Identifier
Mp00081:
Standard tableaux
—reading word permutation⟶
Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Images
=>
Cc0007;cc-rep-0Cc0010;cc-rep-3
[[1]]=>[1]=>[1]=>[.,.]
[[1,2]]=>[1,2]=>[1,2]=>[.,[.,.]]
[[1],[2]]=>[2,1]=>[2,1]=>[[.,.],.]
[[1,2,3]]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[[1,3],[2]]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[[1,2],[3]]=>[3,1,2]=>[2,3,1]=>[[.,[.,.]],.]
[[1],[2],[3]]=>[3,2,1]=>[3,1,2]=>[[.,.],[.,.]]
[[1,2,3,4]]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[[1,3,4],[2]]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[1,2,4],[3]]=>[3,1,2,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[[1,2,3],[4]]=>[4,1,2,3]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[[1,3],[2,4]]=>[2,4,1,3]=>[3,2,4,1]=>[[[.,.],[.,.]],.]
[[1,2],[3,4]]=>[3,4,1,2]=>[2,4,3,1]=>[[.,[[.,.],.]],.]
[[1,4],[2],[3]]=>[3,2,1,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[[1,3],[2],[4]]=>[4,2,1,3]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[[1,2],[3],[4]]=>[4,3,1,2]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[[1],[2],[3],[4]]=>[4,3,2,1]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[[1,2,3,4,5]]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[[1,3,4,5],[2]]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,2,4,5],[3]]=>[3,1,2,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,2,3,5],[4]]=>[4,1,2,3,5]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[[1,2,3,4],[5]]=>[5,1,2,3,4]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[[1,3,5],[2,4]]=>[2,4,1,3,5]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[[1,2,5],[3,4]]=>[3,4,1,2,5]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[[1,3,4],[2,5]]=>[2,5,1,3,4]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]
[[1,2,4],[3,5]]=>[3,5,1,2,4]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[[1,2,3],[4,5]]=>[4,5,1,2,3]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[[1,4,5],[2],[3]]=>[3,2,1,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,3,5],[2],[4]]=>[4,2,1,3,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[[1,2,5],[3],[4]]=>[4,3,1,2,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[[1,3,4],[2],[5]]=>[5,2,1,3,4]=>[3,1,4,5,2]=>[[.,.],[[.,[.,.]],.]]
[[1,2,4],[3],[5]]=>[5,3,1,2,4]=>[2,4,1,5,3]=>[[.,[.,.]],[[.,.],.]]
[[1,2,3],[4],[5]]=>[5,4,1,2,3]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
[[1,4],[2,5],[3]]=>[3,2,5,1,4]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[[1,3],[2,5],[4]]=>[4,2,5,1,3]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.]
[[1,2],[3,5],[4]]=>[4,3,5,1,2]=>[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.]
[[1,3],[2,4],[5]]=>[5,2,4,1,3]=>[3,4,5,1,2]=>[[.,[.,[.,.]]],[.,.]]
[[1,2],[3,4],[5]]=>[5,3,4,1,2]=>[2,5,4,1,3]=>[[.,[[.,.],.]],[.,.]]
[[1,5],[2],[3],[4]]=>[4,3,2,1,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[[1,4],[2],[3],[5]]=>[5,3,2,1,4]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[[1,3],[2],[4],[5]]=>[5,4,2,1,3]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]
[[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[[1,3,4,5,6],[2]]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>[2,3,4,1,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>[2,3,4,5,1,6]=>[[.,[.,[.,[.,.]]]],[.,.]]
[[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>[2,3,4,5,6,1]=>[[.,[.,[.,[.,[.,.]]]]],.]
[[1,3,5,6],[2,4]]=>[2,4,1,3,5,6]=>[3,2,4,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[[1,2,5,6],[3,4]]=>[3,4,1,2,5,6]=>[2,4,3,1,5,6]=>[[.,[[.,.],.]],[.,[.,.]]]
[[1,3,4,6],[2,5]]=>[2,5,1,3,4,6]=>[3,2,4,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>[2,4,3,5,1,6]=>[[.,[[.,.],[.,.]]],[.,.]]
[[1,2,3,6],[4,5]]=>[4,5,1,2,3,6]=>[2,3,5,4,1,6]=>[[.,[.,[[.,.],.]]],[.,.]]
[[1,3,4,5],[2,6]]=>[2,6,1,3,4,5]=>[3,2,4,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[[1,2,4,5],[3,6]]=>[3,6,1,2,4,5]=>[2,4,3,5,6,1]=>[[.,[[.,.],[.,[.,.]]]],.]
[[1,2,3,5],[4,6]]=>[4,6,1,2,3,5]=>[2,3,5,4,6,1]=>[[.,[.,[[.,.],[.,.]]]],.]
[[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>[2,3,4,6,5,1]=>[[.,[.,[.,[[.,.],.]]]],.]
[[1,4,5,6],[2],[3]]=>[3,2,1,4,5,6]=>[3,1,2,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[[1,3,5,6],[2],[4]]=>[4,2,1,3,5,6]=>[3,1,4,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>[2,4,1,3,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,3,4,6],[2],[5]]=>[5,2,1,3,4,6]=>[3,1,4,5,2,6]=>[[.,.],[[.,[.,.]],[.,.]]]
[[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>[2,4,1,5,3,6]=>[[.,[.,.]],[[.,.],[.,.]]]
[[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>[2,3,5,1,4,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[[1,3,4,5],[2],[6]]=>[6,2,1,3,4,5]=>[3,1,4,5,6,2]=>[[.,.],[[.,[.,[.,.]]],.]]
[[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>[2,4,1,5,6,3]=>[[.,[.,.]],[[.,[.,.]],.]]
[[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>[2,3,5,1,6,4]=>[[.,[.,[.,.]]],[[.,.],.]]
[[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>[2,3,4,6,1,5]=>[[.,[.,[.,[.,.]]]],[.,.]]
[[1,3,5],[2,4,6]]=>[2,4,6,1,3,5]=>[3,2,5,4,6,1]=>[[[.,.],[[.,.],[.,.]]],.]
[[1,2,5],[3,4,6]]=>[3,4,6,1,2,5]=>[2,5,3,4,6,1]=>[[.,[[.,.],[.,[.,.]]]],.]
[[1,3,4],[2,5,6]]=>[2,5,6,1,3,4]=>[3,2,4,6,5,1]=>[[[.,.],[.,[[.,.],.]]],.]
[[1,2,4],[3,5,6]]=>[3,5,6,1,2,4]=>[2,4,3,6,5,1]=>[[.,[[.,.],[[.,.],.]]],.]
[[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>[2,3,6,4,5,1]=>[[.,[.,[[.,.],[.,.]]]],.]
[[1,4,6],[2,5],[3]]=>[3,2,5,1,4,6]=>[4,3,2,5,1,6]=>[[[[.,.],.],[.,.]],[.,.]]
[[1,3,6],[2,5],[4]]=>[4,2,5,1,3,6]=>[3,4,5,2,1,6]=>[[[.,[.,[.,.]]],.],[.,.]]
[[1,2,6],[3,5],[4]]=>[4,3,5,1,2,6]=>[2,5,4,3,1,6]=>[[.,[[[.,.],.],.]],[.,.]]
[[1,3,6],[2,4],[5]]=>[5,2,4,1,3,6]=>[3,4,5,1,2,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[[1,2,6],[3,4],[5]]=>[5,3,4,1,2,6]=>[2,5,4,1,3,6]=>[[.,[[.,.],.]],[.,[.,.]]]
[[1,4,5],[2,6],[3]]=>[3,2,6,1,4,5]=>[4,3,2,5,6,1]=>[[[[.,.],.],[.,[.,.]]],.]
[[1,3,5],[2,6],[4]]=>[4,2,6,1,3,5]=>[3,4,5,2,6,1]=>[[[.,[.,[.,.]]],[.,.]],.]
[[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5]=>[2,5,4,3,6,1]=>[[.,[[[.,.],.],[.,.]]],.]
[[1,3,4],[2,6],[5]]=>[5,2,6,1,3,4]=>[3,5,4,6,2,1]=>[[[.,[[.,.],[.,.]]],.],.]
[[1,2,4],[3,6],[5]]=>[5,3,6,1,2,4]=>[2,4,5,6,3,1]=>[[.,[[.,[.,[.,.]]],.]],.]
[[1,2,3],[4,6],[5]]=>[5,4,6,1,2,3]=>[2,3,6,5,4,1]=>[[.,[.,[[[.,.],.],.]]],.]
[[1,3,5],[2,4],[6]]=>[6,2,4,1,3,5]=>[3,4,5,1,6,2]=>[[.,[.,[.,.]]],[[.,.],.]]
[[1,2,5],[3,4],[6]]=>[6,3,4,1,2,5]=>[2,5,4,1,6,3]=>[[.,[[.,.],.]],[[.,.],.]]
[[1,3,4],[2,5],[6]]=>[6,2,5,1,3,4]=>[3,5,4,6,1,2]=>[[.,[[.,.],[.,.]]],[.,.]]
[[1,2,4],[3,5],[6]]=>[6,3,5,1,2,4]=>[2,4,5,6,1,3]=>[[.,[.,[.,[.,.]]]],[.,.]]
[[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3]=>[2,3,6,5,1,4]=>[[.,[.,[[.,.],.]]],[.,.]]
[[1,5,6],[2],[3],[4]]=>[4,3,2,1,5,6]=>[4,1,2,3,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[[1,4,6],[2],[3],[5]]=>[5,3,2,1,4,6]=>[4,1,2,5,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,3,6],[2],[4],[5]]=>[5,4,2,1,3,6]=>[3,1,5,2,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,2,6],[3],[4],[5]]=>[5,4,3,1,2,6]=>[2,5,1,3,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1,4,5],[2],[3],[6]]=>[6,3,2,1,4,5]=>[4,1,2,5,6,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[[1,3,5],[2],[4],[6]]=>[6,4,2,1,3,5]=>[3,1,5,2,6,4]=>[[.,.],[[.,.],[[.,.],.]]]
[[1,2,5],[3],[4],[6]]=>[6,4,3,1,2,5]=>[2,5,1,3,6,4]=>[[.,[.,.]],[.,[[.,.],.]]]
[[1,3,4],[2],[5],[6]]=>[6,5,2,1,3,4]=>[3,1,4,6,2,5]=>[[.,.],[[.,[.,.]],[.,.]]]
[[1,2,4],[3],[5],[6]]=>[6,5,3,1,2,4]=>[2,4,1,6,3,5]=>[[.,[.,.]],[[.,.],[.,.]]]
[[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>[2,3,6,1,4,5]=>[[.,[.,[.,.]]],[.,[.,.]]]
[[1,4],[2,5],[3,6]]=>[3,6,2,5,1,4]=>[4,5,3,6,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[[1,3],[2,5],[4,6]]=>[4,6,2,5,1,3]=>[3,5,6,4,1,2]=>[[.,[[.,[.,.]],.]],[.,.]]
[[1,2],[3,5],[4,6]]=>[4,6,3,5,1,2]=>[2,6,5,4,1,3]=>[[.,[[[.,.],.],.]],[.,.]]
[[1,3],[2,4],[5,6]]=>[5,6,2,4,1,3]=>[3,4,6,1,5,2]=>[[.,[.,[.,.]]],[[.,.],.]]
[[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>[2,6,4,1,5,3]=>[[.,[[.,.],.]],[[.,.],.]]
[[1,5],[2,6],[3],[4]]=>[4,3,2,6,1,5]=>[5,4,2,3,6,1]=>[[[[.,.],.],[.,[.,.]]],.]
[[1,4],[2,6],[3],[5]]=>[5,3,2,6,1,4]=>[4,5,2,6,3,1]=>[[[.,[.,.]],[[.,.],.]],.]
[[1,3],[2,6],[4],[5]]=>[5,4,2,6,1,3]=>[3,5,6,2,4,1]=>[[[.,[.,[.,.]]],[.,.]],.]
[[1,2],[3,6],[4],[5]]=>[5,4,3,6,1,2]=>[2,6,5,3,4,1]=>[[.,[[[.,.],.],[.,.]]],.]
[[1,4],[2,5],[3],[6]]=>[6,3,2,5,1,4]=>[4,5,2,6,1,3]=>[[[.,[.,.]],[.,.]],[.,.]]
[[1,3],[2,5],[4],[6]]=>[6,4,2,5,1,3]=>[3,5,6,2,1,4]=>[[[.,[.,[.,.]]],.],[.,.]]
[[1,2],[3,5],[4],[6]]=>[6,4,3,5,1,2]=>[2,6,5,3,1,4]=>[[.,[[[.,.],.],.]],[.,.]]
[[1,3],[2,4],[5],[6]]=>[6,5,2,4,1,3]=>[3,4,6,1,2,5]=>[[.,[.,[.,.]]],[.,[.,.]]]
[[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2]=>[2,6,4,1,3,5]=>[[.,[[.,.],.]],[.,[.,.]]]
[[1,6],[2],[3],[4],[5]]=>[5,4,3,2,1,6]=>[5,1,2,3,4,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[[1,5],[2],[3],[4],[6]]=>[6,4,3,2,1,5]=>[5,1,2,3,6,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[[1,4],[2],[3],[5],[6]]=>[6,5,3,2,1,4]=>[4,1,2,6,3,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[[1,3],[2],[4],[5],[6]]=>[6,5,4,2,1,3]=>[3,1,6,2,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>[2,6,1,3,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>[6,1,2,3,4,5]=>[[.,.],[.,[.,[.,[.,.]]]]]
[[1,2,3,4,5,6,7]]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,3,4,5,6,7],[2]]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,4,5,6,7],[3]]=>[3,1,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[[1,2,3,5,6,7],[4]]=>[4,1,2,3,5,6,7]=>[2,3,4,1,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[[1,2,3,4,6,7],[5]]=>[5,1,2,3,4,6,7]=>[2,3,4,5,1,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[[1,2,3,4,5,7],[6]]=>[6,1,2,3,4,5,7]=>[2,3,4,5,6,1,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>[2,3,4,5,6,7,1]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[[1,3,5,6,7],[2,4]]=>[2,4,1,3,5,6,7]=>[3,2,4,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[[1,2,5,6,7],[3,4]]=>[3,4,1,2,5,6,7]=>[2,4,3,1,5,6,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]
[[1,3,4,6,7],[2,5]]=>[2,5,1,3,4,6,7]=>[3,2,4,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[[1,2,4,6,7],[3,5]]=>[3,5,1,2,4,6,7]=>[2,4,3,5,1,6,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[[1,2,3,6,7],[4,5]]=>[4,5,1,2,3,6,7]=>[2,3,5,4,1,6,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]
[[1,3,4,5,7],[2,6]]=>[2,6,1,3,4,5,7]=>[3,2,4,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[[1,2,4,5,7],[3,6]]=>[3,6,1,2,4,5,7]=>[2,4,3,5,6,1,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[[1,2,3,5,7],[4,6]]=>[4,6,1,2,3,5,7]=>[2,3,5,4,6,1,7]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[[1,2,3,4,7],[5,6]]=>[5,6,1,2,3,4,7]=>[2,3,4,6,5,1,7]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]
[[1,3,4,5,6],[2,7]]=>[2,7,1,3,4,5,6]=>[3,2,4,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[[1,2,4,5,6],[3,7]]=>[3,7,1,2,4,5,6]=>[2,4,3,5,6,7,1]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[[1,2,3,5,6],[4,7]]=>[4,7,1,2,3,5,6]=>[2,3,5,4,6,7,1]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]
[[1,2,3,4,6],[5,7]]=>[5,7,1,2,3,4,6]=>[2,3,4,6,5,7,1]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]
[[1,2,3,4,5],[6,7]]=>[6,7,1,2,3,4,5]=>[2,3,4,5,7,6,1]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]
[[1,4,5,6,7],[2],[3]]=>[3,2,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[[1,3,5,6,7],[2],[4]]=>[4,2,1,3,5,6,7]=>[3,1,4,2,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[[1,2,5,6,7],[3],[4]]=>[4,3,1,2,5,6,7]=>[2,4,1,3,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[[1,3,4,6,7],[2],[5]]=>[5,2,1,3,4,6,7]=>[3,1,4,5,2,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[[1,2,4,6,7],[3],[5]]=>[5,3,1,2,4,6,7]=>[2,4,1,5,3,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[[1,2,3,6,7],[4],[5]]=>[5,4,1,2,3,6,7]=>[2,3,5,1,4,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[[1,3,4,5,7],[2],[6]]=>[6,2,1,3,4,5,7]=>[3,1,4,5,6,2,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[[1,2,4,5,7],[3],[6]]=>[6,3,1,2,4,5,7]=>[2,4,1,5,6,3,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[[1,2,3,5,7],[4],[6]]=>[6,4,1,2,3,5,7]=>[2,3,5,1,6,4,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[[1,2,3,4,7],[5],[6]]=>[6,5,1,2,3,4,7]=>[2,3,4,6,1,5,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[[1,3,4,5,6],[2],[7]]=>[7,2,1,3,4,5,6]=>[3,1,4,5,6,7,2]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]
[[1,2,4,5,6],[3],[7]]=>[7,3,1,2,4,5,6]=>[2,4,1,5,6,7,3]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[[1,2,3,5,6],[4],[7]]=>[7,4,1,2,3,5,6]=>[2,3,5,1,6,7,4]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[[1,2,3,4,6],[5],[7]]=>[7,5,1,2,3,4,6]=>[2,3,4,6,1,7,5]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[[1,2,3,4,5],[6],[7]]=>[7,6,1,2,3,4,5]=>[2,3,4,5,7,1,6]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[[1,3,5,7],[2,4,6]]=>[2,4,6,1,3,5,7]=>[3,2,5,4,6,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[[1,2,5,7],[3,4,6]]=>[3,4,6,1,2,5,7]=>[2,5,3,4,6,1,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[[1,3,4,7],[2,5,6]]=>[2,5,6,1,3,4,7]=>[3,2,4,6,5,1,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[[1,2,4,7],[3,5,6]]=>[3,5,6,1,2,4,7]=>[2,4,3,6,5,1,7]=>[[.,[[.,.],[[.,.],.]]],[.,.]]
