Identifier
Mp00085: Standard tableaux —Schützenberger involution⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
Images
=>
Cc0007;cc-rep-0Cc0007;cc-rep-1Cc0002;cc-rep-3
[[1]]=>[[1]]=>[1]=>[1] [[1,2]]=>[[1,2]]=>[1,2]=>[1,1] [[1],[2]]=>[[1],[2]]=>[2,1]=>[2] [[1,2,3]]=>[[1,2,3]]=>[1,2,3]=>[1,1,1] [[1,3],[2]]=>[[1,2],[3]]=>[3,1,2]=>[3] [[1,2],[3]]=>[[1,3],[2]]=>[2,1,3]=>[2,1] [[1],[2],[3]]=>[[1],[2],[3]]=>[3,2,1]=>[2,1] [[1,2,3,4]]=>[[1,2,3,4]]=>[1,2,3,4]=>[1,1,1,1] [[1,3,4],[2]]=>[[1,2,3],[4]]=>[4,1,2,3]=>[4] [[1,2,4],[3]]=>[[1,2,4],[3]]=>[3,1,2,4]=>[3,1] [[1,2,3],[4]]=>[[1,3,4],[2]]=>[2,1,3,4]=>[2,1,1] [[1,3],[2,4]]=>[[1,3],[2,4]]=>[2,4,1,3]=>[4] [[1,2],[3,4]]=>[[1,2],[3,4]]=>[3,4,1,2]=>[2,2] [[1,4],[2],[3]]=>[[1,2],[3],[4]]=>[4,3,1,2]=>[4] [[1,3],[2],[4]]=>[[1,3],[2],[4]]=>[4,2,1,3]=>[3,1] [[1,2],[3],[4]]=>[[1,4],[2],[3]]=>[3,2,1,4]=>[2,1,1] [[1],[2],[3],[4]]=>[[1],[2],[3],[4]]=>[4,3,2,1]=>[2,2] [[1,2,3,4,5]]=>[[1,2,3,4,5]]=>[1,2,3,4,5]=>[1,1,1,1,1] [[1,3,4,5],[2]]=>[[1,2,3,4],[5]]=>[5,1,2,3,4]=>[5] [[1,2,4,5],[3]]=>[[1,2,3,5],[4]]=>[4,1,2,3,5]=>[4,1] [[1,2,3,5],[4]]=>[[1,2,4,5],[3]]=>[3,1,2,4,5]=>[3,1,1] [[1,2,3,4],[5]]=>[[1,3,4,5],[2]]=>[2,1,3,4,5]=>[2,1,1,1] [[1,3,5],[2,4]]=>[[1,2,4],[3,5]]=>[3,5,1,2,4]=>[3,2] [[1,2,5],[3,4]]=>[[1,2,3],[4,5]]=>[4,5,1,2,3]=>[5] [[1,3,4],[2,5]]=>[[1,3,4],[2,5]]=>[2,5,1,3,4]=>[5] [[1,2,4],[3,5]]=>[[1,3,5],[2,4]]=>[2,4,1,3,5]=>[4,1] [[1,2,3],[4,5]]=>[[1,2,5],[3,4]]=>[3,4,1,2,5]=>[2,2,1] [[1,4,5],[2],[3]]=>[[1,2,3],[4],[5]]=>[5,4,1,2,3]=>[3,2] [[1,3,5],[2],[4]]=>[[1,2,4],[3],[5]]=>[5,3,1,2,4]=>[5] [[1,2,5],[3],[4]]=>[[1,2,5],[3],[4]]=>[4,3,1,2,5]=>[4,1] [[1,3,4],[2],[5]]=>[[1,3,4],[2],[5]]=>[5,2,1,3,4]=>[4,1] [[1,2,4],[3],[5]]=>[[1,3,5],[2],[4]]=>[4,2,1,3,5]=>[3,1,1] [[1,2,3],[4],[5]]=>[[1,4,5],[2],[3]]=>[3,2,1,4,5]=>[2,1,1,1] [[1,4],[2,5],[3]]=>[[1,3],[2,4],[5]]=>[5,2,4,1,3]=>[4,1] [[1,3],[2,5],[4]]=>[[1,2],[3,4],[5]]=>[5,3,4,1,2]=>[5] [[1,2],[3,5],[4]]=>[[1,2],[3,5],[4]]=>[4,3,5,1,2]=>[3,2] [[1,3],[2,4],[5]]=>[[1,4],[2,5],[3]]=>[3,2,5,1,4]=>[4,1] [[1,2],[3,4],[5]]=>[[1,3],[2,5],[4]]=>[4,2,5,1,3]=>[2,2,1] [[1,5],[2],[3],[4]]=>[[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>[4,1] [[1,4],[2],[3],[5]]=>[[1,3],[2],[4],[5]]=>[5,4,2,1,3]=>[5] [[1,3],[2],[4],[5]]=>[[1,4],[2],[3],[5]]=>[5,3,2,1,4]=>[3,2] [[1,2],[3],[4],[5]]=>[[1,5],[2],[3],[4]]=>[4,3,2,1,5]=>[2,2,1] [[1],[2],[3],[4],[5]]=>[[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>[2,2,1] [[1,2,3,4,5,6]]=>[[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>[1,1,1,1,1,1] [[1,3,4,5,6],[2]]=>[[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>[6] [[1,2,4,5,6],[3]]=>[[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>[5,1] [[1,2,3,5,6],[4]]=>[[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>[4,1,1] [[1,2,3,4,6],[5]]=>[[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>[3,1,1,1] [[1,2,3,4,5],[6]]=>[[1,3,4,5,6],[2]]=>[2,1,3,4,5,6]=>[2,1,1,1,1] [[1,3,5,6],[2,4]]=>[[1,2,3,5],[4,6]]=>[4,6,1,2,3,5]=>[6] [[1,2,5,6],[3,4]]=>[[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>[3,3] [[1,3,4,6],[2,5]]=>[[1,2,4,5],[3,6]]=>[3,6,1,2,4,5]=>[4,2] [[1,2,4,6],[3,5]]=>[[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>[3,2,1] [[1,2,3,6],[4,5]]=>[[1,2,3,6],[4,5]]=>[4,5,1,2,3,6]=>[5,1] [[1,3,4,5],[2,6]]=>[[1,3,4,5],[2,6]]=>[2,6,1,3,4,5]=>[6] [[1,2,4,5],[3,6]]=>[[1,3,4,6],[2,5]]=>[2,5,1,3,4,6]=>[5,1] [[1,2,3,5],[4,6]]=>[[1,3,5,6],[2,4]]=>[2,4,1,3,5,6]=>[4,1,1] [[1,2,3,4],[5,6]]=>[[1,2,5,6],[3,4]]=>[3,4,1,2,5,6]=>[2,2,1,1] [[1,4,5,6],[2],[3]]=>[[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>[6] [[1,3,5,6],[2],[4]]=>[[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>[4,2] [[1,2,5,6],[3],[4]]=>[[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>[3,2,1] [[1,3,4,6],[2],[5]]=>[[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>[6] [[1,2,4,6],[3],[5]]=>[[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>[5,1] [[1,2,3,6],[4],[5]]=>[[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>[4,1,1] [[1,3,4,5],[2],[6]]=>[[1,3,4,5],[2],[6]]=>[6,2,1,3,4,5]=>[5,1] [[1,2,4,5],[3],[6]]=>[[1,3,4,6],[2],[5]]=>[5,2,1,3,4,6]=>[4,1,1] [[1,2,3,5],[4],[6]]=>[[1,3,5,6],[2],[4]]=>[4,2,1,3,5,6]=>[3,1,1,1] [[1,2,3,4],[5],[6]]=>[[1,4,5,6],[2],[3]]=>[3,2,1,4,5,6]=>[2,1,1,1,1] [[1,3,5],[2,4,6]]=>[[1,3,5],[2,4,6]]=>[2,4,6,1,3,5]=>[3,3] [[1,2,5],[3,4,6]]=>[[1,3,4],[2,5,6]]=>[2,5,6,1,3,4]=>[6] [[1,3,4],[2,5,6]]=>[[1,2,5],[3,4,6]]=>[3,4,6,1,2,5]=>[6] [[1,2,4],[3,5,6]]=>[[1,2,4],[3,5,6]]=>[3,5,6,1,2,4]=>[4,2] [[1,2,3],[4,5,6]]=>[[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>[2,2,2] [[1,4,6],[2,5],[3]]=>[[1,2,4],[3,5],[6]]=>[6,3,5,1,2,4]=>[3,3] [[1,3,6],[2,5],[4]]=>[[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3]=>[6] [[1,2,6],[3,5],[4]]=>[[1,2,3],[4,6],[5]]=>[5,4,6,1,2,3]=>[4,2] [[1,3,6],[2,4],[5]]=>[[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5]=>[4,2] [[1,2,6],[3,4],[5]]=>[[1,2,4],[3,6],[5]]=>[5,3,6,1,2,4]=>[6] [[1,4,5],[2,6],[3]]=>[[1,3,4],[2,5],[6]]=>[6,2,5,1,3,4]=>[3,2,1] [[1,3,5],[2,6],[4]]=>[[1,3,5],[2,4],[6]]=>[6,2,4,1,3,5]=>[5,1] [[1,2,5],[3,6],[4]]=>[[1,3,6],[2,4],[5]]=>[5,2,4,1,3,6]=>[4,1,1] [[1,3,4],[2,6],[5]]=>[[1,2,5],[3,4],[6]]=>[6,3,4,1,2,5]=>[6] [[1,2,4],[3,6],[5]]=>[[1,2,6],[3,4],[5]]=>[5,3,4,1,2,6]=>[5,1] [[1,2,3],[4,6],[5]]=>[[1,2,6],[3,5],[4]]=>[4,3,5,1,2,6]=>[3,2,1] [[1,3,5],[2,4],[6]]=>[[1,3,5],[2,6],[4]]=>[4,2,6,1,3,5]=>[3,2,1] [[1,2,5],[3,4],[6]]=>[[1,3,4],[2,6],[5]]=>[5,2,6,1,3,4]=>[5,1] [[1,3,4],[2,5],[6]]=>[[1,4,5],[2,6],[3]]=>[3,2,6,1,4,5]=>[5,1] [[1,2,4],[3,5],[6]]=>[[1,4,6],[2,5],[3]]=>[3,2,5,1,4,6]=>[4,1,1] [[1,2,3],[4,5],[6]]=>[[1,3,6],[2,5],[4]]=>[4,2,5,1,3,6]=>[2,2,1,1] [[1,5,6],[2],[3],[4]]=>[[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>[4,2] [[1,4,6],[2],[3],[5]]=>[[1,2,4],[3],[5],[6]]=>[6,5,3,1,2,4]=>[3,2,1] [[1,3,6],[2],[4],[5]]=>[[1,2,5],[3],[4],[6]]=>[6,4,3,1,2,5]=>[5,1] [[1,2,6],[3],[4],[5]]=>[[1,2,6],[3],[4],[5]]=>[5,4,3,1,2,6]=>[4,1,1] [[1,4,5],[2],[3],[6]]=>[[1,3,4],[2],[5],[6]]=>[6,5,2,1,3,4]=>[3,3] [[1,3,5],[2],[4],[6]]=>[[1,3,5],[2],[4],[6]]=>[6,4,2,1,3,5]=>[6] [[1,2,5],[3],[4],[6]]=>[[1,3,6],[2],[4],[5]]=>[5,4,2,1,3,6]=>[5,1] [[1,3,4],[2],[5],[6]]=>[[1,4,5],[2],[3],[6]]=>[6,3,2,1,4,5]=>[4,2] [[1,2,4],[3],[5],[6]]=>[[1,4,6],[2],[3],[5]]=>[5,3,2,1,4,6]=>[3,2,1] [[1,2,3],[4],[5],[6]]=>[[1,5,6],[2],[3],[4]]=>[4,3,2,1,5,6]=>[2,2,1,1] [[1,4],[2,5],[3,6]]=>[[1,4],[2,5],[3,6]]=>[3,6,2,5,1,4]=>[6] [[1,3],[2,5],[4,6]]=>[[1,3],[2,5],[4,6]]=>[4,6,2,5,1,3]=>[3,3] [[1,2],[3,5],[4,6]]=>[[1,3],[2,4],[5,6]]=>[5,6,2,4,1,3]=>[3,2,1] [[1,3],[2,4],[5,6]]=>[[1,2],[3,5],[4,6]]=>[4,6,3,5,1,2]=>[3,2,1] [[1,2],[3,4],[5,6]]=>[[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>[2,2,1,