Identifier
Mp00081: Standard tableaux reading word permutationPermutations
Mp00235: Permutations descent views to invisible inversion bottomsPermutations
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]=>[3,1,2]=>[[.,.],[.,.]] [[1],[2],[3]]=>[3,2,1]=>[2,3,1]=>[[.,[.,.]],.] [[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]=>[3,1,2,4]=>[[.,.],[.,[.,.]]] [[1,2,3],[4]]=>[4,1,2,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]] [[1,3],[2,4]]=>[2,4,1,3]=>[4,2,1,3]=>[[[.,.],.],[.,.]] [[1,2],[3,4]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]] [[1,4],[2],[3]]=>[3,2,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]] [[1,3],[2],[4]]=>[4,2,1,3]=>[2,4,1,3]=>[[.,[.,.]],[.,.]] [[1,2],[3],[4]]=>[4,3,1,2]=>[3,1,4,2]=>[[.,.],[[.,.],.]] [[1],[2],[3],[4]]=>[4,3,2,1]=>[2,3,4,1]=>[[.,[.,[.,.]]],.] [[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]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]] [[1,2,3,5],[4]]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]] [[1,2,3,4],[5]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]] [[1,3,5],[2,4]]=>[2,4,1,3,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]] [[1,2,5],[3,4]]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]] [[1,3,4],[2,5]]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]] [[1,2,4],[3,5]]=>[3,5,1,2,4]=>[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]] [[1,2,3],[4,5]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]] [[1,4,5],[2],[3]]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]] [[1,3,5],[2],[4]]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]] [[1,2,5],[3],[4]]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]] [[1,3,4],[2],[5]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]] [[1,2,4],[3],[5]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]] [[1,2,3],[4],[5]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]] [[1,4],[2,5],[3]]=>[3,2,5,1,4]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]] [[1,3],[2,5],[4]]=>[4,2,5,1,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]] [[1,2],[3,5],[4]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]] [[1,3],[2,4],[5]]=>[5,2,4,1,3]=>[4,5,1,2,3]=>[[.,[.,.]],[.,[.,.]]] [[1,2],[3,4],[5]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[[.,.],[[[.,.],.],.]] [[1,5],[2],[3],[4]]=>[4,3,2,1,5]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]] [[1,4],[2],[3],[5]]=>[5,3,2,1,4]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]] [[1,3],[2],[4],[5]]=>[5,4,2,1,3]=>[2,4,1,5,3]=>[[.,[.,.]],[[.,.],.]] [[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>[3,1,4,5,2]=>[[.,.],[[.,[.,.]],.]] [[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.] [[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]=>[3,1,2,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>[[.,.],[.,[.,[.,[.,.]]]]] [[1,3,5,6],[2,4]]=>[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>[[[.,.],.],[.,[.,[.,.]]]] [[1,2,5,6],[3,4]]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]] [[1,3,4,6],[2,5]]=>[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>[[[.,.],.],[.,[.,[.,.]]]] [[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>[5,1,3,2,4,6]=>[[.,.],[[.,.],[.,[.,.]]]] [[1,2,3,6],[4,5]]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]] [[1,3,4,5],[2,6]]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>[[[.,.],.],[.,[.,[.,.]]]] [[1,2,4,5],[3,6]]=>[3,6,1,2,4,5]=>[6,1,3,2,4,5]=>[[.,.],[[.,.],[.,[.,.]]]] [[1,2,3,5],[4,6]]=>[4,6,1,2,3,5]=>[6,1,2,4,3,5]=>[[.,.],[.,[[.,.],[.,.]]]] [[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]] [[1,4,5,6],[2],[3]]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [[1,3,5,6],[2],[4]]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]] [[1,3,4,6],[2],[5]]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>[[.,.],[[.,.],[.,[.,.]]]] [[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>[[.,.],[.,[[.,.],[.,.]]]] [[1,3,4,5],[2],[6]]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]] [[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>[[.,.],[[.,.],[.,[.,.]]]] [[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>[[.,.],[.,[[.,.],[.,.]]]] [[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>[[.,.],[.,[.,[[.,.],.]]]] [[1,3,5],[2,4,6]]=>[2,4,6,1,3,5]=>[6,2,1,4,3,5]=>[[[.,.],.],[[.,.],[.,.]]] [[1,2,5],[3,4,6]]=>[3,4,6,1,2,5]=>[6,1,3,4,2,5]=>[[.,.],[[.,[.,.]],[.,.]]] [[1,3,4],[2,5,6]]=>[2,5,6,1,3,4]=>[6,2,1,3,5,4]=>[[[.,.],.],[.,[[.,.],.]]] [[1,2,4],[3,5,6]]=>[3,5,6,1,2,4]=>[6,1,3,2,5,4]=>[[.,.],[[.,.],[[.,.],.]]] [[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]] [[1,4,6],[2,5],[3]]=>[3,2,5,1,4,6]=>[5,3,2,1,4,6]=>[[[[.,.],.],.],[.,[.,.]]] [[1,3,6],[2,5],[4]]=>[4,2,5,1,3,6]=>[5,4,1,2,3,6]=>[[[.,.],.],[.,[.,[.,.]]]] [[1,2,6],[3,5],[4]]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>[[.,.],[[[.,.],.],[.,.]]] [[1,3,6],[2,4],[5]]=>[5,2,4,1,3,6]=>[4,5,1,2,3,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [[1,2,6],[3,4],[5]]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>[[.,.],[[[.,.],.],[.,.]]] [[1,4,5],[2,6],[3]]=>[3,2,6,1,4,5]=>[6,3,2,1,4,5]=>[[[[.,.],.],.],[.,[.,.]]] [[1,3,5],[2,6],[4]]=>[4,2,6,1,3,5]=>[6,4,1,2,3,5]=>[[[.,.],.],[.,[.,[.,.]]]] [[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5]=>[6,1,4,3,2,5]=>[[.,.],[[[.,.],.],[.,.]]] [[1,3,4],[2,6],[5]]=>[5,2,6,1,3,4]=>[6,5,1,3,2,4]=>[[[.,.],.],[[.,.],[.,.]]] [[1,2,4],[3,6],[5]]=>[5,3,6,1,2,4]=>[6,1,5,2,3,4]=>[[.,.],[[.,.],[.,[.,.]]]] [[1,2,3],[4,6],[5]]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>[[.,.],[.,[[[.,.],.],.]]] [[1,3,5],[2,4],[6]]=>[6,2,4,1,3,5]=>[4,6,1,2,3,5]=>[[.,[.,.]],[.,[.,[.,.]]]] [[1,2,5],[3,4],[6]]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>[[.,.],[[[.,.],.],[.,.]]] [[1,3,4],[2,5],[6]]=>[6,2,5,1,3,4]=>[5,6,1,3,2,4]=>[[.,[.,.]],[[.,.],[.,.]]] [[1,2,4],[3,5],[6]]=>[6,3,5,1,2,4]=>[5,1,6,2,3,4]=>[[.,.],[[.,.],[.,[.,.]]]] [[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>[[.,.],[.,[[[.,.],.],.]]] [[1,5,6],[2],[3],[4]]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]] [[1,4,6],[2],[3],[5]]=>[5,3,2,1,4,6]=>[2,3,5,1,4,6]=>[[.,[.,[.,.]]],[.,[.,.]]] [[1,3,6],[2],[4],[5]]=>[5,4,2,1,3,6]=>[2,4,1,5,3,6]=>[[.,[.,.]],[[.,.],[.,.]]] [[1,2,6],[3],[4],[5]]=>[5,4,3,1,2,6]=>[3,1,4,5,2,6]=>[[.,.],[[.,[.,.]],[.,.]]] [[1,4,5],[2],[3],[6]]=>[6,3,2,1,4,5]=>[2,3,6,1,4,5]=>[[.,[.,[.,.]]],[.,[.,.]]] [[1,3,5],[2],[4],[6]]=>[6,4,2,1,3,5]=>[2,4,1,6,3,5]=>[[.,[.,.]],[[.,.],[.,.]]] [[1,2,5],[3],[4],[6]]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]=>[[.,.],[[.,[.,.]],[.,.]]] [[1,3,4],[2],[5],[6]]=>[6,5,2,1,3,4]=>[2,5,1,3,6,4]=>[[.,[.,.]],[.,[[.,.],.]]] [[1,2,4],[3],[5],[6]]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]=>[[.,.],[[.,.],[[.,.],.]]] [[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]=>[[.,.],[.,[[.,[.,.]],.]]] [[1,4],[2,5],[3,6]]=>[3,6,2,5,1,4]=>[5,6,3,1,2,4]=>[[[.,[.,.]],.],[.,[.,.]]] [[1,3],[2,5],[4,6]]=>[4,6,2,5,1,3]=>[5,6,1,4,2,3]=>[[.,[.,.]],[[.,.],[.,.]]] [[1,2],[3,5],[4,6]]=>[4,6,3,5,1,2]=>[5,1,6,4,3,2]=>[[.,.],[[[[.,.],.],.],.]] [[1,3],[2,4],[5,6]]=>[5,6,2,4,1,3]=>[4,6,1,2,5,3]=>[[.,[.,.]],[.,[[.,.],.]]] [[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>[[.,.],[[[.,.],[.,.]],.]] [[1,5],[2,6],[3],[4]]=>[4,3,2,6,1,5]=>[6,3,4,2,1,5]=>[[[[.,.],[.,.]],.],[.,.]] [[1,4],[2,6],[3],[5]]=>[5,3,2,6,1,4]=>[6,3,5,1,2,4]=>[[[.,.],[.,.]],[.,[.,.]]] [[1,3],[2,6],[4],[5]]=>[5,4,2,6,1,3]=>[6,4,1,5,2,3]=>[[[.,.],.],[[.,.],[.,.]]] [[1,2],[3,6],[4],[5]]=>[5,4,3,6,1,2]=>[6,1,4,5,3,2]=>[[.,.],[[[.,[.,.]],.],.]] [[1,4],[2,5],[3],[6]]=>[6,3,2,5,1,4]=>[5,3,6,1,2,4]=>[[[.,.],[.,.]],[.,[.,.]]] [[1,3],[2,5],[4],[6]]=>[6,4,2,5,1,3]=>[5,4,1,6,2,3]=>[[[.,.],.],[[.,.],[.,.]]] [[1,2],[3,5],[4],[6]]=>[6,4,3,5,1,2]=>[5,1,4,6,3,2]=>[[.,.],[[[.,[.,.]],.],.]] [[1,3],[2,4],[5],[6]]=>[6,5,2,4,1,3]=>[4,5,1,2,6,3]=>[[.,[.,.]],[.,[[.,.],.]]] [[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2]=>[4,1,5,3,6,2]=>[[.,.],[[[.,.],[.,.]],.]] [[1,6],[2],[3],[4],[5]]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[[.,[.,[.,[.,.]]]],[.,.]] [[1,5],[2],[3],[4],[6]]=>[6,4,3,2,1,5]=>[2,3,4,6,1,5]=>[[.,[.,[.,[.,.]]]],[.,.]] [[1,4],[2],[3],[5],[6]]=>[6,5,3,2,1,4]=>[2,3,5,1,6,4]=>[[.,[.,[.,.]]],[[.,.],.]] [[1,3],[2],[4],[5],[6]]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]=>[[.,[.,.]],[[.,[.,.]],.]] [[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]=>[[.,.],[[.,[.,[.,.]]],.]] [[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[[.,[.,[.,[.,[.,.]]]]],.] [[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]=>[3,1,2,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[1,2,3,5,6,7],[4]]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[1,2,3,4,6,7],[5]]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[1,2,3,4,5,7],[6]]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[1,3,5,6,7],[2,4]]=>[2,4,1,3,5,6,7]=>[4,2,1,3,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[1,2,5,6,7],[3,4]]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [[1,3,4,6,7],[2,5]]=>[2,5,1,3,4,6,7]=>[5,2,1,3,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[1,2,4,6,7],[3,5]]=>[3,5,1,2,4,6,7]=>[5,1,3,2,4,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [[1,2,3,6,7],[4,5]]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [[1,3,4,5,7],[2,6]]=>[2,6,1,3,4,5,7]=>[6,2,1,3,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[1,2,4,5,7],[3,6]]=>[3,6,1,2,4,5,7]=>[6,1,3,2,4,5,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [[1,2,3,5,7],[4,6]]=>[4,6,1,2,3,5,7]=>[6,1,2,4,3,5,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [[1,2,3,4,7],[5,6]]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [[1,3,4,5,6],[2,7]]=>[2,7,1,3,4,5,6]=>[7,2,1,3,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[1,2,4,5,6],[3,7]]=>[3,7,1,2,4,5,6]=>[7,1,3,2,4,5,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [[1,2,3,5,6],[4,7]]=>[4,7,1,2,3,5,6]=>[7,1,2,4,3,5,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [[1,2,3,4,6],[5,7]]=>[5,7,1,2,3,4,6]=>[7,1,2,3,5,4,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [[1,2,3,4,5],[6,7]]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>[[.,.],[.,[.,[.,[[.,.],.]]]]] [[1,4,5,6,7],[2],[3]]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[1,3,5,6,7],[2],[4]]=>[4,2,1,3,5,6,7]=>[2,4,1,3,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[1,2,5,6,7],[3],[4]]=>[4,3,1,2,5,6,7]=>[3,1,4,2,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [[1,3,4,6,7],[2],[5]]=>[5,2,1,3,4,6,7]=>[2,5,1,3,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[1,2,4,6,7],[3],[5]]=>[5,3,1,2,4,6,7]=>[3,1,5,2,4,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [[1,2,3,6,7],[4],[5]]=>[5,4,1,2,3,6,7]=>[4,1,2,5,3,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [[1,3,4,5,7],[2],[6]]=>[6,2,1,3,4,5,7]=>[2,6,1,3,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[1,2,4,5,7],[3],[6]]=>[6,3,1,2,4,5,7]=>[3,1,6,2,4,5,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [[1,2,3,5,7],[4],[6]]=>[6,4,1,2,3,5,7]=>[4,1,2,6,3,5,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [[1,2,3,4,7],[5],[6]]=>[6,5,1,2,3,4,7]=>[5,1,2,3,6,4,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [[1,3,4,5,6],[2],[7]]=>[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[1,2,4,5,6],[3],[7]]=>[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [[1,2,3,5,6],[4],[7]]=>[7,4,1,2,3,5,6]=>[4,1,2,7,3,5,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [[1,2,3,4,6],[5],[7]]=>[7,5,1,2,3,4,6]=>[5,1,2,3,7,4,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [[1,2,3,4,5],[6],[7]]=>[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]=>[[.,.],[.,[.,[.,[[.,.],.]]]]] [[1,3,5,7],[2,4,6]]=>[2,4,6,1,3,5,7]=>[6,2,1,4,3,5,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [[1,2,5,7],[3,4,6]]=>[3,4,6,1,2,5,7]=>[6,1,3,4,2,5,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [[1,3,4,7],[2,5,6]]=>[2,5,6,1,3,4,7]=>[6,2,1,3,5,4,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [[1,2,4,7],[3,5,6]]=>[3,5,6,1,2,4,7]=>[6,1,3,2,5,4,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [[1,2,3,7],[4,5,6]]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [[1,3,5,6],[2,4,7]]=>[2,4,7,1,3,5,6]=>[7,2,1,4,3,5,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [[1,2,5,6],[3,4,7]]=>[3,4,7,1,2,5,6]=>[7,1,3,4,2,5,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [[1,3,4,6],[2,5,7]]=>[2,5,7,1,3,4,6]=>[7,2,1,3,5,4,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [[1,2,4,6],[3,5,7]]=>[3,5,7,1,2,4,6]=>[7,1,3,2,5,4,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [[1,2,3,6],[4,5,7]]=>[4,5,7,1,2,3,6]=>[7,1,2,4,5,3,6]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [[1,3,4,5],[2,6,7]]=>[2,6,7,1,3,4,5]=>[7,2,1,3,4,6,5]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [[1,2,4,5],[3,6,7]]=>[3,6,7,1,2,4,5]=>[7,1,3,2,4,6,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [[1,2,3,5],[4,6,7]]=>[4,6,7,1,2,3,5]=>[7,1,2,4,3,6,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]] [[1,2,3,4],[5,6,7]]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>[[.,.],[.,[.,[[.,[.,.]],.]]]] [[1,4,6,7],[2,5],[3]]=>[3,2,5,1,4,6,7]=>[5,3,2,1,4,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[1,3,6,7],[2,5],[4]]=>[4,2,5,1,3,6,7]=>[5,4,1,2,3,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[1,2,6,7],[3,5],[4]]=>[4,3,5,1,2,6,7]=>[5,1,4,3,2,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [[1,3,6,7],[2,4],[5]]=>[5,2,4,1,3,6,7]=>[4,5,1,2,3,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[1,2,6,7],[3,4],[5]]=>[5,3,4,1,2,6,7]=>[4,1,5,3,2,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [[1,4,5,7],[2,6],[3]]=>[3,2,6,1,4,5,7]=>[6,3,2,1,4,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[1,3,5,7],[2,6],[4]]=>[4,2,6,1,3,5,7]=>[6,4,1,2,3,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[1