Identifier
Mp00075:
Semistandard tableaux
—reading word permutation⟶
Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Images
=>
Cc0019;cc-rep-0Cc0010;cc-rep-3
[[1,2]]=>[1,2]=>[1,2]=>[.,[.,.]]
[[2,2]]=>[1,2]=>[1,2]=>[.,[.,.]]
[[1],[2]]=>[2,1]=>[2,1]=>[[.,.],.]
[[1,3]]=>[1,2]=>[1,2]=>[.,[.,.]]
[[2,3]]=>[1,2]=>[1,2]=>[.,[.,.]]
[[3,3]]=>[1,2]=>[1,2]=>[.,[.,.]]
[[1],[3]]=>[2,1]=>[2,1]=>[[.,.],.]
[[2],[3]]=>[2,1]=>[2,1]=>[[.,.],.]
[[1,1,2]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[1,2,2]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[2,2,2]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[1,1],[2]]=>[3,1,2]=>[3,1,2]=>[[.,.],[.,.]]
[[1,2],[2]]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[[1,4]]=>[1,2]=>[1,2]=>[.,[.,.]]
[[2,4]]=>[1,2]=>[1,2]=>[.,[.,.]]
[[3,4]]=>[1,2]=>[1,2]=>[.,[.,.]]
[[4,4]]=>[1,2]=>[1,2]=>[.,[.,.]]
[[1],[4]]=>[2,1]=>[2,1]=>[[.,.],.]
[[2],[4]]=>[2,1]=>[2,1]=>[[.,.],.]
[[3],[4]]=>[2,1]=>[2,1]=>[[.,.],.]
[[1,1,3]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[1,2,3]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[1,3,3]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[2,2,3]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[2,3,3]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[3,3,3]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[1,1],[3]]=>[3,1,2]=>[3,1,2]=>[[.,.],[.,.]]
[[1,2],[3]]=>[3,1,2]=>[3,1,2]=>[[.,.],[.,.]]
[[1,3],[2]]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[[1,3],[3]]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[[2,2],[3]]=>[3,1,2]=>[3,1,2]=>[[.,.],[.,.]]
[[2,3],[3]]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[[1],[2],[3]]=>[3,2,1]=>[2,3,1]=>[[.,[.,.]],.]
[[1,1,1,2]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[1,1,2,2]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[1,2,2,2]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[2,2,2,2]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[1,1,1],[2]]=>[4,1,2,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[[1,1,2],[2]]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[1,2,2],[2]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[1,1],[2,2]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[1,5]]=>[1,2]=>[1,2]=>[.,[.,.]]
[[2,5]]=>[1,2]=>[1,2]=>[.,[.,.]]
[[3,5]]=>[1,2]=>[1,2]=>[.,[.,.]]
[[4,5]]=>[1,2]=>[1,2]=>[.,[.,.]]
[[5,5]]=>[1,2]=>[1,2]=>[.,[.,.]]
[[1],[5]]=>[2,1]=>[2,1]=>[[.,.],.]
[[2],[5]]=>[2,1]=>[2,1]=>[[.,.],.]
[[3],[5]]=>[2,1]=>[2,1]=>[[.,.],.]
[[4],[5]]=>[2,1]=>[2,1]=>[[.,.],.]
[[1,1,4]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[1,2,4]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[1,3,4]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[1,4,4]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[2,2,4]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[2,3,4]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[2,4,4]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[3,3,4]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[3,4,4]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[4,4,4]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[1,1],[4]]=>[3,1,2]=>[3,1,2]=>[[.,.],[.,.]]
[[1,2],[4]]=>[3,1,2]=>[3,1,2]=>[[.,.],[.,.]]
[[1,4],[2]]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[[1,3],[4]]=>[3,1,2]=>[3,1,2]=>[[.,.],[.,.]]
[[1,4],[3]]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[[1,4],[4]]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[[2,2],[4]]=>[3,1,2]=>[3,1,2]=>[[.,.],[.,.]]
[[2,3],[4]]=>[3,1,2]=>[3,1,2]=>[[.,.],[.,.]]
[[2,4],[3]]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[[2,4],[4]]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[[3,3],[4]]=>[3,1,2]=>[3,1,2]=>[[.,.],[.,.]]
[[3,4],[4]]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[[1],[2],[4]]=>[3,2,1]=>[2,3,1]=>[[.,[.,.]],.]
[[1],[3],[4]]=>[3,2,1]=>[2,3,1]=>[[.,[.,.]],.]
[[2],[3],[4]]=>[3,2,1]=>[2,3,1]=>[[.,[.,.]],.]
[[1,1,1,3]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[1,1,2,3]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[1,1,3,3]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[1,2,2,3]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[1,2,3,3]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[1,3,3,3]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[2,2,2,3]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[2,2,3,3]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[2,3,3,3]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[3,3,3,3]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[1,1,1],[3]]=>[4,1,2,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[[1,1,2],[3]]=>[4,1,2,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[[1,1,3],[2]]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[1,1,3],[3]]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[1,2,2],[3]]=>[4,1,2,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[[1,2,3],[2]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[1,2,3],[3]]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[1,3,3],[2]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[1,3,3],[3]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[2,2,2],[3]]=>[4,1,2,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[[2,2,3],[3]]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[2,3,3],[3]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[1,1],[2,3]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[1,1],[3,3]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[1,2],[2,3]]=>[2,4,1,3]=>[4,2,1,3]=>[[[.,.],.],[.,.]]
[[1,2],[3,3]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[2,2],[3,3]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[1,1],[2],[3]]=>[4,3,1,2]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[[1,2],[2],[3]]=>[4,2,1,3]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[[1,3],[2],[3]]=>[3,2,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[[1,1,1,1,2]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,1,1,2,2]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,1,2,2,2]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,2,2,2,2]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[2,2,2,2,2]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,1,1,1],[2]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]
[[1,1,1,2],[2]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,1,2,2],[2]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,2,2,2],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,1,1],[2,2]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,1,2],[2,2]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,6]]=>[1,2]=>[1,2]=>[.,[.,.]]
[[2,6]]=>[1,2]=>[1,2]=>[.,[.,.]]
[[3,6]]=>[1,2]=>[1,2]=>[.,[.,.]]
[[4,6]]=>[1,2]=>[1,2]=>[.,[.,.]]
[[5,6]]=>[1,2]=>[1,2]=>[.,[.,.]]
[[6,6]]=>[1,2]=>[1,2]=>[.,[.,.]]
[[1],[6]]=>[2,1]=>[2,1]=>[[.,.],.]
[[2],[6]]=>[2,1]=>[2,1]=>[[.,.],.]
[[3],[6]]=>[2,1]=>[2,1]=>[[.,.],.]
[[4],[6]]=>[2,1]=>[2,1]=>[[.,.],.]
[[5],[6]]=>[2,1]=>[2,1]=>[[.,.],.]
[[1,1,5]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[1,2,5]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[1,3,5]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[1,4,5]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[1,5,5]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[2,2,5]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[2,3,5]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[2,4,5]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[2,5,5]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[3,3,5]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[3,4,5]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[3,5,5]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[4,4,5]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[4,5,5]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[5,5,5]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[1,1],[5]]=>[3,1,2]=>[3,1,2]=>[[.,.],[.,.]]
[[1,2],[5]]=>[3,1,2]=>[3,1,2]=>[[.,.],[.,.]]
[[1,5],[2]]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[[1,3],[5]]=>[3,1,2]=>[3,1,2]=>[[.,.],[.,.]]
[[1,5],[3]]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[[1,4],[5]]=>[3,1,2]=>[3,1,2]=>[[.,.],[.,.]]
[[1,5],[4]]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[[1,5],[5]]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[[2,2],[5]]=>[3,1,2]=>[3,1,2]=>[[.,.],[.,.]]
[[2,3],[5]]=>[3,1,2]=>[3,1,2]=>[[.,.],[.,.]]
[[2,5],[3]]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[[2,4],[5]]=>[3,1,2]=>[3,1,2]=>[[.,.],[.,.]]
[[2,5],[4]]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[[2,5],[5]]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[[3,3],[5]]=>[3,1,2]=>[3,1,2]=>[[.,.],[.,.]]
[[3,4],[5]]=>[3,1,2]=>[3,1,2]=>[[.,.],[.,.]]
[[3,5],[4]]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[[3,5],[5]]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[[4,4],[5]]=>[3,1,2]=>[3,1,2]=>[[.,.],[.,.]]
[[4,5],[5]]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[[1],[2],[5]]=>[3,2,1]=>[2,3,1]=>[[.,[.,.]],.]
[[1],[3],[5]]=>[3,2,1]=>[2,3,1]=>[[.,[.,.]],.]
[[1],[4],[5]]=>[3,2,1]=>[2,3,1]=>[[.,[.,.]],.]
[[2],[3],[5]]=>[3,2,1]=>[2,3,1]=>[[.,[.,.]],.]
[[2],[4],[5]]=>[3,2,1]=>[2,3,1]=>[[.,[.,.]],.]
[[3],[4],[5]]=>[3,2,1]=>[2,3,1]=>[[.,[.,.]],.]