[[1,2,3,7],[4,5,6]]=>[4,5,6,1,2,3,7]=>[2,3,6,4,5,1,7]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[[1,3,5,6],[2,4,7]]=>[2,4,7,1,3,5,6]=>[3,2,5,4,6,7,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[[1,2,5,6],[3,4,7]]=>[3,4,7,1,2,5,6]=>[2,5,3,4,6,7,1]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[[1,3,4,6],[2,5,7]]=>[2,5,7,1,3,4,6]=>[3,2,4,6,5,7,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[[1,2,4,6],[3,5,7]]=>[3,5,7,1,2,4,6]=>[2,4,3,6,5,7,1]=>[[.,[[.,.],[[.,.],[.,.]]]],.]
[[1,2,3,6],[4,5,7]]=>[4,5,7,1,2,3,6]=>[2,3,6,4,5,7,1]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]
[[1,3,4,5],[2,6,7]]=>[2,6,7,1,3,4,5]=>[3,2,4,5,7,6,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.]
[[1,2,4,5],[3,6,7]]=>[3,6,7,1,2,4,5]=>[2,4,3,5,7,6,1]=>[[.,[[.,.],[.,[[.,.],.]]]],.]
[[1,2,3,5],[4,6,7]]=>[4,6,7,1,2,3,5]=>[2,3,5,4,7,6,1]=>[[.,[.,[[.,.],[[.,.],.]]]],.]
[[1,2,3,4],[5,6,7]]=>[5,6,7,1,2,3,4]=>[2,3,4,7,5,6,1]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]
[[1,4,6,7],[2,5],[3]]=>[3,2,5,1,4,6,7]=>[4,3,2,5,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[[1,3,6,7],[2,5],[4]]=>[4,2,5,1,3,6,7]=>[3,4,5,2,1,6,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[[1,2,6,7],[3,5],[4]]=>[4,3,5,1,2,6,7]=>[2,5,4,3,1,6,7]=>[[.,[[[.,.],.],.]],[.,[.,.]]]
[[1,3,6,7],[2,4],[5]]=>[5,2,4,1,3,6,7]=>[3,4,5,1,2,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[[1,2,6,7],[3,4],[5]]=>[5,3,4,1,2,6,7]=>[2,5,4,1,3,6,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]
[[1,4,5,7],[2,6],[3]]=>[3,2,6,1,4,5,7]=>[4,3,2,5,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[[1,3,5,7],[2,6],[4]]=>[4,2,6,1,3,5,7]=>[3,4,5,2,6,1,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[[1,2,5,7],[3,6],[4]]=>[4,3,6,1,2,5,7]=>[2,5,4,3,6,1,7]=>[[.,[[[.,.],.],[.,.]]],[.,.]]
[[1,3,4,7],[2,6],[5]]=>[5,2,6,1,3,4,7]=>[3,5,4,6,2,1,7]=>[[[.,[[.,.],[.,.]]],.],[.,.]]
[[1,2,4,7],[3,6],[5]]=>[5,3,6,1,2,4,7]=>[2,4,5,6,3,1,7]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]
[[1,2,3,7],[4,6],[5]]=>[5,4,6,1,2,3,7]=>[2,3,6,5,4,1,7]=>[[.,[.,[[[.,.],.],.]]],[.,.]]
[[1,3,5,7],[2,4],[6]]=>[6,2,4,1,3,5,7]=>[3,4,5,1,6,2,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[[1,2,5,7],[3,4],[6]]=>[6,3,4,1,2,5,7]=>[2,5,4,1,6,3,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]
[[1,3,4,7],[2,5],[6]]=>[6,2,5,1,3,4,7]=>[3,5,4,6,1,2,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[[1,2,4,7],[3,5],[6]]=>[6,3,5,1,2,4,7]=>[2,4,5,6,1,3,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[[1,2,3,7],[4,5],[6]]=>[6,4,5,1,2,3,7]=>[2,3,6,5,1,4,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]
[[1,4,5,6],[2,7],[3]]=>[3,2,7,1,4,5,6]=>[4,3,2,5,6,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[[1,3,5,6],[2,7],[4]]=>[4,2,7,1,3,5,6]=>[3,4,5,2,6,7,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[[1,2,5,6],[3,7],[4]]=>[4,3,7,1,2,5,6]=>[2,5,4,3,6,7,1]=>[[.,[[[.,.],.],[.,[.,.]]]],.]
[[1,3,4,6],[2,7],[5]]=>[5,2,7,1,3,4,6]=>[3,5,4,6,2,7,1]=>[[[.,[[.,.],[.,.]]],[.,.]],.]
[[1,2,4,6],[3,7],[5]]=>[5,3,7,1,2,4,6]=>[2,4,5,6,3,7,1]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]
[[1,2,3,6],[4,7],[5]]=>[5,4,7,1,2,3,6]=>[2,3,6,5,4,7,1]=>[[.,[.,[[[.,.],.],[.,.]]]],.]
[[1,3,4,5],[2,7],[6]]=>[6,2,7,1,3,4,5]=>[3,6,4,5,7,2,1]=>[[[.,[[.,.],[.,[.,.]]]],.],.]
[[1,2,4,5],[3,7],[6]]=>[6,3,7,1,2,4,5]=>[2,4,6,5,7,3,1]=>[[.,[[.,[[.,.],[.,.]]],.]],.]
[[1,2,3,5],[4,7],[6]]=>[6,4,7,1,2,3,5]=>[2,3,5,6,7,4,1]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]
[[1,2,3,4],[5,7],[6]]=>[6,5,7,1,2,3,4]=>[2,3,4,7,6,5,1]=>[[.,[.,[.,[[[.,.],.],.]]]],.]
[[1,3,5,6],[2,4],[7]]=>[7,2,4,1,3,5,6]=>[3,4,5,1,6,7,2]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[[1,2,5,6],[3,4],[7]]=>[7,3,4,1,2,5,6]=>[2,5,4,1,6,7,3]=>[[.,[[.,.],.]],[[.,[.,.]],.]]
[[1,3,4,6],[2,5],[7]]=>[7,2,5,1,3,4,6]=>[3,5,4,6,1,7,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[[1,2,4,6],[3,5],[7]]=>[7,3,5,1,2,4,6]=>[2,4,5,6,1,7,3]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[[1,2,3,6],[4,5],[7]]=>[7,4,5,1,2,3,6]=>[2,3,6,5,1,7,4]=>[[.,[.,[[.,.],.]]],[[.,.],.]]
[[1,3,4,5],[2,6],[7]]=>[7,2,6,1,3,4,5]=>[3,6,4,5,7,1,2]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[[1,2,4,5],[3,6],[7]]=>[7,3,6,1,2,4,5]=>[2,4,6,5,7,1,3]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[[1,2,3,5],[4,6],[7]]=>[7,4,6,1,2,3,5]=>[2,3,5,6,7,1,4]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[[1,2,3,4],[5,6],[7]]=>[7,5,6,1,2,3,4]=>[2,3,4,7,6,1,5]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]
[[1,5,6,7],[2],[3],[4]]=>[4,3,2,1,5,6,7]=>[4,1,2,3,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[[1,4,6,7],[2],[3],[5]]=>[5,3,2,1,4,6,7]=>[4,1,2,5,3,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[[1,3,6,7],[2],[4],[5]]=>[5,4,2,1,3,6,7]=>[3,1,5,2,4,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[[1,2,6,7],[3],[4],[5]]=>[5,4,3,1,2,6,7]=>[2,5,1,3,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[[1,4,5,7],[2],[3],[6]]=>[6,3,2,1,4,5,7]=>[4,1,2,5,6,3,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[[1,3,5,7],[2],[4],[6]]=>[6,4,2,1,3,5,7]=>[3,1,5,2,6,4,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[[1,2,5,7],[3],[4],[6]]=>[6,4,3,1,2,5,7]=>[2,5,1,3,6,4,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[[1,3,4,7],[2],[5],[6]]=>[6,5,2,1,3,4,7]=>[3,1,4,6,2,5,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[[1,2,4,7],[3],[5],[6]]=>[6,5,3,1,2,4,7]=>[2,4,1,6,3,5,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[[1,2,3,7],[4],[5],[6]]=>[6,5,4,1,2,3,7]=>[2,3,6,1,4,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[[1,4,5,6],[2],[3],[7]]=>[7,3,2,1,4,5,6]=>[4,1,2,5,6,7,3]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]
[[1,3,5,6],[2],[4],[7]]=>[7,4,2,1,3,5,6]=>[3,1,5,2,6,7,4]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[[1,2,5,6],[3],[4],[7]]=>[7,4,3,1,2,5,6]=>[2,5,1,3,6,7,4]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[[1,3,4,6],[2],[5],[7]]=>[7,5,2,1,3,4,6]=>[3,1,4,6,2,7,5]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[[1,2,4,6],[3],[5],[7]]=>[7,5,3,1,2,4,6]=>[2,4,1,6,3,7,5]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[[1,2,3,6],[4],[5],[7]]=>[7,5,4,1,2,3,6]=>[2,3,6,1,4,7,5]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[[1,3,4,5],[2],[6],[7]]=>[7,6,2,1,3,4,5]=>[3,1,4,5,7,2,6]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[[1,2,4,5],[3],[6],[7]]=>[7,6,3,1,2,4,5]=>[2,4,1,5,7,3,6]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[[1,2,3,5],[4],[6],[7]]=>[7,6,4,1,2,3,5]=>[2,3,5,1,7,4,6]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[[1,2,3,4],[5],[6],[7]]=>[7,6,5,1,2,3,4]=>[2,3,4,7,1,5,6]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[[1,4,6],[2,5,7],[3]]=>[3,2,5,7,1,4,6]=>[4,3,2,6,5,7,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[[1,3,6],[2,5,7],[4]]=>[4,2,5,7,1,3,6]=>[3,4,6,2,5,7,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[[1,2,6],[3,5,7],[4]]=>[4,3,5,7,1,2,6]=>[2,6,4,3,5,7,1]=>[[.,[[[.,.],.],[.,[.,.]]]],.]
[[1,3,6],[2,4,7],[5]]=>[5,2,4,7,1,3,6]=>[3,4,6,5,2,7,1]=>[[[.,[.,[[.,.],.]]],[.,.]],.]
[[1,2,6],[3,4,7],[5]]=>[5,3,4,7,1,2,6]=>[2,6,4,5,3,7,1]=>[[.,[[[.,.],[.,.]],[.,.]]],.]
[[1,4,5],[2,6,7],[3]]=>[3,2,6,7,1,4,5]=>[4,3,2,5,7,6,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]
[[1,3,5],[2,6,7],[4]]=>[4,2,6,7,1,3,5]=>[3,4,5,2,7,6,1]=>[[[.,[.,[.,.]]],[[.,.],.]],.]
[[1,2,5],[3,6,7],[4]]=>[4,3,6,7,1,2,5]=>[2,5,4,3,7,6,1]=>[[.,[[[.,.],.],[[.,.],.]]],.]
[[1,3,4],[2,6,7],[5]]=>[5,2,6,7,1,3,4]=>[3,5,4,7,2,6,1]=>[[[.,[[.,.],[.,.]]],[.,.]],.]
[[1,2,4],[3,6,7],[5]]=>[5,3,6,7,1,2,4]=>[2,4,5,7,3,6,1]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]
[[1,2,3],[4,6,7],[5]]=>[5,4,6,7,1,2,3]=>[2,3,7,5,4,6,1]=>[[.,[.,[[[.,.],.],[.,.]]]],.]
[[1,3,5],[2,4,7],[6]]=>[6,2,4,7,1,3,5]=>[3,4,5,6,7,2,1]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]
[[1,2,5],[3,4,7],[6]]=>[6,3,4,7,1,2,5]=>[2,5,4,6,7,3,1]=>[[.,[[[.,.],[.,[.,.]]],.]],.]
[[1,3,4],[2,5,7],[6]]=>[6,2,5,7,1,3,4]=>[3,5,4,7,6,2,1]=>[[[.,[[.,.],[[.,.],.]]],.],.]
[[1,2,4],[3,5,7],[6]]=>[6,3,5,7,1,2,4]=>[2,4,5,7,6,3,1]=>[[.,[[.,[.,[[.,.],.]]],.]],.]
[[1,2,3],[4,5,7],[6]]=>[6,4,5,7,1,2,3]=>[2,3,7,5,6,4,1]=>[[.,[.,[[[.,.],[.,.]],.]]],.]
[[1,3,5],[2,4,6],[7]]=>[7,2,4,6,1,3,5]=>[3,4,5,6,7,1,2]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[[1,2,5],[3,4,6],[7]]=>[7,3,4,6,1,2,5]=>[2,5,4,6,7,1,3]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[[1,3,4],[2,5,6],[7]]=>[7,2,5,6,1,3,4]=>[3,5,4,7,6,1,2]=>[[.,[[.,.],[[.,.],.]]],[.,.]]
[[1,2,4],[3,5,6],[7]]=>[7,3,5,6,1,2,4]=>[2,4,5,7,6,1,3]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]
[[1,2,3],[4,5,6],[7]]=>[7,4,5,6,1,2,3]=>[2,3,7,5,6,1,4]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[[1,4,7],[2,5],[3,6]]=>[3,6,2,5,1,4,7]=>[4,5,3,6,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[[1,3,7],[2,5],[4,6]]=>[4,6,2,5,1,3,7]=>[3,5,6,4,1,2,7]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]
[[1,2,7],[3,5],[4,6]]=>[4,6,3,5,1,2,7]=>[2,6,5,4,1,3,7]=>[[.,[[[.,.],.],.]],[.,[.,.]]]
