Identifier
Mp00081:
Standard tableaux
—reading word permutation⟶
Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00059: Permutations —Robinson-Schensted insertion tableau⟶ Standard tableaux
Mp00069: Permutations —complement⟶ Permutations
Mp00059: Permutations —Robinson-Schensted insertion tableau⟶ Standard tableaux
Images
=>
Cc0007;cc-rep-0Cc0007;cc-rep-3
[[1]]=>[1]=>[1]=>[[1]]
[[1,2]]=>[1,2]=>[2,1]=>[[1],[2]]
[[1],[2]]=>[2,1]=>[1,2]=>[[1,2]]
[[1,2,3]]=>[1,2,3]=>[3,2,1]=>[[1],[2],[3]]
[[1,3],[2]]=>[2,1,3]=>[2,3,1]=>[[1,3],[2]]
[[1,2],[3]]=>[3,1,2]=>[1,3,2]=>[[1,2],[3]]
[[1],[2],[3]]=>[3,2,1]=>[1,2,3]=>[[1,2,3]]
[[1,2,3,4]]=>[1,2,3,4]=>[4,3,2,1]=>[[1],[2],[3],[4]]
[[1,3,4],[2]]=>[2,1,3,4]=>[3,4,2,1]=>[[1,4],[2],[3]]
[[1,2,4],[3]]=>[3,1,2,4]=>[2,4,3,1]=>[[1,3],[2],[4]]
[[1,2,3],[4]]=>[4,1,2,3]=>[1,4,3,2]=>[[1,2],[3],[4]]
[[1,3],[2,4]]=>[2,4,1,3]=>[3,1,4,2]=>[[1,2],[3,4]]
[[1,2],[3,4]]=>[3,4,1,2]=>[2,1,4,3]=>[[1,3],[2,4]]
[[1,4],[2],[3]]=>[3,2,1,4]=>[2,3,4,1]=>[[1,3,4],[2]]
[[1,3],[2],[4]]=>[4,2,1,3]=>[1,3,4,2]=>[[1,2,4],[3]]
[[1,2],[3],[4]]=>[4,3,1,2]=>[1,2,4,3]=>[[1,2,3],[4]]
[[1],[2],[3],[4]]=>[4,3,2,1]=>[1,2,3,4]=>[[1,2,3,4]]
[[1,2,3,4,5]]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[[1],[2],[3],[4],[5]]
[[1,3,4,5],[2]]=>[2,1,3,4,5]=>[4,5,3,2,1]=>[[1,5],[2],[3],[4]]
[[1,2,4,5],[3]]=>[3,1,2,4,5]=>[3,5,4,2,1]=>[[1,4],[2],[3],[5]]
[[1,2,3,5],[4]]=>[4,1,2,3,5]=>[2,5,4,3,1]=>[[1,3],[2],[4],[5]]
[[1,2,3,4],[5]]=>[5,1,2,3,4]=>[1,5,4,3,2]=>[[1,2],[3],[4],[5]]
[[1,3,5],[2,4]]=>[2,4,1,3,5]=>[4,2,5,3,1]=>[[1,3],[2,5],[4]]
[[1,2,5],[3,4]]=>[3,4,1,2,5]=>[3,2,5,4,1]=>[[1,4],[2,5],[3]]
[[1,3,4],[2,5]]=>[2,5,1,3,4]=>[4,1,5,3,2]=>[[1,2],[3,5],[4]]
[[1,2,4],[3,5]]=>[3,5,1,2,4]=>[3,1,5,4,2]=>[[1,2],[3,4],[5]]
[[1,2,3],[4,5]]=>[4,5,1,2,3]=>[2,1,5,4,3]=>[[1,3],[2,4],[5]]
[[1,4,5],[2],[3]]=>[3,2,1,4,5]=>[3,4,5,2,1]=>[[1,4,5],[2],[3]]
[[1,3,5],[2],[4]]=>[4,2,1,3,5]=>[2,4,5,3,1]=>[[1,3,5],[2],[4]]
[[1,2,5],[3],[4]]=>[4,3,1,2,5]=>[2,3,5,4,1]=>[[1,3,4],[2],[5]]
[[1,3,4],[2],[5]]=>[5,2,1,3,4]=>[1,4,5,3,2]=>[[1,2,5],[3],[4]]
[[1,2,4],[3],[5]]=>[5,3,1,2,4]=>[1,3,5,4,2]=>[[1,2,4],[3],[5]]
[[1,2,3],[4],[5]]=>[5,4,1,2,3]=>[1,2,5,4,3]=>[[1,2,3],[4],[5]]
[[1,4],[2,5],[3]]=>[3,2,5,1,4]=>[3,4,1,5,2]=>[[1,2,5],[3,4]]
[[1,3],[2,5],[4]]=>[4,2,5,1,3]=>[2,4,1,5,3]=>[[1,3,5],[2,4]]
[[1,2],[3,5],[4]]=>[4,3,5,1,2]=>[2,3,1,5,4]=>[[1,3,4],[2,5]]
[[1,3],[2,4],[5]]=>[5,2,4,1,3]=>[1,4,2,5,3]=>[[1,2,3],[4,5]]
[[1,2],[3,4],[5]]=>[5,3,4,1,2]=>[1,3,2,5,4]=>[[1,2,4],[3,5]]
[[1,5],[2],[3],[4]]=>[4,3,2,1,5]=>[2,3,4,5,1]=>[[1,3,4,5],[2]]
[[1,4],[2],[3],[5]]=>[5,3,2,1,4]=>[1,3,4,5,2]=>[[1,2,4,5],[3]]
[[1,3],[2],[4],[5]]=>[5,4,2,1,3]=>[1,2,4,5,3]=>[[1,2,3,5],[4]]
[[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>[1,2,3,5,4]=>[[1,2,3,4],[5]]
[[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>[1,2,3,4,5]=>[[1,2,3,4,5]]
[[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6]]
[[1,3,4,5,6],[2]]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[[1,6],[2],[3],[4],[5]]
[[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>[[1,5],[2],[3],[4],[6]]
[[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>[3,6,5,4,2,1]=>[[1,4],[2],[3],[5],[6]]
[[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>[2,6,5,4,3,1]=>[[1,3],[2],[4],[5],[6]]
[[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>[1,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6]]
[[1,3,5,6],[2,4]]=>[2,4,1,3,5,6]=>[5,3,6,4,2,1]=>[[1,4],[2,6],[3],[5]]
[[1,2,5,6],[3,4]]=>[3,4,1,2,5,6]=>[4,3,6,5,2,1]=>[[1,5],[2,6],[3],[4]]
[[1,3,4,6],[2,5]]=>[2,5,1,3,4,6]=>[5,2,6,4,3,1]=>[[1,3],[2,6],[4],[5]]
[[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>[4,2,6,5,3,1]=>[[1,3],[2,5],[4],[6]]
[[1,2,3,6],[4,5]]=>[4,5,1,2,3,6]=>[3,2,6,5,4,1]=>[[1,4],[2,5],[3],[6]]
[[1,3,4,5],[2,6]]=>[2,6,1,3,4,5]=>[5,1,6,4,3,2]=>[[1,2],[3,6],[4],[5]]
[[1,2,4,5],[3,6]]=>[3,6,1,2,4,5]=>[4,1,6,5,3,2]=>[[1,2],[3,5],[4],[6]]
[[1,2,3,5],[4,6]]=>[4,6,1,2,3,5]=>[3,1,6,5,4,2]=>[[1,2],[3,4],[5],[6]]
[[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>[2,1,6,5,4,3]=>[[1,3],[2,4],[5],[6]]
[[1,4,5,6],[2],[3]]=>[3,2,1,4,5,6]=>[4,5,6,3,2,1]=>[[1,5,6],[2],[3],[4]]
[[1,3,5,6],[2],[4]]=>[4,2,1,3,5,6]=>[3,5,6,4,2,1]=>[[1,4,6],[2],[3],[5]]
[[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>[3,4,6,5,2,1]=>[[1,4,5],[2],[3],[6]]
[[1,3,4,6],[2],[5]]=>[5,2,1,3,4,6]=>[2,5,6,4,3,1]=>[[1,3,6],[2],[4],[5]]
[[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>[2,4,6,5,3,1]=>[[1,3,5],[2],[4],[6]]
[[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>[2,3,6,5,4,1]=>[[1,3,4],[2],[5],[6]]
[[1,3,4,5],[2],[6]]=>[6,2,1,3,4,5]=>[1,5,6,4,3,2]=>[[1,2,6],[3],[4],[5]]
[[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>[1,4,6,5,3,2]=>[[1,2,5],[3],[4],[6]]
[[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>[1,3,6,5,4,2]=>[[1,2,4],[3],[5],[6]]
[[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>[1,2,6,5,4,3]=>[[1,2,3],[4],[5],[6]]
[[1,3,5],[2,4,6]]=>[2,4,6,1,3,5]=>[5,3,1,6,4,2]=>[[1,2],[3,4],[5,6]]
[[1,2,5],[3,4,6]]=>[3,4,6,1,2,5]=>[4,3,1,6,5,2]=>[[1,2],[3,5],[4,6]]
[[1,3,4],[2,5,6]]=>[2,5,6,1,3,4]=>[5,2,1,6,4,3]=>[[1,3],[2,4],[5,6]]
[[1,2,4],[3,5,6]]=>[3,5,6,1,2,4]=>[4,2,1,6,5,3]=>[[1,3],[2,5],[4,6]]
[[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>[[1,4],[2,5],[3,6]]
[[1,4,6],[2,5],[3]]=>[3,2,5,1,4,6]=>[4,5,2,6,3,1]=>[[1,3,6],[2,5],[4]]
[[1,3,6],[2,5],[4]]=>[4,2,5,1,3,6]=>[3,5,2,6,4,1]=>[[1,4,6],[2,5],[3]]
[[1,2,6],[3,5],[4]]=>[4,3,5,1,2,6]=>[3,4,2,6,5,1]=>[[1,4,5],[2,6],[3]]
[[1,3,6],[2,4],[5]]=>[5,2,4,1,3,6]=>[2,5,3,6,4,1]=>[[1,3,4],[2,6],[5]]
[[1,2,6],[3,4],[5]]=>[5,3,4,1,2,6]=>[2,4,3,6,5,1]=>[[1,3,5],[2,6],[4]]
[[1,4,5],[2,6],[3]]=>[3,2,6,1,4,5]=>[4,5,1,6,3,2]=>[[1,2,6],[3,5],[4]]
[[1,3,5],[2,6],[4]]=>[4,2,6,1,3,5]=>[3,5,1,6,4,2]=>[[1,2,6],[3,4],[5]]
[[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5]=>[3,4,1,6,5,2]=>[[1,2,5],[3,4],[6]]
[[1,3,4],[2,6],[5]]=>[5,2,6,1,3,4]=>[2,5,1,6,4,3]=>[[1,3,6],[2,4],[5]]
[[1,2,4],[3,6],[5]]=>[5,3,6,1,2,4]=>[2,4,1,6,5,3]=>[[1,3,5],[2,4],[6]]
[[1,2,3],[4,6],[5]]=>[5,4,6,1,2,3]=>[2,3,1,6,5,4]=>[[1,3,4],[2,5],[6]]
[[1,3,5],[2,4],[6]]=>[6,2,4,1,3,5]=>[1,5,3,6,4,2]=>[[1,2,4],[3,6],[5]]
[[1,2,5],[3,4],[6]]=>[6,3,4,1,2,5]=>[1,4,3,6,5,2]=>[[1,2,5],[3,6],[4]]
[[1,3,4],[2,5],[6]]=>[6,2,5,1,3,4]=>[1,5,2,6,4,3]=>[[1,2,3],[4,6],[5]]
[[1,2,4],[3,5],[6]]=>[6,3,5,1,2,4]=>[1,4,2,6,5,3]=>[[1,2,3],[4,5],[6]]
[[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3]=>[1,3,2,6,5,4]=>[[1,2,4],[3,5],[6]]
[[1,5,6],[2],[3],[4]]=>[4,3,2,1,5,6]=>[3,4,5,6,2,1]=>[[1,4,5,6],[2],[3]]
[[1,4,6],[2],[3],[5]]=>[5,3,2,1,4,6]=>[2,4,5,6,3,1]=>[[1,3,5,6],[2],[4]]
[[1,3,6],[2],[4],[5]]=>[5,4,2,1,3,6]=>[2,3,5,6,4,1]=>[[1,3,4,6],[2],[5]]
[[1,2,6],[3],[4],[5]]=>[5,4,3,1,2,6]=>[2,3,4,6,5,1]=>[[1,3,4,5],[2],[6]]
[[1,4,5],[2],[3],[6]]=>[6,3,2,1,4,5]=>[1,4,5,6,3,2]=>[[1,2,5,6],[3],[4]]
[[1,3,5],[2],[4],[6]]=>[6,4,2,1,3,5]=>[1,3,5,6,4,2]=>[[1,2,4,6],[3],[5]]
[[1,2,5],[3],[4],[6]]=>[6,4,3,1,2,5]=>[1,3,4,6,5,2]=>[[1,2,4,5],[3],[6]]
[[1,3,4],[2],[5],[6]]=>[6,5,2,1,3,4]=>[1,2,5,6,4,3]=>[[1,2,3,6],[4],[5]]
[[1,2,4],[3],[5],[6]]=>[6,5,3,1,2,4]=>[1,2,4,6,5,3]=>[[1,2,3,5],[4],[6]]
[[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>[1,2,3,6,5,4]=>[[1,2,3,4],[5],[6]]
[[1,4],[2,5],[3,6]]=>[3,6,2,5,1,4]=>[4,1,5,2,6,3]=>[[1,2,3],[4,5,6]]
[[1,3],[2,5],[4,6]]=>[4,6,2,5,1,3]=>[3,1,5,2,6,4]=>[[1,2,4],[3,5,6]]
[[1,2],[3,5],[4,6]]=>[4,6,3,5,1,2]=>[3,1,4,2,6,5]=>[[1,2,5],[3,4,6]]
[[1,3],[2,4],[5,6]]=>[5,6,2,4,1,3]=>[2,1,5,3,6,4]=>[[1,3,4],[2,5,6]]
[[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>[[1,3,5],[2,4,6]]
[[1,5],[2,6],[3],[4]]=>[4,3,2,6,1,5]=>[3,4,5,1,6,2]=>[[1,2,5,6],[3,4]]
[[1,4],[2,6],[3],[5]]=>[5,3,2,6,1,4]=>[2,4,5,1,6,3]=>[[1,3,5,6],[2,4]]
[[1,3],[2,6],[4],[5]]=>[5,4,2,6,1,3]=>[2,3,5,1,6,4]=>[[1,3,4,6],[2,5]]
[[1,2],[3,6],[4],[5]]=>[5,4,3,6,1,2]=>[2,3,4,1,6,5]=>[[1,3,4,5],[2,6]]
[[1,4],[2,5],[3],[6]]=>[6,3,2,5,1,4]=>[1,4,5,2,6,3]=>[[1,2,3,6],[4,5]]
[[1,3],[2,5],[4],[6]]=>[6,4,2,5,1,3]=>[1,3,5,2,6,4]=>[[1,2,4,6],[3,5]]
[[1,2],[3,5],[4],[6]]=>[6,4,3,5,1,2]=>[1,3,4,2,6,5]=>[[1,2,4,5],[3,6]]
[[1,3],[2,4],[5],[6]]=>[6,5,2,4,1,3]=>[1,2,5,3,6,4]=>[[1,2,3,4],[5,6]]
[[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2]=>[1,2,4,3,6,5]=>[[1,2,3,5],[4,6]]
[[1,6],[2],[3],[4],[5]]=>[5,4,3,2,1,6]=>[2,3,4,5,6,1]=>[[1,3,4,5,6],[2]]
[[1,5],[2],[3],[4],[6]]=>[6,4,3,2,1,5]=>[1,3,4,5,6,2]=>[[1,2,4,5,6],[3]]
[[1,4],[2],[3],[5],[6]]=>[6,5,3,2,1,4]=>[1,2,4,5,6,3]=>[[1,2,3,5,6],[4]]
[[1,3],[2],[4],[5],[6]]=>[6,5,4,2,1,3]=>[1,2,3,5,6,4]=>[[1,2,3,4,6],[5]]
[[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>[1,2,3,4,6,5]=>[[1,2,3,4,5],[6]]
[[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[[1,2,3,4,5,6]]
[[1,2,3,4,5,6,7]]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7]]
[[1,3,4,5,6,7],[2]]=>[2,1,3,4,5,6,7]=>[6,7,5,4,3,2,1]=>[[1,7],[2],[3],[4],[5],[6]]
[[1,2,4,5,6,7],[3]]=>[3,1,2,4,5,6,7]=>[5,7,6,4,3,2,1]=>[[1,6],[2],[3],[4],[5],[7]]
[[1,2,3,5,6,7],[4]]=>[4,1,2,3,5,6,7]=>[4,7,6,5,3,2,1]=>[[1,5],[2],[3],[4],[6],[7]]
[[1,2,3,4,6,7],[5]]=>[5,1,2,3,4,6,7]=>[3,7,6,5,4,2,1]=>[[1,4],[2],[3],[5],[6],[7]]
[[1,2,3,4,5,7],[6]]=>[6,1,2,3,4,5,7]=>[2,7,6,5,4,3,1]=>[[1,3],[2],[4],[5],[6],[7]]
[[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>[1,7,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6],[7]]
[[1,3,5,6,7],[2,4]]=>[2,4,1,3,5,6,7]=>[6,4,7,5,3,2,1]=>[[1,5],[2,7],[3],[4],[6]]
[[1,2,5,6,7],[3,4]]=>[3,4,1,2,5,6,7]=>[5,4,7,6,3,2,1]=>[[1,6],[2,7],[3],[4],[5]]
[[1,3,4,6,7],[2,5]]=>[2,5,1,3,4,6,7]=>[6,3,7,5,4,2,1]=>[[1,4],[2,7],[3],[5],[6]]
[[1,2,4,6,7],[3,5]]=>[3,5,1,2,4,6,7]=>[5,3,7,6,4,2,1]=>[[1,4],[2,6],[3],[5],[7]]
[[1,2,3,6,7],[4,5]]=>[4,5,1,2,3,6,7]=>[4,3,7,6,5,2,1]=>[[1,5],[2,6],[3],[4],[7]]
[[1,3,4,5,7],[2,6]]=>[2,6,1,3,4,5,7]=>[6,2,7,5,4,3,1]=>[[1,3],[2,7],[4],[5],[6]]
[[1,2,4,5,7],[3,6]]=>[3,6,1,2,4,5,7]=>[5,2,7,6,4,3,1]=>[[1,3],[2,6],[4],[5],[7]]
[[1,2,3,5,7],[4,6]]=>[4,6,1,2,3,5,7]=>[4,2,7,6,5,3,1]=>[[1,3],[2,5],[4],[6],[7]]
[[1,2,3,4,7],[5,6]]=>[5,6,1,2,3,4,7]=>[3,2,7,6,5,4,1]=>[[1,4],[2,5],[3],[6],[7]]
[[1,3,4,5,6],[2,7]]=>[2,7,1,3,4,5,6]=>[6,1,7,5,4,3,2]=>[[1,2],[3,7],[4],[5],[6]]
[[1,2,4,5,6],[3,7]]=>[3,7,1,2,4,5,6]=>[5,1,7,6,4,3,2]=>[[1,2],[3,6],[4],[5],[7]]
[[1,2,3,5,6],[4,7]]=>[4,7,1,2,3,5,6]=>[4,1,7,6,5,3,2]=>[[1,2],[3,5],[4],[6],[7]]
[[1,2,3,4,6],[5,7]]=>[5,7,1,2,3,4,6]=>[3,1,7,6,5,4,2]=>[[1,2],[3,4],[5],[6],[7]]
[[1,2,3,4,5],[6,7]]=>[6,7,1,2,3,4,5]=>[2,1,7,6,5,4,3]=>[[1,3],[2,4],[5],[6],[7]]
[[1,4,5,6,7],[2],[3]]=>[3,2,1,4,5,6,7]=>[5,6,7,4,3,2,1]=>[[1,6,7],[2],[3],[4],[5]]
[[1,3,5,6,7],[2],[4]]=>[4,2,1,3,5,6,7]=>[4,6,7,5,3,2,1]=>[[1,5,7],[2],[3],[4],[6]]
[[1,2,5,6,7],[3],[4]]=>[4,3,1,2,5,6,7]=>[4,5,7,6,3,2,1]=>[[1,5,6],[2],[3],[4],[7]]
[[1,3,4,6,7],[2],[5]]=>[5,2,1,3,4,6,7]=>[3,6,7,5,4,2,1]=>[[1,4,7],[2],[3],[5],[6]]
[[1,2,4,6,7],[3],[5]]=>[5,3,1,2,4,6,7]=>[3,5,7,6,4,2,1]=>[[1,4,6],[2],[3],[5],[7]]
[[1,2,3,6,7],[4],[5]]=>[5,4,1,2,3,6,7]=>[3,4,7,6,5,2,1]=>[[1,4,5],[2],[3],[6],[7]]
[[1,3,4,5,7],[2],[6]]=>[6,2,1,3,4,5,7]=>[2,6,7,5,4,3,1]=>[[1,3,7],[2],[4],[5],[6]]
[[1,2,4,5,7],[3],[6]]=>[6,3,1,2,4,5,7]=>[2,5,7,6,4,3,1]=>[[1,3,6],[2],[4],[5],[7]]
[[1,2,3,5,7],[4],[6]]=>[6,4,1,2,3,5,7]=>[2,4,7,6,5,3,1]=>[[1,3,5],[2],[4],[6],[7]]
[[1,2,3,4,7],[5],[6]]=>[6,5,1,2,3,4,7]=>[2,3,7,6,5,4,1]=>[[1,3,4],[2],[5],[6],[7]]
[[1,3,4,5,6],[2],[7]]=>[7,2,1,3,4,5,6]=>[1,6,7,5,4,3,2]=>[[1,2,7],[3],[4],[5],[6]]
[[1,2,4,5,6],[3],[7]]=>[7,3,1,2,4,5,6]=>[1,5,7,6,4,3,2]=>[[1,2,6],[3],[4],[5],[7]]
[[1,2,3,5,6],[4],[7]]=>[7,4,1,2,3,5,6]=>[1,4,7,6,5,3,2]=>[[1,2,5],[3],[4],[6],[7]]
[[1,2,3,4,6],[5],[7]]=>[7,5,1,2,3,4,6]=>[1,3,7,6,5,4,2]=>[[1,2,4],[3],[5],[6],[7]]
[[1,2,3,4,5],[6],[7]]=>[7,6,1,2,3,4,5]=>[1,2,7,6,5,4,3]=>[[1,2,3],[4],[5],[6],[7]]
[[1,3,5,7],[2,4,6]]=>[2,4,6,1,3,5,7]=>[6,4,2,7,5,3,1]=>[[1,3],[2,5],[4,7],[6]]
[[1,2,5,7],[3,4,6]]=>[3,4,6,1,2,5,7]=>[5,4,2,7,6,3,1]=>[[1,3],[2,6],[4,7],[5]]
[[1,3,4,7],[2,5,6]]=>[2,5,6,1,3,4,7]=>[6,3,2,7,5,4,1]=>[[1,4],[2,5],[3,7],[6]]
[[1,2,4,7],[3,5,6]]=>[3,5,6,1,2,4,7]=>[5,3,2,7,6,4,1]=>[[1,4],[2,6],[3,7],[5]]
[[1,2,3,7],[4,5,6]]=>[4,5,6,1,2,3,7]=>[4,3,2,7,6,5,1]=>[[1,5],[2,6],[3,7],[4]]
[[1,3,5,6],[2,4,7]]=>[2,4,7,1,3,5,6]=>[6,4,1,7,5,3,2]=>[[1,2],[3,5],[4,7],[6]]
[[1,2,5,6],[3,4,7]]=>[3,4,7,1,2,5,6]=>[5,4,1,7,6,3,2]=>[[1,2],[3,6],[4,7],[5]]
[[1,3,4,6],[2,5,7]]=>[2,5,7,1,3,4,6]=>[6,3,1,7,5,4,2]=>[[1,2],[3,4],[5,7],[6]]
[[1,2,4,6],[3,5,7]]=>[3,5,7,1,2,4,6]=>[5,3,1,7,6,4,2]=>[[1,2],[3,4],[5,6],[7]]
[[1,2,3,6],[4,5,7]]=>[4,5,7,1,2,3,6]=>[4,3,1,7,6,5,2]=>[[1,2],[3,5],[4,6],[7]]
[[1,3,4,5],[2,6,7]]=>[2,6,7,1,3,4,5]=>[6,2,1,7,5,4,3]=>[[1,3],[2,4],[5,7],[6]]
[[1,2,4,5],[3,6,7]]=>[3,6,7,1,2,4,5]=>[5,2,1,7,6,4,3]=>[[1,3],[2,4],[5,6],[7]]
[[1,2,3,5],[4,6,7]]=>[4,6,7,1,2,3,5]=>[4,2,1,7,6,5,3]=>[[1,3],[2,5],[4,6],[7]]
[[1,2,3,4],[5,6,7]]=>[5,6,7,1,2,3,4]=>[3,2,1,7,6,5,4]=>[[1,4],[2,5],[3,6],[7]]