[[1,1,1,4]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[1,1,2,4]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[1,1,3,4]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[1,1,4,4]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[1,2,2,4]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[1,2,3,4]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[1,2,4,4]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[1,3,3,4]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[1,3,4,4]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[1,4,4,4]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[2,2,2,4]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[2,2,3,4]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[2,2,4,4]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[2,3,3,4]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[2,3,4,4]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[2,4,4,4]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[3,3,3,4]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[3,3,4,4]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[3,4,4,4]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[4,4,4,4]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[1,1,1],[4]]=>[4,1,2,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[[1,1,2],[4]]=>[4,1,2,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[[1,1,4],[2]]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[1,1,3],[4]]=>[4,1,2,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[[1,1,4],[3]]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[1,1,4],[4]]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[1,2,2],[4]]=>[4,1,2,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[[1,2,4],[2]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[1,2,3],[4]]=>[4,1,2,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[[1,2,4],[3]]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[1,3,4],[2]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[1,2,4],[4]]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[1,4,4],[2]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[1,3,3],[4]]=>[4,1,2,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[[1,3,4],[3]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[1,3,4],[4]]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[1,4,4],[3]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[1,4,4],[4]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[2,2,2],[4]]=>[4,1,2,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[[2,2,3],[4]]=>[4,1,2,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[[2,2,4],[3]]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[2,2,4],[4]]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[2,3,3],[4]]=>[4,1,2,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[[2,3,4],[3]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[2,3,4],[4]]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[2,4,4],[3]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[2,4,4],[4]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[3,3,3],[4]]=>[4,1,2,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[[3,3,4],[4]]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[3,4,4],[4]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
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[[2,4,5],[5]]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
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[[3,3,5],[5]]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[3,4,4],[5]]=>[4,1,2,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
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[[3,4,5],[5]]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[3,5,5],[4]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[3,5,5],[5]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[4,4,4],[5]]=>[4,1,2,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[[4,4,5],[5]]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[4,5,5],[5]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
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[[1,3,4,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,4,4,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
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[[2,2,2,3,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[2,2,2,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[2,2,3,3,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[2,2,3,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[2,2,4,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[2,3,3,3,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[2,3,3,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[2,3,4,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[2,4,4,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[3,3,3,3,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[3,3,3,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[3,3,4,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[3,4,4,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[4,4,4,4,4]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
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[[1,1,1,2],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]
[[1,1,1,4],[2]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,1,1,3],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]
[[1,1,1,4],[3]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,1,1,4],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,1,2,2],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]
[[1,1,2,4],[2]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,1,2,3],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]
[[1,1,2,4],[3]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,1,3,4],[2]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,1,2,4],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,1,4,4],[2]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,1,3,3],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]
[[1,1,3,4],[3]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,1,3,4],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,1,4,4],[3]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,1,4,4],[4]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,2,2,2],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]
[[1,2,2,4],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,2,2,3],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]
[[1,2,2,4],[3]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,2,3,4],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,2,2,4],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,2,4,4],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,2,3,3],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]
[[1,2,3,4],[3]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,3,3,4],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,2,3,4],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,2,4,4],[3]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,3,4,4],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,2,4,4],[4]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,4,4,4],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,3,3,3],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]
[[1,3,3,4],[3]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,3,3,4],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,3,4,4],[3]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,3,4,4],[4]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,4,4,4],[3]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,4,4,4],[4]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[2,2,2,2],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]
[[2,2,2,3],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]
[[2,2,2,4],[3]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[[2,2,2,4],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[[2,2,3,3],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]
[[2,2,3,4],[3]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[2,2,3,4],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[[2,2,4,4],[3]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[2,2,4,4],[4]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[2,3,3,3],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]
[[2,3,3,4],[3]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[2,3,3,4],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[[2,3,4,4],[3]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[2,3,4,4],[4]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[2,4,4,4],[3]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[2,4,4,4],[4]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[3,3,3,3],[4]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]
[[3,3,3,4],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[[3,3,4,4],[4]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[3,4,4,4],[4]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,1,1],[2,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,1,1],[3,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,1,1],[4,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,1,2],[2,4]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,1,4],[2,2]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,1,2],[3,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,1,3],[2,4]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,1,4],[2,3]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,1,2],[4,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,1,4],[2,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,1,3],[3,4]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,1,4],[3,3]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,1,3],[4,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,1,4],[3,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,1,4],[4,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,2,2],[2,4]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]
[[1,2,2],[3,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,2,3],[2,4]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]
[[1,2,4],[2,3]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[[1,2,2],[4,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,2,4],[2,4]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[[1,2,3],[3,4]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,2,4],[3,3]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,3,3],[2,4]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]
[[1,2,3],[4,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,2,4],[3,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,3,4],[2,4]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[[1,2,4],[4,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,3,3],[3,4]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]
[[1,3,3],[4,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,3,4],[3,4]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[[1,3,4],[4,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[2,2,2],[3,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[2,2,2],[4,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[2,2,3],[3,4]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]]
[[2,2,4],[3,3]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[2,2,3],[4,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[2,2,4],[3,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[2,2,4],[4,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[2,3,3],[3,4]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]
[[2,3,3],[4,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[2,3,4],[3,4]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[[2,3,4],[4,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[3,3,3],[4,4]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[3,3,4],[4,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,1,1],[2],[4]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[[1,1,1],[3],[4]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[[1,1,2],[2],[4]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,1,2],[3],[4]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[[1,1,3],[2],[4]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,1,4],[2],[3]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,1,4],[2],[4]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,1,3],[3],[4]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,1,4],[3],[4]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,2,2],[2],[4]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[[1,2,2],[3],[4]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[[1,2,3],[2],[4]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[[1,2,4],[2],[3]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,2,4],[2],[4]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,2,3],[3],[4]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,3,3],[2],[4]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[[1,3,4],[2],[3]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,2,4],[3],[4]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,3,4],[2],[4]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,4,4],[2],[3]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,4,4],[2],[4]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,3,3],[3],[4]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[[1,3,4],[3],[4]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,4,4],[3],[4]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[[2,2,2],[3],[4]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[[2,2,3],[3],[4]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[[2,2,4],[3],[4]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[[2,3,3],[3],[4]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[[2,3,4],[3],[4]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[[2,4,4],[3],[4]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,1],[2,2],[4]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[[.,.],[[[.,.],.],.]]
[[1,1],[2,3],[4]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[[.,.],[[[.,.],.],.]]
[[1,1],[2,4],[3]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]]
[[1,1],[2,4],[4]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]]
[[1,1],[3,3],[4]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[[.,.],[[[.,.],.],.]]
[[1,1],[3,4],[4]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]]
[[1,2],[2,3],[4]]=>[5,2,4,1,3]=>[4,5,1,2,3]=>[[.,[.,.]],[.,[.,.]]]
[[1,2],[2,4],[3]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[[1,2],[2,4],[4]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[[1,2],[3,3],[4]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[[.,.],[[[.,.],.],.]]
[[1,3],[2,4],[3]]=>[3,2,5,1,4]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]]
[[1,2],[3,4],[4]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]]
[[1,3],[2,4],[4]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[[1,3],[3,4],[4]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[[2,2],[3,3],[4]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[[.,.],[[[.,.],.],.]]
[[2,2],[3,4],[4]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]]
[[2,3],[3,4],[4]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[[1,1],[2],[3],[4]]=>[5,4,3,1,2]=>[3,1,4,5,2]=>[[.,.],[[.,[.,.]],.]]
[[1,2],[2],[3],[4]]=>[5,4,2,1,3]=>[2,4,1,5,3]=>[[.,[.,.]],[[.,.],.]]
[[1,3],[2],[3],[4]]=>[5,3,2,1,4]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
[[1,4],[2],[3],[4]]=>[4,3,2,1,5]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[[1,1,1,1,1,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,1,1,1,2,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,1,1,1,3,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,1,1,2,2,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,1,1,2,3,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,1,1,3,3,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,1,2,2,2,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,1,2,2,3,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,1,2,3,3,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,1,3,3,3,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,2,2,2,2,3]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
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[[2,2,2,3,3],[3]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
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[[3,8]]=>[1,2]=>[1,2]=>[.,[.,.]]
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[[8,8]]=>[1,2]=>[1,2]=>[.,[.,.]]
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[[4],[8]]=>[2,1]=>[2,1]=>[[.,.],.]
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[[6],[8]]=>[2,1]=>[2,1]=>[[.,.],.]
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[[1,3,7]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[1,4,7]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[1,5,7]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[1,6,7]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[1,7,7]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[2,2,7]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[2,3,7]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[2,4,7]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[2,5,7]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[2,6,7]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[2,7,7]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[3,3,7]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[3,4,7]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[3,5,7]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[3,6,7]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[3,7,7]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[4,4,7]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[4,5,7]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[4,6,7]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[4,7,7]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[5,5,7]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[5,6,7]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[5,7,7]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[6,6,7]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[6,7,7]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
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[[3,4,6],[5]]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[3,5,6],[4]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[3,4,6],[6]]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[3,6,6],[4]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[3,5,5],[6]]=>[4,1,2,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[[3,5,6],[5]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[3,5,6],[6]]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[3,6,6],[5]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[3,6,6],[6]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[4,4,4],[6]]=>[4,1,2,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[[4,4,5],[6]]=>[4,1,2,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[[4,4,6],[5]]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[4,4,6],[6]]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[4,5,5],[6]]=>[4,1,2,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[[4,5,6],[5]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[4,5,6],[6]]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[4,6,6],[5]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[4,6,6],[6]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[5,5,5],[6]]=>[4,1,2,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[[5,5,6],[6]]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[5,6,6],[6]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[1,1],[2,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[1,1],[3,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
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[[1,1],[5,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
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[[1,3],[2,6]]=>[2,4,1,3]=>[4,2,1,3]=>[[[.,.],.],[.,.]]
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[[1,4],[2,6]]=>[2,4,1,3]=>[4,2,1,3]=>[[[.,.],.],[.,.]]
[[1,2],[5,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[1,5],[2,6]]=>[2,4,1,3]=>[4,2,1,3]=>[[[.,.],.],[.,.]]
[[1,2],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[1,3],[3,6]]=>[2,4,1,3]=>[4,2,1,3]=>[[[.,.],.],[.,.]]
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[[1,4],[3,6]]=>[2,4,1,3]=>[4,2,1,3]=>[[[.,.],.],[.,.]]
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[[1,5],[3,6]]=>[2,4,1,3]=>[4,2,1,3]=>[[[.,.],.],[.,.]]
[[1,3],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[1,4],[4,6]]=>[2,4,1,3]=>[4,2,1,3]=>[[[.,.],.],[.,.]]