[[1,3,7],[2,4],[5,6]]=>[5,6,2,4,1,3,7]=>[3,4,6,1,5,2,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[[1,2,7],[3,4],[5,6]]=>[5,6,3,4,1,2,7]=>[2,6,4,1,5,3,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]
[[1,4,6],[2,5],[3,7]]=>[3,7,2,5,1,4,6]=>[4,5,3,6,1,7,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[[1,3,6],[2,5],[4,7]]=>[4,7,2,5,1,3,6]=>[3,5,6,4,1,7,2]=>[[.,[[.,[.,.]],.]],[[.,.],.]]
[[1,2,6],[3,5],[4,7]]=>[4,7,3,5,1,2,6]=>[2,6,5,4,1,7,3]=>[[.,[[[.,.],.],.]],[[.,.],.]]
[[1,3,6],[2,4],[5,7]]=>[5,7,2,4,1,3,6]=>[3,4,6,1,5,7,2]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[[1,2,6],[3,4],[5,7]]=>[5,7,3,4,1,2,6]=>[2,6,4,1,5,7,3]=>[[.,[[.,.],.]],[[.,[.,.]],.]]
[[1,4,5],[2,6],[3,7]]=>[3,7,2,6,1,4,5]=>[4,6,3,5,7,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[[1,3,5],[2,6],[4,7]]=>[4,7,2,6,1,3,5]=>[3,6,5,4,7,1,2]=>[[.,[[[.,.],.],[.,.]]],[.,.]]
[[1,2,5],[3,6],[4,7]]=>[4,7,3,6,1,2,5]=>[2,5,6,4,7,1,3]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]
[[1,3,4],[2,6],[5,7]]=>[5,7,2,6,1,3,4]=>[3,6,4,7,5,1,2]=>[[.,[[.,.],[[.,.],.]]],[.,.]]
[[1,2,4],[3,6],[5,7]]=>[5,7,3,6,1,2,4]=>[2,4,6,7,5,1,3]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]
[[1,2,3],[4,6],[5,7]]=>[5,7,4,6,1,2,3]=>[2,3,7,6,5,1,4]=>[[.,[.,[[[.,.],.],.]]],[.,.]]
[[1,3,5],[2,4],[6,7]]=>[6,7,2,4,1,3,5]=>[3,4,5,1,7,6,2]=>[[.,[.,[.,.]]],[[[.,.],.],.]]
[[1,2,5],[3,4],[6,7]]=>[6,7,3,4,1,2,5]=>[2,5,4,1,7,6,3]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[[1,3,4],[2,5],[6,7]]=>[6,7,2,5,1,3,4]=>[3,5,4,7,1,6,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[[1,2,4],[3,5],[6,7]]=>[6,7,3,5,1,2,4]=>[2,4,5,7,1,6,3]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[[1,2,3],[4,5],[6,7]]=>[6,7,4,5,1,2,3]=>[2,3,7,5,1,6,4]=>[[.,[.,[[.,.],.]]],[[.,.],.]]
[[1,5,7],[2,6],[3],[4]]=>[4,3,2,6,1,5,7]=>[5,4,2,3,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[[1,4,7],[2,6],[3],[5]]=>[5,3,2,6,1,4,7]=>[4,5,2,6,3,1,7]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[[1,3,7],[2,6],[4],[5]]=>[5,4,2,6,1,3,7]=>[3,5,6,2,4,1,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[[1,2,7],[3,6],[4],[5]]=>[5,4,3,6,1,2,7]=>[2,6,5,3,4,1,7]=>[[.,[[[.,.],.],[.,.]]],[.,.]]
[[1,4,7],[2,5],[3],[6]]=>[6,3,2,5,1,4,7]=>[4,5,2,6,1,3,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[[1,3,7],[2,5],[4],[6]]=>[6,4,2,5,1,3,7]=>[3,5,6,2,1,4,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[[1,2,7],[3,5],[4],[6]]=>[6,4,3,5,1,2,7]=>[2,6,5,3,1,4,7]=>[[.,[[[.,.],.],.]],[.,[.,.]]]
[[1,3,7],[2,4],[5],[6]]=>[6,5,2,4,1,3,7]=>[3,4,6,1,2,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[[1,2,7],[3,4],[5],[6]]=>[6,5,3,4,1,2,7]=>[2,6,4,1,3,5,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]
[[1,5,6],[2,7],[3],[4]]=>[4,3,2,7,1,5,6]=>[5,4,2,3,6,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[[1,4,6],[2,7],[3],[5]]=>[5,3,2,7,1,4,6]=>[4,5,2,6,3,7,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]
[[1,3,6],[2,7],[4],[5]]=>[5,4,2,7,1,3,6]=>[3,5,6,2,4,7,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[[1,2,6],[3,7],[4],[5]]=>[5,4,3,7,1,2,6]=>[2,6,5,3,4,7,1]=>[[.,[[[.,.],.],[.,[.,.]]]],.]
[[1,4,5],[2,7],[3],[6]]=>[6,3,2,7,1,4,5]=>[4,6,2,5,7,3,1]=>[[[.,[.,.]],[[.,[.,.]],.]],.]
[[1,3,5],[2,7],[4],[6]]=>[6,4,2,7,1,3,5]=>[3,6,5,2,7,4,1]=>[[[.,[[.,.],.]],[[.,.],.]],.]
[[1,2,5],[3,7],[4],[6]]=>[6,4,3,7,1,2,5]=>[2,5,6,3,7,4,1]=>[[.,[[.,[.,.]],[[.,.],.]]],.]
[[1,3,4],[2,7],[5],[6]]=>[6,5,2,7,1,3,4]=>[3,6,4,7,2,5,1]=>[[[.,[[.,.],[.,.]]],[.,.]],.]
[[1,2,4],[3,7],[5],[6]]=>[6,5,3,7,1,2,4]=>[2,4,6,7,3,5,1]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]
[[1,2,3],[4,7],[5],[6]]=>[6,5,4,7,1,2,3]=>[2,3,7,6,4,5,1]=>[[.,[.,[[[.,.],.],[.,.]]]],.]
[[1,4,6],[2,5],[3],[7]]=>[7,3,2,5,1,4,6]=>[4,5,2,6,1,7,3]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[[1,3,6],[2,5],[4],[7]]=>[7,4,2,5,1,3,6]=>[3,5,6,2,1,7,4]=>[[[.,[.,[.,.]]],.],[[.,.],.]]
[[1,2,6],[3,5],[4],[7]]=>[7,4,3,5,1,2,6]=>[2,6,5,3,1,7,4]=>[[.,[[[.,.],.],.]],[[.,.],.]]
[[1,3,6],[2,4],[5],[7]]=>[7,5,2,4,1,3,6]=>[3,4,6,1,2,7,5]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[[1,2,6],[3,4],[5],[7]]=>[7,5,3,4,1,2,6]=>[2,6,4,1,3,7,5]=>[[.,[[.,.],.]],[.,[[.,.],.]]]
[[1,4,5],[2,6],[3],[7]]=>[7,3,2,6,1,4,5]=>[4,6,2,5,7,1,3]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[[1,3,5],[2,6],[4],[7]]=>[7,4,2,6,1,3,5]=>[3,6,5,2,7,1,4]=>[[[.,[[.,.],.]],[.,.]],[.,.]]
[[1,2,5],[3,6],[4],[7]]=>[7,4,3,6,1,2,5]=>[2,5,6,3,7,1,4]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]
[[1,3,4],[2,6],[5],[7]]=>[7,5,2,6,1,3,4]=>[3,6,4,7,2,1,5]=>[[[.,[[.,.],[.,.]]],.],[.,.]]
[[1,2,4],[3,6],[5],[7]]=>[7,5,3,6,1,2,4]=>[2,4,6,7,3,1,5]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]
[[1,2,3],[4,6],[5],[7]]=>[7,5,4,6,1,2,3]=>[2,3,7,6,4,1,5]=>[[.,[.,[[[.,.],.],.]]],[.,.]]
[[1,3,5],[2,4],[6],[7]]=>[7,6,2,4,1,3,5]=>[3,4,5,1,7,2,6]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[[1,2,5],[3,4],[6],[7]]=>[7,6,3,4,1,2,5]=>[2,5,4,1,7,3,6]=>[[.,[[.,.],.]],[[.,.],[.,.]]]
[[1,3,4],[2,5],[6],[7]]=>[7,6,2,5,1,3,4]=>[3,5,4,7,1,2,6]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[[1,2,4],[3,5],[6],[7]]=>[7,6,3,5,1,2,4]=>[2,4,5,7,1,3,6]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[[1,2,3],[4,5],[6],[7]]=>[7,6,4,5,1,2,3]=>[2,3,7,5,1,4,6]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]
[[1,6,7],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7]=>[5,1,2,3,4,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[[1,5,7],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7]=>[5,1,2,3,6,4,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[[1,4,7],[2],[3],[5],[6]]=>[6,5,3,2,1,4,7]=>[4,1,2,6,3,5,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[[1,3,7],[2],[4],[5],[6]]=>[6,5,4,2,1,3,7]=>[3,1,6,2,4,5,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[[1,2,7],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7]=>[2,6,1,3,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[[1,5,6],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6]=>[5,1,2,3,6,7,4]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[[1,4,6],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6]=>[4,1,2,6,3,7,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[[1,3,6],[2],[4],[5],[7]]=>[7,5,4,2,1,3,6]=>[3,1,6,2,4,7,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[[1,2,6],[3],[4],[5],[7]]=>[7,5,4,3,1,2,6]=>[2,6,1,3,4,7,5]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[[1,4,5],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5]=>[4,1,2,5,7,3,6]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[[1,3,5],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5]=>[3,1,5,2,7,4,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[[1,2,5],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5]=>[2,5,1,3,7,4,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[[1,3,4],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4]=>[3,1,4,7,2,5,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[[1,2,4],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4]=>[2,4,1,7,3,5,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[[1,2,3],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3]=>[2,3,7,1,4,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[[1,5],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5]=>[5,6,4,3,7,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[[1,4],[2,6],[3,7],[5]]=>[5,3,7,2,6,1,4]=>[4,6,5,7,3,1,2]=>[[[.,[[.,.],[.,.]]],.],[.,.]]
[[1,3],[2,6],[4,7],[5]]=>[5,4,7,2,6,1,3]=>[3,6,7,5,4,1,2]=>[[.,[[[.,[.,.]],.],.]],[.,.]]
[[1,2],[3,6],[4,7],[5]]=>[5,4,7,3,6,1,2]=>[2,7,6,5,4,1,3]=>[[.,[[[[.,.],.],.],.]],[.,.]]
[[1,4],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4]=>[4,5,6,7,1,3,2]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[[1,3],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3]=>[3,5,7,6,1,4,2]=>[[.,[.,[[.,.],.]]],[[.,.],.]]
[[1,2],[3,5],[4,7],[6]]=>[6,4,7,3,5,1,2]=>[2,7,5,6,1,4,3]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[[1,3],[2,4],[5,7],[6]]=>[6,5,7,2,4,1,3]=>[3,4,7,1,6,5,2]=>[[.,[.,[.,.]]],[[[.,.],.],.]]
[[1,2],[3,4],[5,7],[6]]=>[6,5,7,3,4,1,2]=>[2,7,4,1,6,5,3]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[[1,4],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4]=>[4,5,6,7,1,2,3]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[[1,3],[2,5],[4,6],[7]]=>[7,4,6,2,5,1,3]=>[3,5,7,6,1,2,4]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]
[[1,2],[3,5],[4,6],[7]]=>[7,4,6,3,5,1,2]=>[2,7,5,6,1,3,4]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[[1,3],[2,4],[5,6],[7]]=>[7,5,6,2,4,1,3]=>[3,4,7,1,6,2,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[[1,2],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2]=>[2,7,4,1,6,3,5]=>[[.,[[.,.],.]],[[.,.],[.,.]]]
[[1,6],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6]=>[6,5,2,3,4,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[[1,5],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5]=>[5,6,2,3,7,4,1]=>[[[.,[.,.]],[.,[[.,.],.]]],.]
[[1,4],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4]=>[4,6,2,7,3,5,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]
[[1,3],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3]=>[3,6,7,2,4,5,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[[1,2],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2]=>[2,7,6,3,4,5,1]=>[[.,[[[.,.],.],[.,[.,.]]]],.]
[[1,5],[2,6],[3],[4],[7]]=>[7,4,3,2,6,1,5]=>[5,6,2,3,7,1,4]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[[1,4],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4]=>[4,6,2,7,3,1,5]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[[1,3],[2,6],[4],[5],[7]]=>[7,5,4,2,6,1,3]=>[3,6,7,2,4,1,5]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[[1,2],[3,6],[4],[5],[7]]=>[7,5,4,3,6,1,2]=>[2,7,6,3,4,1,5]=>[[.,[[[.,.],.],[.,.]]],[.,.]]
[[1,4],[2,5],[3],[6],[7]]=>[7,6,3,2,5,1,4]=>[4,5,2,7,1,3,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[[1,3],[2,5],[4],[6],[7]]=>[7,6,4,2,5,1,3]=>[3,5,7,2,1,4,6]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[[1,2],[3,5],[4],[6],[7]]=>[7,6,4,3,5,1,2]=>[2,7,5,3,1,4,6]=>[[.,[[[.,.],.],.]],[.,[.,.]]]