[[1,4,6,7],[2,5],[3]]=>[3,2,5,1,4,6,7]=>[5,6,3,7,4,2,1]=>[[1,4,7],[2,6],[3],[5]]
[[1,3,6,7],[2,5],[4]]=>[4,2,5,1,3,6,7]=>[4,6,3,7,5,2,1]=>[[1,5,7],[2,6],[3],[4]]
[[1,2,6,7],[3,5],[4]]=>[4,3,5,1,2,6,7]=>[4,5,3,7,6,2,1]=>[[1,5,6],[2,7],[3],[4]]
[[1,3,6,7],[2,4],[5]]=>[5,2,4,1,3,6,7]=>[3,6,4,7,5,2,1]=>[[1,4,5],[2,7],[3],[6]]
[[1,2,6,7],[3,4],[5]]=>[5,3,4,1,2,6,7]=>[3,5,4,7,6,2,1]=>[[1,4,6],[2,7],[3],[5]]
[[1,4,5,7],[2,6],[3]]=>[3,2,6,1,4,5,7]=>[5,6,2,7,4,3,1]=>[[1,3,7],[2,6],[4],[5]]
[[1,3,5,7],[2,6],[4]]=>[4,2,6,1,3,5,7]=>[4,6,2,7,5,3,1]=>[[1,3,7],[2,5],[4],[6]]
[[1,2,5,7],[3,6],[4]]=>[4,3,6,1,2,5,7]=>[4,5,2,7,6,3,1]=>[[1,3,6],[2,5],[4],[7]]
[[1,3,4,7],[2,6],[5]]=>[5,2,6,1,3,4,7]=>[3,6,2,7,5,4,1]=>[[1,4,7],[2,5],[3],[6]]
[[1,2,4,7],[3,6],[5]]=>[5,3,6,1,2,4,7]=>[3,5,2,7,6,4,1]=>[[1,4,6],[2,5],[3],[7]]
[[1,2,3,7],[4,6],[5]]=>[5,4,6,1,2,3,7]=>[3,4,2,7,6,5,1]=>[[1,4,5],[2,6],[3],[7]]
[[1,3,5,7],[2,4],[6]]=>[6,2,4,1,3,5,7]=>[2,6,4,7,5,3,1]=>[[1,3,5],[2,7],[4],[6]]
[[1,2,5,7],[3,4],[6]]=>[6,3,4,1,2,5,7]=>[2,5,4,7,6,3,1]=>[[1,3,6],[2,7],[4],[5]]
[[1,3,4,7],[2,5],[6]]=>[6,2,5,1,3,4,7]=>[2,6,3,7,5,4,1]=>[[1,3,4],[2,7],[5],[6]]
[[1,2,4,7],[3,5],[6]]=>[6,3,5,1,2,4,7]=>[2,5,3,7,6,4,1]=>[[1,3,4],[2,6],[5],[7]]
[[1,2,3,7],[4,5],[6]]=>[6,4,5,1,2,3,7]=>[2,4,3,7,6,5,1]=>[[1,3,5],[2,6],[4],[7]]
[[1,4,5,6],[2,7],[3]]=>[3,2,7,1,4,5,6]=>[5,6,1,7,4,3,2]=>[[1,2,7],[3,6],[4],[5]]
[[1,3,5,6],[2,7],[4]]=>[4,2,7,1,3,5,6]=>[4,6,1,7,5,3,2]=>[[1,2,7],[3,5],[4],[6]]
[[1,2,5,6],[3,7],[4]]=>[4,3,7,1,2,5,6]=>[4,5,1,7,6,3,2]=>[[1,2,6],[3,5],[4],[7]]
[[1,3,4,6],[2,7],[5]]=>[5,2,7,1,3,4,6]=>[3,6,1,7,5,4,2]=>[[1,2,7],[3,4],[5],[6]]
[[1,2,4,6],[3,7],[5]]=>[5,3,7,1,2,4,6]=>[3,5,1,7,6,4,2]=>[[1,2,6],[3,4],[5],[7]]
[[1,2,3,6],[4,7],[5]]=>[5,4,7,1,2,3,6]=>[3,4,1,7,6,5,2]=>[[1,2,5],[3,4],[6],[7]]
[[1,3,4,5],[2,7],[6]]=>[6,2,7,1,3,4,5]=>[2,6,1,7,5,4,3]=>[[1,3,7],[2,4],[5],[6]]
[[1,2,4,5],[3,7],[6]]=>[6,3,7,1,2,4,5]=>[2,5,1,7,6,4,3]=>[[1,3,6],[2,4],[5],[7]]
[[1,2,3,5],[4,7],[6]]=>[6,4,7,1,2,3,5]=>[2,4,1,7,6,5,3]=>[[1,3,5],[2,4],[6],[7]]
[[1,2,3,4],[5,7],[6]]=>[6,5,7,1,2,3,4]=>[2,3,1,7,6,5,4]=>[[1,3,4],[2,5],[6],[7]]
[[1,3,5,6],[2,4],[7]]=>[7,2,4,1,3,5,6]=>[1,6,4,7,5,3,2]=>[[1,2,5],[3,7],[4],[6]]
[[1,2,5,6],[3,4],[7]]=>[7,3,4,1,2,5,6]=>[1,5,4,7,6,3,2]=>[[1,2,6],[3,7],[4],[5]]
[[1,3,4,6],[2,5],[7]]=>[7,2,5,1,3,4,6]=>[1,6,3,7,5,4,2]=>[[1,2,4],[3,7],[5],[6]]
[[1,2,4,6],[3,5],[7]]=>[7,3,5,1,2,4,6]=>[1,5,3,7,6,4,2]=>[[1,2,4],[3,6],[5],[7]]
[[1,2,3,6],[4,5],[7]]=>[7,4,5,1,2,3,6]=>[1,4,3,7,6,5,2]=>[[1,2,5],[3,6],[4],[7]]
[[1,3,4,5],[2,6],[7]]=>[7,2,6,1,3,4,5]=>[1,6,2,7,5,4,3]=>[[1,2,3],[4,7],[5],[6]]
[[1,2,4,5],[3,6],[7]]=>[7,3,6,1,2,4,5]=>[1,5,2,7,6,4,3]=>[[1,2,3],[4,6],[5],[7]]
[[1,2,3,5],[4,6],[7]]=>[7,4,6,1,2,3,5]=>[1,4,2,7,6,5,3]=>[[1,2,3],[4,5],[6],[7]]
[[1,2,3,4],[5,6],[7]]=>[7,5,6,1,2,3,4]=>[1,3,2,7,6,5,4]=>[[1,2,4],[3,5],[6],[7]]
[[1,5,6,7],[2],[3],[4]]=>[4,3,2,1,5,6,7]=>[4,5,6,7,3,2,1]=>[[1,5,6,7],[2],[3],[4]]
[[1,4,6,7],[2],[3],[5]]=>[5,3,2,1,4,6,7]=>[3,5,6,7,4,2,1]=>[[1,4,6,7],[2],[3],[5]]
[[1,3,6,7],[2],[4],[5]]=>[5,4,2,1,3,6,7]=>[3,4,6,7,5,2,1]=>[[1,4,5,7],[2],[3],[6]]
[[1,2,6,7],[3],[4],[5]]=>[5,4,3,1,2,6,7]=>[3,4,5,7,6,2,1]=>[[1,4,5,6],[2],[3],[7]]
[[1,4,5,7],[2],[3],[6]]=>[6,3,2,1,4,5,7]=>[2,5,6,7,4,3,1]=>[[1,3,6,7],[2],[4],[5]]
[[1,3,5,7],[2],[4],[6]]=>[6,4,2,1,3,5,7]=>[2,4,6,7,5,3,1]=>[[1,3,5,7],[2],[4],[6]]
[[1,2,5,7],[3],[4],[6]]=>[6,4,3,1,2,5,7]=>[2,4,5,7,6,3,1]=>[[1,3,5,6],[2],[4],[7]]
[[1,3,4,7],[2],[5],[6]]=>[6,5,2,1,3,4,7]=>[2,3,6,7,5,4,1]=>[[1,3,4,7],[2],[5],[6]]
[[1,2,4,7],[3],[5],[6]]=>[6,5,3,1,2,4,7]=>[2,3,5,7,6,4,1]=>[[1,3,4,6],[2],[5],[7]]
[[1,2,3,7],[4],[5],[6]]=>[6,5,4,1,2,3,7]=>[2,3,4,7,6,5,1]=>[[1,3,4,5],[2],[6],[7]]
[[1,4,5,6],[2],[3],[7]]=>[7,3,2,1,4,5,6]=>[1,5,6,7,4,3,2]=>[[1,2,6,7],[3],[4],[5]]
[[1,3,5,6],[2],[4],[7]]=>[7,4,2,1,3,5,6]=>[1,4,6,7,5,3,2]=>[[1,2,5,7],[3],[4],[6]]
[[1,2,5,6],[3],[4],[7]]=>[7,4,3,1,2,5,6]=>[1,4,5,7,6,3,2]=>[[1,2,5,6],[3],[4],[7]]
[[1,3,4,6],[2],[5],[7]]=>[7,5,2,1,3,4,6]=>[1,3,6,7,5,4,2]=>[[1,2,4,7],[3],[5],[6]]
[[1,2,4,6],[3],[5],[7]]=>[7,5,3,1,2,4,6]=>[1,3,5,7,6,4,2]=>[[1,2,4,6],[3],[5],[7]]
[[1,2,3,6],[4],[5],[7]]=>[7,5,4,1,2,3,6]=>[1,3,4,7,6,5,2]=>[[1,2,4,5],[3],[6],[7]]
[[1,3,4,5],[2],[6],[7]]=>[7,6,2,1,3,4,5]=>[1,2,6,7,5,4,3]=>[[1,2,3,7],[4],[5],[6]]
[[1,2,4,5],[3],[6],[7]]=>[7,6,3,1,2,4,5]=>[1,2,5,7,6,4,3]=>[[1,2,3,6],[4],[5],[7]]
[[1,2,3,5],[4],[6],[7]]=>[7,6,4,1,2,3,5]=>[1,2,4,7,6,5,3]=>[[1,2,3,5],[4],[6],[7]]
[[1,2,3,4],[5],[6],[7]]=>[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>[[1,2,3,4],[5],[6],[7]]
[[1,4,6],[2,5,7],[3]]=>[3,2,5,7,1,4,6]=>[5,6,3,1,7,4,2]=>[[1,2,7],[3,4],[5,6]]
[[1,3,6],[2,5,7],[4]]=>[4,2,5,7,1,3,6]=>[4,6,3,1,7,5,2]=>[[1,2,7],[3,5],[4,6]]
[[1,2,6],[3,5,7],[4]]=>[4,3,5,7,1,2,6]=>[4,5,3,1,7,6,2]=>[[1,2,6],[3,5],[4,7]]
[[1,3,6],[2,4,7],[5]]=>[5,2,4,7,1,3,6]=>[3,6,4,1,7,5,2]=>[[1,2,5],[3,4],[6,7]]
[[1,2,6],[3,4,7],[5]]=>[5,3,4,7,1,2,6]=>[3,5,4,1,7,6,2]=>[[1,2,6],[3,4],[5,7]]
[[1,4,5],[2,6,7],[3]]=>[3,2,6,7,1,4,5]=>[5,6,2,1,7,4,3]=>[[1,3,7],[2,4],[5,6]]
[[1,3,5],[2,6,7],[4]]=>[4,2,6,7,1,3,5]=>[4,6,2,1,7,5,3]=>[[1,3,7],[2,5],[4,6]]
[[1,2,5],[3,6,7],[4]]=>[4,3,6,7,1,2,5]=>[4,5,2,1,7,6,3]=>[[1,3,6],[2,5],[4,7]]
[[1,3,4],[2,6,7],[5]]=>[5,2,6,7,1,3,4]=>[3,6,2,1,7,5,4]=>[[1,4,7],[2,5],[3,6]]
[[1,2,4],[3,6,7],[5]]=>[5,3,6,7,1,2,4]=>[3,5,2,1,7,6,4]=>[[1,4,6],[2,5],[3,7]]
[[1,2,3],[4,6,7],[5]]=>[5,4,6,7,1,2,3]=>[3,4,2,1,7,6,5]=>[[1,4,5],[2,6],[3,7]]
[[1,3,5],[2,4,7],[6]]=>[6,2,4,7,1,3,5]=>[2,6,4,1,7,5,3]=>[[1,3,5],[2,4],[6,7]]
[[1,2,5],[3,4,7],[6]]=>[6,3,4,7,1,2,5]=>[2,5,4,1,7,6,3]=>[[1,3,6],[2,4],[5,7]]
[[1,3,4],[2,5,7],[6]]=>[6,2,5,7,1,3,4]=>[2,6,3,1,7,5,4]=>[[1,3,4],[2,5],[6,7]]
[[1,2,4],[3,5,7],[6]]=>[6,3,5,7,1,2,4]=>[2,5,3,1,7,6,4]=>[[1,3,4],[2,6],[5,7]]
[[1,2,3],[4,5,7],[6]]=>[6,4,5,7,1,2,3]=>[2,4,3,1,7,6,5]=>[[1,3,5],[2,6],[4,7]]
[[1,3,5],[2,4,6],[7]]=>[7,2,4,6,1,3,5]=>[1,6,4,2,7,5,3]=>[[1,2,3],[4,5],[6,7]]
[[1,2,5],[3,4,6],[7]]=>[7,3,4,6,1,2,5]=>[1,5,4,2,7,6,3]=>[[1,2,3],[4,6],[5,7]]
[[1,3,4],[2,5,6],[7]]=>[7,2,5,6,1,3,4]=>[1,6,3,2,7,5,4]=>[[1,2,4],[3,5],[6,7]]
[[1,2,4],[3,5,6],[7]]=>[7,3,5,6,1,2,4]=>[1,5,3,2,7,6,4]=>[[1,2,4],[3,6],[5,7]]
[[1,2,3],[4,5,6],[7]]=>[7,4,5,6,1,2,3]=>[1,4,3,2,7,6,5]=>[[1,2,5],[3,6],[4,7]]
[[1,4,7],[2,5],[3,6]]=>[3,6,2,5,1,4,7]=>[5,2,6,3,7,4,1]=>[[1,3,4],[2,6,7],[5]]
[[1,3,7],[2,5],[4,6]]=>[4,6,2,5,1,3,7]=>[4,2,6,3,7,5,1]=>[[1,3,5],[2,6,7],[4]]
[[1,2,7],[3,5],[4,6]]=>[4,6,3,5,1,2,7]=>[4,2,5,3,7,6,1]=>[[1,3,6],[2,5,7],[4]]
[[1,3,7],[2,4],[5,6]]=>[5,6,2,4,1,3,7]=>[3,2,6,4,7,5,1]=>[[1,4,5],[2,6,7],[3]]
[[1,2,7],[3,4],[5,6]]=>[5,6,3,4,1,2,7]=>[3,2,5,4,7,6,1]=>[[1,4,6],[2,5,7],[3]]
[[1,4,6],[2,5],[3,7]]=>[3,7,2,5,1,4,6]=>[5,1,6,3,7,4,2]=>[[1,2,4],[3,6,7],[5]]
[[1,3,6],[2,5],[4,7]]=>[4,7,2,5,1,3,6]=>[4,1,6,3,7,5,2]=>[[1,2,5],[3,6,7],[4]]
[[1,2,6],[3,5],[4,7]]=>[4,7,3,5,1,2,6]=>[4,1,5,3,7,6,2]=>[[1,2,6],[3,5,7],[4]]
[[1,3,6],[2,4],[5,7]]=>[5,7,2,4,1,3,6]=>[3,1,6,4,7,5,2]=>[[1,2,5],[3,4,7],[6]]
[[1,2,6],[3,4],[5,7]]=>[5,7,3,4,1,2,6]=>[3,1,5,4,7,6,2]=>[[1,2,6],[3,4,7],[5]]
[[1,4,5],[2,6],[3,7]]=>[3,7,2,6,1,4,5]=>[5,1,6,2,7,4,3]=>[[1,2,3],[4,6,7],[5]]
[[1,3,5],[2,6],[4,7]]=>[4,7,2,6,1,3,5]=>[4,1,6,2,7,5,3]=>[[1,2,3],[4,5,7],[6]]
[[1,2,5],[3,6],[4,7]]=>[4,7,3,6,1,2,5]=>[4,1,5,2,7,6,3]=>[[1,2,3],[4,5,6],[7]]
[[1,3,4],[2,6],[5,7]]=>[5,7,2,6,1,3,4]=>[3,1,6,2,7,5,4]=>[[1,2,4],[3,5,7],[6]]
[[1,2,4],[3,6],[5,7]]=>[5,7,3,6,1,2,4]=>[3,1,5,2,7,6,4]=>[[1,2,4],[3,5,6],[7]]
[[1,2,3],[4,6],[5,7]]=>[5,7,4,6,1,2,3]=>[3,1,4,2,7,6,5]=>[[1,2,5],[3,4,6],[7]]
[[1,3,5],[2,4],[6,7]]=>[6,7,2,4,1,3,5]=>[2,1,6,4,7,5,3]=>[[1,3,5],[2,4,7],[6]]
[[1,2,5],[3,4],[6,7]]=>[6,7,3,4,1,2,5]=>[2,1,5,4,7,6,3]=>[[1,3,6],[2,4,7],[5]]
[[1,3,4],[2,5],[6,7]]=>[6,7,2,5,1,3,4]=>[2,1,6,3,7,5,4]=>[[1,3,4],[2,5,7],[6]]
[[1,2,4],[3,5],[6,7]]=>[6,7,3,5,1,2,4]=>[2,1,5,3,7,6,4]=>[[1,3,4],[2,5,6],[7]]
[[1,2,3],[4,5],[6,7]]=>[6,7,4,5,1,2,3]=>[2,1,4,3,7,6,5]=>[[1,3,5],[2,4,6],[7]]
[[1,5,7],[2,6],[3],[4]]=>[4,3,2,6,1,5,7]=>[4,5,6,2,7,3,1]=>[[1,3,6,7],[2,5],[4]]
[[1,4,7],[2,6],[3],[5]]=>[5,3,2,6,1,4,7]=>[3,5,6,2,7,4,1]=>[[1,4,6,7],[2,5],[3]]
[[1,3,7],[2,6],[4],[5]]=>[5,4,2,6,1,3,7]=>[3,4,6,2,7,5,1]=>[[1,4,5,7],[2,6],[3]]
[[1,2,7],[3,6],[4],[5]]=>[5,4,3,6,1,2,7]=>[3,4,5,2,7,6,1]=>[[1,4,5,6],[2,7],[3]]
[[1,4,7],[2,5],[3],[6]]=>[6,3,2,5,1,4,7]=>[2,5,6,3,7,4,1]=>[[1,3,4,7],[2,6],[5]]
[[1,3,7],[2,5],[4],[6]]=>[6,4,2,5,1,3,7]=>[2,4,6,3,7,5,1]=>[[1,3,5,7],[2,6],[4]]
[[1,2,7],[3,5],[4],[6]]=>[6,4,3,5,1,2,7]=>[2,4,5,3,7,6,1]=>[[1,3,5,6],[2,7],[4]]
[[1,3,7],[2,4],[5],[6]]=>[6,5,2,4,1,3,7]=>[2,3,6,4,7,5,1]=>[[1,3,4,5],[2,7],[6]]
[[1,2,7],[3,4],[5],[6]]=>[6,5,3,4,1,2,7]=>[2,3,5,4,7,6,1]=>[[1,3,4,6],[2,7],[5]]
[[1,5,6],[2,7],[3],[4]]=>[4,3,2,7,1,5,6]=>[4,5,6,1,7,3,2]=>[[1,2,6,7],[3,5],[4]]
[[1,4,6],[2,7],[3],[5]]=>[5,3,2,7,1,4,6]=>[3,5,6,1,7,4,2]=>[[1,2,6,7],[3,4],[5]]
[[1,3,6],[2,7],[4],[5]]=>[5,4,2,7,1,3,6]=>[3,4,6,1,7,5,2]=>[[1,2,5,7],[3,4],[6]]
[[1,2,6],[3,7],[4],[5]]=>[5,4,3,7,1,2,6]=>[3,4,5,1,7,6,2]=>[[1,2,5,6],[3,4],[7]]
[[1,4,5],[2,7],[3],[6]]=>[6,3,2,7,1,4,5]=>[2,5,6,1,7,4,3]=>[[1,3,6,7],[2,4],[5]]
[[1,3,5],[2,7],[4],[6]]=>[6,4,2,7,1,3,5]=>[2,4,6,1,7,5,3]=>[[1,3,5,7],[2,4],[6]]
[[1,2,5],[3,7],[4],[6]]=>[6,4,3,7,1,2,5]=>[2,4,5,1,7,6,3]=>[[1,3,5,6],[2,4],[7]]
[[1,3,4],[2,7],[5],[6]]=>[6,5,2,7,1,3,4]=>[2,3,6,1,7,5,4]=>[[1,3,4,7],[2,5],[6]]
[[1,2,4],[3,7],[5],[6]]=>[6,5,3,7,1,2,4]=>[2,3,5,1,7,6,4]=>[[1,3,4,6],[2,5],[7]]
[[1,2,3],[4,7],[5],[6]]=>[6,5,4,7,1,2,3]=>[2,3,4,1,7,6,5]=>[[1,3,4,5],[2,6],[7]]
[[1,4,6],[2,5],[3],[7]]=>[7,3,2,5,1,4,6]=>[1,5,6,3,7,4,2]=>[[1,2,4,7],[3,6],[5]]
[[1,3,6],[2,5],[4],[7]]=>[7,4,2,5,1,3,6]=>[1,4,6,3,7,5,2]=>[[1,2,5,7],[3,6],[4]]
[[1,2,6],[3,5],[4],[7]]=>[7,4,3,5,1,2,6]=>[1,4,5,3,7,6,2]=>[[1,2,5,6],[3,7],[4]]
[[1,3,6],[2,4],[5],[7]]=>[7,5,2,4,1,3,6]=>[1,3,6,4,7,5,2]=>[[1,2,4,5],[3,7],[6]]
[[1,2,6],[3,4],[5],[7]]=>[7,5,3,4,1,2,6]=>[1,3,5,4,7,6,2]=>[[1,2,4,6],[3,7],[5]]
[[1,4,5],[2,6],[3],[7]]=>[7,3,2,6,1,4,5]=>[1,5,6,2,7,4,3]=>[[1,2,3,7],[4,6],[5]]
[[1,3,5],[2,6],[4],[7]]=>[7,4,2,6,1,3,5]=>[1,4,6,2,7,5,3]=>[[1,2,3,7],[4,5],[6]]
[[1,2,5],[3,6],[4],[7]]=>[7,4,3,6,1,2,5]=>[1,4,5,2,7,6,3]=>[[1,2,3,6],[4,5],[7]]
[[1,3,4],[2,6],[5],[7]]=>[7,5,2,6,1,3,4]=>[1,3,6,2,7,5,4]=>[[1,2,4,7],[3,5],[6]]
[[1,2,4],[3,6],[5],[7]]=>[7,5,3,6,1,2,4]=>[1,3,5,2,7,6,4]=>[[1,2,4,6],[3,5],[7]]
[[1,2,3],[4,6],[5],[7]]=>[7,5,4,6,1,2,3]=>[1,3,4,2,7,6,5]=>[[1,2,4,5],[3,6],[7]]
[[1,3,5],[2,4],[6],[7]]=>[7,6,2,4,1,3,5]=>[1,2,6,4,7,5,3]=>[[1,2,3,5],[4,7],[6]]
[[1,2,5],[3,4],[6],[7]]=>[7,6,3,4,1,2,5]=>[1,2,5,4,7,6,3]=>[[1,2,3,6],[4,7],[5]]
[[1,3,4],[2,5],[6],[7]]=>[7,6,2,5,1,3,4]=>[1,2,6,3,7,5,4]=>[[1,2,3,4],[5,7],[6]]
[[1,2,4],[3,5],[6],[7]]=>[7,6,3,5,1,2,4]=>[1,2,5,3,7,6,4]=>[[1,2,3,4],[5,6],[7]]
[[1,2,3],[4,5],[6],[7]]=>[7,6,4,5,1,2,3]=>[1,2,4,3,7,6,5]=>[[1,2,3,5],[4,6],[7]]
[[1,6,7],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7]=>[3,4,5,6,7,2,1]=>[[1,4,5,6,7],[2],[3]]
[[1,5,7],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7]=>[2,4,5,6,7,3,1]=>[[1,3,5,6,7],[2],[4]]
[[1,4,7],[2],[3],[5],[6]]=>[6,5,3,2,1,4,7]=>[2,3,5,6,7,4,1]=>[[1,3,4,6,7],[2],[5]]
[[1,3,7],[2],[4],[5],[6]]=>[6,5,4,2,1,3,7]=>[2,3,4,6,7,5,1]=>[[1,3,4,5,7],[2],[6]]
[[1,2,7],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7]=>[2,3,4,5,7,6,1]=>[[1,3,4,5,6],[2],[7]]
[[1,5,6],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6]=>[1,4,5,6,7,3,2]=>[[1,2,5,6,7],[3],[4]]
[[1,4,6],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6]=>[1,3,5,6,7,4,2]=>[[1,2,4,6,7],[3],[5]]
[[1,3,6],[2],[4],[5],[7]]=>[7,5,4,2,1,3,6]=>[1,3,4,6,7,5,2]=>[[1,2,4,5,7],[3],[6]]
[[1,2,6],[3],[4],[5],[7]]=>[7,5,4,3,1,2,6]=>[1,3,4,5,7,6,2]=>[[1,2,4,5,6],[3],[7]]
[[1,4,5],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5]=>[1,2,5,6,7,4,3]=>[[1,2,3,6,7],[4],[5]]
[[1,3,5],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5]=>[1,2,4,6,7,5,3]=>[[1,2,3,5,7],[4],[6]]
[[1,2,5],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5]=>[1,2,4,5,7,6,3]=>[[1,2,3,5,6],[4],[7]]
[[1,3,4],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4]=>[1,2,3,6,7,5,4]=>[[1,2,3,4,7],[5],[6]]
[[1,2,4],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4]=>[1,2,3,5,7,6,4]=>[[1,2,3,4,6],[5],[7]]
[[1,2,3],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3]=>[1,2,3,4,7,6,5]=>[[1,2,3,4,5],[6],[7]]
[[1,5],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5]=>[4,5,1,6,2,7,3]=>[[1,2,3,7],[4,5,6]]
[[1,4],[2,6],[3,7],[5]]=>[5,3,7,2,6,1,4]=>[3,5,1,6,2,7,4]=>[[1,2,4,7],[3,5,6]]
[[1,3],[2,6],[4,7],[5]]=>[5,4,7,2,6,1,3]=>[3,4,1,6,2,7,5]=>[[1,2,5,7],[3,4,6]]
[[1,2],[3,6],[4,7],[5]]=>[5,4,7,3,6,1,2]=>[3,4,1,5,2,7,6]=>[[1,2,5,6],[3,4,7]]
[[1,4],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4]=>[2,5,1,6,3,7,4]=>[[1,3,4,7],[2,5,6]]
[[1,3],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3]=>[2,4,1,6,3,7,5]=>[[1,3,5,7],[2,4,6]]