[[1,4],[5,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[1,5],[4,6]]=>[2,4,1,3]=>[4,2,1,3]=>[[[.,.],.],[.,.]]
[[1,4],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[1,5],[5,6]]=>[2,4,1,3]=>[4,2,1,3]=>[[[.,.],.],[.,.]]
[[1,5],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[2,2],[3,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[2,2],[4,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[2,2],[5,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[2,2],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[2,3],[3,6]]=>[2,4,1,3]=>[4,2,1,3]=>[[[.,.],.],[.,.]]
[[2,3],[4,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[2,4],[3,6]]=>[2,4,1,3]=>[4,2,1,3]=>[[[.,.],.],[.,.]]
[[2,3],[5,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[2,5],[3,6]]=>[2,4,1,3]=>[4,2,1,3]=>[[[.,.],.],[.,.]]
[[2,3],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[2,4],[4,6]]=>[2,4,1,3]=>[4,2,1,3]=>[[[.,.],.],[.,.]]
[[2,4],[5,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[2,5],[4,6]]=>[2,4,1,3]=>[4,2,1,3]=>[[[.,.],.],[.,.]]
[[2,4],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[2,5],[5,6]]=>[2,4,1,3]=>[4,2,1,3]=>[[[.,.],.],[.,.]]
[[2,5],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[3,3],[4,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[3,3],[5,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[3,3],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[3,4],[4,6]]=>[2,4,1,3]=>[4,2,1,3]=>[[[.,.],.],[.,.]]
[[3,4],[5,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[3,5],[4,6]]=>[2,4,1,3]=>[4,2,1,3]=>[[[.,.],.],[.,.]]
[[3,4],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[3,5],[5,6]]=>[2,4,1,3]=>[4,2,1,3]=>[[[.,.],.],[.,.]]
[[3,5],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[4,4],[5,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[4,4],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[4,5],[5,6]]=>[2,4,1,3]=>[4,2,1,3]=>[[[.,.],.],[.,.]]
[[4,5],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[5,5],[6,6]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[[1,1],[2],[6]]=>[4,3,1,2]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[[1,1],[3],[6]]=>[4,3,1,2]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[[1,1],[4],[6]]=>[4,3,1,2]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[[1,1],[5],[6]]=>[4,3,1,2]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[[1,2],[2],[6]]=>[4,2,1,3]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[[1,2],[3],[6]]=>[4,3,1,2]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[[1,3],[2],[6]]=>[4,2,1,3]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[[1,6],[2],[3]]=>[3,2,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[[1,2],[4],[6]]=>[4,3,1,2]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[[1,4],[2],[6]]=>[4,2,1,3]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[[1,6],[2],[4]]=>[3,2,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[[1,2],[5],[6]]=>[4,3,1,2]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[[1,5],[2],[6]]=>[4,2,1,3]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[[1,6],[2],[5]]=>[3,2,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[[1,6],[2],[6]]=>[3,2,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[[1,3],[3],[6]]=>[4,2,1,3]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[[1,3],[4],[6]]=>[4,3,1,2]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[[1,4],[3],[6]]=>[4,2,1,3]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[[1,6],[3],[4]]=>[3,2,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[[1,3],[5],[6]]=>[4,3,1,2]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[[1,5],[3],[6]]=>[4,2,1,3]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[[1,6],[3],[5]]=>[3,2,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[[1,6],[3],[6]]=>[3,2,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[[1,4],[4],[6]]=>[4,2,1,3]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[[1,4],[5],[6]]=>[4,3,1,2]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[[1,5],[4],[6]]=>[4,2,1,3]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[[1,6],[4],[5]]=>[3,2,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[[1,6],[4],[6]]=>[3,2,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[[1,5],[5],[6]]=>[4,2,1,3]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[[1,6],[5],[6]]=>[3,2,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[[2,2],[3],[6]]=>[4,3,1,2]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[[2,2],[4],[6]]=>[4,3,1,2]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[[2,2],[5],[6]]=>[4,3,1,2]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[[2,3],[3],[6]]=>[4,2,1,3]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[[2,3],[4],[6]]=>[4,3,1,2]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[[2,4],[3],[6]]=>[4,2,1,3]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[[2,6],[3],[4]]=>[3,2,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[[2,3],[5],[6]]=>[4,3,1,2]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[[2,5],[3],[6]]=>[4,2,1,3]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[[2,6],[3],[5]]=>[3,2,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[[2,6],[3],[6]]=>[3,2,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[[2,4],[4],[6]]=>[4,2,1,3]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[[2,4],[5],[6]]=>[4,3,1,2]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[[2,5],[4],[6]]=>[4,2,1,3]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[[2,6],[4],[5]]=>[3,2,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[[2,6],[4],[6]]=>[3,2,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[[2,5],[5],[6]]=>[4,2,1,3]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[[2,6],[5],[6]]=>[3,2,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[[3,3],[4],[6]]=>[4,3,1,2]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[[3,3],[5],[6]]=>[4,3,1,2]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[[3,4],[4],[6]]=>[4,2,1,3]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[[3,4],[5],[6]]=>[4,3,1,2]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[[3,5],[4],[6]]=>[4,2,1,3]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[[3,6],[4],[5]]=>[3,2,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[[3,6],[4],[6]]=>[3,2,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[[3,5],[5],[6]]=>[4,2,1,3]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[[3,6],[5],[6]]=>[3,2,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[[4,4],[5],[6]]=>[4,3,1,2]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[[4,5],[5],[6]]=>[4,2,1,3]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[[4,6],[5],[6]]=>[3,2,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[[1],[2],[3],[6]]=>[4,3,2,1]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[[1],[2],[4],[6]]=>[4,3,2,1]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[[1],[2],[5],[6]]=>[4,3,2,1]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[[1],[3],[4],[6]]=>[4,3,2,1]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[[1],[3],[5],[6]]=>[4,3,2,1]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[[1],[4],[5],[6]]=>[4,3,2,1]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[[2],[3],[4],[6]]=>[4,3,2,1]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[[2],[3],[5],[6]]=>[4,3,2,1]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[[2],[4],[5],[6]]=>[4,3,2,1]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[[3],[4],[5],[6]]=>[4,3,2,1]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
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[[1,1,1,2,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,1,1,3,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,1,1,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,1,1,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,1,2,2,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,1,2,3,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,1,2,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,1,2,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,1,3,3,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,1,3,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,1,3,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,1,4,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,1,4,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,1,5,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,2,2,2,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,2,2,3,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,2,2,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,2,2,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,2,3,3,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,2,3,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,2,3,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,2,4,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,2,4,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,2,5,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,3,3,3,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,3,3,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,3,3,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,3,4,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,3,4,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,3,5,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,4,4,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,4,4,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,4,5,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,5,5,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[2,2,2,2,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[2,2,2,3,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[2,2,2,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[2,2,2,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[2,2,3,3,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[2,2,3,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[2,2,3,5,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[2,2,4,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
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[[3,4,5,5],[5]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[3,5,5,5],[4]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[3,5,5,5],[5]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[4,4,4,4],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]
[[4,4,4,5],[5]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[[4,4,5,5],[5]]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[4,5,5,5],[5]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,1,1],[2,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,1,1],[3,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,1,1],[4,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,1,1],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,1,2],[2,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,1,5],[2,2]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,1,2],[3,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,1,3],[2,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,1,5],[2,3]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,1,2],[4,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,1,4],[2,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,1,5],[2,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,1,2],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,1,5],[2,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,1,3],[3,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,1,5],[3,3]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,1,3],[4,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,1,4],[3,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,1,5],[3,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,1,3],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,1,5],[3,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,1,4],[4,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,1,5],[4,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,1,4],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,1,5],[4,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,1,5],[5,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,2,2],[2,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]
[[1,2,2],[3,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,2,3],[2,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]
[[1,2,5],[2,3]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[[1,2,2],[4,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,2,4],[2,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]
[[1,2,5],[2,4]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[[1,2,2],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,2,5],[2,5]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[[1,2,3],[3,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,2,5],[3,3]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,3,3],[2,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]
[[1,2,3],[4,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,2,4],[3,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,2,5],[3,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,3,4],[2,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]
[[1,3,5],[2,4]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[[1,2,3],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,2,5],[3,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,3,5],[2,5]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[[1,2,4],[4,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,2,5],[4,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,4,4],[2,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]
[[1,2,4],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,2,5],[4,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,4,5],[2,5]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[[1,2,5],[5,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,3,3],[3,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]
[[1,3,3],[4,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,3,4],[3,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]
[[1,3,5],[3,4]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[[1,3,3],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,3,5],[3,5]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[[1,3,4],[4,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,3,5],[4,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,4,4],[3,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]
[[1,3,4],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,3,5],[4,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,4,5],[3,5]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[[1,3,5],[5,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,4,4],[4,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]