1] [[1,5],[2,6],[3],[4]]=>[[1,3],[2,4],[5],[6]]=>[6,5,2,4,1,3]=>[5,1] [[1,4],[2,6],[3],[5]]=>[[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2]=>[4,1,1] [[1,3],[2,6],[4],[5]]=>[[1,2],[3,5],[4],[6]]=>[6,4,3,5,1,2]=>[5,1] [[1,2],[3,6],[4],[5]]=>[[1,2],[3,6],[4],[5]]=>[5,4,3,6,1,2]=>[3,2,1] [[1,4],[2,5],[3],[6]]=>[[1,4],[2,5],[3],[6]]=>[6,3,2,5,1,4]=>[4,2] [[1,3],[2,5],[4],[6]]=>[[1,3],[2,5],[4],[6]]=>[6,4,2,5,1,3]=>[6] [[1,2],[3,5],[4],[6]]=>[[1,3],[2,6],[4],[5]]=>[5,4,2,6,1,3]=>[4,2] [[1,3],[2,4],[5],[6]]=>[[1,5],[2,6],[3],[4]]=>[4,3,2,6,1,5]=>[4,2] [[1,2],[3,4],[5],[6]]=>[[1,4],[2,6],[3],[5]]=>[5,3,2,6,1,4]=>[2,2,2] [[1,6],[2],[3],[4],[5]]=>[[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>[4,2] [[1,5],[2],[3],[4],[6]]=>[[1,3],[2],[4],[5],[6]]=>[6,5,4,2,1,3]=>[6] [[1,4],[2],[3],[5],[6]]=>[[1,4],[2],[3],[5],[6]]=>[6,5,3,2,1,4]=>[5,1] [[1,3],[2],[4],[5],[6]]=>[[1,5],[2],[3],[4],[6]]=>[6,4,3,2,1,5]=>[3,2,1] [[1,2],[3],[4],[5],[6]]=>[[1,6],[2],[3],[4],[5]]=>[5,4,3,2,1,6]=>[2,2,1,1] [[1],[2],[3],[4],[5],[6]]=>[[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>[2,2,2] [[1,2,3,4,5,6,7]]=>[[1,2,3,4,5,6,7]]=>[1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1] [[1,3,4,5,6,7],[2]]=>[[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>[7] [[1,2,4,5,6,7],[3]]=>[[1,2,3,4,5,7],[6]]=>[6,1,2,3,4,5,7]=>[6,1] [[1,2,3,5,6,7],[4]]=>[[1,2,3,4,6,7],[5]]=>[5,1,2,3,4,6,7]=>[5,1,1] [[1,2,3,4,6,7],[5]]=>[[1,2,3,5,6,7],[4]]=>[4,1,2,3,5,6,7]=>[4,1,1,1] [[1,2,3,4,5,7],[6]]=>[[1,2,4,5,6,7],[3]]=>[3,1,2,4,5,6,7]=>[3,1,1,1,1] [[1,2,3,4,5,6],[7]]=>[[1,3,4,5,6,7],[2]]=>[2,1,3,4,5,6,7]=>[2,1,1,1,1,1] [[1,3,5,6,7],[2,4]]=>[[1,2,3,4,6],[5,7]]=>[5,7,1,2,3,4,6]=>[4,3] [[1,2,5,6,7],[3,4]]=>[[1,2,3,4,5],[6,7]]=>[6,7,1,2,3,4,5]=>[7] [[1,3,4,6,7],[2,5]]=>[[1,2,3,5,6],[4,7]]=>[4,7,1,2,3,5,6]=>[7] [[1,2,4,6,7],[3,5]]=>[[1,2,3,5,7],[4,6]]=>[4,6,1,2,3,5,7]=>[6,1] [[1,2,3,6,7],[4,5]]=>[[1,2,3,4,7],[5,6]]=>[5,6,1,2,3,4,7]=>[3,3,1] [[1,3,4,5,7],[2,6]]=>[[1,2,4,5,6],[3,7]]=>[3,7,1,2,4,5,6]=>[5,2] [[1,2,4,5,7],[3,6]]=>[[1,2,4,5,7],[3,6]]=>[3,6,1,2,4,5,7]=>[4,2,1] [[1,2,3,5,7],[4,6]]=>[[1,2,4,6,7],[3,5]]=>[3,5,1,2,4,6,7]=>[3,2,1,1] [[1,2,3,4,7],[5,6]]=>[[1,2,3,6,7],[4,5]]=>[4,5,1,2,3,6,7]=>[5,1,1] [[1,3,4,5,6],[2,7]]=>[[1,3,4,5,6],[2,7]]=>[2,7,1,3,4,5,6]=>[7] [[1,2,4,5,6],[3,7]]=>[[1,3,4,5,7],[2,6]]=>[2,6,1,3,4,5,7]=>[6,1] [[1,2,3,5,6],[4,7]]=>[[1,3,4,6,7],[2,5]]=>[2,5,1,3,4,6,7]=>[5,1,1] [[1,2,3,4,6],[5,7]]=>[[1,3,5,6,7],[2,4]]=>[2,4,1,3,5,6,7]=>[4,1,1,1] [[1,2,3,4,5],[6,7]]=>[[1,2,5,6,7],[3,4]]=>[3,4,1,2,5,6,7]=>[2,2,1,1,1] [[1,4,5,6,7],[2],[3]]=>[[1,2,3,4,5],[6],[7]]=>[7,6,1,2,3,4,5]=>[4,3] [[1,3,5,6,7],[2],[4]]=>[[1,2,3,4,6],[5],[7]]=>[7,5,1,2,3,4,6]=>[7] [[1,2,5,6,7],[3],[4]]=>[[1,2,3,4,7],[5],[6]]=>[6,5,1,2,3,4,7]=>[6,1] [[1,3,4,6,7],[2],[5]]=>[[1,2,3,5,6],[4],[7]]=>[7,4,1,2,3,5,6]=>[5,2] [[1,2,4,6,7],[3],[5]]=>[[1,2,3,5,7],[4],[6]]=>[6,4,1,2,3,5,7]=>[4,2,1] [[1,2,3,6,7],[4],[5]]=>[[1,2,3,6,7],[4],[5]]=>[5,4,1,2,3,6,7]=>[3,2,1,1] [[1,3,4,5,7],[2],[6]]=>[[1,2,4,5,6],[3],[7]]=>[7,3,1,2,4,5,6]=>[7] [[1,2,4,5,7],[3],[6]]=>[[1,2,4,5,7],[3],[6]]=>[6,3,1,2,4,5,7]=>[6,1] [[1,2,3,5,7],[4],[6]]=>[[1,2,4,6,7],[3],[5]]=>[5,3,1,2,4,6,7]=>[5,1,1] [[1,2,3,4,7],[5],[6]]=>[[1,2,5,6,7],[3],[4]]=>[4,3,1,2,5,6,7]=>[4,1,1,1] [[1,3,4,5,6],[2],[7]]=>[[1,3,4,5,6],[2],[7]]=>[7,2,1,3,4,5,6]=>[6,1] [[1,2,4,5,6],[3],[7]]=>[[1,3,4,5,7],[2],[6]]=>[6,2,1,3,4,5,7]=>[5,1,1] [[1,2,3,5,6],[4],[7]]=>[[1,3,4,6,7],[2],[5]]=>[5,2,1,3,4,6,7]=>[4,1,1,1] [[1,2,3,4,6],[5],[7]]=>[[1,3,5,6,7],[2],[4]]=>[4,2,1,3,5,6,7]=>[3,1,1,1,1] [[1,2,3,4,5],[6],[7]]=>[[1,4,5,6,7],[2],[3]]=>[3,2,1,4,5,6,7]=>[2,1,1,1,1,1] [[1,3,5,7],[2,4,6]]=>[[1,2,4,6],[3,5,7]]=>[3,5,7,1,2,4,6]=>[5,2] [[1,2,5,7],[3,4,6]]=>[[1,2,4,5],[3,6,7]]=>[3,6,7,1,2,4,5]=>[7] [[1,3,4,7],[2,5,6]]=>[[1,2,3,6],[4,5,7]]=>[4,5,7,1,2,3,6]=>[3,2,2] [[1,2,4,7],[3,5,6]]=>[[1,2,3,5],[4,6,7]]=>[4,6,7,1,2,3,5]=>[5,2] [[1,2,3,7],[4,5,6]]=>[[1,2,3,4],[5,6,7]]=>[5,6,7,1,2,3,4]=>[7] [[1,3,5,6],[2,4,7]]=>[[1,3,4,6],[2,5,7]]=>[2,5,7,1,3,4,6]=>[7] [[1,2,5,6],[3,4,7]]=>[[1,3,4,5],[2,6,7]]=>[2,6,7,1,3,4,5]=>[4,3] [[1,3,4,6],[2,5,7]]=>[[1,3,5,6],[2,4,7]]=>[2,4,7,1,3,5,6]=>[4,3] [[1,2,4,6],[3,5,7]]=>[[1,3,5,7],[2,4,6]]=>[2,4,6,1,3,5,7]=>[3,3,1] [[1,2,3,6],[4,5,7]]=>[[1,3,4,7],[2,5,6]]=>[2,5,6,1,3,4,7]=>[6,1] [[1,3,4,5],[2,6,7]]=>[[1,2,5,6],[3,4,7]]=>[3,4,7,1,2,5,6]=>[7] [[1,2,4,5],[3,6,7]]=>[[1,2,5,7],[3,4,6]]=>[3,4,6,1,2,5,7]=>[6,1] [[1,2,3,5],[4,6,7]]=>[[1,2,4,7],[3,5,6]]=>[3,5,6,1,2,4,7]=>[4,2,1] [[1,2,3,4],[5,6,7]]=>[[1,2,3,7],[4,5,6]]=>[4,5,6,1,2,3,7]=>[2,2,2,1] [[1,4,6,7],[2,5],[3]]=>[[1,2,3,5],[4,6],[7]]=>[7,4,6,1,2,3,5]=>[5,2] [[1,3,6,7],[2,5],[4]]=>[[1,2,3,4],[5,6],[7]]=>[7,5,6,1,2,3,4]=>[3,2,2] [[1,2,6,7],[3,5],[4]]=>[[1,2,3,4],[5,7],[6]]=>[6,5,7,1,2,3,4]=>[5,2] [[1,3,6,7],[2,4],[5]]=>[[1,2,3,6],[4,7],[5]]=>[5,4,7,1,2,3,6]=>[4,3] [[1,2,6,7],[3,4],[5]]=>[[1,2,3,5],[4,7],[6]]=>[6,4,7,1,2,3,5]=>[7] [[1,4,5,7],[2,6],[3]]=>[[1,2,4,5],[3,6],[7]]=>[7,3,6,1,2,4,5]=>[7] [[1,3,5,7],[2,6],[4]]=>[[1,2,4,6],[3,5],[7]]=>[7,3,5,1,2,4,6]=>[4,3] [[1,2,5,7],[3,6],[4]]=>[[1,2,4,7],[3,5],[6]]=>[6,3,5,1,2,4,7]=>[3,3,1] [[1,3,4,7],[2,6],[5]]=>[[1,2,3,6],[4,5],[7]]=>[7,4,5,1,2,3,6]=>[7] [[1,2,4,7],[3,6],[5]]=>[[1,2,3,7],[4,5],[6]]=>[6,4,5,1,2,3,7]=>[6,1] [[1,2,3,7],[4,6],[5]]=>[[1,2,3,7],[4,6],[5]]=>[5,4,6,1,2,3,7]=>[4,2,1] [[1,3,5,7],[2,4],[6]]=>[[1,2,4,6],[3,7],[5]]=>[5,3,7,1,2,4,6]=>[7] [[1,2,5,7],[3,4],[6]]=>[[1,2,4,5],[3,7],[6]]=>[6,3,7,1,2,4,5]=>[4,3] [[1,3,4,7],[2,5],[6]]=>[[1,2,5,6],[3,7],[4]]=>[4,3,7,1,2,5,6]=>[5,2] [[1,2,4,7],[3,5],[6]]=>[[1,2,5,7],[3,6],[4]]=>[4,3,6,1,2,5,7]=>[4,2,1] [[1,2,3,7],[4,5],[6]]=>[[1,2,4,7],[3,6],[5]]=>[5,3,6,1,2,4,7]=>[6,1] [[1,4,5,6],[2,7],[3]]=>[[1,3,4,5],[2,6],[7]]=>[7,2,6,1,3,4,5]=>[6,1] [[1,3,5,6],[2,7],[4]]=>[[1,3,4,6],[2,5],[7]]=>[7,2,5,1,3,4,6]=>[4,2,1] [[1,2,5,6],[3,7],[4]]=>[[1,3,4,7],[2,5],[6]]=>[6,2,5,1,3,4,7]=>[3,2,1,1] [[1,3,4,6],[2,7],[5]]=>[[1,3,5,6],[2,4],[7]]=>[7,2,4,1,3,5,6]=>[6,1] [[1,2,4,6],[3,7],[5]]=>[[1,3,5,7],[2,4],[6]]=>[6,2,4,1,3,5,7]=>[5,1,1] [[1,2,3,6],[4,7],[5]]=>[[1,3,6,7],[2,4],[5]]=>[5,2,4,1,3,6,7]=>[4,1,1,1] [[1,3,4,5],[2,7],[6]]=>[[1,2,5,6],[3,4],[7]]=>[7,3,4,1,2,5,6]=>[7] [[1,2,4,5],[3,7],[6]]=>[[1,2,5,7],[3,4],[6]]=>[6,3,4,1,2,5,7]=>[6,1] [[1,2,3,5],[4,7],[6]]=>[[1,2,6,7],[3,4],[5]]=>[5,3,4,1,2,6,7]=>[5,1,1] [[1,2,3,4],[5,7],[6]]=>[[1,2,6,7],[3,5],[4]]=>[4,3,5,1,2,6,7]=>[3,2,1,1] [[1,3,5,6],[2,4],[7]]=>[[1,3,4,6],[2,7],[5]]=>[5,2,7,1,3,4,6]=>[6,1] [[1,2,5,6],[3,4],[7]]=>[[1,3,4,5],[2,7],[6]]=>[6,2,7,1,3,4,5]=>[3,3,1] [[1,3,4,6],[2,5],[7]]=>[[1,3,5,6],[2,7],[4]]=>[4,2,7,1,3,5,6]=>[4,2,1] [[1,2,4,6],[3,5],[7]]=>[[1,3,5,7],[2,6],[4]]=>[4,2,6,1,3,5,7]=>[3,2,1,1] [[1,2,3,6],[4,5],[7]]=>[[1,3,4,7],[2,6],[5]]=>[5,2,