[[1,2],[3,5],[4,7],[6]]=>[6,4,7,3,5,1,2]=>[2,4,1,5,3,7,6]=>[[1,3,5,6],[2,4,7]]
[[1,3],[2,4],[5,7],[6]]=>[6,5,7,2,4,1,3]=>[2,3,1,6,4,7,5]=>[[1,3,4,5],[2,6,7]]
[[1,2],[3,4],[5,7],[6]]=>[6,5,7,3,4,1,2]=>[2,3,1,5,4,7,6]=>[[1,3,4,6],[2,5,7]]
[[1,4],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4]=>[1,5,2,6,3,7,4]=>[[1,2,3,4],[5,6,7]]
[[1,3],[2,5],[4,6],[7]]=>[7,4,6,2,5,1,3]=>[1,4,2,6,3,7,5]=>[[1,2,3,5],[4,6,7]]
[[1,2],[3,5],[4,6],[7]]=>[7,4,6,3,5,1,2]=>[1,4,2,5,3,7,6]=>[[1,2,3,6],[4,5,7]]
[[1,3],[2,4],[5,6],[7]]=>[7,5,6,2,4,1,3]=>[1,3,2,6,4,7,5]=>[[1,2,4,5],[3,6,7]]
[[1,2],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2]=>[1,3,2,5,4,7,6]=>[[1,2,4,6],[3,5,7]]
[[1,6],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6]=>[3,4,5,6,1,7,2]=>[[1,2,5,6,7],[3,4]]
[[1,5],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5]=>[2,4,5,6,1,7,3]=>[[1,3,5,6,7],[2,4]]
[[1,4],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4]=>[2,3,5,6,1,7,4]=>[[1,3,4,6,7],[2,5]]
[[1,3],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3]=>[2,3,4,6,1,7,5]=>[[1,3,4,5,7],[2,6]]
[[1,2],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2]=>[2,3,4,5,1,7,6]=>[[1,3,4,5,6],[2,7]]
[[1,5],[2,6],[3],[4],[7]]=>[7,4,3,2,6,1,5]=>[1,4,5,6,2,7,3]=>[[1,2,3,6,7],[4,5]]
[[1,4],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4]=>[1,3,5,6,2,7,4]=>[[1,2,4,6,7],[3,5]]
[[1,3],[2,6],[4],[5],[7]]=>[7,5,4,2,6,1,3]=>[1,3,4,6,2,7,5]=>[[1,2,4,5,7],[3,6]]
[[1,2],[3,6],[4],[5],[7]]=>[7,5,4,3,6,1,2]=>[1,3,4,5,2,7,6]=>[[1,2,4,5,6],[3,7]]
[[1,4],[2,5],[3],[6],[7]]=>[7,6,3,2,5,1,4]=>[1,2,5,6,3,7,4]=>[[1,2,3,4,7],[5,6]]
[[1,3],[2,5],[4],[6],[7]]=>[7,6,4,2,5,1,3]=>[1,2,4,6,3,7,5]=>[[1,2,3,5,7],[4,6]]
[[1,2],[3,5],[4],[6],[7]]=>[7,6,4,3,5,1,2]=>[1,2,4,5,3,7,6]=>[[1,2,3,5,6],[4,7]]
[[1,3],[2,4],[5],[6],[7]]=>[7,6,5,2,4,1,3]=>[1,2,3,6,4,7,5]=>[[1,2,3,4,5],[6,7]]
[[1,2],[3,4],[5],[6],[7]]=>[7,6,5,3,4,1,2]=>[1,2,3,5,4,7,6]=>[[1,2,3,4,6],[5,7]]
[[1,7],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,7,1]=>[[1,3,4,5,6,7],[2]]
[[1,6],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6]=>[1,3,4,5,6,7,2]=>[[1,2,4,5,6,7],[3]]
[[1,5],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5]=>[1,2,4,5,6,7,3]=>[[1,2,3,5,6,7],[4]]
[[1,4],[2],[3],[5],[6],[7]]=>[7,6,5,3,2,1,4]=>[1,2,3,5,6,7,4]=>[[1,2,3,4,6,7],[5]]
[[1,3],[2],[4],[5],[6],[7]]=>[7,6,5,4,2,1,3]=>[1,2,3,4,6,7,5]=>[[1,2,3,4,5,7],[6]]
[[1,2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2]=>[1,2,3,4,5,7,6]=>[[1,2,3,4,5,6],[7]]
[[1],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>[[1,2,3,4,5,6,7]]
[[1,2,3,4,5,6,7,8]]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7],[8]]
[[1,3,4,5,6,7,8],[2]]=>[2,1,3,4,5,6,7,8]=>[7,8,6,5,4,3,2,1]=>[[1,8],[2],[3],[4],[5],[6],[7]]
[[1,2,4,5,6,7,8],[3]]=>[3,1,2,4,5,6,7,8]=>[6,8,7,5,4,3,2,1]=>[[1,7],[2],[3],[4],[5],[6],[8]]
[[1,2,3,5,6,7,8],[4]]=>[4,1,2,3,5,6,7,8]=>[5,8,7,6,4,3,2,1]=>[[1,6],[2],[3],[4],[5],[7],[8]]
[[1,2,3,4,6,7,8],[5]]=>[5,1,2,3,4,6,7,8]=>[4,8,7,6,5,3,2,1]=>[[1,5],[2],[3],[4],[6],[7],[8]]
[[1,2,3,4,5,7,8],[6]]=>[6,1,2,3,4,5,7,8]=>[3,8,7,6,5,4,2,1]=>[[1,4],[2],[3],[5],[6],[7],[8]]
[[1,2,3,4,5,6,8],[7]]=>[7,1,2,3,4,5,6,8]=>[2,8,7,6,5,4,3,1]=>[[1,3],[2],[4],[5],[6],[7],[8]]
[[1,2,3,4,5,6,7],[8]]=>[8,1,2,3,4,5,6,7]=>[1,8,7,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6],[7],[8]]
[[1,3,5,6,7,8],[2,4]]=>[2,4,1,3,5,6,7,8]=>[7,5,8,6,4,3,2,1]=>[[1,6],[2,8],[3],[4],[5],[7]]
[[1,2,5,6,7,8],[3,4]]=>[3,4,1,2,5,6,7,8]=>[6,5,8,7,4,3,2,1]=>[[1,7],[2,8],[3],[4],[5],[6]]
[[1,3,4,6,7,8],[2,5]]=>[2,5,1,3,4,6,7,8]=>[7,4,8,6,5,3,2,1]=>[[1,5],[2,8],[3],[4],[6],[7]]
[[1,2,4,6,7,8],[3,5]]=>[3,5,1,2,4,6,7,8]=>[6,4,8,7,5,3,2,1]=>[[1,5],[2,7],[3],[4],[6],[8]]
[[1,3,4,5,7,8],[2,6]]=>[2,6,1,3,4,5,7,8]=>[7,3,8,6,5,4,2,1]=>[[1,4],[2,8],[3],[5],[6],[7]]
[[1,2,4,5,7,8],[3,6]]=>[3,6,1,2,4,5,7,8]=>[6,3,8,7,5,4,2,1]=>[[1,4],[2,7],[3],[5],[6],[8]]
[[1,2,3,5,7,8],[4,6]]=>[4,6,1,2,3,5,7,8]=>[5,3,8,7,6,4,2,1]=>[[1,4],[2,6],[3],[5],[7],[8]]
[[1,2,3,4,7,8],[5,6]]=>[5,6,1,2,3,4,7,8]=>[4,3,8,7,6,5,2,1]=>[[1,5],[2,6],[3],[4],[7],[8]]
[[1,3,4,5,6,8],[2,7]]=>[2,7,1,3,4,5,6,8]=>[7,2,8,6,5,4,3,1]=>[[1,3],[2,8],[4],[5],[6],[7]]
[[1,2,4,5,6,8],[3,7]]=>[3,7,1,2,4,5,6,8]=>[6,2,8,7,5,4,3,1]=>[[1,3],[2,7],[4],[5],[6],[8]]
[[1,2,3,5,6,8],[4,7]]=>[4,7,1,2,3,5,6,8]=>[5,2,8,7,6,4,3,1]=>[[1,3],[2,6],[4],[5],[7],[8]]
[[1,2,3,4,6,8],[5,7]]=>[5,7,1,2,3,4,6,8]=>[4,2,8,7,6,5,3,1]=>[[1,3],[2,5],[4],[6],[7],[8]]
[[1,2,3,4,5,8],[6,7]]=>[6,7,1,2,3,4,5,8]=>[3,2,8,7,6,5,4,1]=>[[1,4],[2,5],[3],[6],[7],[8]]
[[1,3,4,5,6,7],[2,8]]=>[2,8,1,3,4,5,6,7]=>[7,1,8,6,5,4,3,2]=>[[1,2],[3,8],[4],[5],[6],[7]]
[[1,2,4,5,6,7],[3,8]]=>[3,8,1,2,4,5,6,7]=>[6,1,8,7,5,4,3,2]=>[[1,2],[3,7],[4],[5],[6],[8]]
[[1,2,3,5,6,7],[4,8]]=>[4,8,1,2,3,5,6,7]=>[5,1,8,7,6,4,3,2]=>[[1,2],[3,6],[4],[5],[7],[8]]
[[1,2,3,4,6,7],[5,8]]=>[5,8,1,2,3,4,6,7]=>[4,1,8,7,6,5,3,2]=>[[1,2],[3,5],[4],[6],[7],[8]]
[[1,2,3,4,5,7],[6,8]]=>[6,8,1,2,3,4,5,7]=>[3,1,8,7,6,5,4,2]=>[[1,2],[3,4],[5],[6],[7],[8]]
[[1,2,3,4,5,6],[7,8]]=>[7,8,1,2,3,4,5,6]=>[2,1,8,7,6,5,4,3]=>[[1,3],[2,4],[5],[6],[7],[8]]
[[1,4,5,6,7,8],[2],[3]]=>[3,2,1,4,5,6,7,8]=>[6,7,8,5,4,3,2,1]=>[[1,7,8],[2],[3],[4],[5],[6]]
[[1,3,5,6,7,8],[2],[4]]=>[4,2,1,3,5,6,7,8]=>[5,7,8,6,4,3,2,1]=>[[1,6,8],[2],[3],[4],[5],[7]]
[[1,2,5,6,7,8],[3],[4]]=>[4,3,1,2,5,6,7,8]=>[5,6,8,7,4,3,2,1]=>[[1,6,7],[2],[3],[4],[5],[8]]
[[1,3,4,6,7,8],[2],[5]]=>[5,2,1,3,4,6,7,8]=>[4,7,8,6,5,3,2,1]=>[[1,5,8],[2],[3],[4],[6],[7]]
[[1,2,4,6,7,8],[3],[5]]=>[5,3,1,2,4,6,7,8]=>[4,6,8,7,5,3,2,1]=>[[1,5,7],[2],[3],[4],[6],[8]]
[[1,2,3,6,7,8],[4],[5]]=>[5,4,1,2,3,6,7,8]=>[4,5,8,7,6,3,2,1]=>[[1,5,6],[2],[3],[4],[7],[8]]
[[1,3,4,5,7,8],[2],[6]]=>[6,2,1,3,4,5,7,8]=>[3,7,8,6,5,4,2,1]=>[[1,4,8],[2],[3],[5],[6],[7]]
[[1,2,4,5,7,8],[3],[6]]=>[6,3,1,2,4,5,7,8]=>[3,6,8,7,5,4,2,1]=>[[1,4,7],[2],[3],[5],[6],[8]]
[[1,2,3,5,7,8],[4],[6]]=>[6,4,1,2,3,5,7,8]=>[3,5,8,7,6,4,2,1]=>[[1,4,6],[2],[3],[5],[7],[8]]
[[1,3,4,5,6,8],[2],[7]]=>[7,2,1,3,4,5,6,8]=>[2,7,8,6,5,4,3,1]=>[[1,3,8],[2],[4],[5],[6],[7]]
[[1,2,4,5,6,8],[3],[7]]=>[7,3,1,2,4,5,6,8]=>[2,6,8,7,5,4,3,1]=>[[1,3,7],[2],[4],[5],[6],[8]]
[[1,2,3,5,6,8],[4],[7]]=>[7,4,1,2,3,5,6,8]=>[2,5,8,7,6,4,3,1]=>[[1,3,6],[2],[4],[5],[7],[8]]
[[1,2,3,4,6,8],[5],[7]]=>[7,5,1,2,3,4,6,8]=>[2,4,8,7,6,5,3,1]=>[[1,3,5],[2],[4],[6],[7],[8]]
[[1,2,3,4,5,8],[6],[7]]=>[7,6,1,2,3,4,5,8]=>[2,3,8,7,6,5,4,1]=>[[1,3,4],[2],[5],[6],[7],[8]]
[[1,3,4,5,6,7],[2],[8]]=>[8,2,1,3,4,5,6,7]=>[1,7,8,6,5,4,3,2]=>[[1,2,8],[3],[4],[5],[6],[7]]
[[1,2,4,5,6,7],[3],[8]]=>[8,3,1,2,4,5,6,7]=>[1,6,8,7,5,4,3,2]=>[[1,2,7],[3],[4],[5],[6],[8]]
[[1,2,3,5,6,7],[4],[8]]=>[8,4,1,2,3,5,6,7]=>[1,5,8,7,6,4,3,2]=>[[1,2,6],[3],[4],[5],[7],[8]]
[[1,2,3,4,6,7],[5],[8]]=>[8,5,1,2,3,4,6,7]=>[1,4,8,7,6,5,3,2]=>[[1,2,5],[3],[4],[6],[7],[8]]
[[1,2,3,4,5,7],[6],[8]]=>[8,6,1,2,3,4,5,7]=>[1,3,8,7,6,5,4,2]=>[[1,2,4],[3],[5],[6],[7],[8]]
[[1,2,3,4,5,6],[7],[8]]=>[8,7,1,2,3,4,5,6]=>[1,2,8,7,6,5,4,3]=>[[1,2,3],[4],[5],[6],[7],[8]]
[[1,3,5,7,8],[2,4,6]]=>[2,4,6,1,3,5,7,8]=>[7,5,3,8,6,4,2,1]=>[[1,4],[2,6],[3,8],[5],[7]]
[[1,2,3,7,8],[4,5,6]]=>[4,5,6,1,2,3,7,8]=>[5,4,3,8,7,6,2,1]=>[[1,6],[2,7],[3,8],[4],[5]]
[[1,3,5,6,8],[2,4,7]]=>[2,4,7,1,3,5,6,8]=>[7,5,2,8,6,4,3,1]=>[[1,3],[2,6],[4,8],[5],[7]]
[[1,2,5,6,8],[3,4,7]]=>[3,4,7,1,2,5,6,8]=>[6,5,2,8,7,4,3,1]=>[[1,3],[2,7],[4,8],[5],[6]]
[[1,3,4,6,8],[2,5,7]]=>[2,5,7,1,3,4,6,8]=>[7,4,2,8,6,5,3,1]=>[[1,3],[2,5],[4,8],[6],[7]]
[[1,2,4,6,8],[3,5,7]]=>[3,5,7,1,2,4,6,8]=>[6,4,2,8,7,5,3,1]=>[[1,3],[2,5],[4,7],[6],[8]]
[[1,3,4,5,8],[2,6,7]]=>[2,6,7,1,3,4,5,8]=>[7,3,2,8,6,5,4,1]=>[[1,4],[2,5],[3,8],[6],[7]]
[[1,2,4,5,8],[3,6,7]]=>[3,6,7,1,2,4,5,8]=>[6,3,2,8,7,5,4,1]=>[[1,4],[2,5],[3,7],[6],[8]]
[[1,2,3,5,8],[4,6,7]]=>[4,6,7,1,2,3,5,8]=>[5,3,2,8,7,6,4,1]=>[[1,4],[2,6],[3,7],[5],[8]]
[[1,2,3,4,8],[5,6,7]]=>[5,6,7,1,2,3,4,8]=>[4,3,2,8,7,6,5,1]=>[[1,5],[2,6],[3,7],[4],[8]]
[[1,3,5,6,7],[2,4,8]]=>[2,4,8,1,3,5,6,7]=>[7,5,1,8,6,4,3,2]=>[[1,2],[3,6],[4,8],[5],[7]]
[[1,2,5,6,7],[3,4,8]]=>[3,4,8,1,2,5,6,7]=>[6,5,1,8,7,4,3,2]=>[[1,2],[3,7],[4,8],[5],[6]]
[[1,3,4,6,7],[2,5,8]]=>[2,5,8,1,3,4,6,7]=>[7,4,1,8,6,5,3,2]=>[[1,2],[3,5],[4,8],[6],[7]]
[[1,2,4,6,7],[3,5,8]]=>[3,5,8,1,2,4,6,7]=>[6,4,1,8,7,5,3,2]=>[[1,2],[3,5],[4,7],[6],[8]]
[[1,2,3,6,7],[4,5,8]]=>[4,5,8,1,2,3,6,7]=>[5,4,1,8,7,6,3,2]=>[[1,2],[3,6],[4,7],[5],[8]]
[[1,3,4,5,7],[2,6,8]]=>[2,6,8,1,3,4,5,7]=>[7,3,1,8,6,5,4,2]=>[[1,2],[3,4],[5,8],[6],[7]]
[[1,2,4,5,7],[3,6,8]]=>[3,6,8,1,2,4,5,7]=>[6,3,1,8,7,5,4,2]=>[[1,2],[3,4],[5,7],[6],[8]]
[[1,2,3,5,7],[4,6,8]]=>[4,6,8,1,2,3,5,7]=>[5,3,1,8,7,6,4,2]=>[[1,2],[3,4],[5,6],[7],[8]]
[[1,2,3,4,7],[5,6,8]]=>[5,6,8,1,2,3,4,7]=>[4,3,1,8,7,6,5,2]=>[[1,2],[3,5],[4,6],[7],[8]]
[[1,3,4,5,6],[2,7,8]]=>[2,7,8,1,3,4,5,6]=>[7,2,1,8,6,5,4,3]=>[[1,3],[2,4],[5,8],[6],[7]]
[[1,2,4,5,6],[3,7,8]]=>[3,7,8,1,2,4,5,6]=>[6,2,1,8,7,5,4,3]=>[[1,3],[2,4],[5,7],[6],[8]]
[[1,2,3,5,6],[4,7,8]]=>[4,7,8,1,2,3,5,6]=>[5,2,1,8,7,6,4,3]=>[[1,3],[2,4],[5,6],[7],[8]]
[[1,2,3,4,6],[5,7,8]]=>[5,7,8,1,2,3,4,6]=>[4,2,1,8,7,6,5,3]=>[[1,3],[2,5],[4,6],[7],[8]]
[[1,2,3,4,5],[6,7,8]]=>[6,7,8,1,2,3,4,5]=>[3,2,1,8,7,6,5,4]=>[[1,4],[2,5],[3,6],[7],[8]]
[[1,4,6,7,8],[2,5],[3]]=>[3,2,5,1,4,6,7,8]=>[6,7,4,8,5,3,2,1]=>[[1,5,8],[2,7],[3],[4],[6]]
[[1,3,6,7,8],[2,5],[4]]=>[4,2,5,1,3,6,7,8]=>[5,7,4,8,6,3,2,1]=>[[1,6,8],[2,7],[3],[4],[5]]
[[1,2,6,7,8],[3,5],[4]]=>[4,3,5,1,2,6,7,8]=>[5,6,4,8,7,3,2,1]=>[[1,6,7],[2,8],[3],[4],[5]]
[[1,2,6,7,8],[3,4],[5]]=>[5,3,4,1,2,6,7,8]=>[4,6,5,8,7,3,2,1]=>[[1,5,7],[2,8],[3],[4],[6]]
[[1,3,4,7,8],[2,6],[5]]=>[5,2,6,1,3,4,7,8]=>[4,7,3,8,6,5,2,1]=>[[1,5,8],[2,6],[3],[4],[7]]
[[1,2,4,7,8],[3,6],[5]]=>[5,3,6,1,2,4,7,8]=>[4,6,3,8,7,5,2,1]=>[[1,5,7],[2,6],[3],[4],[8]]
[[1,2,4,7,8],[3,5],[6]]=>[6,3,5,1,2,4,7,8]=>[3,6,4,8,7,5,2,1]=>[[1,4,5],[2,7],[3],[6],[8]]
[[1,3,5,6,8],[2,7],[4]]=>[4,2,7,1,3,5,6,8]=>[5,7,2,8,6,4,3,1]=>[[1,3,8],[2,6],[4],[5],[7]]
[[1,2,5,6,8],[3,7],[4]]=>[4,3,7,1,2,5,6,8]=>[5,6,2,8,7,4,3,1]=>[[1,3,7],[2,6],[4],[5],[8]]
[[1,3,4,5,8],[2,7],[6]]=>[6,2,7,1,3,4,5,8]=>[3,7,2,8,6,5,4,1]=>[[1,4,8],[2,5],[3],[6],[7]]
[[1,2,4,5,8],[3,7],[6]]=>[6,3,7,1,2,4,5,8]=>[3,6,2,8,7,5,4,1]=>[[1,4,7],[2,5],[3],[6],[8]]
[[1,2,3,5,8],[4,7],[6]]=>[6,4,7,1,2,3,5,8]=>[3,5,2,8,7,6,4,1]=>[[1,4,6],[2,5],[3],[7],[8]]
[[1,2,3,4,8],[5,7],[6]]=>[6,5,7,1,2,3,4,8]=>[3,4,2,8,7,6,5,1]=>[[1,4,5],[2,6],[3],[7],[8]]
[[1,3,4,6,8],[2,5],[7]]=>[7,2,5,1,3,4,6,8]=>[2,7,4,8,6,5,3,1]=>[[1,3,5],[2,8],[4],[6],[7]]
[[1,2,4,6,8],[3,5],[7]]=>[7,3,5,1,2,4,6,8]=>[2,6,4,8,7,5,3,1]=>[[1,3,5],[2,7],[4],[6],[8]]
[[1,2,3,6,8],[4,5],[7]]=>[7,4,5,1,2,3,6,8]=>[2,5,4,8,7,6,3,1]=>[[1,3,6],[2,7],[4],[5],[8]]
[[1,2,4,5,8],[3,6],[7]]=>[7,3,6,1,2,4,5,8]=>[2,6,3,8,7,5,4,1]=>[[1,3,4],[2,7],[5],[6],[8]]
[[1,2,3,4,8],[5,6],[7]]=>[7,5,6,1,2,3,4,8]=>[2,4,3,8,7,6,5,1]=>[[1,3,5],[2,6],[4],[7],[8]]
[[1,4,5,6,7],[2,8],[3]]=>[3,2,8,1,4,5,6,7]=>[6,7,1,8,5,4,3,2]=>[[1,2,8],[3,7],[4],[5],[6]]
[[1,3,4,6,7],[2,8],[5]]=>[5,2,8,1,3,4,6,7]=>[4,7,1,8,6,5,3,2]=>[[1,2,8],[3,5],[4],[6],[7]]
[[1,2,4,6,7],[3,8],[5]]=>[5,3,8,1,2,4,6,7]=>[4,6,1,8,7,5,3,2]=>[[1,2,7],[3,5],[4],[6],[8]]
[[1,3,4,5,7],[2,8],[6]]=>[6,2,8,1,3,4,5,7]=>[3,7,1,8,6,5,4,2]=>[[1,2,8],[3,4],[5],[6],[7]]
[[1,2,4,5,7],[3,8],[6]]=>[6,3,8,1,2,4,5,7]=>[3,6,1,8,7,5,4,2]=>[[1,2,7],[3,4],[5],[6],[8]]
[[1,2,3,4,7],[5,8],[6]]=>[6,5,8,1,2,3,4,7]=>[3,4,1,8,7,6,5,2]=>[[1,2,5],[3,4],[6],[7],[8]]
[[1,3,4,5,6],[2,8],[7]]=>[7,2,8,1,3,4,5,6]=>[2,7,1,8,6,5,4,3]=>[[1,3,8],[2,4],[5],[6],[7]]
[[1,2,3,4,6],[5,8],[7]]=>[7,5,8,1,2,3,4,6]=>[2,4,1,8,7,6,5,3]=>[[1,3,5],[2,4],[6],[7],[8]]
[[1,2,3,4,5],[6,8],[7]]=>[7,6,8,1,2,3,4,5]=>[2,3,1,8,7,6,5,4]=>[[1,3,4],[2,5],[6],[7],[8]]
[[1,3,5,6,7],[2,4],[8]]=>[8,2,4,1,3,5,6,7]=>[1,7,5,8,6,4,3,2]=>[[1,2,6],[3,8],[4],[5],[7]]
[[1,2,5,6,7],[3,4],[8]]=>[8,3,4,1,2,5,6,7]=>[1,6,5,8,7,4,3,2]=>[[1,2,7],[3,8],[4],[5],[6]]
[[1,3,4,6,7],[2,5],[8]]=>[8,2,5,1,3,4,6,7]=>[1,7,4,8,6,5,3,2]=>[[1,2,5],[3,8],[4],[6],[7]]
[[1,2,4,6,7],[3,5],[8]]=>[8,3,5,1,2,4,6,7]=>[1,6,4,8,7,5,3,2]=>[[1,2,5],[3,7],[4],[6],[8]]
[[1,2,3,5,7],[4,6],[8]]=>[8,4,6,1,2,3,5,7]=>[1,5,3,8,7,6,4,2]=>[[1,2,4],[3,6],[5],[7],[8]]
[[1,2,3,4,7],[5,6],[8]]=>[8,5,6,1,2,3,4,7]=>[1,4,3,8,7,6,5,2]=>[[1,2,5],[3,6],[4],[7],[8]]
[[1,2,4,5,6],[3,7],[8]]=>[8,3,7,1,2,4,5,6]=>[1,6,2,8,7,5,4,3]=>[[1,2,3],[4,7],[5],[6],[8]]
[[1,2,3,4,6],[5,7],[8]]=>[8,5,7,1,2,3,4,6]=>[1,4,2,8,7,6,5,3]=>[[1,2,3],[4,5],[6],[7],[8]]
[[1,2,3,4,5],[6,7],[8]]=>[8,6,7,1,2,3,4,5]=>[1,3,2,8,7,6,5,4]=>[[1,2,4],[3,5],[6],[7],[8]]
[[1,5,6,7,8],[2],[3],[4]]=>[4,3,2,1,5,6,7,8]=>[5,6,7,8,4,3,2,1]=>[[1,6,7,8],[2],[3],[4],[5]]
[[1,2,6,7,8],[3],[4],[5]]=>[5,4,3,1,2,6,7,8]=>[4,5,6,8,7,3,2,1]=>[[1,5,6,7],[2],[3],[4],[8]]
[[1,3,5,7,8],[2],[4],[6]]=>[6,4,2,1,3,5,7,8]=>[3,5,7,8,6,4,2,1]=>[[1,4,6,8],[2],[3],[5],[7]]
[[1,2,5,7,8],[3],[4],[6]]=>[6,4,3,1,2,5,7,8]=>[3,5,6,8,7,4,2,1]=>[[1,4,6,7],[2],[3],[5],[8]]
