Identifier
Mp00081:
Standard tableaux
—reading word permutation⟶
Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Images
=>
Cc0007;cc-rep-0Cc0010;cc-rep-2
[[1]]=>[1]=>[.,.]=>[1]
[[1,2]]=>[1,2]=>[.,[.,.]]=>[2,1]
[[1],[2]]=>[2,1]=>[[.,.],.]=>[1,2]
[[1,2,3]]=>[1,2,3]=>[.,[.,[.,.]]]=>[3,2,1]
[[1,3],[2]]=>[2,1,3]=>[[.,.],[.,.]]=>[1,3,2]
[[1,2],[3]]=>[3,1,2]=>[[.,.],[.,.]]=>[1,3,2]
[[1],[2],[3]]=>[3,2,1]=>[[[.,.],.],.]=>[1,2,3]
[[1,2,3,4]]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]=>[4,3,2,1]
[[1,3,4],[2]]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]=>[1,4,3,2]
[[1,2,4],[3]]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]=>[1,4,3,2]
[[1,2,3],[4]]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]=>[1,4,3,2]
[[1,3],[2,4]]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]=>[2,1,4,3]
[[1,2],[3,4]]=>[3,4,1,2]=>[[.,[.,.]],[.,.]]=>[2,1,4,3]
[[1,4],[2],[3]]=>[3,2,1,4]=>[[[.,.],.],[.,.]]=>[1,2,4,3]
[[1,3],[2],[4]]=>[4,2,1,3]=>[[[.,.],.],[.,.]]=>[1,2,4,3]
[[1,2],[3],[4]]=>[4,3,1,2]=>[[[.,.],.],[.,.]]=>[1,2,4,3]
[[1],[2],[3],[4]]=>[4,3,2,1]=>[[[[.,.],.],.],.]=>[1,2,3,4]
[[1,2,3,4,5]]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]
[[1,3,4,5],[2]]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]
[[1,2,4,5],[3]]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]
[[1,2,3,5],[4]]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]
[[1,2,3,4],[5]]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]
[[1,3,5],[2,4]]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]
[[1,2,5],[3,4]]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]
[[1,3,4],[2,5]]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]
[[1,2,4],[3,5]]=>[3,5,1,2,4]=>[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]
[[1,2,3],[4,5]]=>[4,5,1,2,3]=>[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]
[[1,4,5],[2],[3]]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]
[[1,3,5],[2],[4]]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]
[[1,2,5],[3],[4]]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]
[[1,3,4],[2],[5]]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]
[[1,2,4],[3],[5]]=>[5,3,1,2,4]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]
[[1,2,3],[4],[5]]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]
[[1,4],[2,5],[3]]=>[3,2,5,1,4]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]
[[1,3],[2,5],[4]]=>[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]
[[1,2],[3,5],[4]]=>[4,3,5,1,2]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]
[[1,3],[2,4],[5]]=>[5,2,4,1,3]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]
[[1,2],[3,4],[5]]=>[5,3,4,1,2]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]
[[1,5],[2],[3],[4]]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]
[[1,4],[2],[3],[5]]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]
[[1,3],[2],[4],[5]]=>[5,4,2,1,3]=>[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]
[[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]
[[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]
[[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]
[[1,3,4,5,6],[2]]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]
[[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]
[[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]
[[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]
[[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]
[[1,3,5,6],[2,4]]=>[2,4,1,3,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]
[[1,2,5,6],[3,4]]=>[3,4,1,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]
[[1,3,4,6],[2,5]]=>[2,5,1,3,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]
[[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]
[[1,2,3,6],[4,5]]=>[4,5,1,2,3,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]
[[1,3,4,5],[2,6]]=>[2,6,1,3,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]
[[1,2,4,5],[3,6]]=>[3,6,1,2,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]
[[1,2,3,5],[4,6]]=>[4,6,1,2,3,5]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]
[[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]
[[1,4,5,6],[2],[3]]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]
[[1,3,5,6],[2],[4]]=>[4,2,1,3,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]
[[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]
[[1,3,4,6],[2],[5]]=>[5,2,1,3,4,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]
[[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]
[[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]
[[1,3,4,5],[2],[6]]=>[6,2,1,3,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]
[[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]
[[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]
[[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]
[[1,3,5],[2,4,6]]=>[2,4,6,1,3,5]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]
[[1,2,5],[3,4,6]]=>[3,4,6,1,2,5]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]
[[1,3,4],[2,5,6]]=>[2,5,6,1,3,4]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]
[[1,2,4],[3,5,6]]=>[3,5,6,1,2,4]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]
[[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]
[[1,4,6],[2,5],[3]]=>[3,2,5,1,4,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]
[[1,3,6],[2,5],[4]]=>[4,2,5,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]
[[1,2,6],[3,5],[4]]=>[4,3,5,1,2,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]
[[1,3,6],[2,4],[5]]=>[5,2,4,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]
[[1,2,6],[3,4],[5]]=>[5,3,4,1,2,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]
[[1,4,5],[2,6],[3]]=>[3,2,6,1,4,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]
[[1,3,5],[2,6],[4]]=>[4,2,6,1,3,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]
[[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]
[[1,3,4],[2,6],[5]]=>[5,2,6,1,3,4]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]
[[1,2,4],[3,6],[5]]=>[5,3,6,1,2,4]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]
[[1,2,3],[4,6],[5]]=>[5,4,6,1,2,3]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]
[[1,3,5],[2,4],[6]]=>[6,2,4,1,3,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]
[[1,2,5],[3,4],[6]]=>[6,3,4,1,2,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]
[[1,3,4],[2,5],[6]]=>[6,2,5,1,3,4]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]
[[1,2,4],[3,5],[6]]=>[6,3,5,1,2,4]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]
[[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]
[[1,5,6],[2],[3],[4]]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]
[[1,4,6],[2],[3],[5]]=>[5,3,2,1,4,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]
[[1,3,6],[2],[4],[5]]=>[5,4,2,1,3,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]
[[1,2,6],[3],[4],[5]]=>[5,4,3,1,2,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]
[[1,4,5],[2],[3],[6]]=>[6,3,2,1,4,5]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]
[[1,3,5],[2],[4],[6]]=>[6,4,2,1,3,5]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]
[[1,2,5],[3],[4],[6]]=>[6,4,3,1,2,5]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]
[[1,3,4],[2],[5],[6]]=>[6,5,2,1,3,4]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]
[[1,2,4],[3],[5],[6]]=>[6,5,3,1,2,4]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]
[[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]
[[1,4],[2,5],[3,6]]=>[3,6,2,5,1,4]=>[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]
[[1,3],[2,5],[4,6]]=>[4,6,2,5,1,3]=>[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]
[[1,2],[3,5],[4,6]]=>[4,6,3,5,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]
[[1,3],[2,4],[5,6]]=>[5,6,2,4,1,3]=>[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]
[[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]
[[1,5],[2,6],[3],[4]]=>[4,3,2,6,1,5]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]
[[1,4],[2,6],[3],[5]]=>[5,3,2,6,1,4]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]
[[1,3],[2,6],[4],[5]]=>[5,4,2,6,1,3]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]
[[1,2],[3,6],[4],[5]]=>[5,4,3,6,1,2]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]
[[1,4],[2,5],[3],[6]]=>[6,3,2,5,1,4]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]
[[1,3],[2,5],[4],[6]]=>[6,4,2,5,1,3]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]
[[1,2],[3,5],[4],[6]]=>[6,4,3,5,1,2]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]
[[1,3],[2,4],[5],[6]]=>[6,5,2,4,1,3]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]
[[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]
[[1,6],[2],[3],[4],[5]]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]
[[1,5],[2],[3],[4],[6]]=>[6,4,3,2,1,5]=>[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]
[[1,4],[2],[3],[5],[6]]=>[6,5,3,2,1,4]=>[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]
[[1,3],[2],[4],[5],[6]]=>[6,5,4,2,1,3]=>[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]
[[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]
[[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]
[[1,2,3,4,5,6,7]]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]
[[1,3,4,5,6,7],[2]]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]
[[1,2,4,5,6,7],[3]]=>[3,1,2,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]
[[1,2,3,5,6,7],[4]]=>[4,1,2,3,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]
[[1,2,3,4,6,7],[5]]=>[5,1,2,3,4,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]
[[1,2,3,4,5,7],[6]]=>[6,1,2,3,4,5,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]
[[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]
[[1,3,5,6,7],[2,4]]=>[2,4,1,3,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]
[[1,2,5,6,7],[3,4]]=>[3,4,1,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]
[[1,3,4,6,7],[2,5]]=>[2,5,1,3,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]
[[1,2,4,6,7],[3,5]]=>[3,5,1,2,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]
[[1,2,3,6,7],[4,5]]=>[4,5,1,2,3,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]
[[1,3,4,5,7],[2,6]]=>[2,6,1,3,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]
[[1,2,4,5,7],[3,6]]=>[3,6,1,2,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]
[[1,2,3,5,7],[4,6]]=>[4,6,1,2,3,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]
[[1,2,3,4,7],[5,6]]=>[5,6,1,2,3,4,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]
[[1,3,4,5,6],[2,7]]=>[2,7,1,3,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]
[[1,2,4,5,6],[3,7]]=>[3,7,1,2,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]
[[1,2,3,5,6],[4,7]]=>[4,7,1,2,3,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]
[[1,2,3,4,6],[5,7]]=>[5,7,1,2,3,4,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]
[[1,2,3,4,5],[6,7]]=>[6,7,1,2,3,4,5]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]
[[1,4,5,6,7],[2],[3]]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[[1,3,5,6,7],[2],[4]]=>[4,2,1,3,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[[1,2,5,6,7],[3],[4]]=>[4,3,1,2,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[[1,3,4,6,7],[2],[5]]=>[5,2,1,3,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[[1,2,4,6,7],[3],[5]]=>[5,3,1,2,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[[1,2,3,6,7],[4],[5]]=>[5,4,1,2,3,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[[1,3,4,5,7],[2],[6]]=>[6,2,1,3,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[[1,2,4,5,7],[3],[6]]=>[6,3,1,2,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[[1,2,3,5,7],[4],[6]]=>[6,4,1,2,3,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[[1,2,3,4,7],[5],[6]]=>[6,5,1,2,3,4,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[[1,3,4,5,6],[2],[7]]=>[7,2,1,3,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[[1,2,4,5,6],[3],[7]]=>[7,3,1,2,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[[1,2,3,5,6],[4],[7]]=>[7,4,1,2,3,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[[1,2,3,4,6],[5],[7]]=>[7,5,1,2,3,4,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[[1,2,3,4,5],[6],[7]]=>[7,6,1,2,3,4,5]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[[1,3,5,7],[2,4,6]]=>[2,4,6,1,3,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]
[[1,2,5,7],[3,4,6]]=>[3,4,6,1,2,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]
[[1,3,4,7],[2,5,6]]=>[2,5,6,1,3,4,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]
[[1,2,4,7],[3,5,6]]=>[3,5,6,1,2,4,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]
[[1,2,3,7],[4,5,6]]=>[4,5,6,1,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]
[[1,3,5,6],[2,4,7]]=>[2,4,7,1,3,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]
[[1,2,5,6],[3,4,7]]=>[3,4,7,1,2,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]
[[1,3,4,6],[2,5,7]]=>[2,5,7,1,3,4,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]
[[1,2,4,6],[3,5,7]]=>[3,5,7,1,2,4,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]
[[1,2,3,6],[4,5,7]]=>[4,5,7,1,2,3,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]
[[1,3,4,5],[2,6,7]]=>[2,6,7,1,3,4,5]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]
[[1,2,4,5],[3,6,7]]=>[3,6,7,1,2,4,5]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]
[[1,2,3,5],[4,6,7]]=>[4,6,7,1,2,3,5]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]
[[1,2,3,4],[5,6,7]]=>[5,6,7,1,2,3,4]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]