,2,5,7],[3,6],[4]]=>[4,3,6,1,2,5,7]=>[6,1,4,3,2,5,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [[1,3,4,7],[2,6],[5]]=>[5,2,6,1,3,4,7]=>[6,5,1,3,2,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [[1,2,4,7],[3,6],[5]]=>[5,3,6,1,2,4,7]=>[6,1,5,2,3,4,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [[1,2,3,7],[4,6],[5]]=>[5,4,6,1,2,3,7]=>[6,1,2,5,4,3,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]] [[1,3,5,7],[2,4],[6]]=>[6,2,4,1,3,5,7]=>[4,6,1,2,3,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[1,2,5,7],[3,4],[6]]=>[6,3,4,1,2,5,7]=>[4,1,6,3,2,5,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [[1,3,4,7],[2,5],[6]]=>[6,2,5,1,3,4,7]=>[5,6,1,3,2,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [[1,2,4,7],[3,5],[6]]=>[6,3,5,1,2,4,7]=>[5,1,6,2,3,4,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [[1,2,3,7],[4,5],[6]]=>[6,4,5,1,2,3,7]=>[5,1,2,6,4,3,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]] [[1,4,5,6],[2,7],[3]]=>[3,2,7,1,4,5,6]=>[7,3,2,1,4,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[1,3,5,6],[2,7],[4]]=>[4,2,7,1,3,5,6]=>[7,4,1,2,3,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[1,2,5,6],[3,7],[4]]=>[4,3,7,1,2,5,6]=>[7,1,4,3,2,5,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [[1,3,4,6],[2,7],[5]]=>[5,2,7,1,3,4,6]=>[7,5,1,3,2,4,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [[1,2,4,6],[3,7],[5]]=>[5,3,7,1,2,4,6]=>[7,1,5,2,3,4,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [[1,2,3,6],[4,7],[5]]=>[5,4,7,1,2,3,6]=>[7,1,2,5,4,3,6]=>[[.,.],[.,[[[.,.],.],[.,.]]]] [[1,3,4,5],[2,7],[6]]=>[6,2,7,1,3,4,5]=>[7,6,1,3,4,2,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [[1,2,4,5],[3,7],[6]]=>[6,3,7,1,2,4,5]=>[7,1,6,2,4,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [[1,2,3,5],[4,7],[6]]=>[6,4,7,1,2,3,5]=>[7,1,2,6,3,4,5]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [[1,2,3,4],[5,7],[6]]=>[6,5,7,1,2,3,4]=>[7,1,2,3,6,5,4]=>[[.,.],[.,[.,[[[.,.],.],.]]]] [[1,3,5,6],[2,4],[7]]=>[7,2,4,1,3,5,6]=>[4,7,1,2,3,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[1,2,5,6],[3,4],[7]]=>[7,3,4,1,2,5,6]=>[4,1,7,3,2,5,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [[1,3,4,6],[2,5],[7]]=>[7,2,5,1,3,4,6]=>[5,7,1,3,2,4,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [[1,2,4,6],[3,5],[7]]=>[7,3,5,1,2,4,6]=>[5,1,7,2,3,4,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [[1,2,3,6],[4,5],[7]]=>[7,4,5,1,2,3,6]=>[5,1,2,7,4,3,6]=>[[.,.],[.,[[[.,.],.],[.,.]]]] [[1,3,4,5],[2,6],[7]]=>[7,2,6,1,3,4,5]=>[6,7,1,3,4,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [[1,2,4,5],[3,6],[7]]=>[7,3,6,1,2,4,5]=>[6,1,7,2,4,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [[1,2,3,5],[4,6],[7]]=>[7,4,6,1,2,3,5]=>[6,1,2,7,3,4,5]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [[1,2,3,4],[5,6],[7]]=>[7,5,6,1,2,3,4]=>[6,1,2,3,7,5,4]=>[[.,.],[.,[.,[[[.,.],.],.]]]] [[1,5,6,7],[2],[3],[4]]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [[1,4,6,7],[2],[3],[5]]=>[5,3,2,1,4,6,7]=>[2,3,5,1,4,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [[1,3,6,7],[2],[4],[5]]=>[5,4,2,1,3,6,7]=>[2,4,1,5,3,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [[1,2,6,7],[3],[4],[5]]=>[5,4,3,1,2,6,7]=>[3,1,4,5,2,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [[1,4,5,7],[2],[3],[6]]=>[6,3,2,1,4,5,7]=>[2,3,6,1,4,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [[1,3,5,7],[2],[4],[6]]=>[6,4,2,1,3,5,7]=>[2,4,1,6,3,5,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [[1,2,5,7],[3],[4],[6]]=>[6,4,3,1,2,5,7]=>[3,1,4,6,2,5,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [[1,3,4,7],[2],[5],[6]]=>[6,5,2,1,3,4,7]=>[2,5,1,3,6,4,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [[1,2,4,7],[3],[5],[6]]=>[6,5,3,1,2,4,7]=>[3,1,5,2,6,4,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [[1,2,3,7],[4],[5],[6]]=>[6,5,4,1,2,3,7]=>[4,1,2,5,6,3,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [[1,4,5,6],[2],[3],[7]]=>[7,3,2,1,4,5,6]=>[2,3,7,1,4,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [[1,3,5,6],[2],[4],[7]]=>[7,4,2,1,3,5,6]=>[2,4,1,7,3,5,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [[1,2,5,6],[3],[4],[7]]=>[7,4,3,1,2,5,6]=>[3,1,4,7,2,5,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [[1,3,4,6],[2],[5],[7]]=>[7,5,2,1,3,4,6]=>[2,5,1,3,7,4,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [[1,2,4,6],[3],[5],[7]]=>[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [[1,2,3,6],[4],[5],[7]]=>[7,5,4,1,2,3,6]=>[4,1,2,5,7,3,6]=>[[.,.],[.,[[.,[.,.]],[.,.]]]] [[1,3,4,5],[2],[6],[7]]=>[7,6,2,1,3,4,5]=>[2,6,1,3,4,7,5]=>[[.,[.,.]],[.,[.,[[.,.],.]]]] [[1,2,4,5],[3],[6],[7]]=>[7,6,3,1,2,4,5]=>[3,1,6,2,4,7,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [[1,2,3,5],[4],[6],[7]]=>[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]] [[1,2,3,4],[5],[6],[7]]=>[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]=>[[.,.],[.,[.,[[.,[.,.]],.]]]] [[1,4,6],[2,5,7],[3]]=>[3,2,5,7,1,4,6]=>[7,3,2,1,5,4,6]=>[[[[.,.],.],.],[[.,.],[.,.]]] [[1,3,6],[2,5,7],[4]]=>[4,2,5,7,1,3,6]=>[7,4,1,2,5,3,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [[1,2,6],[3,5,7],[4]]=>[4,3,5,7,1,2,6]=>[7,1,4,3,5,2,6]=>[[.,.],[[[.,.],[.,.]],[.,.]]] [[1,3,6],[2,4,7],[5]]=>[5,2,4,7,1,3,6]=>[7,5,1,2,4,3,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [[1,2,6],[3,4,7],[5]]=>[5,3,4,7,1,2,6]=>[7,1,5,3,4,2,6]=>[[.,.],[[[.,.],[.,.]],[.,.]]] [[1,4,5],[2,6,7],[3]]=>[3,2,6,7,1,4,5]=>[7,3,2,1,4,6,5]=>[[[[.,.],.],.],[.,[[.,.],.]]] [[1,3,5],[2,6,7],[4]]=>[4,2,6,7,1,3,5]=>[7,4,1,2,3,6,5]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [[1,2,5],[3,6,7],[4]]=>[4,3,6,7,1,2,5]=>[7,1,4,3,2,6,5]=>[[.,.],[[[.,.],.],[[.,.],.]]] [[1,3,4],[2,6,7],[5]]=>[5,2,6,7,1,3,4]=>[7,5,1,3,2,6,4]=>[[[.,.],.],[[.,.],[[.,.],.]]] [[1,2,4],[3,6,7],[5]]=>[5,3,6,7,1,2,4]=>[7,1,5,2,3,6,4]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [[1,2,3],[4,6,7],[5]]=>[5,4,6,7,1,2,3]=>[7,1,2,5,4,6,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]] [[1,3,5],[2,4,7],[6]]=>[6,2,4,7,1,3,5]=>[7,6,1,2,3,4,5]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[1,2,5],[3,4,7],[6]]=>[6,3,4,7,1,2,5]=>[7,1,6,3,2,4,5]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [[1,3,4],[2,5,7],[6]]=>[6,2,5,7,1,3,4]=>[7,6,1,3,2,5,4]=>[[[.,.],.],[[.,.],[[.,.],.]]] [[1,2,4],[3,5,7],[6]]=>[6,3,5,7,1,2,4]=>[7,1,6,2,3,5,4]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [[1,2,3],[4,5,7],[6]]=>[6,4,5,7,1,2,3]=>[7,1,2,6,4,5,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]] [[1,3,5],[2,4,6],[7]]=>[7,2,4,6,1,3,5]=>[6,7,1,2,3,4,5]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[1,2,5],[3,4,6],[7]]=>[7,3,4,6,1,2,5]=>[6,1,7,3,2,4,5]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [[1,3,4],[2,5,6],[7]]=>[7,2,5,6,1,3,4]=>[6,7,1,3,2,5,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [[1,2,4],[3,5,6],[7]]=>[7,3,5,6,1,2,4]=>[6,1,7,2,3,5,4]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [[1,2,3],[4,5,6],[7]]=>[7,4,5,6,1,2,3]=>[6,1,2,7,4,5,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]] [[1,4,7],[2,5],[3,6]]=>[3,6,2,5,1,4,7]=>[5,6,3,1,2,4,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [[1,3,7],[2,5],[4,6]]=>[4,6,2,5,1,3,7]=>[5,6,1,4,2,3,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [[1,2,7],[3,5],[4,6]]=>[4,6,3,5,1,2,7]=>[5,1,6,4,3,2,7]=>[[.,.],[[[[.,.],.],.],[.,.]]] [[1,3,7],[2,4],[5,6]]=>[5,6,2,4,1,3,7]=>[4,6,1,2,5,3,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [[1,2,7],[3,4],[5,6]]=>[5,6,3,4,1,2,7]=>[4,1,6,3,5,2,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]] [[1,4,6],[2,5],[3,7]]=>[3,7,2,5,1,4,6]=>[5,7,3,1,2,4,6]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [[1,3,6],[2,5],[4,7]]=>[4,7,2,5,1,3,6]=>[5,7,1,4,2,3,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]] [[1,2,6],[3,5],[4,7]]=>[4,7,3,5,1,2,6]=>[5,1,7,4,3,2,6]=>[[.,.],[[[[.,.],.],.],[.,.]]] [[1,3,6],[2,4],[5,7]]=>[5,7,2,4,1,3,6]=>[4,7,1,2,5,3,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [[1,2,6],[3,4],[5,7]]=>[5,7,3,4,1,2,6]=>[4,1,7,3,5,2,6]=>[[.,.],[[[.,.],[.,.]],[.,.]]] [[1,4,5],[2,6],[3,7]]=>[3,7,2,6,1,4,5]=>[6,7,3,1,4,2,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]] [[1,3,5],[2,6],[4,7]]=>[4,7,2,6,1,3,5]=>[6,7,1,4,3,2,5]=>[[.,[.,.]],[[[.,.],.],[.,.]]] [[1,2,5],[3,6],[4,7]]=>[4,7,3,6,1,2,5]=>[6,1,7,4,2,3,5]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [[1,3,4],[2,6],[5,7]]=>[5,7,2,6,1,3,4]=>[6,7,1,3,5,2,4]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [[1,2,4],[3,6],[5,7]]=>[5,7,3,6,1,2,4]=>[6,1,7,2,5,3,4]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [[1,2,3],[4,6],[5,7]]=>[5,7,4,6,1,2,3]=>[6,1,2,7,5,4,3]=>[[.,.],[.,[[[[.,.],.],.],.]]] [[1,3,5],[2,4],[6,7]]=>[6,7,2,4,1,3,5]=>[4,7,1,2,3,6,5]=>[[.,[.,.]],[.,[.,[[.,.],.]]]] [[1,2,5],[3,4],[6,7]]=>[6,7,3,4,1,2,5]=>[4,1,7,3,2,6,5]=>[[.,.],[[[.,.],.],[[.,.],.]]] [[1,3,4],[2,5],[6,7]]=>[6,7,2,5,1,3,4]=>[5,7,1,3,2,6,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [[1,2,4],[3,5],[6,7]]=>[6,7,3,5,1,2,4]=>[5,1,7,2,3,6,4]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [[1,2,3],[4,5],[6,7]]=>[6,7,4,5,1,2,3]=>[5,1,2,7,4,6,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]] [[1,5,7],[2,6],[3],[4]]=>[4,3,2,6,1,5,7]=>[6,3,4,2,1,5,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [[1,4,7],[2,6],[3],[5]]=>[5,3,2,6,1,4,7]=>[6,3,5,1,2,4,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[1,3,7],[2,6],[4],[5]]=>[5,4,2,6,1,3,7]=>[6,4,1,5,2,3,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [[1,2,7],[3,6],[4],[5]]=>[5,4,3,6,1,2,7]=>[6,1,4,5,3,2,7]=>[[.,.],[[[.,[.,.]],.],[.,.]]] [[1,4,7],[2,5],[3],[6]]=>[6,3,2,5,1,4,7]=>[5,3,6,1,2,4,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[1,3,7],[2,5],[4],[6]]=>[6,4,2,5,1,3,7]=>[5,4,1,6,2,3,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [[1,2,7],[3,5],[4],[6]]=>[6,4,3,5,1,2,7]=>[5,1,4,6,3,2,7]=>[[.,.],[[[.,[.,.]],.],[.,.]]] [[1,3,7],[2,4],[5],[6]]=>[6,5,2,4,1,3,7]=>[4,5,1,2,6,3,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [[1,2,7],[3,4],[5],[6]]=>[6,5,3,4,1,2,7]=>[4,1,5,3,6,2,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]] [[1,5,6],[2,7],[3],[4]]=>[4,3,2,7,1,5,6]=>[7,3,4,2,1,5,6]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [[1,4,6],[2,7],[3],[5]]=>[5,3,2,7,1,4,6]=>[7,3,5,1,2,4,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[1,3,6],[2,7],[4],[5]]=>[5,4,2,7,1,3,6]=>[7,4,1,5,2,3,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [[1,2,6],[3,7],[4],[5]]=>[5,4,3,7,1,2,6]=>[7,1,4,5,3,2,6]=>[[.,.],[[[.,[.,.]],.],[.,.]]] [[1,4,5],[2,7],[3],[6]]=>[6,3,2,7,1,4,5]=>[7,3,6,1,4,2,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [[1,3,5],[2,7],[4],[6]]=>[6,4,2,7,1,3,5]=>[7,4,1,6,3,2,5]=>[[[.,.],.],[[[.,.],.],[.,.]]] [[1,2,5],[3,7],[4],[6]]=>[6,4,3,7,1,2,5]=>[7,1,4,6,2,3,5]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [[1,3,4],[2,7],[5],[6]]=>[6,5,2,7,1,3,4]=>[7,5,1,3,6,2,4]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [[1,2,4],[3,7],[5],[6]]=>[6,5,3,7,1,2,4]=>[7,1,5,2,6,3,4]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [[1,2,3],[4,7],[5],[6]]=>[6,5,4,7,1,2,3]=>[7,1,2,5,6,4,3]=>[[.,.],[.,[[[.,[.,.]],.],.]]] [[1,4,6],[2,5],[3],[7]]=>[7,3,2,5,1,4,6]=>[5,3,7,1,2,4,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[1,3,6],[2,5],[4],[7]]=>[7,4,2,5,1,3,6]=>[5,4,1,7,2,3,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [[1,2,6],[3,5],[4],[7]]=>[7,4,3,5,1,2,6]=>[5,1,4,7,3,2,6]=>[[.,.],[[[.,[.,.]],.],[.,.]]] [[1,3,6],[2,4],[5],[7]]=>[7,5,2,4,1,3,6]=>[4,5,1,2,7,3,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]] [[1,2,6],[3,4],[5],[7]]=>[7,5,3,4,1,2,6]=>[4,1,5,3,7,2,6]=>[[.,.],[[[.,.],[.,.]],[.,.]]] [[1,4,5],[2,6],[3],[7]]=>[7,3,2,6,1,4,5]=>[6,3,7,1,4,2,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [[1,3,5],[2,6],[4],[7]]=>[7,4,2,6,1,3,5]=>[6,4,1,7,3,2,5]=>[[[.,.],.],[[[.,.],.],[.,.]]] [[1,2,5],[3,6],[4],[7]]=>[7,4,3,6,1,2,5]=>[6,1,4,7,2,3,5]=>[[.,.],[[.,[.,.]],[.,[.,.]]]] [[1,3,4],[2,6],[5],[7]]=>[7,5,2,6,1,3,4]=>[6,5,1,3,7,2,4]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [[1,2,4],[3,6],[5],[7]]=>[7,5,3,6,1,2,4]=>[6,1,5,2,7,3,4]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [[1,2,3],[4,6],[5],[7]]=>[7,5,4,6,1,2,3]=>[6,1,2,5,7,4,3]=>[[.,.],[.,[[[.,[.,.]],.],.]]] [[1,3,5],[2,4],[6],[7]]=>[7,6,2,4,1,3,5]=>[4,6,1,2,3,7,5]=>[[.,[.,.]],[.,[.,[[.,.],.]]]] [[1,2,5],[3,4],[6],[7]]=>[7,6,3,4,1,2,5]=>[4,1,6,3,2,7,5]=>[[.,.],[[[.,.],.],[[.,.],.]]] [[1,3,4],[2,5],[6],[7]]=>[7,6,2,5,1,3,4]=>[5,6,1,3,2,7,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [[1,2,4],[3,5],[6],[7]]=>[7,6,3,5,1,2,4]=>[5,1,6,2,3,7,4]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [[1,2,3],[4,5],[6],[7]]=>[7,6,4,5,1,2,3]=>[5,1,2,6,4,7,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]] [[1,6,7],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [[1,5,7],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7]=>[2,3,4,6,1,5,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [[1,4,7],[2],[3],[5],[6]]=>[6,5,3,2,1,4,7]=>[2,3,5,1,6,4,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [[1,3,7],[2],[4],[5],[6]]=>[6,5,4,2,1,3,7]=>[2,4,1,5,6,3,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [[1,2,7],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7]=>[3,1,4,5,6,2,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]] [[1,5,6],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6]=>[2,3,4,7,1,5,6]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [[1,4,6],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6]=>[2,3,5,1,7,4,6]=>[[.,[.,[.,.]]],[[.,.],[.,.]]] [[1,3,6],[2],[4],[5],[7]]=>[7,5,4,2,1,3,6]=>[2,4,1,5,7,3,6]=>[[.,[.,.]],[[.,[.,.]],[.,.]]] [[1,2,6],[3],[4],[5],[7]]=>[7,5,4,3,1,2,6]=>[3,1,4,5,7,2,6]=>[[.,.],[[.,[.,[.,.]]],[.,.]]] [[1,4,5],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5]=>