[[1,4,4],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[1,4,5],[4,5]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[[1,4,5],[5,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[2,2,2],[3,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[2,2,2],[4,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[2,2,2],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[2,2,3],[3,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]]
[[2,2,5],[3,3]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[2,2,3],[4,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[2,2,4],[3,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]]
[[2,2,5],[3,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[2,2,3],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[2,2,5],[3,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[2,2,4],[4,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]]
[[2,2,5],[4,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[2,2,4],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[2,2,5],[4,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[2,2,5],[5,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[2,3,3],[3,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]
[[2,3,3],[4,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[2,3,4],[3,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]
[[2,3,5],[3,4]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[[2,3,3],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[2,3,5],[3,5]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[[2,3,4],[4,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]]
[[2,3,5],[4,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[2,4,4],[3,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]
[[2,3,4],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[2,3,5],[4,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[2,4,5],[3,5]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[[2,3,5],[5,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[2,4,4],[4,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]
[[2,4,4],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[2,4,5],[4,5]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[[2,4,5],[5,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[3,3,3],[4,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[3,3,3],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[3,3,4],[4,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]]
[[3,3,5],[4,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[3,3,4],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[3,3,5],[4,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[3,3,5],[5,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[3,4,4],[4,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]
[[3,4,4],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[3,4,5],[4,5]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[[3,4,5],[5,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[4,4,4],[5,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[[4,4,5],[5,5]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,1,1],[2],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[[1,1,1],[3],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[[1,1,1],[4],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[[1,1,2],[2],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,1,2],[3],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[[1,1,3],[2],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,1,5],[2],[3]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,1,2],[4],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[[1,1,4],[2],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,1,5],[2],[4]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,1,5],[2],[5]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,1,3],[3],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,1,3],[4],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[[1,1,4],[3],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,1,5],[3],[4]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,1,5],[3],[5]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,1,4],[4],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,1,5],[4],[5]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,2,2],[2],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[[1,2,2],[3],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[[1,2,3],[2],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[[1,2,5],[2],[3]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,2,2],[4],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[[1,2,4],[2],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[[1,2,5],[2],[4]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,2,5],[2],[5]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,2,3],[3],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,3,3],[2],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[[1,3,5],[2],[3]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,2,3],[4],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[[1,2,4],[3],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,2,5],[3],[4]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,3,4],[2],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[[1,3,5],[2],[4]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,4,5],[2],[3]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,2,5],[3],[5]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,3,5],[2],[5]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,5,5],[2],[3]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,2,4],[4],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,4,4],[2],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[[1,4,5],[2],[4]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,2,5],[4],[5]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,4,5],[2],[5]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,5,5],[2],[4]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,5,5],[2],[5]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,3,3],[3],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[[1,3,3],[4],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[[1,3,4],[3],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[[1,3,5],[3],[4]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,3,5],[3],[5]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,3,4],[4],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,4,4],[3],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[[1,4,5],[3],[4]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,3,5],[4],[5]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,4,5],[3],[5]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,5,5],[3],[4]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,5,5],[3],[5]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,4,4],[4],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[[1,4,5],[4],[5]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,5,5],[4],[5]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[[2,2,2],[3],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[[2,2,2],[4],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[[2,2,3],[3],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[[2,2,3],[4],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[[2,2,4],[3],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[[2,2,5],[3],[4]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[[2,2,5],[3],[5]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[[2,2,4],[4],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[[2,2,5],[4],[5]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[[2,3,3],[3],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[[2,3,3],[4],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[[2,3,4],[3],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[[2,3,5],[3],[4]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[[2,3,5],[3],[5]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[[2,3,4],[4],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[[2,4,4],[3],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[[2,4,5],[3],[4]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[[2,3,5],[4],[5]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[[2,4,5],[3],[5]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[[2,5,5],[3],[4]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[[2,5,5],[3],[5]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[[2,4,4],[4],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[[2,4,5],[4],[5]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[[2,5,5],[4],[5]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[[3,3,3],[4],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[[3,3,4],[4],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[[3,3,5],[4],[5]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[[3,4,4],[4],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[[3,4,5],[4],[5]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[[3,5,5],[4],[5]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,1],[2,2],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[[.,.],[[[.,.],.],.]]
[[1,1],[2,3],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[[.,.],[[[.,.],.],.]]
[[1,1],[2,5],[3]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]]
[[1,1],[2,4],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[[.,.],[[[.,.],.],.]]
[[1,1],[2,5],[4]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]]
[[1,1],[2,5],[5]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]]
[[1,1],[3,3],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[[.,.],[[[.,.],.],.]]
[[1,1],[3,4],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[[.,.],[[[.,.],.],.]]
[[1,1],[3,5],[4]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]]
[[1,1],[3,5],[5]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]]
[[1,1],[4,4],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[[.,.],[[[.,.],.],.]]
[[1,1],[4,5],[5]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]]
[[1,2],[2,3],[5]]=>[5,2,4,1,3]=>[4,5,1,2,3]=>[[.,[.,.]],[.,[.,.]]]
[[1,2],[2,5],[3]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[[1,2],[2,4],[5]]=>[5,2,4,1,3]=>[4,5,1,2,3]=>[[.,[.,.]],[.,[.,.]]]
[[1,2],[2,5],[4]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[[1,2],[2,5],[5]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[[1,2],[3,3],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[[.,.],[[[.,.],.],.]]
[[1,3],[2,5],[3]]=>[3,2,5,1,4]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]]
[[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]=>[[.,.],[[[.,.],.],.]]
[[1,3],[2,4],[5]]=>[5,2,4,1,3]=>[4,5,1,2,3]=>[[.,[.,.]],[.,[.,.]]]
[[1,3],[2,5],[4]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[[1,4],[2,5],[3]]=>[3,2,5,1,4]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]]
[[1,2],[3,5],[5]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]]
[[1,3],[2,5],[5]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[[1,2],[4,4],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[[.,.],[[[.,.],.],.]]
[[1,4],[2,5],[4]]=>[3,2,5,1,4]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]]
[[1,2],[4,5],[5]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]]
[[1,4],[2,5],[5]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[[1,3],[3,4],[5]]=>[5,2,4,1,3]=>[4,5,1,2,3]=>[[.,[.,.]],[.,[.,.]]]
[[1,3],[3,5],[4]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[[1,3],[3,5],[5]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[[1,3],[4,4],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[[.,.],[[[.,.],.],.]]
[[1,4],[3,5],[4]]=>[3,2,5,1,4]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]]
[[1,3],[4,5],[5]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]]
[[1,4],[3,5],[5]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[[1,4],[4,5],[5]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[[2,2],[3,3],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[[.,.],[[[.,.],.],.]]
[[2,2],[3,4],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[[.,.],[[[.,.],.],.]]
[[2,2],[3,5],[4]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]]
[[2,2],[3,5],[5]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]]
[[2,2],[4,4],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[[.,.],[[[.,.],.],.]]
[[2,2],[4,5],[5]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]]
[[2,3],[3,4],[5]]=>[5,2,4,1,3]=>[4,5,1,2,3]=>[[.,[.,.]],[.,[.,.]]]
[[2,3],[3,5],[4]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[[2,3],[3,5],[5]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[[2,3],[4,4],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[[.,.],[[[.,.],.],.]]
[[2,4],[3,5],[4]]=>[3,2,5,1,4]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]]
[[2,3],[4,5],[5]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]]
[[2,4],[3,5],[5]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[[2,4],[4,5],[5]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[[3,3],[4,4],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[[.,.],[[[.,.],.],.]]
[[3,3],[4,5],[5]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]]
[[3,4],[4,5],[5]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[[1,1],[2],[3],[5]]=>[5,4,3,1,2]=>[3,1,4,5,2]=>[[.,.],[[.,[.,.]],.]]
[[1,1],[2],[4],[5]]=>[5,4,3,1,2]=>[3,1,4,5,2]=>[[.,.],[[.,[.,.]],.]]
[[1,1],[3],[4],[5]]=>[5,4,3,1,2]=>[3,1,4,5,2]=>[[.,.],[[.,[.,.]],.]]
[[1,2],[2],[3],[5]]=>[5,4,2,1,3]=>[2,4,1,5,3]=>[[.,[.,.]],[[.,.],.]]
[[1,2],[2],[4],[5]]=>[5,4,2,1,3]=>[2,4,1,5,3]=>[[.,[.,.]],[[.,.],.]]
[[1,3],[2],[3],[5]]=>[5,3,2,1,4]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
[[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>[3,1,4,5,2]=>[[.,.],[[.,[.,.]],.]]
[[1,3],[2],[4],[5]]=>[5,4,2,1,3]=>[2,4,1,5,3]=>[[.,[.,.]],[[.,.],.]]
[[1,4],[2],[3],[5]]=>[5,3,2,1,4]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
[[1,5],[2],[3],[4]]=>[4,3,2,1,5]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[[1,5],[2],[3],[5]]=>[4,3,2,1,5]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[[1,4],[2],[4],[5]]=>[5,3,2,1,4]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
[[1,5],[2],[4],[5]]=>[4,3,2,1,5]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[[1,3],[3],[4],[5]]=>[5,4,2,1,3]=>[2,4,1,5,3]=>[[.,[.,.]],[[.,.],.]]
[[1,4],[3],[4],[5]]=>[5,3,2,1,4]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
[[1,5],[3],[4],[5]]=>[4,3,2,1,5]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[[2,2],[3],[4],[5]]=>[5,4,3,1,2]=>[3,1,4,5,2]=>[[.,.],[[.,[.,.]],.]]
[[2,3],[3],[4],[5]]=>[5,4,2,1,3]=>[2,4,1,5,3]=>[[.,[.,.]],[[.,.],.]]
