Identifier
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00020: Binary trees —to Tamari-corresponding Dyck path⟶ Dyck paths
Images
=>
Cc0007;cc-rep-0Cc0010;cc-rep-2Cc0005;cc-rep-3
[[1]]=>[1]=>[.,.]=>[1,0] [[1,2]]=>[1,2]=>[.,[.,.]]=>[1,1,0,0] [[1],[2]]=>[2,1]=>[[.,.],.]=>[1,0,1,0] [[1,2,3]]=>[1,2,3]=>[.,[.,[.,.]]]=>[1,1,1,0,0,0] [[1,3],[2]]=>[2,1,3]=>[[.,.],[.,.]]=>[1,0,1,1,0,0] [[1,2],[3]]=>[3,1,2]=>[[.,.],[.,.]]=>[1,0,1,1,0,0] [[1],[2],[3]]=>[3,2,1]=>[[[.,.],.],.]=>[1,0,1,0,1,0] [[1,2,3,4]]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0] [[1,3,4],[2]]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0] [[1,2,4],[3]]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0] [[1,2,3],[4]]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]=>[1,0,1,1,1,0,0,0] [[1,3],[2,4]]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0] [[1,2],[3,4]]=>[3,4,1,2]=>[[.,[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0] [[1,4],[2],[3]]=>[3,2,1,4]=>[[[.,.],.],[.,.]]=>[1,0,1,0,1,1,0,0] [[1,3],[2],[4]]=>[4,2,1,3]=>[[[.,.],.],[.,.]]=>[1,0,1,0,1,1,0,0] [[1,2],[3],[4]]=>[4,3,1,2]=>[[[.,.],.],[.,.]]=>[1,0,1,0,1,1,0,0] [[1],[2],[3],[4]]=>[4,3,2,1]=>[[[[.,.],.],.],.]=>[1,0,1,0,1,0,1,0] [[1,2,3,4,5]]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>[1,1,1,1,1,0,0,0,0,0] [[1,3,4,5],[2]]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,0] [[1,2,4,5],[3]]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,0] [[1,2,3,5],[4]]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,0] [[1,2,3,4],[5]]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]=>[1,0,1,1,1,1,0,0,0,0] [[1,3,5],[2,4]]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0] [[1,2,5],[3,4]]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0] [[1,3,4],[2,5]]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0] [[1,2,4],[3,5]]=>[3,5,1,2,4]=>[[.,[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0] [[1,2,3],[4,5]]=>[4,5,1,2,3]=>[[.,[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0] [[1,4,5],[2],[3]]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0] [[1,3,5],[2],[4]]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0] [[1,2,5],[3],[4]]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0] [[1,3,4],[2],[5]]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0] [[1,2,4],[3],[5]]=>[5,3,1,2,4]=>[[[.,.],.],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0] [[1,2,3],[4],[5]]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0] [[1,4],[2,5],[3]]=>[3,2,5,1,4]=>[[[.,.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0] [[1,3],[2,5],[4]]=>[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0] [[1,2],[3,5],[4]]=>[4,3,5,1,2]=>[[[.,.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0] [[1,3],[2,4],[5]]=>[5,2,4,1,3]=>[[[.,.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0] [[1,2],[3,4],[5]]=>[5,3,4,1,2]=>[[[.,.],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0] [[1,5],[2],[3],[4]]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]=>[1,0,1,0,1,0,1,1,0,0] [[1,4],[2],[3],[5]]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]]=>[1,0,1,0,1,0,1,1,0,0] [[1,3],[2],[4],[5]]=>[5,4,2,1,3]=>[[[[.,.],.],.],[.,.]]=>[1,0,1,0,1,0,1,1,0,0] [[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]]=>[1,0,1,0,1,0,1,1,0,0] [[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0] [[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[1,1,1,1,1,1,0,0,0,0,0,0] [[1,3,4,5,6],[2]]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,1,1,1,0,0,0,0,0] [[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,1,1,1,0,0,0,0,0] [[1,3,5,6],[2,4]]=>[2,4,1,3,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,5,6],[3,4]]=>[3,4,1,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,4,6],[2,5]]=>[2,5,1,3,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,3,6],[4,5]]=>[4,5,1,2,3,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,4,5],[2,6]]=>[2,6,1,3,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,4,5],[3,6]]=>[3,6,1,2,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,3,5],[4,6]]=>[4,6,1,2,3,5]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,1,1,0,0,0,0] [[1,4,5,6],[2],[3]]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0] [[1,3,5,6],[2],[4]]=>[4,2,1,3,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0] [[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0] [[1,3,4,6],[2],[5]]=>[5,2,1,3,4,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0] [[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0] [[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0] [[1,3,4,5],[2],[6]]=>[6,2,1,3,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0] [[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0] [[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0] [[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,1,1,0,0,0,0] [[1,3,5],[2,4,6]]=>[2,4,6,1,3,5]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,5],[3,4,6]]=>[3,4,6,1,2,5]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0] [[1,3,4],[2,5,6]]=>[2,5,6,1,3,4]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,4],[3,5,6]]=>[3,5,6,1,2,4]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[1,1,1,0,0,0,1,1,1,0,0,0] [[1,4,6],[2,5],[3]]=>[3,2,5,1,4,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0] [[1,3,6],[2,5],[4]]=>[4,2,5,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,6],[3,5],[4]]=>[4,3,5,1,2,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0] [[1,3,6],[2,4],[5]]=>[5,2,4,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,6],[3,4],[5]]=>[5,3,4,1,2,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0] [[1,4,5],[2,6],[3]]=>[3,2,6,1,4,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0] [[1,3,5],[2,6],[4]]=>[4,2,6,1,3,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0] [[1,3,4],[2,6],[5]]=>[5,2,6,1,3,4]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,4],[3,6],[5]]=>[5,3,6,1,2,4]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,3],[4,6],[5]]=>[5,4,6,1,2,3]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0] [[1,3,5],[2,4],[6]]=>[6,2,4,1,3,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,5],[3,4],[6]]=>[6,3,4,1,2,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0] [[1,3,4],[2,5],[6]]=>[6,2,5,1,3,4]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,4],[3,5],[6]]=>[6,3,5,1,2,4]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,1,0,0,0] [[1,5,6],[2],[3],[4]]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,0] [[1,4,6],[2],[3],[5]]=>[5,3,2,1,4,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,0] [[1,3,6],[2],[4],[5]]=>[5,4,2,1,3,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,0] [[1,2,6],[3],[4],[5]]=>[5,4,3,1,2,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,0] [[1,4,5],[2],[3],[6]]=>[6,3,2,1,4,5]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,0] [[1,3,5],[2],[4],[6]]=>[6,4,2,1,3,5]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,0] [[1,2,5],[3],[4],[6]]=>[6,4,3,1,2,5]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,0] [[1,3,4],[2],[5],[6]]=>[6,5,2,1,3,4]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,0] [[1,2,4],[3],[5],[6]]=>[6,5,3,1,2,4]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,0] [[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,1,0,0,0] [[1,4],[2,5],[3,6]]=>[3,6,2,5,1,4]=>[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0] [[1,3],[2,5],[4,6]]=>[4,6,2,5,1,3]=>[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0] [[1,2],[3,5],[4,6]]=>[4,6,3,5,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0] [[1,3],[2,4],[5,6]]=>[5,6,2,4,1,3]=>[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0] [[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0] [[1,5],[2,6],[3],[4]]=>[4,3,2,6,1,5]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0] [[1,4],[2,6],[3],[5]]=>[5,3,2,6,1,4]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0] [[1,3],[2,6],[4],[5]]=>[5,4,2,6,1,3]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0] [[1,2],[3,6],[4],[5]]=>[5,4,3,6,1,2]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0] [[1,4],[2,5],[3],[6]]=>[6,3,2,5,1,4]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0] [[1,3],[2,5],[4],[6]]=>[6,4,2,5,1,3]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0] [[1,2],[3,5],[4],[6]]=>[6,4,3,5,1,2]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0] [[1,3],[2,4],[5],[6]]=>[6,5,2,4,1,3]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0] [[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0] [[1,6],[2],[3],[4],[5]]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0] [[1,5],[2],[3],[4],[6]]=>[6,4,3,2,1,5]=>[[[[[.,.