[[1,4,5,6,8],[2],[3],[7]]=>[7,3,2,1,4,5,6,8]=>[2,6,7,8,5,4,3,1]=>[[1,3,7,8],[2],[4],[5],[6]]
[[1,3,4,6,8],[2],[5],[7]]=>[7,5,2,1,3,4,6,8]=>[2,4,7,8,6,5,3,1]=>[[1,3,5,8],[2],[4],[6],[7]]
[[1,2,4,6,8],[3],[5],[7]]=>[7,5,3,1,2,4,6,8]=>[2,4,6,8,7,5,3,1]=>[[1,3,5,7],[2],[4],[6],[8]]
[[1,2,3,4,8],[5],[6],[7]]=>[7,6,5,1,2,3,4,8]=>[2,3,4,8,7,6,5,1]=>[[1,3,4,5],[2],[6],[7],[8]]
[[1,4,5,6,7],[2],[3],[8]]=>[8,3,2,1,4,5,6,7]=>[1,6,7,8,5,4,3,2]=>[[1,2,7,8],[3],[4],[5],[6]]
[[1,3,4,6,7],[2],[5],[8]]=>[8,5,2,1,3,4,6,7]=>[1,4,7,8,6,5,3,2]=>[[1,2,5,8],[3],[4],[6],[7]]
[[1,2,4,6,7],[3],[5],[8]]=>[8,5,3,1,2,4,6,7]=>[1,4,6,8,7,5,3,2]=>[[1,2,5,7],[3],[4],[6],[8]]
[[1,2,3,6,7],[4],[5],[8]]=>[8,5,4,1,2,3,6,7]=>[1,4,5,8,7,6,3,2]=>[[1,2,5,6],[3],[4],[7],[8]]
[[1,3,4,5,7],[2],[6],[8]]=>[8,6,2,1,3,4,5,7]=>[1,3,7,8,6,5,4,2]=>[[1,2,4,8],[3],[5],[6],[7]]
[[1,2,4,5,7],[3],[6],[8]]=>[8,6,3,1,2,4,5,7]=>[1,3,6,8,7,5,4,2]=>[[1,2,4,7],[3],[5],[6],[8]]
[[1,2,3,5,7],[4],[6],[8]]=>[8,6,4,1,2,3,5,7]=>[1,3,5,8,7,6,4,2]=>[[1,2,4,6],[3],[5],[7],[8]]
[[1,2,3,4,7],[5],[6],[8]]=>[8,6,5,1,2,3,4,7]=>[1,3,4,8,7,6,5,2]=>[[1,2,4,5],[3],[6],[7],[8]]
[[1,3,4,5,6],[2],[7],[8]]=>[8,7,2,1,3,4,5,6]=>[1,2,7,8,6,5,4,3]=>[[1,2,3,8],[4],[5],[6],[7]]
[[1,2,3,5,6],[4],[7],[8]]=>[8,7,4,1,2,3,5,6]=>[1,2,5,8,7,6,4,3]=>[[1,2,3,6],[4],[5],[7],[8]]
[[1,2,3,4,6],[5],[7],[8]]=>[8,7,5,1,2,3,4,6]=>[1,2,4,8,7,6,5,3]=>[[1,2,3,5],[4],[6],[7],[8]]
[[1,2,3,4,5],[6],[7],[8]]=>[8,7,6,1,2,3,4,5]=>[1,2,3,8,7,6,5,4]=>[[1,2,3,4],[5],[6],[7],[8]]
[[1,3,5,7],[2,4,6,8]]=>[2,4,6,8,1,3,5,7]=>[7,5,3,1,8,6,4,2]=>[[1,2],[3,4],[5,6],[7,8]]
[[1,2,5,7],[3,4,6,8]]=>[3,4,6,8,1,2,5,7]=>[6,5,3,1,8,7,4,2]=>[[1,2],[3,4],[5,7],[6,8]]
[[1,3,4,7],[2,5,6,8]]=>[2,5,6,8,1,3,4,7]=>[7,4,3,1,8,6,5,2]=>[[1,2],[3,5],[4,6],[7,8]]
[[1,2,4,7],[3,5,6,8]]=>[3,5,6,8,1,2,4,7]=>[6,4,3,1,8,7,5,2]=>[[1,2],[3,5],[4,7],[6,8]]
[[1,3,5,6],[2,4,7,8]]=>[2,4,7,8,1,3,5,6]=>[7,5,2,1,8,6,4,3]=>[[1,3],[2,4],[5,6],[7,8]]
[[1,2,5,6],[3,4,7,8]]=>[3,4,7,8,1,2,5,6]=>[6,5,2,1,8,7,4,3]=>[[1,3],[2,4],[5,7],[6,8]]
[[1,3,4,6],[2,5,7,8]]=>[2,5,7,8,1,3,4,6]=>[7,4,2,1,8,6,5,3]=>[[1,3],[2,5],[4,6],[7,8]]
[[1,2,4,6],[3,5,7,8]]=>[3,5,7,8,1,2,4,6]=>[6,4,2,1,8,7,5,3]=>[[1,3],[2,5],[4,7],[6,8]]
[[1,2,3,6],[4,5,7,8]]=>[4,5,7,8,1,2,3,6]=>[5,4,2,1,8,7,6,3]=>[[1,3],[2,6],[4,7],[5,8]]
[[1,3,4,5],[2,6,7,8]]=>[2,6,7,8,1,3,4,5]=>[7,3,2,1,8,6,5,4]=>[[1,4],[2,5],[3,6],[7,8]]
[[1,2,4,5],[3,6,7,8]]=>[3,6,7,8,1,2,4,5]=>[6,3,2,1,8,7,5,4]=>[[1,4],[2,5],[3,7],[6,8]]
[[1,2,3,5],[4,6,7,8]]=>[4,6,7,8,1,2,3,5]=>[5,3,2,1,8,7,6,4]=>[[1,4],[2,6],[3,7],[5,8]]
[[1,2,3,4],[5,6,7,8]]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>[[1,5],[2,6],[3,7],[4,8]]
[[1,3,5,8],[2,6,7],[4]]=>[4,2,6,7,1,3,5,8]=>[5,7,3,2,8,6,4,1]=>[[1,4,8],[2,6],[3,7],[5]]
[[1,3,4,8],[2,6,7],[5]]=>[5,2,6,7,1,3,4,8]=>[4,7,3,2,8,6,5,1]=>[[1,5,8],[2,6],[3,7],[4]]
[[1,3,4,8],[2,5,7],[6]]=>[6,2,5,7,1,3,4,8]=>[3,7,4,2,8,6,5,1]=>[[1,4,5],[2,6],[3,8],[7]]
[[1,2,4,8],[3,5,7],[6]]=>[6,3,5,7,1,2,4,8]=>[3,6,4,2,8,7,5,1]=>[[1,4,5],[2,7],[3,8],[6]]
[[1,3,5,8],[2,4,6],[7]]=>[7,2,4,6,1,3,5,8]=>[2,7,5,3,8,6,4,1]=>[[1,3,4],[2,6],[5,8],[7]]
[[1,2,4,8],[3,5,6],[7]]=>[7,3,5,6,1,2,4,8]=>[2,6,4,3,8,7,5,1]=>[[1,3,5],[2,7],[4,8],[6]]
[[1,2,3,8],[4,5,6],[7]]=>[7,4,5,6,1,2,3,8]=>[2,5,4,3,8,7,6,1]=>[[1,3,6],[2,7],[4,8],[5]]
[[1,4,6,7],[2,5,8],[3]]=>[3,2,5,8,1,4,6,7]=>[6,7,4,1,8,5,3,2]=>[[1,2,8],[3,5],[4,7],[6]]
[[1,3,6,7],[2,5,8],[4]]=>[4,2,5,8,1,3,6,7]=>[5,7,4,1,8,6,3,2]=>[[1,2,8],[3,6],[4,7],[5]]
[[1,2,6,7],[3,5,8],[4]]=>[4,3,5,8,1,2,6,7]=>[5,6,4,1,8,7,3,2]=>[[1,2,7],[3,6],[4,8],[5]]
[[1,3,6,7],[2,4,8],[5]]=>[5,2,4,8,1,3,6,7]=>[4,7,5,1,8,6,3,2]=>[[1,2,6],[3,5],[4,8],[7]]
[[1,4,5,7],[2,6,8],[3]]=>[3,2,6,8,1,4,5,7]=>[6,7,3,1,8,5,4,2]=>[[1,2,8],[3,4],[5,7],[6]]
[[1,3,5,7],[2,6,8],[4]]=>[4,2,6,8,1,3,5,7]=>[5,7,3,1,8,6,4,2]=>[[1,2,8],[3,4],[5,6],[7]]
[[1,3,4,7],[2,6,8],[5]]=>[5,2,6,8,1,3,4,7]=>[4,7,3,1,8,6,5,2]=>[[1,2,8],[3,5],[4,6],[7]]
[[1,2,4,7],[3,6,8],[5]]=>[5,3,6,8,1,2,4,7]=>[4,6,3,1,8,7,5,2]=>[[1,2,7],[3,5],[4,6],[8]]
[[1,2,3,7],[4,6,8],[5]]=>[5,4,6,8,1,2,3,7]=>[4,5,3,1,8,7,6,2]=>[[1,2,6],[3,5],[4,7],[8]]
[[1,3,5,7],[2,4,8],[6]]=>[6,2,4,8,1,3,5,7]=>[3,7,5,1,8,6,4,2]=>[[1,2,6],[3,4],[5,8],[7]]
[[1,2,5,7],[3,4,8],[6]]=>[6,3,4,8,1,2,5,7]=>[3,6,5,1,8,7,4,2]=>[[1,2,7],[3,4],[5,8],[6]]
[[1,3,4,7],[2,5,8],[6]]=>[6,2,5,8,1,3,4,7]=>[3,7,4,1,8,6,5,2]=>[[1,2,5],[3,4],[6,8],[7]]
[[1,2,4,7],[3,5,8],[6]]=>[6,3,5,8,1,2,4,7]=>[3,6,4,1,8,7,5,2]=>[[1,2,5],[3,4],[6,7],[8]]
[[1,4,5,6],[2,7,8],[3]]=>[3,2,7,8,1,4,5,6]=>[6,7,2,1,8,5,4,3]=>[[1,3,8],[2,4],[5,7],[6]]
[[1,3,4,6],[2,7,8],[5]]=>[5,2,7,8,1,3,4,6]=>[4,7,2,1,8,6,5,3]=>[[1,3,8],[2,5],[4,6],[7]]
[[1,2,4,6],[3,7,8],[5]]=>[5,3,7,8,1,2,4,6]=>[4,6,2,1,8,7,5,3]=>[[1,3,7],[2,5],[4,6],[8]]
[[1,2,3,6],[4,7,8],[5]]=>[5,4,7,8,1,2,3,6]=>[4,5,2,1,8,7,6,3]=>[[1,3,6],[2,5],[4,7],[8]]
[[1,2,3,5],[4,7,8],[6]]=>[6,4,7,8,1,2,3,5]=>[3,5,2,1,8,7,6,4]=>[[1,4,6],[2,5],[3,7],[8]]
[[1,2,3,4],[5,7,8],[6]]=>[6,5,7,8,1,2,3,4]=>[3,4,2,1,8,7,6,5]=>[[1,4,5],[2,6],[3,7],[8]]
[[1,2,5,6],[3,4,8],[7]]=>[7,3,4,8,1,2,5,6]=>[2,6,5,1,8,7,4,3]=>[[1,3,7],[2,4],[5,8],[6]]
[[1,2,4,6],[3,5,8],[7]]=>[7,3,5,8,1,2,4,6]=>[2,6,4,1,8,7,5,3]=>[[1,3,5],[2,4],[6,7],[8]]
[[1,2,3,6],[4,5,8],[7]]=>[7,4,5,8,1,2,3,6]=>[2,5,4,1,8,7,6,3]=>[[1,3,6],[2,4],[5,7],[8]]
[[1,2,3,4],[5,6,8],[7]]=>[7,5,6,8,1,2,3,4]=>[2,4,3,1,8,7,6,5]=>[[1,3,5],[2,6],[4,7],[8]]
[[1,3,5,7],[2,4,6],[8]]=>[8,2,4,6,1,3,5,7]=>[1,7,5,3,8,6,4,2]=>[[1,2,4],[3,6],[5,8],[7]]
[[1,2,4,7],[3,5,6],[8]]=>[8,3,5,6,1,2,4,7]=>[1,6,4,3,8,7,5,2]=>[[1,2,5],[3,7],[4,8],[6]]
[[1,2,3,7],[4,5,6],[8]]=>[8,4,5,6,1,2,3,7]=>[1,5,4,3,8,7,6,2]=>[[1,2,6],[3,7],[4,8],[5]]
[[1,3,5,6],[2,4,7],[8]]=>[8,2,4,7,1,3,5,6]=>[1,7,5,2,8,6,4,3]=>[[1,2,3],[4,6],[5,8],[7]]
[[1,2,5,6],[3,4,7],[8]]=>[8,3,4,7,1,2,5,6]=>[1,6,5,2,8,7,4,3]=>[[1,2,3],[4,7],[5,8],[6]]
[[1,3,4,6],[2,5,7],[8]]=>[8,2,5,7,1,3,4,6]=>[1,7,4,2,8,6,5,3]=>[[1,2,3],[4,5],[6,8],[7]]
[[1,2,4,6],[3,5,7],[8]]=>[8,3,5,7,1,2,4,6]=>[1,6,4,2,8,7,5,3]=>[[1,2,3],[4,5],[6,7],[8]]
[[1,3,4,5],[2,6,7],[8]]=>[8,2,6,7,1,3,4,5]=>[1,7,3,2,8,6,5,4]=>[[1,2,4],[3,5],[6,8],[7]]
[[1,2,3,5],[4,6,7],[8]]=>[8,4,6,7,1,2,3,5]=>[1,5,3,2,8,7,6,4]=>[[1,2,4],[3,6],[5,7],[8]]
[[1,2,3,4],[5,6,7],[8]]=>[8,5,6,7,1,2,3,4]=>[1,4,3,2,8,7,6,5]=>[[1,2,5],[3,6],[4,7],[8]]
[[1,4,7,8],[2,5],[3,6]]=>[3,6,2,5,1,4,7,8]=>[6,3,7,4,8,5,2,1]=>[[1,4,5],[2,7,8],[3],[6]]
[[1,3,7,8],[2,5],[4,6]]=>[4,6,2,5,1,3,7,8]=>[5,3,7,4,8,6,2,1]=>[[1,4,6],[2,7,8],[3],[5]]
[[1,2,7,8],[3,5],[4,6]]=>[4,6,3,5,1,2,7,8]=>[5,3,6,4,8,7,2,1]=>[[1,4,7],[2,6,8],[3],[5]]
[[1,2,7,8],[3,4],[5,6]]=>[5,6,3,4,1,2,7,8]=>[4,3,6,5,8,7,2,1]=>[[1,5,7],[2,6,8],[3],[4]]
[[1,4,6,8],[2,5],[3,7]]=>[3,7,2,5,1,4,6,8]=>[6,2,7,4,8,5,3,1]=>[[1,3,5],[2,7,8],[4],[6]]
[[1,2,6,8],[3,5],[4,7]]=>[4,7,3,5,1,2,6,8]=>[5,2,6,4,8,7,3,1]=>[[1,3,7],[2,6,8],[4],[5]]
[[1,3,6,8],[2,4],[5,7]]=>[5,7,2,4,1,3,6,8]=>[4,2,7,5,8,6,3,1]=>[[1,3,6],[2,5,8],[4],[7]]
[[1,2,6,8],[3,4],[5,7]]=>[5,7,3,4,1,2,6,8]=>[4,2,6,5,8,7,3,1]=>[[1,3,7],[2,5,8],[4],[6]]
[[1,4,5,8],[2,6],[3,7]]=>[3,7,2,6,1,4,5,8]=>[6,2,7,3,8,5,4,1]=>[[1,3,4],[2,7,8],[5],[6]]
[[1,2,5,8],[3,6],[4,7]]=>[4,7,3,6,1,2,5,8]=>[5,2,6,3,8,7,4,1]=>[[1,3,4],[2,6,7],[5],[8]]
[[1,2,3,8],[4,6],[5,7]]=>[5,7,4,6,1,2,3,8]=>[4,2,5,3,8,7,6,1]=>[[1,3,6],[2,5,7],[4],[8]]
[[1,3,5,8],[2,4],[6,7]]=>[6,7,2,4,1,3,5,8]=>[3,2,7,5,8,6,4,1]=>[[1,4,6],[2,5,8],[3],[7]]
[[1,4,6,7],[2,5],[3,8]]=>[3,8,2,5,1,4,6,7]=>[6,1,7,4,8,5,3,2]=>[[1,2,5],[3,7,8],[4],[6]]
[[1,3,6,7],[2,5],[4,8]]=>[4,8,2,5,1,3,6,7]=>[5,1,7,4,8,6,3,2]=>[[1,2,6],[3,7,8],[4],[5]]
[[1,3,6,7],[2,4],[5,8]]=>[5,8,2,4,1,3,6,7]=>[4,1,7,5,8,6,3,2]=>[[1,2,6],[3,5,8],[4],[7]]
[[1,2,6,7],[3,4],[5,8]]=>[5,8,3,4,1,2,6,7]=>[4,1,6,5,8,7,3,2]=>[[1,2,7],[3,5,8],[4],[6]]
[[1,4,5,7],[2,6],[3,8]]=>[3,8,2,6,1,4,5,7]=>[6,1,7,3,8,5,4,2]=>[[1,2,4],[3,7,8],[5],[6]]
[[1,3,5,7],[2,6],[4,8]]=>[4,8,2,6,1,3,5,7]=>[5,1,7,3,8,6,4,2]=>[[1,2,4],[3,6,8],[5],[7]]
[[1,2,4,7],[3,6],[5,8]]=>[5,8,3,6,1,2,4,7]=>[4,1,6,3,8,7,5,2]=>[[1,2,5],[3,6,7],[4],[8]]
[[1,2,3,7],[4,6],[5,8]]=>[5,8,4,6,1,2,3,7]=>[4,1,5,3,8,7,6,2]=>[[1,2,6],[3,5,7],[4],[8]]
[[1,3,5,7],[2,4],[6,8]]=>[6,8,2,4,1,3,5,7]=>[3,1,7,5,8,6,4,2]=>[[1,2,6],[3,4,8],[5],[7]]
[[1,3,4,7],[2,5],[6,8]]=>[6,8,2,5,1,3,4,7]=>[3,1,7,4,8,6,5,2]=>[[1,2,5],[3,4,8],[6],[7]]
[[1,4,5,6],[2,7],[3,8]]=>[3,8,2,7,1,4,5,6]=>[6,1,7,2,8,5,4,3]=>[[1,2,3],[4,7,8],[5],[6]]
[[1,3,5,6],[2,7],[4,8]]=>[4,8,2,7,1,3,5,6]=>[5,1,7,2,8,6,4,3]=>[[1,2,3],[4,6,8],[5],[7]]
[[1,2,5,6],[3,7],[4,8]]=>[4,8,3,7,1,2,5,6]=>[5,1,6,2,8,7,4,3]=>[[1,2,3],[4,6,7],[5],[8]]
[[1,2,4,6],[3,7],[5,8]]=>[5,8,3,7,1,2,4,6]=>[4,1,6,2,8,7,5,3]=>[[1,2,3],[4,5,7],[6],[8]]
[[1,2,3,6],[4,7],[5,8]]=>[5,8,4,7,1,2,3,6]=>[4,1,5,2,8,7,6,3]=>[[1,2,3],[4,5,6],[7],[8]]
[[1,2,4,5],[3,7],[6,8]]=>[6,8,3,7,1,2,4,5]=>[3,1,6,2,8,7,5,4]=>[[1,2,4],[3,5,7],[6],[8]]
[[1,2,3,5],[4,7],[6,8]]=>[6,8,4,7,1,2,3,5]=>[3,1,5,2,8,7,6,4]=>[[1,2,4],[3,5,6],[7],[8]]
[[1,3,5,6],[2,4],[7,8]]=>[7,8,2,4,1,3,5,6]=>[2,1,7,5,8,6,4,3]=>[[1,3,6],[2,4,8],[5],[7]]
[[1,2,5,6],[3,4],[7,8]]=>[7,8,3,4,1,2,5,6]=>[2,1,6,5,8,7,4,3]=>[[1,3,7],[2,4,8],[5],[6]]
[[1,2,4,6],[3,5],[7,8]]=>[7,8,3,5,1,2,4,6]=>[2,1,6,4,8,7,5,3]=>[[1,3,5],[2,4,7],[6],[8]]
[[1,2,3,6],[4,5],[7,8]]=>[7,8,4,5,1,2,3,6]=>[2,1,5,4,8,7,6,3]=>[[1,3,6],[2,4,7],[5],[8]]
[[1,3,4,5],[2,6],[7,8]]=>[7,8,2,6,1,3,4,5]=>[2,1,7,3,8,6,5,4]=>[[1,3,4],[2,5,8],[6],[7]]
[[1,2,3,5],[4,6],[7,8]]=>[7,8,4,6,1,2,3,5]=>[2,1,5,3,8,7,6,4]=>[[1,3,4],[2,5,6],[7],[8]]
[[1,2,3,4],[5,6],[7,8]]=>[7,8,5,6,1,2,3,4]=>[2,1,4,3,8,7,6,5]=>[[1,3,5],[2,4,6],[7],[8]]
[[1,5,7,8],[2,6],[3],[4]]=>[4,3,2,6,1,5,7,8]=>[5,6,7,3,8,4,2,1]=>[[1,4,7,8],[2,6],[3],[5]]
[[1,4,7,8],[2,6],[3],[5]]=>[5,3,2,6,1,4,7,8]=>[4,6,7,3,8,5,2,1]=>[[1,5,7,8],[2,6],[3],[4]]
[[1,3,7,8],[2,6],[4],[5]]=>[5,4,2,6,1,3,7,8]=>[4,5,7,3,8,6,2,1]=>[[1,5,6,8],[2,7],[3],[4]]
[[1,2,7,8],[3,6],[4],[5]]=>[5,4,3,6,1,2,7,8]=>[4,5,6,3,8,7,2,1]=>[[1,5,6,7],[2,8],[3],[4]]
[[1,3,7,8],[2,5],[4],[6]]=>[6,4,2,5,1,3,7,8]=>[3,5,7,4,8,6,2,1]=>[[1,4,6,8],[2,7],[3],[5]]
[[1,3,7,8],[2,4],[5],[6]]=>[6,5,2,4,1,3,7,8]=>[3,4,7,5,8,6,2,1]=>[[1,4,5,6],[2,8],[3],[7]]
[[1,5,6,8],[2,7],[3],[4]]=>[4,3,2,7,1,5,6,8]=>[5,6,7,2,8,4,3,1]=>[[1,3,7,8],[2,6],[4],[5]]
[[1,4,6,8],[2,7],[3],[5]]=>[5,3,2,7,1,4,6,8]=>[4,6,7,2,8,5,3,1]=>[[1,3,7,8],[2,5],[4],[6]]
[[1,3,6,8],[2,7],[4],[5]]=>[5,4,2,7,1,3,6,8]=>[4,5,7,2,8,6,3,1]=>[[1,3,6,8],[2,5],[4],[7]]
[[1,4,5,8],[2,7],[3],[6]]=>[6,3,2,7,1,4,5,8]=>[3,6,7,2,8,5,4,1]=>[[1,4,7,8],[2,5],[3],[6]]
[[1,3,5,8],[2,7],[4],[6]]=>[6,4,2,7,1,3,5,8]=>[3,5,7,2,8,6,4,1]=>[[1,4,6,8],[2,5],[3],[7]]
[[1,2,5,8],[3,7],[4],[6]]=>[6,4,3,7,1,2,5,8]=>[3,5,6,2,8,7,4,1]=>[[1,4,6,7],[2,5],[3],[8]]
[[1,2,4,8],[3,7],[5],[6]]=>[6,5,3,7,1,2,4,8]=>[3,4,6,2,8,7,5,1]=>[[1,4,5,7],[2,6],[3],[8]]
[[1,4,6,8],[2,5],[3],[7]]=>[7,3,2,5,1,4,6,8]=>[2,6,7,4,8,5,3,1]=>[[1,3,5,8],[2,7],[4],[6]]
[[1,3,6,8],[2,5],[4],[7]]=>[7,4,2,5,1,3,6,8]=>[2,5,7,4,8,6,3,1]=>[[1,3,6,8],[2,7],[4],[5]]
[[1,2,6,8],[3,5],[4],[7]]=>[7,4,3,5,1,2,6,8]=>[2,5,6,4,8,7,3,1]=>[[1,3,6,7],[2,8],[4],[5]]
[[1,2,6,8],[3,4],[5],[7]]=>[7,5,3,4,1,2,6,8]=>[2,4,6,5,8,7,3,1]=>[[1,3,5,7],[2,8],[4],[6]]
[[1,4,5,8],[2,6],[3],[7]]=>[7,3,2,6,1,4,5,8]=>[2,6,7,3,8,5,4,1]=>[[1,3,4,8],[2,7],[5],[6]]
[[1,3,5,8],[2,6],[4],[7]]=>[7,4,2,6,1,3,5,8]=>[2,5,7,3,8,6,4,1]=>[[1,3,4,8],[2,6],[5],[7]]
[[1,3,4,8],[2,6],[5],[7]]=>[7,5,2,6,1,3,4,8]=>[2,4,7,3,8,6,5,1]=>[[1,3,5,8],[2,6],[4],[7]]
[[1,2,4,8],[3,6],[5],[7]]=>[7,5,3,6,1,2,4,8]=>[2,4,6,3,8,7,5,1]=>[[1,3,5,7],[2,6],[4],[8]]
[[1,2,5,8],[3,4],[6],[7]]=>[7,6,3,4,1,2,5,8]=>[2,3,6,5,8,7,4,1]=>[[1,3,4,7],[2,8],[5],[6]]
[[1,5,6,7],[2,8],[3],[4]]=>[4,3,2,8,1,5,6,7]=>[5,6,7,1,8,4,3,2]=>[[1,2,7,8],[3,6],[4],[5]]
[[1,4,6,7],[2,8],[3],[5]]=>[5,3,2,8,1,4,6,7]=>[4,6,7,1,8,5,3,2]=>[[1,2,7,8],[3,5],[4],[6]]
[[1,2,6,7],[3,8],[4],[5]]=>[5,4,3,8,1,2,6,7]=>[4,5,6,1,8,7,3,2]=>[[1,2,6,7],[3,5],[4],[8]]
[[1,4,5,7],[2,8],[3],[6]]=>[6,3,2,8,1,4,5,7]=>[3,6,7,1,8,5,4,2]=>[[1,2,7,8],[3,4],[5],[6]]
[[1,3,5,7],[2,8],[4],[6]]=>[6,4,2,8,1,3,5,7]=>[3,5,7,1,8,6,4,2]=>[[1,2,6,8],[3,4],[5],[7]]
[[1,2,5,7],[3,8],[4],[6]]=>[6,4,3,8,1,2,5,7]=>[3,5,6,1,8,7,4,2]=>[[1,2,6,7],[3,4],[5],[8]]
[[1,3,4,7],[2,8],[5],[6]]=>[6,5,2,8,1,3,4,7]=>[3,4,7,1,8,6,5,2]=>[[1,2,5,8],[3,4],[6],[7]]
[[1,2,3,7],[4,8],[5],[6]]=>[6,5,4,8,1,2,3,7]=>[3,4,5,1,8,7,6,2]=>[[1,2,5,6],[3,4],[7],[8]]
[[1,3,5,6],[2,8],[4],[7]]=>[7,4,2,8,1,3,5,6]=>[2,5,7,1,8,6,4,3]=>[[1,3,6,8],[2,4],[5],[7]]
[[1,2,5,6],[3,8],[4],[7]]=>[7,4,3,8,1,2,5,6]=>[2,5,6,1,8,7,4,3]=>[[1,3,6,7],[2,4],[5],[8]]
[[1,2,4,6],[3,8],[5],[7]]=>[7,5,3,8,1,2,4,6]=>[2,4,6,1,8,7,5,3]=>[[1,3,5,7],[2,4],[6],[8]]
[[1,2,4,5],[3,8],[6],[7]]=>[7,6,3,8,1,2,4,5]=>[2,3,6,1,8,7,5,4]=>[[1,3,4,7],[2,5],[6],[8]]
[[1,2,3,4],[5,8],[6],[7]]=>[7,6,5,8,1,2,3,4]=>[2,3,4,1,8,7,6,5]=>[[1,3,4,5],[2,6],[7],[8]]
[[1,4,6,7],[2,5],[3],[8]]=>[8,3,2,5,1,4,6,7]=>[1,6,7,4,8,5,3,2]=>[[1,2,5,8],[3,7],[4],[6]]
[[1,3,6,7],[2,5],[4],[8]]=>[8,4,2,5,1,3,6,7]=>[1,5,7,4,8,6,3,2]=>[[1,2,6,8],[3,7],[4],[5]]