[2,3,6,1,4,7,5]=>[[.,[.,[.,.]]],[.,[[.,.],.]]] [[1,3,5],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [[1,2,5],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]=>[[.,.],[[.,[.,.]],[[.,.],.]]] [[1,3,4],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4]=>[2,5,1,3,6,7,4]=>[[.,[.,.]],[.,[[.,[.,.]],.]]] [[1,2,4],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]=>[[.,.],[[.,.],[[.,[.,.]],.]]] [[1,2,3],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3]=>[4,1,2,5,6,7,3]=>[[.,.],[.,[[.,[.,[.,.]]],.]]] [[1,5],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5]=>[6,7,4,3,1,2,5]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [[1,4],[2,6],[3,7],[5]]=>[5,3,7,2,6,1,4]=>[6,7,5,1,3,2,4]=>[[[.,[.,.]],.],[[.,.],[.,.]]] [[1,3],[2,6],[4,7],[5]]=>[5,4,7,2,6,1,3]=>[6,7,1,5,4,2,3]=>[[.,[.,.]],[[[.,.],.],[.,.]]] [[1,2],[3,6],[4,7],[5]]=>[5,4,7,3,6,1,2]=>[6,1,7,5,4,3,2]=>[[.,.],[[[[[.,.],.],.],.],.]] [[1,4],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4]=>[5,7,6,1,2,3,4]=>[[.,[[.,.],.]],[.,[.,[.,.]]]] [[1,3],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3]=>[5,7,1,6,2,4,3]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [[1,2],[3,5],[4,7],[6]]=>[6,4,7,3,5,1,2]=>[5,1,7,6,3,4,2]=>[[.,.],[[[[.,.],.],[.,.]],.]] [[1,3],[2,4],[5,7],[6]]=>[6,5,7,2,4,1,3]=>[4,7,1,2,6,5,3]=>[[.,[.,.]],[.,[[[.,.],.],.]]] [[1,2],[3,4],[5,7],[6]]=>[6,5,7,3,4,1,2]=>[4,1,7,3,6,5,2]=>[[.,.],[[[.,.],[[.,.],.]],.]] [[1,4],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4]=>[5,6,7,1,2,3,4]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [[1,3],[2,5],[4,6],[7]]=>[7,4,6,2,5,1,3]=>[5,6,1,7,2,4,3]=>[[.,[.,.]],[[.,.],[[.,.],.]]] [[1,2],[3,5],[4,6],[7]]=>[7,4,6,3,5,1,2]=>[5,1,6,7,3,4,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]] [[1,3],[2,4],[5,6],[7]]=>[7,5,6,2,4,1,3]=>[4,6,1,2,7,5,3]=>[[.,[.,.]],[.,[[[.,.],.],.]]] [[1,2],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2]=>[4,1,6,3,7,5,2]=>[[.,.],[[[.,.],[[.,.],.]],.]] [[1,6],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6]=>[7,3,4,5,2,1,6]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [[1,5],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5]=>[7,3,4,6,1,2,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [[1,4],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4]=>[7,3,5,1,6,2,4]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [[1,3],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3]=>[7,4,1,5,6,2,3]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [[1,2],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2]=>[7,1,4,5,6,3,2]=>[[.,.],[[[.,[.,[.,.]]],.],.]] [[1,5],[2,6],[3],[4],[7]]=>[7,4,3,2,6,1,5]=>[6,3,4,7,1,2,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [[1,4],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4]=>[6,3,5,1,7,2,4]=>[[[.,.],[.,.]],[[.,.],[.,.]]] [[1,3],[2,6],[4],[5],[7]]=>[7,5,4,2,6,1,3]=>[6,4,1,5,7,2,3]=>[[[.,.],.],[[.,[.,.]],[.,.]]] [[1,2],[3,6],[4],[5],[7]]=>[7,5,4,3,6,1,2]=>[6,1,4,5,7,3,2]=>[[.,.],[[[.,[.,[.,.]]],.],.]] [[1,4],[2,5],[3],[6],[7]]=>[7,6,3,2,5,1,4]=>[5,3,6,1,2,7,4]=>[[[.,.],[.,.]],[.,[[.,.],.]]] [[1,3],[2,5],[4],[6],[7]]=>[7,6,4,2,5,1,3]=>[5,4,1,6,2,7,3]=>[[[.,.],.],[[.,.],[[.,.],.]]] [[1,2],[3,5],[4],[6],[7]]=>[7,6,4,3,5,1,2]=>[5,1,4,6,3,7,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]] [[1,3],[2,4],[5],[6],[7]]=>[7,6,5,2,4,1,3]=>[4,5,1,2,6,7,3]=>[[.,[.,.]],[.,[[.,[.,.]],.]]] [[1,2],[3,4],[5],[6],[7]]=>[7,6,5,3,4,1,2]=>[4,1,5,3,6,7,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]] [[1,7],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [[1,6],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6]=>[2,3,4,5,7,1,6]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [[1,5],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5]=>[2,3,4,6,1,7,5]=>[[.,[.,[.,[.,.]]]],[[.,.],.]] [[1,4],[2],[3],[5],[6],[7]]=>[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]=>[[.,[.,[.,.]]],[[.,[.,.]],.]] [[1,3],[2],[4],[5],[6],[7]]=>[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]=>[[.,[.,.]],[[.,[.,[.,.]]],.]] [[1,2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2]=>[3,1,4,5,6,7,2]=>[[.,.],[[.,[.,[.,[.,.]]]],.]] [[1],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.] [[1,2,3,4,5,6,7,8]]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [[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]=>[3,1,2,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] [[1,2,3,5,6,7,8],[4]]=>[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] [[1,2,3,4,6,7,8],[5]]=>[5,1,2,3,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] [[1,2,3,4,5,7,8],[6]]=>[6,1,2,3,4,5,7,8]=>[6,1,2,3,4,5,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] [[1,2,3,4,5,6,8],[7]]=>[7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,6,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] [[1,2,3,4,5,6,7],[8]]=>[8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] [[1,3,5,6,7,8],[2,4]]=>[2,4,1,3,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] [[1,2,5,6,7,8],[3,4]]=>[3,4,1,2,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] [[1,3,4,6,7,8],[2,5]]=>[2,5,1,3,4,6,7,8]=>[5,2,1,3,4,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] [[1,2,3,6,7,8],[4,5]]=>[4,5,1,2,3,6,7,8]=>[5,1,2,4,3,6,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] [[1,2,3,5,7,8],[4,6]]=>[4,6,1,2,3,5,7,8]=>[6,1,2,4,3,5,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] [[1,2,3,4,7,8],[5,6]]=>[5,6,1,2,3,4,7,8]=>[6,1,2,3,5,4,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] [[1,3,4,5,6,8],[2,7]]=>[2,7,1,3,4,5,6,8]=>[7,2,1,3,4,5,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] [[1,2,4,5,6,8],[3,7]]=>[3,7,1,2,4,5,6,8]=>[7,1,3,2,4,5,6,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] [[1,2,3,5,6,8],[4,7]]=>[4,7,1,2,3,5,6,8]=>[7,1,2,4,3,5,6,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] [[1,2,3,4,6,8],[5,7]]=>[5,7,1,2,3,4,6,8]=>[7,1,2,3,5,4,6,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] [[1,2,3,4,5,8],[6,7]]=>[6,7,1,2,3,4,5,8]=>[7,1,2,3,4,6,5,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] [[1,3,4,5,6,7],[2,8]]=>[2,8,1,3,4,5,6,7]=>[8,2,1,3,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] [[1,2,4,5,6,7],[3,8]]=>[3,8,1,2,4,5,6,7]=>[8,1,3,2,4,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] [[1,2,3,5,6,7],[4,8]]=>[4,8,1,2,3,5,6,7]=>[8,1,2,4,3,5,6,7]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] [[1,2,3,4,6,7],[5,8]]=>[5,8,1,2,3,4,6,7]=>[8,1,2,3,5,4,6,7]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] [[1,2,3,4,5,7],[6,8]]=>[6,8,1,2,3,4,5,7]=>[8,1,2,3,4,6,5,7]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] [[1,2,3,4,5,6],[7,8]]=>[7,8,1,2,3,4,5,6]=>[8,1,2,3,4,5,7,6]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] [[1,4,5,6,7,8],[2],[3]]=>[3,2,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] [[1,3,5,6,7,8],[2],[4]]=>[4,2,1,3,5,6,7,8]=>[2,4,1,3,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] [[1,2,5,6,7,8],[3],[4]]=>[4,3,1,2,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] [[1,3,4,6,7,8],[2],[5]]=>[5,2,1,3,4,6,7,8]=>[2,5,1,3,4,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] [[1,2,3,6,7,8],[4],[5]]=>[5,4,1,2,3,6,7,8]=>[4,1,2,5,3,6,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] [[1,3,4,5,7,8],[2],[6]]=>[6,2,1,3,4,5,7,8]=>[2,6,1,3,4,5,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] [[1,2,3,4,7,8],[5],[6]]=>[6,5,1,2,3,4,7,8]=>[5,1,2,3,6,4,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] [[1,3,4,5,6,8],[2],[7]]=>[7,2,1,3,4,5,6,8]=>[2,7,1,3,4,5,6,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] [[1,2,4,5,6,8],[3],[7]]=>[7,3,1,2,4,5,6,8]=>[3,1,7,2,4,5,6,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] [[1,2,3,5,6,8],[4],[7]]=>[7,4,1,2,3,5,6,8]=>[4,1,2,7,3,5,6,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] [[1,2,3,4,5,8],[6],[7]]=>[7,6,1,2,3,4,5,8]=>[6,1,2,3,4,7,5,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] [[1,3,4,5,6,7],[2],[8]]=>[8,2,1,3,4,5,6,7]=>[2,8,1,3,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] [[1,2,4,5,6,7],[3],[8]]=>[8,3,1,2,4,5,6,7]=>[3,1,8,2,4,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] [[1,2,3,5,6,7],[4],[8]]=>[8,4,1,2,3,5,6,7]=>[4,1,2,8,3,5,6,7]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] [[1,2,3,4,6,7],[5],[8]]=>[8,5,1,2,3,4,6,7]=>[5,1,2,3,8,4,6,7]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] [[1,2,3,4,5,7],[6],[8]]=>[8,6,1,2,3,4,5,7]=>[6,1,2,3,4,8,5,7]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] [[1,2,3,4,5,6],[7],[8]]=>[8,7,1,2,3,4,5,6]=>[7,1,2,3,4,5,8,6]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] [[1,3,5,7,8],[2,4,6]]=>[2,4,6,1,3,5,7,8]=>[6,2,1,4,3,5,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] [[1,2,5,7,8],[3,4,6]]=>[3,4,6,1,2,5,7,8]=>[6,1,3,4,2,5,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] [[1,3,5,6,8],[2,4,7]]=>[2,4,7,1,3,5,6,8]=>[7,2,1,4,3,5,6,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] [[1,2,4,6,8],[3,5,7]]=>[3,5,7,1,2,4,6,8]=>[7,1,3,2,5,4,6,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] [[1,2,3,4,8],[5,6,7]]=>[5,6,7,1,2,3,4,8]=>[7,1,2,3,5,6,4,8]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] [[1,2,4,6,7],[3,5,8]]=>[3,5,8,1,2,4,6,7]=>[8,1,3,2,5,4,6,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] [[1,2,3,6,7],[4,5,8]]=>[4,5,8,1,2,3,6,7]=>[8,1,2,4,5,3,6,7]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] [[1,3,4,5,7],[2,6,8]]=>[2,6,8,1,3,4,5,7]=>[8,2,1,3,4,6,5,7]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]] [[1,2,4,5,7],[3,6,8]]=>[3,6,8,1,2,4,5,7]=>[8,1,3,2,4,6,5,7]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]] [[1,2,3,5,7],[4,6,8]]=>[4,6,8,1,2,3,5,7]=>[8,1,2,4,3,6,5,7]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] [[1,2,3,4,7],[5,6,8]]=>[5,6,8,1,2,3,4,7]=>[8,1,2,3,5,6,4,7]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] [[1,3,4,5,6],[2,7,8]]=>[2,7,8,1,3,4,5,6]=>[8,2,1,3,4,5,7,6]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]] [[1,2,4,5,6],[3,7,8]]=>[3,7,8,1,2,4,5,6]=>[8,1,3,2,4,5,7,6]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]] [[1,2,3,5,6],[4,7,8]]=>[4,7,8,1,2,3,5,6]=>[8,1,2,4,3,5,7,6]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] [[1,2,3,4,6],[5,7,8]]=>[5,7,8,1,2,3,4,6]=>[8,1,2,3,5,4,7,6]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]] [[1,2,3,4,5],[6,7,8]]=>[6,7,8,1,2,3,4,5]=>[8,1,2,3,4,6,7,5]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] [[1,4,6,7,8],[2,5],[3]]=>[3,2,5,1,4,6,7,8]=>[5,3,2,1,4,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] [[1,3,6,7,8],[2,5],[4]]=>[4,2,5,1,3,6,7,8]=>[5,4,1,2,3,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] [[1,2,6,7,8],[3,5],[4]]=>[4,3,5,1,2,6,7,8]=>[5,1,4,3,2,6,7,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] [[1,3,6,7,8],[2,4],[5]]=>[5,2,4,1,3,6,7,8]=>[4,5,1,2,3,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] [[1,3,5,7,8],[2,6],[4]]=>[4,2,6,1,3,5,7,8]=>[6,4,1,2,3,5,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] [[1,2,4,7,8],[3,6],[5]]=>[5,3,6,1,2,4,7,8]=>[6,1,5,2,3,4,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] [[1,3,5,7,8],[2,4],[6]]=>[6,2,4,1,3,5,7,8]=>[4,6,1,2,3,5,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] [[1,2,5,7,8],[3,4],[6]]=>[6,3,4,1,2,5,7,8]=>[4,1,6,3,2,5,7,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] [[1,2,4,7,8],[3,5],[6]]=>[6,3,5,1,2,4,7,8]=>[5,1,6,2,3,4,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] [[1,4,5,6,8],[2,7],[3]]=>[3,2,7,1,4,5,6,8]=>[7,3,2,1,4,5,6,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] [[1,3,5,6,8],[2,7],[4]]=>[4,2,7,1,3,5,6,8]=>[7,4,1,2,3,5,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] [[1,3,4,6,8],[2,7],[5]]=>[5,2,7,1,3,4,6,8]=>[7,5,1,3,2,4,6,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] [[1,3,4,5,8],[2,7],[6]]=>[6,2,7,1,3,4,5,8]=>[7,6,1,3,4,2,5,8]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] [[1,2,3,5,8],[4,7],[6]]=>[6,4,7,1,2,3,5,8]=>[7,1,2,6,3,4,5,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] [[1,2,3,4,8],[5,7],[6]]=>[6,5,7,1,2,3,4,8]=>[7,1,2,3,6,5,4,8]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]] [[1,3,4,6,8],[2,5],[7]]=>[7,2,5,1,3,4,6,8]=>[5,7,1,3,2,4,6,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] [[1,2,3,5,8],[4,6],[7]]=>[7,4,6,1,2,3,5,8]=>[6,1,2,7,3,4,5,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] [[1,2,3,4,8],[5,6],[7]]=>[7,5,6,1,2,3,4,8]=>[6,1,2,3,7,5,4,8]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]] [[1,4,5,6,7],[2,8],[3]]=>[3,2,8,1,4,5,6,7]=>[8,3,2,1,4,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] [[1,3,5,6,7],[2,8],[4]]=>[4,2,8,1,3,5,6,7]=>[8,4,1,2,3,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] [[1,2,5,6,7],[3,8],[4]]=>[4,3,8,1,2,5,6,7]=>[8,1,4,3,2,5,6,7]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] [[1,3,4,6,7],[2,8],[5]]=>[5,2,8,1,3,4,6,7]=>[8,5,1,3,2,4,6,7]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] [[1,2,4,6,7],[3,8],[5]]=>[5,3,8,1,2,4,6,7]=>[8,1,5,2,3,4,6,7]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] [[1,2,3,6,7],[4,8],[5]]=>[5,4,8,1,2,3,6,7]=>[8,1,2,5,4,3,6,7]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]] [[1,3,4,5,7],[2,8],[6]]=>[6,2,8,1,3,4,5,7]=>[8,6,1,3,4,2,5,7]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] [[1,2,4,5,7],[3,8],[6]]=>[6,3,8,1,2,4,5,7]=>[8,1,6,2,4,3,5,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] [[1,2,3,5,7],[4,8],[6]]=>[6,4,8,1,2,3,5,7]=>[8,1,2,6,3,4,5,7]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] [[1,2,3,4,7],[5,8],[6]]=>[6,5,8,1,2,3,4,7]=>[8,1,2,3,6,5,4,7]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]] [[1,3,4,5,6],[2,8],[7]]=>[7,2,8,1,3,4,5,6]=>[8,7,1,3,4,5,2,6]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]] [[1,2,4,5,6],[3,8],[7]]=>[7,3,8,1