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0] [[1,4],[2],[3],[5],[6]]=>[6,5,3,2,1,4]=>[[[[[.,.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0] [[1,3],[2],[4],[5],[6]]=>[6,5,4,2,1,3]=>[[[[[.,.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0] [[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>[[[[[.,.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0] [[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0,1,0] [[1,2,3,4,5,6,7]]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0] [[1,3,4,5,6,7],[2]]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0] [[1,2,4,5,6,7],[3]]=>[3,1,2,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0] [[1,2,3,5,6,7],[4]]=>[4,1,2,3,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0] [[1,2,3,4,6,7],[5]]=>[5,1,2,3,4,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0] [[1,2,3,4,5,7],[6]]=>[6,1,2,3,4,5,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0] [[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0] [[1,3,5,6,7],[2,4]]=>[2,4,1,3,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,5,6,7],[3,4]]=>[3,4,1,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,3,4,6,7],[2,5]]=>[2,5,1,3,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,4,6,7],[3,5]]=>[3,5,1,2,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,6,7],[4,5]]=>[4,5,1,2,3,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,3,4,5,7],[2,6]]=>[2,6,1,3,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,4,5,7],[3,6]]=>[3,6,1,2,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,5,7],[4,6]]=>[4,6,1,2,3,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,4,7],[5,6]]=>[5,6,1,2,3,4,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,3,4,5,6],[2,7]]=>[2,7,1,3,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,4,5,6],[3,7]]=>[3,7,1,2,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,5,6],[4,7]]=>[4,7,1,2,3,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,4,6],[5,7]]=>[5,7,1,2,3,4,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,4,5],[6,7]]=>[6,7,1,2,3,4,5]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,4,5,6,7],[2],[3]]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,3,5,6,7],[2],[4]]=>[4,2,1,3,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,2,5,6,7],[3],[4]]=>[4,3,1,2,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,3,4,6,7],[2],[5]]=>[5,2,1,3,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,2,4,6,7],[3],[5]]=>[5,3,1,2,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,6,7],[4],[5]]=>[5,4,1,2,3,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,3,4,5,7],[2],[6]]=>[6,2,1,3,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,2,4,5,7],[3],[6]]=>[6,3,1,2,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,5,7],[4],[6]]=>[6,4,1,2,3,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,4,7],[5],[6]]=>[6,5,1,2,3,4,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,3,4,5,6],[2],[7]]=>[7,2,1,3,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,2,4,5,6],[3],[7]]=>[7,3,1,2,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,5,6],[4],[7]]=>[7,4,1,2,3,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,4,6],[5],[7]]=>[7,5,1,2,3,4,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,4,5],[6],[7]]=>[7,6,1,2,3,4,5]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,3,5,7],[2,4,6]]=>[2,4,6,1,3,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,2,5,7],[3,4,6]]=>[3,4,6,1,2,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,3,4,7],[2,5,6]]=>[2,5,6,1,3,4,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,2,4,7],[3,5,6]]=>[3,5,6,1,2,4,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,2,3,7],[4,5,6]]=>[4,5,6,1,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,3,5,6],[2,4,7]]=>[2,4,7,1,3,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,2,5,6],[3,4,7]]=>[3,4,7,1,2,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,3,4,6],[2,5,7]]=>[2,5,7,1,3,4,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,2,4,6],[3,5,7]]=>[3,5,7,1,2,4,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,2,3,6],[4,5,7]]=>[4,5,7,1,2,3,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,3,4,5],[2,6,7]]=>[2,6,7,1,3,4,5]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,2,4,5],[3,6,7]]=>[3,6,7,1,2,4,5]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,2,3,5],[4,6,7]]=>[4,6,7,1,2,3,5]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,2,3,4],[5,6,7]]=>[5,6,7,1,2,3,4]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,4,6,7],[2,5],[3]]=>[3,2,5,1,4,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,6,7],[2,5],[4]]=>[4,2,5,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,6,7],[3,5],[4]]=>[4,3,5,1,2,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,6,7],[2,4],[5]]=>[5,2,4,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,6,7],[3,4],[5]]=>[5,3,4,1,2,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,4,5,7],[2,6],[3]]=>[3,2,6,1,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,5,7],[2,6],[4]]=>[4,2,6,1,3,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,5,7],[3,6],[4]]=>[4,3,6,1,2,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,4,7],[2,6],[5]]=>[5,2,6,1,3,4,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,4,7],[3,6],[5]]=>[5,3,6,1,2,4,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,3,7],[4,6],[5]]=>[5,4,6,1,2,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,5,7],[2,4],[6]]=>[6,2,4,1,3,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,5,7],[3,4],[6]]=>[6,3,4,1,2,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,4,7],[2,5],[6]]=>[6,2,5,1,3,4,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,4,7],[3,5],[6]]=>[6,3,5,1,2,4,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,3,7],[4,5],[6]]=>[6,4,5,1,2,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,4,5,6],[2,7],[3]]=>[3,2,7,1,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,5,6],[2,7],[4]]=>[4,2,7,1,3,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,5,6],[3,7],[4]]=>[4,3,7,1,2,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,4,6],[2,7],[5]]=>[5,2,7,1,3,4,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,4,6],[3,7],[5]]=>[5,3,7,1,2,4,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,3,6],[4,7],[5]]=>[5,4,7,1,2,3,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,4,5],[2,7],[6]]=>[6,2,7,1,3,4,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,4,5],[3,7],[6]]=>[6,3,7,1,2,4,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,3,5],[4,7],[6]]=>[6,4,7,1,2,3,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,3,4],[5,7],[6]]=>[6,5,7,1,2,3,4]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,5,6],[2,4],