6,1,3,4,7]=>[5,1,1] [[1,3,4,5],[2,6],[7]]=>[[1,4,5,6],[2,7],[3]]=>[3,2,7,1,4,5,6]=>[6,1] [[1,2,4,5],[3,6],[7]]=>[[1,4,5,7],[2,6],[3]]=>[3,2,6,1,4,5,7]=>[5,1,1] [[1,2,3,5],[4,6],[7]]=>[[1,4,6,7],[2,5],[3]]=>[3,2,5,1,4,6,7]=>[4,1,1,1] [[1,2,3,4],[5,6],[7]]=>[[1,3,6,7],[2,5],[4]]=>[4,2,5,1,3,6,7]=>[2,2,1,1,1] [[1,5,6,7],[2],[3],[4]]=>[[1,2,3,4],[5],[6],[7]]=>[7,6,5,1,2,3,4]=>[4,3] [[1,4,6,7],[2],[3],[5]]=>[[1,2,3,5],[4],[6],[7]]=>[7,6,4,1,2,3,5]=>[7] [[1,3,6,7],[2],[4],[5]]=>[[1,2,3,6],[4],[5],[7]]=>[7,5,4,1,2,3,6]=>[5,2] [[1,2,6,7],[3],[4],[5]]=>[[1,2,3,7],[4],[5],[6]]=>[6,5,4,1,2,3,7]=>[4,2,1] [[1,4,5,7],[2],[3],[6]]=>[[1,2,4,5],[3],[6],[7]]=>[7,6,3,1,2,4,5]=>[6,1] [[1,3,5,7],[2],[4],[6]]=>[[1,2,4,6],[3],[5],[7]]=>[7,5,3,1,2,4,6]=>[4,2,1] [[1,2,5,7],[3],[4],[6]]=>[[1,2,4,7],[3],[5],[6]]=>[6,5,3,1,2,4,7]=>[3,2,1,1] [[1,3,4,7],[2],[5],[6]]=>[[1,2,5,6],[3],[4],[7]]=>[7,4,3,1,2,5,6]=>[6,1] [[1,2,4,7],[3],[5],[6]]=>[[1,2,5,7],[3],[4],[6]]=>[6,4,3,1,2,5,7]=>[5,1,1] [[1,2,3,7],[4],[5],[6]]=>[[1,2,6,7],[3],[4],[5]]=>[5,4,3,1,2,6,7]=>[4,1,1,1] [[1,4,5,6],[2],[3],[7]]=>[[1,3,4,5],[2],[6],[7]]=>[7,6,2,1,3,4,5]=>[7] [[1,3,5,6],[2],[4],[7]]=>[[1,3,4,6],[2],[5],[7]]=>[7,5,2,1,3,4,6]=>[4,3] [[1,2,5,6],[3],[4],[7]]=>[[1,3,4,7],[2],[5],[6]]=>[6,5,2,1,3,4,7]=>[3,3,1] [[1,3,4,6],[2],[5],[7]]=>[[1,3,5,6],[2],[4],[7]]=>[7,4,2,1,3,5,6]=>[7] [[1,2,4,6],[3],[5],[7]]=>[[1,3,5,7],[2],[4],[6]]=>[6,4,2,1,3,5,7]=>[6,1] [[1,2,3,6],[4],[5],[7]]=>[[1,3,6,7],[2],[4],[5]]=>[5,4,2,1,3,6,7]=>[5,1,1] [[1,3,4,5],[2],[6],[7]]=>[[1,4,5,6],[2],[3],[7]]=>[7,3,2,1,4,5,6]=>[5,2] [[1,2,4,5],[3],[6],[7]]=>[[1,4,5,7],[2],[3],[6]]=>[6,3,2,1,4,5,7]=>[4,2,1] [[1,2,3,5],[4],[6],[7]]=>[[1,4,6,7],[2],[3],[5]]=>[5,3,2,1,4,6,7]=>[3,2,1,1] [[1,2,3,4],[5],[6],[7]]=>[[1,5,6,7],[2],[3],[4]]=>[4,3,2,1,5,6,7]=>[2,2,1,1,1] [[1,4,6],[2,5,7],[3]]=>[[1,3,5],[2,4,6],[7]]=>[7,2,4,6,1,3,5]=>[3,3,1] [[1,3,6],[2,5,7],[4]]=>[[1,3,4],[2,5,6],[7]]=>[7,2,5,6,1,3,4]=>[6,1] [[1,2,6],[3,5,7],[4]]=>[[1,3,4],[2,5,7],[6]]=>[6,2,5,7,1,3,4]=>[4,2,1] [[1,3,6],[2,4,7],[5]]=>[[1,3,6],[2,4,7],[5]]=>[5,2,4,7,1,3,6]=>[4,2,1] [[1,2,6],[3,4,7],[5]]=>[[1,3,5],[2,4,7],[6]]=>[6,2,4,7,1,3,5]=>[6,1] [[1,4,5],[2,6,7],[3]]=>[[1,2,5],[3,4,6],[7]]=>[7,3,4,6,1,2,5]=>[4,3] [[1,3,5],[2,6,7],[4]]=>[[1,2,4],[3,5,6],[7]]=>[7,3,5,6,1,2,4]=>[7] [[1,2,5],[3,6,7],[4]]=>[[1,2,4],[3,5,7],[6]]=>[6,3,5,7,1,2,4]=>[5,2] [[1,3,4],[2,6,7],[5]]=>[[1,2,3],[4,5,6],[7]]=>[7,4,5,6,1,2,3]=>[4,3] [[1,2,4],[3,6,7],[5]]=>[[1,2,3],[4,5,7],[6]]=>[6,4,5,7,1,2,3]=>[7] [[1,2,3],[4,6,7],[5]]=>[[1,2,3],[4,6,7],[5]]=>[5,4,6,7,1,2,3]=>[5,2] [[1,3,5],[2,4,7],[6]]=>[[1,2,6],[3,4,7],[5]]=>[5,3,4,7,1,2,6]=>[5,2] [[1,2,5],[3,4,7],[6]]=>[[1,2,5],[3,4,7],[6]]=>[6,3,4,7,1,2,5]=>[7] [[1,3,4],[2,5,7],[6]]=>[[1,2,6],[3,5,7],[4]]=>[4,3,5,7,1,2,6]=>[7] [[1,2,4],[3,5,7],[6]]=>[[1,2,5],[3,6,7],[4]]=>[4,3,6,7,1,2,5]=>[4,3] [[1,2,3],[4,5,7],[6]]=>[[1,2,4],[3,6,7],[5]]=>[5,3,6,7,1,2,4]=>[3,2,2] [[1,3,5],[2,4,6],[7]]=>[[1,4,6],[2,5,7],[3]]=>[3,2,5,7,1,4,6]=>[3,3,1] [[1,2,5],[3,4,6],[7]]=>[[1,4,5],[2,6,7],[3]]=>[3,2,6,7,1,4,5]=>[6,1] [[1,3,4],[2,5,6],[7]]=>[[1,3,6],[2,5,7],[4]]=>[4,2,5,7,1,3,6]=>[6,1] [[1,2,4],[3,5,6],[7]]=>[[1,3,5],[2,6,7],[4]]=>[4,2,6,7,1,3,5]=>[4,2,1] [[1,2,3],[4,5,6],[7]]=>[[1,3,4],[2,6,7],[5]]=>[5,2,6,7,1,3,4]=>[2,2,2,1] [[1,4,7],[2,5],[3,6]]=>[[1,2,5],[3,6],[4,7]]=>[4,7,3,6,1,2,5]=>[6,1] [[1,3,7],[2,5],[4,6]]=>[[1,2,4],[3,6],[5,7]]=>[5,7,3,6,1,2,4]=>[4,2,1] [[1,2,7],[3,5],[4,6]]=>[[1,2,4],[3,5],[6,7]]=>[6,7,3,5,1,2,4]=>[6,1] [[1,3,7],[2,4],[5,6]]=>[[1,2,3],[4,6],[5,7]]=>[5,7,4,6,1,2,3]=>[5,2] [[1,2,7],[3,4],[5,6]]=>[[1,2,3],[4,5],[6,7]]=>[6,7,4,5,1,2,3]=>[7] [[1,4,6],[2,5],[3,7]]=>[[1,3,5],[2,6],[4,7]]=>[4,7,2,6,1,3,5]=>[7] [[1,3,6],[2,5],[4,7]]=>[[1,3,4],[2,6],[5,7]]=>[5,7,2,6,1,3,4]=>[5,2] [[1,2,6],[3,5],[4,7]]=>[[1,3,4],[2,5],[6,7]]=>[6,7,2,5,1,3,4]=>[7] [[1,3,6],[2,4],[5,7]]=>[[1,3,6],[2,4],[5,7]]=>[5,7,2,4,1,3,6]=>[4,2,1] [[1,2,6],[3,4],[5,7]]=>[[1,3,5],[2,4],[6,7]]=>[6,7,2,4,1,3,5]=>[6,1] [[1,4,5],[2,6],[3,7]]=>[[1,4,5],[2,6],[3,7]]=>[3,7,2,6,1,4,5]=>[5,2] [[1,3,5],[2,6],[4,7]]=>[[1,4,6],[2,5],[3,7]]=>[3,7,2,5,1,4,6]=>[7] [[1,2,5],[3,6],[4,7]]=>[[1,4,7],[2,5],[3,6]]=>[3,6,2,5,1,4,7]=>[6,1] [[1,3,4],[2,6],[5,7]]=>[[1,3,6],[2,5],[4,7]]=>[4,7,2,5,1,3,6]=>[4,3] [[1,2,4],[3,6],[5,7]]=>[[1,3,7],[2,5],[4,6]]=>[4,6,2,5,1,3,7]=>[3,3,1] [[1,2,3],[4,6],[5,7]]=>[[1,3,7],[2,4],[5,6]]=>[5,6,2,4,1,3,7]=>[3,2,1,1] [[1,3,5],[2,4],[6,7]]=>[[1,2,6],[3,4],[5,7]]=>[5,7,3,4,1,2,6]=>[3,2,1,1] [[1,2,5],[3,4],[6,7]]=>[[1,2,5],[3,4],[6,7]]=>[6,7,3,4,1,2,5]=>[5,1,1] [[1,3,4],[2,5],[6,7]]=>[[1,2,6],[3,5],[4,7]]=>[4,7,3,5,1,2,6]=>[3,3,1] [[1,2,4],[3,5],[6,7]]=>[[1,2,7],[3,5],[4,6]]=>[4,6,3,5,1,2,7]=>[3,2,1,1] [[1,2,3],[4,5],[6,7]]=>[[1,2,7],[3,4],[5,6]]=>[5,6,3,4,1,2,7]=>[2,2,1,1,1] [[1,5,7],[2,6],[3],[4]]=>[[1,2,4],[3,5],[6],[7]]=>[7,6,3,5,1,2,4]=>[4,2,1] [[1,4,7],[2,6],[3],[5]]=>[[1,2,3],[4,5],[6],[7]]=>[7,6,4,5,1,2,3]=>[5,2] [[1,3,7],[2,6],[4],[5]]=>[[1,2,3],[4,6],[5],[7]]=>[7,5,4,6,1,2,3]=>[7] [[1,2,7],[3,6],[4],[5]]=>[[1,2,3],[4,7],[5],[6]]=>[6,5,4,7,1,2,3]=>[4,3] [[1,4,7],[2,5],[3],[6]]=>[[1,2,5],[3,6],[4],[7]]=>[7,4,3,6,1,2,5]=>[3,3,1] [[1,3,7],[2,5],[4],[6]]=>[[1,2,4],[3,6],[5],[7]]=>[7,5,3,6,1,2,4]=>[6,1] [[1,2,7],[3,5],[4],[6]]=>[[1,2,4],[3,7],[5],[6]]=>[6,5,3,7,1,2,4]=>[4,2,1] [[1,3,7],[2,4],[5],[6]]=>[[1,2,6],[3,7],[4],[5]]=>[5,4,3,7,1,2,6]=>[4,2,1] [[1,2,7],[3,4],[5],[6]]=>[[1,2,5],[3,7],[4],[6]]=>[6,4,3,7,1,2,5]=>[6,1] [[1,5,6],[2,7],[3],[4]]=>[[1,3,4],[2,5],[6],[7]]=>[7,6,2,5,1,3,4]=>[4,3] [[1,4,6],[2,7],[3],[5]]=>[[1,3,5],[2,4],[6],[7]]=>[7,6,2,4,1,3,5]=>[3,3,1] [[1,3,6],[2,7],[4],[5]]=>[[1,3,6],[2,4],[5],[7]]=>[7,5,2,4,1,3,6]=>[6,1] [[1,2,6],[3,7],[4],[5]]=>[[1,3,7],[2,4],[5],[6]]=>[6,5,2,4,1,3,7]=>[5,1,1] [[1,4,5],[2,7],[3],[6]]=>[[1,2,5],[3,4],[6],[7]]=>[7,6,3,4,1,2,5]=>[3,2,1,1] [[1,3,5],[2,7],[4],[6]]=>[[1,2,6],[3,4],[5],[7]]=>[7,5,3,4,1,2,6]=>[5,1,1] [[1,2,5],[3,7],[4],[6]]=>[[1,2,7],[3,4],[5],[6]]=>[6,5,3,4,1,2,7]=>[4,1,1,1] [[1,3,4],[2,7],[5],[6]]=>[[1,2,6],[3,5],[4],[7]]=>[7,4,3,5,1,2,6]=>[6,1] [[1,2,4],[3,7],[5],[6]]=>[[1,2,7],[3,5],[4],[6]]=>[6,4,3,5,1,2,7]=>[5,1,1] [[1,2,3],[4,7],[5],[6]]=>[[1,2,7],[3,6],[4],[5]]=>[5,4,3,6,1,2,7]=>[3,2,1,1] [[1,4,6],[2,5],[3],[7]]=>[[1,3,5],[2,6],[4],[7]]=>[7,4,2,6,1,3,5]=>[4,3] [[1,3,6],[2,5],[4],[7]]=>[[1,3,4],[2,6],[5],[7]]=>[7,5,2,6,1,3,4]=>[7] [[1,2,6],[3,5],[4],[7]]=>[[1,3,4],[2,7],[5],[6]]=>[6,5,2,7,1,3,4]=>[5,2] [[1,3,6],[2,4],[5],[7]]=>[[1,3,6],[2,7],[4],[5]]=>[5,4,2,7,1,3,6]=>[5,2] [[1,2,6],[3,4],[5],[7]]=>[[1,3,5],[2,7],[4],[6]]=>[6,4,2,7,1,3,5]=>[7] [[1,4,5],[2,6],[3],[7]]=>[[1,4,5],[2,6],[3],[7]]=>[7,3,2,6,1,4,5]=>[3,2,2] [[1,3,5],[2,6],[4],[7]]=>[[1,4,6],[2,5],[3],[7]]=>[7,3,2,5,1,4,6]=>[5,2] [[1,2,5],[3,6],[4],[7]]=>