,2,4,5,6]=>[8,1,7,2,4,5,3,6]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]] [[1,2,3,5,6],[4,8],[7]]=>[7,4,8,1,2,3,5,6]=>[8,1,2,7,3,5,4,6]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] [[1,2,3,4,6],[5,8],[7]]=>[7,5,8,1,2,3,4,6]=>[8,1,2,3,7,4,5,6]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] [[1,2,3,4,5],[6,8],[7]]=>[7,6,8,1,2,3,4,5]=>[8,1,2,3,4,7,6,5]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] [[1,3,5,6,7],[2,4],[8]]=>[8,2,4,1,3,5,6,7]=>[4,8,1,2,3,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] [[1,2,5,6,7],[3,4],[8]]=>[8,3,4,1,2,5,6,7]=>[4,1,8,3,2,5,6,7]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] [[1,2,4,6,7],[3,5],[8]]=>[8,3,5,1,2,4,6,7]=>[5,1,8,2,3,4,6,7]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] [[1,3,4,5,7],[2,6],[8]]=>[8,2,6,1,3,4,5,7]=>[6,8,1,3,4,2,5,7]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] [[1,2,4,5,7],[3,6],[8]]=>[8,3,6,1,2,4,5,7]=>[6,1,8,2,4,3,5,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] [[1,2,3,5,7],[4,6],[8]]=>[8,4,6,1,2,3,5,7]=>[6,1,2,8,3,4,5,7]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] [[1,2,3,4,7],[5,6],[8]]=>[8,5,6,1,2,3,4,7]=>[6,1,2,3,8,5,4,7]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]] [[1,3,4,5,6],[2,7],[8]]=>[8,2,7,1,3,4,5,6]=>[7,8,1,3,4,5,2,6]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] [[1,2,4,5,6],[3,7],[8]]=>[8,3,7,1,2,4,5,6]=>[7,1,8,2,4,5,3,6]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]] [[1,2,3,5,6],[4,7],[8]]=>[8,4,7,1,2,3,5,6]=>[7,1,2,8,3,5,4,6]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] [[1,2,3,4,6],[5,7],[8]]=>[8,5,7,1,2,3,4,6]=>[7,1,2,3,8,4,5,6]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] [[1,2,3,4,5],[6,7],[8]]=>[8,6,7,1,2,3,4,5]=>[7,1,2,3,4,8,6,5]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] [[1,5,6,7,8],[2],[3],[4]]=>[4,3,2,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] [[1,4,6,7,8],[2],[3],[5]]=>[5,3,2,1,4,6,7,8]=>[2,3,5,1,4,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] [[1,3,6,7,8],[2],[4],[5]]=>[5,4,2,1,3,6,7,8]=>[2,4,1,5,3,6,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] [[1,2,6,7,8],[3],[4],[5]]=>[5,4,3,1,2,6,7,8]=>[3,1,4,5,2,6,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] [[1,4,5,7,8],[2],[3],[6]]=>[6,3,2,1,4,5,7,8]=>[2,3,6,1,4,5,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] [[1,3,5,7,8],[2],[4],[6]]=>[6,4,2,1,3,5,7,8]=>[2,4,1,6,3,5,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] [[1,3,4,7,8],[2],[5],[6]]=>[6,5,2,1,3,4,7,8]=>[2,5,1,3,6,4,7,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] [[1,2,3,7,8],[4],[5],[6]]=>[6,5,4,1,2,3,7,8]=>[4,1,2,5,6,3,7,8]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] [[1,4,5,6,8],[2],[3],[7]]=>[7,3,2,1,4,5,6,8]=>[2,3,7,1,4,5,6,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] [[1,2,4,6,8],[3],[5],[7]]=>[7,5,3,1,2,4,6,8]=>[3,1,5,2,7,4,6,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] [[1,2,3,6,8],[4],[5],[7]]=>[7,5,4,1,2,3,6,8]=>[4,1,2,5,7,3,6,8]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] [[1,2,4,5,8],[3],[6],[7]]=>[7,6,3,1,2,4,5,8]=>[3,1,6,2,4,7,5,8]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]] [[1,2,3,5,8],[4],[6],[7]]=>[7,6,4,1,2,3,5,8]=>[4,1,2,6,3,7,5,8]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] [[1,2,3,4,8],[5],[6],[7]]=>[7,6,5,1,2,3,4,8]=>[5,1,2,3,6,7,4,8]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] [[1,4,5,6,7],[2],[3],[8]]=>[8,3,2,1,4,5,6,7]=>[2,3,8,1,4,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] [[1,3,5,6,7],[2],[4],[8]]=>[8,4,2,1,3,5,6,7]=>[2,4,1,8,3,5,6,7]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] [[1,2,5,6,7],[3],[4],[8]]=>[8,4,3,1,2,5,6,7]=>[3,1,4,8,2,5,6,7]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] [[1,3,4,6,7],[2],[5],[8]]=>[8,5,2,1,3,4,6,7]=>[2,5,1,3,8,4,6,7]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] [[1,2,4,6,7],[3],[5],[8]]=>[8,5,3,1,2,4,6,7]=>[3,1,5,2,8,4,6,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] [[1,2,3,6,7],[4],[5],[8]]=>[8,5,4,1,2,3,6,7]=>[4,1,2,5,8,3,6,7]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] [[1,2,3,5,7],[4],[6],[8]]=>[8,6,4,1,2,3,5,7]=>[4,1,2,6,3,8,5,7]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] [[1,2,3,4,7],[5],[6],[8]]=>[8,6,5,1,2,3,4,7]=>[5,1,2,3,6,8,4,7]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] [[1,3,4,5,6],[2],[7],[8]]=>[8,7,2,1,3,4,5,6]=>[2,7,1,3,4,5,8,6]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] [[1,2,3,5,6],[4],[7],[8]]=>[8,7,4,1,2,3,5,6]=>[4,1,2,7,3,5,8,6]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] [[1,2,3,4,6],[5],[7],[8]]=>[8,7,5,1,2,3,4,6]=>[5,1,2,3,7,4,8,6]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]] [[1,2,3,4,5],[6],[7],[8]]=>[8,7,6,1,2,3,4,5]=>[6,1,2,3,4,7,8,5]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] [[1,3,5,7],[2,4,6,8]]=>[2,4,6,8,1,3,5,7]=>[8,2,1,4,3,6,5,7]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]] [[1,2,5,7],[3,4,6,8]]=>[3,4,6,8,1,2,5,7]=>[8,1,3,4,2,6,5,7]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]] [[1,2,4,7],[3,5,6,8]]=>[3,5,6,8,1,2,4,7]=>[8,1,3,2,5,6,4,7]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]] [[1,2,3,7],[4,5,6,8]]=>[4,5,6,8,1,2,3,7]=>[8,1,2,4,5,6,3,7]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] [[1,3,5,6],[2,4,7,8]]=>[2,4,7,8,1,3,5,6]=>[8,2,1,4,3,5,7,6]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]] [[1,2,4,6],[3,5,7,8]]=>[3,5,7,8,1,2,4,6]=>[8,1,3,2,5,4,7,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]] [[1,2,3,6],[4,5,7,8]]=>[4,5,7,8,1,2,3,6]=>[8,1,2,4,5,3,7,6]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]] [[1,2,4,5],[3,6,7,8]]=>[3,6,7,8,1,2,4,5]=>[8,1,3,2,4,6,7,5]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]] [[1,2,3,4],[5,6,7,8]]=>[5,6,7,8,1,2,3,4]=>[8,1,2,3,5,6,7,4]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] [[1,4,6,8],[2,5,7],[3]]=>[3,2,5,7,1,4,6,8]=>[7,3,2,1,5,4,6,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]] [[1,4,5,8],[2,6,7],[3]]=>[3,2,6,7,1,4,5,8]=>[7,3,2,1,4,6,5,8]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]] [[1,3,4,8],[2,6,7],[5]]=>[5,2,6,7,1,3,4,8]=>[7,5,1,3,2,6,4,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]] [[1,2,4,8],[3,6,7],[5]]=>[5,3,6,7,1,2,4,8]=>[7,1,5,2,3,6,4,8]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]] [[1,2,3,8],[4,6,7],[5]]=>[5,4,6,7,1,2,3,8]=>[7,1,2,5,4,6,3,8]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]] [[1,3,5,8],[2,4,7],[6]]=>[6,2,4,7,1,3,5,8]=>[7,6,1,2,3,4,5,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] [[1,2,3,8],[4,5,7],[6]]=>[6,4,5,7,1,2,3,8]=>[7,1,2,6,4,5,3,8]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]] [[1,3,5,8],[2,4,6],[7]]=>[7,2,4,6,1,3,5,8]=>[6,7,1,2,3,4,5,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] [[1,2,5,8],[3,4,6],[7]]=>[7,3,4,6,1,2,5,8]=>[6,1,7,3,2,4,5,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] [[1,3,4,8],[2,5,6],[7]]=>[7,2,5,6,1,3,4,8]=>[6,7,1,3,2,5,4,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] [[1,4,6,7],[2,5,8],[3]]=>[3,2,5,8,1,4,6,7]=>[8,3,2,1,5,4,6,7]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]] [[1,3,6,7],[2,5,8],[4]]=>[4,2,5,8,1,3,6,7]=>[8,4,1,2,5,3,6,7]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]] [[1,2,6,7],[3,5,8],[4]]=>[4,3,5,8,1,2,6,7]=>[8,1,4,3,5,2,6,7]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]] [[1,3,6,7],[2,4,8],[5]]=>[5,2,4,8,1,3,6,7]=>[8,5,1,2,4,3,6,7]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]] [[1,2,6,7],[3,4,8],[5]]=>[5,3,4,8,1,2,6,7]=>[8,1,5,3,4,2,6,7]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]] [[1,4,5,7],[2,6,8],[3]]=>[3,2,6,8,1,4,5,7]=>[8,3,2,1,4,6,5,7]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]] [[1,2,5,7],[3,6,8],[4]]=>[4,3,6,8,1,2,5,7]=>[8,1,4,3,2,6,5,7]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]] [[1,2,3,7],[4,6,8],[5]]=>[5,4,6,8,1,2,3,7]=>[8,1,2,5,4,6,3,7]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]] [[1,3,5,7],[2,4,8],[6]]=>[6,2,4,8,1,3,5,7]=>[8,6,1,2,3,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] [[1,2,4,7],[3,5,8],[6]]=>[6,3,5,8,1,2,4,7]=>[8,1,6,2,3,5,4,7]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]] [[1,2,3,7],[4,5,8],[6]]=>[6,4,5,8,1,2,3,7]=>[8,1,2,6,4,5,3,7]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]] [[1,4,5,6],[2,7,8],[3]]=>[3,2,7,8,1,4,5,6]=>[8,3,2,1,4,5,7,6]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]] [[1,2,5,6],[3,7,8],[4]]=>[4,3,7,8,1,2,5,6]=>[8,1,4,3,2,5,7,6]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]] [[1,3,4,6],[2,7,8],[5]]=>[5,2,7,8,1,3,4,6]=>[8,5,1,3,2,4,7,6]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]] [[1,2,4,5],[3,7,8],[6]]=>[6,3,7,8,1,2,4,5]=>[8,1,6,2,4,3,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]] [[1,2,3,4],[5,7,8],[6]]=>[6,5,7,8,1,2,3,4]=>[8,1,2,3,6,5,7,4]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]] [[1,2,5,6],[3,4,8],[7]]=>[7,3,4,8,1,2,5,6]=>[8,1,7,3,2,5,4,6]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]] [[1,3,4,6],[2,5,8],[7]]=>[7,2,5,8,1,3,4,6]=>[8,7,1,3,2,4,5,6]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] [[1,2,4,6],[3,5,8],[7]]=>[7,3,5,8,1,2,4,6]=>[8,1,7,2,3,4,5,6]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] [[1,3,4,5],[2,6,8],[7]]=>[7,2,6,8,1,3,4,5]=>[8,7,1,3,4,2,6,5]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]] [[1,2,4,5],[3,6,8],[7]]=>[7,3,6,8,1,2,4,5]=>[8,1,7,2,4,3,6,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]] [[1,2,3,5],[4,6,8],[7]]=>[7,4,6,8,1,2,3,5]=>[8,1,2,7,3,4,6,5]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] [[1,2,3,4],[5,6,8],[7]]=>[7,5,6,8,1,2,3,4]=>[8,1,2,3,7,5,6,4]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]] [[1,3,5,7],[2,4,6],[8]]=>[8,2,4,6,1,3,5,7]=>[6,8,1,2,3,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] [[1,3,4,7],[2,5,6],[8]]=>[8,2,5,6,1,3,4,7]=>[6,8,1,3,2,5,4,7]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] [[1,2,4,7],[3,5,6],[8]]=>[8,3,5,6,1,2,4,7]=>[6,1,8,2,3,5,4,7]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]] [[1,3,5,6],[2,4,7],[8]]=>[8,2,4,7,1,3,5,6]=>[7,8,1,2,3,5,4,6]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] [[1,2,5,6],[3,4,7],[8]]=>[8,3,4,7,1,2,5,6]=>[7,1,8,3,2,5,4,6]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]] [[1,3,4,6],[2,5,7],[8]]=>[8,2,5,7,1,3,4,6]=>[7,8,1,3,2,4,5,6]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] [[1,2,4,6],[3,5,7],[8]]=>[8,3,5,7,1,2,4,6]=>[7,1,8,2,3,4,5,6]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] [[1,3,4,5],[2,6,7],[8]]=>[8,2,6,7,1,3,4,5]=>[7,8,1,3,4,2,6,5]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]] [[1,2,4,5],[3,6,7],[8]]=>[8,3,6,7,1,2,4,5]=>[7,1,8,2,4,3,6,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]] [[1,2,3,4],[5,6,7],[8]]=>[8,5,6,7,1,2,3,4]=>[7,1,2,3,8,5,6,4]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]] [[1,3,7,8],[2,5],[4,6]]=>[4,6,2,5,1,3,7,8]=>[5,6,1,4,2,3,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] [[1,2,7,8],[3,5],[4,6]]=>[4,6,3,5,1,2,7,8]=>[5,1,6,4,3,2,7,8]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]] [[1,3,7,8],[2,4],[5,6]]=>[5,6,2,4,1,3,7,8]=>[4,6,1,2,5,3,7,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] [[1,2,7,8],[3,4],[5,6]]=>[5,6,3,4,1,2,7,8]=>[4,1,6,3,5,2,7,8]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]] [[1,4,6,8],[2,5],[3,7]]=>[3,7,2,5,1,4,6,8]=>[5,7,3,1,2,4,6,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] [[1,3,6,8],[2,5],[4,7]]=>[4,7,2,5,1,3,6,8]=>[5,7,1,4,2,3,6,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] [[1,3,6,8],[2,4],[5,7]]=>[5,7,2,4,1,3,6,8]=>[4,7,1,2,5,3,6,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] [[1,4,5,8],[2,6],[3,7]]=>[3,7,2,6,1,4,5,8]=>[6,7,3,1,4,2,5,8]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]] [[1,3,5,8],[2,6],[4,7]]=>[4,7,2,6,1,3,5,8]=>[6,7,1,4,3,2,5,8]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]] [[1,2,5,8],[3,6],[4,7]]=>[4,7,3,6,1,2,5,8]=>[6,1,7,4,2,3,5,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] [[1,2,4,8],[3,6],[5,7]]=>[5,7,3,6,1,2,4,8]=>[6,1,7,2,5,3,4,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] [[1,2,5,8],[3,4],[6,7]]=>[6,7,3,4,1,2,5,8]=>[4,1,7,3,2,6,5,8]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]] [[1,3,4,8],[2,5],[6,7]]=>[6,7,2,5,1,3,4,8]=>[5,7,1,3,2,6,4,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] [[1,4,6,7],[2,5],[3,8]]=>[3,8,2,5,1,4,6,7]=>[5,8,3,1,2,4,6,7]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] [[1,3,6,7],[2,5],[4,8]]=>[4,8,2,5,1,3,6,7]=>[5,8,1,4,2,3,6,7]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] [[1,3,6,7],[2,4],[5,8]]=>[5,8,2,4,1,3,6,7]=>[4,8,1,2,5,3,6,7]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] [[1,2,6,7],[3,4],[5,8]]=>[5,8,3,4,1,2,6,7]=>[4,1,8,3,5,2,6,7]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]] [[1,4,5,7],[2,6],[3,8]]=>[3,8,2,6,1,4,5,7]=>[6,8,3,1,4,2,5,7]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]] [[1,2,4,7],[3,6],[5,8]]=>[5,8,3,6,1,2,4,7]=>[6,1,8,2,5,3,4,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] [[1,3,5,7],[2,4],[6,8]]=>[6,8,2,4,1,3,5,7]=>[4,8,1,2,3,6,5,7]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] [[1,3,4,7],[2,5],[6,8]]=>[6,8,2,5,1,3,4,7]=>[5,8,1,3,2,6,4,7]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] [[1,3,5,6],[2,7],[4,8]]=>[4,8,2,7,1,3,5,6]=>[7,8,1,4,3,5,2,6]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]] [[1,2,5,6],[3,7],[4,8]]=>[4,8,3,7,1,2,5,6]=>[7,1,8,4,2,5,3,6]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]] [[1,2,4,6],[3,7],[5,8]]=>[5,8,3,7,1,2,4,6]=>[7,1,8,2,5,4,3,6]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]] [[1,2,3,6],[4,7],[5,8]]=>[5,8,4,7,1,2,3,6]=>[7,1,2,8,5,3,4,6]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]] [[1,2,4,5],[3,7],[6,8