[[2,4],[3],[4],[5]]=>[5,3,2,1,4]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
[[2,5],[3],[4],[5]]=>[4,3,2,1,5]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[[1,1,1,1,1,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,1,1,1,2,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,1,1,1,3,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,1,1,1,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,1,1,2,2,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,1,1,2,3,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,1,1,2,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,1,1,3,3,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,1,1,3,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,1,1,4,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,1,2,2,2,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,1,2,2,3,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,1,2,2,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,1,2,3,3,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,1,2,3,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,1,2,4,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,1,3,3,3,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,1,3,3,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,1,3,4,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,1,4,4,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,2,2,2,2,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,2,2,2,3,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,2,2,2,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,2,2,3,3,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,2,2,3,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,2,2,4,4,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,2,3,3,3,4]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
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[[1,1,1,1],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[1,1,1,2],[2,4]]=>[4,6,1,2,3,5]=>[6,1,2,4,3,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,1,1,4],[2,2]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,1,1,2],[3,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[1,1,1,3],[2,4]]=>[4,6,1,2,3,5]=>[6,1,2,4,3,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,1,1,4],[2,3]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,1,1,2],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[1,1,1,4],[2,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,1,1,3],[3,4]]=>[4,6,1,2,3,5]=>[6,1,2,4,3,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,1,1,4],[3,3]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,1,1,3],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[1,1,1,4],[3,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,1,1,4],[4,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,1,2,2],[2,4]]=>[3,6,1,2,4,5]=>[6,1,3,2,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,2,4],[2,2]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,2,2],[3,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[1,1,2,3],[2,4]]=>[3,6,1,2,4,5]=>[6,1,3,2,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,2,4],[2,3]]=>[3,5,1,2,4,6]=>[5,1,3,2,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,3,4],[2,2]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,2,2],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[1,1,2,4],[2,4]]=>[3,5,1,2,4,6]=>[5,1,3,2,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,4,4],[2,2]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,2,3],[3,4]]=>[4,6,1,2,3,5]=>[6,1,2,4,3,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,1,2,4],[3,3]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,1,3,3],[2,4]]=>[3,6,1,2,4,5]=>[6,1,3,2,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,3,4],[2,3]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,2,3],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[1,1,2,4],[3,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,1,3,4],[2,4]]=>[3,5,1,2,4,6]=>[5,1,3,2,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,4,4],[2,3]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,2,4],[4,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,1,4,4],[2,4]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,3,3],[3,4]]=>[3,6,1,2,4,5]=>[6,1,3,2,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,3,4],[3,3]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,3,3],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[1,1,3,4],[3,4]]=>[3,5,1,2,4,6]=>[5,1,3,2,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,4,4],[3,3]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,3,4],[4,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,1,4,4],[3,4]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,4,4],[4,4]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,2,2,2],[2,4]]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]
[[1,2,2,2],[3,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[1,2,2,3],[2,4]]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]
[[1,2,2,4],[2,3]]=>[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[[1,2,2,2],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[1,2,2,4],[2,4]]=>[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[[1,2,2,3],[3,4]]=>[4,6,1,2,3,5]=>[6,1,2,4,3,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,2,2,4],[3,3]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,2,3,3],[2,4]]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]
[[1,2,3,4],[2,3]]=>[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[[1,2,2,3],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[1,2,2,4],[3,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,2,3,4],[2,4]]=>[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[[1,2,4,4],[2,3]]=>[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[[1,2,2,4],[4,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,2,4,4],[2,4]]=>[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[[1,2,3,3],[3,4]]=>[3,6,1,2,4,5]=>[6,1,3,2,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,2,3,4],[3,3]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,3,3,3],[2,4]]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]
[[1,2,3,3],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[1,2,3,4],[3,4]]=>[3,5,1,2,4,6]=>[5,1,3,2,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,2,4,4],[3,3]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,3,3,4],[2,4]]=>[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[[1,2,3,4],[4,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,2,4,4],[3,4]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,3,4,4],[2,4]]=>[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[[1,2,4,4],[4,4]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,3,3,3],[3,4]]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]
[[1,3,3,3],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[1,3,3,4],[3,4]]=>[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[[1,3,3,4],[4,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,3,4,4],[3,4]]=>[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[[1,3,4,4],[4,4]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[2,2,2,2],[3,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[2,2,2,2],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[2,2,2,3],[3,4]]=>[4,6,1,2,3,5]=>[6,1,2,4,3,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[[2,2,2,4],[3,3]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[2,2,2,3],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[2,2,2,4],[3,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[2,2,2,4],[4,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[2,2,3,3],[3,4]]=>[3,6,1,2,4,5]=>[6,1,3,2,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[[2,2,3,4],[3,3]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[2,2,3,3],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[2,2,3,4],[3,4]]=>[3,5,1,2,4,6]=>[5,1,3,2,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[2,2,4,4],[3,3]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[2,2,3,4],[4,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[2,2,4,4],[3,4]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[2,2,4,4],[4,4]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[2,3,3,3],[3,4]]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]
[[2,3,3,3],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[2,3,3,4],[3,4]]=>[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[[2,3,3,4],[4,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[2,3,4,4],[3,4]]=>[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[[2,3,4,4],[4,4]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[3,3,3,3],[4,4]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[3,3,3,4],[4,4]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[3,3,4,4],[4,4]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,1,1],[2],[4]]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[1,1,1,1],[3],[4]]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[1,1,1,2],[2],[4]]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,1,1,2],[3],[4]]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[1,1,1,3],[2],[4]]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,1,1,4],[2],[3]]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,1,1,4],[2],[4]]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,1,1,3],[3],[4]]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,1,1,4],[3],[4]]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,1,2,2],[2],[4]]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,2,2],[3],[4]]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[1,1,2,3],[2],[4]]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,2,4],[2],[3]]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,2,4],[2],[4]]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,2,3],[3],[4]]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,1,3,3],[2],[4]]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,3,4],[2],[3]]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,2,4],[3],[4]]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,1,3,4],[2],[4]]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,4,4],[2],[3]]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,4,4],[2],[4]]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,3,3],[3],[4]]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,3,4],[3],[4]]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,4,4],[3],[4]]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,2,2,2],[2],[4]]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,2,2,2],[3],[4]]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[1,2,2,3],[2],[4]]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,2,2,4],[2],[3]]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,2,2,4],[2],[4]]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,2,2,3],[3],[4]]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,2,3,3],[2],[4]]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,2,3,4],[2],[3]]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,2,2,4],[3],[4]]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,2,3,4],[2],[4]]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,2,4,4],[2],[3]]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,2,4,4],[2],[4]]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,2,3,3],[3],[4]]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,3,3,3],[2],[4]]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,3,3,4],[2],[3]]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,2,3,4],[3],[4]]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,3,3,4],[2],[4]]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,3,4,4],[2],[3]]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,2,4,4],[3],[4]]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,3,4,4],[2],[4]]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,4,4,4],[2],[3]]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,4,4,4],[2],[4]]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,3,3,3],[3],[4]]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,3,3,4],[3],[4]]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,3,4,4],[3],[4]]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,4,4,4],[3],[4]]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[2,2,2,2],[3],[4]]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[2,2,2,3],[3],[4]]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[[2,2,2,4],[3],[4]]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[2,2,3,3],[3],[4]]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[[2,2,3,4],[3],[4]]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[2,2,4,4],[3],[4]]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[2,3,3,3],[3],[4]]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[2,3,3,4],[3],[4]]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[2,3,4,4],[3],[4]]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[2,4,4,4],[3],[4]]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,1,1],[2,2,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[[1,1,1],[2,3,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[[1,1,1],[2,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[[1,1,1],[3,3,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[[1,1,1],[3,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[[1,1,1],[4,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[[1,1,2],[2,2,4]]=>[3,4,6,1,2,5]=>[6,1,3,4,2,5]=>[[.,.],[[.,[.,.]],[.,.]]]
[[1,1,2],[2,3,4]]=>[3,5,6,1,2,4]=>[6,1,3,2,5,4]=>[[.,.],[[.,.],[[.,.],.]]]
[[1,1,3],[2,2,4]]=>[3,4,6,1,2,5]=>[6,1,3,4,2,5]=>[[.,.],[[.,[.,.]],[.,.]]]
[[1,1,2],[2,4,4]]=>[3,5,6,1,2,4]=>[6,1,3,2,5,4]=>[[.,.],[[.,.],[[.,.],.]]]
[[1,1,2],[3,3,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[[1,1,3],[2,3,4]]=>[3,4,6,1,2,5]=>[6,1,3,4,2,5]=>[[.,.],[[.,[.,.]],[.,.]]]
[[1,1,2],[3,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[[1,1,3],[2,4,4]]=>[3,5,6,1,2,4]=>[6,1,3,2,5,4]=>[[.,.],[[.,.],[[.,.],.]]]
[[1,1,2],[4,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[[1,1,3],[3,3,4]]=>[3,4,6,1,2,5]=>[6,1,3,4,2,5]=>[[.,.],[[.,[.,.]],[.,.]]]
[[1,1,3],[3,4,4]]=>[3,5,6,1,2,4]=>[6,1,3,2,5,4]=>[[.,.],[[.,.],[[.,.],.]]]
[[1,1,3],[4,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[[1,2,2],[2,3,4]]=>[2,5,6,1,3,4]=>[6,2,1,3,5,4]=>[[[.,.],.],[.,[[.,.],.]]]
[[1,2,2],[2,4,4]]=>[2,5,6,1,3,4]=>[6,2,1,3,5,4]=>[[[.,.],.],[.,[[.,.],.]]]
[[1,2,2],[3,3,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[[1,2,3],[2,3,4]]=>[2,4,6,1,3,5]=>[6,2,1,4,3,5]=>[[[.,.],.],[[.,.],[.,.]]]
[[1,2,2],[3,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[[1,2,3],[2,4,4]]=>[2,5,6,1,3,4]=>[6,2,1,3,5,4]=>[[[.,.],.],[.,[[.,.],.]]]
[[1,2,2],[4,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[[1,2,3],[3,3,4]]=>[3,4,6,1,2,5]=>[6,1,3,4,2,5]=>[[.,.],[[.,[.,.]],[.,.]]]
[[1,2,3],[3,4,4]]=>[3,5,6,1,2,4]=>[6,1,3,2,5,4]=>[[.,.],[[.,.],[[.,.],.]]]
[[1,3,3],[2,4,4]]=>[2,5,6,1,3,4]=>[6,2,1,3,5,4]=>[[[.,.],.],[.,[[.,.],.]]]
[[1,2,3],[4,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[[1,3,3],[3,4,4]]=>[2,5,6,1,3,4]=>[6,2,1,3,5,4]=>[[[.,.],.],[.,[[.,.],.]]]
[[1,3,3],[4,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[[2,2,2],[3,3,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[[2,2,2],[3,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[[2,2,2],[4,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[[2,2,3],[3,3,4]]=>[3,4,6,1,2,5]=>[6,1,3,4,2,5]=>[[.,.],[[.,[.,.]],[.,.]]]