[[1,4,7],[2,5],[3],[6]]=>[6,3,2,5,1,4,7]=>[4,2,1] [[1,3,4],[2,6],[5],[7]]=>[[1,3,6],[2,5],[4],[7]]=>[7,4,2,5,1,3,6]=>[7] [[1,2,4],[3,6],[5],[7]]=>[[1,3,7],[2,5],[4],[6]]=>[6,4,2,5,1,3,7]=>[6,1] [[1,2,3],[4,6],[5],[7]]=>[[1,3,7],[2,6],[4],[5]]=>[5,4,2,6,1,3,7]=>[4,2,1] [[1,3,5],[2,4],[6],[7]]=>[[1,4,6],[2,7],[3],[5]]=>[5,3,2,7,1,4,6]=>[3,2,2] [[1,2,5],[3,4],[6],[7]]=>[[1,4,5],[2,7],[3],[6]]=>[6,3,2,7,1,4,5]=>[5,2] [[1,3,4],[2,5],[6],[7]]=>[[1,5,6],[2,7],[3],[4]]=>[4,3,2,7,1,5,6]=>[5,2] [[1,2,4],[3,5],[6],[7]]=>[[1,5,7],[2,6],[3],[4]]=>[4,3,2,6,1,5,7]=>[4,2,1] [[1,2,3],[4,5],[6],[7]]=>[[1,4,7],[2,6],[3],[5]]=>[5,3,2,6,1,4,7]=>[2,2,2,1] [[1,6,7],[2],[3],[4],[5]]=>[[1,2,3],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3]=>[4,2,1] [[1,5,7],[2],[3],[4],[6]]=>[[1,2,4],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4]=>[5,2] [[1,4,7],[2],[3],[5],[6]]=>[[1,2,5],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5]=>[3,2,2] [[1,3,7],[2],[4],[5],[6]]=>[[1,2,6],[3],[4],[5],[7]]=>[7,5,4,3,1,2,6]=>[5,2] [[1,2,7],[3],[4],[5],[6]]=>[[1,2,7],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7]=>[4,2,1] [[1,5,6],[2],[3],[4],[7]]=>[[1,3,4],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4]=>[7] [[1,4,6],[2],[3],[5],[7]]=>[[1,3,5],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5]=>[4,3] [[1,3,6],[2],[4],[5],[7]]=>[[1,3,6],[2],[4],[5],[7]]=>[7,5,4,2,1,3,6]=>[7] [[1,2,6],[3],[4],[5],[7]]=>[[1,3,7],[2],[4],[5],[6]]=>[6,5,4,2,1,3,7]=>[6,1] [[1,4,5],[2],[3],[6],[7]]=>[[1,4,5],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5]=>[3,3,1] [[1,3,5],[2],[4],[6],[7]]=>[[1,4,6],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6]=>[6,1] [[1,2,5],[3],[4],[6],[7]]=>[[1,4,7],[2],[3],[5],[6]]=>[6,5,3,2,1,4,7]=>[5,1,1] [[1,3,4],[2],[5],[6],[7]]=>[[1,5,6],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6]=>[4,2,1] [[1,2,4],[3],[5],[6],[7]]=>[[1,5,7],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7]=>[3,2,1,1] [[1,2,3],[4],[5],[6],[7]]=>[[1,6,7],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7]=>[2,2,1,1,1] [[1,5],[2,6],[3,7],[4]]=>[[1,4],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4]=>[6,1] [[1,4],[2,6],[3,7],[5]]=>[[1,3],[2,5],[4,6],[7]]=>[7,4,6,2,5,1,3]=>[4,2,1] [[1,3],[2,6],[4,7],[5]]=>[[1,3],[2,4],[5,6],[7]]=>[7,5,6,2,4,1,3]=>[4,3] [[1,2],[3,6],[4,7],[5]]=>[[1,3],[2,4],[5,7],[6]]=>[6,5,7,2,4,1,3]=>[3,2,2] [[1,4],[2,5],[3,7],[6]]=>[[1,2],[3,5],[4,6],[7]]=>[7,4,6,3,5,1,2]=>[6,1] [[1,3],[2,5],[4,7],[6]]=>[[1,2],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2]=>[7] [[1,2],[3,5],[4,7],[6]]=>[[1,2],[3,4],[5,7],[6]]=>[6,5,7,3,4,1,2]=>[5,2] [[1,3],[2,4],[5,7],[6]]=>[[1,2],[3,6],[4,7],[5]]=>[5,4,7,3,6,1,2]=>[4,3] [[1,2],[3,4],[5,7],[6]]=>[[1,2],[3,5],[4,7],[6]]=>[6,4,7,3,5,1,2]=>[4,2,1] [[1,4],[2,5],[3,6],[7]]=>[[1,5],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5]=>[7] [[1,3],[2,5],[4,6],[7]]=>[[1,4],[2,6],[3,7],[5]]=>[5,3,7,2,6,1,4]=>[4,3] [[1,2],[3,5],[4,6],[7]]=>[[1,4],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4]=>[4,2,1] [[1,3],[2,4],[5,6],[7]]=>[[1,3],[2,6],[4,7],[5]]=>[5,4,7,2,6,1,3]=>[3,2,2] [[1,2],[3,4],[5,6],[7]]=>[[1,3],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3]=>[2,2,2,1] [[1,6],[2,7],[3],[4],[5]]=>[[1,3],[2,4],[5],[6],[7]]=>[7,6,5,2,4,1,3]=>[7] [[1,5],[2,7],[3],[4],[6]]=>[[1,2],[3,4],[5],[6],[7]]=>[7,6,5,3,4,1,2]=>[4,3] [[1,4],[2,7],[3],[5],[6]]=>[[1,2],[3,5],[4],[6],[7]]=>[7,6,4,3,5,1,2]=>[4,2,1] [[1,3],[2,7],[4],[5],[6]]=>[[1,2],[3,6],[4],[5],[7]]=>[7,5,4,3,6,1,2]=>[5,2] [[1,2],[3,7],[4],[5],[6]]=>[[1,2],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2]=>[3,2,2] [[1,5],[2,6],[3],[4],[7]]=>[[1,4],[2,5],[3],[6],[7]]=>[7,6,3,2,5,1,4]=>[5,1,1] [[1,4],[2,6],[3],[5],[7]]=>[[1,3],[2,5],[4],[6],[7]]=>[7,6,4,2,5,1,3]=>[6,1] [[1,3],[2,6],[4],[5],[7]]=>[[1,3],[2,6],[4],[5],[7]]=>[7,5,4,2,6,1,3]=>[7] [[1,2],[3,6],[4],[5],[7]]=>[[1,3],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3]=>[5,2] [[1,4],[2,5],[3],[6],[7]]=>[[1,5],[2,6],[3],[4],[7]]=>[7,4,3,2,6,1,5]=>[4,2,1] [[1,3],[2,5],[4],[6],[7]]=>[[1,4],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4]=>[6,1] [[1,2],[3,5],[4],[6],[7]]=>[[1,4],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4]=>[4,2,1] [[1,3],[2,4],[5],[6],[7]]=>[[1,6],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6]=>[4,2,1] [[1,2],[3,4],[5],[6],[7]]=>[[1,5],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5]=>[2,2,2,1] [[1,7],[2],[3],[4],[5],[6]]=>[[1,2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2]=>[4,2,1] [[1,6],[2],[3],[4],[5],[7]]=>[[1,3],[2],[4],[5],[6],[7]]=>[7,6,5,4,2,1,3]=>[6,1] [[1,5],[2],[3],[4],[6],[7]]=>[[1,4],[2],[3],[5],[6],[7]]=>[7,6,5,3,2,1,4]=>[7] [[1,4],[2],[3],[5],[6],[7]]=>[[1,5],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5]=>[5,2] [[1,3],[2],[4],[5],[6],[7]]=>[[1,6],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6]=>[3,2,2] [[1,2],[3],[4],[5],[6],[7]]=>[[1,7],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7]=>[2,2,2,1] [[1],[2],[3],[4],[5],[6],[7]]=>[[1],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1]=>[2,2,2,1] [[1,2,3,4,5,6,7,8]]=>[[1,2,3,4,5,6,7,8]]=>[1,2,3,4,5,6,7,8]=>[1,1,1,1,1,1,1,1] [[1,3,4,5,6,7,8],[2]]=>[[1,2,3,4,5,6,7],[8]]=>[8,1,2,3,4,5,6,7]=>[8] [[1,2,4,5,6,7,8],[3]]=>[[1,2,3,4,5,6,8],[7]]=>[7,1,2,3,4,5,6,8]=>[7,1] [[1,2,3,4,6,7,8],[5]]=>[[1,2,3,4,6,7,8],[5]]=>[5,1,2,3,4,6,7,8]=>[5,1,1,1] [[1,2,3,4,5,7,8],[6]]=>[[1,2,3,5,6,7,8],[4]]=>[4,1,2,3,5,6,7,8]=>[4,1,1,1,1] [[1,2,3,4,5,6,8],[7]]=>[[1,2,4,5,6,7,8],[3]]=>[3,1,2,4,5,6,7,8]=>[3,1,1,1,1,1] [[1,2,3,4,5,6,7],[8]]=>[[1,3,4,5,6,7,8],[2]]=>[2,1,3,4,5,6,7,8]=>[2,1,1,1,1,1,1] [[1,2,5,6,7,8],[3,4]]=>[[1,2,3,4,5,6],[7,8]]=>[7,8,1,2,3,4,5,6]=>[4,4] [[1,2,4,6,7,8],[3,5]]=>[[1,2,3,4,6,8],[5,7]]=>[5,7,1,2,3,4,6,8]=>[4,3,1] [[1,2,3,6,7,8],[4,5]]=>[[1,2,3,4,5,8],[6,7]]=>[6,7,1,2,3,4,5,8]=>[7,1] [[1,3,4,5,7,8],[2,6]]=>[[1,2,3,5,6,7],[4,8]]=>[4,8,1,2,3,5,6,7]=>[8] [[1,2,4,5,6,8],[3,7]]=>[[1,2,4,5,6,8],[3,7]]=>[3,7,1,2,4,5,6,8]=>[5,2,1] [[1,2,3,4,6,8],[5,7]]=>[[1,2,4,6,7,8],[3,5]]=>[3,5,1,2,4,6,7,8]=>[3,2,1,1,1] [[1,2,3,4,5,8],[6,7]]=>[[1,2,3,6,7,8],[4,5]]=>[4,5,1,2,3,6,7,8]=>[5,1,1,1] [[1,3,4,5,6,7],[2,8]]=>[[1,3,4,5,6,7],[2,8]]=>[2,8,1,3,4,5,6,7]=>[8] [[1,2,3,4,6,7],[5,8]]=>[[1,3,4,6,7,8],[2,5]]=>[2,5,1,3,4,6,7,8]=>[5,1,1,1] [[1,2,3,4,5,7],[6,8]]=>[[1,3,5,6,7,8],[2,4]]=>[2,4,1,3,5,6,7,8]=>[4,1,1,1,1] [[1,2,3,4,5,6],[7,8]]=>[[1,2,5,6,7,8],[3,4]]=>[3,4,1,2,5,6,7,8]=>[2,2,1,1,1,1] [[1,2,4,6,7,8],[3],[5]]=>[[1,2,3,4,6,8],[5],[7]]=>[7,5,1,2,3,4,6,8]=>[7,1] [[1,2,3,4,7,8],[5],[6]]=>[[1,2,3,6,7,8],[4],[5]]=>[5,4,1,2,3,6,7,8]=>[3,2,1,1,1] [[1,3,4,5,6,8],[2],[7]]=>[[1,2,4,5,6,7],[3],[8]]=>[8,3,1,2,4,5,6,7]=>[8] [[1,2,4,5,6,8],[3],[7