]]=>[6,8,3,7,1,2,4,5]=>[7,1,8,2,4,6,3,5]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]] [[1,2,3,5],[4,7],[6,8]]=>[6,8,4,7,1,2,3,5]=>[7,1,2,8,3,6,4,5]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] [[1,2,3,4],[5,7],[6,8]]=>[6,8,5,7,1,2,3,4]=>[7,1,2,3,8,6,5,4]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]] [[1,3,5,6],[2,4],[7,8]]=>[7,8,2,4,1,3,5,6]=>[4,8,1,2,3,5,7,6]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] [[1,3,4,6],[2,5],[7,8]]=>[7,8,2,5,1,3,4,6]=>[5,8,1,3,2,4,7,6]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]] [[1,2,4,6],[3,5],[7,8]]=>[7,8,3,5,1,2,4,6]=>[5,1,8,2,3,4,7,6]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]] [[1,2,3,6],[4,5],[7,8]]=>[7,8,4,5,1,2,3,6]=>[5,1,2,8,4,3,7,6]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]] [[1,3,4,5],[2,6],[7,8]]=>[7,8,2,6,1,3,4,5]=>[6,8,1,3,4,2,7,5]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]] [[1,2,4,5],[3,6],[7,8]]=>[7,8,3,6,1,2,4,5]=>[6,1,8,2,4,3,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]] [[1,2,3,5],[4,6],[7,8]]=>[7,8,4,6,1,2,3,5]=>[6,1,2,8,3,4,7,5]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] [[1,2,3,4],[5,6],[7,8]]=>[7,8,5,6,1,2,3,4]=>[6,1,2,3,8,5,7,4]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]] [[1,5,7,8],[2,6],[3],[4]]=>[4,3,2,6,1,5,7,8]=>[6,3,4,2,1,5,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] [[1,4,7,8],[2,6],[3],[5]]=>[5,3,2,6,1,4,7,8]=>[6,3,5,1,2,4,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] [[1,3,7,8],[2,6],[4],[5]]=>[5,4,2,6,1,3,7,8]=>[6,4,1,5,2,3,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] [[1,2,7,8],[3,6],[4],[5]]=>[5,4,3,6,1,2,7,8]=>[6,1,4,5,3,2,7,8]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]] [[1,4,7,8],[2,5],[3],[6]]=>[6,3,2,5,1,4,7,8]=>[5,3,6,1,2,4,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] [[1,4,6,8],[2,7],[3],[5]]=>[5,3,2,7,1,4,6,8]=>[7,3,5,1,2,4,6,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] [[1,3,6,8],[2,7],[4],[5]]=>[5,4,2,7,1,3,6,8]=>[7,4,1,5,2,3,6,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] [[1,2,6,8],[3,7],[4],[5]]=>[5,4,3,7,1,2,6,8]=>[7,1,4,5,3,2,6,8]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]] [[1,3,4,8],[2,7],[5],[6]]=>[6,5,2,7,1,3,4,8]=>[7,5,1,3,6,2,4,8]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] [[1,2,4,8],[3,7],[5],[6]]=>[6,5,3,7,1,2,4,8]=>[7,1,5,2,6,3,4,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] [[1,4,6,8],[2,5],[3],[7]]=>[7,3,2,5,1,4,6,8]=>[5,3,7,1,2,4,6,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] [[1,3,6,8],[2,4],[5],[7]]=>[7,5,2,4,1,3,6,8]=>[4,5,1,2,7,3,6,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] [[1,2,4,8],[3,6],[5],[7]]=>[7,5,3,6,1,2,4,8]=>[6,1,5,2,7,3,4,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] [[1,2,5,8],[3,4],[6],[7]]=>[7,6,3,4,1,2,5,8]=>[4,1,6,3,2,7,5,8]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]] [[1,2,4,8],[3,5],[6],[7]]=>[7,6,3,5,1,2,4,8]=>[5,1,6,2,3,7,4,8]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]] [[1,5,6,7],[2,8],[3],[4]]=>[4,3,2,8,1,5,6,7]=>[8,3,4,2,1,5,6,7]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]] [[1,4,6,7],[2,8],[3],[5]]=>[5,3,2,8,1,4,6,7]=>[8,3,5,1,2,4,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] [[1,3,6,7],[2,8],[4],[5]]=>[5,4,2,8,1,3,6,7]=>[8,4,1,5,2,3,6,7]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] [[1,2,6,7],[3,8],[4],[5]]=>[5,4,3,8,1,2,6,7]=>[8,1,4,5,3,2,6,7]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]] [[1,3,5,7],[2,8],[4],[6]]=>[6,4,2,8,1,3,5,7]=>[8,4,1,6,3,2,5,7]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]] [[1,2,5,7],[3,8],[4],[6]]=>[6,4,3,8,1,2,5,7]=>[8,1,4,6,2,3,5,7]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] [[1,3,4,7],[2,8],[5],[6]]=>[6,5,2,8,1,3,4,7]=>[8,5,1,3,6,2,4,7]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] [[1,2,4,7],[3,8],[5],[6]]=>[6,5,3,8,1,2,4,7]=>[8,1,5,2,6,3,4,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] [[1,2,3,7],[4,8],[5],[6]]=>[6,5,4,8,1,2,3,7]=>[8,1,2,5,6,4,3,7]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]] [[1,3,5,6],[2,8],[4],[7]]=>[7,4,2,8,1,3,5,6]=>[8,4,1,7,3,5,2,6]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]] [[1,2,5,6],[3,8],[4],[7]]=>[7,4,3,8,1,2,5,6]=>[8,1,4,7,2,5,3,6]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]] [[1,3,4,6],[2,8],[5],[7]]=>[7,5,2,8,1,3,4,6]=>[8,5,1,3,7,4,2,6]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]] [[1,2,4,6],[3,8],[5],[7]]=>[7,5,3,8,1,2,4,6]=>[8,1,5,2,7,4,3,6]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]] [[1,2,3,6],[4,8],[5],[7]]=>[7,5,4,8,1,2,3,6]=>[8,1,2,5,7,3,4,6]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] [[1,2,3,5],[4,8],[6],[7]]=>[7,6,4,8,1,2,3,5]=>[8,1,2,6,3,7,4,5]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] [[1,2,3,4],[5,8],[6],[7]]=>[7,6,5,8,1,2,3,4]=>[8,1,2,3,6,7,5,4]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] [[1,3,6,7],[2,5],[4],[8]]=>[8,4,2,5,1,3,6,7]=>[5,4,1,8,2,3,6,7]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] [[1,2,6,7],[3,5],[4],[8]]=>[8,4,3,5,1,2,6,7]=>[5,1,4,8,3,2,6,7]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]] [[1,3,6,7],[2,4],[5],[8]]=>[8,5,2,4,1,3,6,7]=>[4,5,1,2,8,3,6,7]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] [[1,2,6,7],[3,4],[5],[8]]=>[8,5,3,4,1,2,6,7]=>[4,1,5,3,8,2,6,7]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]] [[1,4,5,7],[2,6],[3],[8]]=>[8,3,2,6,1,4,5,7]=>[6,3,8,1,4,2,5,7]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] [[1,3,5,7],[2,6],[4],[8]]=>[8,4,2,6,1,3,5,7]=>[6,4,1,8,3,2,5,7]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]] [[1,2,4,7],[3,6],[5],[8]]=>[8,5,3,6,1,2,4,7]=>[6,1,5,2,8,3,4,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] [[1,3,5,7],[2,4],[6],[8]]=>[8,6,2,4,1,3,5,7]=>[4,6,1,2,3,8,5,7]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] [[1,2,4,7],[3,5],[6],[8]]=>[8,6,3,5,1,2,4,7]=>[5,1,6,2,3,8,4,7]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]] [[1,2,3,7],[4,5],[6],[8]]=>[8,6,4,5,1,2,3,7]=>[5,1,2,6,4,8,3,7]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]] [[1,4,5,6],[2,7],[3],[8]]=>[8,3,2,7,1,4,5,6]=>[7,3,8,1,4,5,2,6]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]] [[1,3,5,6],[2,7],[4],[8]]=>[8,4,2,7,1,3,5,6]=>[7,4,1,8,3,5,2,6]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]] [[1,3,4,6],[2,7],[5],[8]]=>[8,5,2,7,1,3,4,6]=>[7,5,1,3,8,4,2,6]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]] [[1,2,3,6],[4,7],[5],[8]]=>[8,5,4,7,1,2,3,6]=>[7,1,2,5,8,3,4,6]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] [[1,3,4,5],[2,7],[6],[8]]=>[8,6,2,7,1,3,4,5]=>[7,6,1,3,4,8,2,5]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]] [[1,2,4,5],[3,7],[6],[8]]=>[8,6,3,7,1,2,4,5]=>[7,1,6,2,4,8,3,5]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]] [[1,2,3,5],[4,7],[6],[8]]=>[8,6,4,7,1,2,3,5]=>[7,1,2,6,3,8,4,5]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] [[1,2,3,4],[5,7],[6],[8]]=>[8,6,5,7,1,2,3,4]=>[7,1,2,3,6,8,5,4]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] [[1,3,5,6],[2,4],[7],[8]]=>[8,7,2,4,1,3,5,6]=>[4,7,1,2,3,5,8,6]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] [[1,2,5,6],[3,4],[7],[8]]=>[8,7,3,4,1,2,5,6]=>[4,1,7,3,2,5,8,6]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]] [[1,3,4,6],[2,5],[7],[8]]=>[8,7,2,5,1,3,4,6]=>[5,7,1,3,2,4,8,6]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]] [[1,2,4,6],[3,5],[7],[8]]=>[8,7,3,5,1,2,4,6]=>[5,1,7,2,3,4,8,6]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]] [[1,2,4,5],[3,6],[7],[8]]=>[8,7,3,6,1,2,4,5]=>[6,1,7,2,4,3,8,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]] [[1,2,3,5],[4,6],[7],[8]]=>[8,7,4,6,1,2,3,5]=>[6,1,2,7,3,4,8,5]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] [[1,2,3,4],[5,6],[7],[8]]=>[8,7,5,6,1,2,3,4]=>[6,1,2,3,7,5,8,4]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]] [[1,6,7,8],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] [[1,5,7,8],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7,8]=>[2,3,4,6,1,5,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] [[1,3,7,8],[2],[4],[5],[6]]=>[6,5,4,2,1,3,7,8]=>[2,4,1,5,6,3,7,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] [[1,5,6,8],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6,8]=>[2,3,4,7,1,5,6,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] [[1,3,5,8],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5,8]=>[2,4,1,6,3,7,5,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] [[1,2,3,8],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3,8]=>[4,1,2,5,6,7,3,8]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] [[1,5,6,7],[2],[3],[4],[8]]=>[8,4,3,2,1,5,6,7]=>[2,3,4,8,1,5,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] [[1,4,6,7],[2],[3],[5],[8]]=>[8,5,3,2,1,4,6,7]=>[2,3,5,1,8,4,6,7]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] [[1,3,6,7],[2],[4],[5],[8]]=>[8,5,4,2,1,3,6,7]=>[2,4,1,5,8,3,6,7]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] [[1,2,6,7],[3],[4],[5],[8]]=>[8,5,4,3,1,2,6,7]=>[3,1,4,5,8,2,6,7]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] [[1,4,5,7],[2],[3],[6],[8]]=>[8,6,3,2,1,4,5,7]=>[2,3,6,1,4,8,5,7]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] [[1,3,5,7],[2],[4],[6],[8]]=>[8,6,4,2,1,3,5,7]=>[2,4,1,6,3,8,5,7]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] [[1,2,5,7],[3],[4],[6],[8]]=>[8,6,4,3,1,2,5,7]=>[3,1,4,6,2,8,5,7]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]] [[1,3,4,7],[2],[5],[6],[8]]=>[8,6,5,2,1,3,4,7]=>[2,5,1,3,6,8,4,7]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] [[1,2,4,7],[3],[5],[6],[8]]=>[8,6,5,3,1,2,4,7]=>[3,1,5,2,6,8,4,7]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]] [[1,2,3,7],[4],[5],[6],[8]]=>[8,6,5,4,1,2,3,7]=>[4,1,2,5,6,8,3,7]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] [[1,4,5,6],[2],[3],[7],[8]]=>[8,7,3,2,1,4,5,6]=>[2,3,7,1,4,5,8,6]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] [[1,3,5,6],[2],[4],[7],[8]]=>[8,7,4,2,1,3,5,6]=>[2,4,1,7,3,5,8,6]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]] [[1,2,5,6],[3],[4],[7],[8]]=>[8,7,4,3,1,2,5,6]=>[3,1,4,7,2,5,8,6]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] [[1,3,4,6],[2],[5],[7],[8]]=>[8,7,5,2,1,3,4,6]=>[2,5,1,3,7,4,8,6]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] [[1,2,4,6],[3],[5],[7],[8]]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]] [[1,2,3,6],[4],[5],[7],[8]]=>[8,7,5,4,1,2,3,6]=>[4,1,2,5,7,3,8,6]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]] [[1,3,4,5],[2],[6],[7],[8]]=>[8,7,6,2,1,3,4,5]=>[2,6,1,3,4,7,8,5]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] [[1,2,4,5],[3],[6],[7],[8]]=>[8,7,6,3,1,2,4,5]=>[3,1,6,2,4,7,8,5]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]] [[1,2,3,5],[4],[6],[7],[8]]=>[8,7,6,4,1,2,3,5]=>[4,1,2,6,3,7,8,5]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]] [[1,2,3,4],[5],[6],[7],[8]]=>[8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,4]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] [[1,4,7],[2,5,8],[3,6]]=>[3,6,2,5,8,1,4,7]=>[8,6,3,1,2,5,4,7]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]] [[1,3,7],[2,5,8],[4,6]]=>[4,6,2,5,8,1,3,7]=>[8,6,1,4,2,5,3,7]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]] [[1,2,7],[3,5,8],[4,6]]=>[4,6,3,5,8,1,2,7]=>[8,1,6,4,3,5,2,7]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]] [[1,3,7],[2,4,8],[5,6]]=>[5,6,2,4,8,1,3,7]=>[8,6,1,2,5,4,3,7]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]] [[1,3,6],[2,5,8],[4,7]]=>[4,7,2,5,8,1,3,6]=>[8,7,1,4,2,3,5,6]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] [[1,3,6],[2,4,8],[5,7]]=>[5,7,2,4,8,1,3,6]=>[8,7,1,2,5,3,4,6]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]] [[1,2,6],[3,4,8],[5,7]]=>[5,7,3,4,8,1,2,6]=>[8,1,7,3,5,2,4,6]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]] [[1,4,5],[2,6,8],[3,7]]=>[3,7,2,6,8,1,4,5]=>[8,7,3,1,4,2,6,5]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]] [[1,3,5],[2,6,8],[4,7]]=>[4,7,2,6,8,1,3,5]=>[8,7,1,4,3,2,6,5]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]] [[1,2,5],[3,6,8],[4,7]]=>[4,7,3,6,8,1,2,5]=>[8,1,7,4,2,3,6,5]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]] [[1,3,4],[2,6,8],[5,7]]=>[5,7,2,6,8,1,3,4]=>[8,7,1,3,5,2,6,4]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]] [[1,2,4],[3,6,8],[5,7]]=>[5,7,3,6,8,1,2,4]=>[8,1,7,2,5,3,6,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]] [[1,3,5],[2,4,8],[6,7]]=>[6,7,2,4,8,1,3,5]=>[8,7,1,2,3,6,4,5]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]] [[1,2,4],[3,5,8],[6,7]]=>[6,7,3,5,8,1,2,4]=>[8,1,7,2,3,6,5,4]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]] [[1,2,3],[4,5,8],[6,7]]=>[6,7,4,5,8,1,2,3]=>[8,1,2,7,4,6,5,3]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]] [[1,4,6],[2,5,7],[3,8]]=>[3,8,2,5,7,1,4,6]=>[7,8,3,1,2,4,5,6]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] [[1,3,6],[2,5,7],[4,8]]=>[4,8,2,5,7,1,3,6]=>[7,8,1,4,2,3,5,6]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] [[1,3,6],[2,4,7],[5,8]]=>[5,8,2,4,7,1,3,6]=>[7,8,1,2,5,3,4,6]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] [[1,4,5],[2,6,7],[3,8]]=>[3,8,2,6,7,1,4,5]=>[7,8,3,1,4,2,6,5]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]] [[1,2,5],[3,6,7],[4,8]]=>[4,8,3,6,7,1,2,5]=>[7,1,8,4,2,3,6,5]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]] [[1,3,4],[2,6,7],[5,8]]=>[5,8,2,6,7,1,3,4]=>[7,8,1,3,5,2,6,4]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]] [[1,2,4],[3,6,7],[5,8]]=>[5,8,3,6,7,1,2,4]=>[7,1,8,2,5,3,6,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]] [[1,3,5],[2,4,7],[6,8]]=>[6,8,2,4,7,1,3,5]=>[7,8,1,2,3,6,4,5]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] [[1,3,4],[2,5,7],[6,8]]=>[6,8,2,5,7,1,3,4]=>[7,8,1,3,2,6,5,4]