[[1,4,6,7],[2,5],[3]]=>[3,2,5,1,4,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,3,6,7],[2,5],[4]]=>[4,2,5,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,2,6,7],[3,5],[4]]=>[4,3,5,1,2,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,3,6,7],[2,4],[5]]=>[5,2,4,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,2,6,7],[3,4],[5]]=>[5,3,4,1,2,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,4,5,7],[2,6],[3]]=>[3,2,6,1,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,3,5,7],[2,6],[4]]=>[4,2,6,1,3,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,2,5,7],[3,6],[4]]=>[4,3,6,1,2,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,3,4,7],[2,6],[5]]=>[5,2,6,1,3,4,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,2,4,7],[3,6],[5]]=>[5,3,6,1,2,4,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,2,3,7],[4,6],[5]]=>[5,4,6,1,2,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,3,5,7],[2,4],[6]]=>[6,2,4,1,3,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,2,5,7],[3,4],[6]]=>[6,3,4,1,2,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,3,4,7],[2,5],[6]]=>[6,2,5,1,3,4,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,2,4,7],[3,5],[6]]=>[6,3,5,1,2,4,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,2,3,7],[4,5],[6]]=>[6,4,5,1,2,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,4,5,6],[2,7],[3]]=>[3,2,7,1,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,3,5,6],[2,7],[4]]=>[4,2,7,1,3,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,2,5,6],[3,7],[4]]=>[4,3,7,1,2,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,3,4,6],[2,7],[5]]=>[5,2,7,1,3,4,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,2,4,6],[3,7],[5]]=>[5,3,7,1,2,4,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,2,3,6],[4,7],[5]]=>[5,4,7,1,2,3,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,3,4,5],[2,7],[6]]=>[6,2,7,1,3,4,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,2,4,5],[3,7],[6]]=>[6,3,7,1,2,4,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,2,3,5],[4,7],[6]]=>[6,4,7,1,2,3,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,2,3,4],[5,7],[6]]=>[6,5,7,1,2,3,4]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,3,5,6],[2,4],[7]]=>[7,2,4,1,3,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,2,5,6],[3,4],[7]]=>[7,3,4,1,2,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,3,4,6],[2,5],[7]]=>[7,2,5,1,3,4,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,2,4,6],[3,5],[7]]=>[7,3,5,1,2,4,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,2,3,6],[4,5],[7]]=>[7,4,5,1,2,3,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,3,4,5],[2,6],[7]]=>[7,2,6,1,3,4,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,2,4,5],[3,6],[7]]=>[7,3,6,1,2,4,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,2,3,5],[4,6],[7]]=>[7,4,6,1,2,3,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,2,3,4],[5,6],[7]]=>[7,5,6,1,2,3,4]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[[1,5,6,7],[2],[3],[4]]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[[1,4,6,7],[2],[3],[5]]=>[5,3,2,1,4,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[[1,3,6,7],[2],[4],[5]]=>[5,4,2,1,3,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[[1,2,6,7],[3],[4],[5]]=>[5,4,3,1,2,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[[1,4,5,7],[2],[3],[6]]=>[6,3,2,1,4,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[[1,3,5,7],[2],[4],[6]]=>[6,4,2,1,3,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[[1,2,5,7],[3],[4],[6]]=>[6,4,3,1,2,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[[1,3,4,7],[2],[5],[6]]=>[6,5,2,1,3,4,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[[1,2,4,7],[3],[5],[6]]=>[6,5,3,1,2,4,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[[1,2,3,7],[4],[5],[6]]=>[6,5,4,1,2,3,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[[1,4,5,6],[2],[3],[7]]=>[7,3,2,1,4,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[[1,3,5,6],[2],[4],[7]]=>[7,4,2,1,3,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[[1,2,5,6],[3],[4],[7]]=>[7,4,3,1,2,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[[1,3,4,6],[2],[5],[7]]=>[7,5,2,1,3,4,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[[1,2,4,6],[3],[5],[7]]=>[7,5,3,1,2,4,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[[1,2,3,6],[4],[5],[7]]=>[7,5,4,1,2,3,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[[1,3,4,5],[2],[6],[7]]=>[7,6,2,1,3,4,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[[1,2,4,5],[3],[6],[7]]=>[7,6,3,1,2,4,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[[1,2,3,5],[4],[6],[7]]=>[7,6,4,1,2,3,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[[1,2,3,4],[5],[6],[7]]=>[7,6,5,1,2,3,4]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[[1,4,6],[2,5,7],[3]]=>[3,2,5,7,1,4,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[[1,3,6],[2,5,7],[4]]=>[4,2,5,7,1,3,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[[1,2,6],[3,5,7],[4]]=>[4,3,5,7,1,2,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[[1,3,6],[2,4,7],[5]]=>[5,2,4,7,1,3,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[[1,2,6],[3,4,7],[5]]=>[5,3,4,7,1,2,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[[1,4,5],[2,6,7],[3]]=>[3,2,6,7,1,4,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[[1,3,5],[2,6,7],[4]]=>[4,2,6,7,1,3,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[[1,2,5],[3,6,7],[4]]=>[4,3,6,7,1,2,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[[1,3,4],[2,6,7],[5]]=>[5,2,6,7,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[[1,2,4],[3,6,7],[5]]=>[5,3,6,7,1,2,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[[1,2,3],[4,6,7],[5]]=>[5,4,6,7,1,2,3]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[[1,3,5],[2,4,7],[6]]=>[6,2,4,7,1,3,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[[1,2,5],[3,4,7],[6]]=>[6,3,4,7,1,2,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[[1,3,4],[2,5,7],[6]]=>[6,2,5,7,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[[1,2,4],[3,5,7],[6]]=>[6,3,5,7,1,2,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[[1,2,3],[4,5,7],[6]]=>[6,4,5,7,1,2,3]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[[1,3,5],[2,4,6],[7]]=>[7,2,4,6,1,3,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[[1,2,5],[3,4,6],[7]]=>[7,3,4,6,1,2,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[[1,3,4],[2,5,6],[7]]=>[7,2,5,6,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[[1,2,4],[3,5,6],[7]]=>[7,3,5,6,1,2,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[[1,2,3],[4,5,6],[7]]=>[7,4,5,6,1,2,3]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[[1,4,7],[2,5],[3,6]]=>[3,6,2,5,1,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[[1,3,7],[2,5],[4,6]]=>[4,6,2,5,1,3,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[[1,2,7],[3,5],[4,6]]=>[4,6,3,5,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[[1,3,7],[2,4],[5,6]]=>[5,6,2,4,1,3,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[[1,2,7],[3,4],[5,6]]=>[5,6,3,4,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[[1,4,6],[2,5],[3,7]]=>[3,7,2,5,1,4,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[[1,3,6],[2,5],[4,7]]=>[4,7,2,5,1,3,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[[1,2,6],[3,5],[4,7]]=>[4,7,3,5,1,2,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[[1,3,6],[2,4],[5,7]]=>[5,7,2,4,1,3,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[[1,2,6],[3,4],[5,7]]=>[5,7,3,4,1,2,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[[1,4,5],[2,6],[3,7]]=>[3,7,2,6,1,4,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[[1,3,5],[2,6],[4,7]]=>[4,7,2,6,1,3,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[[1,2,5],[3,6],[4,7]]=>[4,7,3,6,1,2,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[[1,3,4],[2,6],[5,7]]=>[5,7,2,6,1,3,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[[1,2,4],[3,6],[5,7]]=>[5,7,3,6,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[[1,2,3],[4,6],[5,7]]=>[5,7,4,6,1,2,3]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[[1,3,5],[2,4],[6,7]]=>[6,7,2,4,1,3,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[[1,2,5],[3,4],[6,7]]=>[6,7,3,4,1,2,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[[1,3,4],[2,5],[6,7]]=>[6,7,2,5,1,3,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[[1,2,4],[3,5],[6,7]]=>[6,7,3,5,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[[1,2,3],[4,5],[6,7]]=>[6,7,4,5,1,2,3]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[[1,5,7],[2,6],[3],[4]]=>[4,3,2,6,1,5,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,4,7],[2,6],[3],[5]]=>[5,3,2,6,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,3,7],[2,6],[4],[5]]=>[5,4,2,6,1,3,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,2,7],[3,6],[4],[5]]=>[5,4,3,6,1,2,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,4,7],[2,5],[3],[6]]=>[6,3,2,5,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,3,7],[2,5],[4],[6]]=>[6,4,2,5,1,3,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,2,7],[3,5],[4],[6]]=>[6,4,3,5,1,2,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,3,7],[2,4],[5],[6]]=>[6,5,2,4,1,3,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,2,7],[3,4],[5],[6]]=>[6,5,3,4,1,2,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,5,6],[2,7],[3],[4]]=>[4,3,2,7,1,5,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,4,6],[2,7],[3],[5]]=>[5,3,2,7,1,4,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,3,6],[2,7],[4],[5]]=>[5,4,2,7,1,3,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,2,6],[3,7],[4],[5]]=>[5,4,3,7,1,2,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,4,5],[2,7],[3],[6]]=>[6,3,2,7,1,4,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,3,5],[2,7],[4],[6]]=>[6,4,2,7,1,3,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,2,5],[3,7],[4],[6]]=>[6,4,3,7,1,2,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,3,4],[2,7],[5],[6]]=>[6,5,2,7,1,3,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,2,4],[3,7],[5],[6]]=>[6,5,3,7,1,2,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,2,3],[4,7],[5],[6]]=>[6,5,4,7,1,2,3]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,4,6],[2,5],[3],[7]]=>[7,3,2,5,1,4,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,3,6],[2,5],[4],[7]]=>[7,4,2,5,1,3,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,2,6],[3,5],[4],[7]]=>[7,4,3,5,1,2,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,3,6],[2,4],[5],[7]]=>[7,5,2,4,1,3,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,2,6],[3,4],[5],[7]]=>[7,5,3,4,1,2,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,4,5],[2,6],[3],[7]]=>[7,3,2,6,1,4,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,3,5],[2,6],[4],[7]]=>[7,4,2,6,1,3,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,2,5],[3,6],[4],[7]]=>[7,4,3,6,1,2,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,3,4],[2,6],[5],[7]]=>[7,5,2,6,1,3,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,2,4],[3,6],[5],[7]]=>[7,5,3,6,1,2,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,2,3],[4,6],[5],[7]]=>[7,5,4,6,1,2,3]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,3,5],[2,4],[6],[7]]=>[7,6,2,4,1,3,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,2,5],[3,4],[6],[7]]=>[7,6,3,4,1,2,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,3,4],[2,5],[6],[7]]=>[7,6,2,5,1,3,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,2,4],[3,5],[6],[7]]=>[7,6,3,5,1,2,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,2,3],[4,5],[6],[7]]=>[7,6,4,5,1,2,3]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[[1,6,7],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[[1,5,7],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[[1,4,7],[2],[3],[5],[6]]=>[6,5,3,2,1,4,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[[1,3,7],[2],[4],[5],[6]]=>[6,5,4,2,1,3,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[[1,2,7],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[[1,5,6],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[[1,4,6],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[[1,3,6],[2],[4],[5],[7]]=>[7,5,4,2,1,3,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[[1,2,6],[3],[4],[5],[7]]=>[7,5,4,3,1,2,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[[1,4,5],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[[1,3,5],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[[1,2,5],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[[1,3,4],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[[1,2,4],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[[1,2,3],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[[1,5],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]
[[1,4],[2,6],[3,7],[5]]=>[5,3,7,2,6,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]
[[1,3],[2,6],[4,7],[5]]=>[5,4,7,2,6,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]
[[1,2],[3,6],[4,7],[5]]=>[5,4,7,3,6,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]
[[1,4],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]
[[1,3],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]
[[1,2],[3,5],[4,7],[6]]=>[6,4,7,3,5,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]
[[1,3],[2,4],[5,7],[6]]=>[6,5,7,2,4,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]
[[1,2],[3,4],[5,7],[6]]=>[6,5,7,3,4,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]
[[1,4],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]
[[1,3],[2,5],[4,6],[7]]=>[7,4,6,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]
[[1,2],[3,5],[4,6],[7]]=>[7,4,6,3,5,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]
[[1,3],[2,4],[5,6],[7]]=>[7,5,6,2,4,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]
[[1,2],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]
[[1,6],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]
[[1,5],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]
[[1,4],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]
[[1,3],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]
[[1,2],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]
[[1,5],[2,6],[3],[4],[7]]=>[7,4,3,2,6,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]
[[1,4],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]
[[1,3],[2,6],[4],[5],[7]]=>[7,5,4,2,6,1,3]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]
[[1,2],[3,6],[4],[5],[7]]=>[7,5,4,3,6,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]
[[1,4],[2,5],[3],[6],[7]]=>[7,6,3,2,5,1,4]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]
[[1,3],[2,5],[4],[6],[7]]=>[7,6,4,2,5,1,3]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]
[[1,2],[3,5],[4],[6],[7]]=>[7,6,4,3,5,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]
[[1,3],[2,4],[5],[6],[7]]=>[7,6,5,2,4,1,3]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]
[[1,2],[3,4],[5],[6],[7]]=>[7,6,5,3,4,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]
[[1,7],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]
[[1,6],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]
[[1,5],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]
[[1,4],[2],[3],[5],[6],[7]]=>[7,6,5,3,2,1,4]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]
[[1,3],[2],[4],[5],[6],[7]]=>[7,6,5,4,2,1,3]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]
[[1,2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]
[[1],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]
[[1,2,3,4,5,6,7,8]]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]
[[1,3,4,5,6,7,8],[2]]=>[2,1,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]
[[1,2,4,5,6,7,8],[3]]=>[3,1,2,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]
[[1,2,3,5,6,7,8],[4]]=>[4,1,2,3,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]
[[1,2,3,4,6,7,8],[5]]=>[5,1,2,3,4,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]
[[1,2,3,4,5,7,8],[6]]=>[6,1,2,3,4,5,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]
[[1,2,3,4,5,6,8],[7]]=>[7,1,2,3,4,5,6,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]
[[1,2,3,4,5,6,7],[8]]=>[8,1,2,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]
[[1,3,5,6,7,8],[2,4]]=>[2,4,1,3,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]