[[1,3,6,7],[2,4],[5],[8]]=>[8,5,2,4,1,3,6,7]=>[1,4,7,5,8,6,3,2]=>[[1,2,5,6],[3,8],[4],[7]]
[[1,2,6,7],[3,4],[5],[8]]=>[8,5,3,4,1,2,6,7]=>[1,4,6,5,8,7,3,2]=>[[1,2,5,7],[3,8],[4],[6]]
[[1,4,5,7],[2,6],[3],[8]]=>[8,3,2,6,1,4,5,7]=>[1,6,7,3,8,5,4,2]=>[[1,2,4,8],[3,7],[5],[6]]
[[1,3,5,7],[2,6],[4],[8]]=>[8,4,2,6,1,3,5,7]=>[1,5,7,3,8,6,4,2]=>[[1,2,4,8],[3,6],[5],[7]]
[[1,2,4,7],[3,6],[5],[8]]=>[8,5,3,6,1,2,4,7]=>[1,4,6,3,8,7,5,2]=>[[1,2,5,7],[3,6],[4],[8]]
[[1,2,3,7],[4,6],[5],[8]]=>[8,5,4,6,1,2,3,7]=>[1,4,5,3,8,7,6,2]=>[[1,2,5,6],[3,7],[4],[8]]
[[1,3,5,7],[2,4],[6],[8]]=>[8,6,2,4,1,3,5,7]=>[1,3,7,5,8,6,4,2]=>[[1,2,4,6],[3,8],[5],[7]]
[[1,2,4,7],[3,5],[6],[8]]=>[8,6,3,5,1,2,4,7]=>[1,3,6,4,8,7,5,2]=>[[1,2,4,5],[3,7],[6],[8]]
[[1,2,3,7],[4,5],[6],[8]]=>[8,6,4,5,1,2,3,7]=>[1,3,5,4,8,7,6,2]=>[[1,2,4,6],[3,7],[5],[8]]
[[1,4,5,6],[2,7],[3],[8]]=>[8,3,2,7,1,4,5,6]=>[1,6,7,2,8,5,4,3]=>[[1,2,3,8],[4,7],[5],[6]]
[[1,3,5,6],[2,7],[4],[8]]=>[8,4,2,7,1,3,5,6]=>[1,5,7,2,8,6,4,3]=>[[1,2,3,8],[4,6],[5],[7]]
[[1,2,4,6],[3,7],[5],[8]]=>[8,5,3,7,1,2,4,6]=>[1,4,6,2,8,7,5,3]=>[[1,2,3,7],[4,5],[6],[8]]
[[1,2,3,6],[4,7],[5],[8]]=>[8,5,4,7,1,2,3,6]=>[1,4,5,2,8,7,6,3]=>[[1,2,3,6],[4,5],[7],[8]]
[[1,2,3,4],[5,7],[6],[8]]=>[8,6,5,7,1,2,3,4]=>[1,3,4,2,8,7,6,5]=>[[1,2,4,5],[3,6],[7],[8]]
[[1,3,5,6],[2,4],[7],[8]]=>[8,7,2,4,1,3,5,6]=>[1,2,7,5,8,6,4,3]=>[[1,2,3,6],[4,8],[5],[7]]
[[1,2,5,6],[3,4],[7],[8]]=>[8,7,3,4,1,2,5,6]=>[1,2,6,5,8,7,4,3]=>[[1,2,3,7],[4,8],[5],[6]]
[[1,2,4,6],[3,5],[7],[8]]=>[8,7,3,5,1,2,4,6]=>[1,2,6,4,8,7,5,3]=>[[1,2,3,5],[4,7],[6],[8]]
[[1,2,3,6],[4,5],[7],[8]]=>[8,7,4,5,1,2,3,6]=>[1,2,5,4,8,7,6,3]=>[[1,2,3,6],[4,7],[5],[8]]
[[1,3,4,5],[2,6],[7],[8]]=>[8,7,2,6,1,3,4,5]=>[1,2,7,3,8,6,5,4]=>[[1,2,3,4],[5,8],[6],[7]]
[[1,2,4,5],[3,6],[7],[8]]=>[8,7,3,6,1,2,4,5]=>[1,2,6,3,8,7,5,4]=>[[1,2,3,4],[5,7],[6],[8]]
[[1,2,3,5],[4,6],[7],[8]]=>[8,7,4,6,1,2,3,5]=>[1,2,5,3,8,7,6,4]=>[[1,2,3,4],[5,6],[7],[8]]
[[1,2,3,4],[5,6],[7],[8]]=>[8,7,5,6,1,2,3,4]=>[1,2,4,3,8,7,6,5]=>[[1,2,3,5],[4,6],[7],[8]]
[[1,6,7,8],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8]=>[4,5,6,7,8,3,2,1]=>[[1,5,6,7,8],[2],[3],[4]]
[[1,5,7,8],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7,8]=>[3,5,6,7,8,4,2,1]=>[[1,4,6,7,8],[2],[3],[5]]
[[1,4,7,8],[2],[3],[5],[6]]=>[6,5,3,2,1,4,7,8]=>[3,4,6,7,8,5,2,1]=>[[1,4,5,7,8],[2],[3],[6]]
[[1,3,7,8],[2],[4],[5],[6]]=>[6,5,4,2,1,3,7,8]=>[3,4,5,7,8,6,2,1]=>[[1,4,5,6,8],[2],[3],[7]]
[[1,2,7,8],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7,8]=>[3,4,5,6,8,7,2,1]=>[[1,4,5,6,7],[2],[3],[8]]
[[1,5,6,8],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6,8]=>[2,5,6,7,8,4,3,1]=>[[1,3,6,7,8],[2],[4],[5]]
[[1,4,6,8],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6,8]=>[2,4,6,7,8,5,3,1]=>[[1,3,5,7,8],[2],[4],[6]]
[[1,3,6,8],[2],[4],[5],[7]]=>[7,5,4,2,1,3,6,8]=>[2,4,5,7,8,6,3,1]=>[[1,3,5,6,8],[2],[4],[7]]
[[1,4,5,8],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5,8]=>[2,3,6,7,8,5,4,1]=>[[1,3,4,7,8],[2],[5],[6]]
[[1,3,5,8],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5,8]=>[2,3,5,7,8,6,4,1]=>[[1,3,4,6,8],[2],[5],[7]]
[[1,2,5,8],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5,8]=>[2,3,5,6,8,7,4,1]=>[[1,3,4,6,7],[2],[5],[8]]
[[1,3,4,8],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4,8]=>[2,3,4,7,8,6,5,1]=>[[1,3,4,5,8],[2],[6],[7]]
[[1,2,4,8],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4,8]=>[2,3,4,6,8,7,5,1]=>[[1,3,4,5,7],[2],[6],[8]]
[[1,2,3,8],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3,8]=>[2,3,4,5,8,7,6,1]=>[[1,3,4,5,6],[2],[7],[8]]
[[1,5,6,7],[2],[3],[4],[8]]=>[8,4,3,2,1,5,6,7]=>[1,5,6,7,8,4,3,2]=>[[1,2,6,7,8],[3],[4],[5]]
[[1,4,6,7],[2],[3],[5],[8]]=>[8,5,3,2,1,4,6,7]=>[1,4,6,7,8,5,3,2]=>[[1,2,5,7,8],[3],[4],[6]]
[[1,4,5,7],[2],[3],[6],[8]]=>[8,6,3,2,1,4,5,7]=>[1,3,6,7,8,5,4,2]=>[[1,2,4,7,8],[3],[5],[6]]
[[1,3,5,7],[2],[4],[6],[8]]=>[8,6,4,2,1,3,5,7]=>[1,3,5,7,8,6,4,2]=>[[1,2,4,6,8],[3],[5],[7]]
[[1,2,5,7],[3],[4],[6],[8]]=>[8,6,4,3,1,2,5,7]=>[1,3,5,6,8,7,4,2]=>[[1,2,4,6,7],[3],[5],[8]]
[[1,2,3,7],[4],[5],[6],[8]]=>[8,6,5,4,1,2,3,7]=>[1,3,4,5,8,7,6,2]=>[[1,2,4,5,6],[3],[7],[8]]
[[1,4,5,6],[2],[3],[7],[8]]=>[8,7,3,2,1,4,5,6]=>[1,2,6,7,8,5,4,3]=>[[1,2,3,7,8],[4],[5],[6]]
[[1,2,5,6],[3],[4],[7],[8]]=>[8,7,4,3,1,2,5,6]=>[1,2,5,6,8,7,4,3]=>[[1,2,3,6,7],[4],[5],[8]]
[[1,3,4,6],[2],[5],[7],[8]]=>[8,7,5,2,1,3,4,6]=>[1,2,4,7,8,6,5,3]=>[[1,2,3,5,8],[4],[6],[7]]
[[1,2,4,6],[3],[5],[7],[8]]=>[8,7,5,3,1,2,4,6]=>[1,2,4,6,8,7,5,3]=>[[1,2,3,5,7],[4],[6],[8]]
[[1,2,3,6],[4],[5],[7],[8]]=>[8,7,5,4,1,2,3,6]=>[1,2,4,5,8,7,6,3]=>[[1,2,3,5,6],[4],[7],[8]]
[[1,3,4,5],[2],[6],[7],[8]]=>[8,7,6,2,1,3,4,5]=>[1,2,3,7,8,6,5,4]=>[[1,2,3,4,8],[5],[6],[7]]
[[1,2,4,5],[3],[6],[7],[8]]=>[8,7,6,3,1,2,4,5]=>[1,2,3,6,8,7,5,4]=>[[1,2,3,4,7],[5],[6],[8]]
[[1,2,3,5],[4],[6],[7],[8]]=>[8,7,6,4,1,2,3,5]=>[1,2,3,5,8,7,6,4]=>[[1,2,3,4,6],[5],[7],[8]]
[[1,2,3,4],[5],[6],[7],[8]]=>[8,7,6,5,1,2,3,4]=>[1,2,3,4,8,7,6,5]=>[[1,2,3,4,5],[6],[7],[8]]
[[1,4,7],[2,5,8],[3,6]]=>[3,6,2,5,8,1,4,7]=>[6,3,7,4,1,8,5,2]=>[[1,2,5],[3,4,8],[6,7]]
[[1,3,7],[2,5,8],[4,6]]=>[4,6,2,5,8,1,3,7]=>[5,3,7,4,1,8,6,2]=>[[1,2,6],[3,4,8],[5,7]]
[[1,3,7],[2,4,8],[5,6]]=>[5,6,2,4,8,1,3,7]=>[4,3,7,5,1,8,6,2]=>[[1,2,6],[3,5,8],[4,7]]
[[1,2,7],[3,4,8],[5,6]]=>[5,6,3,4,8,1,2,7]=>[4,3,6,5,1,8,7,2]=>[[1,2,7],[3,5,8],[4,6]]
[[1,4,6],[2,5,8],[3,7]]=>[3,7,2,5,8,1,4,6]=>[6,2,7,4,1,8,5,3]=>[[1,3,5],[2,4,8],[6,7]]
[[1,3,6],[2,5,8],[4,7]]=>[4,7,2,5,8,1,3,6]=>[5,2,7,4,1,8,6,3]=>[[1,3,6],[2,4,8],[5,7]]
[[1,2,6],[3,5,8],[4,7]]=>[4,7,3,5,8,1,2,6]=>[5,2,6,4,1,8,7,3]=>[[1,3,7],[2,4,8],[5,6]]
[[1,3,6],[2,4,8],[5,7]]=>[5,7,2,4,8,1,3,6]=>[4,2,7,5,1,8,6,3]=>[[1,3,6],[2,5,8],[4,7]]
[[1,2,6],[3,4,8],[5,7]]=>[5,7,3,4,8,1,2,6]=>[4,2,6,5,1,8,7,3]=>[[1,3,7],[2,5,8],[4,6]]
[[1,2,5],[3,6,8],[4,7]]=>[4,7,3,6,8,1,2,5]=>[5,2,6,3,1,8,7,4]=>[[1,3,4],[2,6,7],[5,8]]
[[1,2,4],[3,6,8],[5,7]]=>[5,7,3,6,8,1,2,4]=>[4,2,6,3,1,8,7,5]=>[[1,3,5],[2,6,7],[4,8]]
[[1,2,3],[4,6,8],[5,7]]=>[5,7,4,6,8,1,2,3]=>[4,2,5,3,1,8,7,6]=>[[1,3,6],[2,5,7],[4,8]]
[[1,3,5],[2,4,8],[6,7]]=>[6,7,2,4,8,1,3,5]=>[3,2,7,5,1,8,6,4]=>[[1,4,6],[2,5,8],[3,7]]
[[1,2,4],[3,5,8],[6,7]]=>[6,7,3,5,8,1,2,4]=>[3,2,6,4,1,8,7,5]=>[[1,4,5],[2,6,7],[3,8]]
[[1,2,3],[4,5,8],[6,7]]=>[6,7,4,5,8,1,2,3]=>[3,2,5,4,1,8,7,6]=>[[1,4,6],[2,5,7],[3,8]]
[[1,4,6],[2,5,7],[3,8]]=>[3,8,2,5,7,1,4,6]=>[6,1,7,4,2,8,5,3]=>[[1,2,3],[4,5,8],[6,7]]
[[1,3,6],[2,5,7],[4,8]]=>[4,8,2,5,7,1,3,6]=>[5,1,7,4,2,8,6,3]=>[[1,2,3],[4,6,8],[5,7]]
[[1,2,6],[3,5,7],[4,8]]=>[4,8,3,5,7,1,2,6]=>[5,1,6,4,2,8,7,3]=>[[1,2,3],[4,6,7],[5,8]]
[[1,3,6],[2,4,7],[5,8]]=>[5,8,2,4,7,1,3,6]=>[4,1,7,5,2,8,6,3]=>[[1,2,3],[4,5,6],[7,8]]
[[1,4,5],[2,6,7],[3,8]]=>[3,8,2,6,7,1,4,5]=>[6,1,7,3,2,8,5,4]=>[[1,2,4],[3,5,8],[6,7]]
[[1,2,5],[3,6,7],[4,8]]=>[4,8,3,6,7,1,2,5]=>[5,1,6,3,2,8,7,4]=>[[1,2,4],[3,6,7],[5,8]]
[[1,3,4],[2,6,7],[5,8]]=>[5,8,2,6,7,1,3,4]=>[4,1,7,3,2,8,6,5]=>[[1,2,5],[3,6,8],[4,7]]
[[1,2,3],[4,6,7],[5,8]]=>[5,8,4,6,7,1,2,3]=>[4,1,5,3,2,8,7,6]=>[[1,2,6],[3,5,7],[4,8]]
[[1,2,5],[3,4,7],[6,8]]=>[6,8,3,4,7,1,2,5]=>[3,1,6,5,2,8,7,4]=>[[1,2,4],[3,5,7],[6,8]]
[[1,3,4],[2,5,7],[6,8]]=>[6,8,2,5,7,1,3,4]=>[3,1,7,4,2,8,6,5]=>[[1,2,5],[3,4,6],[7,8]]
[[1,3,5],[2,4,6],[7,8]]=>[7,8,2,4,6,1,3,5]=>[2,1,7,5,3,8,6,4]=>[[1,3,4],[2,5,6],[7,8]]
[[1,2,5],[3,4,6],[7,8]]=>[7,8,3,4,6,1,2,5]=>[2,1,6,5,3,8,7,4]=>[[1,3,4],[2,5,7],[6,8]]
[[1,3,4],[2,5,6],[7,8]]=>[7,8,2,5,6,1,3,4]=>[2,1,7,4,3,8,6,5]=>[[1,3,5],[2,4,6],[7,8]]
[[1,5,7],[2,6,8],[3],[4]]=>[4,3,2,6,8,1,5,7]=>[5,6,7,3,1,8,4,2]=>[[1,2,7,8],[3,4],[5,6]]
[[1,4,7],[2,6,8],[3],[5]]=>[5,3,2,6,8,1,4,7]=>[4,6,7,3,1,8,5,2]=>[[1,2,7,8],[3,5],[4,6]]
[[1,3,7],[2,6,8],[4],[5]]=>[5,4,2,6,8,1,3,7]=>[4,5,7,3,1,8,6,2]=>[[1,2,6,8],[3,5],[4,7]]
[[1,4,7],[2,5,8],[3],[6]]=>[6,3,2,5,8,1,4,7]=>[3,6,7,4,1,8,5,2]=>[[1,2,5,8],[3,4],[6,7]]
[[1,2,7],[3,5,8],[4],[6]]=>[6,4,3,5,8,1,2,7]=>[3,5,6,4,1,8,7,2]=>[[1,2,6,7],[3,4],[5,8]]
[[1,3,7],[2,4,8],[5],[6]]=>[6,5,2,4,8,1,3,7]=>[3,4,7,5,1,8,6,2]=>[[1,2,5,6],[3,4],[7,8]]
[[1,5,6],[2,7,8],[3],[4]]=>[4,3,2,7,8,1,5,6]=>[5,6,7,2,1,8,4,3]=>[[1,3,7,8],[2,4],[5,6]]
[[1,4,6],[2,7,8],[3],[5]]=>[5,3,2,7,8,1,4,6]=>[4,6,7,2,1,8,5,3]=>[[1,3,7,8],[2,5],[4,6]]
[[1,3,6],[2,7,8],[4],[5]]=>[5,4,2,7,8,1,3,6]=>[4,5,7,2,1,8,6,3]=>[[1,3,6,8],[2,5],[4,7]]
[[1,2,6],[3,7,8],[4],[5]]=>[5,4,3,7,8,1,2,6]=>[4,5,6,2,1,8,7,3]=>[[1,3,6,7],[2,5],[4,8]]
[[1,4,5],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5]=>[3,6,7,2,1,8,5,4]=>[[1,4,7,8],[2,5],[3,6]]
[[1,3,5],[2,7,8],[4],[6]]=>[6,4,2,7,8,1,3,5]=>[3,5,7,2,1,8,6,4]=>[[1,4,6,8],[2,5],[3,7]]
[[1,2,5],[3,7,8],[4],[6]]=>[6,4,3,7,8,1,2,5]=>[3,5,6,2,1,8,7,4]=>[[1,4,6,7],[2,5],[3,8]]
[[1,3,4],[2,7,8],[5],[6]]=>[6,5,2,7,8,1,3,4]=>[3,4,7,2,1,8,6,5]=>[[1,4,5,8],[2,6],[3,7]]
[[1,2,4],[3,7,8],[5],[6]]=>[6,5,3,7,8,1,2,4]=>[3,4,6,2,1,8,7,5]=>[[1,4,5,7],[2,6],[3,8]]
[[1,2,3],[4,7,8],[5],[6]]=>[6,5,4,7,8,1,2,3]=>[3,4,5,2,1,8,7,6]=>[[1,4,5,6],[2,7],[3,8]]
[[1,3,6],[2,5,8],[4],[7]]=>[7,4,2,5,8,1,3,6]=>[2,5,7,4,1,8,6,3]=>[[1,3,6,8],[2,4],[5,7]]
[[1,3,6],[2,4,8],[5],[7]]=>[7,5,2,4,8,1,3,6]=>[2,4,7,5,1,8,6,3]=>[[1,3,5,6],[2,4],[7,8]]
[[1,2,3],[4,6,8],[5],[7]]=>[7,5,4,6,8,1,2,3]=>[2,4,5,3,1,8,7,6]=>[[1,3,5,6],[2,7],[4,8]]
[[1,3,5],[2,4,8],[6],[7]]=>[7,6,2,4,8,1,3,5]=>[2,3,7,5,1,8,6,4]=>[[1,3,4,6],[2,5],[7,8]]
[[1,2,5],[3,4,8],[6],[7]]=>[7,6,3,4,8,1,2,5]=>[2,3,6,5,1,8,7,4]=>[[1,3,4,7],[2,5],[6,8]]
[[1,2,3],[4,5,8],[6],[7]]=>[7,6,4,5,8,1,2,3]=>[2,3,5,4,1,8,7,6]=>[[1,3,4,6],[2,7],[5,8]]
[[1,4,6],[2,5,7],[3],[8]]=>[8,3,2,5,7,1,4,6]=>[1,6,7,4,2,8,5,3]=>[[1,2,3,8],[4,5],[6,7]]
[[1,3,6],[2,5,7],[4],[8]]=>[8,4,2,5,7,1,3,6]=>[1,5,7,4,2,8,6,3]=>[[1,2,3,8],[4,6],[5,7]]
[[1,2,6],[3,5,7],[4],[8]]=>[8,4,3,5,7,1,2,6]=>[1,5,6,4,2,8,7,3]=>[[1,2,3,7],[4,6],[5,8]]
[[1,3,6],[2,4,7],[5],[8]]=>[8,5,2,4,7,1,3,6]=>[1,4,7,5,2,8,6,3]=>[[1,2,3,6],[4,5],[7,8]]
[[1,2,6],[3,4,7],[5],[8]]=>[8,5,3,4,7,1,2,6]=>[1,4,6,5,2,8,7,3]=>[[1,2,3,7],[4,5],[6,8]]
[[1,4,5],[2,6,7],[3],[8]]=>[8,3,2,6,7,1,4,5]=>[1,6,7,3,2,8,5,4]=>[[1,2,4,8],[3,5],[6,7]]
[[1,2,5],[3,6,7],[4],[8]]=>[8,4,3,6,7,1,2,5]=>[1,5,6,3,2,8,7,4]=>[[1,2,4,7],[3,6],[5,8]]
[[1,3,4],[2,6,7],[5],[8]]=>[8,5,2,6,7,1,3,4]=>[1,4,7,3,2,8,6,5]=>[[1,2,5,8],[3,6],[4,7]]
[[1,2,4],[3,6,7],[5],[8]]=>[8,5,3,6,7,1,2,4]=>[1,4,6,3,2,8,7,5]=>[[1,2,5,7],[3,6],[4,8]]
[[1,2,3],[4,6,7],[5],[8]]=>[8,5,4,6,7,1,2,3]=>[1,4,5,3,2,8,7,6]=>[[1,2,5,6],[3,7],[4,8]]
[[1,3,5],[2,4,6],[7],[8]]=>[8,7,2,4,6,1,3,5]=>[1,2,7,5,3,8,6,4]=>[[1,2,3,4],[5,6],[7,8]]
[[1,2,5],[3,4,6],[7],[8]]=>[8,7,3,4,6,1,2,5]=>[1,2,6,5,3,8,7,4]=>[[1,2,3,4],[5,7],[6,8]]
[[1,3,4],[2,5,6],[7],[8]]=>[8,7,2,5,6,1,3,4]=>[1,2,7,4,3,8,6,5]=>[[1,2,3,5],[4,6],[7,8]]
[[1,2,3],[4,5,6],[7],[8]]=>[8,7,4,5,6,1,2,3]=>[1,2,5,4,3,8,7,6]=>[[1,2,3,6],[4,7],[5,8]]
[[1,5,8],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5,8]=>[5,6,2,7,3,8,4,1]=>[[1,3,4,8],[2,6,7],[5]]
[[1,3,8],[2,6],[4,7],[5]]=>[5,4,7,2,6,1,3,8]=>[4,5,2,7,3,8,6,1]=>[[1,3,6,8],[2,5,7],[4]]
[[1,4,8],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4,8]=>[3,6,2,7,4,8,5,1]=>[[1,4,5,8],[2,6,7],[3]]
[[1,3,8],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3,8]=>[3,5,2,7,4,8,6,1]=>[[1,4,6,8],[2,5,7],[3]]
[[1,2,8],[3,5],[4,7],[6]]=>[6,4,7,3,5,1,2,8]=>[3,5,2,6,4,8,7,1]=>[[1,4,6,7],[2,5,8],[3]]
[[1,3,8],[2,4],[5,7],[6]]=>[6,5,7,2,4,1,3,8]=>[3,4,2,7,5,8,6,1]=>[[1,4,5,6],[2,7,8],[3]]
[[1,2,8],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2,8]=>[2,4,3,6,5,8,7,1]=>[[1,3,5,7],[2,6,8],[4]]
[[1,5,7],[2,6],[3,8],[4]]=>[4,3,8,2,6,1,5,7]=>[5,6,1,7,3,8,4,2]=>[[1,2,4,8],[3,6,7],[5]]
[[1,4,7],[2,6],[3,8],[5]]=>[5,3,8,2,6,1,4,7]=>[4,6,1,7,3,8,5,2]=>[[1,2,5,8],[3,6,7],[4]]
[[1,3,7],[2,5],[4,8],[6]]=>[6,4,8,2,5,1,3,7]=>[3,5,1,7,4,8,6,2]=>[[1,2,6,8],[3,4,7],[5]]
[[1,3,7],[2,4],[5,8],[6]]=>[6,5,8,2,4,1,3,7]=>[3,4,1,7,5,8,6,2]=>[[1,2,5,6],[3,4,8],[7]]
[[1,2,7],[3,4],[5,8],[6]]=>[6,5,8,3,4,1,2,7]=>[3,4,1,6,5,8,7,2]=>[[1,2,5,7],[3,4,8],[6]]
[[1,5,6],[2,7],[3,8],[4]]=>[4,3,8,2,7,1,5,6]=>[5,6,1,7,2,8,4,3]=>[[1,2,3,8],[4,6,7],[5]]
[[1,3,6],[2,7],[4,8],[5]]=>[5,4,8,2,7,1,3,6]=>[4,5,1,7,2,8,6,3]=>[[1,2,3,8],[4,5,6],[7]]
[[1,2,6],[3,7],[4,8],[5]]=>[5,4,8,3,7,1,2,6]=>[4,5,1,6,2,8,7,3]=>[[1,2,3,7],[4,5,6],[8]]
[[1,3,5],[2,7],[4,8],[6]]=>[6,4,8,2,7,1,3,5]=>[3,5,1,7,2,8,6,4]=>[[1,2,4,8],[3,5,6],[7]]
[[1,2,5],[3,7],[4,8],[6]]=>[6,4,8,3,7,1,2,5]=>[3,5,1,6,2,8,7,4]=>[[1,2,4,7],[3,5,6],[8]]
[[1,2,3],[4,7],[5,8],[6]]=>[6,5,8,4,7,1,2,3]=>[3,4,1,5,2,8,7,6]=>[[1,2,5,6],[3,4,7],[8]]
[[1,4,6],[2,5],[3,8],[7]]=>[7,3,8,2,5,1,4,6]=>[2,6,1,7,4,8,5,3]=>[[1,3,5,8],[2,4,7],[6]]
[[1,3,6],[2,4],[5,8],[7]]=>[7,5,8,2,4,1,3,6]=>[2,4,1,7,5,8,6,3]=>[[1,3,5,6],[2,4,8],[7]]
[[1,2,6],[3,4],[5,8],[7]]=>[7,5,8,3,4,1,2,6]=>[2,4,1,6,5,8,7,3]=>[[1,3,5,7],[2,4,8],[6]]
[[1,3,5],[2,6],[4,8],[7]]=>[7,4,8,2,6,1,3,5]=>[2,5,1,7,3,8,6,4]=>[[1,3,4,8],[2,5,6],[7]]
[[1,3,4],[2,6],[5,8],[7]]=>[7,5,8,2,6,1,3,4]=>[2,4,1,7,3,8,6,5]=>[[1,3,5,8],[2,4,6],[7]]