[7]]=>[7,2,4,1,3,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,5,6],[3,4],[7]]=>[7,3,4,1,2,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,4,6],[2,5],[7]]=>[7,2,5,1,3,4,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,4,6],[3,5],[7]]=>[7,3,5,1,2,4,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,3,6],[4,5],[7]]=>[7,4,5,1,2,3,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,4,5],[2,6],[7]]=>[7,2,6,1,3,4,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,4,5],[3,6],[7]]=>[7,3,6,1,2,4,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,3,5],[4,6],[7]]=>[7,4,6,1,2,3,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,3,4],[5,6],[7]]=>[7,5,6,1,2,3,4]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,5,6,7],[2],[3],[4]]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,4,6,7],[2],[3],[5]]=>[5,3,2,1,4,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,3,6,7],[2],[4],[5]]=>[5,4,2,1,3,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,2,6,7],[3],[4],[5]]=>[5,4,3,1,2,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,4,5,7],[2],[3],[6]]=>[6,3,2,1,4,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,3,5,7],[2],[4],[6]]=>[6,4,2,1,3,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,2,5,7],[3],[4],[6]]=>[6,4,3,1,2,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,3,4,7],[2],[5],[6]]=>[6,5,2,1,3,4,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,2,4,7],[3],[5],[6]]=>[6,5,3,1,2,4,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,2,3,7],[4],[5],[6]]=>[6,5,4,1,2,3,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,4,5,6],[2],[3],[7]]=>[7,3,2,1,4,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,3,5,6],[2],[4],[7]]=>[7,4,2,1,3,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,2,5,6],[3],[4],[7]]=>[7,4,3,1,2,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,3,4,6],[2],[5],[7]]=>[7,5,2,1,3,4,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,2,4,6],[3],[5],[7]]=>[7,5,3,1,2,4,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,2,3,6],[4],[5],[7]]=>[7,5,4,1,2,3,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,3,4,5],[2],[6],[7]]=>[7,6,2,1,3,4,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,2,4,5],[3],[6],[7]]=>[7,6,3,1,2,4,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,2,3,5],[4],[6],[7]]=>[7,6,4,1,2,3,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,2,3,4],[5],[6],[7]]=>[7,6,5,1,2,3,4]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,4,6],[2,5,7],[3]]=>[3,2,5,7,1,4,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,3,6],[2,5,7],[4]]=>[4,2,5,7,1,3,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,6],[3,5,7],[4]]=>[4,3,5,7,1,2,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,3,6],[2,4,7],[5]]=>[5,2,4,7,1,3,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,6],[3,4,7],[5]]=>[5,3,4,7,1,2,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,4,5],[2,6,7],[3]]=>[3,2,6,7,1,4,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,3,5],[2,6,7],[4]]=>[4,2,6,7,1,3,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,5],[3,6,7],[4]]=>[4,3,6,7,1,2,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,3,4],[2,6,7],[5]]=>[5,2,6,7,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,4],[3,6,7],[5]]=>[5,3,6,7,1,2,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,3],[4,6,7],[5]]=>[5,4,6,7,1,2,3]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,3,5],[2,4,7],[6]]=>[6,2,4,7,1,3,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,5],[3,4,7],[6]]=>[6,3,4,7,1,2,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,3,4],[2,5,7],[6]]=>[6,2,5,7,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,4],[3,5,7],[6]]=>[6,3,5,7,1,2,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,3],[4,5,7],[6]]=>[6,4,5,7,1,2,3]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,3,5],[2,4,6],[7]]=>[7,2,4,6,1,3,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,5],[3,4,6],[7]]=>[7,3,4,6,1,2,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,3,4],[2,5,6],[7]]=>[7,2,5,6,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,4],[3,5,6],[7]]=>[7,3,5,6,1,2,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,3],[4,5,6],[7]]=>[7,4,5,6,1,2,3]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,4,7],[2,5],[3,6]]=>[3,6,2,5,1,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,3,7],[2,5],[4,6]]=>[4,6,2,5,1,3,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,2,7],[3,5],[4,6]]=>[4,6,3,5,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,3,7],[2,4],[5,6]]=>[5,6,2,4,1,3,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,2,7],[3,4],[5,6]]=>[5,6,3,4,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,4,6],[2,5],[3,7]]=>[3,7,2,5,1,4,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,3,6],[2,5],[4,7]]=>[4,7,2,5,1,3,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,2,6],[3,5],[4,7]]=>[4,7,3,5,1,2,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,3,6],[2,4],[5,7]]=>[5,7,2,4,1,3,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,2,6],[3,4],[5,7]]=>[5,7,3,4,1,2,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,4,5],[2,6],[3,7]]=>[3,7,2,6,1,4,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,3,5],[2,6],[4,7]]=>[4,7,2,6,1,3,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,2,5],[3,6],[4,7]]=>[4,7,3,6,1,2,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,3,4],[2,6],[5,7]]=>[5,7,2,6,1,3,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,2,4],[3,6],[5,7]]=>[5,7,3,6,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,2,3],[4,6],[5,7]]=>[5,7,4,6,1,2,3]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,3,5],[2,4],[6,7]]=>[6,7,2,4,1,3,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,2,5],[3,4],[6,7]]=>[6,7,3,4,1,2,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,3,4],[2,5],[6,7]]=>[6,7,2,5,1,3,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,2,4],[3,5],[6,7]]=>[6,7,3,5,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,2,3],[4,5],[6,7]]=>[6,7,4,5,1,2,3]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,5,7],[2,6],[3],[4]]=>[4,3,2,6,1,5,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,4,7],[2,6],[3],[5]]=>[5,3,2,6,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,3,7],[2,6],[4],[5]]=>[5,4,2,6,1,3,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,7],[3,6],[4],[5]]=>[5,4,3,6,1,2,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,4,7],[2,5],[3],[6]]=>[6,3,2,5,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,3,7],[2,5],[4],[6]]=>[6,4,2,5,1,3,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,7],[3,5],[4],[6]]=>[6,4,3,5,1,2,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,3,7],[2,4],[5],[6]]=>[6,5,2,4,1,3,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,7],[3,4],[5],[6]]=>[6,5,3,4,1,2,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,5,6],[2,7],[3],[4]]=>[4,3,2,7,1,5,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,4,6],[2,7],[3],[5]]=>[5,3,2,7,1,4,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,3,6],[2,7],[4],[5]]=>[5,4,2,7,1,3,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,6],[3,7],[4],[5]]=>[5,4,3,7,1,2,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,4,5],[2,7],[3],[6]]=>[6,3,2,7,1,4,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,3,5],[2,7],[4],[6]]=>[6,4,2,7,1,3,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,5],[3,7],[4],[6]]=>[6,4,3,7,1,2,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,3,4],[2,7],[5],[6]]=>[6,5,2,7,1,3,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,4],[3,7],[5],[6]]=>[6,5,3,7,1,2,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,3],[4,7],[5],[6]]=>[6