[[1,2,5,6,7,8],[3,4]]=>[3,4,1,2,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]
[[1,3,4,6,7,8],[2,5]]=>[2,5,1,3,4,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]
[[1,2,4,6,7,8],[3,5]]=>[3,5,1,2,4,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]
[[1,2,3,6,7,8],[4,5]]=>[4,5,1,2,3,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]
[[1,3,4,5,7,8],[2,6]]=>[2,6,1,3,4,5,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]
[[1,2,4,5,7,8],[3,6]]=>[3,6,1,2,4,5,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]
[[1,2,3,5,7,8],[4,6]]=>[4,6,1,2,3,5,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]
[[1,3,4,5,6,8],[2,7]]=>[2,7,1,3,4,5,6,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]
[[1,2,4,5,6,8],[3,7]]=>[3,7,1,2,4,5,6,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]
[[1,2,3,5,6,8],[4,7]]=>[4,7,1,2,3,5,6,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]
[[1,2,3,4,6,8],[5,7]]=>[5,7,1,2,3,4,6,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]
[[1,2,3,4,5,8],[6,7]]=>[6,7,1,2,3,4,5,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]
[[1,3,4,5,6,7],[2,8]]=>[2,8,1,3,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]
[[1,2,4,5,6,7],[3,8]]=>[3,8,1,2,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]
[[1,2,3,5,6,7],[4,8]]=>[4,8,1,2,3,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]
[[1,2,3,4,6,7],[5,8]]=>[5,8,1,2,3,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]
[[1,2,3,4,5,7],[6,8]]=>[6,8,1,2,3,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]
[[1,2,3,4,5,6],[7,8]]=>[7,8,1,2,3,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]
[[1,4,5,6,7,8],[2],[3]]=>[3,2,1,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[[1,3,5,6,7,8],[2],[4]]=>[4,2,1,3,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[[1,2,5,6,7,8],[3],[4]]=>[4,3,1,2,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[[1,3,4,6,7,8],[2],[5]]=>[5,2,1,3,4,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[[1,2,4,6,7,8],[3],[5]]=>[5,3,1,2,4,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[[1,2,3,6,7,8],[4],[5]]=>[5,4,1,2,3,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[[1,2,4,5,7,8],[3],[6]]=>[6,3,1,2,4,5,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[[1,2,3,5,7,8],[4],[6]]=>[6,4,1,2,3,5,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[[1,2,3,4,7,8],[5],[6]]=>[6,5,1,2,3,4,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[[1,3,4,5,6,8],[2],[7]]=>[7,2,1,3,4,5,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[[1,2,4,5,6,8],[3],[7]]=>[7,3,1,2,4,5,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[[1,2,3,5,6,8],[4],[7]]=>[7,4,1,2,3,5,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[[1,2,3,4,6,8],[5],[7]]=>[7,5,1,2,3,4,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[[1,2,3,4,5,8],[6],[7]]=>[7,6,1,2,3,4,5,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[[1,3,4,5,6,7],[2],[8]]=>[8,2,1,3,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[[1,2,4,5,6,7],[3],[8]]=>[8,3,1,2,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[[1,2,3,5,6,7],[4],[8]]=>[8,4,1,2,3,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[[1,2,3,4,6,7],[5],[8]]=>[8,5,1,2,3,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[[1,2,3,4,5,7],[6],[8]]=>[8,6,1,2,3,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[[1,2,3,4,5,6],[7],[8]]=>[8,7,1,2,3,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[[1,3,5,7,8],[2,4,6]]=>[2,4,6,1,3,5,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]
[[1,2,4,7,8],[3,5,6]]=>[3,5,6,1,2,4,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]
[[1,2,3,7,8],[4,5,6]]=>[4,5,6,1,2,3,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]
[[1,2,4,6,8],[3,5,7]]=>[3,5,7,1,2,4,6,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]
[[1,2,3,5,8],[4,6,7]]=>[4,6,7,1,2,3,5,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]
[[1,2,3,4,8],[5,6,7]]=>[5,6,7,1,2,3,4,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]
[[1,3,5,6,7],[2,4,8]]=>[2,4,8,1,3,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]
[[1,2,5,6,7],[3,4,8]]=>[3,4,8,1,2,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]
[[1,2,3,6,7],[4,5,8]]=>[4,5,8,1,2,3,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]
[[1,3,4,5,7],[2,6,8]]=>[2,6,8,1,3,4,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]
[[1,2,4,5,7],[3,6,8]]=>[3,6,8,1,2,4,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]
[[1,2,3,5,7],[4,6,8]]=>[4,6,8,1,2,3,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]
[[1,2,3,4,7],[5,6,8]]=>[5,6,8,1,2,3,4,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]
[[1,3,4,5,6],[2,7,8]]=>[2,7,8,1,3,4,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]
[[1,2,4,5,6],[3,7,8]]=>[3,7,8,1,2,4,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]
[[1,2,3,5,6],[4,7,8]]=>[4,7,8,1,2,3,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]
[[1,2,3,4,6],[5,7,8]]=>[5,7,8,1,2,3,4,6]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]
[[1,2,3,4,5],[6,7,8]]=>[6,7,8,1,2,3,4,5]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]
[[1,4,6,7,8],[2,5],[3]]=>[3,2,5,1,4,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,3,6,7,8],[2,5],[4]]=>[4,2,5,1,3,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,6,7,8],[3,5],[4]]=>[4,3,5,1,2,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,3,5,7,8],[2,6],[4]]=>[4,2,6,1,3,5,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,4,7,8],[3,6],[5]]=>[5,3,6,1,2,4,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,3,5,7,8],[2,4],[6]]=>[6,2,4,1,3,5,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,4,7,8],[3,5],[6]]=>[6,3,5,1,2,4,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,4,6,8],[3,7],[5]]=>[5,3,7,1,2,4,6,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,3,6,8],[4,7],[5]]=>[5,4,7,1,2,3,6,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,3,4,5,8],[2,7],[6]]=>[6,2,7,1,3,4,5,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,4,5,8],[3,7],[6]]=>[6,3,7,1,2,4,5,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,3,5,8],[4,7],[6]]=>[6,4,7,1,2,3,5,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,3,4,8],[5,7],[6]]=>[6,5,7,1,2,3,4,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,5,6,8],[3,4],[7]]=>[7,3,4,1,2,5,6,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,4,6,8],[3,5],[7]]=>[7,3,5,1,2,4,6,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,3,6,8],[4,5],[7]]=>[7,4,5,1,2,3,6,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,4,5,8],[3,6],[7]]=>[7,3,6,1,2,4,5,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,3,5,8],[4,6],[7]]=>[7,4,6,1,2,3,5,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,3,4,8],[5,6],[7]]=>[7,5,6,1,2,3,4,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,4,5,6,7],[2,8],[3]]=>[3,2,8,1,4,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,3,5,6,7],[2,8],[4]]=>[4,2,8,1,3,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,3,6,7],[4,8],[5]]=>[5,4,8,1,2,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,3,4,5,7],[2,8],[6]]=>[6,2,8,1,3,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,4,5,7],[3,8],[6]]=>[6,3,8,1,2,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,3,5,7],[4,8],[6]]=>[6,4,8,1,2,3,5,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,3,4,7],[5,8],[6]]=>[6,5,8,1,2,3,4,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,3,4,5,6],[2,8],[7]]=>[7,2,8,1,3,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,4,5,6],[3,8],[7]]=>[7,3,8,1,2,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,3,5,6],[4,8],[7]]=>[7,4,8,1,2,3,5,6]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,3,4,6],[5,8],[7]]=>[7,5,8,1,2,3,4,6]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,3,4,5],[6,8],[7]]=>[7,6,8,1,2,3,4,5]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,3,5,6,7],[2,4],[8]]=>[8,2,4,1,3,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,5,6,7],[3,4],[8]]=>[8,3,4,1,2,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,4,6,7],[3,5],[8]]=>[8,3,5,1,2,4,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,3,6,7],[4,5],[8]]=>[8,4,5,1,2,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,4,5,7],[3,6],[8]]=>[8,3,6,1,2,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,3,4,7],[5,6],[8]]=>[8,5,6,1,2,3,4,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,4,5,6],[3,7],[8]]=>[8,3,7,1,2,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,3,5,6],[4,7],[8]]=>[8,4,7,1,2,3,5,6]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,3,4,6],[5,7],[8]]=>[8,5,7,1,2,3,4,6]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,2,3,4,5],[6,7],[8]]=>[8,6,7,1,2,3,4,5]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[[1,5,6,7,8],[2],[3],[4]]=>[4,3,2,1,5,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[[1,4,6,7,8],[2],[3],[5]]=>[5,3,2,1,4,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[[1,3,6,7,8],[2],[4],[5]]=>[5,4,2,1,3,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[[1,2,6,7,8],[3],[4],[5]]=>[5,4,3,1,2,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[[1,3,5,7,8],[2],[4],[6]]=>[6,4,2,1,3,5,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[[1,2,5,7,8],[3],[4],[6]]=>[6,4,3,1,2,5,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[[1,2,3,7,8],[4],[5],[6]]=>[6,5,4,1,2,3,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[[1,4,5,6,8],[2],[3],[7]]=>[7,3,2,1,4,5,6,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[[1,2,5,6,8],[3],[4],[7]]=>[7,4,3,1,2,5,6,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[[1,2,4,6,8],[3],[5],[7]]=>[7,5,3,1,2,4,6,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[[1,2,3,4,8],[5],[6],[7]]=>[7,6,5,1,2,3,4,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[[1,4,5,6,7],[2],[3],[8]]=>[8,3,2,1,4,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[[1,3,5,6,7],[2],[4],[8]]=>[8,4,2,1,3,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[[1,3,4,6,7],[2],[5],[8]]=>[8,5,2,1,3,4,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[[1,2,4,6,7],[3],[5],[8]]=>[8,5,3,1,2,4,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[[1,2,3,6,7],[4],[5],[8]]=>[8,5,4,1,2,3,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[[1,2,3,5,7],[4],[6],[8]]=>[8,6,4,1,2,3,5,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[[1,2,3,4,7],[5],[6],[8]]=>[8,6,5,1,2,3,4,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[[1,3,4,5,6],[2],[7],[8]]=>[8,7,2,1,3,4,5,6]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[[1,2,3,5,6],[4],[7],[8]]=>[8,7,4,1,2,3,5,6]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[[1,2,3,4,6],[5],[7],[8]]=>[8,7,5,1,2,3,4,6]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[[1,2,3,4,5],[6],[7],[8]]=>[8,7,6,1,2,3,4,5]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[[1,3,5,7],[2,4,6,8]]=>[2,4,6,8,1,3,5,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]
[[1,2,5,7],[3,4,6,8]]=>[3,4,6,8,1,2,5,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]
[[1,3,4,7],[2,5,6,8]]=>[2,5,6,8,1,3,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]
[[1,2,4,7],[3,5,6,8]]=>[3,5,6,8,1,2,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]
[[1,2,3,7],[4,5,6,8]]=>[4,5,6,8,1,2,3,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]
[[1,3,5,6],[2,4,7,8]]=>[2,4,7,8,1,3,5,6]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]
[[1,2,5,6],[3,4,7,8]]=>[3,4,7,8,1,2,5,6]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]
[[1,3,4,6],[2,5,7,8]]=>[2,5,7,8,1,3,4,6]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]
[[1,2,4,6],[3,5,7,8]]=>[3,5,7,8,1,2,4,6]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]
[[1,2,3,6],[4,5,7,8]]=>[4,5,7,8,1,2,3,6]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]
[[1,3,4,5],[2,6,7,8]]=>[2,6,7,8,1,3,4,5]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]
[[1,2,4,5],[3,6,7,8]]=>[3,6,7,8,1,2,4,5]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]
[[1,2,3,5],[4,6,7,8]]=>[4,6,7,8,1,2,3,5]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]
[[1,2,3,4],[5,6,7,8]]=>[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]
[[1,4,6,8],[2,5,7],[3]]=>[3,2,5,7,1,4,6,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,3,6,8],[2,5,7],[4]]=>[4,2,5,7,1,3,6,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,3,6,8],[2,4,7],[5]]=>[5,2,4,7,1,3,6,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,3,5,8],[2,6,7],[4]]=>[4,2,6,7,1,3,5,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,3,4,8],[2,6,7],[5]]=>[5,2,6,7,1,3,4,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,2,4,8],[3,6,7],[5]]=>[5,3,6,7,1,2,4,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,2,3,8],[4,6,7],[5]]=>[5,4,6,7,1,2,3,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,3,4,8],[2,5,7],[6]]=>[6,2,5,7,1,3,4,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,2,3,8],[4,5,6],[7]]=>[7,4,5,6,1,2,3,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,4,6,7],[2,5,8],[3]]=>[3,2,5,8,1,4,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,3,6,7],[2,5,8],[4]]=>[4,2,5,8,1,3,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,2,6,7],[3,5,8],[4]]=>[4,3,5,8,1,2,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,3,6,7],[2,4,8],[5]]=>[5,2,4,8,1,3,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,4,5,7],[2,6,8],[3]]=>[3,2,6,8,1,4,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,3,5,7],[2,6,8],[4]]=>[4,2,6,8,1,3,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,3,4,7],[2,6,8],[5]]=>[5,2,6,8,1,3,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,3,5,7],[2,4,8],[6]]=>[6,2,4,8,1,3,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,2,5,7],[3,4,8],[6]]=>[6,3,4,8,1,2,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,3,4,7],[2,5,8],[6]]=>[6,2,5,8,1,3,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,2,4,7],[3,5,8],[6]]=>[6,3,5,8,1,2,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,2,3,7],[4,5,8],[6]]=>[6,4,5,8,1,2,3,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,4,5,6],[2,7,8],[3]]=>[3,2,7,8,1,4,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,2,4,6],[3,7,8],[5]]=>[5,3,7,8,1,2,4,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,2,3,6],[4,7,8],[5]]=>[5,4,7,8,1,2,3,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,3,4,5],[2,7,8],[6]]=>[6,2,7,8,1,3,4,5]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,2,4,5],[3,7,8],[6]]=>[6,3,7,8,1,2,4,5]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,2,3,5],[4,7,8],[6]]=>[6,4,7,8,1,2,3,5]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,2,3,4],[5,7,8],[6]]=>[6,5,7,8,1,2,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,3,5,6],[2,4,8],[7]]=>[7,2,4,8,1,3,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,2,5,6],[3,4,8],[7]]=>[7,3,4,8,1,2,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,2,4,6],[3,5,8],[7]]=>[7,3,5,8,1,2,4,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