[[2,2,3],[3,4,4]]=>[3,5,6,1,2,4]=>[6,1,3,2,5,4]=>[[.,.],[[.,.],[[.,.],.]]]
[[2,2,3],[4,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[[2,3,3],[3,4,4]]=>[2,5,6,1,3,4]=>[6,2,1,3,5,4]=>[[[.,.],.],[.,[[.,.],.]]]
[[2,3,3],[4,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[[3,3,3],[4,4,4]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[[1,1,1],[2,2],[4]]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>[[.,.],[.,[[[.,.],.],.]]]
[[1,1,1],[2,3],[4]]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>[[.,.],[.,[[[.,.],.],.]]]
[[1,1,1],[2,4],[3]]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>[[.,.],[.,[[[.,.],.],.]]]
[[1,1,1],[2,4],[4]]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>[[.,.],[.,[[[.,.],.],.]]]
[[1,1,1],[3,3],[4]]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>[[.,.],[.,[[[.,.],.],.]]]
[[1,1,1],[3,4],[4]]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>[[.,.],[.,[[[.,.],.],.]]]
[[1,1,2],[2,2],[4]]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>[[.,.],[[[.,.],.],[.,.]]]
[[1,1,2],[2,3],[4]]=>[6,3,5,1,2,4]=>[5,1,6,2,3,4]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,2],[2,4],[3]]=>[5,3,6,1,2,4]=>[6,1,5,2,3,4]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,3],[2,2],[4]]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>[[.,.],[[[.,.],.],[.,.]]]
[[1,1,4],[2,2],[3]]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>[[.,.],[[[.,.],.],[.,.]]]
[[1,1,2],[2,4],[4]]=>[5,3,6,1,2,4]=>[6,1,5,2,3,4]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,4],[2,2],[4]]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>[[.,.],[[[.,.],.],[.,.]]]
[[1,1,2],[3,3],[4]]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>[[.,.],[.,[[[.,.],.],.]]]
[[1,1,3],[2,3],[4]]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>[[.,.],[[[.,.],.],[.,.]]]
[[1,1,3],[2,4],[3]]=>[4,3,6,1,2,5]=>[6,1,4,3,2,5]=>[[.,.],[[[.,.],.],[.,.]]]
[[1,1,4],[2,3],[3]]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>[[.,.],[[[.,.],.],[.,.]]]
[[1,1,2],[3,4],[4]]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>[[.,.],[.,[[[.,.],.],.]]]
[[1,1,3],[2,4],[4]]=>[5,3,6,1,2,4]=>[6,1,5,2,3,4]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,4],[2,3],[4]]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>[[.,.],[[[.,.],.],[.,.]]]
[[1,1,4],[2,4],[3]]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>[[.,.],[[[.,.],.],[.,.]]]
[[1,1,4],[2,4],[4]]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>[[.,.],[[[.,.],.],[.,.]]]
[[1,1,3],[3,3],[4]]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>[[.,.],[[[.,.],.],[.,.]]]
[[1,1,3],[3,4],[4]]=>[5,3,6,1,2,4]=>[6,1,5,2,3,4]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,1,4],[3,3],[4]]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>[[.,.],[[[.,.],.],[.,.]]]
[[1,1,4],[3,4],[4]]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>[[.,.],[[[.,.],.],[.,.]]]
[[1,2,2],[2,3],[4]]=>[6,2,5,1,3,4]=>[5,6,1,3,2,4]=>[[.,[.,.]],[[.,.],[.,.]]]
[[1,2,2],[2,4],[3]]=>[5,2,6,1,3,4]=>[6,5,1,3,2,4]=>[[[.,.],.],[[.,.],[.,.]]]
[[1,2,2],[2,4],[4]]=>[5,2,6,1,3,4]=>[6,5,1,3,2,4]=>[[[.,.],.],[[.,.],[.,.]]]
[[1,2,2],[3,3],[4]]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>[[.,.],[.,[[[.,.],.],.]]]
[[1,2,3],[2,3],[4]]=>[6,2,4,1,3,5]=>[4,6,1,2,3,5]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,2,3],[2,4],[3]]=>[4,2,6,1,3,5]=>[6,4,1,2,3,5]=>[[[.,.],.],[.,[.,[.,.]]]]
[[1,2,4],[2,3],[3]]=>[4,2,5,1,3,6]=>[5,4,1,2,3,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[[1,2,2],[3,4],[4]]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>[[.,.],[.,[[[.,.],.],.]]]
[[1,2,3],[2,4],[4]]=>[5,2,6,1,3,4]=>[6,5,1,3,2,4]=>[[[.,.],.],[[.,.],[.,.]]]
[[1,2,4],[2,3],[4]]=>[5,2,4,1,3,6]=>[4,5,1,2,3,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,2,4],[2,4],[3]]=>[4,2,5,1,3,6]=>[5,4,1,2,3,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[[1,2,4],[2,4],[4]]=>[4,2,5,1,3,6]=>[5,4,1,2,3,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[[1,2,3],[3,3],[4]]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>[[.,.],[[[.,.],.],[.,.]]]
[[1,3,3],[2,4],[3]]=>[3,2,6,1,4,5]=>[6,3,2,1,4,5]=>[[[[.,.],.],.],[.,[.,.]]]
[[1,2,3],[3,4],[4]]=>[5,3,6,1,2,4]=>[6,1,5,2,3,4]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,2,4],[3,3],[4]]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>[[.,.],[[[.,.],.],[.,.]]]
[[1,3,3],[2,4],[4]]=>[5,2,6,1,3,4]=>[6,5,1,3,2,4]=>[[[.,.],.],[[.,.],[.,.]]]
[[1,3,4],[2,4],[3]]=>[3,2,5,1,4,6]=>[5,3,2,1,4,6]=>[[[[.,.],.],.],[.,[.,.]]]
[[1,2,4],[3,4],[4]]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>[[.,.],[[[.,.],.],[.,.]]]
[[1,3,4],[2,4],[4]]=>[4,2,5,1,3,6]=>[5,4,1,2,3,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[[1,3,3],[3,4],[4]]=>[5,2,6,1,3,4]=>[6,5,1,3,2,4]=>[[[.,.],.],[[.,.],[.,.]]]
[[1,3,4],[3,4],[4]]=>[4,2,5,1,3,6]=>[5,4,1,2,3,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[[2,2,2],[3,3],[4]]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>[[.,.],[.,[[[.,.],.],.]]]
[[2,2,2],[3,4],[4]]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>[[.,.],[.,[[[.,.],.],.]]]
[[2,2,3],[3,3],[4]]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>[[.,.],[[[.,.],.],[.,.]]]
[[2,2,3],[3,4],[4]]=>[5,3,6,1,2,4]=>[6,1,5,2,3,4]=>[[.,.],[[.,.],[.,[.,.]]]]
[[2,2,4],[3,3],[4]]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>[[.,.],[[[.,.],.],[.,.]]]
[[2,2,4],[3,4],[4]]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>[[.,.],[[[.,.],.],[.,.]]]
[[2,3,3],[3,4],[4]]=>[5,2,6,1,3,4]=>[6,5,1,3,2,4]=>[[[.,.],.],[[.,.],[.,.]]]
[[2,3,4],[3,4],[4]]=>[4,2,5,1,3,6]=>[5,4,1,2,3,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[[1,1,1],[2],[3],[4]]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[[1,1,2],[2],[3],[4]]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]=>[[.,.],[[.,.],[[.,.],.]]]
[[1,1,3],[2],[3],[4]]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]=>[[.,.],[[.,[.,.]],[.,.]]]
[[1,1,4],[2],[3],[4]]=>[5,4,3,1,2,6]=>[3,1,4,5,2,6]=>[[.,.],[[.,[.,.]],[.,.]]]
[[1,2,2],[2],[3],[4]]=>[6,5,2,1,3,4]=>[2,5,1,3,6,4]=>[[.,[.,.]],[.,[[.,.],.]]]
[[1,2,3],[2],[3],[4]]=>[6,4,2,1,3,5]=>[2,4,1,6,3,5]=>[[.,[.,.]],[[.,.],[.,.]]]
[[1,2,4],[2],[3],[4]]=>[5,4,2,1,3,6]=>[2,4,1,5,3,6]=>[[.,[.,.]],[[.,.],[.,.]]]
[[1,3,3],[2],[3],[4]]=>[6,3,2,1,4,5]=>[2,3,6,1,4,5]=>[[.,[.,[.,.]]],[.,[.,.]]]
[[1,3,4],[2],[3],[4]]=>[5,3,2,1,4,6]=>[2,3,5,1,4,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[[1,4,4],[2],[3],[4]]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[[1,1],[2,2],[3,4]]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>[[.,.],[[[.,.],[.,.]],.]]
[[1,1],[2,2],[4,4]]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>[[.,.],[[[.,.],[.,.]],.]]
[[1,1],[2,3],[3,4]]=>[4,6,3,5,1,2]=>[5,1,6,4,3,2]=>[[.,.],[[[[.,.],.],.],.]]
[[1,1],[2,3],[4,4]]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>[[.,.],[[[.,.],[.,.]],.]]
[[1,1],[3,3],[4,4]]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>[[.,.],[[[.,.],[.,.]],.]]
[[1,2],[2,3],[3,4]]=>[4,6,2,5,1,3]=>[5,6,1,4,2,3]=>[[.,[.,.]],[[.,.],[.,.]]]
[[1,2],[2,3],[4,4]]=>[5,6,2,4,1,3]=>[4,6,1,2,5,3]=>[[.,[.,.]],[.,[[.,.],.]]]
[[1,2],[3,3],[4,4]]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>[[.,.],[[[.,.],[.,.]],.]]
[[2,2],[3,3],[4,4]]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>[[.,.],[[[.,.],[.,.]],.]]
