,8]=>[4,3,7,2,1,5,6,8]=>[[1,5,6,8],[2,7],[3],[4]]
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,6,8]=>[[1,2,3,4,5,6,8],[7]]
[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>[2,6,4,5,3,1,7,8]=>[[1,3,5,7,8],[2],[4],[6]]
[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[5,4,6,2,3,1,7,8]=>[3,6,2,5,4,1,7,8]=>[[1,4,7,8],[2,5],[3],[6]]
[[[.,[[.,[.,.]],[[.,.],.]]],.],.]=>[5,6,3,2,4,1,7,8]=>[4,3,6,2,5,1,7,8]=>[[1,5,7,8],[2,6],[3],[4]]
[[[.,[[[.,[.,.]],.],[.,.]]],.],.]=>[6,3,2,4,5,1,7,8]=>[5,3,6,2,4,1,7,8]=>[[1,4,7,8],[2,6],[3],[5]]
[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>[6,5,3,4,2,1,7,8]=>[[1,4,7,8],[2],[3],[5],[6]]
[[[.,[[[.,.],[.,[.,.]]],.]],.],.]=>[5,4,2,3,6,1,7,8]=>[6,4,2,5,3,1,7,8]=>[[1,3,7,8],[2,5],[4],[6]]
[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[5,2,3,4,6,1,7,8]=>[6,5,2,3,4,1,7,8]=>[[1,3,4,7,8],[2],[5],[6]]
[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[5,6,4,3,1,2,7,8]=>[3,1,4,6,5,2,7,8]=>[[1,2,5,7,8],[3,4],[6]]
[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[5,4,6,3,1,2,7,8]=>[3,1,6,5,4,2,7,8]=>[[1,2,7,8],[3,4],[5],[6]]
[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>[4,1,6,3,5,2,7,8]=>[[1,2,5,7,8],[3,6],[4]]
[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[5,4,3,6,1,2,7,8]=>[6,1,4,5,3,2,7,8]=>[[1,2,5,7,8],[3],[4],[6]]
[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[5,6,4,2,1,3,7,8]=>[2,4,1,6,5,3,7,8]=>[[1,3,5,7,8],[2,4],[6]]
[[[[.,[.,.]],[[.,.],[.,.]]],.],.]=>[6,4,5,2,1,3,7,8]=>[2,5,1,6,4,3,7,8]=>[[1,3,6,7,8],[2,4],[5]]
[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[5,4,6,2,1,3,7,8]=>[2,6,1,5,4,3,7,8]=>[[1,3,7,8],[2,4],[5],[6]]
[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[6,5,4,1,2,3,7,8]=>[4,1,2,5,6,3,7,8]=>[[1,2,3,6,7,8],[4,5]]
[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>[2,3,6,1,5,4,7,8]=>[[1,3,4,7,8],[2,5],[6]]
[[[[.,[[.,.],.]],[.,[.,.]]],.],.]=>[6,5,2,3,1,4,7,8]=>[3,5,2,1,6,4,7,8]=>[[1,4,6,7,8],[2,5],[3]]
[[[[.,[[.,.],.]],[[.,.],.]],.],.]=>[5,6,2,3,1,4,7,8]=>[3,6,2,1,5,4,7,8]=>[[1,4,7,8],[2,5],[3,6]]
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[[1,3,4,5,6,7,8],[2]]
[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[2,3,5,4,1,6,7,8]=>[[1,3,4,6,7,8],[2],[5]]
[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[5,3,4,2,1,6,7,8]=>[2,4,5,3,1,6,7,8]=>[[1,3,5,6,7,8],[2],[4]]
[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[4,3,5,2,1,6,7,8]=>[2,5,4,3,1,6,7,8]=>[[1,3,6,7,8],[2],[4],[5]]
[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[2,5,3,4,1,6,7,8]=>[[1,3,4,6,7,8],[2],[5]]
[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[5,4,2,3,1,6,7,8]=>[3,4,2,5,1,6,7,8]=>[[1,4,5,6,7,8],[2],[3]]
[[[[.,[[.,.],[[.,.],.]]],.],.],.]=>[4,5,2,3,1,6,7,8]=>[3,5,2,4,1,6,7,8]=>[[1,4,6,7,8],[2,5],[3]]
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[5,3,2,4,1,6,7,8]=>[4,3,5,2,1,6,7,8]=>[[1,5,6,7,8],[2],[3],[4]]
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[4,5,2,3,1,6,7,8]=>[[1,3,6,7,8],[2,5],[4]]
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[4,3,2,5,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>[[1,4,6,7,8],[2],[3],[5]]
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[[1,6,7,8],[2],[3],[4],[5]]
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[4,2,3,5,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>[[1,3,6,7,8],[2],[4],[5]]
[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>[[1,4,6,7,8],[2],[3],[5]]
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[[1,3,4,6,7,8],[2],[5]]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>[[1,2,3,4,6,7,8],[5]]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[[1,3,4,5,6,7,8],[2]]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[[1,5,6,7,8],[2],[3],[4]]
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[[1,2,3,5,6,7,8],[4]]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[[1,2,4,5,6,7,8],[3]]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8]]
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
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
- the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
- the set of left-to-right maximima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
- the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
- the set of maximal elements in the decreasing runs of $\pi$ is the set of deficiency positions of $\chi(\pi)$, and
- the set of minimal elements in the decreasing runs of $\pi$ is the set of deficiency values of $\chi(\pi)$.
Map
Robinson-Schensted insertion tableau
Description
Sends a permutation to its Robinson-Schensted insertion tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding insertion tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding insertion tableau.
searching the database
Sorry, this map was not found in the database.