]]=>[[1,2,4,5,6,8],[3],[7]]=>[7,3,1,2,4,5,6,8]=>[7,1] [[1,2,3,4,6,8],[5],[7]]=>[[1,2,4,6,7,8],[3],[5]]=>[5,3,1,2,4,6,7,8]=>[5,1,1,1] [[1,2,3,4,5,8],[6],[7]]=>[[1,2,5,6,7,8],[3],[4]]=>[4,3,1,2,5,6,7,8]=>[4,1,1,1,1] [[1,2,3,4,6,7],[5],[8]]=>[[1,3,4,6,7,8],[2],[5]]=>[5,2,1,3,4,6,7,8]=>[4,1,1,1,1] [[1,2,3,4,5,7],[6],[8]]=>[[1,3,5,6,7,8],[2],[4]]=>[4,2,1,3,5,6,7,8]=>[3,1,1,1,1,1] [[1,2,3,4,5,6],[7],[8]]=>[[1,4,5,6,7,8],[2],[3]]=>[3,2,1,4,5,6,7,8]=>[2,1,1,1,1,1,1] [[1,2,3,7,8],[4,5,6]]=>[[1,2,3,4,5],[6,7,8]]=>[6,7,8,1,2,3,4,5]=>[8] [[1,2,4,6,8],[3,5,7]]=>[[1,2,4,6,8],[3,5,7]]=>[3,5,7,1,2,4,6,8]=>[5,2,1] [[1,2,3,6,8],[4,5,7]]=>[[1,2,4,5,8],[3,6,7]]=>[3,6,7,1,2,4,5,8]=>[7,1] [[1,3,4,5,8],[2,6,7]]=>[[1,2,3,6,7],[4,5,8]]=>[4,5,8,1,2,3,6,7]=>[4,2,2] [[1,2,3,4,8],[5,6,7]]=>[[1,2,3,4,8],[5,6,7]]=>[5,6,7,1,2,3,4,8]=>[7,1] [[1,2,5,6,7],[3,4,8]]=>[[1,3,4,5,6],[2,7,8]]=>[2,7,8,1,3,4,5,6]=>[8] [[1,2,3,6,7],[4,5,8]]=>[[1,3,4,5,8],[2,6,7]]=>[2,6,7,1,3,4,5,8]=>[4,3,1] [[1,3,4,5,6],[2,7,8]]=>[[1,2,5,6,7],[3,4,8]]=>[3,4,8,1,2,5,6,7]=>[8] [[1,2,3,4,6],[5,7,8]]=>[[1,2,4,7,8],[3,5,6]]=>[3,5,6,1,2,4,7,8]=>[4,2,1,1] [[1,4,6,7,8],[2,5],[3]]=>[[1,2,3,4,6],[5,7],[8]]=>[8,5,7,1,2,3,4,6]=>[6,2] [[1,3,6,7,8],[2,5],[4]]=>[[1,2,3,4,5],[6,7],[8]]=>[8,6,7,1,2,3,4,5]=>[8] [[1,2,6,7,8],[3,5],[4]]=>[[1,2,3,4,5],[6,8],[7]]=>[7,6,8,1,2,3,4,5]=>[5,3] [[1,2,6,7,8],[3,4],[5]]=>[[1,2,3,4,6],[5,8],[7]]=>[7,5,8,1,2,3,4,6]=>[3,3,2] [[1,4,5,7,8],[2,6],[3]]=>[[1,2,3,5,6],[4,7],[8]]=>[8,4,7,1,2,3,5,6]=>[8] [[1,2,5,7,8],[3,6],[4]]=>[[1,2,3,5,8],[4,6],[7]]=>[7,4,6,1,2,3,5,8]=>[5,2,1] [[1,3,4,7,8],[2,5],[6]]=>[[1,2,3,6,7],[4,8],[5]]=>[5,4,8,1,2,3,6,7]=>[4,4] [[1,2,4,7,8],[3,5],[6]]=>[[1,2,3,6,8],[4,7],[5]]=>[5,4,7,1,2,3,6,8]=>[4,3,1] [[1,2,3,7,8],[4,5],[6]]=>[[1,2,3,5,8],[4,7],[6]]=>[6,4,7,1,2,3,5,8]=>[7,1] [[1,3,5,6,8],[2,7],[4]]=>[[1,2,4,5,7],[3,6],[8]]=>[8,3,6,1,2,4,5,7]=>[8] [[1,3,4,6,8],[2,7],[5]]=>[[1,2,4,6,7],[3,5],[8]]=>[8,3,5,1,2,4,6,7]=>[5,3] [[1,2,4,6,8],[3,7],[5]]=>[[1,2,4,6,8],[3,5],[7]]=>[7,3,5,1,2,4,6,8]=>[4,3,1] [[1,2,3,6,8],[4,7],[5]]=>[[1,2,4,7,8],[3,5],[6]]=>[6,3,5,1,2,4,7,8]=>[3,3,1,1] [[1,2,4,5,8],[3,7],[6]]=>[[1,2,3,6,8],[4,5],[7]]=>[7,4,5,1,2,3,6,8]=>[7,1] [[1,2,3,6,8],[4,5],[7]]=>[[1,2,4,5,8],[3,7],[6]]=>[6,3,7,1,2,4,5,8]=>[4,3,1] [[1,2,3,4,7],[5,8],[6]]=>[[1,3,6,7,8],[2,4],[5]]=>[5,2,4,1,3,6,7,8]=>[4,1,1,1,1] [[1,3,4,5,6],[2,8],[7]]=>[[1,2,5,6,7],[3,4],[8]]=>[8,3,4,1,2,5,6,7]=>[8] [[1,2,4,5,6],[3,8],[7]]=>[[1,2,5,6,8],[3,4],[7]]=>[7,3,4,1,2,5,6,8]=>[7,1] [[1,2,3,4,6],[5,8],[7]]=>[[1,2,6,7,8],[3,4],[5]]=>[5,3,4,1,2,6,7,8]=>[5,1,1,1] [[1,3,5,6,7],[2,4],[8]]=>[[1,3,4,5,7],[2,8],[6]]=>[6,2,8,1,3,4,5,7]=>[4,3,1] [[1,2,3,6,7],[4,5],[8]]=>[[1,3,4,5,8],[2,7],[6]]=>[6,2,7,1,3,4,5,8]=>[3,3,1,1] [[1,3,4,5,6],[2,7],[8]]=>[[1,4,5,6,7],[2,8],[3]]=>[3,2,8,1,4,5,6,7]=>[7,1] [[1,2,3,5,6],[4,7],[8]]=>[[1,4,5,7,8],[2,6],[3]]=>[3,2,6,1,4,5,7,8]=>[5,1,1,1] [[1,2,3,4,6],[5,7],[8]]=>[[1,4,6,7,8],[2,5],[3]]=>[3,2,5,1,4,6,7,8]=>[4,1,1,1,1] [[1,5,6,7,8],[2],[3],[4]]=>[[1,2,3,4,5],[6],[7],[8]]=>[8,7,6,1,2,3,4,5]=>[6,2] [[1,4,6,7,8],[2],[3],[5]]=>[[1,2,3,4,6],[5],[7],[8]]=>[8,7,5,1,2,3,4,6]=>[8] [[1,2,6,7,8],[3],[4],[5]]=>[[1,2,3,4,8],[5],[6],[7]]=>[7,6,5,1,2,3,4,8]=>[4,3,1] [[1,3,5,7,8],[2],[4],[6]]=>[[1,2,3,5,7],[4],[6],[8]]=>[8,6,4,1,2,3,5,7]=>[8] [[1,3,4,6,8],[2],[5],[7]]=>[[1,2,4,6,7],[3],[5],[8]]=>[8,5,3,1,2,4,6,7]=>[5,2,1] [[1,2,4,6,8],[3],[5],[7]]=>[[1,2,4,6,8],[3],[5],[7]]=>[7,5,3,1,2,4,6,8]=>[4,2,1,1] [[1,2,4,5,8],[3],[6],[7]]=>[[1,2,5,6,8],[3],[4],[7]]=>[7,4,3,1,2,5,6,8]=>[6,1,1] [[1,2,3,5,8],[4],[6],[7]]=>[[1,2,5,7,8],[3],[4],[6]]=>[6,4,3,1,2,5,7,8]=>[5,1,1,1] [[1,2,3,4,8],[5],[6],[7]]=>[[1,2,6,7,8],[3],[4],[5]]=>[5,4,3,1,2,6,7,8]=>[4,1,1,1,1] [[1,4,5,6,7],[2],[3],[8]]=>[[1,3,4,5,6],[2],[7],[8]]=>[8,7,2,1,3,4,5,6]=>[4,4] [[1,3,4,5,7],[2],[6],[8]]=>[[1,3,5,6,7],[2],[4],[8]]=>[8,4,2,1,3,5,6,7]=>[8] [[1,2,3,4,7],[5],[6],[8]]=>[[1,3,6,7,8],[2],[4],[5]]=>[5,4,2,1,3,6,7,8]=>[5,1,1,1] [[1,3,4,5,6],[2],[7],[8]]=>[[1,4,5,6,7],[2],[3],[8]]=>[8,3,2,1,4,5,6,7]=>[6,2] [[1,2,3,4,6],[5],[7],[8]]=>[[1,4,6,7,8],[2],[3],[5]]=>[5,3,2,1,4,6,7,8]=>[3,2,1,1,1] [[1,2,3,4,5],[6],[7],[8]]=>[[1,5,6,7,8],[2],[3],[4]]=>[4,3,2,1,5,6,7,8]=>[2,2,1,1,1,1] [[1,3,5,7],[2,4,6,8]]=>[[1,3,5,7],[2,4,6,8]]=>[2,4,6,8,1,3,5,7]=>[6,2] [[1,2,3,7],[4,5,6,8]]=>[[1,3,4,5],[2,6,7,8]]=>[2,6,7,8,1,3,4,5]=>[8] [[1,2,4,6],[3,5,7,8]]=>[[1,2,4,6],[3,5,7,8]]=>[3,5,7,8,1,2,4,6]=>[8] [[1,2,3,6],[4,5,7,8]]=>[[1,2,4,5],[3,6,7,8]]=>[3,6,7,8,1,2,4,5]=>[6,2] [[1,3,4,5],[2,6,7,8]]=>[[1,2,3,7],[4,5,6,8]]=>[4,5,6,8,1,2,3,7]=>[8] [[1,2,3,5],[4,6,7,8]]=>[[1,2,3,5],[4,6,7,8]]=>[4,6,7,8,1,2,3,5]=>[4,2,2] [[1,2,3,4],[5,6,7,8]]=>[[1,2,3,4],[5,6,7,8]]=>[5,6,7,8,1,2,3,4]=>[2,2,2,2] [[1,4,6,8],[2,5,7],[3]]=>[[1,2,4,6],[3,5,7],[8]]=>[8,3,5,7,1,2,4,6]=>[6,2] [[1,2,6,8],[3,4,7],[5]]=>[[1,2,4,6],[3,5,8],[7]]=>[7,3,5,8,1,2,4,6]=>[8] [[1,3,4,8],[2,6,7],[5]]=>[[1,2,3,4],[5,6,7],[8]]=>[8,5,6,7,1,2,3,4]=>[8] [[1,2,4,8],[3,6,7],[5]]=>[[1,2,3,4],[5,6,8],[7]]=>[7,5,6,8,1,2,3,4]=>[6,2] [[1,2,3,8],[4,6,7],[5]]=>[[1,2,3,4],[5,7,8],[6]]=>[6,5,7,8,1,2,3,4]=>[4,2,2] [[1,2,5,8],[3,4,7],[6]]=>[[1,2,3,6],[4,5,8],[7]]=>[7,4,5,8,1,2,3,6]=>[4,4] [[1,2,4,8],[3,5,7],[6]]=>[[1,2,3,6],[4,7,8],[5]]=>[5,4,7,8,1,2,3,6]=>[4,2,2] [[1,2,3,8],[4,5,7],[6]]=>[[1,2,3,5],[4,7,8],[6]]=>[6,4,7,8,1,2,3,5]=>[6,2] [[1,2,5,8],[3,4,6],[7]]=>[[1,2,5,6],[3,7,8],[4]]=>[4,3,7,8,1,2,5,6]=>[8] [[1,2,3,8],[4,5,6],[7]]=>[[1,2,4,5],[3,7,8],[6]]=>[6,3,7,8,1,2,4,5]=>[8] [[1,3,6,7],[2,5,8],[4]]=>[[1,3,4,5],[2,6,7],[8]]=>[8,2,6,7,1,3,4,5]=>[3,2,2,1] [[1,3,5,7],[2,4,8],[6]]=>[[1,3,5,7],[2,4,8],[6]]=>[6,2,4,8,1,3,5,7]=>[7,1] [[1,2,5,7],[3,4,8],[6]]=>[[1,3,5,6],[2,4,8],[7]]=>[7,2,4,8,1,3,5,6]=>[4,3,1] [[1,3,4,7],[2,5,8],[6]]=>[[1,3,6,7],[2,4,8],[5]]=>[5,2,4,8,1,3,6,7]=>[5,2,1] [[1,3,4,5],[2,7,8],[6]]=>[[1,2,3,7],[4,5,6],[8]]=>[8,4,5,6,1,2,3,7]=>[5,3] [[1,2,3,4],[5,7,8],[6]]=>[[1,2,3,8],[4,6,7],[5]]=>[5,4,6,7,1,2,3,8]=>[5,2,1] [[1,2,3,4],[5,6,8],[7]]=>[[1,2,4,8],[3,6,7],[5]]=>[5,3,6,7,1,2,4,8]=>[3,2,2,1] [[1,3,4,7],[2,5,6],[8]]=>[[1,3,4,7],[2,6,8],[5]]=>[5,2,6,8,1,3,4,7]=>[3,2,2,1] [[1,2,3,7],[4,5,6],[8]]=>[[1,3,4,5],[2,7,8],[6]]=>[6,2,7,8,1,3,4,5]=>[7,1] [[1,2,5,6],[3,4,7],[8]]=>[[1,4,5,6],[2,7,8],[3]]=>[3,2,7,8,1,4,5,6]=>[4,3,1] [[1,2,4,6],[3,5,7],[8]]=>[[1,4,6,8],[2,5,7],[3]]=>[3,2,5,7,1,4,6,8]=>[3,3,1,1] [[1,2,3,5],[4,6,7],[8]]=>[[1,3,5,8],[2,6,7],[4]]=>[4,2,6,7,1,3,5,8]=>[4,2,1,1] [[1,2,3,4],[5,6,7],[8]]=>[[1,3,4,8],[2,6,7],[5]]=>[5,2,6,7,1,3,4,8]=>[2,2,2,1,1] [[1,2,7,8],[3,5],[4,6]]=>[[1,2,3,5],[4,6],[7,8]]=>[7,8,4,6,1,2,3,5]=>[8] [[1,3,7,8],[2,4],[5,6]]=>[[1,2,3,4],[5,7],[6,8]]=>[6,8,5,7,1,2,3,4]=>[8] [[1,2,7,8],[3,4],[5,6]]=>[[1,2,3,4],[5,6],[7,8]]=>[7,8,5,6,1,2,3,4]=>[4,4] [[1,4,6,8],[2,5],[3,7]]=>[[1,2,4,6],