[[1,1],[2,2],[3],[4]]=>[6,5,3,4,1,2]=>[4,1,5,3,6,2]=>[[.,.],[[[.,.],[.,.]],.]]
[[1,1],[2,3],[3],[4]]=>[6,4,3,5,1,2]=>[5,1,4,6,3,2]=>[[.,.],[[[.,[.,.]],.],.]]
[[1,1],[2,4],[3],[4]]=>[5,4,3,6,1,2]=>[6,1,4,5,3,2]=>[[.,.],[[[.,[.,.]],.],.]]
[[1,2],[2,3],[3],[4]]=>[6,4,2,5,1,3]=>[5,4,1,6,2,3]=>[[[.,.],.],[[.,.],[.,.]]]
[[1,2],[2,4],[3],[4]]=>[5,4,2,6,1,3]=>[6,4,1,5,2,3]=>[[[.,.],.],[[.,.],[.,.]]]
[[1,3],[2,4],[3],[4]]=>[5,3,2,6,1,4]=>[6,3,5,1,2,4]=>[[[.,.],[.,.]],[.,[.,.]]]
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[[3,3,3,3,3,3,3]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
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[[1,1,1,1,3,3],[3]]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
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[[1,1,1,2,3,3],[3]]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
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[[1,1,1,3,3,3],[3]]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
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[[1,2,2,2,2,2],[3]]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,2,2,2,3],[2]]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
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[[1,2,2,3,3,3],[3]]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
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[[1,1,1,1,3],[2,3]]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[[1,1,1,1,3],[3,3]]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[[1,1,1,2,2],[2,3]]=>[4,7,1,2,3,5,6]=>[7,1,2,4,3,5,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
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[[1,1,1,2,2],[3,3]]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
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[[1,1,1,3,3],[2,3]]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
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[[1,2,2,2,3],[2,3]]=>[2,6,1,3,4,5,7]=>[6,2,1,3,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[[1,2,2,2,3],[3,3]]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[[1,2,2,3,3],[2,3]]=>[2,5,1,3,4,6,7]=>[5,2,1,3,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[[1,2,2,3,3],[3,3]]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[[1,2,3,3,3],[2,3]]=>[2,4,1,3,5,6,7]=>[4,2,1,3,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[[1,2,3,3,3],[3,3]]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[[2,2,2,2,2],[3,3]]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[[2,2,2,2,3],[3,3]]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[[2,2,2,3,3],[3,3]]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[[2,2,3,3,3],[3,3]]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[[1,1,1,1,1],[2],[3]]=>[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
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[[1,1,1,1,3],[2],[3]]=>[6,5,1,2,3,4,7]=>[5,1,2,3,6,4,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[[1,1,1,2,2],[2],[3]]=>[7,4,1,2,3,5,6]=>[4,1,2,7,3,5,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[[1,1,1,2,3],[2],[3]]=>[6,4,1,2,3,5,7]=>[4,1,2,6,3,5,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[[1,1,1,3,3],[2],[3]]=>[5,4,1,2,3,6,7]=>[4,1,2,5,3,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[[1,1,2,2,2],[2],[3]]=>[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
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[[1,1,2,3,3],[2],[3]]=>[5,3,1,2,4,6,7]=>[3,1,5,2,4,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
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[[1,2,2,2,2],[2],[3]]=>[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[[1,2,2,2,3],[2],[3]]=>[6,2,1,3,4,5,7]=>[2,6,1,3,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[[1,2,2,3,3],[2],[3]]=>[5,2,1,3,4,6,7]=>[2,5,1,3,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[[1,2,3,3,3],[2],[3]]=>[4,2,1,3,5,6,7]=>[2,4,1,3,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[[1,3,3,3,3],[2],[3]]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[[1,1,1,1],[2,2,3]]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[[1,1,1,1],[2,3,3]]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[[1,1,1,1],[3,3,3]]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[[1,1,1,2],[2,2,3]]=>[4,5,7,1,2,3,6]=>[7,1,2,4,5,3,6]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[[1,1,1,3],[2,2,2]]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[[1,1,1,2],[2,3,3]]=>[4,6,7,1,2,3,5]=>[7,1,2,4,3,6,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[[1,1,1,3],[2,2,3]]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[[1,1,1,2],[3,3,3]]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[[1,1,1,3],[2,3,3]]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[[1,1,1,3],[3,3,3]]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[[1,1,2,2],[2,2,3]]=>[3,4,7,1,2,5,6]=>[7,1,3,4,2,5,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[[1,1,2,2],[2,3,3]]=>[3,6,7,1,2,4,5]=>[7,1,3,2,4,6,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[[1,1,2,3],[2,2,3]]=>[3,4,6,1,2,5,7]=>[6,1,3,4,2,5,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[[1,1,2,2],[3,3,3]]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[[1,1,2,3],[2,3,3]]=>[3,5,6,1,2,4,7]=>[6,1,3,2,5,4,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[[1,1,2,3],[3,3,3]]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[[1,2,2,2],[2,3,3]]=>[2,6,7,1,3,4,5]=>[7,2,1,3,4,6,5]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[[1,2,2,2],[3,3,3]]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[[1,2,2,3],[2,3,3]]=>[2,5,6,1,3,4,7]=>[6,2,1,3,5,4,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[[1,2,2,3],[3,3,3]]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[[2,2,2,2],[3,3,3]]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[[2,2,2,3],[3,3,3]]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[[1,1,1,1],[2,2],[3]]=>[7,5,6,1,2,3,4]=>[6,1,2,3,7,5,4]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[[1,1,1,1],[2,3],[3]]=>[6,5,7,1,2,3,4]=>[7,1,2,3,6,5,4]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[[1,1,1,2],[2,2],[3]]=>[7,4,5,1,2,3,6]=>[5,1,2,7,4,3,6]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[[1,1,1,2],[2,3],[3]]=>[6,4,7,1,2,3,5]=>[7,1,2,6,3,4,5]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[[1,1,1,3],[2,2],[3]]=>[6,4,5,1,2,3,7]=>[5,1,2,6,4,3,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[[1,1,1,3],[2,3],[3]]=>[5,4,6,1,2,3,7]=>[6,1,2,5,4,3,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[[1,1,2,2],[2,2],[3]]=>[7,3,4,1,2,5,6]=>[4,1,7,3,2,5,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[[1,1,2,2],[2,3],[3]]=>[6,3,7,1,2,4,5]=>[7,1,6,2,4,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[[1,1,2,3],[2,2],[3]]=>[6,3,4,1,2,5,7]=>[4,1,6,3,2,5,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[[1,1,2,3],[2,3],[3]]=>[5,3,6,1,2,4,7]=>[6,1,5,2,3,4,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[[1,1,3,3],[2,2],[3]]=>[5,3,4,1,2,6,7]=>[4,1,5,3,2,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[[1,1,3,3],[2,3],[3]]=>[4,3,5,1,2,6,7]=>[5,1,4,3,2,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[[1,2,2,2],[2,3],[3]]=>[6,2,7,1,3,4,5]=>[7,6,1,3,4,2,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[[1,2,2,3],[2,3],[3]]=>[5,2,6,1,3,4,7]=>[6,5,1,3,2,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[[1,2,3,3],[2,3],[3]]=>[4,2,5,1,3,6,7]=>[5,4,1,2,3,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[[1,1,1],[2,2,2],[3]]=>[7,4,5,6,1,2,3]=>[6,1,2,7,4,5,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[[1,1,1],[2,2,3],[3]]=>[6,4,5,7,1,2,3]=>[7,1,2,6,4,5,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[[1,1,1],[2,3,3],[3]]=>[5,4,6,7,1,2,3]=>[7,1,2,5,4,6,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[[1,1,2],[2,2,3],[3]]=>[6,3,4,7,1,2,5]=>[7,1,6,3,2,4,5]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[[1,1,2],[2,3,3],[3]]=>[5,3,6,7,1,2,4]=>[7,1,5,2,3,6,4]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[[1,2,2],[2,3,3],[3]]=>[5,2,6,7,1,3,4]=>[7,5,1,3,2,6,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[[1,1,1],[2,2],[3,3]]=>[6,7,4,5,1,2,3]=>[5,1,2,7,4,6,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[[1,1,2],[2,2],[3,3]]=>[6,7,3,4,1,2,5]=>[4,1,7,3,2,6,5]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[[1,1,3],[2,2],[3,3]]=>[5,6,3,4,1,2,7]=>[4,1,6,3,5,2,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[[1,1,1,1,1,1,1,2]]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,1,1,1,1,1,2,2]]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,1,1,1,1,2,2,2]]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,1,1,1,2,2,2,2]]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,1,1,2,2,2,2,2]]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,1,2,2,2,2,2,2]]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,2,2,2,2,2,2,2]]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[2,2,2,2,2,2,2,2]]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,1,1,1,1,1,1],[2]]=>[8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,1,1,1,1,1,2],[2]]=>[7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,6,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,1,1,1,1,2,2],[2]]=>[6,1,2,3,4,5,7,8]=>[6,1,2,3,4,5,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,1,1,1,2,2,2],[2]]=>[5,1,2,3,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,1,1,2,2,2,2],[2]]=>[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,1,2,2,2,2,2],[2]]=>[3,1,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,2,2,2,2,2,2],[2]]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,1,1,1,1,1],[2,2]]=>[7,8,1,2,3,4,5,6]=>[8,1,2,3,4,5,7,6]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[[1,1,1,1,1,2],[2,2]]=>[6,7,1,2,3,4,5,8]=>[7,1,2,3,4,6,5,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[[1,1,1,1,2,2],[2,2]]=>[5,6,1,2,3,4,7,8]=>[6,1,2,3,5,4,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[[1,1,1,2,2,2],[2,2]]=>[4,5,1,2,3,6,7,8]=>[5,1,2,4,3,6,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[[1,1,2,2,2,2],[2,2]]=>[3,4,1,2,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[[1,1,1,1,1],[2,2,2]]=>[6,7,8,1,2,3,4,5]=>[8,1,2,3,4,6,7,5]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[[1,1,1,1,2],[2,2,2]]=>[5,6,7,1,2,3,4,8]=>[7,1,2,3,5,6,4,8]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[[1,1,1,1],[2,2,2,2]]=>[5,6,7,8,1,2,3,4]=>[8,1,2,3,5,6,7,4]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[[1]]=>[1]=>[1]=>[.,.]
