Identifier
Mp00106: Standard tableaux —catabolism⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Images
=>
Cc0007;cc-rep-0Cc0007;cc-rep-1
[[1]]=>[[1]]=>[1]=>[1]=> [[1,2]]=>[[1,2]]=>[1,2]=>[2,1]=>0 [[1],[2]]=>[[1,2]]=>[1,2]=>[2,1]=>0 [[1,2,3]]=>[[1,2,3]]=>[1,2,3]=>[2,3,1]=>00 [[1,3],[2]]=>[[1,2],[3]]=>[3,1,2]=>[3,1,2]=>00 [[1,2],[3]]=>[[1,2,3]]=>[1,2,3]=>[2,3,1]=>00 [[1],[2],[3]]=>[[1,2],[3]]=>[3,1,2]=>[3,1,2]=>00 [[1,2,3,4]]=>[[1,2,3,4]]=>[1,2,3,4]=>[2,3,4,1]=>000 [[1,3,4],[2]]=>[[1,2,4],[3]]=>[3,1,2,4]=>[3,4,2,1]=>000 [[1,2,4],[3]]=>[[1,2,3],[4]]=>[4,1,2,3]=>[3,4,1,2]=>000 [[1,2,3],[4]]=>[[1,2,3,4]]=>[1,2,3,4]=>[2,3,4,1]=>000 [[1,3],[2,4]]=>[[1,2,4],[3]]=>[3,1,2,4]=>[3,4,2,1]=>000 [[1,2],[3,4]]=>[[1,2,3,4]]=>[1,2,3,4]=>[2,3,4,1]=>000 [[1,4],[2],[3]]=>[[1,2],[3],[4]]=>[4,3,1,2]=>[4,1,3,2]=>000 [[1,3],[2],[4]]=>[[1,2,4],[3]]=>[3,1,2,4]=>[3,4,2,1]=>000 [[1,2],[3],[4]]=>[[1,2,3],[4]]=>[4,1,2,3]=>[3,4,1,2]=>000 [[1],[2],[3],[4]]=>[[1,2],[3],[4]]=>[4,3,1,2]=>[4,1,3,2]=>000 [[1,2,3,4,5]]=>[[1,2,3,4,5]]=>[1,2,3,4,5]=>[2,3,4,5,1]=>0000 [[1,3,4,5],[2]]=>[[1,2,4,5],[3]]=>[3,1,2,4,5]=>[3,4,2,5,1]=>0000 [[1,2,4,5],[3]]=>[[1,2,3,5],[4]]=>[4,1,2,3,5]=>[3,4,5,2,1]=>0000 [[1,2,3,5],[4]]=>[[1,2,3,4],[5]]=>[5,1,2,3,4]=>[3,4,5,1,2]=>0000 [[1,2,3,4],[5]]=>[[1,2,3,4,5]]=>[1,2,3,4,5]=>[2,3,4,5,1]=>0000 [[1,3,5],[2,4]]=>[[1,2,4],[3,5]]=>[3,5,1,2,4]=>[4,5,2,1,3]=>0000 [[1,2,5],[3,4]]=>[[1,2,3,4],[5]]=>[5,1,2,3,4]=>[3,4,5,1,2]=>0000 [[1,3,4],[2,5]]=>[[1,2,4,5],[3]]=>[3,1,2,4,5]=>[3,4,2,5,1]=>0000 [[1,2,4],[3,5]]=>[[1,2,3,5],[4]]=>[4,1,2,3,5]=>[3,4,5,2,1]=>0000 [[1,2,3],[4,5]]=>[[1,2,3,4,5]]=>[1,2,3,4,5]=>[2,3,4,5,1]=>0000 [[1,4,5],[2],[3]]=>[[1,2,5],[3],[4]]=>[4,3,1,2,5]=>[4,5,3,2,1]=>0000 [[1,3,5],[2],[4]]=>[[1,2,4],[3],[5]]=>[5,3,1,2,4]=>[4,5,3,1,2]=>0000 [[1,2,5],[3],[4]]=>[[1,2,3],[4],[5]]=>[5,4,1,2,3]=>[4,5,1,3,2]=>0000 [[1,3,4],[2],[5]]=>[[1,2,4,5],[3]]=>[3,1,2,4,5]=>[3,4,2,5,1]=>0000 [[1,2,4],[3],[5]]=>[[1,2,3,5],[4]]=>[4,1,2,3,5]=>[3,4,5,2,1]=>0000 [[1,2,3],[4],[5]]=>[[1,2,3,4],[5]]=>[5,1,2,3,4]=>[3,4,5,1,2]=>0000 [[1,4],[2,5],[3]]=>[[1,2,5],[3],[4]]=>[4,3,1,2,5]=>[4,5,3,2,1]=>0000 [[1,3],[2,5],[4]]=>[[1,2,4,5],[3]]=>[3,1,2,4,5]=>[3,4,2,5,1]=>0000 [[1,2],[3,5],[4]]=>[[1,2,3,5],[4]]=>[4,1,2,3,5]=>[3,4,5,2,1]=>0000 [[1,3],[2,4],[5]]=>[[1,2,4],[3,5]]=>[3,5,1,2,4]=>[4,5,2,1,3]=>0000 [[1,2],[3,4],[5]]=>[[1,2,3,4],[5]]=>[5,1,2,3,4]=>[3,4,5,1,2]=>0000 [[1,5],[2],[3],[4]]=>[[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>[5,1,4,3,2]=>0000 [[1,4],[2],[3],[5]]=>[[1,2,5],[3],[4]]=>[4,3,1,2,5]=>[4,5,3,2,1]=>0000 [[1,3],[2],[4],[5]]=>[[1,2,4],[3],[5]]=>[5,3,1,2,4]=>[4,5,3,1,2]=>0000 [[1,2],[3],[4],[5]]=>[[1,2,3],[4],[5]]=>[5,4,1,2,3]=>[4,5,1,3,2]=>0000 [[1],[2],[3],[4],[5]]=>[[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>[5,1,4,3,2]=>0000 [[1,2,3,4,5,6]]=>[[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>[2,3,4,5,6,1]=>00000 [[1,3,4,5,6],[2]]=>[[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>[3,4,2,5,6,1]=>00000 [[1,2,4,5,6],[3]]=>[[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>[3,4,5,2,6,1]=>00000 [[1,2,3,5,6],[4]]=>[[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>[3,4,5,6,2,1]=>00000 [[1,2,3,4,6],[5]]=>[[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>[3,4,5,6,1,2]=>00000 [[1,2,3,4,5],[6]]=>[[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>[2,3,4,5,6,1]=>00000 [[1,3,5,6],[2,4]]=>[[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>[4,5,2,6,3,1]=>00000 [[1,2,5,6],[3,4]]=>[[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>[4,5,6,1,2,3]=>00000 [[1,3,4,6],[2,5]]=>[[1,2,4,5],[3,6]]=>[3,6,1,2,4,5]=>[4,5,2,6,1,3]=>00000 [[1,2,4,6],[3,5]]=>[[1,2,3,5],[4,6]]=>[4,6,1,2,3,5]=>[4,5,6,2,1,3]=>00000 [[1,2,3,6],[4,5]]=>[[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>[3,4,5,6,1,2]=>00000 [[1,3,4,5],[2,6]]=>[[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>[3,4,2,5,6,1]=>00000 [[1,2,4,5],[3,6]]=>[[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>[3,4,5,2,6,1]=>00000 [[1,2,3,5],[4,6]]=>[[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>[3,4,5,6,2,1]=>00000 [[1,2,3,4],[5,6]]=>[[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>[2,3,4,5,6,1]=>00000 [[1,4,5,6],[2],[3]]=>[[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>[4,5,3,2,6,1]=>00000 [[1,3,5,6],[2],[4]]=>[[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>[4,5,3,6,2,1]=>00000 [[1,2,5,6],[3],[4]]=>[[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>[4,5,6,3,2,1]=>00000 [[1,3,4,6],[2],[5]]=>[[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>[4,5,3,6,1,2]=>00000 [[1,2,4,6],[3],[5]]=>[[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>[4,5,6,3,1,2]=>00000 [[1,2,3,6],[4],[5]]=>[[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>[4,5,6,1,3,2]=>00000 [[1,3,4,5],[2],[6]]=>[[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>[3,4,2,5,6,1]=>00000 [[1,2,4,5],[3],[6]]=>[[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>[3,4,5,2,6,1]=>00000 [[1,2,3,5],[4],[6]]=>[[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>[3,4,5,6,2,1]=>00000 [[1,2,3,4],[5],[6]]=>[[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>[3,4,5,6,1,2]=>00000 [[1,3,5],[2,4,6]]=>[[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>[4,5,2,6,3,1]=>00000 [[1,2,5],[3,4,6]]=>[[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>[3,4,5,6,2,1]=>00000 [[1,3,4],[2,5,6]]=>[[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>[3,4,2,5,6,1]=>00000 [[1,2,4],[3,5,6]]=>[[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>[3,4,5,2,6,1]=>00000 [[1,2,3],[4,5,6]]=>[[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>[2,3,4,5,6,1]=>00000 [[1,4,6],[2,5],[3]]=>[[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5]=>[5,6,3,2,1,4]=>00000 [[1,3,6],[2,5],[4]]=>[[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>[4,5,3,6,1,2]=>00000 [[1,2,6],[3,5],[4]]=>[[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>[4,5,6,3,1,2]=>00000 [[1,3,6],[2,4],[5]]=>[[1,2,4],[3,5],[6]]=>[6,3,5,1,2,4]=>[5,6,3,1,4,2]=>00000 [[1,2,6],[3,4],[5]]=>[[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>[4,5,6,1,3,2]=>00000 [[1,4,5],[2,6],[3]]=>[[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>[4,5,3,2,6,1]=>00000 [[1,3,5],[2,6],[4]]=>[[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>[4,5,3,6,2,1]=>00000 [[1,2,5],[3,6],[4]]=>[[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>[4,5,6,3,2,1]=>00000 [[1,3,4],[2,6],[5]]=>[[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>[3,4,2,5,6,1]=>00000 [[1,2,4],[3,6],[5]]=>[[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>[3,4,5,2,6,1]=>00000 [[1,2,3],[4,6],[5]]=>[[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>[3,4,5,6,2,1]=>00000 [[1,3,5],[2,4],[6]]=>[[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>[4,5,2,6,3,1]=>00000 [[1,2,5],[3,4],[6]]=>[[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>[4,5,6,1,2,3]=>00000 [[1,3,4],[2,5],[6]]=>[[1,2,4,5],[3,6]]=>[3,6,1,2,4,5]=>[4,5,2,6,1,3]=>00000 [[1,2,4],[3,5],[6]]=>[[1,2,3,5],[4,6]]=>[4,6,1,2,3,5]=>[4,5,6,2,1,3]=>00000 [[1,2,3],[4,5],[6]]=>[[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>[3,4,5,6,1,2]=>00000 [[1,5,6],[2],[3],[4]]=>[[1,2,6],[3],[4],[5]]=>[5,4,3,1,2,6]=>[5,6,4,3,2,1]=>00000 [[1,4,6],[2],[3],[5]]=>[[1,2,5],[3],[4],[6]]=>[6,4,3,1,2,5]=>[5,6,4,3,1,2]=>00000 [[1,3,6],[2],[4],[5]]=>[[1,2,4],[3],[5],[6]]=>[6,5,3,1,2,4]=>[5,6,4,1,3,2]=>00000 [[1,2,6],[3],[4],[5]]=>[[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>[5,6,1,4,3,2]=>00000 [[1,4,5],[2],[3],[6]]=>[[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>[4,5,3,2,6,1]=>00000 [[1,3,5],[2],[4],[6]]=>[[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>[4,5,3,6,2,1]=>00000 [[1,2,5],[3],[4],[6]]=>[[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>[4,5,6,3,2,1]=>00000 [[1,3,4],[2],[5],[6]]=>[[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>[4,5,3,6,1,2]=>00000 [[1,2,4],[3],[5],[6]]=>[[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>[4,5,6,3,1,2]=>00000 [[1,2,3],[4],[5],[6]]=>[[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>[4,5,6,1,3,2]=>00000 [[1,4],[2,5],[3,6]]=>[[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5]=>[5,6,3,2,1,4]=>00000 [[1,3],[2,5],[4,6]]=>[[1,2,4,5],[3,6]]=>[3,6,1,2,4,5]=>[4,5,2,6,1,3]=>00000 [[1,2],[3,5],[4,6]]=>[[1,2,3,5],[4,6]]=>[4,6,1,2,3,5]=>[4,5,6,2,1,3]=>00000 [[1,3],[2,4],[5,6]]=>[[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>[4,5,2,6,3,1]=>00000 [[1,2],[3,4],[5,6]]=>[[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>[4,5,6,1,2,3]=>00000 [[1,5],[2,6],[3],[4]]=>[[1,2,6],[3],[4],[5]]=>[5,4,3,1,2,6]=>[5,6,4,3,2,1]=>00000 [[1,4],[2,6],[3],[5]]=>[[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>[4,5,3,2,6,1]=>00000 [[1,3],[2,6],[4],[5]]=>[[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>[4,5,3,6,2,1]=>00000 [[1,2],[3,6],[4],[5]]=>[[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>[4,5,6,3,2,1]=>00000 [[1,4],[2,5],[3],[6]]=>[[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5]=>[5,6,3,2,1,4]=>00000 [[1,3],[2,5],[4],[6]]=>[[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>[4,5,3,6,1,2]=>00000 [[1,2],[3,5],[4],[6]]=>[[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>[4,5,6,3,1,2]=>00000 [[1,3],[2,4],[5],[6]]=>[[1,2,4],[3,5],[6]]=>[6,3,5,1,2,4]=>[5,6,3,1,4,2]=>00000 [[1,2],[3,4],[5],[6]]=>[[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>[4,5,6,1,3,2]=>00000 [[1,6],[2],[3],[4],[5]]=>[[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>[6,1,5,4,3,2]=>00000 [[1,5],[2],[3],[4],[6]]=>[[1,2,6],[3],[4],[5]]=>[5,4,3,1,2,6]=>[5,6,4,3,2,1]=>00000 [[1,4],[2],[3],[5],[6]]=>[[1,2,5],[3],[4],[6]]=>[6,4,3,1,2,5]=>[5,6,4,3,1,2]=>00000 [[1,3],[2],[4],[5],[6]]=>[[1,2,4],[3],[5],[6]]=>[6,5,3,1,2,4]=>[5,6,4,1,3,2]=>00000 [[1,2],[3],[4],[5],[6]]=>[[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>[5,6,1,4,3,2]=>00000 [[1],[2],[3],[4],[5],[6]]=>[[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>[6,1,5,4,3,2]=>00000 [[1,2,3,4,5,6,7]]=>[[1,2,3,4,5,6,7]]=>[1,2,3,4,5,6,7]=>[2,3,4,5,6,7,1]=>000000 [[1,3,4,5,6,7],[2]]=>[[1,2,4,5,6,7],[3]]=>[3,1,2,4,5,6,7]=>[3,4,2,5,6,7,1]=>000000 [[1,2,4,5,6,7],[3]]=>[[1,2,3,5,6,7],[4]]=>[4,1,2,3,5,6,7]=>[3,4,5,2,6,7,1]=>000000 [[1,2,3,5,6,7],[4]]=>[[1,2,3,4,6,7],[5]]=>[5,1,2,3,4,6,7]=>[3,4,5,6,2,7,1]=>000000 [[1,2,3,4,6,7],[5]]=>[[1,2,3,4,5,7],[6]]=>[6,1,2,3,4,5,7]=>[3,4,5,6,7,2,1]=>000000 [[1,2,3,4,5,7],[6]]=>[[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>[3,4,5,6,7,1,2]=>000000 [[1,2,3,4,5,6],[7]]=>[[1,2,3,4,5,6,7]]=>[1,2,3,4,5,6,7]=>[2,3,4,5,6,7,1]=>000000 [[1,3,5,6,7],[2,4]]=>[[1,2,4,6,7],[3,5]]=>[3,5,1,2,4,6,7]=>[4,5,2,6,3,7,1]=>000000 [[1,2,5,6,7],[3,4]]=>[[1,2,3,4,7],[5,6]]=>[5,6,1,2,3,4,7]=>[4,5,6,7,2,3,1]=>000000 [[1,3,4,6,7],[2,5]]=>[[1,2,4,5,7],[3,6]]=>[3,6,1,2,4,5,7]=>[4,5,2,6,7,3,1]=>000000 [[1,2,4,6,7],[3,5]]=>[[1,2,3,5,7],[4,6]]=>[4,6,1,2,3,5,7]=>[4,5,6,2,7,3,1]=>000000 [[1,2,3,6,7],[4,5]]=>[[1,2,3,4,5],[6,7]]=>[6,7,1,2,3,4,5]=>[4,5,6,7,1,2,3]=>000000 [[1,3,4,5,7],[2,6]]=>[[1,2,4,5,6],[3,7]]=>[3,7,1,2,4,5,6]=>[4,5,2,6,7,1,3]=>000000 [[1,2,4,5,7],[3,6]]=>[[1,2,3,5,6],[4,7]]=>[4,7,1,2,3,5,6]=>[4,5,6,2,7,1,3]=>000000 [[1,2,3,5,7],[4,6]]=>[[1,2,3,4,6],[5,7]]=>[5,7,1,2,3,4,6]=>[4,5,6,7,2,1,3]=>000000 [[1,2,3,4,7],[5,6]]=>[[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>[3,4,5,6,7,1,2]=>000000 [[1,3,4,5,6],[2,7]]=>[[1,2,4,5,6,7],[3]]=>[3,1,2,4,5,6,7]=>[3,4,2,5,6,7,1]=>000000 [[1,2,4,5,6],[3,7]]=>[[1,2,3,5,6,7],[4]]=>[4,1,2,3,5,6,7]=>[3,4,5,2,6,7,1]=>000000 [[1,2,3,5,6],[4,7]]=>[[1,2,3,4,6,7],[5]]=>[5,1,2,3,4,6,7]=>[3,4,5,6,2,7,1]=>000000 [[1,2,3,4,6],[5,7]]=>[[1,2,3,4,5,7],[6]]=>[6,1,2,3,4,5,7]=>[3,4,5,6,7,2,1]=>000000 [[1,2,3,4,5],[6,7]]=>[[1,2,3,4,5,6,7]]=>[1,2,3,4,5,6,7]=>[2,3,4,5,6,7,1]=>000000 [[1,4,5,6,7],[2],[3]]=>[[1,2,5,6,7],[3],[4]]=>[4,3,1,2,5,6,7]=>[4,5,3,2,6,7,1]=>000000 [[1,3,5,6,7],[2],[4]]=>[[1,2,4,6,7],[3],[5]]=>[5,3,1,2,4,6,7]=>[4,5,3,6,2,7,1]=>000000 [[1,2,5,6,7],[3],[4]]=>[[1,2,3,6,7],[4],[5]]=>[5,4,1,2,3,6,7]=>[4,5,6,3,2,7,1]=>000000 [[1,3,4,6,7],[2],[5]]=>[[1,2,4,5,7],[3],[6]]=>[6,3,1,2,4,5,7]=>[4,5,3,6,7,2,1]=>000000 [[1,2,4,6,7],[3],[5]]=>[[1,2,3,5,7],[4],[6]]=>[6,4,1,2,3,5,7]=>[4,5,6,3,7,2,1]=>000000 [[1,2,3,6,7],[4],[5]]=>[[1,2,3,4,7],[5],[6]]=>[6,5,1,2,3,4,7]=>[4,5,6,7,3,2,1]=>000000 [[1,3,4,5,7],[2],[6]]=>[[1,2,4,5,6],[3],[7]]=>[7,3,1,2,4,5,6]=>[4,5,3,6,7,1,2]=>000000 [[1,2,4,5,7],[3],[6]]=>[[1,2,3,5,6],[4],[7]]=>[7,4,1,2,3,5,6]=>[4,5,6,3,7,1,2]=>000000 [[1,2,3,5,7],[4],[6]]=>[[1,2,3,4,6],[5],[7]]=>[7,5,1,2,3,4,6]=>[4,5,6,7,3,1,2]=>000000 [[1,2,3,4,7],[5],[6]]=>[[1,2,3,4,5],[6],[7]]=>[7,6,1,2,3,4,5]=>[4,5,6,7,1,3,2]=>000000 [[1,3,4,5,6],[2],[7]]=>[[1,2,4,5,6,7],[3]]=>[3,1,2,4,5,6,7]=>[3,4,2,5,6,7,1]=>000000 [[1,2,4,5,6],[3],[7]]=>[[1,2,3,5,6,7],[4]]=>[4,1,2,3,5,6,7]=>[3,4,5,2,6,7,1]=>000000 [[1,2,3,5,6],[4],[7]]=>[[1,2,3,4,6,7],[5]]=>[5,1,2,3,4,6,7]=>[3,4,5,6,2,7,1]=>000000 [[1,2,3,4,6],[5],[7]]=>[[1,2,3,4,5,7],[6]]=>[6,1,2,3,4,5,7]=>[3,4,5,6,7,2,1]=>000000 [[1,2,3,4,5],[6],[7]]=>[[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>[3,4,5,6,7,1,2]=>000000 [[1,3,5,7],[2,4,6]]=>[[1,2,4,6],[3,5,7]]=>[3,5,7,1,2,4,6]=>[5,6,2,7,3,1,4]=>000000 [[1,2,5,7],[3,4,6]]=>[[1,2,3,4,6],[5,7]]=>[5,7,1,2,3,4,6]=>[4,5,6,7,2,1,3]=>000000 [[1,3,4,7],[2,5,6]]=>[[1,2,4,5,6],[3,7]]=>[3,7,1,2,4,5,6]=>[4,5,2,6,7,1,3]=>000000 [[1,2,4,7],[3,5,6]]=>[[1,2,3,5,6],[4,7]]=>[4,7,1,2,3,5,6]=>[4,5,6,2,7,1,3]=>000000 [[1,2,3,7],[4,5,6]]=>[[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>[3,4,5,6,7,1,2]=>000000 [[1,3,5,6],[2,4,7]]=>[[1,2,4,6,7],[3,5]]=>[3,5,1,2,4,6,7]=>[4,5,2,6,3,7,1]=>000000 [[1,2,5,6],[3,4,7]]=>[[1,2,3,4,7],[5,6]]=>[5,6,1,2,3,4,7]=>[4,5,6,7,2,3,1]=>000000 [[1,3,4,6],[2,5,7]]=>[[1,2,4,5,7],[3,6]]=>[3,6,1,2,4,5,7]=>[4,5,2,6,7,3,1]=>000000 [[1,2,4,6],[3,5,7]]=>[[1,2,3,5,7],[4,6]]=>[4,6,1,2,3,5,7]=>[4,5,6,2,7,3,1]=>000000 [[1,2,3,6],[4,5,7]]=>[[1,2,3,4,5,7],[6]]=>[6,1,2,3,4,5,7]=>[3,4,5,6,7,2,1]=>000000 [[1,3,4,5],[2,6,7]]=>[[1,2,4,5,6,7],[3]]=>[3,1,2,4,5,6,7]=>[3,4,2,5,6,7,1]=>000000 [[1,2,4,5],[3,6,7]]=>[[1,2,3,5,6,7],[4]]=>[4,1,2,3,5,6,7]=>[3,4,5,2,6,7,1]=>000000 [[1,2,3,5],[4,6,7]]=>[[1,2,3,4,6,7],[5]]=>[5,1,2,3,4,6,7]=>[3,4,5,6,2,7,1]=>000000 [[1,2,3,4],[5,6,7]]=>[[1,2,3,4,5,6,7]]=>[1,2,3,4,5,6,7]=>[2,3,4,5,6,7,1]=>000000 [[1,4,6,7],[2,5],[3]]=>[[1,2,5,7],[3,6],[4]]=>[4,3,6,1,2,5,7]=>[5,6,3,2,7,4,1]=>000000 [[1,3,6,7],[2,5],[4]]=>[[1,2,4,5],[3,7],[6]]=>[6,3,7,1,2,4,5]=>[5,6,3,7,1,2,4]=>000000 [[1,2,6,7],[3,5],[4]]=>[[1,2,3,5],[4,7],[6]]=>[6,4,7,1,2,3,5]=>[5,6,7,3,1,2,4]=>000000 [[1,3,6,7],[2,4],[5]]=>[[1,2,4,7],[3,5],[6]]=>[6,3,5,1,2,4,7]=>[5,6,3,7,4,2,1]=>000000 [[1,2,6,7],[3,4],[5]]=>[[1,2,3,4],[5,7],[6]]=>[6,5,7,1,2,3,4]=>[5,6,7,1,3,2,4]=>000000 [[1,4,5,7],[2,6],[3]]=>[[1,2,5,6],[3,7],[4]]=>[4,3,7,1,2,5,6]=>[5,6,3,2,7,1,4]=>000000 [[1,3,5,7],[2,6],[4]]=>[[1,2,4,6],[3,7],[5]]=>[5,3,7,1,2,4,6]=>[5,6,3,7,2,1,4]=>000000 [[1,2,5,7],[3,6],[4]]=>[[1,2,3,6],[4,7],[5]]=>[5,4,7,1,2,3,6]=>[5,6,7,3,2,1,4]=>000000 [[1,3,4,7],[2,6],[5]]=>[[1,2,4,5,6],[3],[7]]=>[7,3,1,2,4,5,6]=>[4,5,3,6,7,1,2]=>000000 [[1,2,4,7],[3,6],[5]]=>[[1,2,3,5,6],[4],[7]]=>[7,4,1,2,3,5,6]=>[4,5,6,3,7,1,2]=>000000 [[1,2,3,7],[4,6],[5]]=>[[1,2,3,4,6],[5],[7]]=>[7,5,1,2,3,4,6]=>[4,5,6,7,3,1,2]=>000000 [[1,3,5,7],[2,4],[6]]=>[[1,2,4,6],[3,5],[7]]=>[7,3,5,1,2,4,6]=>[5,6,3,7,4,1,2]=>000000 [[1,2,5,7],[3,4],[6]]=>[[1,2,3,4],[5,6],[7]]=>[7,5,6,1,2,3,4]=>[5,6,7,1,3,4,2]=>000000 [[1,3,4,7],[2,5],[6]]=>[[1,2,4,5],[3,6],[7]]=>[7,3,6,1,2,4,5]=>[5,6,3,7,1,4,2]=>000000 [[1,2,4,7],[3,5],[6]]=>[[1,2,3,5],[4,6],[7]]=>[7,4,6,1,2,3,5]=>[5,6,7,3,1,4,2]=>000000 [[1,2,3,7],[4,5],[6]]=>[[1,2,3,4,5],[6],[7]]=>[7,6,1,2,3,4,5]=>[4,5,6,7,1,3,2]=>000000 [[1,4,5,6],[2,7],[3]]=>[[1,2,5,6,7],[3],[4]]=>[4,3,1,2,5,6,7]=>[4,5,3,2,6,7,1]=>000000 [[1,3,5,6],[2,7],[4]]=>[[1,2,4,6,7],[3],[5]]=>[5,3,1,2,4,6,7]=>[4,5,3,6,2,7,1]=>000000 [[1,2,5,6],[3,7],[4]]=>[[1,2,3,6,7],[4],[5]]=>[5,4,1,2,3,6,7]=>[4,5,6,3,2,7,1]=>000000 [[1,3,4,6],[2,7],[5]]=>[[1,2,4,5,7],[3],[6]]=>[6,3,1,2,4,5,7]=>[4,5,3,6,7,2,1]=>000000 [[1,2,4,6],[3,7],[5]]=>[[1,2,3,5,7],[4],[6]]=>[6,4,1,2,3,5,7]=>[4,5,6,3,7,2,1]=>000000 [[1,2,3,6],[4,7],[5]]=>[[1,2,3,4,7],[5],[6]]=>[6,5,1,2,3,4,7]=>[4,5,6,7,3,2,1]=>000000 [[1,3,4,5],[2,7],[6]]=>[[1,2,4,5,6,7],[3]]=>[3,1,2,4,5,6,7]=>[3,4,2,5,6,7,1]=>000000 [[1,2,4,5],[3,7],[6]]=>[[1,2,3,5,6,7],[4]]=>[4,1,2,3,5,6,7]=>[3,4,5,2,6,7,1]=>000000 [[1,2,3,5],[4,7],[6]]=>[[1,2,3,4,6,7],[5]]=>[5,1,2,3,4,6,7]=>[3,4,5,6,2,7,1]=>000000 [[1,2,3,4],[5,7],[6]]=>[[1,2,3,4,5,7],[6]]=>[6,1,2,3,4,5,7]=>[3,4,5,6,7,2,1]=>000000 [[1,3,5,6],[2,4],[7]]=>[[1,2,4,6,7],[3,5]]=>[3,5,1,2,4,6,7]=>[4,5,2,6,3,7,1]=>000000 [[1,2,5,6],[3,4],[7]]=>[[1,2,3,4,7],[5,6]]=>[5,6,1,2,3,4,7]=>[4,5,6,7,2,3,1]=>000000 [[1,3,4,6],[2,5],[7]]=>[[1,2,4,5,7],[3,6]]=>[3,6,1,2,4,5,7]=>[4,5,2,6,7,3,1]=>000000 [[1,2,4,6],[3,5],[7]]=>[[1,2,3,5,7],[4,6]]=>[4,6,1,2,3,5,7]=>[4,5,6,2,7,3,1]=>000000 [[1,2,3,6],[4,5],[7]]=>[[1,2,3,4,5],[6,7]]=>[6,7,1,2,3,4,5]=>[4,5,6,7,1,2,3]=>000000 [[1,3,4,5],[2,6],[7]]=>[[1,2,4,5,6],[3,7]]=>[3,7,1,2,4,5,6]=>[4,5,2,6,7,1,3]=>000000 [[1,2,4,5],[3,6],[7]]=>[[1,2,3,5,6],[4,7]]=>[4,7,1,2,3,5,6]=>[4,5,6,2,7,1,3]=>000000 [[1,2,3,5],[4,6],[7]]=>[[1,2,3,4,6],[5,7]]=>[5,7,1,2,3,4,6]=>[4,5,6,7,2,1,3]=>000000 [[1,2,3,4],[5,6],[7]]=>[[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>[3,4,5,6,7,1,2]=>000000 [[1,5,6,7],[2],[3],[4]]=>[[1,2,6,7],[3],[4],[5]]=>[5,4,3,1,2,6,7]=>[5,6,4,3,2,7,1]=>000000 [[1,4,6,7],[2],[3],[5]]=>[[1,2,5,7],[3],[4],[6]]=>[6,4,3,1,2,5,7]=>[5,6,4,3,7,2,1]=>000000 [[1,3,6,7],[2],[4],[5]]=>[[1,2,4,7],[3],[5],[6]]=>[6,5,3,1,2,4,7]=>[5,6,4,7,3,2,1]=>000000 [[1,2,6,7],[3],[4],[5]]=>[[1,2,3,7],[4],[5],[6]]=>[6,5,4,1,2,3,7]=>[5,6,7,4,3,2,1]=>000000 [[1,4,5,7],[2],[3],[6]]=>[[1,2,5,6],[3],[4],[7]]=>[7,4,3,1,2,5,6]=>[5,6,4,3,7,1,2]=>000000 [[1,3,5,7],[2],[4],[6]]=>[[1,2,4,6],[3],[5],[7]]=>[7,5,3,1,2,4,6]=>[5,6,4,7,3,1,2]=>000000 [[1,2,5,7],[3],[4],[6]]=>[[1,2,3,6],[4],[5],[7]]=>[7,5,4,1,2,3,6]=>[5,6,7,4,3,1,2]=>000000 [[1,3,4,7],[2],[5],[6]]=>[[1,2,4,5],[3],[6],[7]]=>[7,6,3,1,2,4,5]=>[5,6,4,7,1,3,2]=>000000 [[1,2,4,7],[3],[5],[6]]=>[[1,2,3,5],[4],[6],[7]]=>[7,6,4,1,2,3,5]=>[5,6,7,4,1,3,2]=>000000 [[1,2,3,7],[4],[5],[6]]=>[[1,2,3,4],[5],[6],[7]]=>[7,6,5,1,2,3,4]=>[5,6,7,1,4,3,2]=>000000 [[1,4,5,6],[2],[3],[7]]=>[[1,2,5,6,7],[3],[4]]=>[4,3,1,2,5,6,7]=>[4,5,3,2,6,7,1]=>000000 [[1,3,5,6],[2],[4],[7]]=>[[1,2,4,6,7],[3],[5]]=>[5,3,1,2,4,6,7]=>[4,5,3,6,2,7,1]=>000000 [[1,2,5,6],[3],[4],[7]]=>[[1,2,3,6,7],[4],[5]]=>[5,4,1,2,3,6,7]=>[4,5,6,3,2,7,1]=>000000 [[1,3,4,6],[2],[5],[7]]=>[[1,2,4,5,7],[3],[6]]=>[6,3,1,2,4,5,7]=>[4,5,3,6,7,2,1]=>000000 [[1,2,4,6],[3],[5],[7]]=>[[1,2,3,5,7],[4],[6]]=>[6,4,1,2,3,5,7]=>[4,5,6,3,7,2,1]=>000000 [[1,2,3,6],[4],[5],[7]]=>[[1,2,3,4,7],[5],[6]]=>[6,5,1,2,3,4,7]=>[4,5,6,7,3,2,1]=>000000 [[1,3,4,5],[2],[6],[7]]=>[[1,2,4,5,6],[3],[7]]=>[7,3,1,2,4,5,6]=>[4,5,3,6,7,1,2]=>000000 [[1,2,4,5],[3],[6],[7]]=>[[1,2,3,5,6],[4],[7]]=>[7,4,1,2,3,5,6]=>[4,5,6,3,7,1,2]=>000000 [[1,2,3,5],[4],[6],[7]]=>[[1,2,3,4,6],[5],[7]]=>[7,5,1,2,3,4,6]=>[4,5,6,7,3,1,2]=>000000 [[1,2,3,4],[5],[6],[7]]=>[[1,2,3,4,5],[6],[7]]=>[7,6,1,2,3,4,5]=>[4,5,6,7,1,3,2]=>000000 [[1,4,6],[2,5,7],[3]]=>[[1,2,5,7],[3,6],[4]]=>[4,3,6,1,2,5,7]=>[5,6,3,2,7,4,1]=>000000 [[1,3,6],[2,5,7],[4]]=>[[1,2,4,5,7],[3],[6]]=>[6,3,1,2,4,5,7]=>[4,5,3,6,7,2,1]=>000000 [[1,2,6],[3,5,7],[4]]=>[[1,2,3,5,7],[4],[6]]=>[6,4,1,2,3,5,7]=>[4,5,6,3,7,2,1]=>000000 [[1,3,6],[2,4,7],[5]]=>[[1,2,4,7],[3,5],[6]]=>[6,3,5,1,2,4,7]=>[5,6,3,7,4,2,1]=>000000 [[1,2,6],[3,4,7],[5]]=>[[1,2,3,4,7],[5],[6]]=>[6,5,1,2,3,4,7]=>[4,5,6,7,3,2,1]=>000000 [[1,4,5],[2,6,7],[3]]=>[[1,2,5,6,7],[3],[4]]=>[4,3,1,2,5,6,7]=>[4,5,3,2,6,7,1]=>000000 [[1,3,5],[2,6,7],[4]]=>[[1,2,4,6,7],[3],[5]]=>[5,3,1,2,4,6,7]=>[4,5,3,6,2,7,1]=>000000 [[1,2,5],[3,6,7],[4]]=>[[1,2,3,6,7],[4],[5]]=>[5,4,1,2,3,6,7]=>[4,5,6,3,2,7,1]=>000000 [[1,3,4],[2,6,7],[5]]=>[[1,2,4,5,6,7],[3]]=>[3,1,2,4,5,6,7]=>[3,4,2,5,6,7,1]=>000000 [[1,2,4],[3,6,7],[5]]=>[[1,2,3,5,6,7],[4]]=>[4,1,2,3,5,6,7]=>[3,4,5,2,6,7,1]=>000000 [[1,2,3],[4,6,7],[5]]=>[[1,2,3,4,6,7],[5]]=>[5,1,2,3,4,6,7]=>[3,4,5,6,2,7,1]=>000000 [[1,3,5],[2,4,7],[6]]=>[[1,2,4,6,7],[3,5]]=>[3,5,1,2,4,6,7]=>[4,5,2,6,3,7,1]=>000000 [[1,2,5],[3,4,7],[6]]=>[[1,2,3,4,7],[5,6]]=>[5,6,1,2,3,4,7]=>[4,5,6,7,2,3,1]=>000000 [[1,3,4],[2,5,7],[6]]=>[[1,2,4,5,7],[3,6]]=>[3,6,1,2,4,5,7]=>[4,5,2,6,7,3,1]=>000000 [[1,2,4],[3,5,7],[6]]=>[[1,2,3,5,7],[4,6]]=>[4,6,1,2,3,5,7]=>[4,5,6,2,7,3,1]=>000000 [[1,2,3],[4,5,7],[6]]=>[[1,2,3,4,5,7],[6]]=>[6,1,2,3,4,5,7]=>[3,4,5,6,7,2,1]=>000000 [[1,3,5],[2,4,6],[7]]=>[[1,2,4,6],[3,5,7]]=>[3,5,7,1,2,4,6]=>[5,6,2,7,3,1,4]=>000000 [[1,2,5],[3,4,6],[7]]=>[[1,2,3,4,6],[5,7]]=>[5,7,1,2,3,4,6]=>[4,5,6,7,2,1,3]=>000000 [[1,3,4],[2,5,6],[7]]=>[[1,2,4,5,6],[3,7]]=>[3,7,1,2,4,5,6]=>[4,5,2,6,7,1,3]=>000000 [[1,2,4],[3,5,6],[7]]=>[[1,2,3,5,6],[4,7]]=>[4,7,1,2,3,5,6]=>[4,5,6,2,7,1,3]=>000000 [[1,2,3],[4,5,6],[7]]=>[[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>[3,4,5,6,7,1,2]=>000000 [[1,4,7],[2,5],[3,6]]=>[[1,2,5],[3,6],[4,7]]=>[4,7,3,6,1,2,5]=>[6,7,4,2,1,5,3]=>000000 [[1,3,7],[2,5],[4,6]]=>[[1,2,4,5],[3,6],[7]]=>[7,3,6,1,2,4,5]=>[5,6,3,7,1,4,2]=>000000 [[1,2,7],[3,5],[4,6]]=>[[1,2,3,5],[4,6],[7]]=>[7,4,6,1,2,3,5]=>[5,6,7,3,1,4,2]=>000000 [[1,3,7],[2,4],[5,6]]=>[[1,2,4,6],[3,5],[7]]=>[7,3,5,1,2,4,6]=>[5,6,3,7,4,1,2]=>000000 [[1,2,7],[3,4],[5,6]]=>[[1,2,3,4],[5,6],[7]]=>[7,5,6,1,2,3,4]=>[5,6,7,1,3,4,2]=>000000 [[1,4,6],[2,5],[3,7]]=>[[1,2,5,7],[3,6],[4]]=>[4,3,6,1,2,5,7]=>[5,6,3,2,7,4,1]=>000000 [[1,3,6],[2,5],[4,7]]=>[[1,2,4,5],[3,7],[6]]=>[6,3,7,1,2,4,5]=>[5,6,3,7,1,2,4]=>000000 [[1,2,6],[3,5],[4,7]]=>[[1,2,3,5],[4,7],[6]]=>[6,4,7,1,2,3,5]=>[5,6,7,3,1,2,4]=>000000 [[1,3,6],[2,4],[5,7]]=>[[1,2,4,7],[3,5],[6]]=>[6,3,5,1,2,4,7]=>[5,6,3,7,4,2,1]=>000000 [[1,2,6],[3,4],[5,7]]=>[[1,2,3,4],[5,7],[6]]=>[6,5,7,1,2,3,4]=>[5,6,7,1,3,2,4]=>000000 [[1,4,5],[2,6],[3,7]]=>[[1,2,5,6],[3,7],[4]]=>[4,3,7,1,2,5,6]=>[5,6,3,2,7,1,4]=>000000 [[1,3,5],[2,6],[4,7]]=>[[1,2,4,6],[3,7],[5]]=>[5,3,7,1,2,4,6]=>[5,6,3,7,2,1,4]=>000000 [[1,2,5],[3,6],[4,7]]=>[[1,2,3,6],[4,7],[5]]=>[5,4,7,1,2,3,6]=>[5,6,7,3,2,1,4]=>000000 [[1,3,4],[2,6],[5,7]]=>[[1,2,4,5,6],[3,7]]=>[3,7,1,2,4,5,6]=>[4,5,2,6,7,1,3]=>000000 [[1,2,4],[3,6],[5,7]]=>[[1,2,3,5,6],[4,7]]=>[4,7,1,2,3,5,6]=>[4,5,6,2,7,1,3]=>000000 [[1,2,3],[4,6],[5,7]]=>[[1,2,3,4,6],[5,7]]=>[5,7,1,2,3,4,6]=>[4,5,6,7,2,1,3]=>000000 [[1,3,5],[2,4],[6,7]]=>[[1,2,4,6,7],[3,5]]=>[3,5,1,2,4,6,7]=>[4,5,2,6,3,7,1]=>000000 [[1,2,5],[3,4],[6,7]]=>[[1,2,3,4,7],[5,6]]=>[5,6,1,2,3,4,7]=>[4,5,6,7,2,3,1]=>000000 [[1,3,4],[2,5],[6,7]]=>[[1,2,4,5,7],[3,6]]=>[3,6,1,2,4,5,7]=>[4,5,2,6,7,3,1]=>000000 [[1,2,4],[3,5],[6,7]]=>[[1,2,3,5,7],[4,6]]=>[4,6,1,2,3,5,7]=>[4,5,6,2,7,3,1]=>000000 [[1,2,3],[4,5],[6,7]]=>[[1,2,3,4,5],[6,7]]=>[6,7,1,2,3,4,5]=>[4,5,6,7,1,2,3]=>000000 [[1,5,7],[2,6],[3],[4]]=>[[1,2,6],[3,7],[4],[5]]=>[5,4,3,7,1,2,6]=>[6,7,4,3,2,1,5]=>000000 [[1,4,7],[2,6],[3],[5]]=>[[1,2,5,6],[3],[4],[7]]=>[7,4,3,1,2,5,6]=>[5,6,4,3,7,1,2]=>000000 [[1,3,7],[2,6],[4],[5]]=>[[1,2,4,6],[3],[5],[7]]=>[7,5,3,1,2,4,6]=>[5,6,4,7,3,1,2]=>000000 [[1,2,7],[3,6],[4],[5]]=>[[1,2,3,6],[4],[5],[7]]=>[7,5,4,1,2,3,6]=>[5,6,7,4,3,1,2]=>000000 [[1,4,7],[2,5],[3],[6]]=>[[1,2,5],[3,6],[4],[7]]=>[7,4,3,6,1,2,5]=>[6,7,4,3,1,5,2]=>000000 [[1,3,7],[2,5],[4],[6]]=>[[1,2,4,5],[3],[6],[7]]=>[7,6,3,1,2,4,5]=>[5,6,4,7,1,3,2]=>000000 [[1,2,7],[3,5],[4],[6]]=>[[1,2,3,5],[4],[6],[7]]=>[7,6,4,1,2,3,5]=>[5,6,7,4,1,3,2]=>000000 [[1,3,7],[2,4],[5],[6]]=>[[1,2,4],[3,5],[6],[7]]=>[7,6,3,5,1,2,4]=>[6,7,4,1,5,3,2]=>000000 [[1,2,7],[3,4],[5],[6]]=>[[1,2,3,4],[5],[6],[7]]=>[7,6,5,1,2,3,4]=>[5,6,7,1,4,3,2]=>000000 [[1,5,6],[2,7],[3],[4]]=>[[1,2,6,7],[3],[4],[5]]=>[5,4,3,1,2,6,7]=>[5,6,4,3,2,7,1]=>000000 [[1,4,6],[2,7],[3],[5]]=>[[1,2,5,7],[3],[4],[6]]=>[6,4,3,1,2,5,7]=>[5,6,4,3,7,2,1]=>000000 [[1,3,6],[2,7],[4],[5]]=>[[1,2,4,7],[3],[5],[6]]=>[6,5,3,1,2,4,7]=>[5,6,4,7,3,2,1]=>000000 [[1,2,6],[3,7],[4],[5]]=>[[1,2,3,7],[4],[5],[6]]=>[6,5,4,1,2,3,7]=>[5,6,7,4,3,2,1]=>000000 [[1,4,5],[2,7],[3],[6]]=>[[1,2,5,6,7],[3],[4]]=>[4,3,1,2,5,6,7]=>[4,5,3,2,6,7,1]=>000000 [[1,3,5],[2,7],[4],[6]]=>[[1,2,4,6,7],[3],[5]]=>[5,3,1,2,4,6,7]=>[4,5,3,6,2,7,1]=>000000 [[1,2,5],[3,7],[4],[6]]=>[[1,2,3,6,7],[4],[5]]=>[5,4,1,2,3,6,7]=>[4,5,6,3,2,7,1]=>000000 [[1,3,4],[2,7],[5],[6]]=>[[1,2,4,5,7],[3],[6]]=>[6,3,1,2,4,5,7]=>[4,5,3,6,7,2,1]=>000000 [[1,2,4],[3,7],[5],[6]]=>[[1,2,3,5,7],[4],[6]]=>[6,4,1,2,3,5,7]=>[4,5,6,3,7,2,1]=>000000 [[1,2,3],[4,7],[5],[6]]=>[[1,2,3,4,7],[5],[6]]=>[6,5,1,2,3,4,7]=>[4,5,6,7,3,2,1]=>000000 [[1,4,6],[2,5],[3],[7]]=>[[1,2,5,7],[3,6],[4]]=>[4,3,6,1,2,5,7]=>[5,6,3,2,7,4,1]=>000000 [[1,3,6],[2,5],[4],[7]]=>[[1,2,4,5],[3,7],[6]]=>[6,3,7,1,2,4,5]=>[5,6,3,7,1,2,4]=>000000 [[1,2,6],[3,5],[4],[7]]=>[[1,2,3,5],[4,7],[6]]=>[6,4,7,1,2,3,5]=>[5,6,7,3,1,2,4]=>000000 [[1,3,6],[2,4],[5],[7]]=>[[1,2,4,7],[3,5],[6]]=>[6,3,5,1,2,4,7]=>[5,6,3,7,4,2,1]=>000000 [[1,2,6],[3,4],[5],[7]]=>[[1,2,3,4],[5,7],[6]]=>[6,5,7,1,2,3,4]=>[5,6,7,1,3,2,4]=>000000 [[1,4,5],[2,6],[3],[7]]=>[[1,2,5,6],[3,7],[4]]=>[4,3,7,1,2,5,6]=>[5,6,3,2,7,1,4]=>000000 [[1,3,5],[2,6],[4],[7]]=>[[1,2,4,6],[3,7],[5]]=>[5,3,7,1,2,4,6]=>[5,6,3,7,2,1,4]=>000000 [[1,2,5],[3,6],[4],[7]]=>[[1,2,3,6],[4,7],[5]]=>[5,4,7,1,2,3,6]=>[5,6,7,3,2,1,4]=>000000 [[1,3,4],[2,6],[5],[7]]=>[[1,2,4,5,6],[3],[7]]=>[7,3,1,2,4,5,6]=>[4,5,3,6,7,1,2]=>000000 [[1,2,4],[3,6],[5],[7]]=>[[1,2,3,5,6],[4],[7]]=>[7,4,1,2,3,5,6]=>[4,5,6,3,7,1,2]=>000000 [[1,2,3],[4,6],[5],[7]]=>[[1,2,3,4,6],[5],[7]]=>[7,5,1,2,3,4,6]=>[4,5,6,7,3,1,2]=>000000 [[1,3,5],[2,4],[6],[7]]=>[[1,2,4,6],[3,5],[7]]=>[7,3,5,1,2,4,6]=>[5,6,3,7,4,1,2]=>000000 [[1,2,5],[3,4],[6],[7]]=>[[1,2,3,4],[5,6],[7]]=>[7,5,6,1,2,3,4]=>[5,6,7,1,3,4,2]=>000000 [[1,3,4],[2,5],[6],[7]]=>[[1,2,4,5],[3,6],[7]]=>[7,3,6,1,2,4,5]=>[5,6,3,7,1,4,2]=>000000 [[1,2,4],[3,5],[6],[7]]=>[[1,2,3,5],[4,6],[7]]=>[7,4,6,1,2,3,5]=>[5,6,7,3,1,4,2]=>000000 [[1,2,3],[4,5],[6],[7]]=>[[1,2,3,4,5],[6],[7]]=>[7,6,1,2,3,4,5]=>[4,5,6,7,1,3,2]=>000000 [[1,6,7],[2],[3],[4],[5]]=>[[1,2,7],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7]=>[6,7,5,4,3,2,1]=>000000 [[1,5,7],[2],[3],[4],[6]]=>[[1,2,6],[3],[4],[5],[7]]=>[7,5,4,3,1,2,6]=>[6,7,5,4,3,1,2]=>000000 [[1,4,7],[2],[3],[5],[6]]=>[[1,2,5],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5]=>[6,7,5,4,1,3,2]=>000000 [[1,3,7],[2],[4],[5],[6]]=>[[1,2,4],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4]=>[6,7,5,1,4,3,2]=>000000 [[1,2,7],[3],[4],[5],[6]]=>[[1,2,3],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3]=>[6,7,1,5,4,3,2]=>000000 [[1,5,6],[2],[3],[4],[7]]=>[[1,2,6,7],[3],[4],[5]]=>[5,4,3,1,2,6,7]=>[5,6,4,3,2,7,1]=>000000 [[1,4,6],[2],[3],[5],[7]]=>[[1,2,5,7],[3],[4],[6]]=>[6,4,3,1,2,5,7]=>[5,6,4,3,7,2,1]=>000000 [[1,3,6],[2],[4],[5],[7]]=>[[1,2,4,7],[3],[5],[6]]=>[6,5,3,1,2,4,7]=>[5,6,4,7,3,2,1]=>000000 [[1,2,6],[3],[4],[5],[7]]=>[[1,2,3,7],[4],[5],[6]]=>[6,5,4,1,2,3,7]=>[5,6,7,4,3,2,1]=>000000 [[1,4,5],[2],[3],[6],[7]]=>[[1,2,5,6],[3],[4],[7]]=>[7,4,3,1,2,5,6]=>[5,6,4,3,7,1,2]=>000000 [[1,3,5],[2],[4],[6],[7]]=>[[1,2,4,6],[3],[5],[7]]=>[7,5,3,1,2,4,6]=>[5,6,4,7,3,1,2]=>000000 [[1,2,5],[3],[4],[6],[7]]=>[[1,2,3,6],[4],[5],[7]]=>[7,5,4,1,2,3,6]=>[5,6,7,4,3,1,2]=>000000 [[1,3,4],[2],[5],[6],[7]]=>[[1,2,4,5],[3],[6],[7]]=>[7,6,3,1,2,4,5]=>[5,6,4,7,1,3,2]=>000000 [[1,2,4],[3],[5],[6],[7]]=>[[1,2,3,5],[4],[6],[7]]=>[7,6,4,1,2,3,5]=>[5,6,7,4,1,3,2]=>000000 [[1,2,3],[4],[5],[6],[7]]=>[[1,2,3,4],[5],[6],[7]]=>[7,6,5,1,2,3,4]=>[5,6,7,1,4,3,2]=>000000 [[1,5],[2,6],[3,7],[4]]=>[[1,2,6],[3,7],[4],[5]]=>[5,4,3,7,1,2,6]=>[6,7,4,3,2,1,5]=>000000 [[1,4],[2,6],[3,7],[5]]=>[[1,2,5,6],[3,7],[4]]=>[4,3,7,1,2,5,6]=>[5,6,3,2,7,1,4]=>000000 [[1,3],[2,6],[4,7],[5]]=>[[1,2,4,6],[3,7],[5]]=>[5,3,7,1,2,4,6]=>[5,6,3,7,2,1,4]=>000000 [[1,2],[3,6],[4,7],[5]]=>[[1,2,3,6],[4,7],[5]]=>[5,4,7,1,2,3,6]=>[5,6,7,3,2,1,4]=>000000 [[1,4],[2,5],[3,7],[6]]=>[[1,2,5,7],[3,6],[4]]=>[4,3,6,1,2,5,7]=>[5,6,3,2,7,4,1]=>000000 [[1,3],[2,5],[4,7],[6]]=>[[1,2,4,5],[3,7],[6]]=>[6,3,7,1,2,4,5]=>[5,6,3,7,1,2,4]=>000000 [[1,2],[3,5],[4,7],[6]]=>[[1,2,3,5],[4,7],[6]]=>[6,4,7,1,2,3,5]=>[5,6,7,3,1,2,4]=>000000 [[1,3],[2,4],[5,7],[6]]=>[[1,2,4,7],[3,5],[6]]=>[6,3,5,1,2,4,7]=>[5,6,3,7,4,2,1]=>000000 [[1,2],[3,4],[5,7],[6]]=>[[1,2,3,4],[5,7],[6]]=>[6,5,7,1,2,3,4]=>[5,6,7,1,3,2,4]=>000000 [[1,4],[2,5],[3,6],[7]]=>[[1,2,5],[3,6],[4,7]]=>[4,7,3,6,1,2,5]=>[6,7,4,2,1,5,3]=>000000 [[1,3],[2,5],[4,6],[7]]=>[[1,2,4,5],[3,6],[7]]=>[7,3,6,1,2,4,5]=>[5,6,3,7,1,4,2]=>000000 [[1,2],[3,5],[4,6],[7]]=>[[1,2,3,5],[4,6],[7]]=>[7,4,6,1,2,3,5]=>[5,6,7,3,1,4,2]=>000000 [[1,3],[2,4],[5,6],[7]]=>[[1,2,4,6],[3,5],[7]]=>[7,3,5,1,2,4,6]=>[5,6,3,7,4,1,2]=>000000 [[1,2],[3,4],[5,6],[7]]=>[[1,2,3,4],[5,6],[7]]=>[7,5,6,1,2,3,4]=>[5,6,7,1,3,4,2]=>000000 [[1,6],[2,7],[3],[4],[5]]=>[[1,2,7],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7]=>[6,7,5,4,3,2,1]=>000000 [[1,5],[2,7],[3],[4],[6]]=>[[1,2,6,7],[3],[4],[5]]=>[5,4,3,1,2,6,7]=>[5,6,4,3,2,7,1]=>000000 [[1,4],[2,7],[3],[5],[6]]=>[[1,2,5,7],[3],[4],[6]]=>[6,4,3,1,2,5,7]=>[5,6,4,3,7,2,1]=>000000 [[1,3],[2,7],[4],[5],[6]]=>[[1,2,4,7],[3],[5],[6]]=>[6,5,3,1,2,4,7]=>[5,6,4,7,3,2,1]=>000000 [[1,2],[3,7],[4],[5],[6]]=>[[1,2,3,7],[4],[5],[6]]=>[6,5,4,1,2,3,7]=>[5,6,7,4,3,2,1]=>000000 [[1,5],[2,6],[3],[4],[7]]=>[[1,2,6],[3,7],[4],[5]]=>[5,4,3,7,1,2,6]=>[6,7,4,3,2,1,5]=>000000 [[1,4],[2,6],[3],[5],[7]]=>[[1,2,5,6],[3],[4],[7]]=>[7,4,3,1,2,5,6]=>[5,6,4,3,7,1,2]=>000000 [[1,3],[2,6],[4],[5],[7]]=>[[1,2,4,6],[3],[5],[7]]=>[7,5,3,1,2,4,6]=>[5,6,4,7,3,1,2]=>000000 [[1,2],[3,6],[4],[5],[7]]=>[[1,2,3,6],[4],[5],[7]]=>[7,5,4,1,2,3,6]=>[5,6,7,4,3,1,2]=>000000 [[1,4],[2,5],[3],[6],[7]]=>[[1,2,5],[3,6],[4],[7]]=>[7,4,3,6,1,2,5]=>[6,7,4,3,1,5,2]=>000000 [[1,3],[2,5],[4],[6],[7]]=>[[1,2,4,5],[3],[6],[7]]=>[7,6,3,1,2,4,5]=>[5,6,4,7,1,3,2]=>000000 [[1,2],[3,5],[4],[6],[7]]=>[[1,2,3,5],[4],[6],[7]]=>[7,6,4,1,2,3,5]=>[5,6,7,4,1,3,2]=>000000 [[1,3],[2,4],[5],[6],[7]]=>[[1,2,4],[3,5],[6],[7]]=>[7,6,3,5,1,2,4]=>[6,7,4,1,5,3,2]=>000000 [[1,2],[3,4],[5],[6],[7]]=>[[1,2,3,4],[5],[6],[7]]=>[7,6,5,1,2,3,4]=>[5,6,7,1,4,3,2]=>000000 [[1,7],[2],[3],[4],[5],[6]]=>[[1,2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2]=>[7,1,6,5,4,3,2]=>000000 [[1,6],[2],[3],[4],[5],[7]]=>[[1,2,7],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7]=>[6,7,5,4,3,2,1]=>000000 [[1,5],[2],[3],[4],[6],[7]]=>[[1,2,6],[3],[4],[5],[7]]=>[7,5,4,3,1,2,6]=>[6,7,5,4,3,1,2]=>000000 [[1,4],[2],[3],[5],[6],[7]]=>[[1,2,5],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5]=>[6,7,5,4,1,3,2]=>000000 [[1,3],[2],[4],[5],[6],[7]]=>[[1,2,4],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4]=>[6,7,5,1,4,3,2]=>000000 [[1,2],[3],[4],[5],[6],[7]]=>[[1,2,3],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3]=>[6,7,1,5,4,3,2]=>000000 [[1],[2],[3],[4],[5],[6],[7]]=>[[1,2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2]=>[7,1,6,5,4,3,2]=>000000 [[1,2,3,4,5,6,7,8]]=>[[1,2,3,4,5,6,7,8]]=>[1,2,3,4,5,6,7,8]=>[2,3,4,5,6,7,8,1]=>0000000 [[1,2,3,5,6,7,8],[4]]=>[[1,2,3,4,6,7,8],[5]]=>[5,1,2,3,4,6,7,8]=>[3,4,5,6,2,7,8,1]=>0000000 [[1,2,3,4,5,6,8],[7]]=>[[1,2,3,4,5,6,7],[8]]=>[8,1,2,3,4,5,6,7]=>[3,4,5,6,7,8,1,2]=>0000000 [[1,2,3,4,5,6,7],[8]]=>[[1,2,3,4,5,6,7,8]]=>[1,2,3,4,5,6,7,8]=>[2,3,4,5,6,7,8,1]=>0000000 [[1,2,3,6,7,8],[4,5]]=>[[1,2,3,4,5,8],[6,7]]=>[6,7,1,2,3,4,5,8]=>[4,5,6,7,8,2,3,1]=>0000000 [[1,2,4,5,7,8],[3,6]]=>[[1,2,3,5,6,8],[4,7]]=>[4,7,1,2,3,5,6,8]=>[4,5,6,2,7,8,3,1]=>0000000 [[1,2,3,5,7,8],[4,6]]=>[[1,2,3,4,6,8],[5,7]]=>[5,7,1,2,3,4,6,8]=>[4,5,6,7,2,8,3,1]=>0000000 [[1,2,3,4,6,8],[5,7]]=>[[1,2,3,4,5,7],[6,8]]=>[6,8,1,2,3,4,5,7]=>[4,5,6,7,8,2,1,3]=>0000000 [[1,2,3,4,5,8],[6,7]]=>[[1,2,3,4,5,6,7],[8]]=>[8,1,2,3,4,5,6,7]=>[3,4,5,6,7,8,1,2]=>0000000 [[1,2,3,5,6,7],[4,8]]=>[[1,2,3,4,6,7,8],[5]]=>[5,1,2,3,4,6,7,8]=>[3,4,5,6,2,7,8,1]=>0000000 [[1,2,3,4,5,6],[7,8]]=>[[1,2,3,4,5,6,7,8]]=>[1,2,3,4,5,6,7,8]=>[2,3,4,5,6,7,8,1]=>0000000 [[1,2,3,6,7,8],[4],[5]]=>[[1,2,3,4,7,8],[5],[6]]=>[6,5,1,2,3,4,7,8]=>[4,5,6,7,3,2,8,1]=>0000000 [[1,2,3,5,7,8],[4],[6]]=>[[1,2,3,4,6,8],[5],[7]]=>[7,5,1,2,3,4,6,8]=>[4,5,6,7,3,8,2,1]=>0000000 [[1,3,4,5,6,8],[2],[7]]=>[[1,2,4,5,6,7],[3],[8]]=>[8,3,1,2,4,5,6,7]=>[4,5,3,6,7,8,1,2]=>0000000 [[1,2,4,5,6,8],[3],[7]]=>[[1,2,3,5,6,7],[4],[8]]=>[8,4,1,2,3,5,6,7]=>[4,5,6,3,7,8,1,2]=>0000000 [[1,2,3,5,6,8],[4],[7]]=>[[1,2,3,4,6,7],[5],[8]]=>[8,5,1,2,3,4,6,7]=>[4,5,6,7,3,8,1,2]=>0000000 [[1,2,3,4,6,8],[5],[7]]=>[[1,2,3,4,5,7],[6],[8]]=>[8,6,1,2,3,4,5,7]=>[4,5,6,7,8,3,1,2]=>0000000 [[1,2,3,4,5,8],[6],[7]]=>[[1,2,3,4,5,6],[7],[8]]=>[8,7,1,2,3,4,5,6]=>[4,5,6,7,8,1,3,2]=>0000000 [[1,2,3,5,6,7],[4],[8]]=>[[1,2,3,4,6,7,8],[5]]=>[5,1,2,3,4,6,7,8]=>[3,4,5,6,2,7,8,1]=>0000000 [[1,2,3,4,5,6],[7],[8]]=>[[1,2,3,4,5,6,7],[8]]=>[8,1,2,3,4,5,6,7]=>[3,4,5,6,7,8,1,2]=>0000000 [[1,3,5,7,8],[2,4,6]]=>[[1,2,4,6,8],[3,5,7]]=>[3,5,7,1,2,4,6,8]=>[5,6,2,7,3,8,4,1]=>0000000 [[1,3,4,7,8],[2,5,6]]=>[[1,2,4,5,6],[3,7,8]]=>[3,7,8,1,2,4,5,6]=>[5,6,2,7,8,1,3,4]=>0000000 [[1,3,5,6,8],[2,4,7]]=>[[1,2,4,6,7],[3,5,8]]=>[3,5,8,1,2,4,6,7]=>[5,6,2,7,3,8,1,4]=>0000000 [[1,2,5,6,8],[3,4,7]]=>[[1,2,3,4,7],[5,6,8]]=>[5,6,8,1,2,3,4,7]=>[5,6,7,8,2,3,1,4]=>0000000 [[1,3,4,6,8],[2,5,7]]=>[[1,2,4,5,7],[3,6,8]]=>[3,6,8,1,2,4,5,7]=>[5,6,2,7,8,3,1,4]=>0000000 [[1,2,4,6,8],[3,5,7]]=>[[1,2,3,5,7],[4,6,8]]=>[4,6,8,1,2,3,5,7]=>[5,6,7,2,8,3,1,4]=>0000000 [[1,2,3,6,8],[4,5,7]]=>[[1,2,3,4,5,7],[6,8]]=>[6,8,1,2,3,4,5,7]=>[4,5,6,7,8,2,1,3]=>0000000 [[1,2,3,4,8],[5,6,7]]=>[[1,2,3,4,5,6,7],[8]]=>[8,1,2,3,4,5,6,7]=>[3,4,5,6,7,8,1,2]=>0000000 [[1,2,3,6,7],[4,5,8]]=>[[1,2,3,4,5,8],[6,7]]=>[6,7,1,2,3,4,5,8]=>[4,5,6,7,8,2,3,1]=>0000000 [[1,2,4,5,7],[3,6,8]]=>[[1,2,3,5,6,8],[4,7]]=>[4,7,1,2,3,5,6,8]=>[4,5,6,2,7,8,3,1]=>0000000 [[1,2,3,5,7],[4,6,8]]=>[[1,2,3,4,6,8],[5,7]]=>[5,7,1,2,3,4,6,8]=>[4,5,6,7,2,8,3,1]=>0000000 [[1,2,3,5,6],[4,7,8]]=>[[1,2,3,4,6,7,8],[5]]=>[5,1,2,3,4,6,7,8]=>[3,4,5,6,2,7,8,1]=>0000000 [[1,2,3,4,5],[6,7,8]]=>[[1,2,3,4,5,6,7,8]]=>[1,2,3,4,5,6,7,8]=>[2,3,4,5,6,7,8,1]=>0000000 [[1,3,6,7,8],[2,5],[4]]=>[[1,2,4,5,8],[3,7],[6]]=>[6,3,7,1,2,4,5,8]=>[5,6,3,7,8,2,4,1]=>0000000 [[1,2,6,7,8],[3,5],[4]]=>[[1,2,3,5,8],[4,7],[6]]=>[6,4,7,1,2,3,5,8]=>[5,6,7,3,8,2,4,1]=>0000000 [[1,2,5,7,8],[3,6],[4]]=>[[1,2,3,6,8],[4,7],[5]]=>[5,4,7,1,2,3,6,8]=>[5,6,7,3,2,8,4,1]=>0000000 [[1,2,3,7,8],[4,6],[5]]=>[[1,2,3,4,6],[5,8],[7]]=>[7,5,8,1,2,3,4,6]=>[5,6,7,8,3,1,2,4]=>0000000 [[1,3,5,7,8],[2,4],[6]]=>[[1,2,4,6,8],[3,5],[7]]=>[7,3,5,1,2,4,6,8]=>[5,6,3,7,4,8,2,1]=>0000000 [[1,2,5,7,8],[3,4],[6]]=>[[1,2,3,4,8],[5,6],[7]]=>[7,5,6,1,2,3,4,8]=>[5,6,7,8,3,4,2,1]=>0000000 [[1,2,4,7,8],[3,5],[6]]=>[[1,2,3,5,8],[4,6],[7]]=>[7,4,6,1,2,3,5,8]=>[5,6,7,3,8,4,2,1]=>0000000 [[1,2,3,7,8],[4,5],[6]]=>[[1,2,3,4,5],[6,8],[7]]=>[7,6,8,1,2,3,4,5]=>[5,6,7,8,1,3,2,4]=>0000000 [[1,3,5,6,8],[2,7],[4]]=>[[1,2,4,6,7],[3,8],[5]]=>[5,3,8,1,2,4,6,7]=>[5,6,3,7,2,8,1,4]=>0000000 [[1,2,5,6,8],[3,7],[4]]=>[[1,2,3,6,7],[4,8],[5]]=>[5,4,8,1,2,3,6,7]=>[5,6,7,3,2,8,1,4]=>0000000 [[1,2,4,6,8],[3,7],[5]]=>[[1,2,3,5,7],[4,8],[6]]=>[6,4,8,1,2,3,5,7]=>[5,6,7,3,8,2,1,4]=>0000000 [[1,2,3,6,8],[4,7],[5]]=>[[1,2,3,4,7],[5,8],[6]]=>[6,5,8,1,2,3,4,7]=>[5,6,7,8,3,2,1,4]=>0000000 [[1,3,4,5,8],[2,7],[6]]=>[[1,2,4,5,6,7],[3],[8]]=>[8,3,1,2,4,5,6,7]=>[4,5,3,6,7,8,1,2]=>0000000 [[1,2,4,5,8],[3,7],[6]]=>[[1,2,3,5,6,7],[4],[8]]=>[8,4,1,2,3,5,6,7]=>[4,5,6,3,7,8,1,2]=>0000000 [[1,2,3,5,8],[4,7],[6]]=>[[1,2,3,4,6,7],[5],[8]]=>[8,5,1,2,3,4,6,7]=>[4,5,6,7,3,8,1,2]=>0000000 [[1,2,3,4,8],[5,7],[6]]=>[[1,2,3,4,5,7],[6],[8]]=>[8,6,1,2,3,4,5,7]=>[4,5,6,7,8,3,1,2]=>0000000 [[1,3,5,6,8],[2,4],[7]]=>[[1,2,4,6,7],[3,5],[8]]=>[8,3,5,1,2,4,6,7]=>[5,6,3,7,4,8,1,2]=>0000000 [[1,2,4,6,8],[3,5],[7]]=>[[1,2,3,5,7],[4,6],[8]]=>[8,4,6,1,2,3,5,7]=>[5,6,7,3,8,4,1,2]=>0000000 [[1,2,3,6,8],[4,5],[7]]=>[[1,2,3,4,5],[6,7],[8]]=>[8,6,7,1,2,3,4,5]=>[5,6,7,8,1,3,4,2]=>0000000 [[1,2,3,5,8],[4,6],[7]]=>[[1,2,3,4,6],[5,7],[8]]=>[8,5,7,1,2,3,4,6]=>[5,6,7,8,3,1,4,2]=>0000000 [[1,2,3,4,8],[5,6],[7]]=>[[1,2,3,4,5,6],[7],[8]]=>[8,7,1,2,3,4,5,6]=>[4,5,6,7,8,1,3,2]=>0000000 [[1,2,3,6,7],[4,8],[5]]=>[[1,2,3,4,7,8],[5],[6]]=>[6,5,1,2,3,4,7,8]=>[4,5,6,7,3,2,8,1]=>0000000 [[1,2,3,5,7],[4,8],[6]]=>[[1,2,3,4,6,8],[5],[7]]=>[7,5,1,2,3,4,6,8]=>[4,5,6,7,3,8,2,1]=>0000000 [[1,2,3,5,6],[4,8],[7]]=>[[1,2,3,4,6,7,8],[5]]=>[5,1,2,3,4,6,7,8]=>[3,4,5,6,2,7,8,1]=>0000000 [[1,2,3,6,7],[4,5],[8]]=>[[1,2,3,4,5,8],[6,7]]=>[6,7,1,2,3,4,5,8]=>[4,5,6,7,8,2,3,1]=>0000000 [[1,2,4,5,7],[3,6],[8]]=>[[1,2,3,5,6,8],[4,7]]=>[4,7,1,2,3,5,6,8]=>[4,5,6,2,7,8,3,1]=>0000000 [[1,2,3,5,7],[4,6],[8]]=>[[1,2,3,4,6,8],[5,7]]=>[5,7,1,2,3,4,6,8]=>[4,5,6,7,2,8,3,1]=>0000000 [[1,2,3,4,6],[5,7],[8]]=>[[1,2,3,4,5,7],[6,8]]=>[6,8,1,2,3,4,5,7]=>[4,5,6,7,8,2,1,3]=>0000000 [[1,2,3,4,5],[6,7],[8]]=>[[1,2,3,4,5,6,7],[8]]=>[8,1,2,3,4,5,6,7]=>[3,4,5,6,7,8,1,2]=>0000000 [[1,3,4,7,8],[2],[5],[6]]=>[[1,2,4,5,8],[3],[6],[7]]=>[7,6,3,1,2,4,5,8]=>[5,6,4,7,8,3,2,1]=>0000000 [[1,2,4,7,8],[3],[5],[6]]=>[[1,2,3,5,8],[4],[6],[7]]=>[7,6,4,1,2,3,5,8]=>[5,6,7,4,8,3,2,1]=>0000000 [[1,2,3,7,8],[4],[5],[6]]=>[[1,2,3,4,8],[5],[6],[7]]=>[7,6,5,1,2,3,4,8]=>[5,6,7,8,4,3,2,1]=>0000000 [[1,3,5,6,8],[2],[4],[7]]=>[[1,2,4,6,7],[3],[5],[8]]=>[8,5,3,1,2,4,6,7]=>[5,6,4,7,3,8,1,2]=>0000000 [[1,2,3,6,8],[4],[5],[7]]=>[[1,2,3,4,7],[5],[6],[8]]=>[8,6,5,1,2,3,4,7]=>[5,6,7,8,4,3,1,2]=>0000000 [[1,2,3,5,8],[4],[6],[7]]=>[[1,2,3,4,6],[5],[7],[8]]=>[8,7,5,1,2,3,4,6]=>[5,6,7,8,4,1,3,2]=>0000000 [[1,2,3,4,8],[5],[6],[7]]=>[[1,2,3,4,5],[6],[7],[8]]=>[8,7,6,1,2,3,4,5]=>[5,6,7,8,1,4,3,2]=>0000000 [[1,2,3,6,7],[4],[5],[8]]=>[[1,2,3,4,7,8],[5],[6]]=>[6,5,1,2,3,4,7,8]=>[4,5,6,7,3,2,8,1]=>0000000 [[1,2,3,5,7],[4],[6],[8]]=>[[1,2,3,4,6,8],[5],[7]]=>[7,5,1,2,3,4,6,8]=>[4,5,6,7,3,8,2,1]=>0000000 [[1,3,4,5,6],[2],[7],[8]]=>[[1,2,4,5,6,7],[3],[8]]=>[8,3,1,2,4,5,6,7]=>[4,5,3,6,7,8,1,2]=>0000000 [[1,2,4,5,6],[3],[7],[8]]=>[[1,2,3,5,6,7],[4],[8]]=>[8,4,1,2,3,5,6,7]=>[4,5,6,3,7,8,1,2]=>0000000 [[1,2,3,5,6],[4],[7],[8]]=>[[1,2,3,4,6,7],[5],[8]]=>[8,5,1,2,3,4,6,7]=>[4,5,6,7,3,8,1,2]=>0000000 [[1,2,3,4,6],[5],[7],[8]]=>[[1,2,3,4,5,7],[6],[8]]=>[8,6,1,2,3,4,5,7]=>[4,5,6,7,8,3,1,2]=>0000000 [[1,2,3,4,5],[6],[7],[8]]=>[[1,2,3,4,5,6],[7],[8]]=>[8,7,1,2,3,4,5,6]=>[4,5,6,7,8,1,3,2]=>0000000 [[1,3,5,7],[2,4,6,8]]=>[[1,2,4,6,8],[3,5,7]]=>[3,5,7,1,2,4,6,8]=>[5,6,2,7,3,8,4,1]=>0000000 [[1,2,5,7],[3,4,6,8]]=>[[1,2,3,4,6,8],[5,7]]=>[5,7,1,2,3,4,6,8]=>[4,5,6,7,2,8,3,1]=>0000000 [[1,2,4,7],[3,5,6,8]]=>[[1,2,3,5,6,8],[4,7]]=>[4,7,1,2,3,5,6,8]=>[4,5,6,2,7,8,3,1]=>0000000 [[1,2,3,5],[4,6,7,8]]=>[[1,2,3,4,6,7,8],[5]]=>[5,1,2,3,4,6,7,8]=>[3,4,5,6,2,7,8,1]=>0000000 [[1,2,3,4],[5,6,7,8]]=>[[1,2,3,4,5,6,7,8]]=>[1,2,3,4,5,6,7,8]=>[2,3,4,5,6,7,8,1]=>0000000 [[1,4,6,8],[2,5,7],[3]]=>[[1,2,5,7],[3,6,8],[4]]=>[4,3,6,8,1,2,5,7]=>[6,7,3,2,8,4,1,5]=>0000000 [[1,2,6,8],[3,5,7],[4]]=>[[1,2,3,5,7],[4,8],[6]]=>[6,4,8,1,2,3,5,7]=>[5,6,7,3,8,2,1,4]=>0000000 [[1,3,6,8],[2,4,7],[5]]=>[[1,2,4,7],[3,5,8],[6]]=>[6,3,5,8,1,2,4,7]=>[6,7,3,8,4,2,1,5]=>0000000 [[1,2,6,8],[3,4,7],[5]]=>[[1,2,3,4,7],[5,8],[6]]=>[6,5,8,1,2,3,4,7]=>[5,6,7,8,3,2,1,4]=>0000000 [[1,3,5,8],[2,6,7],[4]]=>[[1,2,4,6,7],[3,8],[5]]=>[5,3,8,1,2,4,6,7]=>[5,6,3,7,2,8,1,4]=>0000000 [[1,2,5,8],[3,6,7],[4]]=>[[1,2,3,6,7],[4,8],[5]]=>[5,4,8,1,2,3,6,7]=>[5,6,7,3,2,8,1,4]=>0000000 [[1,3,4,8],[2,6,7],[5]]=>[[1,2,4,5,6,7],[3],[8]]=>[8,3,1,2,4,5,6,7]=>[4,5,3,6,7,8,1,2]=>0000000 [[1,2,4,8],[3,6,7],[5]]=>[[1,2,3,5,6,7],[4],[8]]=>[8,4,1,2,3,5,6,7]=>[4,5,6,3,7,8,1,2]=>0000000 [[1,2,3,8],[4,6,7],[5]]=>[[1,2,3,4,6,7],[5],[8]]=>[8,5,1,2,3,4,6,7]=>[4,5,6,7,3,8,1,2]=>0000000 [[1,3,5,8],[2,4,7],[6]]=>[[1,2,4,6,7],[3,5],[8]]=>[8,3,5,1,2,4,6,7]=>[5,6,3,7,4,8,1,2]=>0000000 [[1,2,4,8],[3,5,7],[6]]=>[[1,2,3,5,7],[4,6],[8]]=>[8,4,6,1,2,3,5,7]=>[5,6,7,3,8,4,1,2]=>0000000 [[1,2,3,8],[4,5,7],[6]]=>[[1,2,3,4,5,7],[6],[8]]=>[8,6,1,2,3,4,5,7]=>[4,5,6,7,8,3,1,2]=>0000000 [[1,3,5,8],[2,4,6],[7]]=>[[1,2,4,6],[3,5,7],[8]]=>[8,3,5,7,1,2,4,6]=>[6,7,3,8,4,1,5,2]=>0000000 [[1,2,5,8],[3,4,6],[7]]=>[[1,2,3,4,6],[5,7],[8]]=>[8,5,7,1,2,3,4,6]=>[5,6,7,8,3,1,4,2]=>0000000 [[1,2,3,8],[4,5,6],[7]]=>[[1,2,3,4,5,6],[7],[8]]=>[8,7,1,2,3,4,5,6]=>[4,5,6,7,8,1,3,2]=>0000000 [[1,3,6,7],[2,5,8],[4]]=>[[1,2,4,5,8],[3,7],[6]]=>[6,3,7,1,2,4,5,8]=>[5,6,3,7,8,2,4,1]=>0000000 [[1,2,6,7],[3,5,8],[4]]=>[[1,2,3,5,8],[4,7],[6]]=>[6,4,7,1,2,3,5,8]=>[5,6,7,3,8,2,4,1]=>0000000 [[1,2,5,7],[3,6,8],[4]]=>[[1,2,3,6,8],[4,7],[5]]=>[5,4,7,1,2,3,6,8]=>[5,6,7,3,2,8,4,1]=>0000000 [[1,2,3,7],[4,6,8],[5]]=>[[1,2,3,4,6,8],[5],[7]]=>[7,5,1,2,3,4,6,8]=>[4,5,6,7,3,8,2,1]=>0000000 [[1,3,5,7],[2,4,8],[6]]=>[[1,2,4,6,8],[3,5],[7]]=>[7,3,5,1,2,4,6,8]=>[5,6,3,7,4,8,2,1]=>0000000 [[1,2,5,7],[3,4,8],[6]]=>[[1,2,3,4,8],[5,6],[7]]=>[7,5,6,1,2,3,4,8]=>[5,6,7,8,3,4,2,1]=>0000000 [[1,2,4,7],[3,5,8],[6]]=>[[1,2,3,5,8],[4,6],[7]]=>[7,4,6,1,2,3,5,8]=>[5,6,7,3,8,4,2,1]=>0000000 [[1,2,3,6],[4,7,8],[5]]=>[[1,2,3,4,7,8],[5],[6]]=>[6,5,1,2,3,4,7,8]=>[4,5,6,7,3,2,8,1]=>0000000 [[1,2,3,5],[4,7,8],[6]]=>[[1,2,3,4,6,7,8],[5]]=>[5,1,2,3,4,6,7,8]=>[3,4,5,6,2,7,8,1]=>0000000 [[1,2,3,6],[4,5,8],[7]]=>[[1,2,3,4,5,8],[6,7]]=>[6,7,1,2,3,4,5,8]=>[4,5,6,7,8,2,3,1]=>0000000 [[1,2,4,5],[3,6,8],[7]]=>[[1,2,3,5,6,8],[4,7]]=>[4,7,1,2,3,5,6,8]=>[4,5,6,2,7,8,3,1]=>0000000 [[1,2,3,5],[4,6,8],[7]]=>[[1,2,3,4,6,8],[5,7]]=>[5,7,1,2,3,4,6,8]=>[4,5,6,7,2,8,3,1]=>0000000 [[1,3,5,7],[2,4,6],[8]]=>[[1,2,4,6,8],[3,5,7]]=>[3,5,7,1,2,4,6,8]=>[5,6,2,7,3,8,4,1]=>0000000 [[1,3,4,7],[2,5,6],[8]]=>[[1,2,4,5,6],[3,7,8]]=>[3,7,8,1,2,4,5,6]=>[5,6,2,7,8,1,3,4]=>0000000 [[1,3,5,6],[2,4,7],[8]]=>[[1,2,4,6,7],[3,5,8]]=>[3,5,8,1,2,4,6,7]=>[5,6,2,7,3,8,1,4]=>0000000 [[1,2,5,6],[3,4,7],[8]]=>[[1,2,3,4,7],[5,6,8]]=>[5,6,8,1,2,3,4,7]=>[5,6,7,8,2,3,1,4]=>0000000 [[1,3,4,6],[2,5,7],[8]]=>[[1,2,4,5,7],[3,6,8]]=>[3,6,8,1,2,4,5,7]=>[5,6,2,7,8,3,1,4]=>0000000 [[1,2,4,6],[3,5,7],[8]]=>[[1,2,3,5,7],[4,6,8]]=>[4,6,8,1,2,3,5,7]=>[5,6,7,2,8,3,1,4]=>0000000 [[1,2,3,6],[4,5,7],[8]]=>[[1,2,3,4,5,7],[6,8]]=>[6,8,1,2,3,4,5,7]=>[4,5,6,7,8,2,1,3]=>0000000 [[1,2,3,4],[5,6,7],[8]]=>[[1,2,3,4,5,6,7],[8]]=>[8,1,2,3,4,5,6,7]=>[3,4,5,6,7,8,1,2]=>0000000 [[1,3,7,8],[2,5],[4,6]]=>[[1,2,4,5],[3,6],[7,8]]=>[7,8,3,6,1,2,4,5]=>[6,7,4,8,1,5,2,3]=>0000000 [[1,2,7,8],[3,4],[5,6]]=>[[1,2,3,4],[5,6],[7,8]]=>[7,8,5,6,1,2,3,4]=>[6,7,8,1,4,5,2,3]=>0000000 [[1,3,6,8],[2,5],[4,7]]=>[[1,2,4,5],[3,7],[6,8]]=>[6,8,3,7,1,2,4,5]=>[6,7,4,8,1,2,5,3]=>0000000 [[1,2,6,8],[3,4],[5,7]]=>[[1,2,3,4],[5,7],[6,8]]=>[6,8,5,7,1,2,3,4]=>[6,7,8,1,4,2,5,3]=>0000000 [[1,4,5,8],[2,6],[3,7]]=>[[1,2,5,6],[3,7],[4,8]]=>[4,8,3,7,1,2,5,6]=>[6,7,4,2,8,1,5,3]=>0000000 [[1,3,5,8],[2,6],[4,7]]=>[[1,2,4,6],[3,7],[5,8]]=>[5,8,3,7,1,2,4,6]=>[6,7,4,8,2,1,5,3]=>0000000 [[1,2,5,8],[3,6],[4,7]]=>[[1,2,3,6],[4,7],[5,8]]=>[5,8,4,7,1,2,3,6]=>[6,7,8,4,2,1,5,3]=>0000000 [[1,2,3,8],[4,6],[5,7]]=>[[1,2,3,4,6],[5,7],[8]]=>[8,5,7,1,2,3,4,6]=>[5,6,7,8,3,1,4,2]=>0000000 [[1,3,5,8],[2,4],[6,7]]=>[[1,2,4,6,7],[3,5],[8]]=>[8,3,5,1,2,4,6,7]=>[5,6,3,7,4,8,1,2]=>0000000 [[1,2,4,8],[3,5],[6,7]]=>[[1,2,3,5,7],[4,6],[8]]=>[8,4,6,1,2,3,5,7]=>[5,6,7,3,8,4,1,2]=>0000000 [[1,2,3,8],[4,5],[6,7]]=>[[1,2,3,4,5],[6,7],[8]]=>[8,6,7,1,2,3,4,5]=>[5,6,7,8,1,3,4,2]=>0000000 [[1,3,6,7],[2,5],[4,8]]=>[[1,2,4,5,8],[3,7],[6]]=>[6,3,7,1,2,4,5,8]=>[5,6,3,7,8,2,4,1]=>0000000 [[1,2,6,7],[3,5],[4,8]]=>[[1,2,3,5,8],[4,7],[6]]=>[6,4,7,1,2,3,5,8]=>[5,6,7,3,8,2,4,1]=>0000000 [[1,2,5,7],[3,6],[4,8]]=>[[1,2,3,6,8],[4,7],[5]]=>[5,4,7,1,2,3,6,8]=>[5,6,7,3,2,8,4,1]=>0000000 [[1,2,3,7],[4,6],[5,8]]=>[[1,2,3,4,6],[5,8],[7]]=>[7,5,8,1,2,3,4,6]=>[5,6,7,8,3,1,2,4]=>0000000 [[1,3,5,7],[2,4],[6,8]]=>[[1,2,4,6,8],[3,5],[7]]=>[7,3,5,1,2,4,6,8]=>[5,6,3,7,4,8,2,1]=>0000000 [[1,2,5,7],[3,4],[6,8]]=>[[1,2,3,4,8],[5,6],[7]]=>[7,5,6,1,2,3,4,8]=>[5,6,7,8,3,4,2,1]=>0000000 [[1,2,4,7],[3,5],[6,8]]=>[[1,2,3,5,8],[4,6],[7]]=>[7,4,6,1,2,3,5,8]=>[5,6,7,3,8,4,2,1]=>0000000 [[1,2,3,7],[4,5],[6,8]]=>[[1,2,3,4,5],[6,8],[7]]=>[7,6,8,1,2,3,4,5]=>[5,6,7,8,1,3,2,4]=>0000000 [[1,3,5,6],[2,7],[4,8]]=>[[1,2,4,6,7],[3,8],[5]]=>[5,3,8,1,2,4,6,7]=>[5,6,3,7,2,8,1,4]=>0000000 [[1,2,5,6],[3,7],[4,8]]=>[[1,2,3,6,7],[4,8],[5]]=>[5,4,8,1,2,3,6,7]=>[5,6,7,3,2,8,1,4]=>0000000 [[1,2,4,6],[3,7],[5,8]]=>[[1,2,3,5,7],[4,8],[6]]=>[6,4,8,1,2,3,5,7]=>[5,6,7,3,8,2,1,4]=>0000000 [[1,2,3,6],[4,7],[5,8]]=>[[1,2,3,4,7],[5,8],[6]]=>[6,5,8,1,2,3,4,7]=>[5,6,7,8,3,2,1,4]=>0000000 [[1,2,3,4],[5,7],[6,8]]=>[[1,2,3,4,5,7],[6,8]]=>[6,8,1,2,3,4,5,7]=>[4,5,6,7,8,2,1,3]=>0000000 [[1,2,3,6],[4,5],[7,8]]=>[[1,2,3,4,5,8],[6,7]]=>[6,7,1,2,3,4,5,8]=>[4,5,6,7,8,2,3,1]=>0000000 [[1,2,4,5],[3,6],[7,8]]=>[[1,2,3,5,6,8],[4,7]]=>[4,7,1,2,3,5,6,8]=>[4,5,6,2,7,8,3,1]=>0000000 [[1,2,3,5],[4,6],[7,8]]=>[[1,2,3,4,6,8],[5,7]]=>[5,7,1,2,3,4,6,8]=>[4,5,6,7,2,8,3,1]=>0000000 [[1,4,7,8],[2,6],[3],[5]]=>[[1,2,5,6],[3,8],[4],[7]]=>[7,4,3,8,1,2,5,6]=>[6,7,4,3,8,1,2,5]=>0000000 [[1,3,7,8],[2,6],[4],[5]]=>[[1,2,4,6],[3,8],[5],[7]]=>[7,5,3,8,1,2,4,6]=>[6,7,4,8,3,1,2,5]=>0000000 [[1,2,7,8],[3,6],[4],[5]]=>[[1,2,3,6],[4,8],[5],[7]]=>[7,5,4,8,1,2,3,6]=>[6,7,8,4,3,1,2,5]=>0000000 [[1,2,7,8],[3,5],[4],[6]]=>[[1,2,3,5],[4,8],[6],[7]]=>[7,6,4,8,1,2,3,5]=>[6,7,8,4,1,3,2,5]=>0000000 [[1,2,7,8],[3,4],[5],[6]]=>[[1,2,3,4],[5,8],[6],[7]]=>[7,6,5,8,1,2,3,4]=>[6,7,8,1,4,3,2,5]=>0000000 [[1,3,6,8],[2,7],[4],[5]]=>[[1,2,4,7],[3,8],[5],[6]]=>[6,5,3,8,1,2,4,7]=>[6,7,4,8,3,2,1,5]=>0000000 [[1,2,6,8],[3,7],[4],[5]]=>[[1,2,3,7],[4,8],[5],[6]]=>[6,5,4,8,1,2,3,7]=>[6,7,8,4,3,2,1,5]=>0000000 [[1,3,5,8],[2,7],[4],[6]]=>[[1,2,4,6,7],[3],[5],[8]]=>[8,5,3,1,2,4,6,7]=>[5,6,4,7,3,8,1,2]=>0000000 [[1,2,3,8],[4,7],[5],[6]]=>[[1,2,3,4,7],[5],[6],[8]]=>[8,6,5,1,2,3,4,7]=>[5,6,7,8,4,3,1,2]=>0000000 [[1,3,6,8],[2,5],[4],[7]]=>[[1,2,4,5],[3,7],[6],[8]]=>[8,6,3,7,1,2,4,5]=>[6,7,4,8,1,3,5,2]=>0000000 [[1,2,6,8],[3,4],[5],[7]]=>[[1,2,3,4],[5,7],[6],[8]]=>[8,6,5,7,1,2,3,4]=>[6,7,8,1,4,3,5,2]=>0000000 [[1,4,5,8],[2,6],[3],[7]]=>[[1,2,5,6],[3,7],[4],[8]]=>[8,4,3,7,1,2,5,6]=>[6,7,4,3,8,1,5,2]=>0000000 [[1,3,5,8],[2,6],[4],[7]]=>[[1,2,4,6],[3,7],[5],[8]]=>[8,5,3,7,1,2,4,6]=>[6,7,4,8,3,1,5,2]=>0000000 [[1,2,5,8],[3,6],[4],[7]]=>[[1,2,3,6],[4,7],[5],[8]]=>[8,5,4,7,1,2,3,6]=>[6,7,8,4,3,1,5,2]=>0000000 [[1,2,3,8],[4,6],[5],[7]]=>[[1,2,3,4,6],[5],[7],[8]]=>[8,7,5,1,2,3,4,6]=>[5,6,7,8,4,1,3,2]=>0000000 [[1,3,5,8],[2,4],[6],[7]]=>[[1,2,4,6],[3,5],[7],[8]]=>[8,7,3,5,1,2,4,6]=>[6,7,4,8,5,1,3,2]=>0000000 [[1,2,5,8],[3,4],[6],[7]]=>[[1,2,3,4],[5,6],[7],[8]]=>[8,7,5,6,1,2,3,4]=>[6,7,8,1,4,5,3,2]=>0000000 [[1,3,4,8],[2,5],[6],[7]]=>[[1,2,4,5],[3,6],[7],[8]]=>[8,7,3,6,1,2,4,5]=>[6,7,4,8,1,5,3,2]=>0000000 [[1,2,4,8],[3,5],[6],[7]]=>[[1,2,3,5],[4,6],[7],[8]]=>[8,7,4,6,1,2,3,5]=>[6,7,8,4,1,5,3,2]=>0000000 [[1,2,3,8],[4,5],[6],[7]]=>[[1,2,3,4,5],[6],[7],[8]]=>[8,7,6,1,2,3,4,5]=>[5,6,7,8,1,4,3,2]=>0000000 [[1,3,4,7],[2,8],[5],[6]]=>[[1,2,4,5,8],[3],[6],[7]]=>[7,6,3,1,2,4,5,8]=>[5,6,4,7,8,3,2,1]=>0000000 [[1,2,4,7],[3,8],[5],[6]]=>[[1,2,3,5,8],[4],[6],[7]]=>[7,6,4,1,2,3,5,8]=>[5,6,7,4,8,3,2,1]=>0000000 [[1,2,3,7],[4,8],[5],[6]]=>[[1,2,3,4,8],[5],[6],[7]]=>[7,6,5,1,2,3,4,8]=>[5,6,7,8,4,3,2,1]=>0000000 [[1,2,3,6],[4,8],[5],[7]]=>[[1,2,3,4,7,8],[5],[6]]=>[6,5,1,2,3,4,7,8]=>[4,5,6,7,3,2,8,1]=>0000000 [[1,2,3,5],[4,8],[6],[7]]=>[[1,2,3,4,6,8],[5],[7]]=>[7,5,1,2,3,4,6,8]=>[4,5,6,7,3,8,2,1]=>0000000 [[1,3,6,7],[2,5],[4],[8]]=>[[1,2,4,5,8],[3,7],[6]]=>[6,3,7,1,2,4,5,8]=>[5,6,3,7,8,2,4,1]=>0000000 [[1,2,6,7],[3,5],[4],[8]]=>[[1,2,3,5,8],[4,7],[6]]=>[6,4,7,1,2,3,5,8]=>[5,6,7,3,8,2,4,1]=>0000000 [[1,2,5,7],[3,6],[4],[8]]=>[[1,2,3,6,8],[4,7],[5]]=>[5,4,7,1,2,3,6,8]=>[5,6,7,3,2,8,4,1]=>0000000 [[1,2,3,7],[4,6],[5],[8]]=>[[1,2,3,4,6],[5,8],[7]]=>[7,5,8,1,2,3,4,6]=>[5,6,7,8,3,1,2,4]=>0000000 [[1,3,5,7],[2,4],[6],[8]]=>[[1,2,4,6,8],[3,5],[7]]=>[7,3,5,1,2,4,6,8]=>[5,6,3,7,4,8,2,1]=>0000000 [[1,2,5,7],[3,4],[6],[8]]=>[[1,2,3,4,8],[5,6],[7]]=>[7,5,6,1,2,3,4,8]=>[5,6,7,8,3,4,2,1]=>0000000 [[1,2,4,7],[3,5],[6],[8]]=>[[1,2,3,5,8],[4,6],[7]]=>[7,4,6,1,2,3,5,8]=>[5,6,7,3,8,4,2,1]=>0000000 [[1,2,3,7],[4,5],[6],[8]]=>[[1,2,3,4,5],[6,8],[7]]=>[7,6,8,1,2,3,4,5]=>[5,6,7,8,1,3,2,4]=>0000000 [[1,3,5,6],[2,7],[4],[8]]=>[[1,2,4,6,7],[3,8],[5]]=>[5,3,8,1,2,4,6,7]=>[5,6,3,7,2,8,1,4]=>0000000 [[1,2,5,6],[3,7],[4],[8]]=>[[1,2,3,6,7],[4,8],[5]]=>[5,4,8,1,2,3,6,7]=>[5,6,7,3,2,8,1,4]=>0000000 [[1,2,4,6],[3,7],[5],[8]]=>[[1,2,3,5,7],[4,8],[6]]=>[6,4,8,1,2,3,5,7]=>[5,6,7,3,8,2,1,4]=>0000000 [[1,2,3,6],[4,7],[5],[8]]=>[[1,2,3,4,7],[5,8],[6]]=>[6,5,8,1,2,3,4,7]=>[5,6,7,8,3,2,1,4]=>0000000 [[1,3,4,5],[2,7],[6],[8]]=>[[1,2,4,5,6,7],[3],[8]]=>[8,3,1,2,4,5,6,7]=>[4,5,3,6,7,8,1,2]=>0000000 [[1,2,4,5],[3,7],[6],[8]]=>[[1,2,3,5,6,7],[4],[8]]=>[8,4,1,2,3,5,6,7]=>[4,5,6,3,7,8,1,2]=>0000000 [[1,2,3,5],[4,7],[6],[8]]=>[[1,2,3,4,6,7],[5],[8]]=>[8,5,1,2,3,4,6,7]=>[4,5,6,7,3,8,1,2]=>0000000 [[1,2,3,4],[5,7],[6],[8]]=>[[1,2,3,4,5,7],[6],[8]]=>[8,6,1,2,3,4,5,7]=>[4,5,6,7,8,3,1,2]=>0000000 [[1,3,5,6],[2,4],[7],[8]]=>[[1,2,4,6,7],[3,5],[8]]=>[8,3,5,1,2,4,6,7]=>[5,6,3,7,4,8,1,2]=>0000000 [[1,2,4,6],[3,5],[7],[8]]=>[[1,2,3,5,7],[4,6],[8]]=>[8,4,6,1,2,3,5,7]=>[5,6,7,3,8,4,1,2]=>0000000 [[1,2,3,6],[4,5],[7],[8]]=>[[1,2,3,4,5],[6,7],[8]]=>[8,6,7,1,2,3,4,5]=>[5,6,7,8,1,3,4,2]=>0000000 [[1,2,3,5],[4,6],[7],[8]]=>[[1,2,3,4,6],[5,7],[8]]=>[8,5,7,1,2,3,4,6]=>[5,6,7,8,3,1,4,2]=>0000000 [[1,2,3,4],[5,6],[7],[8]]=>[[1,2,3,4,5,6],[7],[8]]=>[8,7,1,2,3,4,5,6]=>[4,5,6,7,8,1,3,2]=>0000000 [[1,4,7,8],[2],[3],[5],[6]]=>[[1,2,5,8],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5,8]=>[6,7,5,4,8,3,2,1]=>0000000 [[1,3,7,8],[2],[4],[5],[6]]=>[[1,2,4,8],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4,8]=>[6,7,5,8,4,3,2,1]=>0000000 [[1,3,6,8],[2],[4],[5],[7]]=>[[1,2,4,7],[3],[5],[6],[8]]=>[8,6,5,3,1,2,4,7]=>[6,7,5,8,4,3,1,2]=>0000000 [[1,3,5,8],[2],[4],[6],[7]]=>[[1,2,4,6],[3],[5],[7],[8]]=>[8,7,5,3,1,2,4,6]=>[6,7,5,8,4,1,3,2]=>0000000 [[1,3,4,8],[2],[5],[6],[7]]=>[[1,2,4,5],[3],[6],[7],[8]]=>[8,7,6,3,1,2,4,5]=>[6,7,5,8,1,4,3,2]=>0000000 [[1,2,4,8],[3],[5],[6],[7]]=>[[1,2,3,5],[4],[6],[7],[8]]=>[8,7,6,4,1,2,3,5]=>[6,7,8,5,1,4,3,2]=>0000000 [[1,2,3,8],[4],[5],[6],[7]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[8,7,6,5,1,2,3,4]=>[6,7,8,1,5,4,3,2]=>0000000 [[1,3,4,7],[2],[5],[6],[8]]=>[[1,2,4,5,8],[3],[6],[7]]=>[7,6,3,1,2,4,5,8]=>[5,6,4,7,8,3,2,1]=>0000000 [[1,2,4,7],[3],[5],[6],[8]]=>[[1,2,3,5,8],[4],[6],[7]]=>[7,6,4,1,2,3,5,8]=>[5,6,7,4,8,3,2,1]=>0000000 [[1,2,3,7],[4],[5],[6],[8]]=>[[1,2,3,4,8],[5],[6],[7]]=>[7,6,5,1,2,3,4,8]=>[5,6,7,8,4,3,2,1]=>0000000 [[1,3,5,6],[2],[4],[7],[8]]=>[[1,2,4,6,7],[3],[5],[8]]=>[8,5,3,1,2,4,6,7]=>[5,6,4,7,3,8,1,2]=>0000000 [[1,2,3,6],[4],[5],[7],[8]]=>[[1,2,3,4,7],[5],[6],[8]]=>[8,6,5,1,2,3,4,7]=>[5,6,7,8,4,3,1,2]=>0000000 [[1,2,3,5],[4],[6],[7],[8]]=>[[1,2,3,4,6],[5],[7],[8]]=>[8,7,5,1,2,3,4,6]=>[5,6,7,8,4,1,3,2]=>0000000 [[1,2,3,4],[5],[6],[7],[8]]=>[[1,2,3,4,5],[6],[7],[8]]=>[8,7,6,1,2,3,4,5]=>[5,6,7,8,1,4,3,2]=>0000000 [[1,2,7],[3,5,8],[4,6]]=>[[1,2,3,5,8],[4,6],[7]]=>[7,4,6,1,2,3,5,8]=>[5,6,7,3,8,4,2,1]=>0000000 [[1,3,7],[2,4,8],[5,6]]=>[[1,2,4,6,8],[3,5],[7]]=>[7,3,5,1,2,4,6,8]=>[5,6,3,7,4,8,2,1]=>0000000 [[1,2,7],[3,4,8],[5,6]]=>[[1,2,3,4,8],[5,6],[7]]=>[7,5,6,1,2,3,4,8]=>[5,6,7,8,3,4,2,1]=>0000000 [[1,3,6],[2,5,8],[4,7]]=>[[1,2,4,5,8],[3,7],[6]]=>[6,3,7,1,2,4,5,8]=>[5,6,3,7,8,2,4,1]=>0000000 [[1,2,6],[3,5,8],[4,7]]=>[[1,2,3,5,8],[4,7],[6]]=>[6,4,7,1,2,3,5,8]=>[5,6,7,3,8,2,4,1]=>0000000 [[1,2,5],[3,6,8],[4,7]]=>[[1,2,3,6,8],[4,7],[5]]=>[5,4,7,1,2,3,6,8]=>[5,6,7,3,2,8,4,1]=>0000000 [[1,2,4],[3,6,8],[5,7]]=>[[1,2,3,5,6,8],[4,7]]=>[4,7,1,2,3,5,6,8]=>[4,5,6,2,7,8,3,1]=>0000000 [[1,2,3],[4,6,8],[5,7]]=>[[1,2,3,4,6,8],[5,7]]=>[5,7,1,2,3,4,6,8]=>[4,5,6,7,2,8,3,1]=>0000000 [[1,2,3],[4,5,8],[6,7]]=>[[1,2,3,4,5,8],[6,7]]=>[6,7,1,2,3,4,5,8]=>[4,5,6,7,8,2,3,1]=>0000000 [[1,4,6],[2,5,7],[3,8]]=>[[1,2,5,7],[3,6,8],[4]]=>[4,3,6,8,1,2,5,7]=>[6,7,3,2,8,4,1,5]=>0000000 [[1,2,6],[3,5,7],[4,8]]=>[[1,2,3,5,7],[4,8],[6]]=>[6,4,8,1,2,3,5,7]=>[5,6,7,3,8,2,1,4]=>0000000 [[1,3,6],[2,4,7],[5,8]]=>[[1,2,4,7],[3,5,8],[6]]=>[6,3,5,8,1,2,4,7]=>[6,7,3,8,4,2,1,5]=>0000000 [[1,2,6],[3,4,7],[5,8]]=>[[1,2,3,4,7],[5,8],[6]]=>[6,5,8,1,2,3,4,7]=>[5,6,7,8,3,2,1,4]=>0000000 [[1,3,5],[2,6,7],[4,8]]=>[[1,2,4,6,7],[3,8],[5]]=>[5,3,8,1,2,4,6,7]=>[5,6,3,7,2,8,1,4]=>0000000 [[1,2,5],[3,6,7],[4,8]]=>[[1,2,3,6,7],[4,8],[5]]=>[5,4,8,1,2,3,6,7]=>[5,6,7,3,2,8,1,4]=>0000000 [[1,3,5],[2,4,7],[6,8]]=>[[1,2,4,6,7],[3,5,8]]=>[3,5,8,1,2,4,6,7]=>[5,6,2,7,3,8,1,4]=>0000000 [[1,2,5],[3,4,7],[6,8]]=>[[1,2,3,4,7],[5,6,8]]=>[5,6,8,1,2,3,4,7]=>[5,6,7,8,2,3,1,4]=>0000000 [[1,3,4],[2,5,7],[6,8]]=>[[1,2,4,5,7],[3,6,8]]=>[3,6,8,1,2,4,5,7]=>[5,6,2,7,8,3,1,4]=>0000000 [[1,2,4],[3,5,7],[6,8]]=>[[1,2,3,5,7],[4,6,8]]=>[4,6,8,1,2,3,5,7]=>[5,6,7,2,8,3,1,4]=>0000000 [[1,2,3],[4,5,7],[6,8]]=>[[1,2,3,4,5,7],[6,8]]=>[6,8,1,2,3,4,5,7]=>[4,5,6,7,8,2,1,3]=>0000000 [[1,3,5],[2,4,6],[7,8]]=>[[1,2,4,6,8],[3,5,7]]=>[3,5,7,1,2,4,6,8]=>[5,6,2,7,3,8,4,1]=>0000000 [[1,3,4],[2,5,6],[7,8]]=>[[1,2,4,5,6],[3,7,8]]=>[3,7,8,1,2,4,5,6]=>[5,6,2,7,8,1,3,4]=>0000000 [[1,3,7],[2,5,8],[4],[6]]=>[[1,2,4,5,8],[3],[6],[7]]=>[7,6,3,1,2,4,5,8]=>[5,6,4,7,8,3,2,1]=>0000000 [[1,2,7],[3,5,8],[4],[6]]=>[[1,2,3,5,8],[4],[6],[7]]=>[7,6,4,1,2,3,5,8]=>[5,6,7,4,8,3,2,1]=>0000000 [[1,2,7],[3,4,8],[5],[6]]=>[[1,2,3,4,8],[5],[6],[7]]=>[7,6,5,1,2,3,4,8]=>[5,6,7,8,4,3,2,1]=>0000000 [[1,2,3],[4,7,8],[5],[6]]=>[[1,2,3,4,7,8],[5],[6]]=>[6,5,1,2,3,4,7,8]=>[4,5,6,7,3,2,8,1]=>0000000 [[1,3,6],[2,5,8],[4],[7]]=>[[1,2,4,5,8],[3,7],[6]]=>[6,3,7,1,2,4,5,8]=>[5,6,3,7,8,2,4,1]=>0000000 [[1,2,6],[3,5,8],[4],[7]]=>[[1,2,3,5,8],[4,7],[6]]=>[6,4,7,1,2,3,5,8]=>[5,6,7,3,8,2,4,1]=>0000000 [[1,2,5],[3,6,8],[4],[7]]=>[[1,2,3,6,8],[4,7],[5]]=>[5,4,7,1,2,3,6,8]=>[5,6,7,3,2,8,4,1]=>0000000 [[1,2,3],[4,6,8],[5],[7]]=>[[1,2,3,4,6,8],[5],[7]]=>[7,5,1,2,3,4,6,8]=>[4,5,6,7,3,8,2,1]=>0000000 [[1,3,5],[2,4,8],[6],[7]]=>[[1,2,4,6,8],[3,5],[7]]=>[7,3,5,1,2,4,6,8]=>[5,6,3,7,4,8,2,1]=>0000000 [[1,2,5],[3,4,8],[6],[7]]=>[[1,2,3,4,8],[5,6],[7]]=>[7,5,6,1,2,3,4,8]=>[5,6,7,8,3,4,2,1]=>0000000 [[1,2,4],[3,5,8],[6],[7]]=>[[1,2,3,5,8],[4,6],[7]]=>[7,4,6,1,2,3,5,8]=>[5,6,7,3,8,4,2,1]=>0000000 [[1,4,6],[2,5,7],[3],[8]]=>[[1,2,5,7],[3,6,8],[4]]=>[4,3,6,8,1,2,5,7]=>[6,7,3,2,8,4,1,5]=>0000000 [[1,2,6],[3,5,7],[4],[8]]=>[[1,2,3,5,7],[4,8],[6]]=>[6,4,8,1,2,3,5,7]=>[5,6,7,3,8,2,1,4]=>0000000 [[1,3,6],[2,4,7],[5],[8]]=>[[1,2,4,7],[3,5,8],[6]]=>[6,3,5,8,1,2,4,7]=>[6,7,3,8,4,2,1,5]=>0000000 [[1,2,6],[3,4,7],[5],[8]]=>[[1,2,3,4,7],[5,8],[6]]=>[6,5,8,1,2,3,4,7]=>[5,6,7,8,3,2,1,4]=>0000000 [[1,3,5],[2,6,7],[4],[8]]=>[[1,2,4,6,7],[3,8],[5]]=>[5,3,8,1,2,4,6,7]=>[5,6,3,7,2,8,1,4]=>0000000 [[1,2,5],[3,6,7],[4],[8]]=>[[1,2,3,6,7],[4,8],[5]]=>[5,4,8,1,2,3,6,7]=>[5,6,7,3,2,8,1,4]=>0000000 [[1,3,4],[2,6,7],[5],[8]]=>[[1,2,4,5,6,7],[3],[8]]=>[8,3,1,2,4,5,6,7]=>[4,5,3,6,7,8,1,2]=>0000000 [[1,2,4],[3,6,7],[5],[8]]=>[[1,2,3,5,6,7],[4],[8]]=>[8,4,1,2,3,5,6,7]=>[4,5,6,3,7,8,1,2]=>0000000 [[1,2,3],[4,6,7],[5],[8]]=>[[1,2,3,4,6,7],[5],[8]]=>[8,5,1,2,3,4,6,7]=>[4,5,6,7,3,8,1,2]=>0000000 [[1,3,5],[2,4,7],[6],[8]]=>[[1,2,4,6,7],[3,5],[8]]=>[8,3,5,1,2,4,6,7]=>[5,6,3,7,4,8,1,2]=>0000000 [[1,2,4],[3,5,7],[6],[8]]=>[[1,2,3,5,7],[4,6],[8]]=>[8,4,6,1,2,3,5,7]=>[5,6,7,3,8,4,1,2]=>0000000 [[1,2,3],[4,5,7],[6],[8]]=>[[1,2,3,4,5,7],[6],[8]]=>[8,6,1,2,3,4,5,7]=>[4,5,6,7,8,3,1,2]=>0000000 [[1,3,5],[2,4,6],[7],[8]]=>[[1,2,4,6],[3,5,7],[8]]=>[8,3,5,7,1,2,4,6]=>[6,7,3,8,4,1,5,2]=>0000000 [[1,2,5],[3,4,6],[7],[8]]=>[[1,2,3,4,6],[5,7],[8]]=>[8,5,7,1,2,3,4,6]=>[5,6,7,8,3,1,4,2]=>0000000 [[1,2,3],[4,5,6],[7],[8]]=>[[1,2,3,4,5,6],[7],[8]]=>[8,7,1,2,3,4,5,6]=>[4,5,6,7,8,1,3,2]=>0000000 [[1,4,8],[2,6],[3,7],[5]]=>[[1,2,5,6],[3,7],[4],[8]]=>[8,4,3,7,1,2,5,6]=>[6,7,4,3,8,1,5,2]=>0000000 [[1,3,8],[2,6],[4,7],[5]]=>[[1,2,4,6],[3,7],[5],[8]]=>[8,5,3,7,1,2,4,6]=>[6,7,4,8,3,1,5,2]=>0000000 [[1,2,8],[3,6],[4,7],[5]]=>[[1,2,3,6],[4,7],[5],[8]]=>[8,5,4,7,1,2,3,6]=>[6,7,8,4,3,1,5,2]=>0000000 [[1,3,8],[2,5],[4,7],[6]]=>[[1,2,4,5],[3,7],[6],[8]]=>[8,6,3,7,1,2,4,5]=>[6,7,4,8,1,3,5,2]=>0000000 [[1,2,8],[3,4],[5,7],[6]]=>[[1,2,3,4],[5,7],[6],[8]]=>[8,6,5,7,1,2,3,4]=>[6,7,8,1,4,3,5,2]=>0000000 [[1,4,8],[2,5],[3,6],[7]]=>[[1,2,5],[3,6],[4,7],[8]]=>[8,4,7,3,6,1,2,5]=>[7,8,5,3,1,6,4,2]=>0000000 [[1,3,8],[2,5],[4,6],[7]]=>[[1,2,4,5],[3,6],[7],[8]]=>[8,7,3,6,1,2,4,5]=>[6,7,4,8,1,5,3,2]=>0000000 [[1,2,8],[3,5],[4,6],[7]]=>[[1,2,3,5],[4,6],[7],[8]]=>[8,7,4,6,1,2,3,5]=>[6,7,8,4,1,5,3,2]=>0000000 [[1,3,8],[2,4],[5,6],[7]]=>[[1,2,4,6],[3,5],[7],[8]]=>[8,7,3,5,1,2,4,6]=>[6,7,4,8,5,1,3,2]=>0000000 [[1,2,8],[3,4],[5,6],[7]]=>[[1,2,3,4],[5,6],[7],[8]]=>[8,7,5,6,1,2,3,4]=>[6,7,8,1,4,5,3,2]=>0000000 [[1,4,7],[2,6],[3,8],[5]]=>[[1,2,5,6],[3,8],[4],[7]]=>[7,4,3,8,1,2,5,6]=>[6,7,4,3,8,1,2,5]=>0000000 [[1,3,7],[2,6],[4,8],[5]]=>[[1,2,4,6],[3,8],[5],[7]]=>[7,5,3,8,1,2,4,6]=>[6,7,4,8,3,1,2,5]=>0000000 [[1,2,7],[3,6],[4,8],[5]]=>[[1,2,3,6],[4,8],[5],[7]]=>[7,5,4,8,1,2,3,6]=>[6,7,8,4,3,1,2,5]=>0000000 [[1,2,7],[3,5],[4,8],[6]]=>[[1,2,3,5],[4,8],[6],[7]]=>[7,6,4,8,1,2,3,5]=>[6,7,8,4,1,3,2,5]=>0000000 [[1,2,7],[3,4],[5,8],[6]]=>[[1,2,3,4],[5,8],[6],[7]]=>[7,6,5,8,1,2,3,4]=>[6,7,8,1,4,3,2,5]=>0000000 [[1,3,6],[2,7],[4,8],[5]]=>[[1,2,4,7],[3,8],[5],[6]]=>[6,5,3,8,1,2,4,7]=>[6,7,4,8,3,2,1,5]=>0000000 [[1,2,6],[3,7],[4,8],[5]]=>[[1,2,3,7],[4,8],[5],[6]]=>[6,5,4,8,1,2,3,7]=>[6,7,8,4,3,2,1,5]=>0000000 [[1,3,5],[2,7],[4,8],[6]]=>[[1,2,4,6,7],[3,8],[5]]=>[5,3,8,1,2,4,6,7]=>[5,6,3,7,2,8,1,4]=>0000000 [[1,2,5],[3,7],[4,8],[6]]=>[[1,2,3,6,7],[4,8],[5]]=>[5,4,8,1,2,3,6,7]=>[5,6,7,3,2,8,1,4]=>0000000 [[1,2,4],[3,7],[5,8],[6]]=>[[1,2,3,5,7],[4,8],[6]]=>[6,4,8,1,2,3,5,7]=>[5,6,7,3,8,2,1,4]=>0000000 [[1,2,3],[4,7],[5,8],[6]]=>[[1,2,3,4,7],[5,8],[6]]=>[6,5,8,1,2,3,4,7]=>[5,6,7,8,3,2,1,4]=>0000000 [[1,3,6],[2,5],[4,8],[7]]=>[[1,2,4,5,8],[3,7],[6]]=>[6,3,7,1,2,4,5,8]=>[5,6,3,7,8,2,4,1]=>0000000 [[1,2,6],[3,5],[4,8],[7]]=>[[1,2,3,5,8],[4,7],[6]]=>[6,4,7,1,2,3,5,8]=>[5,6,7,3,8,2,4,1]=>0000000 [[1,2,5],[3,6],[4,8],[7]]=>[[1,2,3,6,8],[4,7],[5]]=>[5,4,7,1,2,3,6,8]=>[5,6,7,3,2,8,4,1]=>0000000 [[1,2,3],[4,6],[5,8],[7]]=>[[1,2,3,4,6],[5,8],[7]]=>[7,5,8,1,2,3,4,6]=>[5,6,7,8,3,1,2,4]=>0000000 [[1,3,5],[2,4],[6,8],[7]]=>[[1,2,4,6,8],[3,5],[7]]=>[7,3,5,1,2,4,6,8]=>[5,6,3,7,4,8,2,1]=>0000000 [[1,2,5],[3,4],[6,8],[7]]=>[[1,2,3,4,8],[5,6],[7]]=>[7,5,6,1,2,3,4,8]=>[5,6,7,8,3,4,2,1]=>0000000 [[1,2,4],[3,5],[6,8],[7]]=>[[1,2,3,5,8],[4,6],[7]]=>[7,4,6,1,2,3,5,8]=>[5,6,7,3,8,4,2,1]=>0000000 [[1,2,3],[4,5],[6,8],[7]]=>[[1,2,3,4,5],[6,8],[7]]=>[7,6,8,1,2,3,4,5]=>[5,6,7,8,1,3,2,4]=>0000000 [[1,3,7],[2,5],[4,6],[8]]=>[[1,2,4,5],[3,6],[7,8]]=>[7,8,3,6,1,2,4,5]=>[6,7,4,8,1,5,2,3]=>0000000 [[1,2,7],[3,4],[5,6],[8]]=>[[1,2,3,4],[5,6],[7,8]]=>[7,8,5,6,1,2,3,4]=>[6,7,8,1,4,5,2,3]=>0000000 [[1,3,6],[2,5],[4,7],[8]]=>[[1,2,4,5],[3,7],[6,8]]=>[6,8,3,7,1,2,4,5]=>[6,7,4,8,1,2,5,3]=>0000000 [[1,2,6],[3,4],[5,7],[8]]=>[[1,2,3,4],[5,7],[6,8]]=>[6,8,5,7,1,2,3,4]=>[6,7,8,1,4,2,5,3]=>0000000 [[1,4,5],[2,6],[3,7],[8]]=>[[1,2,5,6],[3,7],[4,8]]=>[4,8,3,7,1,2,5,6]=>[6,7,4,2,8,1,5,3]=>0000000 [[1,3,5],[2,6],[4,7],[8]]=>[[1,2,4,6],[3,7],[5,8]]=>[5,8,3,7,1,2,4,6]=>[6,7,4,8,2,1,5,3]=>0000000 [[1,2,5],[3,6],[4,7],[8]]=>[[1,2,3,6],[4,7],[5,8]]=>[5,8,4,7,1,2,3,6]=>[6,7,8,4,2,1,5,3]=>0000000 [[1,2,3],[4,6],[5,7],[8]]=>[[1,2,3,4,6],[5,7],[8]]=>[8,5,7,1,2,3,4,6]=>[5,6,7,8,3,1,4,2]=>0000000 [[1,3,5],[2,4],[6,7],[8]]=>[[1,2,4,6,7],[3,5],[8]]=>[8,3,5,1,2,4,6,7]=>[5,6,3,7,4,8,1,2]=>0000000 [[1,2,4],[3,5],[6,7],[8]]=>[[1,2,3,5,7],[4,6],[8]]=>[8,4,6,1,2,3,5,7]=>[5,6,7,3,8,4,1,2]=>0000000 [[1,2,3],[4,5],[6,7],[8]]=>[[1,2,3,4,5],[6,7],[8]]=>[8,6,7,1,2,3,4,5]=>[5,6,7,8,1,3,4,2]=>0000000 [[1,6,8],[2,7],[3],[4],[5]]=>[[1,2,7],[3,8],[4],[5],[6]]=>[6,5,4,3,8,1,2,7]=>[7,8,5,4,3,2,1,6]=>0000000 [[1,3,8],[2,7],[4],[5],[6]]=>[[1,2,4,7],[3],[5],[6],[8]]=>[8,6,5,3,1,2,4,7]=>[6,7,5,8,4,3,1,2]=>0000000 [[1,3,8],[2,6],[4],[5],[7]]=>[[1,2,4,6],[3],[5],[7],[8]]=>[8,7,5,3,1,2,4,6]=>[6,7,5,8,4,1,3,2]=>0000000 [[1,4,8],[2,5],[3],[6],[7]]=>[[1,2,5],[3,6],[4],[7],[8]]=>[8,7,4,3,6,1,2,5]=>[7,8,5,4,1,6,3,2]=>0000000 [[1,3,8],[2,5],[4],[6],[7]]=>[[1,2,4,5],[3],[6],[7],[8]]=>[8,7,6,3,1,2,4,5]=>[6,7,5,8,1,4,3,2]=>0000000 [[1,2,8],[3,5],[4],[6],[7]]=>[[1,2,3,5],[4],[6],[7],[8]]=>[8,7,6,4,1,2,3,5]=>[6,7,8,5,1,4,3,2]=>0000000 [[1,3,8],[2,4],[5],[6],[7]]=>[[1,2,4],[3,5],[6],[7],[8]]=>[8,7,6,3,5,1,2,4]=>[7,8,5,1,6,4,3,2]=>0000000 [[1,2,8],[3,4],[5],[6],[7]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[8,7,6,5,1,2,3,4]=>[6,7,8,1,5,4,3,2]=>0000000 [[1,4,7],[2,8],[3],[5],[6]]=>[[1,2,5,8],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5,8]=>[6,7,5,4,8,3,2,1]=>0000000 [[1,3,7],[2,8],[4],[5],[6]]=>[[1,2,4,8],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4,8]=>[6,7,5,8,4,3,2,1]=>0000000 [[1,3,4],[2,8],[5],[6],[7]]=>[[1,2,4,5,8],[3],[6],[7]]=>[7,6,3,1,2,4,5,8]=>[5,6,4,7,8,3,2,1]=>0000000 [[1,2,4],[3,8],[5],[6],[7]]=>[[1,2,3,5,8],[4],[6],[7]]=>[7,6,4,1,2,3,5,8]=>[5,6,7,4,8,3,2,1]=>0000000 [[1,2,3],[4,8],[5],[6],[7]]=>[[1,2,3,4,8],[5],[6],[7]]=>[7,6,5,1,2,3,4,8]=>[5,6,7,8,4,3,2,1]=>0000000 [[1,4,7],[2,6],[3],[5],[8]]=>[[1,2,5,6],[3,8],[4],[7]]=>[7,4,3,8,1,2,5,6]=>[6,7,4,3,8,1,2,5]=>0000000 [[1,3,7],[2,6],[4],[5],[8]]=>[[1,2,4,6],[3,8],[5],[7]]=>[7,5,3,8,1,2,4,6]=>[6,7,4,8,3,1,2,5]=>0000000 [[1,2,7],[3,6],[4],[5],[8]]=>[[1,2,3,6],[4,8],[5],[7]]=>[7,5,4,8,1,2,3,6]=>[6,7,8,4,3,1,2,5]=>0000000 [[1,2,7],[3,5],[4],[6],[8]]=>[[1,2,3,5],[4,8],[6],[7]]=>[7,6,4,8,1,2,3,5]=>[6,7,8,4,1,3,2,5]=>0000000 [[1,2,7],[3,4],[5],[6],[8]]=>[[1,2,3,4],[5,8],[6],[7]]=>[7,6,5,8,1,2,3,4]=>[6,7,8,1,4,3,2,5]=>0000000 [[1,3,6],[2,7],[4],[5],[8]]=>[[1,2,4,7],[3,8],[5],[6]]=>[6,5,3,8,1,2,4,7]=>[6,7,4,8,3,2,1,5]=>0000000 [[1,2,6],[3,7],[4],[5],[8]]=>[[1,2,3,7],[4,8],[5],[6]]=>[6,5,4,8,1,2,3,7]=>[6,7,8,4,3,2,1,5]=>0000000 [[1,3,5],[2,7],[4],[6],[8]]=>[[1,2,4,6,7],[3],[5],[8]]=>[8,5,3,1,2,4,6,7]=>[5,6,4,7,3,8,1,2]=>0000000 [[1,2,3],[4,7],[5],[6],[8]]=>[[1,2,3,4,7],[5],[6],[8]]=>[8,6,5,1,2,3,4,7]=>[5,6,7,8,4,3,1,2]=>0000000 [[1,3,6],[2,5],[4],[7],[8]]=>[[1,2,4,5],[3,7],[6],[8]]=>[8,6,3,7,1,2,4,5]=>[6,7,4,8,1,3,5,2]=>0000000 [[1,2,6],[3,4],[5],[7],[8]]=>[[1,2,3,4],[5,7],[6],[8]]=>[8,6,5,7,1,2,3,4]=>[6,7,8,1,4,3,5,2]=>0000000 [[1,4,5],[2,6],[3],[7],[8]]=>[[1,2,5,6],[3,7],[4],[8]]=>[8,4,3,7,1,2,5,6]=>[6,7,4,3,8,1,5,2]=>0000000 [[1,3,5],[2,6],[4],[7],[8]]=>[[1,2,4,6],[3,7],[5],[8]]=>[8,5,3,7,1,2,4,6]=>[6,7,4,8,3,1,5,2]=>0000000 [[1,2,5],[3,6],[4],[7],[8]]=>[[1,2,3,6],[4,7],[5],[8]]=>[8,5,4,7,1,2,3,6]=>[6,7,8,4,3,1,5,2]=>0000000 [[1,2,3],[4,6],[5],[7],[8]]=>[[1,2,3,4,6],[5],[7],[8]]=>[8,7,5,1,2,3,4,6]=>[5,6,7,8,4,1,3,2]=>0000000 [[1,3,5],[2,4],[6],[7],[8]]=>[[1,2,4,6],[3,5],[7],[8]]=>[8,7,3,5,1,2,4,6]=>[6,7,4,8,5,1,3,2]=>0000000 [[1,2,5],[3,4],[6],[7],[8]]=>[[1,2,3,4],[5,6],[7],[8]]=>[8,7,5,6,1,2,3,4]=>[6,7,8,1,4,5,3,2]=>0000000 [[1,3,4],[2,5],[6],[7],[8]]=>[[1,2,4,5],[3,6],[7],[8]]=>[8,7,3,6,1,2,4,5]=>[6,7,4,8,1,5,3,2]=>0000000 [[1,2,4],[3,5],[6],[7],[8]]=>[[1,2,3,5],[4,6],[7],[8]]=>[8,7,4,6,1,2,3,5]=>[6,7,8,4,1,5,3,2]=>0000000 [[1,2,3],[4,5],[6],[7],[8]]=>[[1,2,3,4,5],[6],[7],[8]]=>[8,7,6,1,2,3,4,5]=>[5,6,7,8,1,4,3,2]=>0000000 [[1,6,8],[2],[3],[4],[5],[7]]=>[[1,2,7],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,1,2,7]=>[7,8,6,5,4,3,1,2]=>0000000 [[1,4,8],[2],[3],[5],[6],[7]]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,1,2,5]=>[7,8,6,5,1,4,3,2]=>0000000 [[1,3,8],[2],[4],[5],[6],[7]]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[8,7,6,5,3,1,2,4]=>[7,8,6,1,5,4,3,2]=>0000000 [[1,2,8],[3],[4],[5],[6],[7]]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,1,2,3]=>[7,8,1,6,5,4,3,2]=>0000000 [[1,4,7],[2],[3],[5],[6],[8]]=>[[1,2,5,8],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5,8]=>[6,7,5,4,8,3,2,1]=>0000000 [[1,3,7],[2],[4],[5],[6],[8]]=>[[1,2,4,8],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4,8]=>[6,7,5,8,4,3,2,1]=>0000000 [[1,3,6],[2],[4],[5],[7],[8]]=>[[1,2,4,7],[3],[5],[6],[8]]=>[8,6,5,3,1,2,4,7]=>[6,7,5,8,4,3,1,2]=>0000000 [[1,3,5],[2],[4],[6],[7],[8]]=>[[1,2,4,6],[3],[5],[7],[8]]=>[8,7,5,3,1,2,4,6]=>[6,7,5,8,4,1,3,2]=>0000000 [[1,3,4],[2],[5],[6],[7],[8]]=>[[1,2,4,5],[3],[6],[7],[8]]=>[8,7,6,3,1,2,4,5]=>[6,7,5,8,1,4,3,2]=>0000000 [[1,2,4],[3],[5],[6],[7],[8]]=>[[1,2,3,5],[4],[6],[7],[8]]=>[8,7,6,4,1,2,3,5]=>[6,7,8,5,1,4,3,2]=>0000000 [[1,2,3],[4],[5],[6],[7],[8]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[8,7,6,5,1,2,3,4]=>[6,7,8,1,5,4,3,2]=>0000000 [[1,4],[2,6],[3,7],[5,8]]=>[[1,2,5,6],[3,7],[4,8]]=>[4,8,3,7,1,2,5,6]=>[6,7,4,2,8,1,5,3]=>0000000 [[1,3],[2,6],[4,7],[5,8]]=>[[1,2,4,6],[3,7],[5,8]]=>[5,8,3,7,1,2,4,6]=>[6,7,4,8,2,1,5,3]=>0000000 [[1,2],[3,6],[4,7],[5,8]]=>[[1,2,3,6],[4,7],[5,8]]=>[5,8,4,7,1,2,3,6]=>[6,7,8,4,2,1,5,3]=>0000000 [[1,3],[2,5],[4,7],[6,8]]=>[[1,2,4,5],[3,7],[6,8]]=>[6,8,3,7,1,2,4,5]=>[6,7,4,8,1,2,5,3]=>0000000 [[1,2],[3,4],[5,7],[6,8]]=>[[1,2,3,4],[5,7],[6,8]]=>[6,8,5,7,1,2,3,4]=>[6,7,8,1,4,2,5,3]=>0000000 [[1,3],[2,5],[4,6],[7,8]]=>[[1,2,4,5],[3,6],[7,8]]=>[7,8,3,6,1,2,4,5]=>[6,7,4,8,1,5,2,3]=>0000000 [[1,2],[3,4],[5,6],[7,8]]=>[[1,2,3,4],[5,6],[7,8]]=>[7,8,5,6,1,2,3,4]=>[6,7,8,1,4,5,2,3]=>0000000 [[1,6],[2,7],[3,8],[4],[5]]=>[[1,2,7],[3,8],[4],[5],[6]]=>[6,5,4,3,8,1,2,7]=>[7,8,5,4,3,2,1,6]=>0000000 [[1,3],[2,7],[4,8],[5],[6]]=>[[1,2,4,7],[3,8],[5],[6]]=>[6,5,3,8,1,2,4,7]=>[6,7,4,8,3,2,1,5]=>0000000 [[1,2],[3,7],[4,8],[5],[6]]=>[[1,2,3,7],[4,8],[5],[6]]=>[6,5,4,8,1,2,3,7]=>[6,7,8,4,3,2,1,5]=>0000000 [[1,4],[2,6],[3,8],[5],[7]]=>[[1,2,5,6],[3,8],[4],[7]]=>[7,4,3,8,1,2,5,6]=>[6,7,4,3,8,1,2,5]=>0000000 [[1,3],[2,6],[4,8],[5],[7]]=>[[1,2,4,6],[3,8],[5],[7]]=>[7,5,3,8,1,2,4,6]=>[6,7,4,8,3,1,2,5]=>0000000 [[1,2],[3,6],[4,8],[5],[7]]=>[[1,2,3,6],[4,8],[5],[7]]=>[7,5,4,8,1,2,3,6]=>[6,7,8,4,3,1,2,5]=>0000000 [[1,2],[3,5],[4,8],[6],[7]]=>[[1,2,3,5],[4,8],[6],[7]]=>[7,6,4,8,1,2,3,5]=>[6,7,8,4,1,3,2,5]=>0000000 [[1,2],[3,4],[5,8],[6],[7]]=>[[1,2,3,4],[5,8],[6],[7]]=>[7,6,5,8,1,2,3,4]=>[6,7,8,1,4,3,2,5]=>0000000 [[1,4],[2,6],[3,7],[5],[8]]=>[[1,2,5,6],[3,7],[4],[8]]=>[8,4,3,7,1,2,5,6]=>[6,7,4,3,8,1,5,2]=>0000000 [[1,3],[2,6],[4,7],[5],[8]]=>[[1,2,4,6],[3,7],[5],[8]]=>[8,5,3,7,1,2,4,6]=>[6,7,4,8,3,1,5,2]=>0000000 [[1,2],[3,6],[4,7],[5],[8]]=>[[1,2,3,6],[4,7],[5],[8]]=>[8,5,4,7,1,2,3,6]=>[6,7,8,4,3,1,5,2]=>0000000 [[1,3],[2,5],[4,7],[6],[8]]=>[[1,2,4,5],[3,7],[6],[8]]=>[8,6,3,7,1,2,4,5]=>[6,7,4,8,1,3,5,2]=>0000000 [[1,2],[3,4],[5,7],[6],[8]]=>[[1,2,3,4],[5,7],[6],[8]]=>[8,6,5,7,1,2,3,4]=>[6,7,8,1,4,3,5,2]=>0000000 [[1,4],[2,5],[3,6],[7],[8]]=>[[1,2,5],[3,6],[4,7],[8]]=>[8,4,7,3,6,1,2,5]=>[7,8,5,3,1,6,4,2]=>0000000 [[1,3],[2,5],[4,6],[7],[8]]=>[[1,2,4,5],[3,6],[7],[8]]=>[8,7,3,6,1,2,4,5]=>[6,7,4,8,1,5,3,2]=>0000000 [[1,2],[3,5],[4,6],[7],[8]]=>[[1,2,3,5],[4,6],[7],[8]]=>[8,7,4,6,1,2,3,5]=>[6,7,8,4,1,5,3,2]=>0000000 [[1,3],[2,4],[5,6],[7],[8]]=>[[1,2,4,6],[3,5],[7],[8]]=>[8,7,3,5,1,2,4,6]=>[6,7,4,8,5,1,3,2]=>0000000 [[1,2],[3,4],[5,6],[7],[8]]=>[[1,2,3,4],[5,6],[7],[8]]=>[8,7,5,6,1,2,3,4]=>[6,7,8,1,4,5,3,2]=>0000000 [[1,4],[2,8],[3],[5],[6],[7]]=>[[1,2,5,8],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5,8]=>[6,7,5,4,8,3,2,1]=>0000000 [[1,3],[2,8],[4],[5],[6],[7]]=>[[1,2,4,8],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4,8]=>[6,7,5,8,4,3,2,1]=>0000000 [[1,6],[2,7],[3],[4],[5],[8]]=>[[1,2,7],[3,8],[4],[5],[6]]=>[6,5,4,3,8,1,2,7]=>[7,8,5,4,3,2,1,6]=>0000000 [[1,3],[2,7],[4],[5],[6],[8]]=>[[1,2,4,7],[3],[5],[6],[8]]=>[8,6,5,3,1,2,4,7]=>[6,7,5,8,4,3,1,2]=>0000000 [[1,3],[2,6],[4],[5],[7],[8]]=>[[1,2,4,6],[3],[5],[7],[8]]=>[8,7,5,3,1,2,4,6]=>[6,7,5,8,4,1,3,2]=>0000000 [[1,4],[2,5],[3],[6],[7],[8]]=>[[1,2,5],[3,6],[4],[7],[8]]=>[8,7,4,3,6,1,2,5]=>[7,8,5,4,1,6,3,2]=>0000000 [[1,3],[2,5],[4],[6],[7],[8]]=>[[1,2,4,5],[3],[6],[7],[8]]=>[8,7,6,3,1,2,4,5]=>[6,7,5,8,1,4,3,2]=>0000000 [[1,2],[3,5],[4],[6],[7],[8]]=>[[1,2,3,5],[4],[6],[7],[8]]=>[8,7,6,4,1,2,3,5]=>[6,7,8,5,1,4,3,2]=>0000000 [[1,3],[2,4],[5],[6],[7],[8]]=>[[1,2,4],[3,5],[6],[7],[8]]=>[8,7,6,3,5,1,2,4]=>[7,8,5,1,6,4,3,2]=>0000000 [[1,2],[3,4],[5],[6],[7],[8]]=>[[1,2,3,4],[5],[6],[7],[8]]=>[8,7,6,5,1,2,3,4]=>[6,7,8,1,5,4,3,2]=>0000000 [[1,8],[2],[3],[4],[5],[6],[7]]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,1,2]=>[8,1,7,6,5,4,3,2]=>0000000 [[1,6],[2],[3],[4],[5],[7],[8]]=>[[1,2,7],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,1,2,7]=>[7,8,6,5,4,3,1,2]=>0000000 [[1,4],[2],[3],[5],[6],[7],[8]]=>[[1,2,5],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,1,2,5]=>[7,8,6,5,1,4,3,2]=>0000000 [[1,3],[2],[4],[5],[6],[7],[8]]=>[[1,2,4],[3],[5],[6],[7],[8]]=>[8,7,6,5,3,1,2,4]=>[7,8,6,1,5,4,3,2]=>0000000 [[1,2],[3],[4],[5],[6],[7],[8]]=>[[1,2,3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,1,2,3]=>[7,8,1,6,5,4,3,2]=>0000000 [[1],[2],[3],[4],[5],[6],[7],[8]]=>[[1,2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,1,2]=>[8,1,7,6,5,4,3,2]=>0000000
Map
catabolism
Description
Remove the first row of the standard tableau and insert it back using column Schensted insertion, starting with the largest number.
The algorithm for column-inserting an entry $k$ into tableau $T$ is as follows:
If $k$ is larger than all entries in the first column, place $k$ at the bottom of the first column and the procedure is finished. Otherwise, place $k$ in the first column, replacing the smallest entry, $y$, greater than $k$. Now insert $y$ into the second column using the same procedure: if $y$ is greater than all entries in the second column, place it at the bottom of that column (provided that the result is still a tableau). Otherwise, place $y$ in the second column, replacing, or 'bumping', the smallest entry, $z$, larger than $y$. Continue the procedure until we have placed a bumped entry at the bottom of a column (or on its own in a new column).
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
Kreweras complement
Description
Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $\pi^{-1}c$ where $c = (1,\ldots,n)$ is the long cycle.
Map
connectivity set
Description
The connectivity set of a permutation as a binary word.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.