[3,7],[5,8]]=>[5,8,3,7,1,2,4,6]=>[3,2,2,1] [[1,3,6,8],[2,4],[5,7]]=>[[1,2,4,7],[3,5],[6,8]]=>[6,8,3,5,1,2,4,7]=>[7,1] [[1,2,6,8],[3,4],[5,7]]=>[[1,2,4,6],[3,5],[7,8]]=>[7,8,3,5,1,2,4,6]=>[4,3,1] [[1,4,5,8],[2,6],[3,7]]=>[[1,2,5,6],[3,7],[4,8]]=>[4,8,3,7,1,2,5,6]=>[4,3,1] [[1,3,4,8],[2,6],[5,7]]=>[[1,2,4,7],[3,6],[5,8]]=>[5,8,3,6,1,2,4,7]=>[5,2,1] [[1,4,6,7],[2,5],[3,8]]=>[[1,3,4,6],[2,7],[5,8]]=>[5,8,2,7,1,3,4,6]=>[4,2,2] [[1,3,6,7],[2,5],[4,8]]=>[[1,3,4,5],[2,7],[6,8]]=>[6,8,2,7,1,3,4,5]=>[6,2] [[1,2,6,7],[3,4],[5,8]]=>[[1,3,4,6],[2,5],[7,8]]=>[7,8,2,5,1,3,4,6]=>[4,4] [[1,4,5,7],[2,6],[3,8]]=>[[1,3,5,6],[2,7],[4,8]]=>[4,8,2,7,1,3,5,6]=>[4,4] [[1,2,5,7],[3,4],[6,8]]=>[[1,3,5,6],[2,4],[7,8]]=>[7,8,2,4,1,3,5,6]=>[4,3,1] [[1,2,4,7],[3,5],[6,8]]=>[[1,3,6,8],[2,4],[5,7]]=>[5,7,2,4,1,3,6,8]=>[4,2,1,1] [[1,4,5,6],[2,7],[3,8]]=>[[1,4,5,6],[2,7],[3,8]]=>[3,8,2,7,1,4,5,6]=>[8] [[1,2,5,6],[3,7],[4,8]]=>[[1,4,5,8],[2,6],[3,7]]=>[3,7,2,6,1,4,5,8]=>[5,2,1] [[1,2,3,5],[4,7],[6,8]]=>[[1,3,7,8],[2,5],[4,6]]=>[4,6,2,5,1,3,7,8]=>[3,3,1,1] [[1,2,3,4],[5,7],[6,8]]=>[[1,3,7,8],[2,4],[5,6]]=>[5,6,2,4,1,3,7,8]=>[3,2,1,1,1] [[1,2,5,6],[3,4],[7,8]]=>[[1,2,5,6],[3,4],[7,8]]=>[7,8,3,4,1,2,5,6]=>[3,3,1,1] [[1,3,4,6],[2,5],[7,8]]=>[[1,2,6,7],[3,4],[5,8]]=>[5,8,3,4,1,2,6,7]=>[4,2,1,1] [[1,2,4,5],[3,6],[7,8]]=>[[1,2,6,8],[3,5],[4,7]]=>[4,7,3,5,1,2,6,8]=>[3,3,1,1] [[1,2,3,5],[4,6],[7,8]]=>[[1,2,7,8],[3,5],[4,6]]=>[4,6,3,5,1,2,7,8]=>[3,2,1,1,1] [[1,2,3,4],[5,6],[7,8]]=>[[1,2,7,8],[3,4],[5,6]]=>[5,6,3,4,1,2,7,8]=>[2,2,1,1,1,1] [[1,5,7,8],[2,6],[3],[4]]=>[[1,2,3,5],[4,6],[7],[8]]=>[8,7,4,6,1,2,3,5]=>[5,3] [[1,4,7,8],[2,6],[3],[5]]=>[[1,2,3,4],[5,6],[7],[8]]=>[8,7,5,6,1,2,3,4]=>[8] [[1,3,7,8],[2,6],[4],[5]]=>[[1,2,3,4],[5,7],[6],[8]]=>[8,6,5,7,1,2,3,4]=>[6,2] [[1,2,7,8],[3,6],[4],[5]]=>[[1,2,3,4],[5,8],[6],[7]]=>[7,6,5,8,1,2,3,4]=>[4,2,2] [[1,5,6,8],[2,7],[3],[4]]=>[[1,2,4,5],[3,6],[7],[8]]=>[8,7,3,6,1,2,4,5]=>[4,3,1] [[1,4,6,8],[2,7],[3],[5]]=>[[1,2,4,6],[3,5],[7],[8]]=>[8,7,3,5,1,2,4,6]=>[7,1] [[1,2,6,8],[3,7],[4],[5]]=>[[1,2,4,8],[3,5],[6],[7]]=>[7,6,3,5,1,2,4,8]=>[4,2,1,1] [[1,4,5,8],[2,7],[3],[6]]=>[[1,2,3,6],[4,5],[7],[8]]=>[8,7,4,5,1,2,3,6]=>[8] [[1,4,6,8],[2,5],[3],[7]]=>[[1,2,4,6],[3,7],[5],[8]]=>[8,5,3,7,1,2,4,6]=>[5,2,1] [[1,3,6,8],[2,5],[4],[7]]=>[[1,2,4,5],[3,7],[6],[8]]=>[8,6,3,7,1,2,4,5]=>[3,2,2,1] [[1,3,6,8],[2,4],[5],[7]]=>[[1,2,4,7],[3,8],[5],[6]]=>[6,5,3,8,1,2,4,7]=>[4,3,1] [[1,2,6,8],[3,4],[5],[7]]=>[[1,2,4,6],[3,8],[5],[7]]=>[7,5,3,8,1,2,4,6]=>[7,1] [[1,2,5,8],[3,6],[4],[7]]=>[[1,2,5,8],[3,6],[4],[7]]=>[7,4,3,6,1,2,5,8]=>[3,3,1,1] [[1,3,4,8],[2,6],[5],[7]]=>[[1,2,4,7],[3,6],[5],[8]]=>[8,5,3,6,1,2,4,7]=>[7,1] [[1,2,3,8],[4,6],[5],[7]]=>[[1,2,4,8],[3,7],[5],[6]]=>[6,5,3,7,1,2,4,8]=>[4,2,1,1] [[1,3,5,8],[2,4],[6],[7]]=>[[1,2,5,7],[3,8],[4],[6]]=>[6,4,3,8,1,2,5,7]=>[7,1] [[1,2,3,8],[4,5],[6],[7]]=>[[1,2,5,8],[3,7],[4],[6]]=>[6,4,3,7,1,2,5,8]=>[6,1,1] [[1,5,6,7],[2,8],[3],[4]]=>[[1,3,4,5],[2,6],[7],[8]]=>[8,7,2,6,1,3,4,5]=>[5,3] [[1,4,6,7],[2,8],[3],[5]]=>[[1,3,4,6],[2,5],[7],[8]]=>[8,7,2,5,1,3,4,6]=>[8] [[1,3,6,7],[2,8],[4],[5]]=>[[1,3,4,7],[2,5],[6],[8]]=>[8,6,2,5,1,3,4,7]=>[5,3] [[1,4,5,7],[2,8],[3],[6]]=>[[1,3,5,6],[2,4],[7],[8]]=>[8,7,2,4,1,3,5,6]=>[7,1] [[1,3,5,7],[2,8],[4],[6]]=>[[1,3,5,7],[2,4],[6],[8]]=>[8,6,2,4,1,3,5,7]=>[4,3,1] [[1,2,3,7],[4,8],[5],[6]]=>[[1,3,7,8],[2,4],[5],[6]]=>[6,5,2,4,1,3,7,8]=>[5,1,1,1] [[1,4,5,6],[2,8],[3],[7]]=>[[1,2,5,6],[3,4],[7],[8]]=>[8,7,3,4,1,2,5,6]=>[6,1,1] [[1,3,5,6],[2,8],[4],[7]]=>[[1,2,5,7],[3,4],[6],[8]]=>[8,6,3,4,1,2,5,7]=>[4,2,1,1] [[1,3,4,6],[2,8],[5],[7]]=>[[1,2,6,7],[3,4],[5],[8]]=>[8,5,3,4,1,2,6,7]=>[6,1,1] [[1,2,3,5],[4,8],[6],[7]]=>[[1,2,7,8],[3,5],[4],[6]]=>[6,4,3,5,1,2,7,8]=>[5,1,1,1] [[1,2,3,4],[5,8],[6],[7]]=>[[1,2,7,8],[3,6],[4],[5]]=>[5,4,3,6,1,2,7,8]=>[3,2,1,1,1] [[1,4,6,7],[2,5],[3],[8]]=>[[1,3,4,6],[2,7],[5],[8]]=>[8,5,2,7,1,3,4,6]=>[6,2] [[1,2,6,7],[3,5],[4],[8]]=>[[1,3,4,5],[2,8],[6],[7]]=>[7,6,2,8,1,3,4,5]=>[5,3] [[1,3,6,7],[2,4],[5],[8]]=>[[1,3,4,7],[2,8],[5],[6]]=>[6,5,2,8,1,3,4,7]=>[5,3] [[1,4,5,7],[2,6],[3],[8]]=>[[1,3,5,6],[2,7],[4],[8]]=>[8,4,2,7,1,3,5,6]=>[8] [[1,3,5,7],[2,6],[4],[8]]=>[[1,3,5,7],[2,6],[4],[8]]=>[8,4,2,6,1,3,5,7]=>[4,4] [[1,2,5,7],[3,4],[6],[8]]=>[[1,3,5,6],[2,8],[4],[7]]=>[7,4,2,8,1,3,5,6]=>[5,3] [[1,4,5,6],[2,7],[3],[8]]=>[[1,4,5,6],[2,7],[3],[8]]=>[8,3,2,7,1,4,5,6]=>[6,2] [[1,3,5,6],[2,7],[4],[8]]=>[[1,4,5,7],[2,6],[3],[8]]=>[8,3,2,6,1,4,5,7]=>[4,2,2] [[1,2,5,6],[3,7],[4],[8]]=>[[1,4,5,8],[2,6],[3],[7]]=>[7,3,2,6,1,4,5,8]=>[3,2,2,1] [[1,2,4,6],[3,7],[5],[8]]=>[[1,4,6,8],[2,5],[3],[7]]=>[7,3,2,5,1,4,6,8]=>[5,2,1] [[1,2,3,4],[5,7],[6],[8]]=>[[1,3,7,8],[2,6],[4],[5]]=>[5,4,2,6,1,3,7,8]=>[4,2,1,1] [[1,2,5,6],[3,4],[7],[8]]=>[[1,4,5,6],[2,8],[3],[7]]=>[7,3,2,8,1,4,5,6]=>[3,3,2] [[1,2,3,6],[4,5],[7],[8]]=>[[1,4,5,8],[2,7],[3],[6]]=>[6,3,2,7,1,4,5,8]=>[5,2,1] [[1,3,4,5],[2,6],[7],[8]]=>[[1,5,6,7],[2,8],[3],[4]]=>[4,3,2,8,1,5,6,7]=>[6,2] [[1,2,4,5],[3,6],[7],[8]]=>[[1,5,6,8],[2,7],[3],[4]]=>[4,3,2,7,1,5,6,8]=>[5,2,1] [[1,2,3,5],[4,6],[7],[8]]=>[[1,5,7,8],[2,6],[3],[4]]=>[4,3,2,6,1,5,7,8]=>[4,2,1,1] [[1,2,3,4],[5,6],[7],[8]]=>[[1,4,7,8],[2,6],[3],[5]]=>[5,3,2,6,1,4,7,8]=>[2,2,2,1,1] [[1,6,7,8],[2],[3],[4],[5]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[8,7,6,5,1,2,3,4]=>[4,4] [[1,5,7,8],[2],[3],[4],[6]]=>[[1,2,3,5],[4],[6],[7],[8]]=>[8,7,6,4,1,2,3,5]=>[4,3,1] [[1,2,7,8],[3],[4],[5],[6]]=>[[1,2,3,8],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3,8]=>[4,2,1,1] [[1,5,6,8],[2],[3],[4],[7]]=>[[1,2,4,5],[3],[6],[7],[8]]=>[8,7,6,3,1,2,4,5]=>[5,3] [[1,4,6,8],[2],[3],[5],[7]]=>[[1,2,4,6],[3],[5],[7],[8]]=>[8,7,5,3,1,2,4,6]=>[8] [[1,2,3,8],[4],[5],[6],[7]]=>[[1,2,7,8],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7,8]=>[4,2,1,1] [[1,5,6,7],[2],[3],[4],[8]]=>[[1,3,4,5],[2],[6],[7],[8]]=>[8,7,6,2,1,3,4,5]=>[3,3,2] [[1,4,6,7],[2],[3],[5],[8]]=>[[1,3,4,6],[2],[5],[7],[8]]=>[8,7,5,2,1,3,4,6]=>[5,3] [[1,3,6,7],[2],[4],[5],[8]]=>[[1,3,4,7],[2],[5],[6],[8]]=>[8,6,5,2,1,3,4,7]=>[8] [[1,2,6,7],[3],[4],[5],[8]]=>[[1,3,4,8],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4,8]=>[7,1] [[1,3,5,7],[2],[4],[6],[8]]=>[[1,3,5,7],[2],[4],[6],[8]]=>[8,6,4,2,1,3,5,7]=>[4,4] [[1,2,5,7],[3],[4],[6],[8]]=>[[1,3,5,8],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5,8]=>[4,3,1] [[1,3,4,7],[2],[5],[6],[8]]=>[[1,3,6,7],[2],[4],[5],[8]]=>[8,5,4,2,1,3,6,7]=>[8] [[1,4,5,6],[2],[3],[7],[8]]=>[[1,4,5,6],[2],[3],[7],[8]]=>[8,7,3,2,1,4,5,6]=>[7,1] [[1,3,5,6],[2],[4],[7],[8]]=>[[1,4,5,7],[2],[3],[6],[8]]=>[8,6,3,2,1,4,5,7]=>[4,3,1] [[1,2,5,6],[3],[4],[7],[8]]=>[[1,4,5,8],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5,8]=>[3,3,1,1] [[1,3,4,6],[2],[5],[7],[8]]=>[[1,4,6,7],[2],[3],[