[[1,3],[2,4],[5],[6],[7]]=>[7,6,5,2,4,1,3]=>[3,4,7,1,2,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[[1,2],[3,4],[5],[6],[7]]=>[7,6,5,3,4,1,2]=>[2,7,4,1,3,5,6]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]
[[1,7],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7]=>[6,1,2,3,4,5,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[[1,6],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6]=>[6,1,2,3,4,7,5]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[[1,5],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,7,4,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[[1,4],[2],[3],[5],[6],[7]]=>[7,6,5,3,2,1,4]=>[4,1,2,7,3,5,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[[1,3],[2],[4],[5],[6],[7]]=>[7,6,5,4,2,1,3]=>[3,1,7,2,4,5,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[[1,2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2]=>[2,7,1,3,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[[1],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1]=>[7,1,2,3,4,5,6]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,3,4,5,6,7,8]]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,3,4,5,6,7,8],[2]]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,2,4,5,6,7,8],[3]]=>[3,1,2,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,3,5,6,7,8],[4]]=>[4,1,2,3,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[[1,2,3,4,6,7,8],[5]]=>[5,1,2,3,4,6,7,8]=>[2,3,4,5,1,6,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[[1,2,3,4,5,7,8],[6]]=>[6,1,2,3,4,5,7,8]=>[2,3,4,5,6,1,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[[1,2,3,4,5,6,8],[7]]=>[7,1,2,3,4,5,6,8]=>[2,3,4,5,6,7,1,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[[1,2,3,4,5,6,7],[8]]=>[8,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,8,1]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[[1,3,5,6,7,8],[2,4]]=>[2,4,1,3,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[[1,2,5,6,7,8],[3,4]]=>[3,4,1,2,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[[1,3,4,6,7,8],[2,5]]=>[2,5,1,3,4,6,7,8]=>[3,2,4,5,1,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[[1,2,4,6,7,8],[3,5]]=>[3,5,1,2,4,6,7,8]=>[2,4,3,5,1,6,7,8]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[[1,2,3,6,7,8],[4,5]]=>[4,5,1,2,3,6,7,8]=>[2,3,5,4,1,6,7,8]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[[1,3,4,5,7,8],[2,6]]=>[2,6,1,3,4,5,7,8]=>[3,2,4,5,6,1,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[[1,2,3,4,7,8],[5,6]]=>[5,6,1,2,3,4,7,8]=>[2,3,4,6,5,1,7,8]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[[1,3,4,5,6,8],[2,7]]=>[2,7,1,3,4,5,6,8]=>[3,2,4,5,6,7,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[[1,2,4,5,6,8],[3,7]]=>[3,7,1,2,4,5,6,8]=>[2,4,3,5,6,7,1,8]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[[1,2,3,5,6,8],[4,7]]=>[4,7,1,2,3,5,6,8]=>[2,3,5,4,6,7,1,8]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[[1,2,3,4,6,8],[5,7]]=>[5,7,1,2,3,4,6,8]=>[2,3,4,6,5,7,1,8]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[[1,2,3,4,5,8],[6,7]]=>[6,7,1,2,3,4,5,8]=>[2,3,4,5,7,6,1,8]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]
[[1,3,4,5,6,7],[2,8]]=>[2,8,1,3,4,5,6,7]=>[3,2,4,5,6,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[[1,2,4,5,6,7],[3,8]]=>[3,8,1,2,4,5,6,7]=>[2,4,3,5,6,7,8,1]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[[1,2,3,5,6,7],[4,8]]=>[4,8,1,2,3,5,6,7]=>[2,3,5,4,6,7,8,1]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[[1,2,3,4,6,7],[5,8]]=>[5,8,1,2,3,4,6,7]=>[2,3,4,6,5,7,8,1]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[[1,2,3,4,5,7],[6,8]]=>[6,8,1,2,3,4,5,7]=>[2,3,4,5,7,6,8,1]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]
[[1,2,3,4,5,6],[7,8]]=>[7,8,1,2,3,4,5,6]=>[2,3,4,5,6,8,7,1]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]
[[1,4,5,6,7,8],[2],[3]]=>[3,2,1,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,3,5,6,7,8],[2],[4]]=>[4,2,1,3,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[[1,2,5,6,7,8],[3],[4]]=>[4,3,1,2,5,6,7,8]=>[2,4,1,3,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
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[[1,2,4,7,8],[3,5,6]]=>[3,5,6,1,2,4,7,8]=>[2,4,3,6,5,1,7,8]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]
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[[1,2,5,6,8],[3,4],[7]]=>[7,3,4,1,2,5,6,8]=>[2,5,4,1,6,7,3,8]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[[1,3,4,6,8],[2,5],[7]]=>[7,2,5,1,3,4,6,8]=>[3,5,4,6,1,7,2,8]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
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[[1,2,3,6,8],[4,5],[7]]=>[7,4,5,1,2,3,6,8]=>[2,3,6,5,1,7,4,8]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
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[[1,3,6,7],[2,5],[4],[8]]=>[8,4,2,5,1,3,6,7]=>[3,5,6,2,1,7,8,4]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]
[[1,3,6,7],[2,4],[5],[8]]=>[8,5,2,4,1,3,6,7]=>[3,4,6,1,2,7,8,5]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[[1,2,6,7],[3,4],[5],[8]]=>[8,5,3,4,1,2,6,7]=>[2,6,4,1,3,7,8,5]=>[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]
[[1,4,5,7],[2,6],[3],[8]]=>[8,3,2,6,1,4,5,7]=>[4,6,2,5,7,1,8,3]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[[1,2,4,7],[3,6],[5],[8]]=>[8,5,3,6,1,2,4,7]=>[2,4,6,7,3,1,8,5]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]
[[1,2,5,7],[3,4],[6],[8]]=>[8,6,3,4,1,2,5,7]=>[2,5,4,1,7,3,8,6]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[[1,3,4,7],[2,5],[6],[8]]=>[8,6,2,5,1,3,4,7]=>[3,5,4,7,1,2,8,6]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]
[[1,2,3,7],[4,5],[6],[8]]=>[8,6,4,5,1,2,3,7]=>[2,3,7,5,1,4,8,6]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]
[[1,3,5,6],[2,7],[4],[8]]=>[8,4,2,7,1,3,5,6]=>[3,7,5,2,6,8,1,4]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]
[[1,2,5,6],[3,7],[4],[8]]=>[8,4,3,7,1,2,5,6]=>[2,5,7,3,6,8,1,4]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]
[[1,2,4,6],[3,7],[5],[8]]=>[8,5,3,7,1,2,4,6]=>[2,4,7,6,3,8,1,5]=>[[.,[[.,[[.,.],.]],[.,.]]],[.,.]]
[[1,3,4,5],[2,7],[6],[8]]=>[8,6,2,7,1,3,4,5]=>[3,7,4,5,8,2,1,6]=>[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]
[[1,2,4,5],[3,7],[6],[8]]=>[8,6,3,7,1,2,4,5]=>[2,4,7,5,8,3,1,6]=>[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]
[[1,2,3,4],[5,7],[6],[8]]=>[8,6,5,7,1,2,3,4]=>[2,3,4,8,7,5,1,6]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]
[[1,2,5,6],[3,4],[7],[8]]=>[8,7,3,4,1,2,5,6]=>[2,5,4,1,6,8,3,7]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[[1,3,4,6],[2,5],[7],[8]]=>[8,7,2,5,1,3,4,6]=>[3,5,4,6,1,8,2,7]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[[1,2,4,6],[3,5],[7],[8]]=>[8,7,3,5,1,2,4,6]=>[2,4,5,6,1,8,3,7]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[[1,2,3,6],[4,5],[7],[8]]=>[8,7,4,5,1,2,3,6]=>[2,3,6,5,1,8,4,7]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
[[1,2,4,5],[3,6],[7],[8]]=>[8,7,3,6,1,2,4,5]=>[2,4,6,5,8,1,3,7]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[[1,2,3,5],[4,6],[7],[8]]=>[8,7,4,6,1,2,3,5]=>[2,3,5,6,8,1,4,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[[1,2,3,4],[5,6],[7],[8]]=>[8,7,5,6,1,2,3,4]=>[2,3,4,8,6,1,5,7]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[[1,6,7,8],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,5,7,8],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7,8]=>[5,1,2,3,6,4,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[[1,2,7,8],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7,8]=>[2,6,1,3,4,5,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[[1,5,6,8],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6,8]=>[5,1,2,3,6,7,4,8]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[[1,4,6,8],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6,8]=>[4,1,2,6,3,7,5,8]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[[1,2,6,8],[3],[4],[5],[7]]=>[7,5,4,3,1,2,6,8]=>[2,6,1,3,4,7,5,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[[1,4,5,8],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5,8]=>[4,1,2,5,7,3,6,8]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[[1,3,5,8],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5,8]=>[3,1,5,2,7,4,6,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[[1,2,3,8],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3,8]=>[2,3,7,1,4,5,6,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[[1,5,6,7],[2],[3],[4],[8]]=>[8,4,3,2,1,5,6,7]=>[5,1,2,3,6,7,8,4]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[[1,4,6,7],[2],[3],[5],[8]]=>[8,5,3,2,1,4,6,7]=>[4,1,2,6,3,7,8,5]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[[1,3,6,7],[2],[4],[5],[8]]=>[8,5,4,2,1,3,6,7]=>[3,1,6,2,4,7,8,5]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[[1,2,6,7],[3],[4],[5],[8]]=>[8,5,4,3,1,2,6,7]=>[2,6,1,3,4,7,8,5]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[[1,4,5,7],[2],[3],[6],[8]]=>[8,6,3,2,1,4,5,7]=>[4,1,2,5,7,3,8,6]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[[1,3,5,7],[2],[4],[6],[8]]=>[8,6,4,2,1,3,5,7]=>[3,1,5,2,7,4,8,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[[1,2,5,7],[3],[4],[6],[8]]=>[8,6,4,3,1,2,5,7]=>[2,5,1,3,7,4,8,6]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[[1,3,4,7],[2],[5],[6],[8]]=>[8,6,5,2,1,3,4,7]=>[3,1,4,7,2,5,8,6]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[[1,2,4,7],[3],[5],[6],[8]]=>[8,6,5,3,1,2,4,7]=>[2,4,1,7,3,5,8,6]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[[1,2,3,7],[4],[5],[6],[8]]=>[8,6,5,4,1,2,3,7]=>[2,3,7,1,4,5,8,6]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[[1,4,5,6],[2],[3],[7],[8]]=>[8,7,3,2,1,4,5,6]=>[4,1,2,5,6,8,3,7]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[[1,3,5,6],[2],[4],[7],[8]]=>[8,7,4,2,1,3,5,6]=>[3,1,5,2,6,8,4,7]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[[1,2,5,6],[3],[4],[7],[8]]=>[8,7,4,3,1,2,5,6]=>[2,5,1,3,6,8,4,7]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[[1,3,4,6],[2],[5],[7],[8]]=>[8,7,5,2,1,3,4,6]=>[3,1,4,6,2,8,5,7]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[[1,2,4,6],[3],[5],[7],[8]]=>[8,7,5,3,1,2,4,6]=>[2,4,1,6,3,8,5,7]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[[1,2,3,6],[4],[5],[7],[8]]=>[8,7,5,4,1,2,3,6]=>[2,3,6,1,4,8,5,7]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[[1,3,4,5],[2],[6],[7],[8]]=>[8,7,6,2,1,3,4,5]=>[3,1,4,5,8,2,6,7]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[[1,2,4,5],[3],[6],[7],[8]]=>[8,7,6,3,1,2,4,5]=>[2,4,1,5,8,3,6,7]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[[1,2,3,5],[4],[6],[7],[8]]=>[8,7,6,4,1,2,3,5]=>[2,3,5,1,8,4,6,7]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[[1,2,3,4],[5],[6],[7],[8]]=>[8,7,6,5,1,2,3,4]=>[2,3,4,8,1,5,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[[1,3,7],[2,5,8],[4,6]]=>[4,6,2,5,8,1,3,7]=>[3,5,7,4,6,2,8,1]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]
[[1,2,7],[3,5,8],[4,6]]=>[4,6,3,5,8,1,2,7]=>[2,7,5,4,6,3,8,1]=>[[.,[[[[.,.],.],[.,.]],[.,.]]],.]
[[1,3,7],[2,4,8],[5,6]]=>[5,6,2,4,8,1,3,7]=>[3,4,7,6,5,2,8,1]=>[[[.,[.,[[[.,.],.],.]]],[.,.]],.]
[[1,2,7],[3,4,8],[5,6]]=>[5,6,3,4,8,1,2,7]=>[2,7,4,6,5,3,8,1]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]
[[1,3,6],[2,5,8],[4,7]]=>[4,7,2,5,8,1,3,6]=>[3,5,6,4,7,8,2,1]=>[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]
[[1,2,6],[3,5,8],[4,7]]=>[4,7,3,5,8,1,2,6]=>[2,6,5,4,7,8,3,1]=>[[.,[[[[.,.],.],[.,[.,.]]],.]],.]
[[1,3,6],[2,4,8],[5,7]]=>[5,7,2,4,8,1,3,6]=>[3,4,6,7,5,8,2,1]=>[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]
[[1,4,5],[2,6,8],[3,7]]=>[3,7,2,6,8,1,4,5]=>[4,6,3,5,8,7,2,1]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]
[[1,2,5],[3,6,8],[4,7]]=>[4,7,3,6,8,1,2,5]=>[2,5,6,4,8,7,3,1]=>[[.,[[[.,[.,.]],[[.,.],.]],.]],.]
[[1,3,4],[2,6,8],[5,7]]=>[5,7,2,6,8,1,3,4]=>[3,6,4,8,5,7,2,1]=>[[[.,[[.,.],[[.,.],[.,.]]]],.],.]
[[1,2,4],[3,6,8],[5,7]]=>[5,7,3,6,8,1,2,4]=>[2,4,6,8,5,7,3,1]=>[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]
[[1,3,5],[2,4,8],[6,7]]=>[6,7,2,4,8,1,3,5]=>[3,4,5,7,8,6,2,1]=>[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]
[[1,2,5],[3,4,8],[6,7]]=>[6,7,3,4,8,1,2,5]=>[2,5,4,7,8,6,3,1]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],.]
[[1,2,3],[4,5,8],[6,7]]=>[6,7,4,5,8,1,2,3]=>[2,3,8,5,7,6,4,1]=>[[.,[.,[[[.,.],[[.,.],.]],.]]],.]
[[1,4,6],[2,5,7],[3,8]]=>[3,8,2,5,7,1,4,6]=>[4,5,3,6,7,8,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[[1,3,6],[2,5,7],[4,8]]=>[4,8,2,5,7,1,3,6]=>[3,5,6,4,7,8,1,2]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]
[[1,3,6],[2,4,7],[5,8]]=>[5,8,2,4,7,1,3,6]=>[3,4,6,7,5,8,1,2]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]
[[1,4,5],[2,6,7],[3,8]]=>[3,8,2,6,7,1,4,5]=>[4,6,3,5,8,7,1,2]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]
[[1,3,4],[2,6,7],[5,8]]=>[5,8,2,6,7,1,3,4]=>[3,6,4,8,5,7,1,2]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[[1,2,4],[3,6,7],[5,8]]=>[5,8,3,6,7,1,2,4]=>[2,4,6,8,5,7,1,3]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]
[[1,3,5],[2,4,7],[6,8]]=>[6,8,2,4,7,1,3,5]=>[3,4,5,7,8,6,1,2]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]
[[1,3,4],[2,5,7],[6,8]]=>[6,8,2,5,7,1,3,4]=>[3,5,4,8,7,6,1,2]=>[[.,[[.,.],[[[.,.],.],.]]],[.,.]]
[[1,2,4],[3,5,7],[6,8]]=>[6,8,3,5,7,1,2,4]=>[2,4,5,8,7,6,1,3]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]
[[1,3,5],[2,4,6],[7,8]]=>[7,8,2,4,6,1,3,5]=>[3,4,5,6,8,1,7,2]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[[1,2,5],[3,4,6],[7,8]]=>[7,8,3,4,6,1,2,5]=>[2,5,4,6,8,1,7,3]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[[1,3,4],[2,5,6],[7,8]]=>[7,8,2,5,6,1,3,4]=>[3,5,4,8,6,1,7,2]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[[1,2,3],[4,5,6],[7,8]]=>[7,8,4,5,6,1,2,3]=>[2,3,8,5,6,1,7,4]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[[1,5,7],[2,6,8],[3],[4]]=>[4,3,2,6,8,1,5,7]=>[5,4,2,3,7,6,8,1]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]
[[1,3,7],[2,6,8],[4],[5]]=>[5,4,2,6,8,1,3,7]=>[3,5,7,2,4,6,8,1]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
[[1,3,7],[2,5,8],[4],[6]]=>[6,4,2,5,8,1,3,7]=>[3,5,7,2,6,4,8,1]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]
[[1,2,7],[3,5,8],[4],[6]]=>[6,4,3,5,8,1,2,7]=>[2,7,5,3,6,4,8,1]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]
[[1,3,7],[2,4,8],[5],[6]]=>[6,5,2,4,8,1,3,7]=>[3,4,7,6,2,5,8,1]=>[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]
[[1,3,6],[2,7,8],[4],[5]]=>[5,4,2,7,8,1,3,6]=>[3,5,6,2,4,8,7,1]=>[[[.,[.,[.,.]]],[.,[[.,.],.]]],.]
[[1,4,5],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5]=>[4,6,2,5,8,3,7,1]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]
[[1,2,5],[3,7,8],[4],[6]]=>[6,4,3,7,8,1,2,5]=>[2,5,6,3,8,4,7,1]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]
[[1,3,4],[2,7,8],[5],[6]]=>[6,5,2,7,8,1,3,4]=>[3,6,4,8,2,5,7,1]=>[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]
[[1,2,4],[3,7,8],[5],[6]]=>[6,5,3,7,8,1,2,4]=>[2,4,6,8,3,5,7,1]=>[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]
[[1,2,3],[4,7,8],[5],[6]]=>[6,5,4,7,8,1,2,3]=>[2,3,8,6,4,5,7,1]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[[1,3,6],[2,5,8],[4],[7]]=>[7,4,2,5,8,1,3,6]=>[3,5,6,2,7,8,4,1]=>[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]
[[1,2,6],[3,5,8],[4],[7]]=>[7,4,3,5,8,1,2,6]=>[2,6,5,3,7,8,4,1]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],.]