,2,3,6],[4,5,8],[7]]=>[7,4,5,8,1,2,3,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,2,3,5],[4,6,8],[7]]=>[7,4,6,8,1,2,3,5]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,2,3,4],[5,6,8],[7]]=>[7,5,6,8,1,2,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,2,5,7],[3,4,6],[8]]=>[8,3,4,6,1,2,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,2,4,7],[3,5,6],[8]]=>[8,3,5,6,1,2,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,2,3,7],[4,5,6],[8]]=>[8,4,5,6,1,2,3,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,3,5,6],[2,4,7],[8]]=>[8,2,4,7,1,3,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,3,4,6],[2,5,7],[8]]=>[8,2,5,7,1,3,4,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,2,4,6],[3,5,7],[8]]=>[8,3,5,7,1,2,4,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,3,4,5],[2,6,7],[8]]=>[8,2,6,7,1,3,4,5]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,2,3,5],[4,6,7],[8]]=>[8,4,6,7,1,2,3,5]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,2,3,4],[5,6,7],[8]]=>[8,5,6,7,1,2,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[[1,4,7,8],[2,5],[3,6]]=>[3,6,2,5,1,4,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,3,7,8],[2,5],[4,6]]=>[4,6,2,5,1,3,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,2,7,8],[3,5],[4,6]]=>[4,6,3,5,1,2,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,3,7,8],[2,4],[5,6]]=>[5,6,2,4,1,3,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,2,7,8],[3,4],[5,6]]=>[5,6,3,4,1,2,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,4,6,8],[2,5],[3,7]]=>[3,7,2,5,1,4,6,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,2,6,8],[3,5],[4,7]]=>[4,7,3,5,1,2,6,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,4,5,8],[2,6],[3,7]]=>[3,7,2,6,1,4,5,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,2,5,8],[3,6],[4,7]]=>[4,7,3,6,1,2,5,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,3,4,8],[2,6],[5,7]]=>[5,7,2,6,1,3,4,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,3,4,8],[2,5],[6,7]]=>[6,7,2,5,1,3,4,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,3,6,7],[2,5],[4,8]]=>[4,8,2,5,1,3,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,3,6,7],[2,4],[5,8]]=>[5,8,2,4,1,3,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,2,6,7],[3,4],[5,8]]=>[5,8,3,4,1,2,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,2,4,7],[3,6],[5,8]]=>[5,8,3,6,1,2,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,2,3,7],[4,6],[5,8]]=>[5,8,4,6,1,2,3,7]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,2,4,7],[3,5],[6,8]]=>[6,8,3,5,1,2,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,4,5,6],[2,7],[3,8]]=>[3,8,2,7,1,4,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,3,5,6],[2,7],[4,8]]=>[4,8,2,7,1,3,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,2,5,6],[3,7],[4,8]]=>[4,8,3,7,1,2,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,3,4,6],[2,7],[5,8]]=>[5,8,2,7,1,3,4,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,2,4,6],[3,7],[5,8]]=>[5,8,3,7,1,2,4,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,2,3,6],[4,7],[5,8]]=>[5,8,4,7,1,2,3,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,3,4,5],[2,7],[6,8]]=>[6,8,2,7,1,3,4,5]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,2,4,5],[3,7],[6,8]]=>[6,8,3,7,1,2,4,5]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,2,3,4],[5,7],[6,8]]=>[6,8,5,7,1,2,3,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,3,5,6],[2,4],[7,8]]=>[7,8,2,4,1,3,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,2,5,6],[3,4],[7,8]]=>[7,8,3,4,1,2,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,3,4,6],[2,5],[7,8]]=>[7,8,2,5,1,3,4,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,2,4,6],[3,5],[7,8]]=>[7,8,3,5,1,2,4,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,2,3,6],[4,5],[7,8]]=>[7,8,4,5,1,2,3,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,2,3,5],[4,6],[7,8]]=>[7,8,4,6,1,2,3,5]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,2,3,4],[5,6],[7,8]]=>[7,8,5,6,1,2,3,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[[1,5,7,8],[2,6],[3],[4]]=>[4,3,2,6,1,5,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,4,7,8],[2,6],[3],[5]]=>[5,3,2,6,1,4,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,3,7,8],[2,6],[4],[5]]=>[5,4,2,6,1,3,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,2,7,8],[3,6],[4],[5]]=>[5,4,3,6,1,2,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,4,7,8],[2,5],[3],[6]]=>[6,3,2,5,1,4,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,2,7,8],[3,5],[4],[6]]=>[6,4,3,5,1,2,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,3,7,8],[2,4],[5],[6]]=>[6,5,2,4,1,3,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,5,6,8],[2,7],[3],[4]]=>[4,3,2,7,1,5,6,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,4,6,8],[2,7],[3],[5]]=>[5,3,2,7,1,4,6,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,4,5,8],[2,7],[3],[6]]=>[6,3,2,7,1,4,5,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,3,5,8],[2,7],[4],[6]]=>[6,4,2,7,1,3,5,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,2,5,8],[3,7],[4],[6]]=>[6,4,3,7,1,2,5,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,3,4,8],[2,7],[5],[6]]=>[6,5,2,7,1,3,4,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,2,4,8],[3,7],[5],[6]]=>[6,5,3,7,1,2,4,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,4,6,8],[2,5],[3],[7]]=>[7,3,2,5,1,4,6,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,3,6,8],[2,5],[4],[7]]=>[7,4,2,5,1,3,6,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,4,5,8],[2,6],[3],[7]]=>[7,3,2,6,1,4,5,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,3,5,8],[2,6],[4],[7]]=>[7,4,2,6,1,3,5,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,2,5,8],[3,6],[4],[7]]=>[7,4,3,6,1,2,5,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,3,4,8],[2,6],[5],[7]]=>[7,5,2,6,1,3,4,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,2,4,8],[3,6],[5],[7]]=>[7,5,3,6,1,2,4,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,5,6,7],[2,8],[3],[4]]=>[4,3,2,8,1,5,6,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,4,6,7],[2,8],[3],[5]]=>[5,3,2,8,1,4,6,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,4,5,7],[2,8],[3],[6]]=>[6,3,2,8,1,4,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,3,5,7],[2,8],[4],[6]]=>[6,4,2,8,1,3,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,2,5,7],[3,8],[4],[6]]=>[6,4,3,8,1,2,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,3,4,7],[2,8],[5],[6]]=>[6,5,2,8,1,3,4,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,2,4,7],[3,8],[5],[6]]=>[6,5,3,8,1,2,4,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,4,5,6],[2,8],[3],[7]]=>[7,3,2,8,1,4,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,3,5,6],[2,8],[4],[7]]=>[7,4,2,8,1,3,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,2,5,6],[3,8],[4],[7]]=>[7,4,3,8,1,2,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,2,4,6],[3,8],[5],[7]]=>[7,5,3,8,1,2,4,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,2,3,6],[4,8],[5],[7]]=>[7,5,4,8,1,2,3,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,3,4,5],[2,8],[6],[7]]=>[7,6,2,8,1,3,4,5]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,2,3,4],[5,8],[6],[7]]=>[7,6,5,8,1,2,3,4]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,4,6,7],[2,5],[3],[8]]=>[8,3,2,5,1,4,6,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,3,6,7],[2,5],[4],[8]]=>[8,4,2,5,1,3,6,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,2,6,7],[3,4],[5],[8]]=>[8,5,3,4,1,2,6,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,4,5,7],[2,6],[3],[8]]=>[8,3,2,6,1,4,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,3,5,7],[2,6],[4],[8]]=>[8,4,2,6,1,3,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,2,4,7],[3,6],[5],[8]]=>[8,5,3,6,1,2,4,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,3,5,7],[2,4],[6],[8]]=>[8,6,2,4,1,3,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,2,5,7],[3,4],[6],[8]]=>[8,6,3,4,1,2,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,3,4,7],[2,5],[6],[8]]=>[8,6,2,5,1,3,4,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,2,3,7],[4,5],[6],[8]]=>[8,6,4,5,1,2,3,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,4,5,6],[2,7],[3],[8]]=>[8,3,2,7,1,4,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,3,5,6],[2,7],[4],[8]]=>[8,4,2,7,1,3,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,2,5,6],[3,7],[4],[8]]=>[8,4,3,7,1,2,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,3,4,6],[2,7],[5],[8]]=>[8,5,2,7,1,3,4,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,2,4,6],[3,7],[5],[8]]=>[8,5,3,7,1,2,4,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,2,4,5],[3,7],[6],[8]]=>[8,6,3,7,1,2,4,5]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,2,3,4],[5,7],[6],[8]]=>[8,6,5,7,1,2,3,4]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,3,5,6],[2,4],[7],[8]]=>[8,7,2,4,1,3,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,2,5,6],[3,4],[7],[8]]=>[8,7,3,4,1,2,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,3,4,6],[2,5],[7],[8]]=>[8,7,2,5,1,3,4,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,2,4,6],[3,5],[7],[8]]=>[8,7,3,5,1,2,4,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,3,4,5],[2,6],[7],[8]]=>[8,7,2,6,1,3,4,5]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,2,4,5],[3,6],[7],[8]]=>[8,7,3,6,1,2,4,5]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,2,3,5],[4,6],[7],[8]]=>[8,7,4,6,1,2,3,5]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,2,3,4],[5,6],[7],[8]]=>[8,7,5,6,1,2,3,4]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[[1,6,7,8],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,5,7,8],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,3,7,8],[2],[4],[5],[6]]=>[6,5,4,2,1,3,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,2,7,8],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,5,6,8],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,4,6,8],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,2,6,8],[3],[4],[5],[7]]=>[7,5,4,3,1,2,6,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,4,5,8],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,3,5,8],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,2,5,8],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,3,4,8],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,2,3,8],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,5,6,7],[2],[3],[4],[8]]=>[8,4,3,2,1,5,6,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,4,6,7],[2],[3],[5],[8]]=>[8,5,3,2,1,4,6,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,3,6,7],[2],[4],[5],[8]]=>[8,5,4,2,1,3,6,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,4,5,7],[2],[3],[6],[8]]=>[8,6,3,2,1,4,5,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,3,5,7],[2],[4],[6],[8]]=>[8,6,4,2,1,3,5,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,2,5,7],[3],[4],[6],[8]]=>[8,6,4,3,1,2,5,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,3,4,7],[2],[5],[6],[8]]=>[8,6,5,2,1,3,4,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,2,3,7],[4],[5],[6],[8]]=>[8,6,5,4,1,2,3,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,4,5,6],[2],[3],[7],[8]]=>[8,7,3,2,1,4,5,6]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,3,5,6],[2],[4],[7],[8]]=>[8,7,4,2,1,3,5,6]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,3,4,6],[2],[5],[7],[8]]=>[8,7,5,2,1,3,4,6]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,2,4,6],[3],[5],[7],[8]]=>[8,7,5,3,1,2,4,6]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,2,3,6],[4],[5],[7],[8]]=>[8,7,5,4,1,2,3,6]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,3,4,5],[2],[6],[7],[8]]=>[8,7,6,2,1,3,4,5]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,2,4,5],[3],[6],[7],[8]]=>[8,7,6,3,1,2,4,5]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,2,3,5],[4],[6],[7],[8]]=>[8,7,6,4,1,2,3,5]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,2,3,4],[5],[6],[7],[8]]=>[8,7,6,5,1,2,3,4]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[[1,4,7],[2,5,8],[3,6]]=>[3,6,2,5,8,1,4,7]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[[1,2,7],[3,5,8],[4,6]]=>[4,6,3,5,8,1,2,7]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[[1,3,7],[2,4,8],[5,6]]=>[5,6,2,4,8,1,3,7]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[[1,3,6],[2,5,8],[4,7]]=>[4,7,2,5,8,1,3,6]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[[1,2,6],[3,5,8],[4,7]]=>[4,7,3,5,8,1,2,6]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[[1,3,6],[2,4,8],[5,7]]=>[5,7,2,4,8,1,3,6]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[[1,2,6],[3,4,8],[5,7]]=>[5,7,3,4,8,1,2,6]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[[1,2,5],[3,6,8],[4,7]]=>[4,7,3,6,8,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[[1,3,4],[2,6,8],[5,7]]=>[5,7,2,6,8,1,3,4]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[[1,2,3],[4,6,8],[5,7]]=>[5,7,4,6,8,1,2,3]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[[1,2,5],[3,4,8],[6,7]]=>[6,7,3,4,8,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[[1,2,4],[3,5,8],[6,7]]=>[6,7,3,5,8,1,2,4]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[[1,2,3],[4,5,8],[6,7]]=>[6,7,4,5,8,1,2,3]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[[1,4,6],[2,5,7],[3,8]]=>[3,8,2,5,7,1,4,6]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[[1,2,6],[3,5,7],[4,8]]=>[4,8,3,5,7,1,2,6]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[[1,3,6],[2,4,7],[5,8]]=>[5,8,2,4,7,1,3,6]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[[1,4,5],[2,6,7],[3,8]]=>[3,8,2,6,7,1,4,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[[1,3,4],[2,6,7],[5,8]]=>[5,8,2,6,7,1,3,4]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[[1,2,4],[3,6,7],[5,8]]=>[5,8,3,6,7,1,2,4]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[[1,3,4],[2,5,7],[6,8]]=>[6,8,2,5,7,1,3,4]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[[1,3,5],[2,4,6],[7,8]]=>[7,8,2,4,6,1,3,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[[1,2,5],[3,4,6],[7,8]]=>[7,8,3,4,6,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[[1,3,4],[2,5,6],[7,8]]=>[7,8,2,5,6,1,3,4]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[[1,2,4],[3,5,6],[7,8]]=>[7,8,3,5,6,1,2,4]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[[1,2,3],[4,5,6],[7,8]]=>[7,8,4,5,6,1,2,3]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[[1,5,7],[2,6,8],[3],[4]]=>[4,3,2,6,8,1,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,4,7],[2,6,8],[3],[5]]=>[5,3,2,6,8,1,4,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,3,7],[2,6,8],[4],[5]]=>[5,4,2,6,8,1,3,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,2,7],[3,6,8],[4],[5]]=>[5,4,3,6,8,1,2,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,4,7],[2,5,8],[3],[6]]=>[6,3,2,5,8,1,4,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