,5,4,7,1,2,3]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,4,6],[2,5],[3],[7]]=>[7,3,2,5,1,4,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,3,6],[2,5],[4],[7]]=>[7,4,2,5,1,3,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,6],[3,5],[4],[7]]=>[7,4,3,5,1,2,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,3,6],[2,4],[5],[7]]=>[7,5,2,4,1,3,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,6],[3,4],[5],[7]]=>[7,5,3,4,1,2,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,4,5],[2,6],[3],[7]]=>[7,3,2,6,1,4,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,3,5],[2,6],[4],[7]]=>[7,4,2,6,1,3,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,5],[3,6],[4],[7]]=>[7,4,3,6,1,2,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,3,4],[2,6],[5],[7]]=>[7,5,2,6,1,3,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,4],[3,6],[5],[7]]=>[7,5,3,6,1,2,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,3],[4,6],[5],[7]]=>[7,5,4,6,1,2,3]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,3,5],[2,4],[6],[7]]=>[7,6,2,4,1,3,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,5],[3,4],[6],[7]]=>[7,6,3,4,1,2,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,3,4],[2,5],[6],[7]]=>[7,6,2,5,1,3,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,4],[3,5],[6],[7]]=>[7,6,3,5,1,2,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,3],[4,5],[6],[7]]=>[7,6,4,5,1,2,3]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,6,7],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[1,5,7],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[1,4,7],[2],[3],[5],[6]]=>[6,5,3,2,1,4,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[1,3,7],[2],[4],[5],[6]]=>[6,5,4,2,1,3,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[1,2,7],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[1,5,6],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[1,4,6],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[1,3,6],[2],[4],[5],[7]]=>[7,5,4,2,1,3,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[1,2,6],[3],[4],[5],[7]]=>[7,5,4,3,1,2,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[1,4,5],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[1,3,5],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[1,2,5],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[1,3,4],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[1,2,4],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[1,2,3],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[1,5],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,4],[2,6],[3,7],[5]]=>[5,3,7,2,6,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,3],[2,6],[4,7],[5]]=>[5,4,7,2,6,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,2],[3,6],[4,7],[5]]=>[5,4,7,3,6,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,4],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,3],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,2],[3,5],[4,7],[6]]=>[6,4,7,3,5,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,3],[2,4],[5,7],[6]]=>[6,5,7,2,4,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,2],[3,4],[5,7],[6]]=>[6,5,7,3,4,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,4],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,3],[2,5],[4,6],[7]]=>[7,4,6,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,2],[3,5],[4,6],[7]]=>[7,4,6,3,5,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,3],[2,4],[5,6],[7]]=>[7,5,6,2,4,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,2],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,6],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[1,5],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[1,4],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[1,3],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[1,2],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[1,5],[2,6],[3],[4],[7]]=>[7,4,3,2,6,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[1,4],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[1,3],[2,6],[4],[5],[7]]=>[7,5,4,2,6,1,3]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[1,2],[3,6],[4],[5],[7]]=>[7,5,4,3,6,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[1,4],[2,5],[3],[6],[7]]=>[7,6,3,2,5,1,4]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[1,3],[2,5],[4],[6],[7]]=>[7,6,4,2,5,1,3]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[1,2],[3,5],[4],[6],[7]]=>[7,6,4,3,5,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[1,3],[2,4],[5],[6],[7]]=>[7,6,5,2,4,1,3]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[1,2],[3,4],[5],[6],[7]]=>[7,6,5,3,4,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[1,7],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0] [[1,6],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0] [[1,5],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0] [[1,4],[2],[3],[5],[6],[7]]=>[7,6,5,3,2,1,4]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0] [[1,3],[2],[4],[5],[6],[7]]=>[7,6,5,4,2,1,3]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0] [[1,2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0] [[1],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0] [[1,2,3,4,5,6,7,8]]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] [[1,2,4,5,6,7,8],[3]]=>[3,1,2,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] [[1,2,3,5,6,7,8],[4]]=>[4,1,2,3,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] [[1,2,3,4,6,7,8],[5]]=>[5,1,2,3,4,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] [[1,2,3,4,5,6,8],[7]]=>[7,1,2,3,4,5,6,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] [[1,2,3,4,5,6,7],[8]]=>[8,1,2,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] [[1,2,5,6,7,8],[3,4]]=>[3,4,1,2,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] [[1,3,4,6,7,8],[2,5]]=>[2,5,1,3,4,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] [[1,2,4,6,7,8],[3,5]]=>[3,5,1,2,4,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] [[1,2,3,6,7,8],[4,5]]=>[4,5,1,2,3,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] [[1,2,4,5,6,8],[3,7]]=>[3,7,1,2,4,5,6,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] [[1,2,3,4,6,8],[5,7]]=>[5,7,1,2,3,4,6,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] [[1,2,3,4,5,8],[6,7]]=>[6,7,1,2,3,4,5,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] [[1,3,4,5,6,7],[2,8]]=>[2,8,1,3,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] [[1,2,3,5,6,7],[4,8]]=>[4,8,1,2,3,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] [[1,2,3,4,6,7],[5,8]]=>[5,8,1,2,3,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] [[1,2,3,4,5,6],[7,8]]=>[7,8,1,2,3,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] [[1,3,4,6,7,8],[2],[5]]=>[5,2,1,3,4,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] [[1,2,4,6,7,8],[3],[5]]=>[5,3,1,2,4,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] [[1,2,3,6,7,8],[4],[5]]=>[5,4,1,2,3,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] [[1,2,3,4,7,8],[5],[6]]=>[6,5,1,2,3,4,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] [[1,2,4,5,6,8],[3],[7]]=>[7,3,1,2,4,5,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] [[1,2,3,4,6,8],[5],[7]]=>[7,5,1,2,3,4,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] [[1,2,4,5,6,7],[3],[8]]=>[8,3,1,2,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] [[1,2,3,4,6,7],[5],[8]]=>[8,5,1,2,3,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] [[1,2,4,7,8],[3,5,6]]=>[3,5,6,1,2,4,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,4,6,8],[3,5,7]]=>[3,5,7,1,2,4,6,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,4,8],[5,6,7]]=>[5,6,7,1,2,3,4,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