[[1,3,5],[2,4],[6,8],[7]]=>[7,6,8,2,4,1,3,5]=>[2,3,1,7,5,8,6,4]=>[[1,3,4,6],[2,5,8],[7]]
[[1,2,5],[3,4],[6,8],[7]]=>[7,6,8,3,4,1,2,5]=>[2,3,1,6,5,8,7,4]=>[[1,3,4,7],[2,5,8],[6]]
[[1,3,4],[2,5],[6,8],[7]]=>[7,6,8,2,5,1,3,4]=>[2,3,1,7,4,8,6,5]=>[[1,3,4,5],[2,6,8],[7]]
[[1,4,7],[2,5],[3,6],[8]]=>[8,3,6,2,5,1,4,7]=>[1,6,3,7,4,8,5,2]=>[[1,2,4,5],[3,7,8],[6]]
[[1,3,7],[2,5],[4,6],[8]]=>[8,4,6,2,5,1,3,7]=>[1,5,3,7,4,8,6,2]=>[[1,2,4,6],[3,7,8],[5]]
[[1,2,7],[3,4],[5,6],[8]]=>[8,5,6,3,4,1,2,7]=>[1,4,3,6,5,8,7,2]=>[[1,2,5,7],[3,6,8],[4]]
[[1,4,6],[2,5],[3,7],[8]]=>[8,3,7,2,5,1,4,6]=>[1,6,2,7,4,8,5,3]=>[[1,2,3,5],[4,7,8],[6]]
[[1,3,6],[2,5],[4,7],[8]]=>[8,4,7,2,5,1,3,6]=>[1,5,2,7,4,8,6,3]=>[[1,2,3,6],[4,7,8],[5]]
[[1,2,6],[3,5],[4,7],[8]]=>[8,4,7,3,5,1,2,6]=>[1,5,2,6,4,8,7,3]=>[[1,2,3,7],[4,6,8],[5]]
[[1,3,6],[2,4],[5,7],[8]]=>[8,5,7,2,4,1,3,6]=>[1,4,2,7,5,8,6,3]=>[[1,2,3,6],[4,5,8],[7]]
[[1,2,6],[3,4],[5,7],[8]]=>[8,5,7,3,4,1,2,6]=>[1,4,2,6,5,8,7,3]=>[[1,2,3,7],[4,5,8],[6]]
[[1,4,5],[2,6],[3,7],[8]]=>[8,3,7,2,6,1,4,5]=>[1,6,2,7,3,8,5,4]=>[[1,2,3,4],[5,7,8],[6]]
[[1,3,5],[2,6],[4,7],[8]]=>[8,4,7,2,6,1,3,5]=>[1,5,2,7,3,8,6,4]=>[[1,2,3,4],[5,6,8],[7]]
[[1,2,5],[3,6],[4,7],[8]]=>[8,4,7,3,6,1,2,5]=>[1,5,2,6,3,8,7,4]=>[[1,2,3,4],[5,6,7],[8]]
[[1,3,4],[2,6],[5,7],[8]]=>[8,5,7,2,6,1,3,4]=>[1,4,2,7,3,8,6,5]=>[[1,2,3,5],[4,6,8],[7]]
[[1,2,3],[4,6],[5,7],[8]]=>[8,5,7,4,6,1,2,3]=>[1,4,2,5,3,8,7,6]=>[[1,2,3,6],[4,5,7],[8]]
[[1,3,5],[2,4],[6,7],[8]]=>[8,6,7,2,4,1,3,5]=>[1,3,2,7,5,8,6,4]=>[[1,2,4,6],[3,5,8],[7]]
[[1,2,5],[3,4],[6,7],[8]]=>[8,6,7,3,4,1,2,5]=>[1,3,2,6,5,8,7,4]=>[[1,2,4,7],[3,5,8],[6]]
[[1,3,4],[2,5],[6,7],[8]]=>[8,6,7,2,5,1,3,4]=>[1,3,2,7,4,8,6,5]=>[[1,2,4,5],[3,6,8],[7]]
[[1,2,4],[3,5],[6,7],[8]]=>[8,6,7,3,5,1,2,4]=>[1,3,2,6,4,8,7,5]=>[[1,2,4,5],[3,6,7],[8]]
[[1,2,3],[4,5],[6,7],[8]]=>[8,6,7,4,5,1,2,3]=>[1,3,2,5,4,8,7,6]=>[[1,2,4,6],[3,5,7],[8]]
[[1,6,8],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6,8]=>[4,5,6,7,2,8,3,1]=>[[1,3,6,7,8],[2,5],[4]]
[[1,5,8],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5,8]=>[3,5,6,7,2,8,4,1]=>[[1,4,6,7,8],[2,5],[3]]
[[1,4,8],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4,8]=>[3,4,6,7,2,8,5,1]=>[[1,4,5,7,8],[2,6],[3]]
[[1,3,8],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3,8]=>[3,4,5,7,2,8,6,1]=>[[1,4,5,6,8],[2,7],[3]]
[[1,2,8],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2,8]=>[3,4,5,6,2,8,7,1]=>[[1,4,5,6,7],[2,8],[3]]
[[1,4,8],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4,8]=>[2,4,6,7,3,8,5,1]=>[[1,3,5,7,8],[2,6],[4]]
[[1,3,8],[2,6],[4],[5],[7]]=>[7,5,4,2,6,1,3,8]=>[2,4,5,7,3,8,6,1]=>[[1,3,5,6,8],[2,7],[4]]
[[1,2,8],[3,6],[4],[5],[7]]=>[7,5,4,3,6,1,2,8]=>[2,4,5,6,3,8,7,1]=>[[1,3,5,6,7],[2,8],[4]]
[[1,3,8],[2,5],[4],[6],[7]]=>[7,6,4,2,5,1,3,8]=>[2,3,5,7,4,8,6,1]=>[[1,3,4,6,8],[2,7],[5]]
[[1,2,8],[3,5],[4],[6],[7]]=>[7,6,4,3,5,1,2,8]=>[2,3,5,6,4,8,7,1]=>[[1,3,4,6,7],[2,8],[5]]
[[1,3,8],[2,4],[5],[6],[7]]=>[7,6,5,2,4,1,3,8]=>[2,3,4,7,5,8,6,1]=>[[1,3,4,5,6],[2,8],[7]]
[[1,2,8],[3,4],[5],[6],[7]]=>[7,6,5,3,4,1,2,8]=>[2,3,4,6,5,8,7,1]=>[[1,3,4,5,7],[2,8],[6]]
[[1,6,7],[2,8],[3],[4],[5]]=>[5,4,3,2,8,1,6,7]=>[4,5,6,7,1,8,3,2]=>[[1,2,6,7,8],[3,5],[4]]
[[1,5,7],[2,8],[3],[4],[6]]=>[6,4,3,2,8,1,5,7]=>[3,5,6,7,1,8,4,2]=>[[1,2,6,7,8],[3,4],[5]]
[[1,4,7],[2,8],[3],[5],[6]]=>[6,5,3,2,8,1,4,7]=>[3,4,6,7,1,8,5,2]=>[[1,2,5,7,8],[3,4],[6]]
[[1,2,7],[3,8],[4],[5],[6]]=>[6,5,4,3,8,1,2,7]=>[3,4,5,6,1,8,7,2]=>[[1,2,5,6,7],[3,4],[8]]
[[1,5,6],[2,8],[3],[4],[7]]=>[7,4,3,2,8,1,5,6]=>[2,5,6,7,1,8,4,3]=>[[1,3,6,7,8],[2,4],[5]]
[[1,2,6],[3,8],[4],[5],[7]]=>[7,5,4,3,8,1,2,6]=>[2,4,5,6,1,8,7,3]=>[[1,3,5,6,7],[2,4],[8]]
[[1,2,4],[3,8],[5],[6],[7]]=>[7,6,5,3,8,1,2,4]=>[2,3,4,6,1,8,7,5]=>[[1,3,4,5,7],[2,6],[8]]
[[1,2,3],[4,8],[5],[6],[7]]=>[7,6,5,4,8,1,2,3]=>[2,3,4,5,1,8,7,6]=>[[1,3,4,5,6],[2,7],[8]]
[[1,4,7],[2,6],[3],[5],[8]]=>[8,5,3,2,6,1,4,7]=>[1,4,6,7,3,8,5,2]=>[[1,2,5,7,8],[3,6],[4]]
[[1,3,7],[2,6],[4],[5],[8]]=>[8,5,4,2,6,1,3,7]=>[1,4,5,7,3,8,6,2]=>[[1,2,5,6,8],[3,7],[4]]
[[1,2,7],[3,6],[4],[5],[8]]=>[8,5,4,3,6,1,2,7]=>[1,4,5,6,3,8,7,2]=>[[1,2,5,6,7],[3,8],[4]]
[[1,3,7],[2,5],[4],[6],[8]]=>[8,6,4,2,5,1,3,7]=>[1,3,5,7,4,8,6,2]=>[[1,2,4,6,8],[3,7],[5]]
[[1,5,6],[2,7],[3],[4],[8]]=>[8,4,3,2,7,1,5,6]=>[1,5,6,7,2,8,4,3]=>[[1,2,3,7,8],[4,6],[5]]
[[1,2,3],[4,7],[5],[6],[8]]=>[8,6,5,4,7,1,2,3]=>[1,3,4,5,2,8,7,6]=>[[1,2,4,5,6],[3,7],[8]]
[[1,4,6],[2,5],[3],[7],[8]]=>[8,7,3,2,5,1,4,6]=>[1,2,6,7,4,8,5,3]=>[[1,2,3,5,8],[4,7],[6]]
[[1,3,6],[2,5],[4],[7],[8]]=>[8,7,4,2,5,1,3,6]=>[1,2,5,7,4,8,6,3]=>[[1,2,3,6,8],[4,7],[5]]
[[1,3,6],[2,4],[5],[7],[8]]=>[8,7,5,2,4,1,3,6]=>[1,2,4,7,5,8,6,3]=>[[1,2,3,5,6],[4,8],[7]]
[[1,4,5],[2,6],[3],[7],[8]]=>[8,7,3,2,6,1,4,5]=>[1,2,6,7,3,8,5,4]=>[[1,2,3,4,8],[5,7],[6]]
[[1,3,5],[2,6],[4],[7],[8]]=>[8,7,4,2,6,1,3,5]=>[1,2,5,7,3,8,6,4]=>[[1,2,3,4,8],[5,6],[7]]
[[1,2,5],[3,6],[4],[7],[8]]=>[8,7,4,3,6,1,2,5]=>[1,2,5,6,3,8,7,4]=>[[1,2,3,4,7],[5,6],[8]]
[[1,3,4],[2,6],[5],[7],[8]]=>[8,7,5,2,6,1,3,4]=>[1,2,4,7,3,8,6,5]=>[[1,2,3,5,8],[4,6],[7]]
[[1,2,3],[4,6],[5],[7],[8]]=>[8,7,5,4,6,1,2,3]=>[1,2,4,5,3,8,7,6]=>[[1,2,3,5,6],[4,7],[8]]
[[1,3,5],[2,4],[6],[7],[8]]=>[8,7,6,2,4,1,3,5]=>[1,2,3,7,5,8,6,4]=>[[1,2,3,4,6],[5,8],[7]]
[[1,2,5],[3,4],[6],[7],[8]]=>[8,7,6,3,4,1,2,5]=>[1,2,3,6,5,8,7,4]=>[[1,2,3,4,7],[5,8],[6]]
[[1,3,4],[2,5],[6],[7],[8]]=>[8,7,6,2,5,1,3,4]=>[1,2,3,7,4,8,6,5]=>[[1,2,3,4,5],[6,8],[7]]
[[1,2,4],[3,5],[6],[7],[8]]=>[8,7,6,3,5,1,2,4]=>[1,2,3,6,4,8,7,5]=>[[1,2,3,4,5],[6,7],[8]]
[[1,2,3],[4,5],[6],[7],[8]]=>[8,7,6,4,5,1,2,3]=>[1,2,3,5,4,8,7,6]=>[[1,2,3,4,6],[5,7],[8]]
[[1,7,8],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7,8]=>[3,4,5,6,7,8,2,1]=>[[1,4,5,6,7,8],[2],[3]]
[[1,6,8],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6,8]=>[2,4,5,6,7,8,3,1]=>[[1,3,5,6,7,8],[2],[4]]
[[1,5,8],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5,8]=>[2,3,5,6,7,8,4,1]=>[[1,3,4,6,7,8],[2],[5]]
[[1,4,8],[2],[3],[5],[6],[7]]=>[7,6,5,3,2,1,4,8]=>[2,3,4,6,7,8,5,1]=>[[1,3,4,5,7,8],[2],[6]]
[[1,3,8],[2],[4],[5],[6],[7]]=>[7,6,5,4,2,1,3,8]=>[2,3,4,5,7,8,6,1]=>[[1,3,4,5,6,8],[2],[7]]
[[1,2,8],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2,8]=>[2,3,4,5,6,8,7,1]=>[[1,3,4,5,6,7],[2],[8]]
[[1,6,7],[2],[3],[4],[5],[8]]=>[8,5,4,3,2,1,6,7]=>[1,4,5,6,7,8,3,2]=>[[1,2,5,6,7,8],[3],[4]]
[[1,5,7],[2],[3],[4],[6],[8]]=>[8,6,4,3,2,1,5,7]=>[1,3,5,6,7,8,4,2]=>[[1,2,4,6,7,8],[3],[5]]
[[1,4,7],[2],[3],[5],[6],[8]]=>[8,6,5,3,2,1,4,7]=>[1,3,4,6,7,8,5,2]=>[[1,2,4,5,7,8],[3],[6]]
[[1,3,7],[2],[4],[5],[6],[8]]=>[8,6,5,4,2,1,3,7]=>[1,3,4,5,7,8,6,2]=>[[1,2,4,5,6,8],[3],[7]]
[[1,2,7],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,1,2,7]=>[1,3,4,5,6,8,7,2]=>[[1,2,4,5,6,7],[3],[8]]
[[1,5,6],[2],[3],[4],[7],[8]]=>[8,7,4,3,2,1,5,6]=>[1,2,5,6,7,8,4,3]=>[[1,2,3,6,7,8],[4],[5]]
[[1,4,6],[2],[3],[5],[7],[8]]=>[8,7,5,3,2,1,4,6]=>[1,2,4,6,7,8,5,3]=>[[1,2,3,5,7,8],[4],[6]]
[[1,3,6],[2],[4],[5],[7],[8]]=>[8,7,5,4,2,1,3,6]=>[1,2,4,5,7,8,6,3]=>[[1,2,3,5,6,8],[4],[7]]
[[1,2,6],[3],[4],[5],[7],[8]]=>[8,7,5,4,3,1,2,6]=>[1,2,4,5,6,8,7,3]=>[[1,2,3,5,6,7],[4],[8]]
[[1,4,5],[2],[3],[6],[7],[8]]=>[8,7,6,3,2,1,4,5]=>[1,2,3,6,7,8,5,4]=>[[1,2,3,4,7,8],[5],[6]]
[[1,3,5],[2],[4],[6],[7],[8]]=>[8,7,6,4,2,1,3,5]=>[1,2,3,5,7,8,6,4]=>[[1,2,3,4,6,8],[5],[7]]
[[1,2,5],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,1,2,5]=>[1,2,3,5,6,8,7,4]=>[[1,2,3,4,6,7],[5],[8]]
[[1,3,4],[2],[5],[6],[7],[8]]=>[8,7,6,5,2,1,3,4]=>[1,2,3,4,7,8,6,5]=>[[1,2,3,4,5,8],[6],[7]]
[[1,2,4],[3],[5],[6],[7],[8]]=>[8,7,6,5,3,1,2,4]=>[1,2,3,4,6,8,7,5]=>[[1,2,3,4,5,7],[6],[8]]
[[1,2,3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,1,2,3]=>[1,2,3,4,5,8,7,6]=>[[1,2,3,4,5,6],[7],[8]]
[[1,5],[2,6],[3,7],[4,8]]=>[4,8,3,7,2,6,1,5]=>[5,1,6,2,7,3,8,4]=>[[1,2,3,4],[5,6,7,8]]
[[1,4],[2,6],[3,7],[5,8]]=>[5,8,3,7,2,6,1,4]=>[4,1,6,2,7,3,8,5]=>[[1,2,3,5],[4,6,7,8]]
[[1,3],[2,6],[4,7],[5,8]]=>[5,8,4,7,2,6,1,3]=>[4,1,5,2,7,3,8,6]=>[[1,2,3,6],[4,5,7,8]]
[[1,2],[3,6],[4,7],[5,8]]=>[5,8,4,7,3,6,1,2]=>[4,1,5,2,6,3,8,7]=>[[1,2,3,7],[4,5,6,8]]
[[1,4],[2,5],[3,7],[6,8]]=>[6,8,3,7,2,5,1,4]=>[3,1,6,2,7,4,8,5]=>[[1,2,4,5],[3,6,7,8]]
[[1,3],[2,5],[4,7],[6,8]]=>[6,8,4,7,2,5,1,3]=>[3,1,5,2,7,4,8,6]=>[[1,2,4,6],[3,5,7,8]]
[[1,2],[3,5],[4,7],[6,8]]=>[6,8,4,7,3,5,1,2]=>[3,1,5,2,6,4,8,7]=>[[1,2,4,7],[3,5,6,8]]
[[1,3],[2,4],[5,7],[6,8]]=>[6,8,5,7,2,4,1,3]=>[3,1,4,2,7,5,8,6]=>[[1,2,5,6],[3,4,7,8]]
[[1,2],[3,4],[5,7],[6,8]]=>[6,8,5,7,3,4,1,2]=>[3,1,4,2,6,5,8,7]=>[[1,2,5,7],[3,4,6,8]]
[[1,4],[2,5],[3,6],[7,8]]=>[7,8,3,6,2,5,1,4]=>[2,1,6,3,7,4,8,5]=>[[1,3,4,5],[2,6,7,8]]
[[1,3],[2,5],[4,6],[7,8]]=>[7,8,4,6,2,5,1,3]=>[2,1,5,3,7,4,8,6]=>[[1,3,4,6],[2,5,7,8]]
[[1,2],[3,5],[4,6],[7,8]]=>[7,8,4,6,3,5,1,2]=>[2,1,5,3,6,4,8,7]=>[[1,3,4,7],[2,5,6,8]]
[[1,3],[2,4],[5,6],[7,8]]=>[7,8,5,6,2,4,1,3]=>[2,1,4,3,7,5,8,6]=>[[1,3,5,6],[2,4,7,8]]
[[1,2],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>[[1,3,5,7],[2,4,6,8]]
[[1,6],[2,7],[3,8],[4],[5]]=>[5,4,3,8,2,7,1,6]=>[4,5,6,1,7,2,8,3]=>[[1,2,3,7,8],[4,5,6]]
[[1,5],[2,7],[3,8],[4],[6]]=>[6,4,3,8,2,7,1,5]=>[3,5,6,1,7,2,8,4]=>[[1,2,4,7,8],[3,5,6]]
[[1,4],[2,7],[3,8],[5],[6]]=>[6,5,3,8,2,7,1,4]=>[3,4,6,1,7,2,8,5]=>[[1,2,5,7,8],[3,4,6]]
[[1,2],[3,7],[4,8],[5],[6]]=>[6,5,4,8,3,7,1,2]=>[3,4,5,1,6,2,8,7]=>[[1,2,5,6,7],[3,4,8]]
[[1,4],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4]=>[2,4,6,1,7,3,8,5]=>[[1,3,5,7,8],[2,4,6]]
[[1,3],[2,6],[4,8],[5],[7]]=>[7,5,4,8,2,6,1,3]=>[2,4,5,1,7,3,8,6]=>[[1,3,5,6,8],[2,4,7]]
[[1,2],[3,6],[4,8],[5],[7]]=>[7,5,4,8,3,6,1,2]=>[2,4,5,1,6,3,8,7]=>[[1,3,5,6,7],[2,4,8]]
[[1,3],[2,5],[4,8],[6],[7]]=>[7,6,4,8,2,5,1,3]=>[2,3,5,1,7,4,8,6]=>[[1,3,4,6,8],[2,5,7]]
[[1,2],[3,5],[4,8],[6],[7]]=>[7,6,4,8,3,5,1,2]=>[2,3,5,1,6,4,8,7]=>[[1,3,4,6,7],[2,5,8]]
[[1,3],[2,4],[5,8],[6],[7]]=>[7,6,5,8,2,4,1,3]=>[2,3,4,1,7,5,8,6]=>[[1,3,4,5,6],[2,7,8]]
[[1,2],[3,4],[5,8],[6],[7]]=>[7,6,5,8,3,4,1,2]=>[2,3,4,1,6,5,8,7]=>[[1,3,4,5,7],[2,6,8]]
[[1,4],[2,6],[3,7],[5],[8]]=>[8,5,3,7,2,6,1,4]=>[1,4,6,2,7,3,8,5]=>[[1,2,3,5,8],[4,6,7]]
[[1,3],[2,6],[4,7],[5],[8]]=>[8,5,4,7,2,6,1,3]=>[1,4,5,2,7,3,8,6]=>[[1,2,3,6,8],[4,5,7]]
[[1,2],[3,6],[4,7],[5],[8]]=>[8,5,4,7,3,6,1,2]=>[1,4,5,2,6,3,8,7]=>[[1,2,3,6,7],[4,5,8]]
[[1,4],[2,5],[3,7],[6],[8]]=>[8,6,3,7,2,5,1,4]=>[1,3,6,2,7,4,8,5]=>[[1,2,4,5,8],[3,6,7]]
[[1,3],[2,5],[4,7],[6],[8]]=>[8,6,4,7,2,5,1,3]=>[1,3,5,2,7,4,8,6]=>[[1,2,4,6,8],[3,5,7]]
[[1,3],[2,4],[5,7],[6],[8]]=>[8,6,5,7,2,4,1,3]=>[1,3,4,2,7,5,8,6]=>[[1,2,4,5,6],[3,7,8]]
[[1,2],[3,4],[5,7],[6],[8]]=>[8,6,5,7,3,4,1,2]=>[1,3,4,2,6,5,8,7]=>[[1,2,4,5,7],[3,6,8]]
[[1,4],[2,5],[3,6],[7],[8]]=>[8,7,3,6,2,5,1,4]=>[1,2,6,3,7,4,8,5]=>[[1,2,3,4,5],[6,7,8]]
[[1,3],[2,5],[4,6],[7],[8]]=>[8,7,4,6,2,5,1,3]=>[1,2,5,3,7,4,8,6]=>[[1,2,3,4,6],[5,7,8]]
[[1,2],[3,5],[4,6],[7],[8]]=>[8,7,4,6,3,5,1,2]=>[1,2,5,3,6,4,8,7]=>[[1,2,3,4,7],[5,6,8]]
[[1,3],[2,4],[5,6],[7],[8]]=>[8,7,5,6,2,4,1,3]=>[1,2,4,3,7,5,8,6]=>[[1,2,3,5,6],[4,7,8]]
[[1,2],[3,4],[5,6],[7],[8]]=>[8,7,5,6,3,4,1,2]=>[1,2,4,3,6,5,8,7]=>[[1,2,3,5,7],[4,6,8]]
[[1,7],[2,8],[3],[4],[5],[6]]=>[6,5,4,3,2,8,1,7]=>[3,4,5,6,7,1,8,2]=>[[1,2,5,6,7,8],[3,4]]
[[1,6],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6]=>[2,4,5,6,7,1,8,3]=>[[1,3,5,6,7,8],[2,4]]
[[1,3],[2,8],[4],[5],[6],[7]]=>[7,6,5,4,2,8,1,3]=>[2,3,4,5,7,1,8,6]=>[[1,3,4,5,6,8],[2,7]]
[[1,2],[3,8],[4],[5],[6],[7]]=>[7,6,5,4,3,8,1,2]=>[2,3,4,5,6,1,8,7]=>[[1,3,4,5,6,7],[2,8]]
[[1,6],[2,7],[3],[4],[5],[8]]=>[8,5,4,3,2,7,1,6]=>[1,4,5,6,7,2,8,3]=>[[1,2,3,6,7,8],[4,5]]
[[1,5],[2,7],[3],[4],[6],[8]]=>[8,6,4,3,2,7,1,5]=>[1,3,5,6,7,2,8,4]=>[[1,2,4,6,7,8],[3,5]]
[[1,4],[2,7],[3],[5],[6],[8]]=>[8,6,5,3,2,7,1,4]=>[1,3,4,6,7,2,8,5]=>[[1,2,4,5,7,8],[3,6]]
[[1,2],[3,7],[4],[5],[6],[8]]=>[8,6,5,4,3,7,1,2]=>[1,3,4,5,6,2,8,7]=>[[1,2,4,5,6,7],[3,8]]
[[1,5],[2,6],[3],[4],[7],[8]]=>[8,7,4,3,2,6,1,5]=>[1,2,5,6,7,3,8,4]=>[[1,2,3,4,7,8],[5,6]]
[[1,3],[2,6],[4],[5],[7],[8]]=>[8,7,5,4,2,6,1,3]=>[1,2,4,5,7,3,8,6]=>[[1,2,3,5,6,8],[4,7]]
[[1,2],[3,6],[4],[5],[7],[8]]=>[8,7,5,4,3,6,1,2]=>[1,2,4,5,6,3,8,7]=>[[1,2,3,5,6,7],[4,8]]
[[1,4],[2,5],[3],[6],[7],[8]]=>[8,7,6,3,2,5,1,4]=>[1,2,3,6,7,4,8,5]=>[[1,2,3,4,5,8],[6,7]]
[[1,3],[2,5],[4],[6],[7],[8]]=>[8,7,6,4,2,5,1,3]=>[1,2,3,5,7,4,8,6]=>[[1,2,3,4,6,8],[5,7]]
[[1,2],[3,5],[4],[6],[7],[8]]=>[8,7,6,4,3,5,1,2]=>[1,2,3,5,6,4,8,7]=>[[1,2,3,4,6,7],[5,8]]
[[1,3],[2,4],[5],[6],[7],[8]]=>[8,7,6,5,2,4,1,3]=>[1,2,3,4,7,5,8,6]=>[[1,2,3,4,5,6],[7,8]]
[[1,2],[3,4],[5],[6],[7],[8]]=>[8,7,6,5,3,4,1,2]=>[1,2,3,4,6,5,8,7]=>[[1,2,3,4,5,7],[6,8]]
[[1,8],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,8,1]=>[[1,3,4,5,6,7,8],[2]]
[[1,7],[2],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,1,7]=>[1,3,4,5,6,7,8,2]=>[[1,2,4,5,6,7,8],[3]]
[[1,6],[2],[3],[4],[5],[7],[8]]=>[8,7,5,4,3,2,1,6]=>[1,2,4,5,6,7,8,3]=>[[1,2,3,5,6,7,8],[4]]