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]] [[1,2,4],[3,5,7],[6,8]]=>[6,8,3,5,7,1,2,4]=>[7,1,8,2,3,6,5,4]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]] [[1,2,3],[4,5,7],[6,8]]=>[6,8,4,5,7,1,2,3]=>[7,1,2,8,4,6,5,3]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]] [[1,3,5],[2,4,6],[7,8]]=>[7,8,2,4,6,1,3,5]=>[6,8,1,2,3,4,7,5]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] [[1,2,5],[3,4,6],[7,8]]=>[7,8,3,4,6,1,2,5]=>[6,1,8,3,2,4,7,5]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]] [[1,3,4],[2,5,6],[7,8]]=>[7,8,2,5,6,1,3,4]=>[6,8,1,3,2,5,7,4]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]] [[1,2,4],[3,5,6],[7,8]]=>[7,8,3,5,6,1,2,4]=>[6,1,8,2,3,5,7,4]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]] [[1,2,3],[4,5,6],[7,8]]=>[7,8,4,5,6,1,2,3]=>[6,1,2,8,4,5,7,3]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]] [[1,5,7],[2,6,8],[3],[4]]=>[4,3,2,6,8,1,5,7]=>[8,3,4,2,1,6,5,7]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]] [[1,4,7],[2,6,8],[3],[5]]=>[5,3,2,6,8,1,4,7]=>[8,3,5,1,2,6,4,7]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] [[1,3,7],[2,6,8],[4],[5]]=>[5,4,2,6,8,1,3,7]=>[8,4,1,5,2,6,3,7]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]] [[1,2,7],[3,6,8],[4],[5]]=>[5,4,3,6,8,1,2,7]=>[8,1,4,5,3,6,2,7]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] [[1,3,7],[2,5,8],[4],[6]]=>[6,4,2,5,8,1,3,7]=>[8,4,1,6,2,5,3,7]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]] [[1,2,7],[3,5,8],[4],[6]]=>[6,4,3,5,8,1,2,7]=>[8,1,4,6,3,5,2,7]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] [[1,3,7],[2,4,8],[5],[6]]=>[6,5,2,4,8,1,3,7]=>[8,5,1,2,6,4,3,7]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]] [[1,4,6],[2,7,8],[3],[5]]=>[5,3,2,7,8,1,4,6]=>[8,3,5,1,2,4,7,6]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]] [[1,3,6],[2,7,8],[4],[5]]=>[5,4,2,7,8,1,3,6]=>[8,4,1,5,2,3,7,6]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]] [[1,2,6],[3,7,8],[4],[5]]=>[5,4,3,7,8,1,2,6]=>[8,1,4,5,3,2,7,6]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]] [[1,4,5],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5]=>[8,3,6,1,4,2,7,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]] [[1,2,4],[3,7,8],[5],[6]]=>[6,5,3,7,8,1,2,4]=>[8,1,5,2,6,3,7,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]] [[1,4,6],[2,5,8],[3],[7]]=>[7,3,2,5,8,1,4,6]=>[8,3,7,1,2,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] [[1,3,6],[2,5,8],[4],[7]]=>[7,4,2,5,8,1,3,6]=>[8,4,1,7,2,3,5,6]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] [[1,2,6],[3,5,8],[4],[7]]=>[7,4,3,5,8,1,2,6]=>[8,1,4,7,3,2,5,6]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]] [[1,3,6],[2,4,8],[5],[7]]=>[7,5,2,4,8,1,3,6]=>[8,5,1,2,7,3,4,6]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]] [[1,2,6],[3,4,8],[5],[7]]=>[7,5,3,4,8,1,2,6]=>[8,1,5,3,7,2,4,6]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]] [[1,4,5],[2,6,8],[3],[7]]=>[7,3,2,6,8,1,4,5]=>[8,3,7,1,4,2,6,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]] [[1,3,5],[2,6,8],[4],[7]]=>[7,4,2,6,8,1,3,5]=>[8,4,1,7,3,2,6,5]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]] [[1,2,5],[3,6,8],[4],[7]]=>[7,4,3,6,8,1,2,5]=>[8,1,4,7,2,3,6,5]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] [[1,3,4],[2,6,8],[5],[7]]=>[7,5,2,6,8,1,3,4]=>[8,5,1,3,7,2,6,4]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]] [[1,2,4],[3,6,8],[5],[7]]=>[7,5,3,6,8,1,2,4]=>[8,1,5,2,7,3,6,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]] [[1,2,3],[4,6,8],[5],[7]]=>[7,5,4,6,8,1,2,3]=>[8,1,2,5,7,4,6,3]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]] [[1,3,5],[2,4,8],[6],[7]]=>[7,6,2,4,8,1,3,5]=>[8,6,1,2,3,7,4,5]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]] [[1,2,5],[3,4,8],[6],[7]]=>[7,6,3,4,8,1,2,5]=>[8,1,6,3,2,7,4,5]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]] [[1,2,4],[3,5,8],[6],[7]]=>[7,6,3,5,8,1,2,4]=>[8,1,6,2,3,7,5,4]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]] [[1,2,3],[4,5,8],[6],[7]]=>[7,6,4,5,8,1,2,3]=>[8,1,2,6,4,7,5,3]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]] [[1,4,6],[2,5,7],[3],[8]]=>[8,3,2,5,7,1,4,6]=>[7,3,8,1,2,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] [[1,3,6],[2,5,7],[4],[8]]=>[8,4,2,5,7,1,3,6]=>[7,4,1,8,2,3,5,6]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] [[1,3,6],[2,4,7],[5],[8]]=>[8,5,2,4,7,1,3,6]=>[7,5,1,2,8,3,4,6]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]] [[1,4,5],[2,6,7],[3],[8]]=>[8,3,2,6,7,1,4,5]=>[7,3,8,1,4,2,6,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]] [[1,3,5],[2,6,7],[4],[8]]=>[8,4,2,6,7,1,3,5]=>[7,4,1,8,3,2,6,5]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]] [[1,2,5],[3,6,7],[4],[8]]=>[8,4,3,6,7,1,2,5]=>[7,1,4,8,2,3,6,5]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] [[1,3,4],[2,6,7],[5],[8]]=>[8,5,2,6,7,1,3,4]=>[7,5,1,3,8,2,6,4]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]] [[1,2,4],[3,6,7],[5],[8]]=>[8,5,3,6,7,1,2,4]=>[7,1,5,2,8,3,6,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]] [[1,2,3],[4,6,7],[5],[8]]=>[8,5,4,6,7,1,2,3]=>[7,1,2,5,8,4,6,3]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]] [[1,3,5],[2,4,7],[6],[8]]=>[8,6,2,4,7,1,3,5]=>[7,6,1,2,3,8,4,5]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]] [[1,2,5],[3,4,7],[6],[8]]=>[8,6,3,4,7,1,2,5]=>[7,1,6,3,2,8,4,5]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]] [[1,2,4],[3,5,7],[6],[8]]=>[8,6,3,5,7,1,2,4]=>[7,1,6,2,3,8,5,4]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]] [[1,3,5],[2,4,6],[7],[8]]=>[8,7,2,4,6,1,3,5]=>[6,7,1,2,3,4,8,5]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] [[1,3,4],[2,5,6],[7],[8]]=>[8,7,2,5,6,1,3,4]=>[6,7,1,3,2,5,8,4]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]] [[1,2,4],[3,5,6],[7],[8]]=>[8,7,3,5,6,1,2,4]=>[6,1,7,2,3,5,8,4]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]] [[1,2,3],[4,5,6],[7],[8]]=>[8,7,4,5,6,1,2,3]=>[6,1,2,7,4,5,8,3]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]] [[1,4,8],[2,6],[3,7],[5]]=>[5,3,7,2,6,1,4,8]=>[6,7,5,1,3,2,4,8]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]] [[1,4,8],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4,8]=>[5,7,6,1,2,3,4,8]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] [[1,3,8],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3,8]=>[5,7,1,6,2,4,3,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] [[1,2,8],[3,5],[4,7],[6]]=>[6,4,7,3,5,1,2,8]=>[5,1,7,6,3,4,2,8]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]] [[1,4,8],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4,8]=>[5,6,7,1,2,3,4,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] [[1,3,8],[2,5],[4,6],[7]]=>[7,4,6,2,5,1,3,8]=>[5,6,1,7,2,4,3,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] [[1,2,8],[3,5],[4,6],[7]]=>[7,4,6,3,5,1,2,8]=>[5,1,6,7,3,4,2,8]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] [[1,2,8],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2,8]=>[4,1,6,3,7,5,2,8]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]] [[1,3,7],[2,6],[4,8],[5]]=>[5,4,8,2,6,1,3,7]=>[6,8,1,5,4,2,3,7]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]] [[1,4,7],[2,5],[3,8],[6]]=>[6,3,8,2,5,1,4,7]=>[5,8,6,1,2,3,4,7]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] [[1,3,7],[2,5],[4,8],[6]]=>[6,4,8,2,5,1,3,7]=>[5,8,1,6,2,4,3,7]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] [[1,2,7],[3,5],[4,8],[6]]=>[6,4,8,3,5,1,2,7]=>[5,1,8,6,3,4,2,7]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]] [[1,3,7],[2,4],[5,8],[6]]=>[6,5,8,2,4,1,3,7]=>[4,8,1,2,6,5,3,7]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]] [[1,2,7],[3,4],[5,8],[6]]=>[6,5,8,3,4,1,2,7]=>[4,1,8,3,6,5,2,7]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]] [[1,5,6],[2,7],[3,8],[4]]=>[4,3,8,2,7,1,5,6]=>[7,8,4,3,1,5,2,6]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]] [[1,2,6],[3,7],[4,8],[5]]=>[5,4,8,3,7,1,2,6]=>[7,1,8,5,4,2,3,6]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]] [[1,4,5],[2,7],[3,8],[6]]=>[6,3,8,2,7,1,4,5]=>[7,8,6,1,4,3,2,5]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]] [[1,3,5],[2,7],[4,8],[6]]=>[6,4,8,2,7,1,3,5]=>[7,8,1,6,3,4,2,5]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]] [[1,2,5],[3,7],[4,8],[6]]=>[6,4,8,3,7,1,2,5]=>[7,1,8,6,2,4,3,5]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]] [[1,3,4],[2,7],[5,8],[6]]=>[6,5,8,2,7,1,3,4]=>[7,8,1,3,6,5,2,4]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]] [[1,2,3],[4,7],[5,8],[6]]=>[6,5,8,4,7,1,2,3]=>[7,1,2,8,6,5,4,3]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]] [[1,4,6],[2,5],[3,8],[7]]=>[7,3,8,2,5,1,4,6]=>[5,8,7,1,2,4,3,6]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]] [[1,3,6],[2,4],[5,8],[7]]=>[7,5,8,2,4,1,3,6]=>[4,8,1,2,7,3,5,6]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] [[1,3,5],[2,6],[4,8],[7]]=>[7,4,8,2,6,1,3,5]=>[6,8,1,7,3,2,4,5]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]] [[1,2,5],[3,6],[4,8],[7]]=>[7,4,8,3,6,1,2,5]=>[6,1,8,7,2,3,4,5]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] [[1,3,4],[2,6],[5,8],[7]]=>[7,5,8,2,6,1,3,4]=>[6,8,1,3,7,2,5,4]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]] [[1,2,4],[3,6],[5,8],[7]]=>[7,5,8,3,6,1,2,4]=>[6,1,8,2,7,3,5,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]] [[1,2,3],[4,6],[5,8],[7]]=>[7,5,8,4,6,1,2,3]=>[6,1,2,8,7,4,5,3]=>[[.,.],[.,[[[[.,.],.],[.,.]],.]]] [[1,2,5],[3,4],[6,8],[7]]=>[7,6,8,3,4,1,2,5]=>[4,1,8,3,2,7,6,5]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]] [[1,4,7],[2,5],[3,6],[8]]=>[8,3,6,2,5,1,4,7]=>[5,6,8,1,2,3,4,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] [[1,2,7],[3,5],[4,6],[8]]=>[8,4,6,3,5,1,2,7]=>[5,1,6,8,3,4,2,7]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] [[1,2,7],[3,4],[5,6],[8]]=>[8,5,6,3,4,1,2,7]=>[4,1,6,3,8,5,2,7]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]] [[1,4,6],[2,5],[3,7],[8]]=>[8,3,7,2,5,1,4,6]=>[5,7,8,1,2,4,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] [[1,2,6],[3,5],[4,7],[8]]=>[8,4,7,3,5,1,2,6]=>[5,1,7,8,3,2,4,6]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]] [[1,3,6],[2,4],[5,7],[8]]=>[8,5,7,2,4,1,3,6]=>[4,7,1,2,8,3,5,6]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] [[1,4,5],[2,6],[3,7],[8]]=>[8,3,7,2,6,1,4,5]=>[6,7,8,1,4,2,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] [[1,3,5],[2,6],[4,7],[8]]=>[8,4,7,2,6,1,3,5]=>[6,7,1,8,3,2,4,5]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]] [[1,2,5],[3,6],[4,7],[8]]=>[8,4,7,3,6,1,2,5]=>[6,1,7,8,2,3,4,5]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] [[1,3,5],[2,4],[6,7],[8]]=>[8,6,7,2,4,1,3,5]=>[4,7,1,2,3,8,6,5]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]] [[1,2,5],[3,4],[6,7],[8]]=>[8,6,7,3,4,1,2,5]=>[4,1,7,3,2,8,6,5]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]] [[1,3,4],[2,5],[6,7],[8]]=>[8,6,7,2,5,1,3,4]=>[5,7,1,3,2,8,6,4]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]] [[1,2,4],[3,5],[6,7],[8]]=>[8,6,7,3,5,1,2,4]=>[5,1,7,2,3,8,6,4]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]] [[1,6,8],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6,8]=>[7,3,4,5,2,1,6,8]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]] [[1,4,8],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4,8]=>[7,3,5,1,6,2,4,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] [[1,3,8],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3,8]=>[7,4,1,5,6,2,3,8]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] [[1,4,8],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4,8]=>[6,3,5,1,7,2,4,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] [[1,3,8],[2,6],[4],[5],[7]]=>[7,5,4,2,6,1,3,8]=>[6,4,1,5,7,2,3,8]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] [[1,4,8],[2,5],[3],[6],[7]]=>[7,6,3,2,5,1,4,8]=>[5,3,6,1,2,7,4,8]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] [[1,3,8],[2,5],[4],[6],[7]]=>[7,6,4,2,5,1,3,8]=>[5,4,1,6,2,7,3,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]] [[1,3,8],[2,4],[5],[6],[7]]=>[7,6,5,2,4,1,3,8]=>[4,5,1,2,6,7,3,8]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] [[1,6,7],[2,8],[3],[4],[5]]=>[5,4,3,2,8,1,6,7]=>[8,3,4,5,2,1,6,7]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]] [[1,4,7],[2,8],[3],[5],[6]]=>[6,5,3,2,8,1,4,7]=>[8,3,5,1,6,2,4,7]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] [[1,3,7],[2,8],[4],[5],[6]]=>[6,5,4,2,8,1,3,7]=>[8,4,1,5,6,2,3,7]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]] [[1,2,7],[3,8],[4],[5],[6]]=>[6,5,4,3,8,1,2,7]=>[8,1,4,5,6,3,2,7]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]] [[1,4,6],[2,8],[3],[5],[7]]=>[7,5,3,2,8,1,4,6]=>[8,3,5,1,7,4,2,6]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]] [[1,3,6],[2,8],[4],[5],[7]]=>[7,5,4,2,8,1,3,6]=>[8,4,1,5,7,3,2,6]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]] [[1,2,6],[3,8],[4],[5],[7]]=>[7,5,4,3,8,1,2,6]=>[8,1,4,5,7,2,3,6]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] [[1,4,5],[2,8],[3],[6],[7]]=>[7,6,3,2,8,1,4,5]=>[8,3,6,1,4,7,2,5]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]] [[1,2,5],[3,8],[4],[6],[7]]=>[7,6,4,3,8,1,2,5]=>[8,1,4,6,2,7,3,5]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]] [[1,3,4],[2,8],[5],[6],[7]]=>[7,6,5,2,8,1,3,4]=>[8,5,1,3,6,7,2,4]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]] [[1,2,4],[3,8],[5],[6],[7]]=>[7,6,5,3,8,1,2,4]=>[8,1,5,2,6,7,3,4]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]] [[1,2,3],[4,8],[5],[6],[7]]=>[7,6,5,4,8,1,2,3]=>[8,1,2,5,6,7,4,3]=>[[.,.],[.,[[[.,[.,[.,.]]],.],.]]] [[1,4,7],[2,6],[3],[5],[8]]=>[8,5,3,2,6,1,4,7]=>[6,3,5,1,8,2,4,7]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] [[1,2,7],[3,6],[4],[5],[8]]=>[8,5,4,3,6,1,2,7]=>[6,1,4,5,8,3,2,7]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]] [[1,4,7],[2,5],[3],[6],[8]]=>[8,6,3,2,5,1,4,7]=>[5,3,6,1