5],[8]]=>[8,5,3,2,1,4,6,7]=>[7,1] [[1,2,4,6],[3],[5],[7],[8]]=>[[1,4,6,8],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6,8]=>[6,1,1] [[1,3,4,5],[2],[6],[7],[8]]=>[[1,5,6,7],[2],[3],[4],[8]]=>[8,4,3,2,1,5,6,7]=>[5,2,1] [[1,2,3,5],[4],[6],[7],[8]]=>[[1,5,7,8],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7,8]=>[3,2,1,1,1] [[1,2,3,4],[5],[6],[7],[8]]=>[[1,6,7,8],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8]=>[2,2,1,1,1,1] [[1,2,7],[3,5,8],[4,6]]=>[[1,3,5],[2,4,6],[7,8]]=>[7,8,2,4,6,1,3,5]=>[7,1] [[1,3,7],[2,4,8],[5,6]]=>[[1,3,4],[2,5,7],[6,8]]=>[6,8,2,5,7,1,3,4]=>[6,2] [[1,2,7],[3,4,8],[5,6]]=>[[1,3,4],[2,5,6],[7,8]]=>[7,8,2,5,6,1,3,4]=>[8] [[1,2,6],[3,5,8],[4,7]]=>[[1,2,5],[3,4,6],[7,8]]=>[7,8,3,4,6,1,2,5]=>[6,1,1] [[1,2,6],[3,4,8],[5,7]]=>[[1,2,4],[3,5,6],[7,8]]=>[7,8,3,5,6,1,2,4]=>[7,1] [[1,2,5],[3,6,8],[4,7]]=>[[1,2,5],[3,6,8],[4,7]]=>[4,7,3,6,8,1,2,5]=>[3,2,2,1] [[1,2,3],[4,6,8],[5,7]]=>[[1,2,4],[3,5,8],[6,7]]=>[6,7,3,5,8,1,2,4]=>[3,2,2,1] [[1,3,5],[2,4,8],[6,7]]=>[[1,2,3],[4,5,7],[6,8]]=>[6,8,4,5,7,1,2,3]=>[6,2] [[1,4,6],[2,5,7],[3,8]]=>[[1,4,6],[2,5,7],[3,8]]=>[3,8,2,5,7,1,4,6]=>[5,3] [[1,3,6],[2,5,7],[4,8]]=>[[1,4,5],[2,6,7],[3,8]]=>[3,8,2,6,7,1,4,5]=>[8] [[1,3,4],[2,5,7],[6,8]]=>[[1,3,7],[2,4,8],[5,6]]=>[5,6,2,4,8,1,3,7]=>[7,1] [[1,5,7],[2,6,8],[3],[4]]=>[[1,3,5],[2,4,6],[7],[8]]=>[8,7,2,4,6,1,3,5]=>[4,3,1] [[1,4,7],[2,6,8],[3],[5]]=>[[1,3,4],[2,5,6],[7],[8]]=>[8,7,2,5,6,1,3,4]=>[5,3] [[1,3,7],[2,6,8],[4],[5]]=>[[1,3,4],[2,5,7],[6],[8]]=>[8,6,2,5,7,1,3,4]=>[8] [[1,3,7],[2,4,8],[5],[6]]=>[[1,3,7],[2,4,8],[5],[6]]=>[6,5,2,4,8,1,3,7]=>[5,2,1] [[1,5,6],[2,7,8],[3],[4]]=>[[1,2,5],[3,4,6],[7],[8]]=>[8,7,3,4,6,1,2,5]=>[4,2,1,1] [[1,3,6],[2,7,8],[4],[5]]=>[[1,2,4],[3,5,7],[6],[8]]=>[8,6,3,5,7,1,2,4]=>[7,1] [[1,2,3],[4,7,8],[5],[6]]=>[[1,2,3],[4,7,8],[5],[6]]=>[6,5,4,7,8,1,2,3]=>[6,2] [[1,3,4],[2,6,8],[5],[7]]=>[[1,2,4],[3,6,7],[5],[8]]=>[8,5,3,6,7,1,2,4]=>[4,3,1] [[1,2,4],[3,6,8],[5],[7]]=>[[1,2,4],[3,6,8],[5],[7]]=>[7,5,3,6,8,1,2,4]=>[7,1] [[1,3,5],[2,4,8],[6],[7]]=>[[1,2,7],[3,5,8],[4],[6]]=>[6,4,3,5,8,1,2,7]=>[5,2,1] [[1,3,4],[2,5,8],[6],[7]]=>[[1,2,7],[3,6,8],[4],[5]]=>[5,4,3,6,8,1,2,7]=>[7,1] [[1,4,5],[2,6,7],[3],[8]]=>[[1,3,6],[2,5,7],[4],[8]]=>[8,4,2,5,7,1,3,6]=>[5,3] [[1,3,4],[2,6,7],[5],[8]]=>[[1,3,4],[2,6,7],[5],[8]]=>[8,5,2,6,7,1,3,4]=>[4,4] [[1,2,3],[4,6,7],[5],[8]]=>[[1,3,4],[2,7,8],[5],[6]]=>[6,5,2,7,8,1,3,4]=>[6,2] [[1,2,5],[3,4,7],[6],[8]]=>[[1,3,6],[2,5,8],[4],[7]]=>[7,4,2,5,8,1,3,6]=>[8] [[1,3,5],[2,4,6],[7],[8]]=>[[1,5,7],[2,6,8],[3],[4]]=>[4,3,2,6,8,1,5,7]=>[3,3,2] [[1,2,5],[3,4,6],[7],[8]]=>[[1,5,6],[2,7,8],[3],[4]]=>[4,3,2,7,8,1,5,6]=>[6,2] [[1,2,3],[4,5,6],[7],[8]]=>[[1,4,5],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5]=>[2,2,2,2] [[1,5,8],[2,6],[3,7],[4]]=>[[1,2,5],[3,6],[4,7],[8]]=>[8,4,7,3,6,1,2,5]=>[4,4] [[1,3,8],[2,6],[4,7],[5]]=>[[1,2,4],[3,5],[6,7],[8]]=>[8,6,7,3,5,1,2,4]=>[7,1] [[1,3,8],[2,5],[4,7],[6]]=>[[1,2,3],[4,5],[6,7],[8]]=>[8,6,7,4,5,1,2,3]=>[6,1,1] [[1,2,8],[3,4],[5,7],[6]]=>[[1,2,3],[4,6],[5,8],[7]]=>[7,5,8,4,6,1,2,3]=>[5,2,1] [[1,5,7],[2,6],[3,8],[4]]=>[[1,3,5],[2,6],[4,7],[8]]=>[8,4,7,2,6,1,3,5]=>[4,2,2] [[1,4,7],[2,6],[3,8],[5]]=>[[1,3,4],[2,6],[5,7],[8]]=>[8,5,7,2,6,1,3,4]=>[6,2] [[1,3,7],[2,6],[4,8],[5]]=>[[1,3,4],[2,5],[6,7],[8]]=>[8,6,7,2,5,1,3,4]=>[5,2,1] [[1,3,7],[2,5],[4,8],[6]]=>[[1,3,5],[2,4],[6,7],[8]]=>[8,6,7,2,4,1,3,5]=>[6,2] [[1,2,7],[3,4],[5,8],[6]]=>[[1,3,6],[2,4],[5,8],[7]]=>[7,5,8,2,4,1,3,6]=>[5,3] [[1,5,6],[2,7],[3,8],[4]]=>[[1,4,5],[2,6],[3,7],[8]]=>[8,3,7,2,6,1,4,5]=>[4,4] [[1,4,6],[2,7],[3,8],[5]]=>[[1,4,6],[2,5],[3,7],[8]]=>[8,3,7,2,5,1,4,6]=>[4,3,1] [[1,3,6],[2,7],[4,8],[5]]=>[[1,4,7],[2,5],[3,6],[8]]=>[8,3,6,2,5,1,4,7]=>[7,1] [[1,2,6],[3,7],[4,8],[5]]=>[[1,4,8],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4,8]=>[6,1,1] [[1,3,5],[2,7],[4,8],[6]]=>[[1,3,7],[2,5],[4,6],[8]]=>[8,4,6,2,5,1,3,7]=>[5,2,1] [[1,4,5],[2,6],[3,8],[7]]=>[[1,2,6],[3,5],[4,7],[8]]=>[8,4,7,3,5,1,2,6]=>[4,3,1] [[1,2,3],[4,6],[5,8],[7]]=>[[1,2,8],[3,4],[5,7],[6]]=>[6,5,7,3,4,1,2,8]=>[5,2,1] [[1,3,5],[2,4],[6,8],[7]]=>[[1,2,7],[3,5],[4,8],[6]]=>[6,4,8,3,5,1,2,7]=>[5,2,1] [[1,2,5],[3,4],[6,8],[7]]=>[[1,2,6],[3,5],[4,8],[7]]=>[7,4,8,3,5,1,2,6]=>[7,1] [[1,4,7],[2,5],[3,6],[8]]=>[[1,3,6],[2,7],[4,8],[5]]=>[5,4,8,2,7,1,3,6]=>[6,2] [[1,3,7],[2,5],[4,6],[8]]=>[[1,3,5],[2,7],[4,8],[6]]=>[6,4,8,2,7,1,3,5]=>[4,2,2] [[1,2,7],[3,4],[5,6],[8]]=>[[1,3,4],[2,6],[5,8],[7]]=>[7,5,8,2,6,1,3,4]=>[8] [[1,4,6],[2,5],[3,7],[8]]=>[[1,4,6],[2,7],[3,8],[5]]=>[5,3,8,2,7,1,4,6]=>[8] [[1,2,6],[3,4],[5,7],[8]]=>[[1,4,6],[2,5],[3,8],[7]]=>[7,3,8,2,5,1,4,6]=>[7,1] [[1,4,5],[2,6],[3,7],[8]]=>[[1,5,6],[2,7],[3,8],[4]]=>[4,3,8,2,7,1,5,6]=>[6,2] [[1,3,5],[2,6],[4,7],[8]]=>[[1,5,7],[2,6],[3,8],[4]]=>[4,3,8,2,6,1,5,7]=>[8] [[1,2,5],[3,6],[4,7],[8]]=>[[1,5,8],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5,8]=>[7,1] [[1,3,4],[2,6],[5,7],[8]]=>[[1,4,7],[2,6],[3,8],[5]]=>[5,3,8,2,6,1,4,7]=>[5,3] [[1,2,4],[3,6],[5,7],[8]]=>[[1,4,8],[2,6],[3,7],[5]]=>[5,3,7,2,6,1,4,8]=>[4,3,1] [[1,3,4],[2,5],[6,7],[8]]=>[[1,3,7],[2,6],[4,8],[5]]=>[5,4,8,2,6,1,3,7]=>[3,3,2] [[1,2,3],[4,5],[6,7],[8]]=>[[1,3,8],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3,8]=>[2,2,2,1,1] [[1,6,8],[2,7],[3],[4],[5]]=>[[1,2,4],[3,5],[6],[7],[8]]=>[8,7,6,3,5,1,2,4]=>[5,2,1] [[1,4,8],[2,7],[3],[5],[6]]=>[[1,2,3],[4,6],[5],[7],[8]]=>[8,7,5,4,6,1,2,3]=>[5,2,1] [[1,3,8],[2,7],[4],[5],[6]]=>[[1,2,3],[4,7],[5],[6],[8]]=>[8,6,5,4,7,1,2,3]=>[7,1] [[1,2,8],[3,7],[4],[5],[6]]=>[[1,2,3],[4,8],[5],[6],[7]]=>[7,6,5,4,8,1,2,3]=>[4,3,1] [[1,5,8],[2,6],[3],[4],[7]]=>[[1,2,5],[3,6],[4],[7],[8]]=>[8,7,4,3,6,1,2,5]=>[4,2,2] [[1,2,8],[3,5],[4],[6],[7]]=>[[1,2,5],[3,8],[4],[6],[7]]=>[7,6,4,3,8,1,2,5]=>[4,2,2] [[1,3,8],[2,4],[5],[6],[7]]=>[[1,2,7],[3,8],[4],[5],[6]]=>[6,5,4,3,8,1,2,7]=>[4,2,2] [[1,6,7],[2,8],[3],[4],[5]]=>[[1,3,4],[2,5],[6],[7],[8]]=>[8,7,6,2,5,1,3,4]=>[7,1] [[1,5,7],[2,8],[3],[4],[6]]=>[[1,3,5],[2,4],[6],[7],[8]]=>[8,7,6,2,4,1,3,5]=>[8] [[1,3,7],[2,8],[4],[5],[6]]=>[[1,3,7],[2,4],[5],[6],[8]]=>[8,6,5,2,4,1,3,7]=>[8] [[1,5,6],[2,8],[3],[4],[7]]=>[[1,2,5],[3,4],[6],[7],[8]]=>[8,7,6,3,4,1,2,5]=>[6,2] [[1,4,6],[2,8],[3],[5],[7]]=>[[1,2,6],[3,4],[5],[7],[8]]=>[8,7,5,3,4,1,2,6]=>[3,3,2] [[1,2,3],[4,8],[5],[6],[7]]=>[[1,2,8],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2,8]=>[3,2,2,1] [[1,5,7],[2,6],[3],[4],[8]]=>[[1,3,5],[2,6],[4],[7],[8]]=>[8,7,4,2,6,1,3,5]=>[4,4] [[1,4,7],[2,6],[3],[5],[8]]=>[[1,3,4],[2,6],[5],[7],[8]]=>[8,7,5,2,6,1,3,4]=>[8] [[1,5,6],[2,7],[3],[4],[8]]=>[[1,4,5],[2,6],[3],[7],[8]]=>[8,7,3,2,6,1,4,5]=>[4,3,1] [[1,3,4],[2,7],[5],[6],[8]]=>[[1,3,7],[2,6],[4],[5],[8]]=>[8,5,4,2,6,1,3,7]=>[8] [[1,2,3],[4,7],[5],[6],[8