,5,6,7],[3,4,8]]=>[3,4,8,1,2,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,6,7],[4,5,8]]=>[4,5,8,1,2,3,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,4,7],[5,6,8]]=>[5,6,8,1,2,3,4,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,4,6],[5,7,8]]=>[5,7,8,1,2,3,4,6]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,4,5],[6,7,8]]=>[6,7,8,1,2,3,4,5]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] [[1,4,6,7,8],[2,5],[3]]=>[3,2,5,1,4,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,4,7,8],[3,5],[6]]=>[6,3,5,1,2,4,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,6,8],[4,7],[5]]=>[5,4,7,1,2,3,6,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,4,5,8],[3,7],[6]]=>[6,3,7,1,2,4,5,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,5,8],[4,7],[6]]=>[6,4,7,1,2,3,5,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,4,8],[5,7],[6]]=>[6,5,7,1,2,3,4,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,5,6,8],[3,4],[7]]=>[7,3,4,1,2,5,6,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,4,6,8],[3,5],[7]]=>[7,3,5,1,2,4,6,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,6,8],[4,5],[7]]=>[7,4,5,1,2,3,6,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,5,8],[4,6],[7]]=>[7,4,6,1,2,3,5,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,4,8],[5,6],[7]]=>[7,5,6,1,2,3,4,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,4,5,6,7],[2,8],[3]]=>[3,2,8,1,4,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,6,7],[4,8],[5]]=>[5,4,8,1,2,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,3,4,5,7],[2,8],[6]]=>[6,2,8,1,3,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,4,7],[5,8],[6]]=>[6,5,8,1,2,3,4,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,4,6],[5,8],[7]]=>[7,5,8,1,2,3,4,6]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,4,5],[6,8],[7]]=>[7,6,8,1,2,3,4,5]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,5,6,7],[3,4],[8]]=>[8,3,4,1,2,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,4,6,7],[3,5],[8]]=>[8,3,5,1,2,4,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,4,5,7],[3,6],[8]]=>[8,3,6,1,2,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,4,7],[5,6],[8]]=>[8,5,6,1,2,3,4,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,5,6],[4,7],[8]]=>[8,4,7,1,2,3,5,6]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,4,6],[5,7],[8]]=>[8,5,7,1,2,3,4,6]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,4,5],[6,7],[8]]=>[8,6,7,1,2,3,4,5]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] [[1,5,6,7,8],[2],[3],[4]]=>[4,3,2,1,5,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,4,6,7,8],[2],[3],[5]]=>[5,3,2,1,4,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,3,6,7,8],[2],[4],[5]]=>[5,4,2,1,3,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,2,6,7,8],[3],[4],[5]]=>[5,4,3,1,2,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,3,5,7,8],[2],[4],[6]]=>[6,4,2,1,3,5,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,2,5,7,8],[3],[4],[6]]=>[6,4,3,1,2,5,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,2,5,6,8],[3],[4],[7]]=>[7,4,3,1,2,5,6,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,2,4,6,8],[3],[5],[7]]=>[7,5,3,1,2,4,6,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,4,8],[5],[6],[7]]=>[7,6,5,1,2,3,4,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,4,5,6,7],[2],[3],[8]]=>[8,3,2,1,4,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,3,5,6,7],[2],[4],[8]]=>[8,4,2,1,3,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,2,4,6,7],[3],[5],[8]]=>[8,5,3,1,2,4,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,5,7],[4],[6],[8]]=>[8,6,4,1,2,3,5,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,4,7],[5],[6],[8]]=>[8,6,5,1,2,3,4,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,3,4,5,6],[2],[7],[8]]=>[8,7,2,1,3,4,5,6]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,4,6],[5],[7],[8]]=>[8,7,5,1,2,3,4,6]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,2,3,4,5],[6],[7],[8]]=>[8,7,6,1,2,3,4,5]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] [[1,3,5,7],[2,4,6,8]]=>[2,4,6,8,1,3,5,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] [[1,2,3,7],[4,5,6,8]]=>[4,5,6,8,1,2,3,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] [[1,2,4,6],[3,5,7,8]]=>[3,5,7,8,1,2,4,6]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] [[1,3,4,5],[2,6,7,8]]=>[2,6,7,8,1,3,4,5]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] [[1,2,4,5],[3,6,7,8]]=>[3,6,7,8,1,2,4,5]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] [[1,2,3,5],[4,6,7,8]]=>[4,6,7,8,1,2,3,5]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] [[1,2,3,4],[5,6,7,8]]=>[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] [[1,4,6,8],[2,5,7],[3]]=>[3,2,5,7,1,4,6,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,3,5,8],[2,6,7],[4]]=>[4,2,6,7,1,3,5,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,3,4,8],[2,6,7],[5]]=>[5,2,6,7,1,3,4,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,2,4,8],[3,6,7],[5]]=>[5,3,6,7,1,2,4,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,2,3,8],[4,6,7],[5]]=>[5,4,6,7,1,2,3,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,4,6,7],[2,5,8],[3]]=>[3,2,5,8,1,4,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,3,6,7],[2,5,8],[4]]=>[4,2,5,8,1,3,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,2,6,7],[3,5,8],[4]]=>[4,3,5,8,1,2,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,3,6,7],[2,4,8],[5]]=>[5,2,4,8,1,3,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,4,5,7],[2,6,8],[3]]=>[3,2,6,8,1,4,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,3,4,7],[2,6,8],[5]]=>[5,2,6,8,1,3,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,3,5,7],[2,4,8],[6]]=>[6,2,4,8,1,3,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,3,4,7],[2,5,8],[6]]=>[6,2,5,8,1,3,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,4,5,6],[2,7,8],[3]]=>[3,2,7,8,1,4,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,2,3,6],[4,7,8],[5]]=>[5,4,7,8,1,2,3,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,3,4,5],[2,7,8],[6]]=>[6,2,7,8,1,3,4,5]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,2,4,5],[3,7,8],[6]]=>[6,3,7,8,1,2,4,5]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,2,3,5],[4,7,8],[6]]=>[6,4,7,8,1,2,3,5]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,2,3,4],[5,7,8],[6]]=>[6,5,7,8,1,2,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,3,5,6],[2,4,8],[7]]=>[7,2,4,8,1,3,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,2,4,6],[3,5,8],[7]]=>[7,3,5,8,1,2,4,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,2,3,6],[4,5,8],[7]]=>[7,4,5,8,1,2,3,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,2,3,4],[5,6,8],[7]]=>[7,5,6,8,1,2,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,2,3,7],[4,5,6],[8]]=>[8,4,5,6,1,2,3,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,3,5,6],[2,4,7],[8]]=>[8,2,4,7,1,3,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,3,4,6],[2,5,7],[8]]=>[8,2,5,7,1,3,4,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,2,4,6],[3,5,7],[8]]=>[8,3,5,7,1,2,4,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,3,4,5],[2,6,7],[8]]=>[8,2,6,7,1,3,4,5]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,2,3,5],[4,6,7],[8]]=>[8,4,6,7,1,2,3,5]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,2,3,4],[5,6,7],[8]]=>[8,5,6,7,1,2,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] [[1,3,7,8],[2,5],[4,6]]=>[4,6,2,5,1,3,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,7,8],[3,5],[4,6]]=>[4,6,3,5,1,2,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,7,8],[2,4],[5,6]]=>[5,6,2,4,1,3,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