[[1,3,6],[2,4,8],[5],[7]]=>[7,5,2,4,8,1,3,6]=>[3,4,6,7,2,8,5,1]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]
[[1,2,6],[3,4,8],[5],[7]]=>[7,5,3,4,8,1,2,6]=>[2,6,4,7,3,8,5,1]=>[[.,[[[.,.],[.,.]],[[.,.],.]]],.]
[[1,3,4],[2,6,8],[5],[7]]=>[7,5,2,6,8,1,3,4]=>[3,6,4,8,2,7,5,1]=>[[[.,[[.,.],[.,.]]],[[.,.],.]],.]
[[1,2,4],[3,6,8],[5],[7]]=>[7,5,3,6,8,1,2,4]=>[2,4,6,8,3,7,5,1]=>[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]
[[1,3,5],[2,4,8],[6],[7]]=>[7,6,2,4,8,1,3,5]=>[3,4,5,7,8,2,6,1]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]
[[1,3,4],[2,5,8],[6],[7]]=>[7,6,2,5,8,1,3,4]=>[3,5,4,8,7,2,6,1]=>[[[.,[[.,.],[[.,.],.]]],[.,.]],.]
[[1,4,6],[2,5,7],[3],[8]]=>[8,3,2,5,7,1,4,6]=>[4,5,2,6,7,8,1,3]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[[1,3,6],[2,5,7],[4],[8]]=>[8,4,2,5,7,1,3,6]=>[3,5,6,2,7,8,1,4]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]
[[1,3,6],[2,4,7],[5],[8]]=>[8,5,2,4,7,1,3,6]=>[3,4,6,7,2,8,1,5]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[[1,3,4],[2,6,7],[5],[8]]=>[8,5,2,6,7,1,3,4]=>[3,6,4,8,2,7,1,5]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]
[[1,2,4],[3,6,7],[5],[8]]=>[8,5,3,6,7,1,2,4]=>[2,4,6,8,3,7,1,5]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]
[[1,2,5],[3,4,7],[6],[8]]=>[8,6,3,4,7,1,2,5]=>[2,5,4,7,8,3,1,6]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]
[[1,2,4],[3,5,7],[6],[8]]=>[8,6,3,5,7,1,2,4]=>[2,4,5,8,7,3,1,6]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]
[[1,3,5],[2,4,6],[7],[8]]=>[8,7,2,4,6,1,3,5]=>[3,4,5,6,8,1,2,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[[1,2,5],[3,4,6],[7],[8]]=>[8,7,3,4,6,1,2,5]=>[2,5,4,6,8,1,3,7]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[[1,3,4],[2,5,6],[7],[8]]=>[8,7,2,5,6,1,3,4]=>[3,5,4,8,6,1,2,7]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]
[[1,2,3],[4,5,6],[7],[8]]=>[8,7,4,5,6,1,2,3]=>[2,3,8,5,6,1,4,7]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[[1,2,8],[3,6],[4,7],[5]]=>[5,4,7,3,6,1,2,8]=>[2,7,6,5,4,1,3,8]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]
[[1,4,8],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4,8]=>[4,5,6,7,1,3,2,8]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[[1,3,8],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3,8]=>[3,5,7,6,1,4,2,8]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
[[1,2,8],[3,4],[5,7],[6]]=>[6,5,7,3,4,1,2,8]=>[2,7,4,1,6,5,3,8]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[[1,4,8],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4,8]=>[4,5,6,7,1,2,3,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[[1,2,8],[3,5],[4,6],[7]]=>[7,4,6,3,5,1,2,8]=>[2,7,5,6,1,3,4,8]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[[1,3,8],[2,4],[5,6],[7]]=>[7,5,6,2,4,1,3,8]=>[3,4,7,1,6,2,5,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[[1,5,7],[2,6],[3,8],[4]]=>[4,3,8,2,6,1,5,7]=>[5,6,4,3,7,1,8,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[[1,4,7],[2,5],[3,8],[6]]=>[6,3,8,2,5,1,4,7]=>[4,5,6,7,1,3,8,2]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[[1,3,7],[2,5],[4,8],[6]]=>[6,4,8,2,5,1,3,7]=>[3,5,7,6,1,4,8,2]=>[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]
[[1,2,7],[3,4],[5,8],[6]]=>[6,5,8,3,4,1,2,7]=>[2,7,4,1,6,5,8,3]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[[1,4,6],[2,7],[3,8],[5]]=>[5,3,8,2,7,1,4,6]=>[4,7,5,6,3,8,1,2]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]
[[1,2,6],[3,7],[4,8],[5]]=>[5,4,8,3,7,1,2,6]=>[2,6,7,5,4,8,1,3]=>[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]
[[1,3,5],[2,7],[4,8],[6]]=>[6,4,8,2,7,1,3,5]=>[3,7,5,6,8,4,1,2]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]
[[1,3,4],[2,7],[5,8],[6]]=>[6,5,8,2,7,1,3,4]=>[3,7,4,8,6,5,1,2]=>[[.,[[.,.],[[[.,.],.],.]]],[.,.]]
[[1,2,4],[3,7],[5,8],[6]]=>[6,5,8,3,7,1,2,4]=>[2,4,7,8,6,5,1,3]=>[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]
[[1,2,3],[4,7],[5,8],[6]]=>[6,5,8,4,7,1,2,3]=>[2,3,8,7,6,5,1,4]=>[[.,[.,[[[[.,.],.],.],.]]],[.,.]]
[[1,4,6],[2,5],[3,8],[7]]=>[7,3,8,2,5,1,4,6]=>[4,5,7,6,1,8,3,2]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]
[[1,3,6],[2,5],[4,8],[7]]=>[7,4,8,2,5,1,3,6]=>[3,5,6,7,1,8,4,2]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[[1,2,6],[3,5],[4,8],[7]]=>[7,4,8,3,5,1,2,6]=>[2,6,5,7,1,8,4,3]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[[1,3,6],[2,4],[5,8],[7]]=>[7,5,8,2,4,1,3,6]=>[3,4,6,1,7,8,5,2]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]
[[1,2,6],[3,4],[5,8],[7]]=>[7,5,8,3,4,1,2,6]=>[2,6,4,1,7,8,5,3]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]
[[1,3,4],[2,6],[5,8],[7]]=>[7,5,8,2,6,1,3,4]=>[3,6,4,8,7,1,5,2]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[[1,2,4],[3,6],[5,8],[7]]=>[7,5,8,3,6,1,2,4]=>[2,4,6,8,7,1,5,3]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]
[[1,2,3],[4,6],[5,8],[7]]=>[7,5,8,4,6,1,2,3]=>[2,3,8,6,7,1,5,4]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[[1,3,5],[2,4],[6,8],[7]]=>[7,6,8,2,4,1,3,5]=>[3,4,5,1,8,7,6,2]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]
[[1,2,5],[3,4],[6,8],[7]]=>[7,6,8,3,4,1,2,5]=>[2,5,4,1,8,7,6,3]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[[1,4,7],[2,5],[3,6],[8]]=>[8,3,6,2,5,1,4,7]=>[4,5,6,7,1,2,8,3]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[[1,3,7],[2,4],[5,6],[8]]=>[8,5,6,2,4,1,3,7]=>[3,4,7,1,6,2,8,5]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[[1,2,7],[3,4],[5,6],[8]]=>[8,5,6,3,4,1,2,7]=>[2,7,4,1,6,3,8,5]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[[1,4,6],[2,5],[3,7],[8]]=>[8,3,7,2,5,1,4,6]=>[4,5,7,6,1,8,2,3]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
[[1,2,6],[3,5],[4,7],[8]]=>[8,4,7,3,5,1,2,6]=>[2,6,5,7,1,8,3,4]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[[1,3,6],[2,4],[5,7],[8]]=>[8,5,7,2,4,1,3,6]=>[3,4,6,1,7,8,2,5]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[[1,2,6],[3,4],[5,7],[8]]=>[8,5,7,3,4,1,2,6]=>[2,6,4,1,7,8,3,5]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[[1,4,5],[2,6],[3,7],[8]]=>[8,3,7,2,6,1,4,5]=>[4,6,7,5,8,1,2,3]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]
[[1,2,5],[3,6],[4,7],[8]]=>[8,4,7,3,6,1,2,5]=>[2,5,6,7,8,1,3,4]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[[1,3,5],[2,4],[6,7],[8]]=>[8,6,7,2,4,1,3,5]=>[3,4,5,1,8,7,2,6]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[[1,2,5],[3,4],[6,7],[8]]=>[8,6,7,3,4,1,2,5]=>[2,5,4,1,8,7,3,6]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[[1,3,4],[2,5],[6,7],[8]]=>[8,6,7,2,5,1,3,4]=>[3,5,4,8,1,7,2,6]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[[1,2,3],[4,5],[6,7],[8]]=>[8,6,7,4,5,1,2,3]=>[2,3,8,5,1,7,4,6]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
[[1,5,8],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5,8]=>[5,6,2,3,7,4,1,8]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]
[[1,4,8],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4,8]=>[4,6,2,7,3,5,1,8]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[[1,3,8],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3,8]=>[3,6,7,2,4,5,1,8]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]
[[1,3,8],[2,5],[4],[6],[7]]=>[7,6,4,2,5,1,3,8]=>[3,5,7,2,1,4,6,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[[1,6,7],[2,8],[3],[4],[5]]=>[5,4,3,2,8,1,6,7]=>[6,5,2,3,4,7,8,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[[1,3,7],[2,8],[4],[5],[6]]=>[6,5,4,2,8,1,3,7]=>[3,6,7,2,4,5,8,1]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
[[1,2,7],[3,8],[4],[5],[6]]=>[6,5,4,3,8,1,2,7]=>[2,7,6,3,4,5,8,1]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[[1,4,6],[2,8],[3],[5],[7]]=>[7,5,3,2,8,1,4,6]=>[4,7,2,6,3,8,5,1]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]
[[1,4,5],[2,8],[3],[6],[7]]=>[7,6,3,2,8,1,4,5]=>[4,7,2,5,8,3,6,1]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]
[[1,2,5],[3,8],[4],[6],[7]]=>[7,6,4,3,8,1,2,5]=>[2,5,7,3,8,4,6,1]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]
[[1,2,4],[3,8],[5],[6],[7]]=>[7,6,5,3,8,1,2,4]=>[2,4,7,8,3,5,6,1]=>[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]
[[1,2,3],[4,8],[5],[6],[7]]=>[7,6,5,4,8,1,2,3]=>[2,3,8,7,4,5,6,1]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[[1,4,7],[2,6],[3],[5],[8]]=>[8,5,3,2,6,1,4,7]=>[4,6,2,7,3,1,8,5]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[[1,3,7],[2,6],[4],[5],[8]]=>[8,5,4,2,6,1,3,7]=>[3,6,7,2,4,1,8,5]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]
[[1,2,7],[3,6],[4],[5],[8]]=>[8,5,4,3,6,1,2,7]=>[2,7,6,3,4,1,8,5]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[[1,3,7],[2,5],[4],[6],[8]]=>[8,6,4,2,5,1,3,7]=>[3,5,7,2,1,4,8,6]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]
[[1,2,7],[3,5],[4],[6],[8]]=>[8,6,4,3,5,1,2,7]=>[2,7,5,3,1,4,8,6]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]
[[1,3,7],[2,4],[5],[6],[8]]=>[8,6,5,2,4,1,3,7]=>[3,4,7,1,2,5,8,6]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[[1,2,7],[3,4],[5],[6],[8]]=>[8,6,5,3,4,1,2,7]=>[2,7,4,1,3,5,8,6]=>[[.,[[.,.],.]],[.,[.,[[.,.],.]]]]
[[1,4,6],[2,7],[3],[5],[8]]=>[8,5,3,2,7,1,4,6]=>[4,7,2,6,3,8,1,5]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[[1,3,6],[2,7],[4],[5],[8]]=>[8,5,4,2,7,1,3,6]=>[3,7,6,2,4,8,1,5]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]
[[1,4,5],[2,7],[3],[6],[8]]=>[8,6,3,2,7,1,4,5]=>[4,7,2,5,8,3,1,6]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]
[[1,3,5],[2,7],[4],[6],[8]]=>[8,6,4,2,7,1,3,5]=>[3,7,5,2,8,4,1,6]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]
[[1,2,5],[3,7],[4],[6],[8]]=>[8,6,4,3,7,1,2,5]=>[2,5,7,3,8,4,1,6]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]
[[1,3,4],[2,7],[5],[6],[8]]=>[8,6,5,2,7,1,3,4]=>[3,7,4,8,2,5,1,6]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]
[[1,2,4],[3,7],[5],[6],[8]]=>[8,6,5,3,7,1,2,4]=>[2,4,7,8,3,5,1,6]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]
[[1,2,3],[4,7],[5],[6],[8]]=>[8,6,5,4,7,1,2,3]=>[2,3,8,7,4,5,1,6]=>[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]
[[1,4,6],[2,5],[3],[7],[8]]=>[8,7,3,2,5,1,4,6]=>[4,5,2,6,1,8,3,7]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[[1,3,6],[2,5],[4],[7],[8]]=>[8,7,4,2,5,1,3,6]=>[3,5,6,2,1,8,4,7]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[[1,2,6],[3,4],[5],[7],[8]]=>[8,7,5,3,4,1,2,6]=>[2,6,4,1,3,8,5,7]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]
[[1,3,5],[2,6],[4],[7],[8]]=>[8,7,4,2,6,1,3,5]=>[3,6,5,2,8,1,4,7]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]
[[1,2,5],[3,6],[4],[7],[8]]=>[8,7,4,3,6,1,2,5]=>[2,5,6,3,8,1,4,7]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]
[[1,3,4],[2,6],[5],[7],[8]]=>[8,7,5,2,6,1,3,4]=>[3,6,4,8,2,1,5,7]=>[[[.,[[.,.],[.,.]]],.],[.,[.,.]]]