,2,8,4,7]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] [[1,3,7],[2,5],[4],[6],[8]]=>[8,6,4,2,5,1,3,7]=>[5,4,1,6,2,8,3,7]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]] [[1,3,7],[2,4],[5],[6],[8]]=>[8,6,5,2,4,1,3,7]=>[4,5,1,2,6,8,3,7]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] [[1,2,7],[3,4],[5],[6],[8]]=>[8,6,5,3,4,1,2,7]=>[4,1,5,3,6,8,2,7]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]] [[1,4,6],[2,7],[3],[5],[8]]=>[8,5,3,2,7,1,4,6]=>[7,3,5,1,8,4,2,6]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]] [[1,3,6],[2,7],[4],[5],[8]]=>[8,5,4,2,7,1,3,6]=>[7,4,1,5,8,3,2,6]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]] [[1,4,5],[2,7],[3],[6],[8]]=>[8,6,3,2,7,1,4,5]=>[7,3,6,1,4,8,2,5]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]] [[1,3,5],[2,7],[4],[6],[8]]=>[8,6,4,2,7,1,3,5]=>[7,4,1,6,3,8,2,5]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]] [[1,2,4],[3,7],[5],[6],[8]]=>[8,6,5,3,7,1,2,4]=>[7,1,5,2,6,8,3,4]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]] [[1,2,6],[3,5],[4],[7],[8]]=>[8,7,4,3,5,1,2,6]=>[5,1,4,7,3,2,8,6]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]] [[1,3,6],[2,4],[5],[7],[8]]=>[8,7,5,2,4,1,3,6]=>[4,5,1,2,7,3,8,6]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] [[1,2,6],[3,4],[5],[7],[8]]=>[8,7,5,3,4,1,2,6]=>[4,1,5,3,7,2,8,6]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]] [[1,4,5],[2,6],[3],[7],[8]]=>[8,7,3,2,6,1,4,5]=>[6,3,7,1,4,2,8,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]] [[1,3,5],[2,6],[4],[7],[8]]=>[8,7,4,2,6,1,3,5]=>[6,4,1,7,3,2,8,5]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]] [[1,2,5],[3,6],[4],[7],[8]]=>[8,7,4,3,6,1,2,5]=>[6,1,4,7,2,3,8,5]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] [[1,3,4],[2,6],[5],[7],[8]]=>[8,7,5,2,6,1,3,4]=>[6,5,1,3,7,2,8,4]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]] [[1,2,4],[3,6],[5],[7],[8]]=>[8,7,5,3,6,1,2,4]=>[6,1,5,2,7,3,8,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]] [[1,2,5],[3,4],[6],[7],[8]]=>[8,7,6,3,4,1,2,5]=>[4,1,6,3,2,7,8,5]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]] [[1,3,4],[2,5],[6],[7],[8]]=>[8,7,6,2,5,1,3,4]=>[5,6,1,3,2,7,8,4]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]] [[1,2,4],[3,5],[6],[7],[8]]=>[8,7,6,3,5,1,2,4]=>[5,1,6,2,3,7,8,4]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]] [[1,7,8],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7,8]=>[2,3,4,5,6,1,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] [[1,6,8],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6,8]=>[2,3,4,5,7,1,6,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] [[1,5,8],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5,8]=>[2,3,4,6,1,7,5,8]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] [[1,3,8],[2],[4],[5],[6],[7]]=>[7,6,5,4,2,1,3,8]=>[2,4,1,5,6,7,3,8]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] [[1,2,8],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2,8]=>[3,1,4,5,6,7,2,8]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] [[1,6,7],[2],[3],[4],[5],[8]]=>[8,5,4,3,2,1,6,7]=>[2,3,4,5,8,1,6,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] [[1,5,7],[2],[3],[4],[6],[8]]=>[8,6,4,3,2,1,5,7]=>[2,3,4,6,1,8,5,7]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] [[1,4,7],[2],[3],[5],[6],[8]]=>[8,6,5,3,2,1,4,7]=>[2,3,5,1,6,8,4,7]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] [[1,3,7],[2],[4],[5],[6],[8]]=>[8,6,5,4,2,1,3,7]=>[2,4,1,5,6,8,3,7]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] [[1,2,7],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,1,2,7]=>[3,1,4,5,6,8,2,7]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] [[1,5,6],[2],[3],[4],[7],[8]]=>[8,7,4,3,2,1,5,6]=>[2,3,4,7,1,5,8,6]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] [[1,4,6],[2],[3],[5],[7],[8]]=>[8,7,5,3,2,1,4,6]=>[2,3,5,1,7,4,8,6]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] [[1,3,6],[2],[4],[5],[7],[8]]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]] [[1,2,6],[3],[4],[5],[7],[8]]=>[8,7,5,4,3,1,2,6]=>[3,1,4,5,7,2,8,6]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]] [[1,4,5],[2],[3],[6],[7],[8]]=>[8,7,6,3,2,1,4,5]=>[2,3,6,1,4,7,8,5]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] [[1,3,5],[2],[4],[6],[7],[8]]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]] [[1,2,5],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,1,2,5]=>[3,1,4,6,2,7,8,5]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]] [[1,3,4],[2],[5],[6],[7],[8]]=>[8,7,6,5,2,1,3,4]=>[2,5,1,3,6,7,8,4]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] [[1,2,4],[3],[5],[6],[7],[8]]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]] [[1,2,3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,3]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] [[1,5],[2,6],[3,7],[4,8]]=>[4,8,3,7,2,6,1,5]=>[6,7,8,4,1,2,3,5]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] [[1,4],[2,6],[3,7],[5,8]]=>[5,8,3,7,2,6,1,4]=>[6,7,8,1,5,2,3,4]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] [[1,3],[2,6],[4,7],[5,8]]=>[5,8,4,7,2,6,1,3]=>[6,7,1,8,5,2,4,3]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]] [[1,2],[3,6],[4,7],[5,8]]=>[5,8,4,7,3,6,1,2]=>[6,1,7,8,5,3,4,2]=>[[.,.],[[[[.,[.,.]],.],[.,.]],.]] [[1,4],[2,5],[3,7],[6,8]]=>[6,8,3,7,2,5,1,4]=>[5,7,8,1,2,6,3,4]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] [[1,2],[3,5],[4,7],[6,8]]=>[6,8,4,7,3,5,1,2]=>[5,1,7,8,3,6,4,2]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]] [[1,3],[2,4],[5,7],[6,8]]=>[6,8,5,7,2,4,1,3]=>[4,7,1,2,8,6,5,3]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]] [[1,4],[2,5],[3,6],[7,8]]=>[7,8,3,6,2,5,1,4]=>[5,6,8,1,2,3,7,4]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] [[1,2],[3,5],[4,6],[7,8]]=>[7,8,4,6,3,5,1,2]=>[5,1,6,8,3,4,7,2]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]] [[1,3],[2,4],[5,6],[7,8]]=>[7,8,5,6,2,4,1,3]=>[4,6,1,2,8,5,7,3]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]] [[1,2],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2]=>[4,1,6,3,8,5,7,2]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]] [[1,5],[2,7],[3,8],[4],[6]]=>[6,4,3,8,2,7,1,5]=>[7,8,4,6,1,3,2,5]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]] [[1,4],[2,7],[3,8],[5],[6]]=>[6,5,3,8,2,7,1,4]=>[7,8,5,1,6,3,2,4]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]] [[1,3],[2,7],[4,8],[5],[6]]=>[6,5,4,8,2,7,1,3]=>[7,8,1,5,6,4,2,3]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]] [[1,4],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4]=>[6,8,5,1,7,2,3,4]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]] [[1,2],[3,5],[4,8],[6],[7]]=>[7,6,4,8,3,5,1,2]=>[5,1,8,6,3,7,4,2]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]] [[1,3],[2,4],[5,8],[6],[7]]=>[7,6,5,8,2,4,1,3]=>[4,8,1,2,6,7,5,3]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]] [[1,2],[3,4],[5,8],[6],[7]]=>[7,6,5,8,3,4,1,2]=>[4,1,8,3,6,7,5,2]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]] [[1,5],[2,6],[3,7],[4],[8]]=>[8,4,3,7,2,6,1,5]=>[6,7,4,8,1,2,3,5]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] [[1,4],[2,6],[3,7],[5],[8]]=>[8,5,3,7,2,6,1,4]=>[6,7,5,1,8,2,3,4]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]] [[1,3],[2,6],[4,7],[5],[8]]=>[8,5,4,7,2,6,1,3]=>[6,7,1,5,8,2,4,3]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]] [[1,2],[3,6],[4,7],[5],[8]]=>[8,5,4,7,3,6,1,2]=>[6,1,7,5,8,3,4,2]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]] [[1,4],[2,5],[3,7],[6],[8]]=>[8,6,3,7,2,5,1,4]=>[5,7,6,1,2,8,3,4]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]] [[1,3],[2,5],[4,7],[6],[8]]=>[8,6,4,7,2,5,1,3]=>[5,7,1,6,2,8,4,3]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]] [[1,2],[3,4],[5,7],[6],[8]]=>[8,6,5,7,3,4,1,2]=>[4,1,7,3,6,8,5,2]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]] [[1,4],[2,5],[3,6],[7],[8]]=>[8,7,3,6,2,5,1,4]=>[5,6,7,1,2,3,8,4]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] [[1,3],[2,5],[4,6],[7],[8]]=>[8,7,4,6,2,5,1,3]=>[5,6,1,7,2,4,8,3]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]] [[1,2],[3,5],[4,6],[7],[8]]=>[8,7,4,6,3,5,1,2]=>[5,1,6,7,3,4,8,2]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]] [[1,3],[2,4],[5,6],[7],[8]]=>[8,7,5,6,2,4,1,3]=>[4,6,1,2,7,5,8,3]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]] [[1,2],[3,4],[5,6],[7],[8]]=>[8,7,5,6,3,4,1,2]=>[4,1,6,3,7,5,8,2]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]] [[1,7],[2,8],[3],[4],[5],[6]]=>[6,5,4,3,2,8,1,7]=>[8,3,4,5,6,2,1,7]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]] [[1,6],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6]=>[8,3,4,5,7,1,2,6]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] [[1,5],[2,8],[3],[4],[6],[7]]=>[7,6,4,3,2,8,1,5]=>[8,3,4,6,1,7,2,5]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]] [[1,4],[2,8],[3],[5],[6],[7]]=>[7,6,5,3,2,8,1,4]=>[8,3,5,1,6,7,2,4]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]] [[1,3],[2,8],[4],[5],[6],[7]]=>[7,6,5,4,2,8,1,3]=>[8,4,1,5,6,7,2,3]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]] [[1,2],[3,8],[4],[5],[6],[7]]=>[7,6,5,4,3,8,1,2]=>[8,1,4,5,6,7,3,2]=>[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] [[1,6],[2,7],[3],[4],[5],[8]]=>[8,5,4,3,2,7,1,6]=>[7,3,4,5,8,1,2,6]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] [[1,4],[2,7],[3],[5],[6],[8]]=>[8,6,5,3,2,7,1,4]=>[7,3,5,1,6,8,2,4]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]] [[1,3],[2,7],[4],[5],[6],[8]]=>[8,6,5,4,2,7,1,3]=>[7,4,1,5,6,8,2,3]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]] [[1,2],[3,7],[4],[5],[6],[8]]=>[8,6,5,4,3,7,1,2]=>[7,1,4,5,6,8,3,2]=>[[.,.],[[[.,[.,[.,[.,.]]]],.],.]] [[1,4],[2,6],[3],[5],[7],[8]]=>[8,7,5,3,2,6,1,4]=>[6,3,5,1,7,2,8,4]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]] [[1,3],[2,6],[4],[5],[7],[8]]=>[8,7,5,4,2,6,1,3]=>[6,4,1,5,7,2,8,3]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]] [[1,4],[2,5],[3],[6],[7],[8]]=>[8,7,6,3,2,5,1,4]=>[5,3,6,1,2,7,8,4]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]] [[1,3],[2,5],[4],[6],[7],[8]]=>[8,7,6,4,2,5,1,3]=>[5,4,1,6,2,7,8,3]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]] [[1,3],[2,4],[5],[6],[7],[8]]=>[8,7,6,5,2,4,1,3]=>[4,5,1,2,6,7,8,3]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] [[1,2],[3,4],[5],[6],[7],[8]]=>[8,7,6,5,3,4,1,2]=>[4,1,5,3,6,7,8,2]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]] [[1,8],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,1,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] [[1,7],[2],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,1,7]=>[2,3,4,5,6,8,1,7]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] [[1,6],[2],[3],[4],[5],[7],[8]]=>[8,7,5,4,3,2,1,6]=>[2,3,4,5,7,1,8,6]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] [[1,5],[2],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,2,1,5]=>[2,3,4,6,1,7,8,5]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] [[1,4],[2],[3],[5],[6],[7],[8]]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] [[1,3],[2],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,3]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] [[1,2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,2]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] [[1],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] [[1,2,4,6,8],[3,5,7,9,10]]=>[3,5,7,9,10,1,2,4,6,8]=>[10,1,3,2,5,4,7,6,9,8]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] [[1,2,3,4,5],[6,7,8,9,10]]=>[6,7,8,9,10,1,2,3,4,5]=>[10,1,2,3,4,6,7,8,9,5]=>[[.,.],[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]] [[1,2,4,6,8,10],[3,5,7,9,11,12]]=>[3,5,7,9,11,12,1,2,4,6,8,10]=>[12,1,3,2,5,4,7,6,9,8,11,10]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] [[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[7,8,9,10,11,12,1,2,3,4,5,6]=>[12,1,2,3,4,5,7,8,9,10,11,6]=>[[.,.],[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]] [[1,2,3,4,5,6,7,8,9]]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] [[1,2,3,4,5,6,7,8],[9]]=>[9,1,2,3,4,5,6,7,8]=>[9,1,2,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [[1,2,3,4,5,6,7],[8,9]]=>[8,9,1,2,3,4,5,6,7]=>[9,1,2,3,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] [[1,2,3,4,5,6,7],[8],[9]]=>[9,8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,9,7]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] [[1,2,3,4,5,6],[7,8,9]]=>[7,8,9,1,2,3,4,5,6]=>[9,1,2,3,4,5,7,8,6]=>[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] [[1,2,3,4,5,6],[7],[8],[9]]=>[9,8,7,1,2,3,4,5,6]=>[7,1,2,3,4,5,8,9,6]=>[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] [[1,2,3,4,5],[6],[7],[8],[9]]=>[9,8,7,6,1,2,3,4,5]=>[6,1,2,3,4,7,8,9,5]=>[[.,.],[.,[.,[.,[[.,[.,[.,.]]],.]]]]] [[1,2,3,4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,9,4]=>[[.,.],[.,[.,[[.,[.,[.,[.,.]]]],.]]]] [[1,2,3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,9,3]=>[[.,.],[.,[[.,[.,[.,[.,[.,.]]]]],.]]] [[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,9,2]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] [[1],[2],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] [[1,2,3,4,5,6,7,8,9,10]]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] [[1,2,3,4,5,6,7,8,9],[10]]=>[10,1,2,3,4,5,6,7,8,9]=>[10,1,2,3,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] [[1,2,3,4,5,6,7,8],[9,10]]=>[9,10,1,2,3,4,5,6,7,8]=>[10,1,2,3,4,5,6,7,9,8]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] [[1,2,3,4,5,6,7,8],[9],[10]]=>[10,9,1,2,3,4,5,6,7,8]=>[9,1,2,3,4,5,6,7,10,8]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] [[1,2,3,4,5,6,7],[8],[9],[10]]=>[10,9,8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,9,10,7]=>[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] [[1,2,3,4,5,6],[7],[8],[9],[10]]=>[10,9,8,7,1,2,3,4,5,6]=>[7,1,2,3,4,5,8,9,