[[1,5],[2],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,2,1,5]=>[1,2,3,5,6,7,8,4]=>[[1,2,3,4,6,7,8],[5]]
[[1,4],[2],[3],[5],[6],[7],[8]]=>[8,7,6,5,3,2,1,4]=>[1,2,3,4,6,7,8,5]=>[[1,2,3,4,5,7,8],[6]]
[[1,3],[2],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,2,1,3]=>[1,2,3,4,5,7,8,6]=>[[1,2,3,4,5,6,8],[7]]
[[1,2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,8,7]=>[[1,2,3,4,5,6,7],[8]]
[[1],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[[1,2,3,4,5,6,7,8]]
[[1,3,5,7,9],[2,4,6,8,10]]=>[2,4,6,8,10,1,3,5,7,9]=>[9,7,5,3,1,10,8,6,4,2]=>[[1,2],[3,4],[5,6],[7,8],[9,10]]
[[1,2,3,4,5],[6,7,8,9,10]]=>[6,7,8,9,10,1,2,3,4,5]=>[5,4,3,2,1,10,9,8,7,6]=>[[1,6],[2,7],[3,8],[4,9],[5,10]]
[[1,2,3,4,5,6],[7,8,9,10,11,12]]=>[7,8,9,10,11,12,1,2,3,4,5,6]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]
[[1,2,3,4,5,6,7,8,9]]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9]]
[[1,2,3,4,5,6,7,8],[9]]=>[9,1,2,3,4,5,6,7,8]=>[1,9,8,7,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6],[7],[8],[9]]
[[1,2,3,4,5,6,7],[8,9]]=>[8,9,1,2,3,4,5,6,7]=>[2,1,9,8,7,6,5,4,3]=>[[1,3],[2,4],[5],[6],[7],[8],[9]]
[[1,2,3,4,5,6,7],[8],[9]]=>[9,8,1,2,3,4,5,6,7]=>[1,2,9,8,7,6,5,4,3]=>[[1,2,3],[4],[5],[6],[7],[8],[9]]
[[1,2,3,4,5,6],[7,8,9]]=>[7,8,9,1,2,3,4,5,6]=>[3,2,1,9,8,7,6,5,4]=>[[1,4],[2,5],[3,6],[7],[8],[9]]
[[1,2,3,4,5,6],[7],[8],[9]]=>[9,8,7,1,2,3,4,5,6]=>[1,2,3,9,8,7,6,5,4]=>[[1,2,3,4],[5],[6],[7],[8],[9]]
[[1,2,3,4,5],[6,7,8,9]]=>[6,7,8,9,1,2,3,4,5]=>[4,3,2,1,9,8,7,6,5]=>[[1,5],[2,6],[3,7],[4,8],[9]]
[[1,2,3,4,5],[6],[7],[8],[9]]=>[9,8,7,6,1,2,3,4,5]=>[1,2,3,4,9,8,7,6,5]=>[[1,2,3,4,5],[6],[7],[8],[9]]
[[1,2,3,4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,1,2,3,4]=>[1,2,3,4,5,9,8,7,6]=>[[1,2,3,4,5,6],[7],[8],[9]]
[[1,2,3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,1,2,3]=>[1,2,3,4,5,6,9,8,7]=>[[1,2,3,4,5,6,7],[8],[9]]
[[1,2],[3,4],[5,6],[7,8],[9]]=>[9,7,8,5,6,3,4,1,2]=>[1,3,2,5,4,7,6,9,8]=>[[1,2,4,6,8],[3,5,7,9]]
[[1,2],[3,4],[5,6],[7],[8],[9]]=>[9,8,7,5,6,3,4,1,2]=>[1,2,3,5,4,7,6,9,8]=>[[1,2,3,4,6,8],[5,7,9]]
[[1,2],[3,4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,3,4,1,2]=>[1,2,3,4,5,7,6,9,8]=>[[1,2,3,4,5,6,8],[7,9]]
[[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,9,8]=>[[1,2,3,4,5,6,7,8],[9]]
[[1],[2],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9]=>[[1,2,3,4,5,6,7,8,9]]
[[1,2,3,4,5,6,7,8,9,10]]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]
[[1,2,3,4,5,6,7,8,9],[10]]=>[10,1,2,3,4,5,6,7,8,9]=>[1,10,9,8,7,6,5,4,3,2]=>[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]
[[1,2,3,4,5,6,7,8],[9,10]]=>[9,10,1,2,3,4,5,6,7,8]=>[2,1,10,9,8,7,6,5,4,3]=>[[1,3],[2,4],[5],[6],[7],[8],[9],[10]]
[[1,2,3,4,5,6,7,8],[9],[10]]=>[10,9,1,2,3,4,5,6,7,8]=>[1,2,10,9,8,7,6,5,4,3]=>[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]
[[1,2,3,4,5,6,7],[8,9,10]]=>[8,9,10,1,2,3,4,5,6,7]=>[3,2,1,10,9,8,7,6,5,4]=>[[1,4],[2,5],[3,6],[7],[8],[9],[10]]
[[1,2,3,4,5,6,7],[8],[9],[10]]=>[10,9,8,1,2,3,4,5,6,7]=>[1,2,3,10,9,8,7,6,5,4]=>[[1,2,3,4],[5],[6],[7],[8],[9],[10]]
[[1,2,3,4,5,6],[7,8,9,10]]=>[7,8,9,10,1,2,3,4,5,6]=>[4,3,2,1,10,9,8,7,6,5]=>[[1,5],[2,6],[3,7],[4,8],[9],[10]]
[[1,2,3,4,5,6],[7,8],[9,10]]=>[9,10,7,8,1,2,3,4,5,6]=>[2,1,4,3,10,9,8,7,6,5]=>[[1,3,5],[2,4,6],[7],[8],[9],[10]]
[[1,2,3,4,5,6],[7],[8],[9],[10]]=>[10,9,8,7,1,2,3,4,5,6]=>[1,2,3,4,10,9,8,7,6,5]=>[[1,2,3,4,5],[6],[7],[8],[9],[10]]
[[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,1,2,3,4,5]=>[1,2,3,4,5,10,9,8,7,6]=>[[1,2,3,4,5,6],[7],[8],[9],[10]]
[[1,2,3,4],[5,6,7,8],[9,10]]=>[9,10,5,6,7,8,1,2,3,4]=>[2,1,6,5,4,3,10,9,8,7]=>[[1,3,7],[2,4,8],[5,9],[6,10]]
[[1,2,3,4],[5,6,7],[8,9],[10]]=>[10,8,9,5,6,7,1,2,3,4]=>[1,3,2,6,5,4,10,9,8,7]=>[[1,2,4,7],[3,5,8],[6,9],[10]]
[[1,2,3,4],[5,6],[7,8],[9,10]]=>[9,10,7,8,5,6,1,2,3,4]=>[2,1,4,3,6,5,10,9,8,7]=>[[1,3,5,7],[2,4,6,8],[9],[10]]
[[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,1,2,3,4]=>[1,2,3,4,5,6,10,9,8,7]=>[[1,2,3,4,5,6,7],[8],[9],[10]]
[[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,1,2,3]=>[1,2,3,4,5,6,7,10,9,8]=>[[1,2,3,4,5,6,7,8],[9],[10]]
[[1,2],[3,4],[5,6],[7,8],[9,10]]=>[9,10,7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7,10,9]=>[[1,3,5,7,9],[2,4,6,8,10]]
[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,8,10,9]=>[[1,2,3,4,5,6,7,8,9],[10]]
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10]=>[[1,2,3,4,5,6,7,8,9,10]]
[[1,2,3,4,5,6,7,8,9,10,11,12]]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]]
[[1,2,3,4,5,6],[7,8,9,10],[11,12]]=>[11,12,7,8,9,10,1,2,3,4,5,6]=>[2,1,6,5,4,3,12,11,10,9,8,7]=>[[1,3,7],[2,4,8],[5,9],[6,10],[11],[12]]
[[1,2,3,4],[5,6,7,8],[9,10],[11,12]]=>[11,12,9,10,5,6,7,8,1,2,3,4]=>[2,1,4,3,8,7,6,5,12,11,10,9]=>[[1,3,5,9],[2,4,6,10],[7,11],[8,12]]
[[1,2,3,4],[5,6],[7,8],[9,10],[11,12]]=>[11,12,9,10,7,8,5,6,1,2,3,4]=>[2,1,4,3,6,5,8,7,12,11,10,9]=>[[1,3,5,7,9],[2,4,6,8,10],[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]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[[1,3,5,7,9,11],[2,4,6,8,10,12]]
[[1,3,4,5,6,7,8,9],[2]]=>[2,1,3,4,5,6,7,8,9]=>[8,9,7,6,5,4,3,2,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8]]
[[1,4,5,6,7,8,9],[2],[3]]=>[3,2,1,4,5,6,7,8,9]=>[7,8,9,6,5,4,3,2,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]]
[[1,7,8,9],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7,8,9]=>[4,5,6,7,8,9,3,2,1]=>[[1,5,6,7,8,9],[2],[3],[4]]
[[1,2,9],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2,9]=>[3,2,5,4,7,6,9,8,1]=>[[1,4,6,8],[2,5,7,9],[3]]
[[1,8,9],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8,9]=>[3,4,5,6,7,8,9,2,1]=>[[1,4,5,6,7,8,9],[2],[3]]
[[1,3],[2,5],[4,7],[6,9],[8]]=>[8,6,9,4,7,2,5,1,3]=>[2,4,1,6,3,8,5,9,7]=>[[1,3,5,7,9],[2,4,6,8]]
[[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1,9]=>[2,3,4,5,6,7,8,9,1]=>[[1,3,4,5,6,7,8,9],[2]]
[[1,3,4,5,6,7,8,9,10],[2]]=>[2,1,3,4,5,6,7,8,9,10]=>[9,10,8,7,6,5,4,3,2,1]=>[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]
[[1,6,7,8,9,10],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8,9,10]=>[6,7,8,9,10,5,4,3,2,1]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]]
[[1,5,8,9,10],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5,8,9,10]=>[5,7,8,9,4,10,6,3,2,1]=>[[1,6,8,9,10],[2,7],[3],[4],[5]]
[[1,3,6,10],[2,5,9],[4,8],[7]]=>[7,4,8,2,5,9,1,3,6,10]=>[4,7,3,9,6,2,10,8,5,1]=>[[1,5,8,10],[2,6,9],[3,7],[4]]
[[1,4,9,10],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4,9,10]=>[4,6,8,3,9,5,10,7,2,1]=>[[1,5,7,9,10],[2,6,8],[3],[4]]
[[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8,9,10]=>[4,5,6,7,8,9,10,3,2,1]=>[[1,5,6,7,8,9,10],[2],[3],[4]]
[[1,3,10],[2,5],[4,7],[6,9],[8]]=>[8,6,9,4,7,2,5,1,3,10]=>[3,5,2,7,4,9,6,10,8,1]=>[[1,4,6,8,10],[2,5,7,9],[3]]
[[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1,9,10]=>[3,4,5,6,7,8,9,10,2,1]=>[[1,4,5,6,7,8,9,10],[2],[3]]
[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,2,1,10]=>[2,3,4,5,6,7,8,9,10,1]=>[[1,3,4,5,6,7,8,9,10],[2]]
[[1,8],[2,9],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,9,1,8]=>[3,4,5,6,7,8,1,9,2]=>[[1,2,5,6,7,8,9],[3,4]]
[[1,7],[2,8],[3,9],[4],[5],[6]]=>[6,5,4,3,9,2,8,1,7]=>[4,5,6,7,1,8,2,9,3]=>[[1,2,3,7,8,9],[4,5,6]]
[[1,7,9],[2,8],[3],[4],[5],[6]]=>[6,5,4,3,2,8,1,7,9]=>[4,5,6,7,8,2,9,3,1]=>[[1,3,6,7,8,9],[2,5],[4]]
[[1,5,9],[2,6],[3,7],[4,8]]=>[4,8,3,7,2,6,1,5,9]=>[6,2,7,3,8,4,9,5,1]=>[[1,3,4,5],[2,7,8,9],[6]]
[[1,4,7],[2,5,8],[3,6,9]]=>[3,6,9,2,5,8,1,4,7]=>[7,4,1,8,5,2,9,6,3]=>[[1,2,3],[4,5,6],[7,8,9]]
[[1,3,5,7,9],[2,4,6,8]]=>[2,4,6,8,1,3,5,7,9]=>[8,6,4,2,9,7,5,3,1]=>[[1,3],[2,5],[4,7],[6,9],[8]]
[[1,3,5,7,8,9],[2,4,6]]=>[2,4,6,1,3,5,7,8,9]=>[8,6,4,9,7,5,3,2,1]=>[[1,5],[2,7],[3,9],[4],[6],[8]]
[[1,3,5,6,7,8,9],[2,4]]=>[2,4,1,3,5,6,7,8,9]=>[8,6,9,7,5,4,3,2,1]=>[[1,7],[2,9],[3],[4],[5],[6],[8]]
[[1,9],[2,10],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,10,1,9]=>[3,4,5,6,7,8,9,1,10,2]=>[[1,2,5,6,7,8,9,10],[3,4]]
[[1,6],[2,7],[3,8],[4,9],[5,10]]=>[5,10,4,9,3,8,2,7,1,6]=>[6,1,7,2,8,3,9,4,10,5]=>[[1,2,3,4,5],[6,7,8,9,10]]
[[1,5,9],[2,6,10],[3,7],[4,8]]=>[4,8,3,7,2,6,10,1,5,9]=>[7,3,8,4,9,5,1,10,6,2]=>[[1,2,5,6],[3,4,9,10],[7,8]]
[[1,4,7,10],[2,5,8],[3,6,9]]=>[3,6,9,2,5,8,1,4,7,10]=>[8,5,2,9,6,3,10,7,4,1]=>[[1,3,4],[2,6,7],[5,9,10],[8]]
[[1,3,5,7,8,9,10],[2,4,6]]=>[2,4,6,1,3,5,7,8,9,10]=>[9,7,5,10,8,6,4,3,2,1]=>[[1,6],[2,8],[3,10],[4],[5],[7],[9]]
[[1,3,5,6,7,8,9,10],[2,4]]=>[2,4,1,3,5,6,7,8,9,10]=>[9,7,10,8,6,5,4,3,2,1]=>[[1,8],[2,10],[3],[4],[5],[6],[7],[9]]
[[1,3],[2,4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,2,4,1,3]=>[1,2,3,4,5,8,6,9,7]=>[[1,2,3,4,5,6,7],[8,9]]
[[1,4],[2,5],[3,6],[7],[8],[9]]=>[9,8,7,3,6,2,5,1,4]=>[1,2,3,7,4,8,5,9,6]=>[[1,2,3,4,5,6],[7,8,9]]
[[1,2,4],[3,5],[6],[7],[8],[9]]=>[9,8,7,6,3,5,1,2,4]=>[1,2,3,4,7,5,9,8,6]=>[[1,2,3,4,5,6],[7,8],[9]]
[[1,5],[2,6],[3,7],[4,8],[9]]=>[9,4,8,3,7,2,6,1,5]=>[1,6,2,7,3,8,4,9,5]=>[[1,2,3,4,5],[6,7,8,9]]
[[1,2,5],[3,6],[4,7],[8],[9]]=>[9,8,4,7,3,6,1,2,5]=>[1,2,6,3,7,4,9,8,5]=>[[1,2,3,4,5],[6,7,8],[9]]
[[1,3,5],[2,4,6],[7],[8],[9]]=>[9,8,7,2,4,6,1,3,5]=>[1,2,3,8,6,4,9,7,5]=>[[1,2,3,4,5],[6,7],[8,9]]
[[1,2,3,5],[4,6],[7],[8],[9]]=>[9,8,7,4,6,1,2,3,5]=>[1,2,3,6,4,9,8,7,5]=>[[1,2,3,4,5],[6,7],[8],[9]]
[[1,2,6],[3,7],[4,8],[5,9]]=>[5,9,4,8,3,7,1,2,6]=>[5,1,6,2,7,3,9,8,4]=>[[1,2,3,4],[5,6,7,8],[9]]
[[1,3,6],[2,4,7],[5,8],[9]]=>[9,5,8,2,4,7,1,3,6]=>[1,5,2,8,6,3,9,7,4]=>[[1,2,3,4],[5,6,7],[8,9]]
[[1,2,3,6],[4,7],[5,8],[9]]=>[9,5,8,4,7,1,2,3,6]=>[1,5,2,6,3,9,8,7,4]=>[[1,2,3,4],[5,6,7],[8],[9]]
[[1,2,4,6],[3,5,7],[8],[9]]=>[9,8,3,5,7,1,2,4,6]=>[1,2,7,5,3,9,8,6,4]=>[[1,2,3,4],[5,6],[7,8],[9]]
[[1,2,3,4,6],[5,7],[8],[9]]=>[9,8,5,7,1,2,3,4,6]=>[1,2,5,3,9,8,7,6,4]=>[[1,2,3,4],[5,6],[7],[8],[9]]
[[1,2,4,7],[3,5,8],[6,9]]=>[6,9,3,5,8,1,2,4,7]=>[4,1,7,5,2,9,8,6,3]=>[[1,2,3],[4,5,6],[7,8],[9]]
[[1,2,3,4,7],[5,8],[6,9]]=>[6,9,5,8,1,2,3,4,7]=>[4,1,5,2,9,8,7,6,3]=>[[1,2,3],[4,5,6],[7],[8],[9]]
[[1,3,5,7],[2,4,6,8],[9]]=>[9,2,4,6,8,1,3,5,7]=>[1,8,6,4,2,9,7,5,3]=>[[1,2,3],[4,5],[6,7],[8,9]]
[[1,2,3,5,7],[4,6,8],[9]]=>[9,4,6,8,1,2,3,5,7]=>[1,6,4,2,9,8,7,5,3]=>[[1,2,3],[4,5],[6,7],[8],[9]]
[[1,2,3,4,5,7],[6,8],[9]]=>[9,6,8,1,2,3,4,5,7]=>[1,4,2,9,8,7,6,5,3]=>[[1,2,3],[4,5],[6],[7],[8],[9]]
[[1,2,4,6,8],[3,5,7,9]]=>[3,5,7,9,1,2,4,6,8]=>[7,5,3,1,9,8,6,4,2]=>[[1,2],[3,4],[5,6],[7,8],[9]]
[[1,2,3,4,6,8],[5,7,9]]=>[5,7,9,1,2,3,4,6,8]=>[5,3,1,9,8,7,6,4,2]=>[[1,2],[3,4],[5,6],[7],[8],[9]]
[[1,2,3,4,5,6,8],[7,9]]=>[7,9,1,2,3,4,5,6,8]=>[3,1,9,8,7,6,5,4,2]=>[[1,2],[3,4],[5],[6],[7],[8],[9]]
[[1,3],[2,4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,2,4,1,3]=>[1,2,3,4,5,6,9,7,10,8]=>[[1,2,3,4,5,6,7,8],[9,10]]
[[1,4],[2,5],[3,6],[7],[8],[9],[10]]=>[10,9,8,7,3,6,2,5,1,4]=>[1,2,3,4,8,5,9,6,10,7]=>[[1,2,3,4,5,6,7],[8,9,10]]
[[1,2,4],[3,5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,3,5,1,2,4]=>[1,2,3,4,5,8,6,10,9,7]=>[[1,2,3,4,5,6,7],[8,9],[10]]
[[1,5],[2,6],[3,7],[4,8],[9],[10]]=>[10,9,4,8,3,7,2,6,1,5]=>[1,2,7,3,8,4,9,5,10,6]=>[[1,2,3,4,5,6],[7,8,9,10]]
[[1,2,5],[3,6],[4,7],[8],[9],[10]]=>[10,9,8,4,7,3,6,1,2,5]=>[1,2,3,7,4,8,5,10,9,6]=>[[1,2,3,4,5,6],[7,8,9],[10]]
[[1,3,5],[2,4,6],[7],[8],[9],[10]]=>[10,9,8,7,2,4,6,1,3,5]=>[1,2,3,4,9,7,5,10,8,6]=>[[1,2,3,4,5,6],[7,8],[9,10]]
[[1,2,3,5],[4,6],[7],[8],[9],[10]]=>[10,9,8,7,4,6,1,2,3,5]=>[1,2,3,4,7,5,10,9,8,6]=>[[1,2,3,4,5,6],[7,8],[9],[10]]
[[1,2,6],[3,7],[4,8],[5,9],[10]]=>[10,5,9,4,8,3,7,1,2,6]=>[1,6,2,7,3,8,4,10,9,5]=>[[1,2,3,4,5],[6,7,8,9],[10]]
[[1,3,6],[2,4,7],[5,8],[9],[10]]=>[10,9,5,8,2,4,7,1,3,6]=>[1,2,6,3,9,7,4,10,8,5]=>[[1,2,3,4,5],[6,7,8],[9,10]]
[[1,2,3,6],[4,7],[5,8],[9],[10]]=>[10,9,5,8,4,7,1,2,3,6]=>[1,2,6,3,7,4,10,9,8,5]=>[[1,2,3,4,5],[6,7,8],[9],[10]]
[[1,2,4,6],[3,5,7],[8],[9],[10]]=>[10,9,8,3,5,7,1,2,4,6]=>[1,2,3,8,6,4,10,9,7,5]=>[[1,2,3,4,5],[6,7],[8,9],[10]]
[[1,2,3,4,6],[5,7],[8],[9],[10]]=>[10,9,8,5,7,1,2,3,4,6]=>[1,2,3,6,4,10,9,8,7,5]=>[[1,2,3,4,5],[6,7],[8],[9],[10]]
[[1,3,7],[2,4,8],[5,9],[6,10]]=>[6,10,5,9,2,4,8,1,3,7]=>[5,1,6,2,9,7,3,10,8,4]=>[[1,2,3,4],[5,6,7,8],[9,10]]
[[1,2,3,7],[4,8],[5,9],[6,10]]=>[6,10,5,9,4,8,1,2,3,7]=>[5,1,6,2,7,3,10,9,8,4]=>[[1,2,3,4],[5,6,7,8],[9],[10]]
[[1,4,7],[2,5,8],[3,6,9],[10]]=>[10,3,6,9,2,5,8,1,4,7]=>[1,8,5,2,9,6,3,10,7,4]=>[[1,2,3,4],[5,6,7],[8,9,10]]
[[1,2,4,7],[3,5,8],[6,9],[10]]=>[10,6,9,3,5,8,1,2,4,7]=>[1,5,2,8,6,3,10,9,7,4]=>[[1,2,3,4],[5,6,7],[8,9],[10]]
[[1,2,3,4,7],[5,8],[6,9],[10]]=>[10,6,9,5,8,1,2,3,4,7]=>[1,5,2,6,3,10,9,8,7,4]=>[[1,2,3,4],[5,6,7],[8],[9],[10]]
[[1,3,5,7],[2,4,6,8],[9],[10]]=>[10,9,2,4,6,8,1,3,5,7]=>[1,2,9,7,5,3,10,8,6,4]=>[[1,2,3,4],[5,6],[7,8],[9,10]]
[[1,2,3,5,7],[4,6,8],[9],[10]]=>[10,9,4,6,8,1,2,3,5,7]=>[1,2,7,5,3,10,9,8,6,4]=>[[1,2,3,4],[5,6],[7,8],[9],[10]]
[[1,2,3,4,5,7],[6,8],[9],[10]]=>[10,9,6,8,1,2,3,4,5,7]=>[1,2,5,3,10,9,8,7,6,4]=>[[1,2,3,4],[5,6],[7],[8],[9],[10]]
[[1,2,5,8],[3,6,9],[4,7,10]]=>[4,7,10,3,6,9,1,2,5,8]=>[7,4,1,8,5,2,10,9,6,3]=>[[1,2,3],[4,5,6],[7,8,9],[10]]