[[1,2,4],[3,6],[5],[7],[8]]=>[8,7,5,3,6,1,2,4]=>[2,4,6,8,3,1,5,7]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]
[[1,2,3],[4,6],[5],[7],[8]]=>[8,7,5,4,6,1,2,3]=>[2,3,8,6,4,1,5,7]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]
[[1,2,5],[3,4],[6],[7],[8]]=>[8,7,6,3,4,1,2,5]=>[2,5,4,1,8,3,6,7]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[[1,2,3],[4,5],[6],[7],[8]]=>[8,7,6,4,5,1,2,3]=>[2,3,8,5,1,4,6,7]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[[1,7,8],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7,8]=>[6,1,2,3,4,5,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,6,8],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6,8]=>[6,1,2,3,4,7,5,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[[1,4,8],[2],[3],[5],[6],[7]]=>[7,6,5,3,2,1,4,8]=>[4,1,2,7,3,5,6,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[[1,3,8],[2],[4],[5],[6],[7]]=>[7,6,5,4,2,1,3,8]=>[3,1,7,2,4,5,6,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[[1,2,8],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2,8]=>[2,7,1,3,4,5,6,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[[1,6,7],[2],[3],[4],[5],[8]]=>[8,5,4,3,2,1,6,7]=>[6,1,2,3,4,7,8,5]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[[1,5,7],[2],[3],[4],[6],[8]]=>[8,6,4,3,2,1,5,7]=>[5,1,2,3,7,4,8,6]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[[1,4,7],[2],[3],[5],[6],[8]]=>[8,6,5,3,2,1,4,7]=>[4,1,2,7,3,5,8,6]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[[1,3,7],[2],[4],[5],[6],[8]]=>[8,6,5,4,2,1,3,7]=>[3,1,7,2,4,5,8,6]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[[1,2,7],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,1,2,7]=>[2,7,1,3,4,5,8,6]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[[1,5,6],[2],[3],[4],[7],[8]]=>[8,7,4,3,2,1,5,6]=>[5,1,2,3,6,8,4,7]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[[1,4,6],[2],[3],[5],[7],[8]]=>[8,7,5,3,2,1,4,6]=>[4,1,2,6,3,8,5,7]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[[1,3,6],[2],[4],[5],[7],[8]]=>[8,7,5,4,2,1,3,6]=>[3,1,6,2,4,8,5,7]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[[1,2,6],[3],[4],[5],[7],[8]]=>[8,7,5,4,3,1,2,6]=>[2,6,1,3,4,8,5,7]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[[1,4,5],[2],[3],[6],[7],[8]]=>[8,7,6,3,2,1,4,5]=>[4,1,2,5,8,3,6,7]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[[1,3,5],[2],[4],[6],[7],[8]]=>[8,7,6,4,2,1,3,5]=>[3,1,5,2,8,4,6,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[[1,2,5],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,1,2,5]=>[2,5,1,3,8,4,6,7]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[[1,3,4],[2],[5],[6],[7],[8]]=>[8,7,6,5,2,1,3,4]=>[3,1,4,8,2,5,6,7]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[[1,2,4],[3],[5],[6],[7],[8]]=>[8,7,6,5,3,1,2,4]=>[2,4,1,8,3,5,6,7]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[[1,2,3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,1,2,3]=>[2,3,8,1,4,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[[1,5],[2,6],[3,7],[4,8]]=>[4,8,3,7,2,6,1,5]=>[5,6,7,4,8,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[[1,2],[3,6],[4,7],[5,8]]=>[5,8,4,7,3,6,1,2]=>[2,8,6,7,5,1,3,4]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]
[[1,3],[2,5],[4,7],[6,8]]=>[6,8,4,7,2,5,1,3]=>[3,5,8,7,1,6,2,4]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
[[1,2],[3,5],[4,7],[6,8]]=>[6,8,4,7,3,5,1,2]=>[2,8,5,7,1,6,3,4]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[[1,3],[2,4],[5,7],[6,8]]=>[6,8,5,7,2,4,1,3]=>[3,4,8,1,7,6,2,5]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[[1,2],[3,4],[5,7],[6,8]]=>[6,8,5,7,3,4,1,2]=>[2,8,4,1,7,6,3,5]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[[1,4],[2,5],[3,6],[7,8]]=>[7,8,3,6,2,5,1,4]=>[4,5,6,8,1,2,7,3]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[[1,3],[2,5],[4,6],[7,8]]=>[7,8,4,6,2,5,1,3]=>[3,5,8,6,1,2,7,4]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]
[[1,3],[2,4],[5,6],[7,8]]=>[7,8,5,6,2,4,1,3]=>[3,4,8,1,6,2,7,5]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[[1,2],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2]=>[2,8,4,1,6,3,7,5]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[[1,5],[2,7],[3,8],[4],[6]]=>[6,4,3,8,2,7,1,5]=>[5,7,6,3,8,4,1,2]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]
[[1,4],[2,7],[3,8],[5],[6]]=>[6,5,3,8,2,7,1,4]=>[4,7,6,8,3,5,1,2]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]
[[1,2],[3,7],[4,8],[5],[6]]=>[6,5,4,8,3,7,1,2]=>[2,8,7,6,4,5,1,3]=>[[.,[[[[.,.],.],.],[.,.]]],[.,.]]
[[1,4],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4]=>[4,6,7,8,3,1,5,2]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]
[[1,3],[2,5],[4,8],[6],[7]]=>[7,6,4,8,2,5,1,3]=>[3,5,8,7,1,4,6,2]=>[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]
[[1,3],[2,4],[5,8],[6],[7]]=>[7,6,5,8,2,4,1,3]=>[3,4,8,1,7,5,6,2]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[[1,5],[2,6],[3,7],[4],[8]]=>[8,4,3,7,2,6,1,5]=>[5,6,7,3,8,1,2,4]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[[1,3],[2,6],[4,7],[5],[8]]=>[8,5,4,7,2,6,1,3]=>[3,6,8,7,4,1,2,5]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]
[[1,2],[3,6],[4,7],[5],[8]]=>[8,5,4,7,3,6,1,2]=>[2,8,6,7,4,1,3,5]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]
[[1,3],[2,5],[4,7],[6],[8]]=>[8,6,4,7,2,5,1,3]=>[3,5,8,7,1,4,2,6]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
[[1,2],[3,5],[4,7],[6],[8]]=>[8,6,4,7,3,5,1,2]=>[2,8,5,7,1,4,3,6]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[[1,2],[3,4],[5,7],[6],[8]]=>[8,6,5,7,3,4,1,2]=>[2,8,4,1,7,5,3,6]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[[1,4],[2,5],[3,6],[7],[8]]=>[8,7,3,6,2,5,1,4]=>[4,5,6,8,1,2,3,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[[1,3],[2,5],[4,6],[7],[8]]=>[8,7,4,6,2,5,1,3]=>[3,5,8,6,1,2,4,7]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[[1,3],[2,4],[5,6],[7],[8]]=>[8,7,5,6,2,4,1,3]=>[3,4,8,1,6,2,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[[1,2],[3,4],[5,6],[7],[8]]=>[8,7,5,6,3,4,1,2]=>[2,8,4,1,6,3,5,7]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[[1,7],[2,8],[3],[4],[5],[6]]=>[6,5,4,3,2,8,1,7]=>[7,6,2,3,4,5,8,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[[1,6],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6]=>[6,7,2,3,4,8,5,1]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]
[[1,4],[2,8],[3],[5],[6],[7]]=>[7,6,5,3,2,8,1,4]=>[4,7,2,8,3,5,6,1]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]
[[1,3],[2,8],[4],[5],[6],[7]]=>[7,6,5,4,2,8,1,3]=>[3,7,8,2,4,5,6,1]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
[[1,2],[3,8],[4],[5],[6],[7]]=>[7,6,5,4,3,8,1,2]=>[2,8,7,3,4,5,6,1]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[[1,6],[2,7],[3],[4],[5],[8]]=>[8,5,4,3,2,7,1,6]=>[6,7,2,3,4,8,1,5]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[[1,3],[2,7],[4],[5],[6],[8]]=>[8,6,5,4,2,7,1,3]=>[3,7,8,2,4,5,1,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]
[[1,4],[2,6],[3],[5],[7],[8]]=>[8,7,5,3,2,6,1,4]=>[4,6,2,8,3,1,5,7]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[[1,3],[2,6],[4],[5],[7],[8]]=>[8,7,5,4,2,6,1,3]=>[3,6,8,2,4,1,5,7]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[[1,3],[2,5],[4],[6],[7],[8]]=>[8,7,6,4,2,5,1,3]=>[3,5,8,2,1,4,6,7]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[[1,2],[3,5],[4],[6],[7],[8]]=>[8,7,6,4,3,5,1,2]=>[2,8,5,3,1,4,6,7]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]
[[1,3],[2,4],[5],[6],[7],[8]]=>[8,7,6,5,2,4,1,3]=>[3,4,8,1,2,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[[1,2],[3,4],[5],[6],[7],[8]]=>[8,7,6,5,3,4,1,2]=>[2,8,4,1,3,5,6,7]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[[1,8],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8]=>[7,1,2,3,4,5,6,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,7],[2],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,8,6]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[[1,6],[2],[3],[4],[5],[7],[8]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,8,5,7]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[[1,5],[2],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,8,4,6,7]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[[1,4],[2],[3],[5],[6],[7],[8]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,8,3,5,6,7]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[[1,3],[2],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,2,1,3]=>[3,1,8,2,4,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[[1,2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,1,2]=>[2,8,1,3,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[[1],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1]=>[8,1,2,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,3,5,7,9],[2,4,6,8,10]]=>[2,4,6,8,10,1,3,5,7,9]=>[3,2,5,4,7,6,9,8,10,1]=>[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]
[[1,3,5,7,8],[2,4,6,9,10]]=>[2,4,6,9,10,1,3,5,7,8]=>[3,2,5,4,7,6,8,10,9,1]=>[[[.,.],[[.,.],[[.,.],[.,[[.,.],.]]]]],.]
[[1,3,5,6,9],[2,4,7,8,10]]=>[2,4,7,8,10,1,3,5,6,9]=>[3,2,5,4,6,9,7,8,10,1]=>[[[.,.],[[.,.],[.,[[.,.],[.,[.,.]]]]]],.]
[[1,3,5,6,8],[2,4,7,9,10]]=>[2,4,7,9,10,1,3,5,6,8]=>[3,2,5,4,6,8,7,10,9,1]=>[[[.,.],[[.,.],[.,[[.,.],[[.,.],.]]]]],.]
[[1,3,5,6,7],[2,4,8,9,10]]=>[2,4,8,9,10,1,3,5,6,7]=>[3,2,5,4,6,7,10,8,9,1]=>[[[.,.],[[.,.],[.,[.,[[.,.],[.,.]]]]]],.]
[[1,3,4,7,9],[2,5,6,8,10]]=>[2,5,6,8,10,1,3,4,7,9]=>[3,2,4,7,5,6,9,8,10,1]=>[[[.,.],[.,[[.,.],[.,[[.,.],[.,.]]]]]],.]
[[1,3,4,7,8],[2,5,6,9,10]]=>[2,5,6,9,10,1,3,4,7,8]=>[3,2,4,7,5,6,8,10,9,1]=>[[[.,.],[.,[[.,.],[.,[.,[[.,.],.]]]]]],.]
[[1,3,4,6,9],[2,5,7,8,10]]=>[2,5,7,8,10,1,3,4,6,9]=>[3,2,4,6,5,9,7,8,10,1]=>[[[.,.],[.,[[.,.],[[.,.],[.,[.,.]]]]]],.]
[[1,3,4,6,8],[2,5,7,9,10]]=>[2,5,7,9,10,1,3,4,6,8]=>[3,2,4,6,5,8,7,10,9,1]=>[[[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]],.]
[[1,3,4,6,7],[2,5,8,9,10]]=>[2,5,8,9,10,1,3,4,6,7]=>[3,2,4,6,5,7,10,8,9,1]=>[[[.,.],[.,[[.,.],[.,[[.,.],[.,.]]]]]],.]
[[1,3,4,5,9],[2,6,7,8,10]]=>[2,6,7,8,10,1,3,4,5,9]=>[3,2,4,5,9,6,7,8,10,1]=>[[[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]],.]
[[1,3,4,5,8],[2,6,7,9,10]]=>[2,6,7,9,10,1,3,4,5,8]=>[3,2,4,5,8,6,7,10,9,1]=>[[[.,.],[.,[.,[[.,.],[.,[[.,.],.]]]]]],.]
[[1,3,4,5,7],[2,6,8,9,10]]=>[2,6,8,9,10,1,3,4,5,7]=>[3,2,4,5,7,6,10,8,9,1]=>[[[.,.],[.,[.,[[.,.],[[.,.],[.,.]]]]]],.]
[[1,3,4,5,6],[2,7,8,9,10]]=>[2,7,8,9,10,1,3,4,5,6]=>[3,2,4,5,6,10,7,8,9,1]=>[[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[[1,2,5,7,9],[3,4,6,8,10]]=>[3,4,6,8,10,1,2,5,7,9]=>[2,5,3,4,7,6,9,8,10,1]=>[[.,[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]],.]
[[1,2,5,7,8],[3,4,6,9,10]]=>[3,4,6,9,10,1,2,5,7,8]=>[2,5,3,4,7,6,8,10,9,1]=>[[.,[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]],.]
[[1,2,5,6,9],[3,4,7,8,10]]=>[3,4,7,8,10,1,2,5,6,9]=>[2,5,3,4,6,9,7,8,10,1]=>[[.,[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[[1,2,5,6,8],[3,4,7,9,10]]=>[3,4,7,9,10,1,2,5,6,8]=>[2,5,3,4,6,8,7,10,9,1]=>[[.,[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]],.]
[[1,2,5,6,7],[3,4,8,9,10]]=>[3,4,8,9,10,1,2,5,6,7]=>[2,5,3,4,6,7,10,8,9,1]=>[[.,[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[[1,2,4,7,9],[3,5,6,8,10]]=>[3,5,6,8,10,1,2,4,7,9]=>[2,4,3,7,5,6,9,8,10,1]=>[[.,[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]],.]
[[1,2,4,7,8],[3,5,6,9,10]]=>[3,5,6,9,10,1,2,4,7,8]=>[2,4,3,7,5,6,8,10,9,1]=>[[.,[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]],.]
[[1,2,4,6,9],[3,5,7,8,10]]=>[3,5,7,8,10,1,2,4,6,9]=>[2,4,3,6,5,9,7,8,10,1]=>[[.,[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]],.]
[[1,2,4,6,8],[3,5,7,9,10]]=>[3,5,7,9,10,1,2,4,6,8]=>[2,4,3,6,5,8,7,10,9,1]=>[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]
[[1,2,4,6,7],[3,5,8,9,10]]=>[3,5,8,9,10,1,2,4,6,7]=>[2,4,3,6,5,7,10,8,9,1]=>[[.,[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]],.]
[[1,2,4,5,9],[3,6,7,8,10]]=>[3,6,7,8,10,1,2,4,5,9]=>[2,4,3,5,9,6,7,8,10,1]=>[[.,[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]],.]
[[1,2,4,5,8],[3,6,7,9,10]]=>[3,6,7,9,10,1,2,4,5,8]=>[2,4,3,5,8,6,7,10,9,1]=>[[.,[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]],.]
[[1,2,4,5,7],[3,6,8,9,10]]=>[3,6,8,9,10,1,2,4,5,7]=>[2,4,3,5,7,6,10,8,9,1]=>[[.,[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]],.]
[[1,2,4,5,6],[3,7,8,9,10]]=>[3,7,8,9,10,1,2,4,5,6]=>[2,4,3,5,6,10,7,8,9,1]=>[[.,[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[[1,2,3,7,9],[4,5,6,8,10]]=>[4,5,6,8,10,1,2,3,7,9]=>[2,3,7,4,5,6,9,8,10,1]=>[[.,[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]],.]
[[1,2,3,7,8],[4,5,6,9,10]]=>[4,5,6,9,10,1,2,3,7,8]=>[2,3,7,4,5,6,8,10,9,1]=>[[.,[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]],.]
[[1,2,3,6,9],[4,5,7,8,10]]=>[4,5,7,8,10,1,2,3,6,9]=>[2,3,6,4,5,9,7,8,10,1]=>[[.,[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]],.]
[[1,2,3,6,8],[4,5,7,9,10]]=>[4,5,7,9,10,1,2,3,6,8]=>[2,3,6,4,5,8,7,10,9,1]=>[[.,[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]],.]
[[1,2,3,6,7],[4,5,8,9,10]]=>[4,5,8,9,10,1,2,3,6,7]=>[2,3,6,4,5,7,10,8,9,1]=>[[.,[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]],.]
[[1,2,3,5,9],[4,6,7,8,10]]=>[4,6,7,8,10,1,2,3,5,9]=>[2,3,5,4,9,6,7,8,10,1]=>[[.,[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]],.]
[[1,2,3,5,8],[4,6,7,9,10]]=>[4,6,7,9,10,1,2,3,5,8]=>[2,3,5,4,8,6,7,10,9,1]=>[[.,[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]],.]
[[1,2,3,5,7],[4,6,8,9,10]]=>[4,6,8,9,10,1,2,3,5,7]=>[2,3,5,4,7,6,10,8,9,1]=>[[.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]],.]
[[1,2,3,5,6],[4,7,8,9,10]]=>[4,7,8,9,10,1,2,3,5,6]=>[2,3,5,4,6,10,7,8,9,1]=>[[.,[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]],.]
[[1,2,3,4,9],[5,6,7,8,10]]=>[5,6,7,8,10,1,2,3,4,9]=>[2,3,4,9,5,6,7,8,10,1]=>[[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]
[[1,2,3,4,8],[5,6,7,9,10]]=>[5,6,7,9,10,1,2,3,4,8]=>[2,3,4,8,5,6,7,10,9,1]=>[[.,[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]],.]