10,6]=>[[.,.],[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]] [[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,1,2,3,4,5]=>[6,1,2,3,4,7,8,9,10,5]=>[[.,.],[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]] [[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,9,10,4]=>[[.,.],[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] [[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,9,10,3]=>[[.,.],[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,9,10,2]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,10,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,10,11,12,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]],.] [[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]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [[1,4,5,6,7,8,9],[2],[3]]=>[3,2,1,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] [[1,5,6,7,8,9],[2],[3],[4]]=>[4,3,2,1,5,6,7,8,9]=>[2,3,4,1,5,6,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] [[1,6,7,8,9],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8,9]=>[2,3,4,5,1,6,7,8,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] [[1,7,8,9],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7,8,9]=>[2,3,4,5,6,1,7,8,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] [[1,8,9],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8,9]=>[2,3,4,5,6,7,1,8,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] [[1,7],[2,9],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,9,1,7]=>[9,3,4,5,6,8,1,2,7]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]] [[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1,9]=>[2,3,4,5,6,7,8,1,9]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] [[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]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] [[1,4,5,6,7,8,9,10],[2],[3]]=>[3,2,1,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [[1,5,6,7,8,9,10],[2],[3],[4]]=>[4,3,2,1,5,6,7,8,9,10]=>[2,3,4,1,5,6,7,8,9,10]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] [[1,6,7,8,9,10],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8,9,10]=>[2,3,4,5,1,6,7,8,9,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] [[1,7,8,9,10],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7,8,9,10]=>[2,3,4,5,6,1,7,8,9,10]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] [[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8,9,10]=>[2,3,4,5,6,7,1,8,9,10]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] [[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1,9,10]=>[2,3,4,5,6,7,8,1,9,10]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] [[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>[9,7,6,5,4,3,2,10,1,8]=>[10,3,4,5,6,7,9,1,2,8]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,2,1,10]=>[2,3,4,5,6,7,8,9,1,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] [[1,8],[2,9],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,9,1,8]=>[9,3,4,5,6,7,2,1,8]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],[.,.]] [[1,3,5,7,9],[2,4,6,8]]=>[2,4,6,8,1,3,5,7,9]=>[8,2,1,4,3,6,5,7,9]=>[[[.,.],.],[[.,.],[[.,.],[.,[.,.]]]]] [[1,9],[2,10],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,10,1,9]=>[10,3,4,5,6,7,8,2,1,9]=>[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],[.,.]] [[1,3],[2,4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,2,4,1,3]=>[4,5,1,2,6,7,8,9,3]=>[[.,[.,.]],[.,[[.,[.,[.,[.,.]]]],.]]] [[1,5],[2,6],[3,7],[4,8],[9]]=>[9,4,8,3,7,2,6,1,5]=>[6,7,8,9,1,2,3,4,5]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] [[1,3,5],[2,4,6],[7],[8],[9]]=>[9,8,7,2,4,6,1,3,5]=>[6,7,1,2,3,4,8,9,5]=>[[.,[.,.]],[.,[.,[.,[[.,[.,.]],.]]]]] [[1,2,4,6],[3,5,7],[8],[9]]=>[9,8,3,5,7,1,2,4,6]=>[7,1,8,2,3,4,5,9,6]=>[[.,.],[[.,.],[.,[.,[.,[[.,.],.]]]]]] [[1,3,5,7],[2,4,6,8],[9]]=>[9,2,4,6,8,1,3,5,7]=>[8,9,1,2,3,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] [[1,2,3,5,7],[4,6,8],[9]]=>[9,4,6,8,1,2,3,5,7]=>[8,1,2,9,3,4,5,6,7]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]] [[1,2,3,4,5,7],[6,8],[9]]=>[9,6,8,1,2,3,4,5,7]=>[8,1,2,3,4,9,5,6,7]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]] [[1,2,3,4,5,6,8],[7,9]]=>[7,9,1,2,3,4,5,6,8]=>[9,1,2,3,4,5,7,6,8]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] [[1,2,6],[3,7],[4,8],[5,9],[10]]=>[10,5,9,4,8,3,7,1,2,6]=>[7,1,8,9,10,2,3,4,5,6]=>[[.,.],[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]] [[1,4,7],[2,5,8],[3,6,9],[10]]=>[10,3,6,9,2,5,8,1,4,7]=>[8,9,10,1,2,3,4,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] [[1,3,5,7],[2,4,6,8],[9],[10]]=>[10,9,2,4,6,8,1,3,5,7]=>[8,9,1,2,3,4,5,6,10,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] [[1,2,4,6,8],[3,5,7,9],[10]]=>[10,3,5,7,9,1,2,4,6,8]=>[9,1,10,2,3,4,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] [[1,2,3,4,5,6,7,9],[8]]=>[8,1,2,3,4,5,6,7,9]=>[8,1,2,3,4,5,6,7,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [[1,2,3,4,5,6,9],[7,8]]=>[7,8,1,2,3,4,5,6,9]=>[8,1,2,3,4,5,7,6,9]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] [[1,2,3,4,5,6,9],[7],[8]]=>[8,7,1,2,3,4,5,6,9]=>[7,1,2,3,4,5,8,6,9]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] [[1,2,9],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,1,2,9]=>[3,1,4,5,6,7,8,2,9]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]] [[1,3],[2,9],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,2,9,1,3]=>[9,4,1,5,6,7,8,2,3]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],[.,.]]] [[1,2,3,4,5,6,7,8,10],[9]]=>[9,1,2,3,4,5,6,7,8,10]=>[9,1,2,3,4,5,6,7,8,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] [[1,2,3,4,5,6,7,10],[8,9]]=>[8,9,1,2,3,4,5,6,7,10]=>[9,1,2,3,4,5,6,8,7,10]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] [[1,3],[2,10],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,2,10,1,3]=>[10,4,1,5,6,7,8,9,2,3]=>[[[.,.],.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]] []=>[]=>[]=>. [[1,2,4,5,6,7,8,9],[3]]=>[3,1,2,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [[1,3,5,6,7,8,9],[2],[4]]=>[4,2,1,3,5,6,7,8,9]=>[2,4,1,3,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] [[1,4,6,7,8,9],[2],[3],[5]]=>[5,3,2,1,4,6,7,8,9]=>[2,3,5,1,4,6,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] [[1,5,7,8,9],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7,8,9]=>[2,3,4,6,1,5,7,8,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] [[1,6,8,9],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6,8,9]=>[2,3,4,5,7,1,6,8,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] [[1,7,9],[2],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,1,7,9]=>[2,3,4,5,6,8,1,7,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] [[1,8],[2],[3],[4],[5],[6],[7],[9]]=>[9,7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,9,1,8]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] [[1,2,4,5,6,7,8,9,10],[3]]=>[3,1,2,4,5,6,7,8,9,10]=>[3,1,2,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] [[1,3,5,6,7,8,9,10],[2],[4]]=>[4,2,1,3,5,6,7,8,9,10]=>[2,4,1,3,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [[1,9],[2],[3],[4],[5],[6],[7],[8],[10]]=>[10,8,7,6,5,4,3,2,1,9]=>[2,3,4,5,6,7,8,10,1,9]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] [[1,3,4,5,6,7,8],[2,9]]=>[2,9,1,3,4,5,6,7,8]=>[9,2,1,3,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] [[1,3,4,5,6,7,8],[2],[9]]=>[9,2,1,3,4,5,6,7,8]=>[2,9,1,3,4,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] [[1,3,4,5,6,7],[2],[8],[9]]=>[9,8,2,1,3,4,5,6,7]=>[2,8,1,3,4,5,6,9,7]=>[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]] [[1,3,4,5,6],[2],[7],[8],[9]]=>[9,8,7,2,1,3,4,5,6]=>[2,7,1,3,4,5,8,9,6]=>[[.,[.,.]],[.,[.,[.,[[.,[.,.]],.]]]]] [[1,3,4],[2],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,2,1,3,4]=>[2,5,1,3,6,7,8,9,4]=>[[.,[.,.]],[.,[[.,[.,[.,[.,.]]]],.]]] [[1,3],[2],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,9,3]=>[[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]] [[1,3,4,5,6,7,8,9],[2,10]]=>[2,10,1,3,4,5,6,7,8,9]=>[10,2,1,3,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [[1,3,4,5,6,7,8,9],[2],[10]]=>[10,2,1,3,4,5,6,7,8,9]=>[2,10,1,3,4,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [[1,3,4,5,6,7,8],[2,9,10]]=>[2,9,10,1,3,4,5,6,7,8]=>[10,2,1,3,4,5,6,7,9,8]=>[[[.,.],.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] [[1,3,4,5,6,7,8],[2],[9],[10]]=>[10,9,2,1,3,4,5,6,7,8]=>[2,9,1,3,4,5,6,7,10,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] [[1,3,4],[2],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,2,1,3,4]=>[2,5,1,3,6,7,8,9,10,4]=>[[.,[.,.]],[.,[[.,[.,[.,[.,[.,.]]]]],.]]] [[1,3],[2],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,9,10,3]=>[[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] [[1,2,3,5,6,7,8,9,10],[4]]=>[4,1,2,3,5,6,7,8,9,10]=>[4,1,2,3,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] [[1,2,3,4,6,7,8,9,10],[5]]=>[5,1,2,3,4,6,7,8,9,10]=>[5,1,2,3,4,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] [[1,2,3,4,5,6,7,9,10],[8]]=>[8,1,2,3,4,5,6,7,9,10]=>[8,1,2,3,4,5,6,7,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] [[1,2,3,4,5,6,8,9,10],[7]]=>[7,1,2,3,4,5,6,8,9,10]=>[7,1,2,3,4,5,6,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] [[1,2,3,4,5,7,8,9,10],[6]]=>[6,1,2,3,4,5,7,8,9,10]=>[6,1,2,3,4,5,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] [[1,2,4,5,6,7,8,9,10,11,12],[3]]=>[3,1,2,4,5,6,7,8,9,10,11,12]=>[3,1,2,4,5,6,7,8,9,10,11,12]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]] [[1,4,5,6,7,8],[2],[3],[9]]=>[9,3,2,1,4,5,6,7,8]=>[2,3,9,1,4,5,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] [[1,5,6,7,8],[2],[3],[4],[9]]=>[9,4,3,2,1,5,6,7,8]=>[2,3,4,9,1,5,6,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] [[1,6,7,8],[2],[3],[4],[5],[9]]=>[9,5,4,3,2,1,6,7,8]=>[2,3,4,5,9,1,6,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] [[1,7,8],[2],[3],[4],[5],[6],[9]]=>[9,6,5,4,3,2,1,7,8]=>[2,3,4,5,6,9,1,7,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] [[1,4,5,6,7,8,9],[2],[3],[10]]=>[10,3,2,1,4,5,6,7,8,9]=>[2,3,10,1,4,5,6,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] [[1,5,6,7,8,9],[2],[3],[4],[10]]=>[10,4,3,2,1,5,6,7,8,9]=>[2,3,4,10,1,5,6,7,8,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] [[1,6,7,8,9],[2],[3],[4],[5],[10]]=>[10,5,4,3,2,1,6,7,8,9]=>[2,3,4,5,10,1,6,7,8,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] [[1,7,8,9],[2],[3],[4],[5],[6],[10]]=>[10,6,5,4,3,2,1,7,8,9]=>[2,3,4,5,6,10,1,7,8,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] [[1,8,9],[2],[3],[4],[5],[6],[7],[10]]=>[10,7,6,5,4,3,2,1,8,9]=>[2,3,4,5,6,7,10,1,8,9]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] [[1,2,5,6,7,8,9],[3],[4]]=>[4,3,1,2,5,6,7,8,9]=>[3,1,4,2,5,6,7,8,9]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]] [[1,2,5,6,7,8,9,10],[3],[4]]=>[4,3,1,2,5,6,7,8,9,10]=>[3,1,4,2,5,6,7,8,9,10]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] [[1,2,5,6,7,8],[3],[4],[9]]=>[9,4,3,1,2,5,6,7,8]=>[3,1,4,9,2,5,6,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,[.,.]]]]]] [[1,2,7,8],[3],[4],[5],[6],[9]]=>[9,6,5,4,3,1,2,7,8]=>[3,1,4,5,6,9,2,7,8]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,[.,.]]]] [[1,4],[2],[3],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,9,10,4]=>[[.,[.,[.,.]]],[[.,[.,[.,[.,[.,.]]]]],.]] [[1,5],[2],[3],[4],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,4,3,2,1,5]=>[2,3,4,6,1,7,8,9,10,5]=>[[.,[.,[.,[.,.]]]],[[.,[.,[.,[.,.]]]],.]] [[1,8],[2],[3],[4],[5],[6],[7],[9],[10]]=>[10,9,7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,9,1,10,8]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]] [[1,7],[2],[3],[4],[5],[6],[8],[9],[10]]=>[10,9,8,6,5,4,3,2,1,7]=>[2,3,4,5,6,8,1,9,10,7]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,[.,.]],.]] [[1,6],[2],[3],[4],[5],[7],[8],[9],[10]]=>[10,9,8,7,5,4,3,2,1,6]=>[2,3,4,5,7,1,8,9,10,6]=>[[.,[.,[.,[.,[.,.]]]]],[[.,[.,[.,.]]],.]] [[1,11],[2],[3],[4],[5],[6],[7],[8],[9],[10],[12]]=>[12,10,9,8,7,6,5,4,3,2,1,11]=>[2,3,4,5,6,7,8,9,10,12,1,11]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],[.,.]] [[1,2,3,4,5,7],[6],[8],[9]]=>[9,8,6,1,2,3,4,5,7]=>[6,1,2,3,4,8,5,9,7]=>[[.,.],[.,[.,[.,[[.,.],[[.,.],.]]]]]] [[1,2,3,4,5,6,8],[7],[9]]=>[9,7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,9,6,8]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] [[1,2,3,4,5,7,9],[6,8]]=>[6,8,1,2,3,4,5,7,9]=>[8,1,2,3,4,6,5,7,9]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]] [[1,2,4,5,6,7,8],[3,9]]=>[3,9,1,2,4,5,6,7,8]=>[9,1,3,2,4,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]] [[1,2,3,4,5,6],[7,9],[8]]=>[8,7,9,1,2,3,4,5,6]=>[9,1,2,3,4,5,8,7,6]=>[[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]] [[1,2,3,4,5,6,7],[8,10],[9]]=>[9,8,10,1,2,3,4,5,6,7]=>[10,1,2,3,4,5,6,9,8,7]=>[[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] [[1,3,4,5,6,7,9],[2,8]]=>[2,8,1,3,4,5,6,7,9]=>[8,2,1,3,4,5,6,7,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] [[1,3,4,5,6,7,8,10],[2,9]]=>[2,9,1,3,4,5,6,7,8,10]=>[9,2,1,3,4,5,6,7,8,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [[1,2,3,4,5,6,8],[7,10],[9]]=>[9,7,10,1,2,3,4,5,6,8]=>[10,1,2,3,4,5,9,6,7,8]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]] [[1,7,8],[2,9],[3],[4],[5],[6]]=>[6,5,4,3,2,9,1,7,8]=>[9,3,4,5,6,2,1,7,8]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,[.,.]]]
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
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
  • the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
  • the set of left-to-right maxima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
  • the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
  • the set of maximal elements in the decreasing runs of $\pi$ is the set of weak deficiency positions of $\chi(\pi)$, and
  • the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.