[[1,3,5,8],[2,4,6,9],[7,10]]=>[7,10,2,4,6,9,1,3,5,8]=>[4,1,9,7,5,2,10,8,6,3]=>[[1,2,3],[4,5,6],[7,8],[9,10]]
[[1,2,3,5,8],[4,6,9],[7,10]]=>[7,10,4,6,9,1,2,3,5,8]=>[4,1,7,5,2,10,9,8,6,3]=>[[1,2,3],[4,5,6],[7,8],[9],[10]]
[[1,2,3,4,5,8],[6,9],[7,10]]=>[7,10,6,9,1,2,3,4,5,8]=>[4,1,5,2,10,9,8,7,6,3]=>[[1,2,3],[4,5,6],[7],[8],[9],[10]]
[[1,2,4,6,8],[3,5,7,9],[10]]=>[10,3,5,7,9,1,2,4,6,8]=>[1,8,6,4,2,10,9,7,5,3]=>[[1,2,3],[4,5],[6,7],[8,9],[10]]
[[1,2,3,4,6,8],[5,7,9],[10]]=>[10,5,7,9,1,2,3,4,6,8]=>[1,6,4,2,10,9,8,7,5,3]=>[[1,2,3],[4,5],[6,7],[8],[9],[10]]
[[1,2,3,4,5,6,8],[7,9],[10]]=>[10,7,9,1,2,3,4,5,6,8]=>[1,4,2,10,9,8,7,6,5,3]=>[[1,2,3],[4,5],[6],[7],[8],[9],[10]]
[[1,2,3,5,7,9],[4,6,8,10]]=>[4,6,8,10,1,2,3,5,7,9]=>[7,5,3,1,10,9,8,6,4,2]=>[[1,2],[3,4],[5,6],[7,8],[9],[10]]
[[1,2,3,4,5,7,9],[6,8,10]]=>[6,8,10,1,2,3,4,5,7,9]=>[5,3,1,10,9,8,7,6,4,2]=>[[1,2],[3,4],[5,6],[7],[8],[9],[10]]
[[1,2,3,4,5,6,7,9],[8,10]]=>[8,10,1,2,3,4,5,6,7,9]=>[3,1,10,9,8,7,6,5,4,2]=>[[1,2],[3,4],[5],[6],[7],[8],[9],[10]]
[[1,2],[3,4],[5,6],[7,9],[8,10]]=>[8,10,7,9,5,6,3,4,1,2]=>[3,1,4,2,6,5,8,7,10,9]=>[[1,2,5,7,9],[3,4,6,8,10]]
[[1,2],[3,4],[5,8],[6,9],[7,10]]=>[7,10,6,9,5,8,3,4,1,2]=>[4,1,5,2,6,3,8,7,10,9]=>[[1,2,3,7,9],[4,5,6,8,10]]
[[1,2],[3,7],[4,8],[5,9],[6,10]]=>[6,10,5,9,4,8,3,7,1,2]=>[5,1,6,2,7,3,8,4,10,9]=>[[1,2,3,4,9],[5,6,7,8,10]]
[[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]=>[6,12,5,11,4,10,3,9,2,8,1,7]=>[7,1,8,2,9,3,10,4,11,5,12,6]=>[[1,2,3,4,5,6],[7,8,9,10,11,12]]
[[1,2,3,4,5,6,7,9],[8]]=>[8,1,2,3,4,5,6,7,9]=>[2,9,8,7,6,5,4,3,1]=>[[1,3],[2],[4],[5],[6],[7],[8],[9]]
[[1,2,3,4,5,6,9],[7,8]]=>[7,8,1,2,3,4,5,6,9]=>[3,2,9,8,7,6,5,4,1]=>[[1,4],[2,5],[3],[6],[7],[8],[9]]
[[1,2,3,4,5,6,9],[7],[8]]=>[8,7,1,2,3,4,5,6,9]=>[2,3,9,8,7,6,5,4,1]=>[[1,3,4],[2],[5],[6],[7],[8],[9]]
[[1,2,3,9],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,1,2,3,9]=>[2,3,4,5,6,9,8,7,1]=>[[1,3,4,5,6,7],[2],[8],[9]]
[[1,2,9],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,1,2,9]=>[2,3,4,5,6,7,9,8,1]=>[[1,3,4,5,6,7,8],[2],[9]]
[[1,3],[2,9],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,2,9,1,3]=>[2,3,4,5,6,8,1,9,7]=>[[1,3,4,5,6,7,9],[2,8]]
[[1,2,3,4,5,6,7,8,10],[9]]=>[9,1,2,3,4,5,6,7,8,10]=>[2,10,9,8,7,6,5,4,3,1]=>[[1,3],[2],[4],[5],[6],[7],[8],[9],[10]]
[[1,2,3,4,5,6,7,10],[8,9]]=>[8,9,1,2,3,4,5,6,7,10]=>[3,2,10,9,8,7,6,5,4,1]=>[[1,4],[2,5],[3],[6],[7],[8],[9],[10]]
[[1,2,3,10],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,1,2,3,10]=>[2,3,4,5,6,7,10,9,8,1]=>[[1,3,4,5,6,7,8],[2],[9],[10]]
[[1,2,10],[3,4],[5,6],[7,8],[9]]=>[9,7,8,5,6,3,4,1,2,10]=>[2,4,3,6,5,8,7,10,9,1]=>[[1,3,5,7,9],[2,6,8,10],[4]]
[[1,2,10],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,1,2,10]=>[2,3,4,5,6,7,8,10,9,1]=>[[1,3,4,5,6,7,8,9],[2],[10]]
[[1,3],[2,10],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,2,10,1,3]=>[2,3,4,5,6,7,9,1,10,8]=>[[1,3,4,5,6,7,8,10],[2,9]]
[]=>[]=>[]=>[]
[[1,2,4,5,6,7,8,9],[3]]=>[3,1,2,4,5,6,7,8,9]=>[7,9,8,6,5,4,3,2,1]=>[[1,8],[2],[3],[4],[5],[6],[7],[9]]
[[1,6,8,9],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6,8,9]=>[3,5,6,7,8,9,4,2,1]=>[[1,4,6,7,8,9],[2],[3],[5]]
[[1,7,9],[2],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,1,7,9]=>[2,4,5,6,7,8,9,3,1]=>[[1,3,5,6,7,8,9],[2],[4]]
[[1,4],[2,6],[3,8],[5],[7],[9]]=>[9,7,5,3,8,2,6,1,4]=>[1,3,5,7,2,8,4,9,6]=>[[1,2,4,6,8,9],[3,5,7]]
[[1,8],[2],[3],[4],[5],[6],[7],[9]]=>[9,7,6,5,4,3,2,1,8]=>[1,3,4,5,6,7,8,9,2]=>[[1,2,4,5,6,7,8,9],[3]]
[[1,2,4,5,6,7,8,9,10],[3]]=>[3,1,2,4,5,6,7,8,9,10]=>[8,10,9,7,6,5,4,3,2,1]=>[[1,9],[2],[3],[4],[5],[6],[7],[8],[10]]
[[1,2,8],[3,4],[5,6],[7,9],[10]]=>[10,7,9,5,6,3,4,1,2,8]=>[1,4,2,6,5,8,7,10,9,3]=>[[1,2,3,7,9],[4,5,8,10],[6]]
[[1,8,10],[2],[3],[4],[5],[6],[7],[9]]=>[9,7,6,5,4,3,2,1,8,10]=>[2,4,5,6,7,8,9,10,3,1]=>[[1,3,5,6,7,8,9,10],[2],[4]]
[[1,9],[2],[3],[4],[5],[6],[7],[8],[10]]=>[10,8,7,6,5,4,3,2,1,9]=>[1,3,4,5,6,7,8,9,10,2]=>[[1,2,4,5,6,7,8,9,10],[3]]
[[1,3,4,5,6,7,8],[2,9]]=>[2,9,1,3,4,5,6,7,8]=>[8,1,9,7,6,5,4,3,2]=>[[1,2],[3,9],[4],[5],[6],[7],[8]]
[[1,3,4,5,6,7,8],[2],[9]]=>[9,2,1,3,4,5,6,7,8]=>[1,8,9,7,6,5,4,3,2]=>[[1,2,9],[3],[4],[5],[6],[7],[8]]
[[1,3,4],[2],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,2,1,3,4]=>[1,2,3,4,5,8,9,7,6]=>[[1,2,3,4,5,6,9],[7],[8]]
[[1,3],[2],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,2,1,3]=>[1,2,3,4,5,6,8,9,7]=>[[1,2,3,4,5,6,7,9],[8]]
[[1,3,4,5,6,7,8,9],[2,10]]=>[2,10,1,3,4,5,6,7,8,9]=>[9,1,10,8,7,6,5,4,3,2]=>[[1,2],[3,10],[4],[5],[6],[7],[8],[9]]
[[1,3,4,5,6,7,8,9],[2],[10]]=>[10,2,1,3,4,5,6,7,8,9]=>[1,9,10,8,7,6,5,4,3,2]=>[[1,2,10],[3],[4],[5],[6],[7],[8],[9]]
[[1,3,4,5,6,7,8],[2,9,10]]=>[2,9,10,1,3,4,5,6,7,8]=>[9,2,1,10,8,7,6,5,4,3]=>[[1,3],[2,4],[5,10],[6],[7],[8],[9]]
[[1,3,4,5],[2,7,8],[6,10],[9]]=>[9,6,10,2,7,8,1,3,4,5]=>[2,5,1,9,4,3,10,8,7,6]=>[[1,3,6,10],[2,4,7],[5,8],[9]]
[[1,3],[2],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,2,1,3]=>[1,2,3,4,5,6,7,9,10,8]=>[[1,2,3,4,5,6,7,8,10],[9]]
[[1,2,3,5,6,7,8,9,10],[4]]=>[4,1,2,3,5,6,7,8,9,10]=>[7,10,9,8,6,5,4,3,2,1]=>[[1,8],[2],[3],[4],[5],[6],[7],[9],[10]]
[[1,2,3,4,6,7,8,9,10],[5]]=>[5,1,2,3,4,6,7,8,9,10]=>[6,10,9,8,7,5,4,3,2,1]=>[[1,7],[2],[3],[4],[5],[6],[8],[9],[10]]
[[1,2,3,4,5,6,7,9,10],[8]]=>[8,1,2,3,4,5,6,7,9,10]=>[3,10,9,8,7,6,5,4,2,1]=>[[1,4],[2],[3],[5],[6],[7],[8],[9],[10]]
[[1,2,3,4,5,6,8,9,10],[7]]=>[7,1,2,3,4,5,6,8,9,10]=>[4,10,9,8,7,6,5,3,2,1]=>[[1,5],[2],[3],[4],[6],[7],[8],[9],[10]]
[[1,2,3,4,5,7,8,9,10],[6]]=>[6,1,2,3,4,5,7,8,9,10]=>[5,10,9,8,7,6,4,3,2,1]=>[[1,6],[2],[3],[4],[5],[7],[8],[9],[10]]
[[1,4,5,6,7,8],[2],[3],[9]]=>[9,3,2,1,4,5,6,7,8]=>[1,7,8,9,6,5,4,3,2]=>[[1,2,8,9],[3],[4],[5],[6],[7]]
[[1,5,6,7,8],[2],[3],[4],[9]]=>[9,4,3,2,1,5,6,7,8]=>[1,6,7,8,9,5,4,3,2]=>[[1,2,7,8,9],[3],[4],[5],[6]]
[[1,6,7,8],[2],[3],[4],[5],[9]]=>[9,5,4,3,2,1,6,7,8]=>[1,5,6,7,8,9,4,3,2]=>[[1,2,6,7,8,9],[3],[4],[5]]
[[1,7,8],[2],[3],[4],[5],[6],[9]]=>[9,6,5,4,3,2,1,7,8]=>[1,4,5,6,7,8,9,3,2]=>[[1,2,5,6,7,8,9],[3],[4]]
[[1,4,5,6,7,8,9],[2],[3],[10]]=>[10,3,2,1,4,5,6,7,8,9]=>[1,8,9,10,7,6,5,4,3,2]=>[[1,2,9,10],[3],[4],[5],[6],[7],[8]]
[[1,5,6,7,8,9],[2],[3],[4],[10]]=>[10,4,3,2,1,5,6,7,8,9]=>[1,7,8,9,10,6,5,4,3,2]=>[[1,2,8,9,10],[3],[4],[5],[6],[7]]
[[1,2,3,4,9],[5,6,7,8],[10]]=>[10,5,6,7,8,1,2,3,4,9]=>[1,6,5,4,3,10,9,8,7,2]=>[[1,2,7],[3,8],[4,9],[5,10],[6]]
[[1,6,7,8,9],[2],[3],[4],[5],[10]]=>[10,5,4,3,2,1,6,7,8,9]=>[1,6,7,8,9,10,5,4,3,2]=>[[1,2,7,8,9,10],[3],[4],[5],[6]]
[[1,2,5,9],[3,4,8],[6,7],[10]]=>[10,6,7,3,4,8,1,2,5,9]=>[1,5,4,8,7,3,10,9,6,2]=>[[1,2,6,9],[3,7,10],[4,8],[5]]
[[1,7,8,9],[2],[3],[4],[5],[6],[10]]=>[10,6,5,4,3,2,1,7,8,9]=>[1,5,6,7,8,9,10,4,3,2]=>[[1,2,6,7,8,9,10],[3],[4],[5]]
[[1,2,9],[3,4],[5,6],[7,8],[10]]=>[10,7,8,5,6,3,4,1,2,9]=>[1,4,3,6,5,8,7,10,9,2]=>[[1,2,5,7,9],[3,6,8,10],[4]]
[[1,8,9],[2],[3],[4],[5],[6],[7],[10]]=>[10,7,6,5,4,3,2,1,8,9]=>[1,4,5,6,7,8,9,10,3,2]=>[[1,2,5,6,7,8,9,10],[3],[4]]
[[1,2,5,6,7,8,9],[3],[4]]=>[4,3,1,2,5,6,7,8,9]=>[6,7,9,8,5,4,3,2,1]=>[[1,7,8],[2],[3],[4],[5],[6],[9]]
[[1,2,6,7,8,9],[3],[4],[5]]=>[5,4,3,1,2,6,7,8,9]=>[5,6,7,9,8,4,3,2,1]=>[[1,6,7,8],[2],[3],[4],[5],[9]]
[[1,2,7,8,9],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7,8,9]=>[4,5,6,7,9,8,3,2,1]=>[[1,5,6,7,8],[2],[3],[4],[9]]
[[1,2],[3,6],[4,8],[5],[7],[9]]=>[9,7,5,4,8,3,6,1,2]=>[1,3,5,6,2,7,4,9,8]=>[[1,2,4,6,7,8],[3,5,9]]
[[1,2],[3,8],[4],[5],[6],[7],[9]]=>[9,7,6,5,4,3,8,1,2]=>[1,3,4,5,6,7,2,9,8]=>[[1,2,4,5,6,7,8],[3,9]]
[[1,2,5,6,7,8,9,10],[3],[4]]=>[4,3,1,2,5,6,7,8,9,10]=>[7,8,10,9,6,5,4,3,2,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7],[10]]
[[1,2,7,8,9,10],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7,8,9,10]=>[5,6,7,8,10,9,4,3,2,1]=>[[1,6,7,8,9],[2],[3],[4],[5],[10]]
[[1,2,8,9,10],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2,8,9,10]=>[4,5,6,7,8,10,9,3,2,1]=>[[1,5,6,7,8,9],[2],[3],[4],[10]]
[[1,2,4,7],[3,6,10],[5,9],[8]]=>[8,5,9,3,6,10,1,2,4,7]=>[3,6,2,8,5,1,10,9,7,4]=>[[1,4,7,9],[2,5,8],[3,6],[10]]
[[1,4],[2,6],[3,9],[5],[7],[8],[10]]=>[10,8,7,5,3,9,2,6,1,4]=>[1,3,4,6,8,2,9,5,10,7]=>[[1,2,4,5,7,9,10],[3,6,8]]
[[1,4],[2],[3],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,3,2,1,4]=>[1,2,3,4,5,6,8,9,10,7]=>[[1,2,3,4,5,6,7,9,10],[8]]
[[1,5],[2],[3],[4],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,4,3,2,1,5]=>[1,2,3,4,5,7,8,9,10,6]=>[[1,2,3,4,5,6,8,9,10],[7]]
[[1,8],[2],[3],[4],[5],[6],[7],[9],[10]]=>[10,9,7,6,5,4,3,2,1,8]=>[1,2,4,5,6,7,8,9,10,3]=>[[1,2,3,5,6,7,8,9,10],[4]]
[[1,7],[2],[3],[4],[5],[6],[8],[9],[10]]=>[10,9,8,6,5,4,3,2,1,7]=>[1,2,3,5,6,7,8,9,10,4]=>[[1,2,3,4,6,7,8,9,10],[5]]
[[1,6],[2],[3],[4],[5],[7],[8],[9],[10]]=>[10,9,8,7,5,4,3,2,1,6]=>[1,2,3,4,6,7,8,9,10,5]=>[[1,2,3,4,5,7,8,9,10],[6]]
[[1,11],[2],[3],[4],[5],[6],[7],[8],[9],[10],[12]]=>[12,10,9,8,7,6,5,4,3,2,1,11]=>[1,3,4,5,6,7,8,9,10,11,12,2]=>[[1,2,4,5,6,7,8,9,10,11,12],[3]]
[[1,7],[2],[3],[4],[5],[6],[8],[9],[10],[11],[12]]=>[12,11,10,9,8,6,5,4,3,2,1,7]=>[1,2,3,4,5,7,8,9,10,11,12,6]=>[[1,2,3,4,5,6,8,9,10,11,12],[7]]
[[1,2,4],[3],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,3,1,2,4]=>[1,2,3,4,5,7,9,8,6]=>[[1,2,3,4,5,6,8],[7],[9]]
[[1,2,3,5],[4],[6],[7],[8],[9]]=>[9,8,7,6,4,1,2,3,5]=>[1,2,3,4,6,9,8,7,5]=>[[1,2,3,4,5,7],[6],[8],[9]]
[[1,2],[3,4],[5,6],[7,9],[8]]=>[8,7,9,5,6,3,4,1,2]=>[2,3,1,5,4,7,6,9,8]=>[[1,3,4,6,8],[2,5,7,9]]
[[1,2,3,4,6],[5],[7],[8],[9]]=>[9,8,7,5,1,2,3,4,6]=>[1,2,3,5,9,8,7,6,4]=>[[1,2,3,4,6],[5],[7],[8],[9]]
[[1,2,3,4,5,7],[6],[8],[9]]=>[9,8,6,1,2,3,4,5,7]=>[1,2,4,9,8,7,6,5,3]=>[[1,2,3,5],[4],[6],[7],[8],[9]]
[[1,2,3,4,5,6,8],[7],[9]]=>[9,7,1,2,3,4,5,6,8]=>[1,3,9,8,7,6,5,4,2]=>[[1,2,4],[3],[5],[6],[7],[8],[9]]
[[1,2,3,4,5,7,9],[6,8]]=>[6,8,1,2,3,4,5,7,9]=>[4,2,9,8,7,6,5,3,1]=>[[1,3],[2,5],[4],[6],[7],[8],[9]]
[[1,2,4],[3],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,3,1,2,4]=>[1,2,3,4,5,6,8,10,9,7]=>[[1,2,3,4,5,6,7,9],[8],[10]]
[[1,2,3,5],[4],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,4,1,2,3,5]=>[1,2,3,4,5,7,10,9,8,6]=>[[1,2,3,4,5,6,8],[7],[9],[10]]
[[1,2],[3,4],[5,6],[7,9],[8],[10]]=>[10,8,7,9,5,6,3,4,1,2]=>[1,3,4,2,6,5,8,7,10,9]=>[[1,2,4,5,7,9],[3,6,8,10]]
[[1,2,3,4,6],[5],[7],[8],[9],[10]]=>[10,9,8,7,5,1,2,3,4,6]=>[1,2,3,4,6,10,9,8,7,5]=>[[1,2,3,4,5,7],[6],[8],[9],[10]]
[[1,2,3,4,5,7],[6],[8],[9],[10]]=>[10,9,8,6,1,2,3,4,5,7]=>[1,2,3,5,10,9,8,7,6,4]=>[[1,2,3,4,6],[5],[7],[8],[9],[10]]
[[1,2,3,4,5,6,8],[7],[9],[10]]=>[10,9,7,1,2,3,4,5,6,8]=>[1,2,4,10,9,8,7,6,5,3]=>[[1,2,3,5],[4],[6],[7],[8],[9],[10]]
[[1,2,3,4,5,6,7,9],[8],[10]]=>[10,8,1,2,3,4,5,6,7,9]=>[1,3,10,9,8,7,6,5,4,2]=>[[1,2,4],[3],[5],[6],[7],[8],[9],[10]]
[[1,2,8],[3,9],[4],[5],[6],[7]]=>[7,6,5,4,3,9,1,2,8]=>[3,4,5,6,7,1,9,8,2]=>[[1,2,5,6,7,8],[3,4],[9]]
[[1,3,4,9],[2],[5],[6],[7],[8]]=>[8,7,6,5,2,1,3,4,9]=>[2,3,4,5,8,9,7,6,1]=>[[1,3,4,5,6,9],[2],[7],[8]]
[[1,3,4,9],[2,10],[5],[6],[7],[8]]=>[8,7,6,5,2,10,1,3,4,9]=>[3,4,5,6,9,1,10,8,7,2]=>[[1,2,5,6,7,10],[3,4],[8],[9]]
[[1,6],[2,8],[3,9],[4],[5],[7]]=>[7,5,4,3,9,2,8,1,6]=>[3,5,6,7,1,8,2,9,4]=>[[1,2,4,7,8,9],[3,5,6]]
[[1,7],[2,8],[3],[4],[5],[6],[9]]=>[9,6,5,4,3,2,8,1,7]=>[1,4,5,6,7,8,2,9,3]=>[[1,2,3,6,7,8,9],[4,5]]
[[1,2],[3,9],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,9,1,2]=>[2,3,4,5,6,7,1,9,8]=>[[1,3,4,5,6,7,8],[2,9]]
[[1,2],[3,8],[4,9],[5],[6],[7]]=>[7,6,5,4,9,3,8,1,2]=>[3,4,5,6,1,7,2,9,8]=>[[1,2,5,6,7,8],[3,4,9]]
[[1,2],[3,10],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,10,1,2]=>[2,3,4,5,6,7,8,1,10,9]=>[[1,3,4,5,6,7,8,9],[2,10]]
[[1,2],[3,9],[4,10],[5],[6],[7],[8]]=>[8,7,6,5,4,10,3,9,1,2]=>[3,4,5,6,7,1,8,2,10,9]=>[[1,2,5,6,7,8,9],[3,4,10]]
[[1,2,3],[4,9],[5],[6],[7],[8]]=>[8,7,6,5,4,9,1,2,3]=>[2,3,4,5,6,1,9,8,7]=>[[1,3,4,5,6,7],[2,8],[9]]
[[1,2,3,4],[5,9],[6],[7],[8]]=>[8,7,6,5,9,1,2,3,4]=>[2,3,4,5,1,9,8,7,6]=>[[1,3,4,5,6],[2,7],[8],[9]]
[[1,4,9],[2,5],[3,7],[6,8]]=>[6,8,3,7,2,5,1,4,9]=>[4,2,7,3,8,5,9,6,1]=>[[1,3,5,6],[2,7,8,9],[4]]
[[1,2,3,4,5,6],[7,9],[8]]=>[8,7,9,1,2,3,4,5,6]=>[2,3,1,9,8,7,6,5,4]=>[[1,3,4],[2,5],[6],[7],[8],[9]]
[[1,3],[2,4],[5,9],[6],[7],[8]]=>[8,7,6,5,9,2,4,1,3]=>[2,3,4,5,1,8,6,9,7]=>[[1,3,4,5,6,7],[2,8,9]]
[[1,4],[2,5],[3],[6],[7],[8],[9]]=>[9,8,7,6,3,2,5,1,4]=>[1,2,3,4,7,8,5,9,6]=>[[1,2,3,4,5,6,9],[7,8]]
[[1,3,4,5,6,7,9],[2,8]]=>[2,8,1,3,4,5,6,7,9]=>[8,2,9,7,6,5,4,3,1]=>[[1,3],[2,9],[4],[5],[6],[7],[8]]
[[1,3,6,7],[2,5,10],[4,9],[8]]=>[8,4,9,2,5,10,1,3,6,7]=>[3,7,2,9,6,1,10,8,5,4]=>[[1,4,8,10],[2,5,9],[3,6],[7]]
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
Map
Robinson-Schensted insertion tableau
Description
Sends a permutation to its Robinson-Schensted insertion tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding insertion tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding insertion tableau.
searching the database
Sorry, this map was not found in the database.