,7,8],[3,4],[5,6]]=>[5,6,3,4,1,2,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,6,8],[3,5],[4,7]]=>[4,7,3,5,1,2,6,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,4,5,8],[2,6],[3,7]]=>[3,7,2,6,1,4,5,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,4,8],[2,6],[5,7]]=>[5,7,2,6,1,3,4,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,4,8],[2,5],[6,7]]=>[6,7,2,5,1,3,4,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,6,7],[2,5],[4,8]]=>[4,8,2,5,1,3,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,6,7],[3,4],[5,8]]=>[5,8,3,4,1,2,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,4,7],[3,6],[5,8]]=>[5,8,3,6,1,2,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,4,7],[3,5],[6,8]]=>[6,8,3,5,1,2,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,4,5,6],[2,7],[3,8]]=>[3,8,2,7,1,4,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,5,6],[2,7],[4,8]]=>[4,8,2,7,1,3,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,4,6],[2,7],[5,8]]=>[5,8,2,7,1,3,4,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,4,6],[3,7],[5,8]]=>[5,8,3,7,1,2,4,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,4,5],[2,7],[6,8]]=>[6,8,2,7,1,3,4,5]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,4,5],[3,7],[6,8]]=>[6,8,3,7,1,2,4,5]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,3,4],[5,7],[6,8]]=>[6,8,5,7,1,2,3,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,5,6],[2,4],[7,8]]=>[7,8,2,4,1,3,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,5,6],[3,4],[7,8]]=>[7,8,3,4,1,2,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,4,6],[2,5],[7,8]]=>[7,8,2,5,1,3,4,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,4,6],[3,5],[7,8]]=>[7,8,3,5,1,2,4,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,3,5],[4,6],[7,8]]=>[7,8,4,6,1,2,3,5]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,3,4],[5,6],[7,8]]=>[7,8,5,6,1,2,3,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,5,7,8],[2,6],[3],[4]]=>[4,3,2,6,1,5,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,4,7,8],[2,6],[3],[5]]=>[5,3,2,6,1,4,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,7,8],[2,6],[4],[5]]=>[5,4,2,6,1,3,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,7,8],[3,6],[4],[5]]=>[5,4,3,6,1,2,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,7,8],[3,5],[4],[6]]=>[6,4,3,5,1,2,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,7,8],[2,4],[5],[6]]=>[6,5,2,4,1,3,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,5,6,8],[2,7],[3],[4]]=>[4,3,2,7,1,5,6,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,4,6,8],[2,7],[3],[5]]=>[5,3,2,7,1,4,6,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,4,5,8],[2,7],[3],[6]]=>[6,3,2,7,1,4,5,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,5,8],[3,7],[4],[6]]=>[6,4,3,7,1,2,5,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,4,8],[3,7],[5],[6]]=>[6,5,3,7,1,2,4,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,4,6,8],[2,5],[3],[7]]=>[7,3,2,5,1,4,6,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,6,8],[2,5],[4],[7]]=>[7,4,2,5,1,3,6,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,4,5,8],[2,6],[3],[7]]=>[7,3,2,6,1,4,5,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,5,8],[3,6],[4],[7]]=>[7,4,3,6,1,2,5,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,4,8],[2,6],[5],[7]]=>[7,5,2,6,1,3,4,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,4,8],[3,6],[5],[7]]=>[7,5,3,6,1,2,4,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,5,6,7],[2,8],[3],[4]]=>[4,3,2,8,1,5,6,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,4,6,7],[2,8],[3],[5]]=>[5,3,2,8,1,4,6,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,4,5,7],[2,8],[3],[6]]=>[6,3,2,8,1,4,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,5,7],[3,8],[4],[6]]=>[6,4,3,8,1,2,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,4,7],[2,8],[5],[6]]=>[6,5,2,8,1,3,4,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,4,7],[3,8],[5],[6]]=>[6,5,3,8,1,2,4,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,4,5,6],[2,8],[3],[7]]=>[7,3,2,8,1,4,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,5,6],[2,8],[4],[7]]=>[7,4,2,8,1,3,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,4,6],[3,8],[5],[7]]=>[7,5,3,8,1,2,4,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,4,5],[2,8],[6],[7]]=>[7,6,2,8,1,3,4,5]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,3,4],[5,8],[6],[7]]=>[7,6,5,8,1,2,3,4]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,6,7],[2,5],[4],[8]]=>[8,4,2,5,1,3,6,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,6,7],[3,4],[5],[8]]=>[8,5,3,4,1,2,6,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,4,5,7],[2,6],[3],[8]]=>[8,3,2,6,1,4,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,5,7],[2,6],[4],[8]]=>[8,4,2,6,1,3,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,4,7],[3,6],[5],[8]]=>[8,5,3,6,1,2,4,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,5,7],[2,4],[6],[8]]=>[8,6,2,4,1,3,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,5,7],[3,4],[6],[8]]=>[8,6,3,4,1,2,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,4,7],[2,5],[6],[8]]=>[8,6,2,5,1,3,4,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,4,5,6],[2,7],[3],[8]]=>[8,3,2,7,1,4,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,5,6],[2,7],[4],[8]]=>[8,4,2,7,1,3,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,5,6],[3,7],[4],[8]]=>[8,4,3,7,1,2,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,4,6],[2,7],[5],[8]]=>[8,5,2,7,1,3,4,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,4,6],[3,7],[5],[8]]=>[8,5,3,7,1,2,4,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,4,5],[3,7],[6],[8]]=>[8,6,3,7,1,2,4,5]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,3,4],[5,7],[6],[8]]=>[8,6,5,7,1,2,3,4]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,5,6],[2,4],[7],[8]]=>[8,7,2,4,1,3,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,5,6],[3,4],[7],[8]]=>[8,7,3,4,1,2,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,4,6],[2,5],[7],[8]]=>[8,7,2,5,1,3,4,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,4,6],[3,5],[7],[8]]=>[8,7,3,5,1,2,4,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,3,4,5],[2,6],[7],[8]]=>[8,7,2,6,1,3,4,5]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,4,5],[3,6],[7],[8]]=>[8,7,3,6,1,2,4,5]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,3,5],[4,6],[7],[8]]=>[8,7,4,6,1,2,3,5]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,2,3,4],[5,6],[7],[8]]=>[8,7,5,6,1,2,3,4]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] [[1,6,7,8],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,5,7,8],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,2,7,8],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,5,6,8],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,4,6,8],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,4,5,8],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,3,5,8],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,3,4,8],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,2,3,8],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,5,6,7],[2],[3],[4],[8]]=>[8,4,3,2,1,5,6,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,4,6,7],[2],[3],[5],[8]]=>[8,5,3,2,1,4,6,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,3,6,7],[2],[4],[5],[8]]=>[8,5,4,2,1,3,6,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,4,5,7],[2],[3],[6],[8]]=>[8,6,3,2,1,4,5,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,3,5,7],[2],[4],[6],[8]]=>[8,6,4,2,1,3,5,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,3,4,7],[2],[5],[6],[8]]=>[8,6,5,2,1,3,4,