[[1,2,3,4,7],[5,6,8,9,10]]=>[5,6,8,9,10,1,2,3,4,7]=>[2,3,4,7,5,6,10,8,9,1]=>[[.,[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]],.]
[[1,2,3,4,6],[5,7,8,9,10]]=>[5,7,8,9,10,1,2,3,4,6]=>[2,3,4,6,5,10,7,8,9,1]=>[[.,[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]],.]
[[1,2,3,4,5],[6,7,8,9,10]]=>[6,7,8,9,10,1,2,3,4,5]=>[2,3,4,5,10,6,7,8,9,1]=>[[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.]
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[[1,2,3,4,5,6],[7,8],[9,10]]=>[9,10,7,8,1,2,3,4,5,6]=>[2,3,4,5,6,10,8,1,9,7]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[[.,.],.]]
[[1,2,3,4,5,6],[7,8],[9],[10]]=>[10,9,7,8,1,2,3,4,5,6]=>[2,3,4,5,6,10,8,1,7,9]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,[.,.]]]
[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[10,9,8,7,1,2,3,4,5,6]=>[2,3,4,5,6,10,1,7,8,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[[1,2,3,4,5],[6,7,8,9],[10]]=>[10,6,7,8,9,1,2,3,4,5]=>[2,3,4,5,10,7,8,9,1,6]=>[[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],[.,.]]
[[1,2,3,4,5],[6,7,8],[9,10]]=>[9,10,6,7,8,1,2,3,4,5]=>[2,3,4,5,10,7,8,1,9,6]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],[[.,.],.]]
[[1,2,3,4,5],[6,7,8],[9],[10]]=>[10,9,6,7,8,1,2,3,4,5]=>[2,3,4,5,10,7,8,1,6,9]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],[.,[.,.]]]
[[1,2,3,4,5],[6,7],[8,9],[10]]=>[10,8,9,6,7,1,2,3,4,5]=>[2,3,4,5,10,7,1,9,6,8]=>[[.,[.,[.,[.,[[.,.],.]]]]],[[.,.],[.,.]]]
[[1,2,3,4,5],[6,7],[8],[9],[10]]=>[10,9,8,6,7,1,2,3,4,5]=>[2,3,4,5,10,7,1,6,8,9]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,[.,.]]]]
[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,1,2,3,4,5]=>[2,3,4,5,10,1,6,7,8,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[[1,2,3,4],[5,6,7,8],[9,10]]=>[9,10,5,6,7,8,1,2,3,4]=>[2,3,4,10,6,7,8,1,9,5]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],[[.,.],.]]
[[1,2,3,4],[5,6,7,8],[9],[10]]=>[10,9,5,6,7,8,1,2,3,4]=>[2,3,4,10,6,7,8,1,5,9]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],[.,[.,.]]]
[[1,2,3,4],[5,6,7],[8,9,10]]=>[8,9,10,5,6,7,1,2,3,4]=>[2,3,4,10,6,7,1,8,9,5]=>[[.,[.,[.,[[.,.],[.,.]]]]],[[.,[.,.]],.]]
[[1,2,3,4],[5,6,7],[8,9],[10]]=>[10,8,9,5,6,7,1,2,3,4]=>[2,3,4,10,6,7,1,9,5,8]=>[[.,[.,[.,[[.,.],[.,.]]]]],[[.,.],[.,.]]]
[[1,2,3,4],[5,6,7],[8],[9],[10]]=>[10,9,8,5,6,7,1,2,3,4]=>[2,3,4,10,6,7,1,5,8,9]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,[.,[.,.]]]]
[[1,2,3,4],[5,6],[7,8],[9,10]]=>[9,10,7,8,5,6,1,2,3,4]=>[2,3,4,10,6,1,8,5,9,7]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],[[.,.],.]]]
[[1,2,3,4],[5,6],[7,8],[9],[10]]=>[10,9,7,8,5,6,1,2,3,4]=>[2,3,4,10,6,1,8,5,7,9]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],[.,[.,.]]]]
[[1,2,3,4],[5,6],[7],[8],[9],[10]]=>[10,9,8,7,5,6,1,2,3,4]=>[2,3,4,10,6,1,5,7,8,9]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,[.,[.,.]]]]]
[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,1,2,3,4]=>[2,3,4,10,1,5,6,7,8,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,3],[4,5,6],[7,8,9],[10]]=>[10,7,8,9,4,5,6,1,2,3]=>[2,3,10,5,6,1,8,9,4,7]=>[[.,[.,[[.,.],[.,.]]]],[[.,[.,.]],[.,.]]]
[[1,2,3],[4,5,6],[7,8],[9,10]]=>[9,10,7,8,4,5,6,1,2,3]=>[2,3,10,5,6,1,8,4,9,7]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],[[.,.],.]]]
[[1,2,3],[4,5,6],[7,8],[9],[10]]=>[10,9,7,8,4,5,6,1,2,3]=>[2,3,10,5,6,1,8,4,7,9]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],[.,[.,.]]]]
[[1,2,3],[4,5,6],[7],[8],[9],[10]]=>[10,9,8,7,4,5,6,1,2,3]=>[2,3,10,5,6,1,4,7,8,9]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,[.,[.,.]]]]]
[[1,2,3],[4,5],[6,7],[8,9],[10]]=>[10,8,9,6,7,4,5,1,2,3]=>[2,3,10,5,1,7,4,9,6,8]=>[[.,[.,[[.,.],.]]],[[.,.],[[.,.],[.,.]]]]
[[1,2,3],[4,5],[6,7],[8],[9],[10]]=>[10,9,8,6,7,4,5,1,2,3]=>[2,3,10,5,1,7,4,6,8,9]=>[[.,[.,[[.,.],.]]],[[.,.],[.,[.,[.,.]]]]]
[[1,2,3],[4,5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,4,5,1,2,3]=>[2,3,10,5,1,4,6,7,8,9]=>[[.,[.,[[.,.],.]]],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,1,2,3]=>[2,3,10,1,4,5,6,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,2],[3,4],[5,6],[7,8],[9,10]]=>[9,10,7,8,5,6,3,4,1,2]=>[2,10,4,1,6,3,8,5,9,7]=>[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]
[[1,2],[3,4],[5,6],[7,8],[9],[10]]=>[10,9,7,8,5,6,3,4,1,2]=>[2,10,4,1,6,3,8,5,7,9]=>[[.,[[.,.],.]],[[.,.],[[.,.],[.,[.,.]]]]]
[[1,2],[3,4],[5,6],[7],[8],[9],[10]]=>[10,9,8,7,5,6,3,4,1,2]=>[2,10,4,1,6,3,5,7,8,9]=>[[.,[[.,.],.]],[[.,.],[.,[.,[.,[.,.]]]]]]
[[1,2],[3,4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,3,4,1,2]=>[2,10,4,1,3,5,6,7,8,9]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,3,1,2]=>[2,10,1,3,4,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,3,2,1]=>[10,1,2,3,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,1,2,3,4,5,6,7,8,9,10,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[[1,3,4,5,6,7,8,9],[2]]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,2,5,6,7,8,9],[3,4]]=>[3,4,1,2,5,6,7,8,9]=>[2,4,3,1,5,6,7,8,9]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]
[[1,4,5,6,7,8,9],[2],[3]]=>[3,2,1,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,2,3,7,8,9],[4,5,6]]=>[4,5,6,1,2,3,7,8,9]=>[2,3,6,4,5,1,7,8,9]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,[.,.]]]]
[[1,3,6,7,8,9],[2,5],[4]]=>[4,2,5,1,3,6,7,8,9]=>[3,4,5,2,1,6,7,8,9]=>[[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]]
[[1,5,6,7,8,9],[2],[3],[4]]=>[4,3,2,1,5,6,7,8,9]=>[4,1,2,3,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,2,3,4,9],[5,6,7,8]]=>[5,6,7,8,1,2,3,4,9]=>[2,3,4,8,5,6,7,1,9]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],[.,.]]
[[1,3,4,8,9],[2,6,7],[5]]=>[5,2,6,7,1,3,4,8,9]=>[3,5,4,7,2,6,1,8,9]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,[.,.]]]
[[1,2,7,8,9],[3,4],[5,6]]=>[5,6,3,4,1,2,7,8,9]=>[2,6,4,1,5,3,7,8,9]=>[[.,[[.,.],.]],[[.,.],[.,[.,[.,.]]]]]
[[1,4,7,8,9],[2,6],[3],[5]]=>[5,3,2,6,1,4,7,8,9]=>[4,5,2,6,3,1,7,8,9]=>[[[.,[.,.]],[[.,.],.]],[.,[.,[.,.]]]]
[[1,6,7,8,9],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8,9]=>[5,1,2,3,4,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,3,4,5],[2,7,8,9],[6]]=>[6,2,7,8,9,1,3,4,5]=>[3,6,4,5,9,2,7,8,1]=>[[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]],.]
[[1,2,5,9],[3,4,8],[6,7]]=>[6,7,3,4,8,1,2,5,9]=>[2,5,4,7,8,6,3,1,9]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],[.,.]]
[[1,4,5,9],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5,9]=>[4,6,2,5,8,3,7,1,9]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],[.,.]]
[[1,3,8,9],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3,8,9]=>[3,5,7,6,1,4,2,8,9]=>[[.,[.,[[.,.],.]]],[[.,.],[.,[.,.]]]]
[[1,5,8,9],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5,8,9]=>[5,6,2,3,7,4,1,8,9]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,[.,.]]]
[[1,7,8,9],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7,8,9]=>[6,1,2,3,4,5,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,3,6],[2,5,9],[4,8],[7]]=>[7,4,8,2,5,9,1,3,6]=>[3,5,6,7,8,9,4,2,1]=>[[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.]
[[1,5,6],[2,8,9],[3],[4],[7]]=>[7,4,3,2,8,9,1,5,6]=>[5,7,2,3,6,9,4,8,1]=>[[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]],.]
[[1,2,9],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2,9]=>[2,8,4,1,6,3,7,5,9]=>[[.,[[.,.],.]],[[.,.],[[.,.],[.,.]]]]
[[1,4,9],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4,9]=>[4,6,7,8,3,1,5,2,9]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],[.,.]]]
[[1,6,9],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6,9]=>[6,7,2,3,4,8,5,1,9]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],[.,.]]
[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,3],[2,5],[4,7],[6,9],[8]]=>[8,6,9,4,7,2,5,1,3]=>[3,5,9,7,1,8,2,6,4]=>[[.,[.,[[.,.],.]]],[[.,.],[[.,.],.]]]
[[1,5],[2,7],[3,9],[4],[6],[8]]=>[8,6,4,3,9,2,7,1,5]=>[5,7,8,3,9,4,1,6,2]=>[[[.,[.,[.,.]]],[[.,.],.]],[[.,.],.]]
[[1,7],[2,9],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,9,1,7]=>[7,8,2,3,4,5,9,6,1]=>[[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]],.]
[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1,9]=>[8,1,2,3,4,5,6,7,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,3,4,5,6,7,8,9,10],[2]]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[[1,2,5,6,7,8,9,10],[3,4]]=>[3,4,1,2,5,6,7,8,9,10]=>[2,4,3,1,5,6,7,8,9,10]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,4,5,6,7,8,9,10],[2],[3]]=>[3,2,1,4,5,6,7,8,9,10]=>[3,1,2,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[[1,2,3,7,8,9,10],[4,5,6]]=>[4,5,6,1,2,3,7,8,9,10]=>[2,3,6,4,5,1,7,8,9,10]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,[.,[.,.]]]]]
[[1,3,6,7,8,9,10],[2,5],[4]]=>[4,2,5,1,3,6,7,8,9,10]=>[3,4,5,2,1,6,7,8,9,10]=>[[[.,[.,[.,.]]],.],[.,[.,[.,[.,[.,.]]]]]]
[[1,5,6,7,8,9,10],[2],[3],[4]]=>[4,3,2,1,5,6,7,8,9,10]=>[4,1,2,3,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[[1,2,3,4,9,10],[5,6,7,8]]=>[5,6,7,8,1,2,3,4,9,10]=>[2,3,4,8,5,6,7,1,9,10]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],[.,[.,.]]]
[[1,3,4,8,9,10],[2,6,7],[5]]=>[5,2,6,7,1,3,4,8,9,10]=>[3,5,4,7,2,6,1,8,9,10]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,[.,[.,.]]]]
[[1,2,7,8,9,10],[3,4],[5,6]]=>[5,6,3,4,1,2,7,8,9,10]=>[2,6,4,1,5,3,7,8,9,10]=>[[.,[[.,.],.]],[[.,.],[.,[.,[.,[.,.]]]]]]
[[1,4,7,8,9,10],[2,6],[3],[5]]=>[5,3,2,6,1,4,7,8,9,10]=>[4,5,2,6,3,1,7,8,9,10]=>[[[.,[.,.]],[[.,.],.]],[.,[.,[.,[.,.]]]]]
[[1,6,7,8,9,10],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8,9,10]=>[5,1,2,3,4,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[[1,3,4,5,10],[2,7,8,9],[6]]=>[6,2,7,8,9,1,3,4,5,10]=>[3,6,4,5,9,2,7,8,1,10]=>[[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]],[.,.]]
[[1,2,5,9,10],[3,4,8],[6,7]]=>[6,7,3,4,8,1,2,5,9,10]=>[2,5,4,7,8,6,3,1,9,10]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],[.,[.,.]]]
[[1,4,5,9,10],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5,9,10]=>[4,6,2,5,8,3,7,1,9,10]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],[.,[.,.]]]
[[1,3,8,9,10],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3,8,9,10]=>[3,5,7,6,1,4,2,8,9,10]=>[[.,[.,[[.,.],.]]],[[.,.],[.,[.,[.,.]]]]]
[[1,5,8,9,10],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5,8,9,10]=>[5,6,2,3,7,4,1,8,9,10]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,[.,[.,.]]]]
[[1,7,8,9,10],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7,8,9,10]=>[6,1,2,3,4,5,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[[1,2,5,6],[3,4,9,10],[7,8]]=>[7,8,3,4,9,10,1,2,5,6]=>[2,5,4,8,6,10,7,3,9,1]=>[[.,[[[.,.],[[.,.],[[.,.],.]]],[.,.]]],.]
[[1,4,5,6],[2,8,9,10],[3],[7]]=>[7,3,2,8,9,10,1,4,5,6]=>[4,7,2,5,6,10,3,8,9,1]=>[[[.,[.,.]],[[.,[.,[.,.]]],[.,[.,.]]]],.]
[[1,2,3,10],[4,5,6],[7,8,9]]=>[7,8,9,4,5,6,1,2,3,10]=>[2,3,9,5,6,1,7,8,4,10]=>[[.,[.,[[.,.],[.,.]]]],[[.,[.,.]],[.,.]]]
[[1,3,6,10],[2,5,9],[4,8],[7]]=>[7,4,8,2,5,9,1,3,6,10]=>[3,5,6,7,8,9,4,2,1,10]=>[[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],[.,.]]
[[1,5,6,10],[2,8,9],[3],[4],[7]]=>[7,4,3,2,8,9,1,5,6,10]=>[5,7,2,3,6,9,4,8,1,10]=>[[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]],[.,.]]
[[1,2,9,10],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2,9,10]=>[2,8,4,1,6,3,7,5,9,10]=>[[.,[[.,.],.]],[[.,.],[[.,.],[.,[.,.]]]]]
[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4,9,10]=>[4,6,7,8,3,1,5,2,9,10]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],[.,[.,.]]]]
[[1,6,9,10],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6,9,10]=>[6,7,2,3,4,8,5,1,9,10]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],[.,[.,.]]]