,2,7],[3,5,8],[4],[6]]=>[6,4,3,5,8,1,2,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,3,7],[2,4,8],[5],[6]]=>[6,5,2,4,8,1,3,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,5,6],[2,7,8],[3],[4]]=>[4,3,2,7,8,1,5,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,4,6],[2,7,8],[3],[5]]=>[5,3,2,7,8,1,4,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,3,6],[2,7,8],[4],[5]]=>[5,4,2,7,8,1,3,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,2,6],[3,7,8],[4],[5]]=>[5,4,3,7,8,1,2,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,4,5],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,3,5],[2,7,8],[4],[6]]=>[6,4,2,7,8,1,3,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,2,5],[3,7,8],[4],[6]]=>[6,4,3,7,8,1,2,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,2,3],[4,7,8],[5],[6]]=>[6,5,4,7,8,1,2,3]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,3,6],[2,5,8],[4],[7]]=>[7,4,2,5,8,1,3,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,2,6],[3,5,8],[4],[7]]=>[7,4,3,5,8,1,2,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,3,4],[2,6,8],[5],[7]]=>[7,5,2,6,8,1,3,4]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,2,4],[3,6,8],[5],[7]]=>[7,5,3,6,8,1,2,4]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,2,3],[4,6,8],[5],[7]]=>[7,5,4,6,8,1,2,3]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,3,5],[2,4,8],[6],[7]]=>[7,6,2,4,8,1,3,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,2,3],[4,5,8],[6],[7]]=>[7,6,4,5,8,1,2,3]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,4,6],[2,5,7],[3],[8]]=>[8,3,2,5,7,1,4,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,3,6],[2,5,7],[4],[8]]=>[8,4,2,5,7,1,3,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,3,6],[2,4,7],[5],[8]]=>[8,5,2,4,7,1,3,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,4,5],[2,6,7],[3],[8]]=>[8,3,2,6,7,1,4,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,3,4],[2,6,7],[5],[8]]=>[8,5,2,6,7,1,3,4]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,2,4],[3,6,7],[5],[8]]=>[8,5,3,6,7,1,2,4]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,3,5],[2,4,7],[6],[8]]=>[8,6,2,4,7,1,3,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,3,4],[2,5,7],[6],[8]]=>[8,6,2,5,7,1,3,4]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,2,4],[3,5,7],[6],[8]]=>[8,6,3,5,7,1,2,4]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,2,3],[4,5,7],[6],[8]]=>[8,6,4,5,7,1,2,3]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,3,5],[2,4,6],[7],[8]]=>[8,7,2,4,6,1,3,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,2,5],[3,4,6],[7],[8]]=>[8,7,3,4,6,1,2,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,3,4],[2,5,6],[7],[8]]=>[8,7,2,5,6,1,3,4]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,2,3],[4,5,6],[7],[8]]=>[8,7,4,5,6,1,2,3]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[[1,5,8],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,3,8],[2,6],[4,7],[5]]=>[5,4,7,2,6,1,3,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,4,8],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,3,8],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,2,8],[3,5],[4,7],[6]]=>[6,4,7,3,5,1,2,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,2,8],[3,4],[5,7],[6]]=>[6,5,7,3,4,1,2,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,5,7],[2,6],[3,8],[4]]=>[4,3,8,2,6,1,5,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,4,7],[2,6],[3,8],[5]]=>[5,3,8,2,6,1,4,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,3,7],[2,6],[4,8],[5]]=>[5,4,8,2,6,1,3,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,2,7],[3,6],[4,8],[5]]=>[5,4,8,3,6,1,2,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,4,7],[2,5],[3,8],[6]]=>[6,3,8,2,5,1,4,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,3,7],[2,5],[4,8],[6]]=>[6,4,8,2,5,1,3,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,2,7],[3,5],[4,8],[6]]=>[6,4,8,3,5,1,2,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,3,7],[2,4],[5,8],[6]]=>[6,5,8,2,4,1,3,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,2,7],[3,4],[5,8],[6]]=>[6,5,8,3,4,1,2,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,5,6],[2,7],[3,8],[4]]=>[4,3,8,2,7,1,5,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,4,6],[2,7],[3,8],[5]]=>[5,3,8,2,7,1,4,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,3,6],[2,7],[4,8],[5]]=>[5,4,8,2,7,1,3,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,2,6],[3,7],[4,8],[5]]=>[5,4,8,3,7,1,2,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,4,5],[2,7],[3,8],[6]]=>[6,3,8,2,7,1,4,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,3,5],[2,7],[4,8],[6]]=>[6,4,8,2,7,1,3,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,4,6],[2,5],[3,8],[7]]=>[7,3,8,2,5,1,4,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,2,6],[3,5],[4,8],[7]]=>[7,4,8,3,5,1,2,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,3,6],[2,4],[5,8],[7]]=>[7,5,8,2,4,1,3,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,3,4],[2,6],[5,8],[7]]=>[7,5,8,2,6,1,3,4]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,2,3],[4,6],[5,8],[7]]=>[7,5,8,4,6,1,2,3]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,3,4],[2,5],[6,8],[7]]=>[7,6,8,2,5,1,3,4]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,2,4],[3,5],[6,8],[7]]=>[7,6,8,3,5,1,2,4]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,3,7],[2,5],[4,6],[8]]=>[8,4,6,2,5,1,3,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,3,7],[2,4],[5,6],[8]]=>[8,5,6,2,4,1,3,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,2,7],[3,4],[5,6],[8]]=>[8,5,6,3,4,1,2,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,2,6],[3,5],[4,7],[8]]=>[8,4,7,3,5,1,2,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,3,6],[2,4],[5,7],[8]]=>[8,5,7,2,4,1,3,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,4,5],[2,6],[3,7],[8]]=>[8,3,7,2,6,1,4,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,3,5],[2,6],[4,7],[8]]=>[8,4,7,2,6,1,3,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,2,5],[3,6],[4,7],[8]]=>[8,4,7,3,6,1,2,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,3,4],[2,6],[5,7],[8]]=>[8,5,7,2,6,1,3,4]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,3,5],[2,4],[6,7],[8]]=>[8,6,7,2,4,1,3,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,2,5],[3,4],[6,7],[8]]=>[8,6,7,3,4,1,2,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,3,4],[2,5],[6,7],[8]]=>[8,6,7,2,5,1,3,4]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,2,4],[3,5],[6,7],[8]]=>[8,6,7,3,5,1,2,4]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,2,3],[4,5],[6,7],[8]]=>[8,6,7,4,5,1,2,3]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[[1,6,8],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,5,8],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,4,8],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,3,8],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,2,8],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,4,8],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,3,8],[2,6],[4],[5],[7]]=>[7,5,4,2,6,1,3,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,2,8],[3,4],[5],[6],[7]]=>[7,6,5,3,4,1,2,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,6,7],[2,8],[3],[4],[5]]=>[5,4,3,2,8,1,6,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,4,7],[2,8],[3],[5],[6]]=>[6,5,3,2,8,1,4,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,2,7],[3,8],[4],[5],[6]]=>[6,5,4,3,8,1,2,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,4,6],[2,8],[3],[5],[7]]=>[7,5,3,2,8,1,4,6]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,3,6],[2,8],[4],[5],[7]]=>[7,5,4,2,8,1,3,6]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,4,5],[2,8],[3],[6],[7]]=>[7,6,3,2,8,1,4,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,2,5],[3,8],[4],[6],[7]]=>[7,6,4,3,8,1,2,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,3,4],[2,8],[5],[6],[7]]=>[7,6,5,2,8,1,3,4]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,2,3],[4,8],[5],[6],[7]]=>[7,6,5,4,8,1,2,3]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,4,7],[2,6],[3],[5],[8]]=>[8,5,3,2,6,1,4,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,3,7],[2,6],[4],[5],[8]]=>[8,5,4,2,6,1,3,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,2,7],[3,6],[4],[5],[8]]=>[8,5,4,3,6,1,2,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,4,7],[2,5],[3],[6],[8]]=>[8,6,3,2,5,1,4,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,3,7],[2,4],[5],[6],[8]]=>[8,6,5,2,4,1,3,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,2,7],[3,4],[5],[6],[8]]=>[8,6,5,3,4,1,2,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,4,6],[2,7],[3],[5],[8]]=>[8,5,3,2,7,1,4,6]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,4,5],[2,7],[3],[6],[8]]=>[8,6,3,2,7,1,4,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,2,5],[3,7],[4],[6],[8]]=>[8,6,4,3,7,1,2,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,4,6],[2,5],[3],[7],[8]]=>[8,7,3,2,5,1,4,6]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,2,6],[3,4],[5],[7],[8]]=>[8,7,5,3,4,1,2,6]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,4,5],[2,6],[3],[7],[8]]=>[8,7,3,2,6,1,4,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,3,5],[2,6],[4],[7],[8]]=>[8,7,4,2,6,1,3,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,2,5],[3,6],[4],[7],[8]]=>[8,7,4,3,6,1,2,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,3,4],[2,6],[5],[7],[8]]=>[8,7,5,2,6,1,3,4]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,2,4],[3,6],[5],[7],[8]]=>[8,7,5,3,6,1,2,4]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,2,3],[4,6],[5],[7],[8]]=>[8,7,5,4,6,1,2,3]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,3,5],[2,4],[6],[7],[8]]=>[8,7,6,2,4,1,3,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,2,5],[3,4],[6],[7],[8]]=>[8,7,6,3,4,1,2,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,3,4],[2,5],[6],[7],[8]]=>[8,7,6,2,5,1,3,4]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,2,4],[3,5],[6],[7],[8]]=>[8,7,6,3,5,1,2,4]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,2,3],[4,5],[6],[7],[8]]=>[8,7,6,4,5,1,2,3]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[[1,7,8],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[[1,6,8],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[[1,5,8],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[[1,4,8],[2],[3],[5],[6],[7]]=>[7,6,5,3,2,1,4,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[[1,3,8],[2],[4],[5],[6],[7]]=>[7,6,5,4,2,1,3,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[[1,2,8],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[[1,6,7],[2],[3],[4],[5],[8]]=>[8,5,4,3,2,1,6,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[[1,5,7],[2],[3],[4],[6],[8]]=>[8,6,4,3,2,1,5,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[[1,4,7],[2],[3],[5],[6],[8]]=>[8,6,5,3,2,1,4,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[[1,3,7],[2],[4],[5],[6],[8]]=>[8,6,5,4,2,1,3,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[[1,2,7],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,1,2,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[[1,5,6],[2],[3],[4],[7],[8]]=>[8,7,4,3,2,1,5,6]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[[1,4,6],[2],[3],[5],[7],[8]]=>[8,7,5,3,2,1,4,6]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[[1,2,6],[3],[4],[5],[7],[8]]=>[8,7,5,4,3,1,2,6]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[[1,4,5],[2],[3],[6],[7],[8]]=>[8,7,6,3,2,1,4,5]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[[1,3,5],[2],[4],[6],[7],[8]]=>[8,7,6,4,2,1,3,5]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[[1,2,5],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,1,2,5]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[[1,3,4],[2],[5],[6],[7],[8]]=>[8,7,6,5,2,1,3,4]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[[1,2,4],[3],[5],[6],[7],[8]]=>[8,7,6,5,3,1,2,4]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[[1,2,3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,1,2,3]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[[1,5],[2,6],[3,7],[4,8]]=>[4,8,3,7,2,6,1,5]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]
[[1,4],[2,6],[3,7],[5,8]]=>[5,8,3,7,2,6,1,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]
[[1,3],[2,6],[4,7],[5,8]]=>[5,8,4,7,2,6,1,3]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]
[[1,2],[3,6],[4,7],[5,8]]=>[5,8,4,7,3,6,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]
[[1,4],[2,5],[3,7],[6,8]]=>[6,8,3,7,2,5,1,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]
[[1,3],[2,5],[4,7],[6,8]]=>[6,8,4,7,2,5,1,3]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]
[[1,2],[3,5],[4,7],[6,8]]=>[6,8,4,7,3,5,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]
[[1,3],[2,4],[5,7],[6,8]]=>[6,8,5,7,2,4,1,3]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]
[[1,2],[3,4],[5,7],[6,8]]=>[6,8,5,7,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]
[[1,4],[2,5],[3,6],[7,8]]=>[7,8,3,6,2,5,1,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]
[[1,3],[2,5],[4,6],[7,8]]=>[7,8,4,6,2,5,1,3]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]
[[1,2],[3,5],[4,6],[7,8]]=>[7,8,4,6,3,5,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]
[[1,3],[2,4],[5,6],[7,8]]=>[7,8,5,6,2,4,1,3]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]
[[1,2],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]