[[2]]=>[1]=>[1]=>[.,.]
[[1,1]]=>[1,2]=>[1,2]=>[.,[.,.]]
[[3]]=>[1]=>[1]=>[.,.]
[[1,1,1]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[4]]=>[1]=>[1]=>[.,.]
[[1,1,1,1]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[5]]=>[1]=>[1]=>[.,.]
[[1,1,1,1,1]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[6]]=>[1]=>[1]=>[.,.]
[[1,1,1,1,1,1]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>[[.,.],[.,[.,[.,[.,.]]]]]
[[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[[1,2,3,5],[4,6]]=>[4,6,1,2,3,5]=>[6,1,2,4,3,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[[1,2,4,5],[3,6]]=>[3,6,1,2,4,5]=>[6,1,3,2,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>[5,1,3,2,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,2,4],[3,5],[6]]=>[6,3,5,1,2,4]=>[5,1,6,2,3,4]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,2,4],[3],[5],[6]]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]=>[[.,.],[[.,.],[[.,.],.]]]
[[1,2,3,6],[4,5]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>[[.,.],[.,[[[.,.],.],.]]]
[[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5]=>[6,1,4,3,2,5]=>[[.,.],[[[.,.],.],[.,.]]]
[[1,2,5],[3],[4],[6]]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]=>[[.,.],[[.,[.,.]],[.,.]]]
[[1,2,3],[4,6],[5]]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>[[.,.],[.,[[[.,.],.],.]]]
[[1,2,4],[3,6],[5]]=>[5,3,6,1,2,4]=>[6,1,5,2,3,4]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,2,6],[3],[4],[5]]=>[5,4,3,1,2,6]=>[3,1,4,5,2,6]=>[[.,.],[[.,[.,.]],[.,.]]]
[[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]=>[[.,.],[[.,[.,[.,.]]],.]]
[[1,3,4,5,6],[2]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[[1,3,4,5],[2,6]]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]
[[1,3,4,6],[2,5]]=>[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[[1,3,4],[2,5],[6]]=>[6,2,5,1,3,4]=>[5,6,1,3,2,4]=>[[.,[.,.]],[[.,.],[.,.]]]
[[1,3,5,6],[2,4]]=>[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[[1,3,5],[2,4,6]]=>[2,4,6,1,3,5]=>[6,2,1,4,3,5]=>[[[.,.],.],[[.,.],[.,.]]]
[[1,3,5],[2,4],[6]]=>[6,2,4,1,3,5]=>[4,6,1,2,3,5]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,3,4],[2,5,6]]=>[2,5,6,1,3,4]=>[6,2,1,3,5,4]=>[[[.,.],.],[.,[[.,.],.]]]
[[1,3,6],[2,4],[5]]=>[5,2,4,1,3,6]=>[4,5,1,2,3,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,3],[2,4],[5],[6]]=>[6,5,2,4,1,3]=>[4,5,1,2,6,3]=>[[.,[.,.]],[.,[[.,.],.]]]
[[1,3,4,5],[2],[6]]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,3,4,6],[2],[5]]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,3,4],[2],[5],[6]]=>[6,5,2,1,3,4]=>[2,5,1,3,6,4]=>[[.,[.,.]],[.,[[.,.],.]]]
[[1,3,5,6],[2],[4]]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,3,5],[2,6],[4]]=>[4,2,6,1,3,5]=>[6,4,1,2,3,5]=>[[[.,.],.],[.,[.,[.,.]]]]
[[1,3,5],[2],[4],[6]]=>[6,4,2,1,3,5]=>[2,4,1,6,3,5]=>[[.,[.,.]],[[.,.],[.,.]]]
[[1,3,4],[2,6],[5]]=>[5,2,6,1,3,4]=>[6,5,1,3,2,4]=>[[[.,.],.],[[.,.],[.,.]]]
[[1,3,6],[2],[4],[5]]=>[5,4,2,1,3,6]=>[2,4,1,5,3,6]=>[[.,[.,.]],[[.,.],[.,.]]]
[[1,3],[2],[4],[5],[6]]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]=>[[.,[.,.]],[[.,[.,.]],.]]
[[1,2,5,6],[3,4]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,2,5],[3,4,6]]=>[3,4,6,1,2,5]=>[6,1,3,4,2,5]=>[[.,.],[[.,[.,.]],[.,.]]]
[[1,2,5],[3,4],[6]]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>[[.,.],[[[.,.],.],[.,.]]]
[[1,2,4],[3,5,6]]=>[3,5,6,1,2,4]=>[6,1,3,2,5,4]=>[[.,.],[[.,.],[[.,.],.]]]
[[1,2,6],[3,4],[5]]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>[[.,.],[[[.,.],.],[.,.]]]
[[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2]=>[4,1,5,3,6,2]=>[[.,.],[[[.,.],[.,.]],.]]
[[1,4,5,6],[2],[3]]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,4,5],[2,6],[3]]=>[3,2,6,1,4,5]=>[6,3,2,1,4,5]=>[[[[.,.],.],.],[.,[.,.]]]
[[1,4,6],[2,5],[3]]=>[3,2,5,1,4,6]=>[5,3,2,1,4,6]=>[[[[.,.],.],.],[.,[.,.]]]
[[1,4],[2,5],[3,6]]=>[3,6,2,5,1,4]=>[5,6,3,1,2,4]=>[[[.,[.,.]],.],[.,[.,.]]]
[[1,4],[2,5],[3],[6]]=>[6,3,2,5,1,4]=>[5,3,6,1,2,4]=>[[[.,.],[.,.]],[.,[.,.]]]
[[1,4,5],[2],[3],[6]]=>[6,3,2,1,4,5]=>[2,3,6,1,4,5]=>[[.,[.,[.,.]]],[.,[.,.]]]
[[1,4,6],[2],[3],[5]]=>[5,3,2,1,4,6]=>[2,3,5,1,4,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[[1,4],[2],[3],[5],[6]]=>[6,5,3,2,1,4]=>[2,3,5,1,6,4]=>[[.,[.,[.,.]]],[[.,.],.]]
[[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[[1,2,6],[3,5],[4]]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>[[.,.],[[[.,.],.],[.,.]]]
[[1,2],[3,5],[4],[6]]=>[6,4,3,5,1,2]=>[5,1,4,6,3,2]=>[[.,.],[[[.,[.,.]],.],.]]
[[1,3,6],[2,5],[4]]=>[4,2,5,1,3,6]=>[5,4,1,2,3,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[[1,3],[2,5],[4,6]]=>[4,6,2,5,1,3]=>[5,6,1,4,2,3]=>[[.,[.,.]],[[.,.],[.,.]]]
[[1,3],[2,5],[4],[6]]=>[6,4,2,5,1,3]=>[5,4,1,6,2,3]=>[[[.,.],.],[[.,.],[.,.]]]
[[1,2],[3,5],[4,6]]=>[4,6,3,5,1,2]=>[5,1,6,4,3,2]=>[[.,.],[[[[.,.],.],.],.]]
[[1,5,6],[2],[3],[4]]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[[1,5],[2,6],[3],[4]]=>[4,3,2,6,1,5]=>[6,3,4,2,1,5]=>[[[[.,.],[.,.]],.],[.,.]]
[[1,5],[2],[3],[4],[6]]=>[6,4,3,2,1,5]=>[2,3,4,6,1,5]=>[[.,[.,[.,[.,.]]]],[.,.]]
[[1,2],[3,6],[4],[5]]=>[5,4,3,6,1,2]=>[6,1,4,5,3,2]=>[[.,.],[[[.,[.,.]],.],.]]
[[1,3],[2,4],[5,6]]=>[5,6,2,4,1,3]=>[4,6,1,2,5,3]=>[[.,[.,.]],[.,[[.,.],.]]]
[[1,3],[2,6],[4],[5]]=>[5,4,2,6,1,3]=>[6,4,1,5,2,3]=>[[[.,.],.],[[.,.],[.,.]]]
[[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>[[.,.],[[[.,.],[.,.]],.]]
[[1,4],[2,6],[3],[5]]=>[5,3,2,6,1,4]=>[6,3,5,1,2,4]=>[[[.,.],[.,.]],[.,[.,.]]]
[[1,6],[2],[3],[4],[5]]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[[.,[.,[.,[.,.]]]],[.,.]]
[[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[[.,[.,[.,[.,[.,.]]]]],.]
[[1,1,1,1,2,2,2],[3,4],[4]]=>[9,8,10,1,2,3,4,5,6,7]=>[10,1,2,3,4,5,6,9,8,7]=>[[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[[1,1,1,2,2,2,2],[3,4],[4]]=>[9,8,10,1,2,3,4,5,6,7]=>[10,1,2,3,4,5,6,9,8,7]=>[[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[[1,1,1,1,2,2,3],[3,4],[4]]=>[9,7,10,1,2,3,4,5,6,8]=>[10,1,2,3,4,5,9,6,7,8]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[[1,1,1,2,2,2,3],[3,4],[4]]=>[9,7,10,1,2,3,4,5,6,8]=>[10,1,2,3,4,5,9,6,7,8]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[[1,1,2,2,2,2,3],[3,4],[4]]=>[9,7,10,1,2,3,4,5,6,8]=>[10,1,2,3,4,5,9,6,7,8]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottommost row (in English notation).
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 maxima 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 weak deficiency positions of $\chi(\pi)$, and
- the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
searching the database
Sorry, this map was not found in the database.