[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8,9,10]=>[7,1,2,3,4,5,6,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[[1,3,4],[2,6,7],[5,9,10],[8]]=>[8,5,9,10,2,6,7,1,3,4]=>[3,6,4,10,8,7,1,5,9,2]=>[[.,[[.,.],[[[.,.],.],.]]],[[.,[.,.]],.]]
[[1,2,7],[3,4,10],[5,6],[8,9]]=>[8,9,5,6,3,4,10,1,2,7]=>[2,7,4,9,6,3,10,8,5,1]=>[[.,[[[.,.],[[.,.],.]],[[[.,.],.],.]]],.]
[[1,4,7],[2,6,10],[3,9],[5],[8]]=>[8,5,3,9,2,6,10,1,4,7]=>[4,6,8,7,3,9,10,5,2,1]=>[[[[.,[.,[[.,.],.]]],[[.,[.,.]],.]],.],.]
[[1,6,7],[2,9,10],[3],[4],[5],[8]]=>[8,5,4,3,2,9,10,1,6,7]=>[6,8,2,3,4,7,10,5,9,1]=>[[[.,[.,.]],[.,[.,[[.,[.,.]],[.,.]]]]],.]
[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[8,6,9,4,7,2,5,1,3,10]=>[3,5,9,7,1,8,2,6,4,10]=>[[.,[.,[[.,.],.]]],[[.,.],[[.,.],[.,.]]]]
[[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[8,6,4,3,9,2,7,1,5,10]=>[5,7,8,3,9,4,1,6,2,10]=>[[[.,[.,[.,.]]],[[.,.],.]],[[.,.],[.,.]]]
[[1,7,10],[2,9],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,9,1,7,10]=>[7,8,2,3,4,5,9,6,1,10]=>[[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]],[.,.]]
[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1,9,10]=>[8,1,2,3,4,5,6,7,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[[1,4],[2,6],[3,8],[5,10],[7],[9]]=>[9,7,5,10,3,8,2,6,1,4]=>[4,6,8,10,9,1,5,2,7,3]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],[[.,.],.]]]
[[1,6],[2,8],[3,10],[4],[5],[7],[9]]=>[9,7,5,4,3,10,2,8,1,6]=>[6,8,9,3,4,10,5,1,7,2]=>[[[.,[.,[.,.]]],[.,[[.,.],.]]],[[.,.],.]]
[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>[9,7,6,5,4,3,2,10,1,8]=>[8,9,2,3,4,5,6,10,7,1]=>[[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]],.]
[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,2,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[[1,4,6,7,8,9],[2,5],[3]]=>[3,2,5,1,4,6,7,8,9]=>[4,3,2,5,1,6,7,8,9]=>[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]]
[[1,3,5,6,7,8,9],[2,4]]=>[2,4,1,3,5,6,7,8,9]=>[3,2,4,1,5,6,7,8,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[[1,3,5,6,7,8,9,10],[2,4]]=>[2,4,1,3,5,6,7,8,9,10]=>[3,2,4,1,5,6,7,8,9,10]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,5],[2,6],[3,7],[4,8],[9]]=>[9,4,8,3,7,2,6,1,5]=>[5,6,7,8,9,1,2,3,4]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[[1,3,5],[2,4,6],[7],[8],[9]]=>[9,8,7,2,4,6,1,3,5]=>[3,4,5,6,9,1,2,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[[1,2,3,6],[4,7],[5,8],[9]]=>[9,5,8,4,7,1,2,3,6]=>[2,3,6,7,8,9,1,4,5]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[[1,3,5,7],[2,4,6,8],[9]]=>[9,2,4,6,8,1,3,5,7]=>[3,4,5,6,7,8,9,1,2]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[[1,2,3,5,7],[4,6,8],[9]]=>[9,4,6,8,1,2,3,5,7]=>[2,3,5,6,7,8,9,1,4]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[[1,2,3,4,5,7],[6,8],[9]]=>[9,6,8,1,2,3,4,5,7]=>[2,3,4,5,7,8,9,1,6]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[[1,2,3,4,5,6,8],[7,9]]=>[7,9,1,2,3,4,5,6,8]=>[2,3,4,5,6,8,7,9,1]=>[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[[1,5],[2,6],[3,7],[4,8],[9],[10]]=>[10,9,4,8,3,7,2,6,1,5]=>[5,6,7,8,10,1,2,3,4,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[[1,2,6],[3,7],[4,8],[5,9],[10]]=>[10,5,9,4,8,3,7,1,2,6]=>[2,6,7,8,9,10,1,3,4,5]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[[1,4,7],[2,5,8],[3,6,9],[10]]=>[10,3,6,9,2,5,8,1,4,7]=>[4,5,6,7,8,9,10,1,2,3]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[[1,2,3,4,7],[5,8],[6,9],[10]]=>[10,6,9,5,8,1,2,3,4,7]=>[2,3,4,7,8,9,10,1,5,6]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[[1,2,4,6,8],[3,5,7,9],[10]]=>[10,3,5,7,9,1,2,4,6,8]=>[2,4,5,6,7,8,9,10,1,3]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[[1,2,3,4,6,8],[5,7,9],[10]]=>[10,5,7,9,1,2,3,4,6,8]=>[2,3,4,6,7,8,9,10,1,5]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[[1,2,3,4,5,6,8],[7,9],[10]]=>[10,7,9,1,2,3,4,5,6,8]=>[2,3,4,5,6,8,9,10,1,7]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[[1,2,3,4,5,6,7,9],[8]]=>[8,1,2,3,4,5,6,7,9]=>[2,3,4,5,6,7,8,1,9]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[[1,2,3,4,5,6,9],[7,8]]=>[7,8,1,2,3,4,5,6,9]=>[2,3,4,5,6,8,7,1,9]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]
[[1,2,3,4,5,6,9],[7],[8]]=>[8,7,1,2,3,4,5,6,9]=>[2,3,4,5,6,8,1,7,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[[1,2,9],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,1,2,9]=>[2,8,1,3,4,5,6,7,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,2,3,4,5,6,7,8,10],[9]]=>[9,1,2,3,4,5,6,7,8,10]=>[2,3,4,5,6,7,8,9,1,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[[1,2,3,4,5,6,7,10],[8,9]]=>[8,9,1,2,3,4,5,6,7,10]=>[2,3,4,5,6,7,9,8,1,10]=>[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],[.,.]]
[]=>[]=>[]=>.
[[1,2,4,5,6,7,8,9],[3]]=>[3,1,2,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,3,5,6,7,8,9],[2],[4]]=>[4,2,1,3,5,6,7,8,9]=>[3,1,4,2,5,6,7,8,9]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[[1,4,6,7,8,9],[2],[3],[5]]=>[5,3,2,1,4,6,7,8,9]=>[4,1,2,5,3,6,7,8,9]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[[1,5,7,8,9],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7,8,9]=>[5,1,2,3,6,4,7,8,9]=>[[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[[1,6,8,9],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6,8,9]=>[6,1,2,3,4,7,5,8,9]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[[1,7,9],[2],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,1,7,9]=>[7,1,2,3,4,5,8,6,9]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[[1,8],[2],[3],[4],[5],[6],[7],[9]]=>[9,7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,9,7]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[[1,2,4,5,6,7,8,9,10],[3]]=>[3,1,2,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,3,5,6,7,8,9,10],[2],[4]]=>[4,2,1,3,5,6,7,8,9,10]=>[3,1,4,2,5,6,7,8,9,10]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,9],[2],[3],[4],[5],[6],[7],[8],[10]]=>[10,8,7,6,5,4,3,2,1,9]=>[9,1,2,3,4,5,6,7,10,8]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[[1,3,4,5,6,7,8],[2,9]]=>[2,9,1,3,4,5,6,7,8]=>[3,2,4,5,6,7,8,9,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[[1,3,4,5,6,7,8],[2],[9]]=>[9,2,1,3,4,5,6,7,8]=>[3,1,4,5,6,7,8,9,2]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[[1,3,4,5,6,7],[2],[8],[9]]=>[9,8,2,1,3,4,5,6,7]=>[3,1,4,5,6,7,9,2,8]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[[1,3,4,5,6],[2],[7],[8],[9]]=>[9,8,7,2,1,3,4,5,6]=>[3,1,4,5,6,9,2,7,8]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[[1,3,4],[2],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,2,1,3,4]=>[3,1,4,9,2,5,6,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[[1,3],[2],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,2,1,3]=>[3,1,9,2,4,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[[1,3,4,5,6,7,8,9],[2,10]]=>[2,10,1,3,4,5,6,7,8,9]=>[3,2,4,5,6,7,8,9,10,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[[1,3,4,5,6,7,8,9],[2],[10]]=>[10,2,1,3,4,5,6,7,8,9]=>[3,1,4,5,6,7,8,9,10,2]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[[1,3,4,5,6,7,8],[2,9,10]]=>[2,9,10,1,3,4,5,6,7,8]=>[3,2,4,5,6,7,8,10,9,1]=>[[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[[1,3,4,5,6,7,8],[2],[9],[10]]=>[10,9,2,1,3,4,5,6,7,8]=>[3,1,4,5,6,7,8,10,2,9]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[[1,3,4,5],[2,7,8],[6,10],[9]]=>[9,6,10,2,7,8,1,3,4,5]=>[3,7,4,5,10,9,8,1,6,2]=>[[.,[[.,.],[.,[[[.,.],.],.]]]],[[.,.],.]]
[[1,3,4],[2],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,2,1,3,4]=>[3,1,4,10,2,5,6,7,8,9]=>[[.,.],[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]
[[1,2,3,5,6,7,8,9,10],[4]]=>[4,1,2,3,5,6,7,8,9,10]=>[2,3,4,1,5,6,7,8,9,10]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,2,3,4,6,7,8,9,10],[5]]=>[5,1,2,3,4,6,7,8,9,10]=>[2,3,4,5,1,6,7,8,9,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[[1,2,3,4,5,6,7,9,10],[8]]=>[8,1,2,3,4,5,6,7,9,10]=>[2,3,4,5,6,7,8,1,9,10]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[[1,2,3,4,5,6,8,9,10],[7]]=>[7,1,2,3,4,5,6,8,9,10]=>[2,3,4,5,6,7,1,8,9,10]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[[1,2,3,4,5,7,8,9,10],[6]]=>[6,1,2,3,4,5,7,8,9,10]=>[2,3,4,5,6,1,7,8,9,10]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[[1,4,5,6,7,8],[2],[3],[9]]=>[9,3,2,1,4,5,6,7,8]=>[4,1,2,5,6,7,8,9,3]=>[[.,.],[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[[1,5,6,7,8],[2],[3],[4],[9]]=>[9,4,3,2,1,5,6,7,8]=>[5,1,2,3,6,7,8,9,4]=>[[.,.],[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[[1,6,7,8],[2],[3],[4],[5],[9]]=>[9,5,4,3,2,1,6,7,8]=>[6,1,2,3,4,7,8,9,5]=>[[.,.],[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[[1,7,8],[2],[3],[4],[5],[6],[9]]=>[9,6,5,4,3,2,1,7,8]=>[7,1,2,3,4,5,8,9,6]=>[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[[1,4,5,6,7,8,9],[2],[3],[10]]=>[10,3,2,1,4,5,6,7,8,9]=>[4,1,2,5,6,7,8,9,10,3]=>[[.,.],[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[[1,5,6,7,8,9],[2],[3],[4],[10]]=>[10,4,3,2,1,5,6,7,8,9]=>[5,1,2,3,6,7,8,9,10,4]=>[[.,.],[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]
[[1,6,7,8,9],[2],[3],[4],[5],[10]]=>[10,5,4,3,2,1,6,7,8,9]=>[6,1,2,3,4,7,8,9,10,5]=>[[.,.],[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[[1,2,5,9],[3,4,8],[6,7],[10]]=>[10,6,7,3,4,8,1,2,5,9]=>[2,5,4,8,9,7,3,1,10,6]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],[[.,.],.]]
[[1,7,8,9],[2],[3],[4],[5],[6],[10]]=>[10,6,5,4,3,2,1,7,8,9]=>[7,1,2,3,4,5,8,9,10,6]=>[[.,.],[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[[1,8,9],[2],[3],[4],[5],[6],[7],[10]]=>[10,7,6,5,4,3,2,1,8,9]=>[8,1,2,3,4,5,6,9,10,7]=>[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[[1,2,3,6,7,8,9],[4,5]]=>[4,5,1,2,3,6,7,8,9]=>[2,3,5,4,1,6,7,8,9]=>[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]
[[1,2,5,6,7,8,9],[3],[4]]=>[4,3,1,2,5,6,7,8,9]=>[2,4,1,3,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[1,2,5,6,7,8,9,10],[3],[4]]=>[4,3,1,2,5,6,7,8,9,10]=>[2,4,1,3,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[[1,2,4,7],[3,6,10],[5,9],[8]]=>[8,5,9,3,6,10,1,2,4,7]=>[2,4,6,7,8,9,10,5,3,1]=>[[.,[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]],.]
[[1,2,3,4,7,8,9],[5,6]]=>[5,6,1,2,3,4,7,8,9]=>[2,3,4,6,5,1,7,8,9]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]]
[[1,2,5,6,7,8],[3],[4],[9]]=>[9,4,3,1,2,5,6,7,8]=>[2,5,1,3,6,7,8,9,4]=>[[.,[.,.]],[.,[[.,[.,[.,[.,.]]]],.]]]
[[1,2,7,8],[3],[4],[5],[6],[9]]=>[9,6,5,4,3,1,2,7,8]=>[2,7,1,3,4,5,8,9,6]=>[[.,[.,.]],[.,[.,[.,[[.,[.,.]],.]]]]]
[[1,2,4,5,6,7,8,9],[3],[10]]=>[10,3,1,2,4,5,6,7,8,9]=>[2,4,1,5,6,7,8,9,10,3]=>[[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[[1,4],[2],[3],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,3,2,1,4]=>[4,1,2,10,3,5,6,7,8,9]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[[1,5],[2],[3],[4],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,4,3,2,1,5]=>[5,1,2,3,10,4,6,7,8,9]=>[[.,.],[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[[1,11],[2],[3],[4],[5],[6],[7],[8],[9],[10],[12]]=>[12,10,9,8,7,6,5,4,3,2,1,11]=>[11,1,2,3,4,5,6,7,8,9,12,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[[1,2,3,4,5,6,8],[7],[9]]=>[9,7,1,2,3,4,5,6,8]=>[2,3,4,5,6,8,1,9,7]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[[1,2,3,4,5,7,9],[6,8]]=>[6,8,1,2,3,4,5,7,9]=>[2,3,4,5,7,6,8,1,9]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],[.,.]]
[[1,2,4,5,6,7,8],[3,9]]=>[3,9,1,2,4,5,6,7,8]=>[2,4,3,5,6,7,8,9,1]=>[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[[1,2,3,4,5,6],[7,9],[8]]=>[8,7,9,1,2,3,4,5,6]=>[2,3,4,5,6,9,8,7,1]=>[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]
[[1,2,3,4,5,6,7],[8,10],[9]]=>[9,8,10,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,10,9,8,1]=>[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]
[[1,3,4,5,6,7,9],[2,8]]=>[2,8,1,3,4,5,6,7,9]=>[3,2,4,5,6,7,8,1,9]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[[1,2,3,4,5,8],[6,9],[7]]=>[7,6,9,1,2,3,4,5,8]=>[2,3,4,5,8,7,6,9,1]=>[[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]],.]
[[1,2,3,4,5,7,8],[6,9]]=>[6,9,1,2,3,4,5,7,8]=>[2,3,4,5,7,6,8,9,1]=>[[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[[1,3,6,7],[2,5,10],[4,9],[8]]=>[8,4,9,2,5,10,1,3,6,7]=>[3,5,6,8,9,7,10,4,2,1]=>[[[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]],.],.]
[[1,4,5,6,7,8],[2,9],[3]]=>[3,2,9,1,4,5,6,7,8]=>[4,3,2,5,6,7,8,9,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
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
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
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.
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