[[1,6],[2,7],[3,8],[4],[5]]=>[5,4,3,8,2,7,1,6]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[[1,5],[2,7],[3,8],[4],[6]]=>[6,4,3,8,2,7,1,5]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[[1,4],[2,7],[3,8],[5],[6]]=>[6,5,3,8,2,7,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[[1,2],[3,7],[4,8],[5],[6]]=>[6,5,4,8,3,7,1,2]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[[1,5],[2,6],[3,8],[4],[7]]=>[7,4,3,8,2,6,1,5]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[[1,4],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[[1,3],[2,6],[4,8],[5],[7]]=>[7,5,4,8,2,6,1,3]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[[1,4],[2,5],[3,8],[6],[7]]=>[7,6,3,8,2,5,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[[1,3],[2,5],[4,8],[6],[7]]=>[7,6,4,8,2,5,1,3]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[[1,3],[2,4],[5,8],[6],[7]]=>[7,6,5,8,2,4,1,3]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[[1,2],[3,4],[5,8],[6],[7]]=>[7,6,5,8,3,4,1,2]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[[1,5],[2,6],[3,7],[4],[8]]=>[8,4,3,7,2,6,1,5]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[[1,4],[2,6],[3,7],[5],[8]]=>[8,5,3,7,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[[1,3],[2,6],[4,7],[5],[8]]=>[8,5,4,7,2,6,1,3]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[[1,2],[3,6],[4,7],[5],[8]]=>[8,5,4,7,3,6,1,2]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[[1,4],[2,5],[3,7],[6],[8]]=>[8,6,3,7,2,5,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[[1,3],[2,5],[4,7],[6],[8]]=>[8,6,4,7,2,5,1,3]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[[1,2],[3,5],[4,7],[6],[8]]=>[8,6,4,7,3,5,1,2]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[[1,3],[2,4],[5,7],[6],[8]]=>[8,6,5,7,2,4,1,3]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[[1,2],[3,4],[5,7],[6],[8]]=>[8,6,5,7,3,4,1,2]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[[1,4],[2,5],[3,6],[7],[8]]=>[8,7,3,6,2,5,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[[1,3],[2,5],[4,6],[7],[8]]=>[8,7,4,6,2,5,1,3]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[[1,2],[3,5],[4,6],[7],[8]]=>[8,7,4,6,3,5,1,2]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[[1,3],[2,4],[5,6],[7],[8]]=>[8,7,5,6,2,4,1,3]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[[1,2],[3,4],[5,6],[7],[8]]=>[8,7,5,6,3,4,1,2]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[[1,7],[2,8],[3],[4],[5],[6]]=>[6,5,4,3,2,8,1,7]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[[1,6],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[[1,3],[2,8],[4],[5],[6],[7]]=>[7,6,5,4,2,8,1,3]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[[1,2],[3,8],[4],[5],[6],[7]]=>[7,6,5,4,3,8,1,2]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[[1,6],[2,7],[3],[4],[5],[8]]=>[8,5,4,3,2,7,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[[1,2],[3,7],[4],[5],[6],[8]]=>[8,6,5,4,3,7,1,2]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[[1,5],[2,6],[3],[4],[7],[8]]=>[8,7,4,3,2,6,1,5]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[[1,4],[2,6],[3],[5],[7],[8]]=>[8,7,5,3,2,6,1,4]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[[1,3],[2,6],[4],[5],[7],[8]]=>[8,7,5,4,2,6,1,3]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[[1,4],[2,5],[3],[6],[7],[8]]=>[8,7,6,3,2,5,1,4]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[[1,3],[2,5],[4],[6],[7],[8]]=>[8,7,6,4,2,5,1,3]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[[1,3],[2,4],[5],[6],[7],[8]]=>[8,7,6,5,2,4,1,3]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[[1,2],[3,4],[5],[6],[7],[8]]=>[8,7,6,5,3,4,1,2]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[[1,8],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]
[[1,7],[2],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,1,7]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]
[[1,6],[2],[3],[4],[5],[7],[8]]=>[8,7,5,4,3,2,1,6]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]
[[1,5],[2],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,2,1,5]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]
[[1,4],[2],[3],[5],[6],[7],[8]]=>[8,7,6,5,3,2,1,4]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]
[[1,3],[2],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,2,1,3]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]
[[1,2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,1,2]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]
[[1],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]
[[1,3,5,7,9],[2,4,6,8,10]]=>[2,4,6,8,10,1,3,5,7,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,3,5,7,8],[2,4,6,9,10]]=>[2,4,6,9,10,1,3,5,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,3,5,6,9],[2,4,7,8,10]]=>[2,4,7,8,10,1,3,5,6,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,3,5,6,8],[2,4,7,9,10]]=>[2,4,7,9,10,1,3,5,6,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,3,5,6,7],[2,4,8,9,10]]=>[2,4,8,9,10,1,3,5,6,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,3,4,7,9],[2,5,6,8,10]]=>[2,5,6,8,10,1,3,4,7,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,3,4,7,8],[2,5,6,9,10]]=>[2,5,6,9,10,1,3,4,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,3,4,6,9],[2,5,7,8,10]]=>[2,5,7,8,10,1,3,4,6,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,3,4,6,8],[2,5,7,9,10]]=>[2,5,7,9,10,1,3,4,6,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,3,4,6,7],[2,5,8,9,10]]=>[2,5,8,9,10,1,3,4,6,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,3,4,5,9],[2,6,7,8,10]]=>[2,6,7,8,10,1,3,4,5,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,3,4,5,8],[2,6,7,9,10]]=>[2,6,7,9,10,1,3,4,5,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,3,4,5,7],[2,6,8,9,10]]=>[2,6,8,9,10,1,3,4,5,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,3,4,5,6],[2,7,8,9,10]]=>[2,7,8,9,10,1,3,4,5,6]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,5,7,9],[3,4,6,8,10]]=>[3,4,6,8,10,1,2,5,7,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,5,7,8],[3,4,6,9,10]]=>[3,4,6,9,10,1,2,5,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,5,6,9],[3,4,7,8,10]]=>[3,4,7,8,10,1,2,5,6,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,5,6,8],[3,4,7,9,10]]=>[3,4,7,9,10,1,2,5,6,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,5,6,7],[3,4,8,9,10]]=>[3,4,8,9,10,1,2,5,6,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,4,7,9],[3,5,6,8,10]]=>[3,5,6,8,10,1,2,4,7,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,4,7,8],[3,5,6,9,10]]=>[3,5,6,9,10,1,2,4,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,4,6,9],[3,5,7,8,10]]=>[3,5,7,8,10,1,2,4,6,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,4,6,8],[3,5,7,9,10]]=>[3,5,7,9,10,1,2,4,6,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,4,6,7],[3,5,8,9,10]]=>[3,5,8,9,10,1,2,4,6,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,4,5,9],[3,6,7,8,10]]=>[3,6,7,8,10,1,2,4,5,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,4,5,8],[3,6,7,9,10]]=>[3,6,7,9,10,1,2,4,5,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,4,5,7],[3,6,8,9,10]]=>[3,6,8,9,10,1,2,4,5,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,4,5,6],[3,7,8,9,10]]=>[3,7,8,9,10,1,2,4,5,6]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,3,7,9],[4,5,6,8,10]]=>[4,5,6,8,10,1,2,3,7,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,3,7,8],[4,5,6,9,10]]=>[4,5,6,9,10,1,2,3,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,3,6,9],[4,5,7,8,10]]=>[4,5,7,8,10,1,2,3,6,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,3,6,8],[4,5,7,9,10]]=>[4,5,7,9,10,1,2,3,6,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,3,6,7],[4,5,8,9,10]]=>[4,5,8,9,10,1,2,3,6,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,3,5,9],[4,6,7,8,10]]=>[4,6,7,8,10,1,2,3,5,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,3,5,8],[4,6,7,9,10]]=>[4,6,7,9,10,1,2,3,5,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,3,5,7],[4,6,8,9,10]]=>[4,6,8,9,10,1,2,3,5,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,3,5,6],[4,7,8,9,10]]=>[4,7,8,9,10,1,2,3,5,6]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,3,4,9],[5,6,7,8,10]]=>[5,6,7,8,10,1,2,3,4,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,3,4,8],[5,6,7,9,10]]=>[5,6,7,9,10,1,2,3,4,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,3,4,7],[5,6,8,9,10]]=>[5,6,8,9,10,1,2,3,4,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,3,4,6],[5,7,8,9,10]]=>[5,7,8,9,10,1,2,3,4,6]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,3,4,5],[6,7,8,9,10]]=>[6,7,8,9,10,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[[1,2,3,4,5,6,7,8,9]]=>[1,2,3,4,5,6,7,8,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]
[[1,2,3,4,5,6,7,8],[9]]=>[9,1,2,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,9,8,7,6,5,4,3,2]
[[1,2,3,4,5,6,7],[8,9]]=>[8,9,1,2,3,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[2,1,9,8,7,6,5,4,3]
[[1,2,3,4,5,6,7],[8],[9]]=>[9,8,1,2,3,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,9,8,7,6,5,4,3]
[[1,2,3,4,5,6],[7,8,9]]=>[7,8,9,1,2,3,4,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[3,2,1,9,8,7,6,5,4]
[[1,2,3,4,5,6],[7,8],[9]]=>[9,7,8,1,2,3,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,3,2,9,8,7,6,5,4]
[[1,2,3,4,5,6],[7],[8],[9]]=>[9,8,7,1,2,3,4,5,6]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,9,8,7,6,5,4]
[[1,2,3,4,5],[6,7,8,9]]=>[6,7,8,9,1,2,3,4,5]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[4,3,2,1,9,8,7,6,5]
[[1,2,3,4,5],[6,7],[8],[9]]=>[9,8,6,7,1,2,3,4,5]=>[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,2,4,3,9,8,7,6,5]
[[1,2,3,4,5],[6],[7],[8],[9]]=>[9,8,7,6,1,2,3,4,5]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,9,8,7,6,5]
[[1,2,3,4],[5,6],[7],[8],[9]]=>[9,8,7,5,6,1,2,3,4]=>[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,3,5,4,9,8,7,6]
[[1,2,3,4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,1,2,3,4]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,9,8,7,6]
[[1,2,3],[4,5],[6],[7],[8],[9]]=>[9,8,7,6,4,5,1,2,3]=>[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,4,6,5,9,8,7]
[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,1,2,3]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]
[[1,2],[3,4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,3,4,1,2]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,7,6,9,8]
[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,1,2]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,9,8]
[[1],[2],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]
[[1,2,3,4,5,6,7,8,9,10]]=>[1,2,3,4,5,6,7,8,9,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]
[[1,2,3,4,5,6,7,8,9],[10]]=>[10,1,2,3,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]
[[1,2,3,4,5,6,7,8],[9,10]]=>[9,10,1,2,3,4,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,1,10,9,8,7,6,5,4,3]
[[1,2,3,4,5,6,7,8],[9],[10]]=>[10,9,1,2,3,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,2,10,9,8,7,6,5,4,3]
[[1,2,3,4,5,6,7],[8,9,10]]=>[8,9,10,1,2,3,4,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[3,2,1,10,9,8,7,6,5,4]
[[1,2,3,4,5,6,7],[8],[9],[10]]=>[10,9,8,1,2,3,4,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,3,10,9,8,7,6,5,4]
[[1,2,3,4,5,6],[7,8,9,10]]=>[7,8,9,10,1,2,3,4,5,6]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[4,3,2,1,10,9,8,7,6,5]
[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[10,9,8,7,1,2,3,4,5,6]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,4,10,9,8,7,6,5]
[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,1,2,3,4,5]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,5,10,9,8,7,6]
[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,1,2,3,4]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,6,10,9,8,7]
[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,1,2,3]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,7,10,9,8]
[[1,2],[3,4],[5,6],[7,8],[9,10]]=>[9,10,7,8,5,6,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,2],[3,4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,3,4,1,2]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,6,8,7,10,9]
[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,3,1,2]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]
[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3,4,5,6,7,8,9],[2]]=>[2,1,3,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,9,8,7,6,5,4,3,2]
[[1,2,5,6,7,8,9],[3,4]]=>[3,4,1,2,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[2,1,9,8,7,6,5,4,3]
[[1,4,5,6,7,8,9],[2],[3]]=>[3,2,1,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,9,8,7,6,5,4,3]
[[1,2,3,7,8,9],[4,5,6]]=>[4,5,6,1,2,3,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[3,2,1,9,8,7,6,5,4]
[[1,3,6,7,8,9],[2,5],[4]]=>[4,2,5,1,3,6,7,8,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,3,2,9,8,7,6,5,4]
[[1,5,6,7,8,9],[2],[3],[4]]=>[4,3,2,1,5,6,7,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,9,8,7,6,5,4]
[[1,2,3,4,9],[5,6,7,8]]=>[5,6,7,8,1,2,3,4,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[4,3,2,1,9,8,7,6,5]
[[1,4,7,8,9],[2,6],[3],[5]]=>[5,3,2,6,1,4,7,8,9]=>[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,2,4,3,9,8,7,6,5]
[[1,6,7,8,9],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,9,8,7,6,5]
[[1,5,8,9],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5,8,9]=>[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,3,5,4,9,8,7,6]
[[1,7,8,9],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7,8,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,9,8,7,6]
[[1,6,9],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6,9]=>[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,4,6,5,9,8,7]
[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]
[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,9,1,7]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,7,6,9,8]
[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,9,8]
[[1,3,4,5,6,7,8,9,10],[2]]=>[2,1,3,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]
[[1,2,5,6,7,8,9,10],[3,4]]=>[3,4,1,2,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,1,10,9,8,7,6,5,4,3]
[[1,4,5,6,7,8,9,10],[2],[3]]=>[3,2,1,4,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,2,10,9,8,7,6,5,4,3]
[[1,2,3,7,8,9,10],[4,5,6]]=>[4,5,6,1,2,3,7,8,9,10]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[3,2,1,10,9,8,7,6,5,4]
[[1,5,6,7,8,9,10],[2],[3],[4]]=>[4,3,2,1,5,6,7,8,9,10]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,3,10,9,8,7,6,5,4]
[[1,2,3,4,9,10],[5,6,7,8]]=>[5,6,7,8,1,2,3,4,9,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[4,3,2,1,10,9,8,7,6,5]
[[1,6,7,8,9,10],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8,9,10]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,4,10,9,8,7,6,5]
[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7,8,9,10]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,5,10,9,8,7,6]
[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8,9,10]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,6,10,9,8,7]
[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1,9,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,7,10,9,8]
[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>[9,7,6,5,4,3,2,10,1,8]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,6,8,7,10,9]
[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]
[[1,8],[2,9],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,9,1,8]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,7,6,9,8]
[[1,7,9],[2,8],[3],[4],[5],[6]]=>[6,5,4,3,2,8,1,7,9]=>[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,4,6,5,9,8,7]
[[1,6,8,9],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6,8,9]=>[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,3,5,4,9,8,7,6]
[[1,5,7,8,9],[2,6],[3],[4]]=>[4,3,2,6,1,5,7,8,9]=>[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,2,4,3,9,8,7,6,5]
[[1,4,6,7,8,9],[2,5],[3]]=>[3,2,5,1,4,6,7,8,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,3,2,9,8,7,6,5,4]
[[1,3,5,7,9],[2,4,6,8]]=>[2,4,6,8,1,3,5,7,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[4,3,2,1,9,8,7,6,5]
[[1,3,5,7,8,9],[2,4,6]]=>[2,4,6,1,3,5,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[3,2,1,9,8,7,6,5,4]