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,4,5,6],[2],[3],[7],[8]]=>[8,7,3,2,1,4,5,6]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,3,4,6],[2],[5],[7],[8]]=>[8,7,5,2,1,3,4,6]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,2,4,6],[3],[5],[7],[8]]=>[8,7,5,3,1,2,4,6]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,3,4,5],[2],[6],[7],[8]]=>[8,7,6,2,1,3,4,5]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,2,4,5],[3],[6],[7],[8]]=>[8,7,6,3,1,2,4,5]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,2,3,5],[4],[6],[7],[8]]=>[8,7,6,4,1,2,3,5]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,2,3,4],[5],[6],[7],[8]]=>[8,7,6,5,1,2,3,4]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] [[1,3,7],[2,4,8],[5,6]]=>[5,6,2,4,8,1,3,7]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,6],[3,5,8],[4,7]]=>[4,7,3,5,8,1,2,6]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,3],[4,6,8],[5,7]]=>[5,7,4,6,8,1,2,3]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,4],[3,5,8],[6,7]]=>[6,7,3,5,8,1,2,4]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,3],[4,5,8],[6,7]]=>[6,7,4,5,8,1,2,3]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,4,6],[2,5,7],[3,8]]=>[3,8,2,5,7,1,4,6]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,6],[3,5,7],[4,8]]=>[4,8,3,5,7,1,2,6]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,4,5],[2,6,7],[3,8]]=>[3,8,2,6,7,1,4,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,3,4],[2,5,7],[6,8]]=>[6,8,2,5,7,1,3,4]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,3,5],[2,4,6],[7,8]]=>[7,8,2,4,6,1,3,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,5],[3,4,6],[7,8]]=>[7,8,3,4,6,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,3,4],[2,5,6],[7,8]]=>[7,8,2,5,6,1,3,4]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,4],[3,5,6],[7,8]]=>[7,8,3,5,6,1,2,4]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,5,7],[2,6,8],[3],[4]]=>[4,3,2,6,8,1,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,3,7],[2,6,8],[4],[5]]=>[5,4,2,6,8,1,3,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,7],[3,6,8],[4],[5]]=>[5,4,3,6,8,1,2,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,4,7],[2,5,8],[3],[6]]=>[6,3,2,5,8,1,4,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,7],[3,5,8],[4],[6]]=>[6,4,3,5,8,1,2,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,3,7],[2,4,8],[5],[6]]=>[6,5,2,4,8,1,3,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,5,6],[2,7,8],[3],[4]]=>[4,3,2,7,8,1,5,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,4,6],[2,7,8],[3],[5]]=>[5,3,2,7,8,1,4,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,3,6],[2,7,8],[4],[5]]=>[5,4,2,7,8,1,3,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,4,5],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,5],[3,7,8],[4],[6]]=>[6,4,3,7,8,1,2,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,3],[4,7,8],[5],[6]]=>[6,5,4,7,8,1,2,3]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,3,6],[2,5,8],[4],[7]]=>[7,4,2,5,8,1,3,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,4],[3,6,8],[5],[7]]=>[7,5,3,6,8,1,2,4]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,3],[4,6,8],[5],[7]]=>[7,5,4,6,8,1,2,3]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,3],[4,5,8],[6],[7]]=>[7,6,4,5,8,1,2,3]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,3,6],[2,5,7],[4],[8]]=>[8,4,2,5,7,1,3,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,3,4],[2,6,7],[5],[8]]=>[8,5,2,6,7,1,3,4]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,4],[3,6,7],[5],[8]]=>[8,5,3,6,7,1,2,4]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,3,4],[2,5,7],[6],[8]]=>[8,6,2,5,7,1,3,4]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,4],[3,5,7],[6],[8]]=>[8,6,3,5,7,1,2,4]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,3],[4,5,7],[6],[8]]=>[8,6,4,5,7,1,2,3]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,3,5],[2,4,6],[7],[8]]=>[8,7,2,4,6,1,3,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,2,5],[3,4,6],[7],[8]]=>[8,7,3,4,6,1,2,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,3,4],[2,5,6],[7],[8]]=>[8,7,2,5,6,1,3,4]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] [[1,5,8],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,3,8],[2,6],[4,7],[5]]=>[5,4,7,2,6,1,3,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,4,8],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,3,8],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,2,8],[3,4],[5,7],[6]]=>[6,5,7,3,4,1,2,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,5,7],[2,6],[3,8],[4]]=>[4,3,8,2,6,1,5,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,4,7],[2,6],[3,8],[5]]=>[5,3,8,2,6,1,4,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,3,7],[2,6],[4,8],[5]]=>[5,4,8,2,6,1,3,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,3,7],[2,5],[4,8],[6]]=>[6,4,8,2,5,1,3,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,2,7],[3,5],[4,8],[6]]=>[6,4,8,3,5,1,2,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,5,6],[2,7],[3,8],[4]]=>[4,3,8,2,7,1,5,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,4,6],[2,7],[3,8],[5]]=>[5,3,8,2,7,1,4,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,3,6],[2,7],[4,8],[5]]=>[5,4,8,2,7,1,3,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,3,5],[2,7],[4,8],[6]]=>[6,4,8,2,7,1,3,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,4,6],[2,5],[3,8],[7]]=>[7,3,8,2,5,1,4,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,2,6],[3,5],[4,8],[7]]=>[7,4,8,3,5,1,2,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,3,6],[2,4],[5,8],[7]]=>[7,5,8,2,4,1,3,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,3,4],[2,6],[5,8],[7]]=>[7,5,8,2,6,1,3,4]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,2,3],[4,6],[5,8],[7]]=>[7,5,8,4,6,1,2,3]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,3,7],[2,5],[4,6],[8]]=>[8,4,6,2,5,1,3,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,2,7],[3,4],[5,6],[8]]=>[8,5,6,3,4,1,2,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,2,6],[3,5],[4,7],[8]]=>[8,4,7,3,5,1,2,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,4,5],[2,6],[3,7],[8]]=>[8,3,7,2,6,1,4,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,3,5],[2,6],[4,7],[8]]=>[8,4,7,2,6,1,3,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,2,5],[3,6],[4,7],[8]]=>[8,4,7,3,6,1,2,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,3,4],[2,6],[5,7],[8]]=>[8,5,7,2,6,1,3,4]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,3,5],[2,4],[6,7],[8]]=>[8,6,7,2,4,1,3,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,3,4],[2,5],[6,7],[8]]=>[8,6,7,2,5,1,3,4]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,2,4],[3,5],[6,7],[8]]=>[8,6,7,3,5,1,2,4]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,2,3],[4,5],[6,7],[8]]=>[8,6,7,4,5,1,2,3]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] [[1,6,8],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,5,8],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,4,8],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,3,8],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,8],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,6,7],[2,8],[3],[4],[5]]=>[5,4,3,2,8,1,6,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,7],[3,8],[4],[5],[6]]=>[6,5,4,3,8,1,2,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,3],[4,8],[5],[6],[7]]=>[7,6,5,4,8,1,2,3]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,3,7],[2,6],[4],[5],[8]]=>[8,5,4,2,6,1,3,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,4,7],[2,5],[3],[6],[8]]=>[8,6,3,2,5,1,4,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,3,7],[2,4],[5],[6],[8]]=>[8,6,5,2,