]]=>[[1,3,8],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3,8]=>[5,2,1] [[1,4,6],[2,5],[3],[7],[8]]=>[[1,4,6],[2,7],[3],[5],[8]]=>[8,5,3,2,7,1,4,6]=>[4,3,1] [[1,3,6],[2,5],[4],[7],[8]]=>[[1,4,5],[2,7],[3],[6],[8]]=>[8,6,3,2,7,1,4,5]=>[7,1] [[1,2,3],[4,6],[5],[7],[8]]=>[[1,4,8],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4,8]=>[4,2,1,1] [[1,3,4],[2,5],[6],[7],[8]]=>[[1,6,7],[2,8],[3],[4],[5]]=>[5,4,3,2,8,1,6,7]=>[5,2,1] [[1,2,4],[3,5],[6],[7],[8]]=>[[1,6,8],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6,8]=>[4,2,1,1] [[1,2,3],[4,5],[6],[7],[8]]=>[[1,5,8],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5,8]=>[2,2,2,1,1] [[1,7,8],[2],[3],[4],[5],[6]]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,1,2,3]=>[4,2,2] [[1,6,8],[2],[3],[4],[5],[7]]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[8,7,6,5,3,1,2,4]=>[6,2] [[1,5,8],[2],[3],[4],[6],[7]]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,1,2,5]=>[5,2,1] [[1,4,8],[2],[3],[5],[6],[7]]=>[[1,2,6],[3],[4],[5],[7],[8]]=>[8,7,5,4,3,1,2,6]=>[3,2,2,1] [[1,6,7],[2],[3],[4],[5],[8]]=>[[1,3,4],[2],[5],[6],[7],[8]]=>[8,7,6,5,2,1,3,4]=>[8] [[1,5,7],[2],[3],[4],[6],[8]]=>[[1,3,5],[2],[4],[6],[7],[8]]=>[8,7,6,4,2,1,3,5]=>[7,1] [[1,3,7],[2],[4],[5],[6],[8]]=>[[1,3,7],[2],[4],[5],[6],[8]]=>[8,6,5,4,2,1,3,7]=>[7,1] [[1,5,6],[2],[3],[4],[7],[8]]=>[[1,4,5],[2],[3],[6],[7],[8]]=>[8,7,6,3,2,1,4,5]=>[8] [[1,4,6],[2],[3],[5],[7],[8]]=>[[1,4,6],[2],[3],[5],[7],[8]]=>[8,7,5,3,2,1,4,6]=>[5,3] [[1,3,6],[2],[4],[5],[7],[8]]=>[[1,4,7],[2],[3],[5],[6],[8]]=>[8,6,5,3,2,1,4,7]=>[8] [[1,3,5],[2],[4],[6],[7],[8]]=>[[1,5,7],[2],[3],[4],[6],[8]]=>[8,6,4,3,2,1,5,7]=>[6,2] [[1,5],[2,6],[3,7],[4,8]]=>[[1,5],[2,6],[3,7],[4,8]]=>[4,8,3,7,2,6,1,5]=>[3,3,1,1] [[1,4],[2,6],[3,7],[5,8]]=>[[1,4],[2,6],[3,7],[5,8]]=>[5,8,3,7,2,6,1,4]=>[6,1,1] [[1,3],[2,6],[4,7],[5,8]]=>[[1,4],[2,5],[3,7],[6,8]]=>[6,8,3,7,2,5,1,4]=>[7,1] [[1,2],[3,6],[4,7],[5,8]]=>[[1,4],[2,5],[3,6],[7,8]]=>[7,8,3,6,2,5,1,4]=>[5,2,1] [[1,4],[2,5],[3,7],[6,8]]=>[[1,3],[2,6],[4,7],[5,8]]=>[5,8,4,7,2,6,1,3]=>[7,1] [[1,3],[2,5],[4,7],[6,8]]=>[[1,3],[2,5],[4,7],[6,8]]=>[6,8,4,7,2,5,1,3]=>[8] [[1,2],[3,5],[4,7],[6,8]]=>[[1,3],[2,5],[4,6],[7,8]]=>[7,8,4,6,2,5,1,3]=>[6,2] [[1,3],[2,4],[5,7],[6,8]]=>[[1,3],[2,4],[5,7],[6,8]]=>[6,8,5,7,2,4,1,3]=>[4,4] [[1,2],[3,4],[5,7],[6,8]]=>[[1,3],[2,4],[5,6],[7,8]]=>[7,8,5,6,2,4,1,3]=>[4,2,2] [[1,4],[2,5],[3,6],[7,8]]=>[[1,2],[3,6],[4,7],[5,8]]=>[5,8,4,7,3,6,1,2]=>[5,2,1] [[1,3],[2,5],[4,6],[7,8]]=>[[1,2],[3,5],[4,7],[6,8]]=>[6,8,4,7,3,5,1,2]=>[6,2] [[1,2],[3,5],[4,6],[7,8]]=>[[1,2],[3,5],[4,6],[7,8]]=>[7,8,4,6,3,5,1,2]=>[4,2,2] [[1,3],[2,4],[5,6],[7,8]]=>[[1,2],[3,4],[5,7],[6,8]]=>[6,8,5,7,3,4,1,2]=>[4,2,2] [[1,2],[3,4],[5,6],[7,8]]=>[[1,2],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2]=>[2,2,2,2] [[1,6],[2,7],[3,8],[4],[5]]=>[[1,4],[2,5],[3,6],[7],[8]]=>[8,7,3,6,2,5,1,4]=>[7,1] [[1,4],[2,7],[3,8],[5],[6]]=>[[1,3],[2,4],[5,6],[7],[8]]=>[8,7,5,6,2,4,1,3]=>[6,2] [[1,3],[2,7],[4,8],[5],[6]]=>[[1,3],[2,4],[5,7],[6],[8]]=>[8,6,5,7,2,4,1,3]=>[8] [[1,2],[3,7],[4,8],[5],[6]]=>[[1,3],[2,4],[5,8],[6],[7]]=>[7,6,5,8,2,4,1,3]=>[6,2] [[1,5],[2,6],[3,8],[4],[7]]=>[[1,2],[3,5],[4,6],[7],[8]]=>[8,7,4,6,3,5,1,2]=>[4,4] [[1,4],[2,6],[3,8],[5],[7]]=>[[1,2],[3,4],[5,6],[7],[8]]=>[8,7,5,6,3,4,1,2]=>[4,2,2] [[1,2],[3,6],[4,8],[5],[7]]=>[[1,2],[3,4],[5,8],[6],[7]]=>[7,6,5,8,3,4,1,2]=>[4,2,2] [[1,3],[2,5],[4,8],[6],[7]]=>[[1,2],[3,5],[4,7],[6],[8]]=>[8,6,4,7,3,5,1,2]=>[8] [[1,5],[2,6],[3,7],[4],[8]]=>[[1,5],[2,6],[3,7],[4],[8]]=>[8,4,3,7,2,6,1,5]=>[6,1,1] [[1,4],[2,6],[3,7],[5],[8]]=>[[1,4],[2,6],[3,7],[5],[8]]=>[8,5,3,7,2,6,1,4]=>[4,2,1,1] [[1,2],[3,6],[4,7],[5],[8]]=>[[1,4],[2,5],[3,8],[6],[7]]=>[7,6,3,8,2,5,1,4]=>[3,2,2,1] [[1,3],[2,5],[4,7],[6],[8]]=>[[1,3],[2,5],[4,7],[6],[8]]=>[8,6,4,7,2,5,1,3]=>[5,3] [[1,2],[3,4],[5,7],[6],[8]]=>[[1,3],[2,6],[4,8],[5],[7]]=>[7,5,4,8,2,6,1,3]=>[3,2,2,1] [[1,3],[2,5],[4,6],[7],[8]]=>[[1,5],[2,7],[3,8],[4],[6]]=>[6,4,3,8,2,7,1,5]=>[4,3,1] [[1,2],[3,5],[4,6],[7],[8]]=>[[1,5],[2,6],[3,8],[4],[7]]=>[7,4,3,8,2,6,1,5]=>[4,2,1,1] [[1,3],[2,4],[5,6],[7],[8]]=>[[1,4],[2,7],[3,8],[5],[6]]=>[6,5,3,8,2,7,1,4]=>[3,2,2,1] [[1,2],[3,4],[5,6],[7],[8]]=>[[1,4],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4]=>[2,2,2,1,1] [[1,7],[2,8],[3],[4],[5],[6]]=>[[1,3],[2,4],[5],[6],[7],[8]]=>[8,7,6,5,2,4,1,3]=>[8] [[1,6],[2,8],[3],[4],[5],[7]]=>[[1,2],[3,4],[5],[6],[7],[8]]=>[8,7,6,5,3,4,1,2]=>[4,4] [[1,2],[3,8],[4],[5],[6],[7]]=>[[1,2],[3,8],[4],[5],[6],[7]]=>[7,6,5,4,3,8,1,2]=>[3,2,2,1] [[1,6],[2,7],[3],[4],[5],[8]]=>[[1,4],[2,5],[3],[6],[7],[8]]=>[8,7,6,3,2,5,1,4]=>[8] [[1,4],[2,7],[3],[5],[6],[8]]=>[[1,3],[2,6],[4],[5],[7],[8]]=>[8,7,5,4,2,6,1,3]=>[6,1,1] [[1,5],[2,6],[3],[4],[7],[8]]=>[[1,5],[2,6],[3],[4],[7],[8]]=>[8,7,4,3,2,6,1,5]=>[5,2,1] [[1,4],[2,6],[3],[5],[7],[8]]=>[[1,4],[2,6],[3],[5],[7],[8]]=>[8,7,5,3,2,6,1,4]=>[7,1] [[1,4],[2,5],[3],[6],[7],[8]]=>[[1,6],[2,7],[3],[4],[5],[8]]=>[8,5,4,3,2,7,1,6]=>[4,2,2] [[1,3],[2,4],[5],[6],[7],[8]]=>[[1,7],[2,8],[3],[4],[5],[6]]=>[6,5,4,3,2,8,1,7]=>[4,2,2] [[1,2],[3,4],[5],[6],[7],[8]]=>[[1,6],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6]=>[2,2,2,2] [[1,8],[2],[3],[4],[5],[6],[7]]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,1,2]=>[4,2,2] [[1,7],[2],[3],[4],[5],[6],[8]]=>[[1,3],[2],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,2,1,3]=>[6,2] [[1,6],[2],[3],[4],[5],[7],[8]]=>[[1,4],[2],[3],[5],[6],[7],[8]]=>[8,7,6,5,3,2,1,4]=>[8] [[1,5],[2],[3],[4],[6],[7],[8]]=>[[1,5],[2],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,2,1,5]=>[7,1] [[1,4],[2],[3],[5],[6],[7],[8]]=>[[1,6],[2],[3],[4],[5],[7],[8]]=>[8,7,5,4,3,2,1,6]=>[5,2,1] [[1,3],[2],[4],[5],[6],[7],[8]]=>[[1,7],[2],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,1,7]=>[3,2,2,1] [[1,2],[3],[4],[5],[6],[7],[8]]=>[[1,8],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8]=>[2,2,2,1,1] [[1],[2],[3],[4],[5],[6],[7],[8]]=>[[1],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1]=>[2,2,2,2] [[1,3,5,7,9],[2,4,6,8,10]]=>[[1,3,5,7,9],[2,4,6,8,10]]=>[2,4,6,8,10,1,3,5,7,9]=>[10] [[1,3,5,7,9,11],[2,4,6,8,10,12]]=>[[1,3,5,7,9,11],[2,4,6,8,10,12]]=>[2,4,6,8,10,12,1,3,5,7,9,11]=>[12] [[1,2],[3,4],[5,6],[7,8],[9,10]]=>[[1,2],[3,4],[5,6],[7,8],[9,10]]=>[9,10,7,8,5,6,3,4,1,2]=>[2,2,2,2,1,1] [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]]=>[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[2,2,2,2,2,2]
Map
Schützenberger involution
Description
Sends a standard tableau to the standard tableau obtained via the Schützenberger involution.
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
cycle type
Description
The cycle type of a permutation as a partition.