[[1,3,5,6,7,8,9],[2,4]]=>[2,4,1,3,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[2,1,9,8,7,6,5,4,3]
[[1,9],[2,10],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,10,1,9]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,6,8,7,10,9]
[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[5,10,4,9,3,8,2,7,1,6]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,3,5,7,9,10],[2,4,6,8]]=>[2,4,6,8,1,3,5,7,9,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[4,3,2,1,10,9,8,7,6,5]
[[1,3,5,7,8,9,10],[2,4,6]]=>[2,4,6,1,3,5,7,8,9,10]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[3,2,1,10,9,8,7,6,5,4]
[[1,3,5,6,7,8,9,10],[2,4]]=>[2,4,1,3,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,1,10,9,8,7,6,5,4,3]
[[1,3],[2,4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,2,4,1,3]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,7,6,9,8]
[[1,2,4],[3,5],[6],[7],[8],[9]]=>[9,8,7,6,3,5,1,2,4]=>[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,4,6,5,9,8,7]
[[1,2,3,5],[4,6],[7],[8],[9]]=>[9,8,7,4,6,1,2,3,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,3,5,4,9,8,7,6]
[[1,2,3,4,6],[5,7],[8],[9]]=>[9,8,5,7,1,2,3,4,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,2,4,3,9,8,7,6,5]
[[1,2,3,4,5,7],[6,8],[9]]=>[9,6,8,1,2,3,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,3,2,9,8,7,6,5,4]
[[1,2,4,6,8],[3,5,7,9]]=>[3,5,7,9,1,2,4,6,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[4,3,2,1,9,8,7,6,5]
[[1,2,3,4,6,8],[5,7,9]]=>[5,7,9,1,2,3,4,6,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[3,2,1,9,8,7,6,5,4]
[[1,2,3,4,5,6,8],[7,9]]=>[7,9,1,2,3,4,5,6,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[2,1,9,8,7,6,5,4,3]
[[1,3],[2,4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,2,4,1,3]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,6,8,7,10,9]
[[1,2,3,5,7,9],[4,6,8,10]]=>[4,6,8,10,1,2,3,5,7,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[4,3,2,1,10,9,8,7,6,5]
[[1,2,3,4,5,7,9],[6,8,10]]=>[6,8,10,1,2,3,4,5,7,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[3,2,1,10,9,8,7,6,5,4]
[[1,2,3,4,5,6,7,9],[8,10]]=>[8,10,1,2,3,4,5,6,7,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,1,10,9,8,7,6,5,4,3]
[[1,2],[3,4],[5,6],[7,9],[8,10]]=>[8,10,7,9,5,6,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,2],[3,4],[5,7],[6,8],[9,10]]=>[9,10,6,8,5,7,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,2],[3,4],[5,7],[6,9],[8,10]]=>[8,10,6,9,5,7,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,2],[3,4],[5,8],[6,9],[7,10]]=>[7,10,6,9,5,8,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,2],[3,5],[4,6],[7,8],[9,10]]=>[9,10,7,8,4,6,3,5,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,2],[3,5],[4,6],[7,9],[8,10]]=>[8,10,7,9,4,6,3,5,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,2],[3,5],[4,7],[6,8],[9,10]]=>[9,10,6,8,4,7,3,5,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,2],[3,5],[4,7],[6,9],[8,10]]=>[8,10,6,9,4,7,3,5,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,2],[3,5],[4,8],[6,9],[7,10]]=>[7,10,6,9,4,8,3,5,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,2],[3,6],[4,7],[5,8],[9,10]]=>[9,10,5,8,4,7,3,6,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,2],[3,6],[4,7],[5,9],[8,10]]=>[8,10,5,9,4,7,3,6,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,2],[3,6],[4,8],[5,9],[7,10]]=>[7,10,5,9,4,8,3,6,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,2],[3,7],[4,8],[5,9],[6,10]]=>[6,10,5,9,4,8,3,7,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,3],[2,4],[5,6],[7,8],[9,10]]=>[9,10,7,8,5,6,2,4,1,3]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,3],[2,4],[5,6],[7,9],[8,10]]=>[8,10,7,9,5,6,2,4,1,3]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,3],[2,4],[5,7],[6,8],[9,10]]=>[9,10,6,8,5,7,2,4,1,3]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,3],[2,4],[5,7],[6,9],[8,10]]=>[8,10,6,9,5,7,2,4,1,3]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,3],[2,4],[5,8],[6,9],[7,10]]=>[7,10,6,9,5,8,2,4,1,3]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,3],[2,5],[4,6],[7,8],[9,10]]=>[9,10,7,8,4,6,2,5,1,3]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,3],[2,5],[4,6],[7,9],[8,10]]=>[8,10,7,9,4,6,2,5,1,3]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,3],[2,5],[4,7],[6,8],[9,10]]=>[9,10,6,8,4,7,2,5,1,3]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,3],[2,5],[4,7],[6,9],[8,10]]=>[8,10,6,9,4,7,2,5,1,3]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,3],[2,5],[4,8],[6,9],[7,10]]=>[7,10,6,9,4,8,2,5,1,3]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,3],[2,6],[4,7],[5,8],[9,10]]=>[9,10,5,8,4,7,2,6,1,3]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,3],[2,6],[4,7],[5,9],[8,10]]=>[8,10,5,9,4,7,2,6,1,3]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,3],[2,6],[4,8],[5,9],[7,10]]=>[7,10,5,9,4,8,2,6,1,3]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,3],[2,7],[4,8],[5,9],[6,10]]=>[6,10,5,9,4,8,2,7,1,3]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,4],[2,5],[3,6],[7,8],[9,10]]=>[9,10,7,8,3,6,2,5,1,4]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,4],[2,5],[3,6],[7,9],[8,10]]=>[8,10,7,9,3,6,2,5,1,4]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,4],[2,5],[3,7],[6,8],[9,10]]=>[9,10,6,8,3,7,2,5,1,4]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,4],[2,5],[3,7],[6,9],[8,10]]=>[8,10,6,9,3,7,2,5,1,4]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,4],[2,5],[3,8],[6,9],[7,10]]=>[7,10,6,9,3,8,2,5,1,4]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,4],[2,6],[3,7],[5,8],[9,10]]=>[9,10,5,8,3,7,2,6,1,4]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,4],[2,6],[3,7],[5,9],[8,10]]=>[8,10,5,9,3,7,2,6,1,4]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,4],[2,6],[3,8],[5,9],[7,10]]=>[7,10,5,9,3,8,2,6,1,4]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,4],[2,7],[3,8],[5,9],[6,10]]=>[6,10,5,9,3,8,2,7,1,4]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,5],[2,6],[3,7],[4,8],[9,10]]=>[9,10,4,8,3,7,2,6,1,5]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,5],[2,6],[3,7],[4,9],[8,10]]=>[8,10,4,9,3,7,2,6,1,5]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,5],[2,6],[3,8],[4,9],[7,10]]=>[7,10,4,9,3,8,2,6,1,5]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,5],[2,7],[3,8],[4,9],[6,10]]=>[6,10,4,9,3,8,2,7,1,5]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[[1,2],[3,4],[5,6],[7,8],[9,11],[10,12]]=>[10,12,9,11,7,8,5,6,3,4,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,4],[5,6],[7,9],[8,10],[11,12]]=>[11,12,8,10,7,9,5,6,3,4,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,4],[5,6],[7,9],[8,11],[10,12]]=>[10,12,8,11,7,9,5,6,3,4,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,4],[5,6],[7,10],[8,11],[9,12]]=>[9,12,8,11,7,10,5,6,3,4,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,4],[5,7],[6,8],[9,10],[11,12]]=>[11,12,9,10,6,8,5,7,3,4,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,4],[5,7],[6,8],[9,11],[10,12]]=>[10,12,9,11,6,8,5,7,3,4,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,4],[5,7],[6,9],[8,10],[11,12]]=>[11,12,8,10,6,9,5,7,3,4,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,4],[5,7],[6,9],[8,11],[10,12]]=>[10,12,8,11,6,9,5,7,3,4,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,4],[5,7],[6,10],[8,11],[9,12]]=>[9,12,8,11,6,10,5,7,3,4,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,4],[5,8],[6,9],[7,10],[11,12]]=>[11,12,7,10,6,9,5,8,3,4,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,4],[5,8],[6,9],[7,11],[10,12]]=>[10,12,7,11,6,9,5,8,3,4,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,4],[5,8],[6,10],[7,11],[9,12]]=>[9,12,7,11,6,10,5,8,3,4,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,4],[5,9],[6,10],[7,11],[8,12]]=>[8,12,7,11,6,10,5,9,3,4,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,5],[4,6],[7,8],[9,10],[11,12]]=>[11,12,9,10,7,8,4,6,3,5,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,5],[4,6],[7,8],[9,11],[10,12]]=>[10,12,9,11,7,8,4,6,3,5,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,5],[4,6],[7,9],[8,10],[11,12]]=>[11,12,8,10,7,9,4,6,3,5,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,5],[4,6],[7,9],[8,11],[10,12]]=>[10,12,8,11,7,9,4,6,3,5,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,5],[4,6],[7,10],[8,11],[9,12]]=>[9,12,8,11,7,10,4,6,3,5,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,5],[4,7],[6,8],[9,10],[11,12]]=>[11,12,9,10,6,8,4,7,3,5,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,5],[4,7],[6,8],[9,11],[10,12]]=>[10,12,9,11,6,8,4,7,3,5,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,5],[4,7],[6,9],[8,10],[11,12]]=>[11,12,8,10,6,9,4,7,3,5,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,5],[4,7],[6,9],[8,11],[10,12]]=>[10,12,8,11,6,9,4,7,3,5,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,5],[4,7],[6,10],[8,11],[9,12]]=>[9,12,8,11,6,10,4,7,3,5,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,5],[4,8],[6,9],[7,10],[11,12]]=>[11,12,7,10,6,9,4,8,3,5,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,5],[4,8],[6,9],[7,11],[10,12]]=>[10,12,7,11,6,9,4,8,3,5,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,5],[4,8],[6,10],[7,11],[9,12]]=>[9,12,7,11,6,10,4,8,3,5,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,5],[4,9],[6,10],[7,11],[8,12]]=>[8,12,7,11,6,10,4,9,3,5,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,6],[4,7],[5,8],[9,10],[11,12]]=>[11,12,9,10,5,8,4,7,3,6,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,6],[4,7],[5,8],[9,11],[10,12]]=>[10,12,9,11,5,8,4,7,3,6,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,6],[4,7],[5,9],[8,10],[11,12]]=>[11,12,8,10,5,9,4,7,3,6,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,6],[4,7],[5,9],[8,11],[10,12]]=>[10,12,8,11,5,9,4,7,3,6,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,6],[4,7],[5,10],[8,11],[9,12]]=>[9,12,8,11,5,10,4,7,3,6,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,6],[4,8],[5,9],[7,10],[11,12]]=>[11,12,7,10,5,9,4,8,3,6,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,6],[4,8],[5,9],[7,11],[10,12]]=>[10,12,7,11,5,9,4,8,3,6,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,6],[4,8],[5,10],[7,11],[9,12]]=>[9,12,7,11,5,10,4,8,3,6,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,6],[4,9],[5,10],[7,11],[8,12]]=>[8,12,7,11,5,10,4,9,3,6,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,7],[4,8],[5,9],[6,10],[11,12]]=>[11,12,6,10,5,9,4,8,3,7,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,7],[4,8],[5,9],[6,11],[10,12]]=>[10,12,6,11,5,9,4,8,3,7,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,7],[4,8],[5,10],[6,11],[9,12]]=>[9,12,6,11,5,10,4,8,3,7,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,7],[4,9],[5,10],[6,11],[8,12]]=>[8,12,6,11,5,10,4,9,3,7,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2],[3,8],[4,9],[5,10],[6,11],[7,12]]=>[7,12,6,11,5,10,4,9,3,8,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,4],[5,6],[7,8],[9,10],[11,12]]=>[11,12,9,10,7,8,5,6,2,4,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,4],[5,6],[7,8],[9,11],[10,12]]=>[10,12,9,11,7,8,5,6,2,4,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,4],[5,6],[7,9],[8,10],[11,12]]=>[11,12,8,10,7,9,5,6,2,4,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,4],[5,6],[7,9],[8,11],[10,12]]=>[10,12,8,11,7,9,5,6,2,4,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,4],[5,6],[7,10],[8,11],[9,12]]=>[9,12,8,11,7,10,5,6,2,4,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,4],[5,7],[6,8],[9,10],[11,12]]=>[11,12,9,10,6,8,5,7,2,4,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,4],[5,7],[6,8],[9,11],[10,12]]=>[10,12,9,11,6,8,5,7,2,4,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,4],[5,7],[6,9],[8,10],[11,12]]=>[11,12,8,10,6,9,5,7,2,4,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,4],[5,7],[6,9],[8,11],[10,12]]=>[10,12,8,11,6,9,5,7,2,4,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,4],[5,7],[6,10],[8,11],[9,12]]=>[9,12,8,11,6,10,5,7,2,4,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,4],[5,8],[6,9],[7,10],[11,12]]=>[11,12,7,10,6,9,5,8,2,4,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,4],[5,8],[6,9],[7,11],[10,12]]=>[10,12,7,11,6,9,5,8,2,4,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,4],[5,8],[6,10],[7,11],[9,12]]=>[9,12,7,11,6,10,5,8,2,4,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,4],[5,9],[6,10],[7,11],[8,12]]=>[8,12,7,11,6,10,5,9,2,4,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,5],[4,6],[7,8],[9,10],[11,12]]=>[11,12,9,10,7,8,4,6,2,5,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,5],[4,6],[7,8],[9,11],[10,12]]=>[10,12,9,11,7,8,4,6,2,5,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,5],[4,6],[7,9],[8,10],[11,12]]=>[11,12,8,10,7,9,4,6,2,5,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,5],[4,6],[7,9],[8,11],[10,12]]=>[10,12,8,11,7,9,4,6,2,5,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,5],[4,6],[7,10],[8,11],[9,12]]=>[9,12,8,11,7,10,4,6,2,5,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,5],[4,7],[6,8],[9,10],[11,12]]=>[11,12,9,10,6,8,4,7,2,5,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,5],[4,7],[6,8],[9,11],[10,12]]=>[10,12,9,11,6,8,4,7,2,5,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,5],[4,7],[6,9],[8,10],[11,12]]=>[11,12,8,10,6,9,4,7,2,5,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,5],[4,7],[6,9],[8,11],[10,12]]=>[10,12,8,11,6,9,4,7,2,5,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,5],[4,7],[6,10],[8,11],[9,12]]=>[9,12,8,11,6,10,4,7,2,5,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,5],[4,8],[6,9],[7,10],[11,12]]=>[11,12,7,10,6,9,4,8,2,5,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,5],[4,8],[6,9],[7,11],[10,12]]=>[10,12,7,11,6,9,4,8,2,5,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,5],[4,8],[6,10],[7,11],[9,12]]=>[9,12,7,11,6,10,4,8,2,5,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,5],[4,9],[6,10],[7,11],[8,12]]=>[8,12,7,11,6,10,4,9,2,5,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,6],[4,7],[5,8],[9,10],[11,12]]=>[11,12,9,10,5,8,4,7,2,6,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,6],[4,7],[5,8],[9,11],[10,12]]=>[10,12,9,11,5,8,4,7,2,6,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,6],[4,7],[5,9],[8,10],[11,12]]=>[11,12,8,10,5,9,4,7,2,6,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,6],[4,7],[5,9],[8,11],[10,12]]=>[10,12,8,11,5,9,4,7,2,6,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,6],[4,7],[5,10],[8,11],[9,12]]=>[9,12,8,11,5,10,4,7,2,6,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,6],[4,8],[5,9],[7,10],[11,12]]=>[11,12,7,10,5,9,4,8,2,6,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,6],[4,8],[5,9],[7,11],[10,12]]=>[10,12,7,11,5,9,4,8,2,6,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,6],[4,8],[5,10],[7,11],[9,12]]=>[9,12,7,11