4,1,3,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,4,6],[2,7],[3],[5],[8]]=>[8,5,3,2,7,1,4,6]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,4,5],[2,7],[3],[6],[8]]=>[8,6,3,2,7,1,4,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,4,6],[2,5],[3],[7],[8]]=>[8,7,3,2,5,1,4,6]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,6],[3,4],[5],[7],[8]]=>[8,7,5,3,4,1,2,6]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,4,5],[2,6],[3],[7],[8]]=>[8,7,3,2,6,1,4,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,3,5],[2,6],[4],[7],[8]]=>[8,7,4,2,6,1,3,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,5],[3,6],[4],[7],[8]]=>[8,7,4,3,6,1,2,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,3,4],[2,6],[5],[7],[8]]=>[8,7,5,2,6,1,3,4]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,3],[4,6],[5],[7],[8]]=>[8,7,5,4,6,1,2,3]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,3,5],[2,4],[6],[7],[8]]=>[8,7,6,2,4,1,3,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,5],[3,4],[6],[7],[8]]=>[8,7,6,3,4,1,2,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,3,4],[2,5],[6],[7],[8]]=>[8,7,6,2,5,1,3,4]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,2,4],[3,5],[6],[7],[8]]=>[8,7,6,3,5,1,2,4]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] [[1,5,8],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[1,5,7],[2],[3],[4],[6],[8]]=>[8,6,4,3,2,1,5,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[1,4,7],[2],[3],[5],[6],[8]]=>[8,6,5,3,2,1,4,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[1,3,7],[2],[4],[5],[6],[8]]=>[8,6,5,4,2,1,3,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[1,5,6],[2],[3],[4],[7],[8]]=>[8,7,4,3,2,1,5,6]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[1,4,6],[2],[3],[5],[7],[8]]=>[8,7,5,3,2,1,4,6]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[1,2,6],[3],[4],[5],[7],[8]]=>[8,7,5,4,3,1,2,6]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[1,4,5],[2],[3],[6],[7],[8]]=>[8,7,6,3,2,1,4,5]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[1,3,5],[2],[4],[6],[7],[8]]=>[8,7,6,4,2,1,3,5]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[1,2,5],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,1,2,5]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[1,3,4],[2],[5],[6],[7],[8]]=>[8,7,6,5,2,1,3,4]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[1,2,4],[3],[5],[6],[7],[8]]=>[8,7,6,5,3,1,2,4]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[1,2,3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,1,2,3]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] [[1,5],[2,6],[3,7],[4,8]]=>[4,8,3,7,2,6,1,5]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,4],[2,6],[3,7],[5,8]]=>[5,8,3,7,2,6,1,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,3],[2,6],[4,7],[5,8]]=>[5,8,4,7,2,6,1,3]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,2],[3,6],[4,7],[5,8]]=>[5,8,4,7,3,6,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,4],[2,5],[3,7],[6,8]]=>[6,8,3,7,2,5,1,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,3],[2,5],[4,7],[6,8]]=>[6,8,4,7,2,5,1,3]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,2],[3,5],[4,7],[6,8]]=>[6,8,4,7,3,5,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,3],[2,4],[5,7],[6,8]]=>[6,8,5,7,2,4,1,3]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,2],[3,4],[5,7],[6,8]]=>[6,8,5,7,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,4],[2,5],[3,6],[7,8]]=>[7,8,3,6,2,5,1,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,3],[2,5],[4,6],[7,8]]=>[7,8,4,6,2,5,1,3]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,2],[3,5],[4,6],[7,8]]=>[7,8,4,6,3,5,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,3],[2,4],[5,6],[7,8]]=>[7,8,5,6,2,4,1,3]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,2],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,6],[2,7],[3,8],[4],[5]]=>[5,4,3,8,2,7,1,6]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,5],[2,7],[3,8],[4],[6]]=>[6,4,3,8,2,7,1,5]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,4],[2,7],[3,8],[5],[6]]=>[6,5,3,8,2,7,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,5],[2,6],[3,8],[4],[7]]=>[7,4,3,8,2,6,1,5]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,4],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,3],[2,6],[4,8],[5],[7]]=>[7,5,4,8,2,6,1,3]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,3],[2,4],[5,8],[6],[7]]=>[7,6,5,8,2,4,1,3]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,2],[3,4],[5,8],[6],[7]]=>[7,6,5,8,3,4,1,2]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,5],[2,6],[3,7],[4],[8]]=>[8,4,3,7,2,6,1,5]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,4],[2,6],[3,7],[5],[8]]=>[8,5,3,7,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,3],[2,5],[4,7],[6],[8]]=>[8,6,4,7,2,5,1,3]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,2],[3,5],[4,7],[6],[8]]=>[8,6,4,7,3,5,1,2]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,3],[2,4],[5,7],[6],[8]]=>[8,6,5,7,2,4,1,3]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,4],[2,5],[3,6],[7],[8]]=>[8,7,3,6,2,5,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,2],[3,5],[4,6],[7],[8]]=>[8,7,4,6,3,5,1,2]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,3],[2,4],[5,6],[7],[8]]=>[8,7,5,6,2,4,1,3]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,2],[3,4],[5,6],[7],[8]]=>[8,7,5,6,3,4,1,2]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] [[1,7],[2,8],[3],[4],[5],[6]]=>[6,5,4,3,2,8,1,7]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[1,6],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[1,2],[3,8],[4],[5],[6],[7]]=>[7,6,5,4,3,8,1,2]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[1,6],[2,7],[3],[4],[5],[8]]=>[8,5,4,3,2,7,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[1,5],[2,6],[3],[4],[7],[8]]=>[8,7,4,3,2,6,1,5]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[1,4],[2,6],[3],[5],[7],[8]]=>[8,7,5,3,2,6,1,4]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[1,3],[2,6],[4],[5],[7],[8]]=>[8,7,5,4,2,6,1,3]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[1,4],[2,5],[3],[6],[7],[8]]=>[8,7,6,3,2,5,1,4]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[1,3],[2,4],[5],[6],[7],[8]]=>[8,7,6,5,2,4,1,3]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[1,2],[3,4],[5],[6],[7],[8]]=>[8,7,6,5,3,4,1,2]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] [[1,8],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] [[1,7],[2],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,1,7]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] [[1,6],[2],[3],[4],[5],[7],[8]]=>[8,7,5,4,3,2,1,6]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] [[1,5],[2],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,2,1,5]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] [[1,4],[2],[3],[5],[6],[7],[8]]=>[8,7,6,5,3,2,1,4]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] [[1,3],[2],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,2,1,3]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] [[1,2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,1,2]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] [[1],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
Map
to Tamari-corresponding Dyck path
Description
Return the Dyck path associated with a binary tree in consistency with the Tamari order on Dyck words and binary trees.
The bijection is defined recursively as follows:
  • a leaf is associated with an empty Dyck path,
  • a tree with children $l,r$ is associated with the Dyck word $T(l) 1 T(r) 0$ where $T(l)$ and $T(r)$ are the images of this bijection to $l$ and $r$.