,5,10,4,8,2,6,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,6],[4,9],[5,10],[7,11],[8,12]]=>[8,12,7,11,5,10,4,9,2,6,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,7],[4,8],[5,9],[6,10],[11,12]]=>[11,12,6,10,5,9,4,8,2,7,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,7],[4,8],[5,9],[6,11],[10,12]]=>[10,12,6,11,5,9,4,8,2,7,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,7],[4,8],[5,10],[6,11],[9,12]]=>[9,12,6,11,5,10,4,8,2,7,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,7],[4,9],[5,10],[6,11],[8,12]]=>[8,12,6,11,5,10,4,9,2,7,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,3],[2,8],[4,9],[5,10],[6,11],[7,12]]=>[7,12,6,11,5,10,4,9,2,8,1,3]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,4],[2,5],[3,6],[7,8],[9,10],[11,12]]=>[11,12,9,10,7,8,3,6,2,5,1,4]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,4],[2,5],[3,6],[7,8],[9,11],[10,12]]=>[10,12,9,11,7,8,3,6,2,5,1,4]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,4],[2,5],[3,6],[7,9],[8,10],[11,12]]=>[11,12,8,10,7,9,3,6,2,5,1,4]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,4],[2,5],[3,6],[7,9],[8,11],[10,12]]=>[10,12,8,11,7,9,3,6,2,5,1,4]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,4],[2,5],[3,6],[7,10],[8,11],[9,12]]=>[9,12,8,11,7,10,3,6,2,5,1,4]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,4],[2,5],[3,7],[6,8],[9,10],[11,12]]=>[11,12,9,10,6,8,3,7,2,5,1,4]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,4],[2,5],[3,7],[6,8],[9,11],[10,12]]=>[10,12,9,11,6,8,3,7,2,5,1,4]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,4],[2,5],[3,7],[6,9],[8,10],[11,12]]=>[11,12,8,10,6,9,3,7,2,5,1,4]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,4],[2,5],[3,7],[6,9],[8,11],[10,12]]=>[10,12,8,11,6,9,3,7,2,5,1,4]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,4],[2,5],[3,7],[6,10],[8,11],[9,12]]=>[9,12,8,11,6,10,3,7,2,5,1,4]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,4],[2,5],[3,8],[6,9],[7,10],[11,12]]=>[11,12,7,10,6,9,3,8,2,5,1,4]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,4],[2,5],[3,8],[6,9],[7,11],[10,12]]=>[10,12,7,11,6,9,3,8,2,5,1,4]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,4],[2,5],[3,8],[6,10],[7,11],[9,12]]=>[9,12,7,11,6,10,3,8,2,5,1,4]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,4],[2,5],[3,9],[6,10],[7,11],[8,12]]=>[8,12,7,11,6,10,3,9,2,5,1,4]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,4],[2,6],[3,7],[5,8],[9,10],[11,12]]=>[11,12,9,10,5,8,3,7,2,6,1,4]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,4],[2,6],[3,7],[5,8],[9,11],[10,12]]=>[10,12,9,11,5,8,3,7,2,6,1,4]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,4],[2,6],[3,7],[5,9],[8,10],[11,12]]=>[11,12,8,10,5,9,3,7,2,6,1,4]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,4],[2,6],[3,7],[5,9],[8,11],[10,12]]=>[10,12,8,11,5,9,3,7,2,6,1,4]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,4],[2,6],[3,7],[5,10],[8,11],[9,12]]=>[9,12,8,11,5,10,3,7,2,6,1,4]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,4],[2,6],[3,8],[5,9],[7,10],[11,12]]=>[11,12,7,10,5,9,3,8,2,6,1,4]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,4],[2,6],[3,8],[5,9],[7,11],[10,12]]=>[10,12,7,11,5,9,3,8,2,6,1,4]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,4],[2,6],[3,8],[5,10],[7,11],[9,12]]=>[9,12,7,11,5,10,3,8,2,6,1,4]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,4],[2,6],[3,9],[5,10],[7,11],[8,12]]=>[8,12,7,11,5,10,3,9,2,6,1,4]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,4],[2,7],[3,8],[5,9],[6,10],[11,12]]=>[11,12,6,10,5,9,3,8,2,7,1,4]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,4],[2,7],[3,8],[5,9],[6,11],[10,12]]=>[10,12,6,11,5,9,3,8,2,7,1,4]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,4],[2,7],[3,8],[5,10],[6,11],[9,12]]=>[9,12,6,11,5,10,3,8,2,7,1,4]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,4],[2,7],[3,9],[5,10],[6,11],[8,12]]=>[8,12,6,11,5,10,3,9,2,7,1,4]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,4],[2,8],[3,9],[5,10],[6,11],[7,12]]=>[7,12,6,11,5,10,3,9,2,8,1,4]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,5],[2,6],[3,7],[4,8],[9,10],[11,12]]=>[11,12,9,10,4,8,3,7,2,6,1,5]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,5],[2,6],[3,7],[4,8],[9,11],[10,12]]=>[10,12,9,11,4,8,3,7,2,6,1,5]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,5],[2,6],[3,7],[4,9],[8,10],[11,12]]=>[11,12,8,10,4,9,3,7,2,6,1,5]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,5],[2,6],[3,7],[4,9],[8,11],[10,12]]=>[10,12,8,11,4,9,3,7,2,6,1,5]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,5],[2,6],[3,7],[4,10],[8,11],[9,12]]=>[9,12,8,11,4,10,3,7,2,6,1,5]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,5],[2,6],[3,8],[4,9],[7,10],[11,12]]=>[11,12,7,10,4,9,3,8,2,6,1,5]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,5],[2,6],[3,8],[4,9],[7,11],[10,12]]=>[10,12,7,11,4,9,3,8,2,6,1,5]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,5],[2,6],[3,8],[4,10],[7,11],[9,12]]=>[9,12,7,11,4,10,3,8,2,6,1,5]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,5],[2,6],[3,9],[4,10],[7,11],[8,12]]=>[8,12,7,11,4,10,3,9,2,6,1,5]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,5],[2,7],[3,8],[4,9],[6,10],[11,12]]=>[11,12,6,10,4,9,3,8,2,7,1,5]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,5],[2,7],[3,8],[4,9],[6,11],[10,12]]=>[10,12,6,11,4,9,3,8,2,7,1,5]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,5],[2,7],[3,8],[4,10],[6,11],[9,12]]=>[9,12,6,11,4,10,3,8,2,7,1,5]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,5],[2,7],[3,9],[4,10],[6,11],[8,12]]=>[8,12,6,11,4,10,3,9,2,7,1,5]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,5],[2,8],[3,9],[4,10],[6,11],[7,12]]=>[7,12,6,11,4,10,3,9,2,8,1,5]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,6],[2,7],[3,8],[4,9],[5,10],[11,12]]=>[11,12,5,10,4,9,3,8,2,7,1,6]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,6],[2,7],[3,8],[4,9],[5,11],[10,12]]=>[10,12,5,11,4,9,3,8,2,7,1,6]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,6],[2,7],[3,8],[4,10],[5,11],[9,12]]=>[9,12,5,11,4,10,3,8,2,7,1,6]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,6],[2,7],[3,9],[4,10],[5,11],[8,12]]=>[8,12,5,11,4,10,3,9,2,7,1,6]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,6],[2,8],[3,9],[4,10],[5,11],[7,12]]=>[7,12,5,11,4,10,3,9,2,8,1,6]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]=>[6,12,5,11,4,10,3,9,2,8,1,7]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[1,2,3,4,5,6,7,9],[8]]=>[8,1,2,3,4,5,6,7,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,9,8,7,6,5,4,3,2]
[[1,2,3,4,5,6,9],[7,8]]=>[7,8,1,2,3,4,5,6,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[2,1,9,8,7,6,5,4,3]
[[1,2,3,4,5,9],[6,7,8]]=>[6,7,8,1,2,3,4,5,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[3,2,1,9,8,7,6,5,4]
[[1,2,3,9],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,1,2,3,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,9,8,7,6]
[[1,2,9],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,1,2,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]
[[1,2,3,4,5,6,7,8,10],[9]]=>[9,1,2,3,4,5,6,7,8,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]
[[1,2,3,4,5,6,7,10],[8,9]]=>[8,9,1,2,3,4,5,6,7,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,1,10,9,8,7,6,5,4,3]
[[1,2,3,4,5,10],[6,7,8,9]]=>[6,7,8,9,1,2,3,4,5,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[4,3,2,1,10,9,8,7,6,5]
[[1,2,3,4,5,10],[6],[7],[8],[9]]=>[9,8,7,6,1,2,3,4,5,10]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,4,10,9,8,7,6,5]
[[1,2,10],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,1,2,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,7,10,9,8]
[[1,2,4,5,6,7,8,9],[3]]=>[3,1,2,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,9,8,7,6,5,4,3,2]
[[1,7,9],[2],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,1,7,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]
[[1,8],[2],[3],[4],[5],[6],[7],[9]]=>[9,7,6,5,4,3,2,1,8]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,9,8]
[[1,2,4,5,6,7,8,9,10],[3]]=>[3,1,2,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]
[[1,8,10],[2],[3],[4],[5],[6],[7],[9]]=>[9,7,6,5,4,3,2,1,8,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,7,10,9,8]
[[1,9],[2],[3],[4],[5],[6],[7],[8],[10]]=>[10,8,7,6,5,4,3,2,1,9]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]
[[1,3,4,5,6,7,8],[2,9]]=>[2,9,1,3,4,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[2,1,9,8,7,6,5,4,3]
[[1,3,4,5,6,7,8],[2],[9]]=>[9,2,1,3,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,9,8,7,6,5,4,3]
[[1,3,4,5,6,7],[2,8,9]]=>[2,8,9,1,3,4,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[3,2,1,9,8,7,6,5,4]
[[1,3,4,5,6],[2,7,8,9]]=>[2,7,8,9,1,3,4,5,6]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[4,3,2,1,9,8,7,6,5]
[[1,3,4],[2],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,2,1,3,4]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]
[[1,3],[2],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,2,1,3]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,9,8]
[[1,3,4,5,6,7,8,9],[2,10]]=>[2,10,1,3,4,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,1,10,9,8,7,6,5,4,3]
[[1,3,4,5,6,7,8,9],[2],[10]]=>[10,2,1,3,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,2,10,9,8,7,6,5,4,3]
[[1,3,4,5,6,7,8],[2,9,10]]=>[2,9,10,1,3,4,5,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[3,2,1,10,9,8,7,6,5,4]
[[1,3,4,5,6,7],[2,8,9,10]]=>[2,8,9,10,1,3,4,5,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[4,3,2,1,10,9,8,7,6,5]
[[1,3],[2],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,2,1,3]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]
[[1,2,4,6,8,10],[3,5,7,9]]=>[3,5,7,9,1,2,4,6,8,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[4,3,2,1,10,9,8,7,6,5]
[[1,2,3,5,6,7,8,9,10],[4]]=>[4,1,2,3,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]
[[1,2,3,4,6,7,8,9,10],[5]]=>[5,1,2,3,4,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]
[[1,2,3,4,5,6,7,9,10],[8]]=>[8,1,2,3,4,5,6,7,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]
[[1,2,3,4,5,6,8,9,10],[7]]=>[7,1,2,3,4,5,6,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]
[[1,2,3,4,5,7,8,9,10],[6]]=>[6,1,2,3,4,5,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]
[[1,2,5,6,7,8],[3,4],[9]]=>[9,3,4,1,2,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,3,2,9,8,7,6,5,4]
[[1,6,7,8],[2],[3],[4],[5],[9]]=>[9,5,4,3,2,1,6,7,8]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,9,8,7,6]
[[1,7,8],[2],[3],[4],[5],[6],[9]]=>[9,6,5,4,3,2,1,7,8]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]
[[1,8,9],[2],[3],[4],[5],[6],[7],[10]]=>[10,7,6,5,4,3,2,1,8,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,7,10,9,8]
[[1,2,5,6,7,8,9],[3],[4]]=>[4,3,1,2,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,9,8,7,6,5,4,3]
[[1,2,6,7,8,9],[3],[4],[5]]=>[5,4,3,1,2,6,7,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,9,8,7,6,5,4]
[[1,2,7,8,9],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7,8,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,9,8,7,6,5]
[[1,2,5,6,7,8,9,10],[3],[4]]=>[4,3,1,2,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,2,10,9,8,7,6,5,4,3]
[[1,2,7,8,9,10],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7,8,9,10]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,4,10,9,8,7,6,5]
[[1,2,8,9,10],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2,8,9,10]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,5,10,9,8,7,6]
[[1,2,6,7],[3,9],[4],[5],[8]]=>[8,5,4,3,9,1,2,6,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,3,5,4,9,8,7,6]
[[1,2,4,5,6,7,8,9],[3],[10]]=>[10,3,1,2,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,2,10,9,8,7,6,5,4,3]
[[1,4],[2],[3],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,3,2,1,4]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]
[[1,5],[2],[3],[4],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,4,3,2,1,5]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]
[[1,8],[2],[3],[4],[5],[6],[7],[9],[10]]=>[10,9,7,6,5,4,3,2,1,8]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]
[[1,7],[2],[3],[4],[5],[6],[8],[9],[10]]=>[10,9,8,6,5,4,3,2,1,7]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]
[[1,6],[2],[3],[4],[5],[7],[8],[9],[10]]=>[10,9,8,7,5,4,3,2,1,6]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]
[[1,2],[3,5],[4],[6],[7],[8],[9]]=>[9,8,7,6,4,3,5,1,2]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,7,6,9,8]
[[1,2,4],[3],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,3,1,2,4]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]
[[1,2,3,5],[4],[6],[7],[8],[9]]=>[9,8,7,6,4,1,2,3,5]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,9,8,7,6]
[[1,2,3,4,6],[5],[7],[8],[9]]=>[9,8,7,5,1,2,3,4,6]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,9,8,7,6,5]
[[1,2,3,4,5,7],[6],[8],[9]]=>[9,8,6,1,2,3,4,5,7]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,9,8,7,6,5,4]
[[1,2,3,4,5,6,8],[7],[9]]=>[9,7,1,2,3,4,5,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,9,8,7,6,5,4,3]
[[1,2,3,4,5,7,9],[6,8]]=>[6,8,1,2,3,4,5,7,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[2,1,9,8,7,6,5,4,3]
[[1,3,10],[2],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,2,1,3,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,7,10,9,8]
[[1,2,4,5,6,7,8],[3,9]]=>[3,9,1,2,4,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[2,1,9,8,7,6,5,4,3]
[[1,2,4,5,6,7,8,9],[3,10]]=>[3,10,1,2,4,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,1,10,9,8,7,6,5,4,3]
[[1,2,3,4,5,6],[7,9],[8]]=>[8,7,9,1,2,3,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,3,2,9,8,7,6,5,4]
[[1,2,3,4,5,7],[6,8,9]]=>[6,8,9,1,2,3,4,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[3,2,1,9,8,7,6,5,4]
[[1,3,4,5,6,7,9],[2,8]]=>[2,8,1,3,4,5,6,7,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[2,1,9,8,7,6,5,4,3]
[[1,2,3,4,5,6,8,9],[7,10]]=>[7,10,1,2,3,4,5,6,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,1,10,9,8,7,6,5,4,3]
[[1,2,3,4,6],[5,7,8,9]]=>[5,7,8,9,1,2,3,4,6]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[4,3,2,1,9,8,7,6,5]
[[1,2,3,4,5,7,8],[6,9]]=>[6,9,1,2,3,4,5,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[2,1,9,8,7,6,5,4,3]
[[1,3,4,5,6,7,8,10],[2],[9]]=>[9,2,1,3,4,5,6,7,8,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,2,10,9,8,7,6,5,4,3]
[[1,4,5,6,7,8],[2,9],[3]]=>[3,2,9,1,4,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,3,2,9,8,7,6,5,4]
[[1,7,8],[2,9],[3],[4],[5],[6]]=>[6,5,4,3,2,9,1,7,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,4,6,5,9,8,7]
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.
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.
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
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