Identifier
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Images
=>
Cc0007;cc-rep-0
[[1]]=>[1]=>[1]=> [[1,2]]=>[1,2]=>[2,1]=>0 [[1],[2]]=>[2,1]=>[1,2]=>1 [[1,2,3]]=>[1,2,3]=>[3,2,1]=>00 [[1,3],[2]]=>[2,1,3]=>[3,1,2]=>00 [[1,2],[3]]=>[3,1,2]=>[2,1,3]=>01 [[1],[2],[3]]=>[3,2,1]=>[1,2,3]=>11 [[1,2,3,4]]=>[1,2,3,4]=>[4,3,2,1]=>000 [[1,3,4],[2]]=>[2,1,3,4]=>[4,3,1,2]=>000 [[1,2,4],[3]]=>[3,1,2,4]=>[4,2,1,3]=>000 [[1,2,3],[4]]=>[4,1,2,3]=>[3,2,1,4]=>001 [[1,3],[2,4]]=>[2,4,1,3]=>[3,1,4,2]=>000 [[1,2],[3,4]]=>[3,4,1,2]=>[2,1,4,3]=>010 [[1,4],[2],[3]]=>[3,2,1,4]=>[4,1,2,3]=>000 [[1,3],[2],[4]]=>[4,2,1,3]=>[3,1,2,4]=>001 [[1,2],[3],[4]]=>[4,3,1,2]=>[2,1,3,4]=>011 [[1],[2],[3],[4]]=>[4,3,2,1]=>[1,2,3,4]=>111 [[1,2,3,4,5]]=>[1,2,3,4,5]=>[5,4,3,2,1]=>0000 [[1,3,4,5],[2]]=>[2,1,3,4,5]=>[5,4,3,1,2]=>0000 [[1,2,4,5],[3]]=>[3,1,2,4,5]=>[5,4,2,1,3]=>0000 [[1,2,3,5],[4]]=>[4,1,2,3,5]=>[5,3,2,1,4]=>0000 [[1,2,3,4],[5]]=>[5,1,2,3,4]=>[4,3,2,1,5]=>0001 [[1,3,5],[2,4]]=>[2,4,1,3,5]=>[5,3,1,4,2]=>0000 [[1,2,5],[3,4]]=>[3,4,1,2,5]=>[5,2,1,4,3]=>0000 [[1,3,4],[2,5]]=>[2,5,1,3,4]=>[4,3,1,5,2]=>0000 [[1,2,4],[3,5]]=>[3,5,1,2,4]=>[4,2,1,5,3]=>0000 [[1,2,3],[4,5]]=>[4,5,1,2,3]=>[3,2,1,5,4]=>0010 [[1,4,5],[2],[3]]=>[3,2,1,4,5]=>[5,4,1,2,3]=>0000 [[1,3,5],[2],[4]]=>[4,2,1,3,5]=>[5,3,1,2,4]=>0000 [[1,2,5],[3],[4]]=>[4,3,1,2,5]=>[5,2,1,3,4]=>0000 [[1,3,4],[2],[5]]=>[5,2,1,3,4]=>[4,3,1,2,5]=>0001 [[1,2,4],[3],[5]]=>[5,3,1,2,4]=>[4,2,1,3,5]=>0001 [[1,2,3],[4],[5]]=>[5,4,1,2,3]=>[3,2,1,4,5]=>0011 [[1,4],[2,5],[3]]=>[3,2,5,1,4]=>[4,1,5,2,3]=>0000 [[1,3],[2,5],[4]]=>[4,2,5,1,3]=>[3,1,5,2,4]=>0000 [[1,2],[3,5],[4]]=>[4,3,5,1,2]=>[2,1,5,3,4]=>0100 [[1,3],[2,4],[5]]=>[5,2,4,1,3]=>[3,1,4,2,5]=>0001 [[1,2],[3,4],[5]]=>[5,3,4,1,2]=>[2,1,4,3,5]=>0101 [[1,5],[2],[3],[4]]=>[4,3,2,1,5]=>[5,1,2,3,4]=>0000 [[1,4],[2],[3],[5]]=>[5,3,2,1,4]=>[4,1,2,3,5]=>0001 [[1,3],[2],[4],[5]]=>[5,4,2,1,3]=>[3,1,2,4,5]=>0011 [[1,2],[3],[4],[5]]=>[5,4,3,1,2]=>[2,1,3,4,5]=>0111 [[1],[2],[3],[4],[5]]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1111 [[1,2,3,4,5,6]]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>00000 [[1,3,4,5,6],[2]]=>[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>00000 [[1,2,4,5,6],[3]]=>[3,1,2,4,5,6]=>[6,5,4,2,1,3]=>00000 [[1,2,3,5,6],[4]]=>[4,1,2,3,5,6]=>[6,5,3,2,1,4]=>00000 [[1,2,3,4,6],[5]]=>[5,1,2,3,4,6]=>[6,4,3,2,1,5]=>00000 [[1,2,3,4,5],[6]]=>[6,1,2,3,4,5]=>[5,4,3,2,1,6]=>00001 [[1,3,5,6],[2,4]]=>[2,4,1,3,5,6]=>[6,5,3,1,4,2]=>00000 [[1,2,5,6],[3,4]]=>[3,4,1,2,5,6]=>[6,5,2,1,4,3]=>00000 [[1,3,4,6],[2,5]]=>[2,5,1,3,4,6]=>[6,4,3,1,5,2]=>00000 [[1,2,4,6],[3,5]]=>[3,5,1,2,4,6]=>[6,4,2,1,5,3]=>00000 [[1,2,3,6],[4,5]]=>[4,5,1,2,3,6]=>[6,3,2,1,5,4]=>00000 [[1,3,4,5],[2,6]]=>[2,6,1,3,4,5]=>[5,4,3,1,6,2]=>00000 [[1,2,4,5],[3,6]]=>[3,6,1,2,4,5]=>[5,4,2,1,6,3]=>00000 [[1,2,3,5],[4,6]]=>[4,6,1,2,3,5]=>[5,3,2,1,6,4]=>00000 [[1,2,3,4],[5,6]]=>[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>00010 [[1,4,5,6],[2],[3]]=>[3,2,1,4,5,6]=>[6,5,4,1,2,3]=>00000 [[1,3,5,6],[2],[4]]=>[4,2,1,3,5,6]=>[6,5,3,1,2,4]=>00000 [[1,2,5,6],[3],[4]]=>[4,3,1,2,5,6]=>[6,5,2,1,3,4]=>00000 [[1,3,4,6],[2],[5]]=>[5,2,1,3,4,6]=>[6,4,3,1,2,5]=>00000 [[1,2,4,6],[3],[5]]=>[5,3,1,2,4,6]=>[6,4,2,1,3,5]=>00000 [[1,2,3,6],[4],[5]]=>[5,4,1,2,3,6]=>[6,3,2,1,4,5]=>00000 [[1,3,4,5],[2],[6]]=>[6,2,1,3,4,5]=>[5,4,3,1,2,6]=>00001 [[1,2,4,5],[3],[6]]=>[6,3,1,2,4,5]=>[5,4,2,1,3,6]=>00001 [[1,2,3,5],[4],[6]]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>00001 [[1,2,3,4],[5],[6]]=>[6,5,1,2,3,4]=>[4,3,2,1,5,6]=>00011 [[1,3,5],[2,4,6]]=>[2,4,6,1,3,5]=>[5,3,1,6,4,2]=>00000 [[1,2,5],[3,4,6]]=>[3,4,6,1,2,5]=>[5,2,1,6,4,3]=>00000 [[1,3,4],[2,5,6]]=>[2,5,6,1,3,4]=>[4,3,1,6,5,2]=>00000 [[1,2,4],[3,5,6]]=>[3,5,6,1,2,4]=>[4,2,1,6,5,3]=>00000 [[1,2,3],[4,5,6]]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>00100 [[1,4,6],[2,5],[3]]=>[3,2,5,1,4,6]=>[6,4,1,5,2,3]=>00000 [[1,3,6],[2,5],[4]]=>[4,2,5,1,3,6]=>[6,3,1,5,2,4]=>00000 [[1,2,6],[3,5],[4]]=>[4,3,5,1,2,6]=>[6,2,1,5,3,4]=>00000 [[1,3,6],[2,4],[5]]=>[5,2,4,1,3,6]=>[6,3,1,4,2,5]=>00000 [[1,2,6],[3,4],[5]]=>[5,3,4,1,2,6]=>[6,2,1,4,3,5]=>00000 [[1,4,5],[2,6],[3]]=>[3,2,6,1,4,5]=>[5,4,1,6,2,3]=>00000 [[1,3,5],[2,6],[4]]=>[4,2,6,1,3,5]=>[5,3,1,6,2,4]=>00000 [[1,2,5],[3,6],[4]]=>[4,3,6,1,2,5]=>[5,2,1,6,3,4]=>00000 [[1,3,4],[2,6],[5]]=>[5,2,6,1,3,4]=>[4,3,1,6,2,5]=>00000 [[1,2,4],[3,6],[5]]=>[5,3,6,1,2,4]=>[4,2,1,6,3,5]=>00000 [[1,2,3],[4,6],[5]]=>[5,4,6,1,2,3]=>[3,2,1,6,4,5]=>00100 [[1,3,5],[2,4],[6]]=>[6,2,4,1,3,5]=>[5,3,1,4,2,6]=>00001 [[1,2,5],[3,4],[6]]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>00001 [[1,3,4],[2,5],[6]]=>[6,2,5,1,3,4]=>[4,3,1,5,2,6]=>00001 [[1,2,4],[3,5],[6]]=>[6,3,5,1,2,4]=>[4,2,1,5,3,6]=>00001 [[1,2,3],[4,5],[6]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>00101 [[1,5,6],[2],[3],[4]]=>[4,3,2,1,5,6]=>[6,5,1,2,3,4]=>00000 [[1,4,6],[2],[3],[5]]=>[5,3,2,1,4,6]=>[6,4,1,2,3,5]=>00000 [[1,3,6],[2],[4],[5]]=>[5,4,2,1,3,6]=>[6,3,1,2,4,5]=>00000 [[1,2,6],[3],[4],[5]]=>[5,4,3,1,2,6]=>[6,2,1,3,4,5]=>00000 [[1,4,5],[2],[3],[6]]=>[6,3,2,1,4,5]=>[5,4,1,2,3,6]=>00001 [[1,3,5],[2],[4],[6]]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>00001 [[1,2,5],[3],[4],[6]]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>00001 [[1,3,4],[2],[5],[6]]=>[6,5,2,1,3,4]=>[4,3,1,2,5,6]=>00011 [[1,2,4],[3],[5],[6]]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>00011 [[1,2,3],[4],[5],[6]]=>[6,5,4,1,2,3]=>[3,2,1,4,5,6]=>00111 [[1,4],[2,5],[3,6]]=>[3,6,2,5,1,4]=>[4,1,5,2,6,3]=>00000 [[1,3],[2,5],[4,6]]=>[4,6,2,5,1,3]=>[3,1,5,2,6,4]=>00000 [[1,2],[3,5],[4,6]]=>[4,6,3,5,1,2]=>[2,1,5,3,6,4]=>01000 [[1,3],[2,4],[5,6]]=>[5,6,2,4,1,3]=>[3,1,4,2,6,5]=>00010 [[1,2],[3,4],[5,6]]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>01010 [[1,5],[2,6],[3],[4]]=>[4,3,2,6,1,5]=>[5,1,6,2,3,4]=>00000 [[1,4],[2,6],[3],[5]]=>[5,3,2,6,1,4]=>[4,1,6,2,3,5]=>00000 [[1,3],[2,6],[4],[5]]=>[5,4,2,6,1,3]=>[3,1,6,2,4,5]=>00000 [[1,2],[3,6],[4],[5]]=>[5,4,3,6,1,2]=>[2,1,6,3,4,5]=>01000 [[1,4],[2,5],[3],[6]]=>[6,3,2,5,1,4]=>[4,1,5,2,3,6]=>00001 [[1,3],[2,5],[4],[6]]=>[6,4,2,5,1,3]=>[3,1,5,2,4,6]=>00001 [[1,2],[3,5],[4],[6]]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>01001 [[1,3],[2,4],[5],[6]]=>[6,5,2,4,1,3]=>[3,1,4,2,5,6]=>00011 [[1,2],[3,4],[5],[6]]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>01011 [[1,6],[2],[3],[4],[5]]=>[5,4,3,2,1,6]=>[6,1,2,3,4,5]=>00000 [[1,5],[2],[3],[4],[6]]=>[6,4,3,2,1,5]=>[5,1,2,3,4,6]=>00001 [[1,4],[2],[3],[5],[6]]=>[6,5,3,2,1,4]=>[4,1,2,3,5,6]=>00011 [[1,3],[2],[4],[5],[6]]=>[6,5,4,2,1,3]=>[3,1,2,4,5,6]=>00111 [[1,2],[3],[4],[5],[6]]=>[6,5,4,3,1,2]=>[2,1,3,4,5,6]=>01111 [[1],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>11111 [[1,2,3,4,5,6,7]]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>000000 [[1,3,4,5,6,7],[2]]=>[2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2]=>000000 [[1,2,4,5,6,7],[3]]=>[3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3]=>000000 [[1,2,3,5,6,7],[4]]=>[4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4]=>000000 [[1,2,3,4,6,7],[5]]=>[5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5]=>000000 [[1,2,3,4,5,7],[6]]=>[6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6]=>000000 [[1,2,3,4,5,6],[7]]=>[7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7]=>000001 [[1,3,5,6,7],[2,4]]=>[2,4,1,3,5,6,7]=>[7,6,5,3,1,4,2]=>000000 [[1,2,5,6,7],[3,4]]=>[3,4,1,2,5,6,7]=>[7,6,5,2,1,4,3]=>000000 [[1,3,4,6,7],[2,5]]=>[2,5,1,3,4,6,7]=>[7,6,4,3,1,5,2]=>000000 [[1,2,4,6,7],[3,5]]=>[3,5,1,2,4,6,7]=>[7,6,4,2,1,5,3]=>000000 [[1,2,3,6,7],[4,5]]=>[4,5,1,2,3,6,7]=>[7,6,3,2,1,5,4]=>000000 [[1,3,4,5,7],[2,6]]=>[2,6,1,3,4,5,7]=>[7,5,4,3,1,6,2]=>000000 [[1,2,4,5,7],[3,6]]=>[3,6,1,2,4,5,7]=>[7,5,4,2,1,6,3]=>000000 [[1,2,3,5,7],[4,6]]=>[4,6,1,2,3,5,7]=>[7,5,3,2,1,6,4]=>000000 [[1,2,3,4,7],[5,6]]=>[5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5]=>000000 [[1,3,4,5,6],[2,7]]=>[2,7,1,3,4,5,6]=>[6,5,4,3,1,7,2]=>000000 [[1,2,4,5,6],[3,7]]=>[3,7,1,2,4,5,6]=>[6,5,4,2,1,7,3]=>000000 [[1,2,3,5,6],[4,7]]=>[4,7,1,2,3,5,6]=>[6,5,3,2,1,7,4]=>000000 [[1,2,3,4,6],[5,7]]=>[5,7,1,2,3,4,6]=>[6,4,3,2,1,7,5]=>000000 [[1,2,3,4,5],[6,7]]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>000010 [[1,4,5,6,7],[2],[3]]=>[3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3]=>000000 [[1,3,5,6,7],[2],[4]]=>[4,2,1,3,5,6,7]=>[7,6,5,3,1,2,4]=>000000 [[1,2,5,6,7],[3],[4]]=>[4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4]=>000000 [[1,3,4,6,7],[2],[5]]=>[5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5]=>000000 [[1,2,4,6,7],[3],[5]]=>[5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5]=>000000 [[1,2,3,6,7],[4],[5]]=>[5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5]=>000000 [[1,3,4,5,7],[2],[6]]=>[6,2,1,3,4,5,7]=>[7,5,4,3,1,2,6]=>000000 [[1,2,4,5,7],[3],[6]]=>[6,3,1,2,4,5,7]=>[7,5,4,2,1,3,6]=>000000 [[1,2,3,5,7],[4],[6]]=>[6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6]=>000000 [[1,2,3,4,7],[5],[6]]=>[6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6]=>000000 [[1,3,4,5,6],[2],[7]]=>[7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7]=>000001 [[1,2,4,5,6],[3],[7]]=>[7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7]=>000001 [[1,2,3,5,6],[4],[7]]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>000001 [[1,2,3,4,6],[5],[7]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>000001 [[1,2,3,4,5],[6],[7]]=>[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>000011 [[1,3,5,7],[2,4,6]]=>[2,4,6,1,3,5,7]=>[7,5,3,1,6,4,2]=>000000 [[1,2,5,7],[3,4,6]]=>[3,4,6,1,2,5,7]=>[7,5,2,1,6,4,3]=>000000 [[1,3,4,7],[2,5,6]]=>[2,5,6,1,3,4,7]=>[7,4,3,1,6,5,2]=>000000 [[1,2,4,7],[3,5,6]]=>[3,5,6,1,2,4,7]=>[7,4,2,1,6,5,3]=>000000 [[1,2,3,7],[4,5,6]]=>[4,5,6,1,2,3,7]=>[7,3,2,1,6,5,4]=>000000 [[1,3,5,6],[2,4,7]]=>[2,4,7,1,3,5,6]=>[6,5,3,1,7,4,2]=>000000 [[1,2,5,6],[3,4,7]]=>[3,4,7,1,2,5,6]=>[6,5,2,1,7,4,3]=>000000 [[1,3,4,6],[2,5,7]]=>[2,5,7,1,3,4,6]=>[6,4,3,1,7,5,2]=>000000 [[1,2,4,6],[3,5,7]]=>[3,5,7,1,2,4,6]=>[6,4,2,1,7,5,3]=>000000 [[1,2,3,6],[4,5,7]]=>[4,5,7,1,2,3,6]=>[6,3,2,1,7,5,4]=>000000 [[1,3,4,5],[2,6,7]]=>[2,6,7,1,3,4,5]=>[5,4,3,1,7,6,2]=>000000 [[1,2,4,5],[3,6,7]]=>[3,6,7,1,2,4,5]=>[5,4,2,1,7,6,3]=>000000 [[1,2,3,5],[4,6,7]]=>[4,6,7,1,2,3,5]=>[5,3,2,1,7,6,4]=>000000 [[1,2,3,4],[5,6,7]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>000100 [[1,4,6,7],[2,5],[3]]=>[3,2,5,1,4,6,7]=>[7,6,4,1,5,2,3]=>000000 [[1,3,6,7],[2,5],[4]]=>[4,2,5,1,3,6,7]=>[7,6,3,1,5,2,4]=>000000 [[1,2,6,7],[3,5],[4]]=>[4,3,5,1,2,6,7]=>[7,6,2,1,5,3,4]=>000000 [[1,3,6,7],[2,4],[5]]=>[5,2,4,1,3,6,7]=>[7,6,3,1,4,2,5]=>000000 [[1,2,6,7],[3,4],[5]]=>[5,3,4,1,2,6,7]=>[7,6,2,1,4,3,5]=>000000 [[1,4,5,7],[2,6],[3]]=>[3,2,6,1,4,5,7]=>[7,5,4,1,6,2,3]=>000000 [[1,3,5,7],[2,6],[4]]=>[4,2,6,1,3,5,7]=>[7,5,3,1,6,2,4]=>000000 [[1,2,5,7],[3,6],[4]]=>[4,3,6,1,2,5,7]=>[7,5,2,1,6,3,4]=>000000 [[1,3,4,7],[2,6],[5]]=>[5,2,6,1,3,4,7]=>[7,4,3,1,6,2,5]=>000000 [[1,2,4,7],[3,6],[5]]=>[5,3,6,1,2,4,7]=>[7,4,2,1,6,3,5]=>000000 [[1,2,3,7],[4,6],[5]]=>[5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5]=>000000 [[1,3,5,7],[2,4],[6]]=>[6,2,4,1,3,5,7]=>[7,5,3,1,4,2,6]=>000000 [[1,2,5,7],[3,4],[6]]=>[6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6]=>000000 [[1,3,4,7],[2,5],[6]]=>[6,2,5,1,3,4,7]=>[7,4,3,1,5,2,6]=>000000 [[1,2,4,7],[3,5],[6]]=>[6,3,5,1,2,4,7]=>[7,4,2,1,5,3,6]=>000000 [[1,2,3,7],[4,5],[6]]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>000000 [[1,4,5,6],[2,7],[3]]=>[3,2,7,1,4,5,6]=>[6,5,4,1,7,2,3]=>000000 [[1,3,5,6],[2,7],[4]]=>[4,2,7,1,3,5,6]=>[6,5,3,1,7,2,4]=>000000 [[1,2,5,6],[3,7],[4]]=>[4,3,7,1,2,5,6]=>[6,5,2,1,7,3,4]=>000000 [[1,3,4,6],[2,7],[5]]=>[5,2,7,1,3,4,6]=>[6,4,3,1,7,2,5]=>000000 [[1,2,4,6],[3,7],[5]]=>[5,3,7,1,2,4,6]=>[6,4,2,1,7,3,5]=>000000 [[1,2,3,6],[4,7],[5]]=>[5,4,7,1,2,3,6]=>[6,3,2,1,7,4,5]=>000000 [[1,3,4,5],[2,7],[6]]=>[6,2,7,1,3,4,5]=>[5,4,3,1,7,2,6]=>000000 [[1,2,4,5],[3,7],[6]]=>[6,3,7,1,2,4,5]=>[5,4,2,1,7,3,6]=>000000 [[1,2,3,5],[4,7],[6]]=>[6,4,7,1,2,3,5]=>[5,3,2,1,7,4,6]=>000000 [[1,2,3,4],[5,7],[6]]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>000100 [[1,3,5,6],[2,4],[7]]=>[7,2,4,1,3,5,6]=>[6,5,3,1,4,2,7]=>000001 [[1,2,5,6],[3,4],[7]]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>000001 [[1,3,4,6],[2,5],[7]]=>[7,2,5,1,3,4,6]=>[6,4,3,1,5,2,7]=>000001 [[1,2,4,6],[3,5],[7]]=>[7,3,5,1,2,4,6]=>[6,4,2,1,5,3,7]=>000001 [[1,2,3,6],[4,5],[7]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>000001 [[1,3,4,5],[2,6],[7]]=>[7,2,6,1,3,4,5]=>[5,4,3,1,6,2,7]=>000001 [[1,2,4,5],[3,6],[7]]=>[7,3,6,1,2,4,5]=>[5,4,2,1,6,3,7]=>000001 [[1,2,3,5],[4,6],[7]]=>[7,4,6,1,2,3,5]=>[5,3,2,1,6,4,7]=>000001 [[1,2,3,4],[5,6],[7]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>000101 [[1,5,6,7],[2],[3],[4]]=>[4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4]=>000000 [[1,4,6,7],[2],[3],[5]]=>[5,3,2,1,4,6,7]=>[7,6,4,1,2,3,5]=>000000 [[1,3,6,7],[2],[4],[5]]=>[5,4,2,1,3,6,7]=>[7,6,3,1,2,4,5]=>000000 [[1,2,6,7],[3],[4],[5]]=>[5,4,3,1,2,6,7]=>[7,6,2,1,3,4,5]=>000000 [[1,4,5,7],[2],[3],[6]]=>[6,3,2,1,4,5,7]=>[7,5,4,1,2,3,6]=>000000 [[1,3,5,7],[2],[4],[6]]=>[6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6]=>000000 [[1,2,5,7],[3],[4],[6]]=>[6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6]=>000000 [[1,3,4,7],[2],[5],[6]]=>[6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6]=>000000 [[1,2,4,7],[3],[5],[6]]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>000000 [[1,2,3,7],[4],[5],[6]]=>[6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6]=>000000 [[1,4,5,6],[2],[3],[7]]=>[7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7]=>000001 [[1,3,5,6],[2],[4],[7]]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>000001 [[1,2,5,6],[3],[4],[7]]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>000001 [[1,3,4,6],[2],[5],[7]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>000001 [[1,2,4,6],[3],[5],[7]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>000001 [[1,2,3,6],[4],[5],[7]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>000001 [[1,3,4,5],[2],[6],[7]]=>[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>000011 [[1,2,4,5],[3],[6],[7]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>000011 [[1,2,3,5],[4],[6],[7]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>000011 [[1,2,3,4],[5],[6],[7]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>000111 [[1,4,6],[2,5,7],[3]]=>[3,2,5,7,1,4,6]=>[6,4,1,7,5,2,3]=>000000 [[1,3,6],[2,5,7],[4]]=>[4,2,5,7,1,3,6]=>[6,3,1,7,5,2,4]=>000000 [[1,2,6],[3,5,7],[4]]=>[4,3,5,7,1,2,6]=>[6,2,1,7,5,3,4]=>000000 [[1,3,6],[2,4,7],[5]]=>[5,2,4,7,1,3,6]=>[6,3,1,7,4,2,5]=>000000 [[1,2,6],[3,4,7],[5]]=>[5,3,4,7,1,2,6]=>[6,2,1,7,4,3,5]=>000000 [[1,4,5],[2,6,7],[3]]=>[3,2,6,7,1,4,5]=>[5,4,1,7,6,2,3]=>000000 [[1,3,5],[2,6,7],[4]]=>[4,2,6,7,1,3,5]=>[5,3,1,7,6,2,4]=>000000 [[1,2,5],[3,6,7],[4]]=>[4,3,6,7,1,2,5]=>[5,2,1,7,6,3,4]=>000000 [[1,3,4],[2,6,7],[5]]=>[5,2,6,7,1,3,4]=>[4,3,1,7,6,2,5]=>000000 [[1,2,4],[3,6,7],[5]]=>[5,3,6,7,1,2,4]=>[4,2,1,7,6,3,5]=>000000 [[1,2,3],[4,6,7],[5]]=>[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>001000 [[1,3,5],[2,4,7],[6]]=>[6,2,4,7,1,3,5]=>[5,3,1,7,4,2,6]=>000000 [[1,2,5],[3,4,7],[6]]=>[6,3,4,7,1,2,5]=>[5,2,1,7,4,3,6]=>000000 [[1,3,4],[2,5,7],[6]]=>[6,2,5,7,1,3,4]=>[4,3,1,7,5,2,6]=>000000 [[1,2,4],[3,5,7],[6]]=>[6,3,5,7,1,2,4]=>[4,2,1,7,5,3,6]=>000000 [[1,2,3],[4,5,7],[6]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>001000 [[1,3,5],[2,4,6],[7]]=>[7,2,4,6,1,3,5]=>[5,3,1,6,4,2,7]=>000001 [[1,2,5],[3,4,6],[7]]=>[7,3,4,6,1,2,5]=>[5,2,1,6,4,3,7]=>000001 [[1,3,4],[2,5,6],[7]]=>[7,2,5,6,1,3,4]=>[4,3,1,6,5,2,7]=>000001 [[1,2,4],[3,5,6],[7]]=>[7,3,5,6,1,2,4]=>[4,2,1,6,5,3,7]=>000001 [[1,2,3],[4,5,6],[7]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>001001 [[1,4,7],[2,5],[3,6]]=>[3,6,2,5,1,4,7]=>[7,4,1,5,2,6,3]=>000000 [[1,3,7],[2,5],[4,6]]=>[4,6,2,5,1,3,7]=>[7,3,1,5,2,6,4]=>000000 [[1,2,7],[3,5],[4,6]]=>[4,6,3,5,1,2,7]=>[7,2,1,5,3,6,4]=>000000 [[1,3,7],[2,4],[5,6]]=>[5,6,2,4,1,3,7]=>[7,3,1,4,2,6,5]=>000000 [[1,2,7],[3,4],[5,6]]=>[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>000000 [[1,4,6],[2,5],[3,7]]=>[3,7,2,5,1,4,6]=>[6,4,1,5,2,7,3]=>000000 [[1,3,6],[2,5],[4,7]]=>[4,7,2,5,1,3,6]=>[6,3,1,5,2,7,4]=>000000 [[1,2,6],[3,5],[4,7]]=>[4,7,3,5,1,2,6]=>[6,2,1,5,3,7,4]=>000000 [[1,3,6],[2,4],[5,7]]=>[5,7,2,4,1,3,6]=>[6,3,1,4,2,7,5]=>000000 [[1,2,6],[3,4],[5,7]]=>[5,7,3,4,1,2,6]=>[6,2,1,4,3,7,5]=>000000 [[1,4,5],[2,6],[3,7]]=>[3,7,2,6,1,4,5]=>[5,4,1,6,2,7,3]=>000000 [[1,3,5],[2,6],[4,7]]=>[4,7,2,6,1,3,5]=>[5,3,1,6,2,7,4]=>000000 [[1,2,5],[3,6],[4,7]]=>[4,7,3,6,1,2,5]=>[5,2,1,6,3,7,4]=>000000 [[1,3,4],[2,6],[5,7]]=>[5,7,2,6,1,3,4]=>[4,3,1,6,2,7,5]=>000000 [[1,2,4],[3,6],[5,7]]=>[5,7,3,6,1,2,4]=>[4,2,1,6,3,7,5]=>000000 [[1,2,3],[4,6],[5,7]]=>[5,7,4,6,1,2,3]=>[3,2,1,6,4,7,5]=>001000 [[1,3,5],[2,4],[6,7]]=>[6,7,2,4,1,3,5]=>[5,3,1,4,2,7,6]=>000010 [[1,2,5],[3,4],[6,7]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>000010 [[1,3,4],[2,5],[6,7]]=>[6,7,2,5,1,3,4]=>[4,3,1,5,2,7,6]=>000010 [[1,2,4],[3,5],[6,7]]=>[6,7,3,5,1,2,4]=>[4,2,1,5,3,7,6]=>000010 [[1,2,3],[4,5],[6,7]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>001010 [[1,5,7],[2,6],[3],[4]]=>[4,3,2,6,1,5,7]=>[7,5,1,6,2,3,4]=>000000 [[1,4,7],[2,6],[3],[5]]=>[5,3,2,6,1,4,7]=>[7,4,1,6,2,3,5]=>000000 [[1,3,7],[2,6],[4],[5]]=>[5,4,2,6,1,3,7]=>[7,3,1,6,2,4,5]=>000000 [[1,2,7],[3,6],[4],[5]]=>[5,4,3,6,1,2,7]=>[7,2,1,6,3,4,5]=>000000 [[1,4,7],[2,5],[3],[6]]=>[6,3,2,5,1,4,7]=>[7,4,1,5,2,3,6]=>000000 [[1,3,7],[2,5],[4],[6]]=>[6,4,2,5,1,3,7]=>[7,3,1,5,2,4,6]=>000000 [[1,2,7],[3,5],[4],[6]]=>[6,4,3,5,1,2,7]=>[7,2,1,5,3,4,6]=>000000 [[1,3,7],[2,4],[5],[6]]=>[6,5,2,4,1,3,7]=>[7,3,1,4,2,5,6]=>000000 [[1,2,7],[3,4],[5],[6]]=>[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>000000 [[1,5,6],[2,7],[3],[4]]=>[4,3,2,7,1,5,6]=>[6,5,1,7,2,3,4]=>000000 [[1,4,6],[2,7],[3],[5]]=>[5,3,2,7,1,4,6]=>[6,4,1,7,2,3,5]=>000000 [[1,3,6],[2,7],[4],[5]]=>[5,4,2,7,1,3,6]=>[6,3,1,7,2,4,5]=>000000 [[1,2,6],[3,7],[4],[5]]=>[5,4,3,7,1,2,6]=>[6,2,1,7,3,4,5]=>000000 [[1,4,5],[2,7],[3],[6]]=>[6,3,2,7,1,4,5]=>[5,4,1,7,2,3,6]=>000000 [[1,3,5],[2,7],[4],[6]]=>[6,4,2,7,1,3,5]=>[5,3,1,7,2,4,6]=>000000 [[1,2,5],[3,7],[4],[6]]=>[6,4,3,7,1,2,5]=>[5,2,1,7,3,4,6]=>000000 [[1,3,4],[2,7],[5],[6]]=>[6,5,2,7,1,3,4]=>[4,3,1,7,2,5,6]=>000000 [[1,2,4],[3,7],[5],[6]]=>[6,5,3,7,1,2,4]=>[4,2,1,7,3,5,6]=>000000 [[1,2,3],[4,7],[5],[6]]=>[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>001000 [[1,4,6],[2,5],[3],[7]]=>[7,3,2,5,1,4,6]=>[6,4,1,5,2,3,7]=>000001 [[1,3,6],[2,5],[4],[7]]=>[7,4,2,5,1,3,6]=>[6,3,1,5,2,4,7]=>000001 [[1,2,6],[3,5],[4],[7]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>000001 [[1,3,6],[2,4],[5],[7]]=>[7,5,2,4,1,3,6]=>[6,3,1,4,2,5,7]=>000001 [[1,2,6],[3,4],[5],[7]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>000001 [[1,4,5],[2,6],[3],[7]]=>[7,3,2,6,1,4,5]=>[5,4,1,6,2,3,7]=>000001 [[1,3,5],[2,6],[4],[7]]=>[7,4,2,6,1,3,5]=>[5,3,1,6,2,4,7]=>000001 [[1,2,5],[3,6],[4],[7]]=>[7,4,3,6,1,2,5]=>[5,2,1,6,3,4,7]=>000001 [[1,3,4],[2,6],[5],[7]]=>[7,5,2,6,1,3,4]=>[4,3,1,6,2,5,7]=>000001 [[1,2,4],[3,6],[5],[7]]=>[7,5,3,6,1,2,4]=>[4,2,1,6,3,5,7]=>000001 [[1,2,3],[4,6],[5],[7]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>001001 [[1,3,5],[2,4],[6],[7]]=>[7,6,2,4,1,3,5]=>[5,3,1,4,2,6,7]=>000011 [[1,2,5],[3,4],[6],[7]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>000011 [[1,3,4],[2,5],[6],[7]]=>[7,6,2,5,1,3,4]=>[4,3,1,5,2,6,7]=>000011 [[1,2,4],[3,5],[6],[7]]=>[7,6,3,5,1,2,4]=>[4,2,1,5,3,6,7]=>000011 [[1,2,3],[4,5],[6],[7]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>001011 [[1,6,7],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5]=>000000 [[1,5,7],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6]=>000000 [[1,4,7],[2],[3],[5],[6]]=>[6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6]=>000000 [[1,3,7],[2],[4],[5],[6]]=>[6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6]=>000000 [[1,2,7],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6]=>000000 [[1,5,6],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6]=>[6,5,1,2,3,4,7]=>000001 [[1,4,6],[2],[3],[5],[7]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>000001 [[1,3,6],[2],[4],[5],[7]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>000001 [[1,2,6],[3],[4],[5],[7]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>000001 [[1,4,5],[2],[3],[6],[7]]=>[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>000011 [[1,3,5],[2],[4],[6],[7]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>000011 [[1,2,5],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>000011 [[1,3,4],[2],[5],[6],[7]]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>000111 [[1,2,4],[3],[5],[6],[7]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>000111 [[1,2,3],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>001111 [[1,5],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5]=>[5,1,6,2,7,3,4]=>000000 [[1,4],[2,6],[3,7],[5]]=>[5,3,7,2,6,1,4]=>[4,1,6,2,7,3,5]=>000000 [[1,3],[2,6],[4,7],[5]]=>[5,4,7,2,6,1,3]=>[3,1,6,2,7,4,5]=>000000 [[1,2],[3,6],[4,7],[5]]=>[5,4,7,3,6,1,2]=>[2,1,6,3,7,4,5]=>010000 [[1,4],[2,5],[3,7],[6]]=>[6,3,7,2,5,1,4]=>[4,1,5,2,7,3,6]=>000000 [[1,3],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3]=>[3,1,5,2,7,4,6]=>000000 [[1,2],[3,5],[4,7],[6]]=>[6,4,7,3,5,1,2]=>[2,1,5,3,7,4,6]=>010000 [[1,3],[2,4],[5,7],[6]]=>[6,5,7,2,4,1,3]=>[3,1,4,2,7,5,6]=>000100 [[1,2],[3,4],[5,7],[6]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>010100 [[1,4],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4]=>[4,1,5,2,6,3,7]=>000001 [[1,3],[2,5],[4,6],[7]]=>[7,4,6,2,5,1,3]=>[3,1,5,2,6,4,7]=>000001 [[1,2],[3,5],[4,6],[7]]=>[7,4,6,3,5,1,2]=>[2,1,5,3,6,4,7]=>010001 [[1,3],[2,4],[5,6],[7]]=>[7,5,6,2,4,1,3]=>[3,1,4,2,6,5,7]=>000101 [[1,2],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>010101 [[1,6],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6]=>[6,1,7,2,3,4,5]=>000000 [[1,5],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5]=>[5,1,7,2,3,4,6]=>000000 [[1,4],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4]=>[4,1,7,2,3,5,6]=>000000 [[1,3],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3]=>[3,1,7,2,4,5,6]=>000000 [[1,2],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6]=>010000 [[1,5],[2,6],[3],[4],[7]]=>[7,4,3,2,6,1,5]=>[5,1,6,2,3,4,7]=>000001 [[1,4],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4]=>[4,1,6,2,3,5,7]=>000001 [[1,3],[2,6],[4],[5],[7]]=>[7,5,4,2,6,1,3]=>[3,1,6,2,4,5,7]=>000001 [[1,2],[3,6],[4],[5],[7]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>010001 [[1,4],[2,5],[3],[6],[7]]=>[7,6,3,2,5,1,4]=>[4,1,5,2,3,6,7]=>000011 [[1,3],[2,5],[4],[6],[7]]=>[7,6,4,2,5,1,3]=>[3,1,5,2,4,6,7]=>000011 [[1,2],[3,5],[4],[6],[7]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>010011 [[1,3],[2,4],[5],[6],[7]]=>[7,6,5,2,4,1,3]=>[3,1,4,2,5,6,7]=>000111 [[1,2],[3,4],[5],[6],[7]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>010111 [[1,7],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6]=>000000 [[1,6],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7]=>000001 [[1,5],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>000011 [[1,4],[2],[3],[5],[6],[7]]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>000111 [[1,3],[2],[4],[5],[6],[7]]=>[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>001111 [[1,2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7]=>011111 [[1],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>111111 [[1,2,3,4,5,6,7,8]]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>0000000 [[1,3,4,5,6,7,8],[2]]=>[2,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,2]=>0000000 [[1,2,4,5,6,7,8],[3]]=>[3,1,2,4,5,6,7,8]=>[8,7,6,5,4,2,1,3]=>0000000 [[1,2,3,5,6,7,8],[4]]=>[4,1,2,3,5,6,7,8]=>[8,7,6,5,3,2,1,4]=>0000000 [[1,2,3,4,6,7,8],[5]]=>[5,1,2,3,4,6,7,8]=>[8,7,6,4,3,2,1,5]=>0000000 [[1,2,3,4,5,7,8],[6]]=>[6,1,2,3,4,5,7,8]=>[8,7,5,4,3,2,1,6]=>0000000 [[1,2,3,4,5,6,8],[7]]=>[7,1,2,3,4,5,6,8]=>[8,6,5,4,3,2,1,7]=>0000000 [[1,2,3,4,5,6,7],[8]]=>[8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8]=>0000001 [[1,3,5,6,7,8],[2,4]]=>[2,4,1,3,5,6,7,8]=>[8,7,6,5,3,1,4,2]=>0000000 [[1,2,5,6,7,8],[3,4]]=>[3,4,1,2,5,6,7,8]=>[8,7,6,5,2,1,4,3]=>0000000 [[1,3,4,6,7,8],[2,5]]=>[2,5,1,3,4,6,7,8]=>[8,7,6,4,3,1,5,2]=>0000000 [[1,2,4,6,7,8],[3,5]]=>[3,5,1,2,4,6,7,8]=>[8,7,6,4,2,1,5,3]=>0000000 [[1,3,4,5,7,8],[2,6]]=>[2,6,1,3,4,5,7,8]=>[8,7,5,4,3,1,6,2]=>0000000 [[1,2,4,5,7,8],[3,6]]=>[3,6,1,2,4,5,7,8]=>[8,7,5,4,2,1,6,3]=>0000000 [[1,2,3,5,7,8],[4,6]]=>[4,6,1,2,3,5,7,8]=>[8,7,5,3,2,1,6,4]=>0000000 [[1,2,3,4,7,8],[5,6]]=>[5,6,1,2,3,4,7,8]=>[8,7,4,3,2,1,6,5]=>0000000 [[1,3,4,5,6,8],[2,7]]=>[2,7,1,3,4,5,6,8]=>[8,6,5,4,3,1,7,2]=>0000000 [[1,2,4,5,6,8],[3,7]]=>[3,7,1,2,4,5,6,8]=>[8,6,5,4,2,1,7,3]=>0000000 [[1,2,3,5,6,8],[4,7]]=>[4,7,1,2,3,5,6,8]=>[8,6,5,3,2,1,7,4]=>0000000 [[1,2,3,4,6,8],[5,7]]=>[5,7,1,2,3,4,6,8]=>[8,6,4,3,2,1,7,5]=>0000000 [[1,2,3,4,5,8],[6,7]]=>[6,7,1,2,3,4,5,8]=>[8,5,4,3,2,1,7,6]=>0000000 [[1,3,4,5,6,7],[2,8]]=>[2,8,1,3,4,5,6,7]=>[7,6,5,4,3,1,8,2]=>0000000 [[1,2,4,5,6,7],[3,8]]=>[3,8,1,2,4,5,6,7]=>[7,6,5,4,2,1,8,3]=>0000000 [[1,2,3,5,6,7],[4,8]]=>[4,8,1,2,3,5,6,7]=>[7,6,5,3,2,1,8,4]=>0000000 [[1,2,3,4,6,7],[5,8]]=>[5,8,1,2,3,4,6,7]=>[7,6,4,3,2,1,8,5]=>0000000 [[1,2,3,4,5,7],[6,8]]=>[6,8,1,2,3,4,5,7]=>[7,5,4,3,2,1,8,6]=>0000000 [[1,2,3,4,5,6],[7,8]]=>[7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7]=>0000010 [[1,4,5,6,7,8],[2],[3]]=>[3,2,1,4,5,6,7,8]=>[8,7,6,5,4,1,2,3]=>0000000 [[1,3,5,6,7,8],[2],[4]]=>[4,2,1,3,5,6,7,8]=>[8,7,6,5,3,1,2,4]=>0000000 [[1,2,5,6,7,8],[3],[4]]=>[4,3,1,2,5,6,7,8]=>[8,7,6,5,2,1,3,4]=>0000000 [[1,3,4,6,7,8],[2],[5]]=>[5,2,1,3,4,6,7,8]=>[8,7,6,4,3,1,2,5]=>0000000 [[1,2,4,6,7,8],[3],[5]]=>[5,3,1,2,4,6,7,8]=>[8,7,6,4,2,1,3,5]=>0000000 [[1,2,3,6,7,8],[4],[5]]=>[5,4,1,2,3,6,7,8]=>[8,7,6,3,2,1,4,5]=>0000000 [[1,3,4,5,7,8],[2],[6]]=>[6,2,1,3,4,5,7,8]=>[8,7,5,4,3,1,2,6]=>0000000 [[1,2,3,5,7,8],[4],[6]]=>[6,4,1,2,3,5,7,8]=>[8,7,5,3,2,1,4,6]=>0000000 [[1,2,3,4,7,8],[5],[6]]=>[6,5,1,2,3,4,7,8]=>[8,7,4,3,2,1,5,6]=>0000000 [[1,3,4,5,6,8],[2],[7]]=>[7,2,1,3,4,5,6,8]=>[8,6,5,4,3,1,2,7]=>0000000 [[1,2,4,5,6,8],[3],[7]]=>[7,3,1,2,4,5,6,8]=>[8,6,5,4,2,1,3,7]=>0000000 [[1,2,3,5,6,8],[4],[7]]=>[7,4,1,2,3,5,6,8]=>[8,6,5,3,2,1,4,7]=>0000000 [[1,2,3,4,6,8],[5],[7]]=>[7,5,1,2,3,4,6,8]=>[8,6,4,3,2,1,5,7]=>0000000 [[1,2,3,4,5,8],[6],[7]]=>[7,6,1,2,3,4,5,8]=>[8,5,4,3,2,1,6,7]=>0000000 [[1,3,4,5,6,7],[2],[8]]=>[8,2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2,8]=>0000001 [[1,2,4,5,6,7],[3],[8]]=>[8,3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3,8]=>0000001 [[1,2,3,5,6,7],[4],[8]]=>[8,4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4,8]=>0000001 [[1,2,3,4,6,7],[5],[8]]=>[8,5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5,8]=>0000001 [[1,2,3,4,5,7],[6],[8]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>0000001 [[1,2,3,4,5,6],[7],[8]]=>[8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8]=>0000011 [[1,3,5,7,8],[2,4,6]]=>[2,4,6,1,3,5,7,8]=>[8,7,5,3,1,6,4,2]=>0000000 [[1,2,5,7,8],[3,4,6]]=>[3,4,6,1,2,5,7,8]=>[8,7,5,2,1,6,4,3]=>0000000 [[1,2,3,7,8],[4,5,6]]=>[4,5,6,1,2,3,7,8]=>[8,7,3,2,1,6,5,4]=>0000000 [[1,2,5,6,8],[3,4,7]]=>[3,4,7,1,2,5,6,8]=>[8,6,5,2,1,7,4,3]=>0000000 [[1,2,4,6,8],[3,5,7]]=>[3,5,7,1,2,4,6,8]=>[8,6,4,2,1,7,5,3]=>0000000 [[1,2,3,4,8],[5,6,7]]=>[5,6,7,1,2,3,4,8]=>[8,4,3,2,1,7,6,5]=>0000000 [[1,2,5,6,7],[3,4,8]]=>[3,4,8,1,2,5,6,7]=>[7,6,5,2,1,8,4,3]=>0000000 [[1,2,3,6,7],[4,5,8]]=>[4,5,8,1,2,3,6,7]=>[7,6,3,2,1,8,5,4]=>0000000 [[1,3,4,5,7],[2,6,8]]=>[2,6,8,1,3,4,5,7]=>[7,5,4,3,1,8,6,2]=>0000000 [[1,2,4,5,7],[3,6,8]]=>[3,6,8,1,2,4,5,7]=>[7,5,4,2,1,8,6,3]=>0000000 [[1,2,3,5,7],[4,6,8]]=>[4,6,8,1,2,3,5,7]=>[7,5,3,2,1,8,6,4]=>0000000 [[1,2,3,4,7],[5,6,8]]=>[5,6,8,1,2,3,4,7]=>[7,4,3,2,1,8,6,5]=>0000000 [[1,3,4,5,6],[2,7,8]]=>[2,7,8,1,3,4,5,6]=>[6,5,4,3,1,8,7,2]=>0000000 [[1,2,3,5,6],[4,7,8]]=>[4,7,8,1,2,3,5,6]=>[6,5,3,2,1,8,7,4]=>0000000 [[1,2,3,4,6],[5,7,8]]=>[5,7,8,1,2,3,4,6]=>[6,4,3,2,1,8,7,5]=>0000000 [[1,2,3,4,5],[6,7,8]]=>[6,7,8,1,2,3,4,5]=>[5,4,3,2,1,8,7,6]=>0000100 [[1,4,6,7,8],[2,5],[3]]=>[3,2,5,1,4,6,7,8]=>[8,7,6,4,1,5,2,3]=>0000000 [[1,3,6,7,8],[2,5],[4]]=>[4,2,5,1,3,6,7,8]=>[8,7,6,3,1,5,2,4]=>0000000 [[1,3,6,7,8],[2,4],[5]]=>[5,2,4,1,3,6,7,8]=>[8,7,6,3,1,4,2,5]=>0000000 [[1,2,6,7,8],[3,4],[5]]=>[5,3,4,1,2,6,7,8]=>[8,7,6,2,1,4,3,5]=>0000000 [[1,3,4,7,8],[2,6],[5]]=>[5,2,6,1,3,4,7,8]=>[8,7,4,3,1,6,2,5]=>0000000 [[1,2,4,7,8],[3,6],[5]]=>[5,3,6,1,2,4,7,8]=>[8,7,4,2,1,6,3,5]=>0000000 [[1,2,4,7,8],[3,5],[6]]=>[6,3,5,1,2,4,7,8]=>[8,7,4,2,1,5,3,6]=>0000000 [[1,4,5,6,8],[2,7],[3]]=>[3,2,7,1,4,5,6,8]=>[8,6,5,4,1,7,2,3]=>0000000 [[1,2,3,6,8],[4,7],[5]]=>[5,4,7,1,2,3,6,8]=>[8,6,3,2,1,7,4,5]=>0000000 [[1,3,4,5,8],[2,7],[6]]=>[6,2,7,1,3,4,5,8]=>[8,5,4,3,1,7,2,6]=>0000000 [[1,2,3,4,8],[5,7],[6]]=>[6,5,7,1,2,3,4,8]=>[8,4,3,2,1,7,5,6]=>0000000 [[1,2,5,6,8],[3,4],[7]]=>[7,3,4,1,2,5,6,8]=>[8,6,5,2,1,4,3,7]=>0000000 [[1,2,4,6,8],[3,5],[7]]=>[7,3,5,1,2,4,6,8]=>[8,6,4,2,1,5,3,7]=>0000000 [[1,2,3,6,8],[4,5],[7]]=>[7,4,5,1,2,3,6,8]=>[8,6,3,2,1,5,4,7]=>0000000 [[1,2,4,5,8],[3,6],[7]]=>[7,3,6,1,2,4,5,8]=>[8,5,4,2,1,6,3,7]=>0000000 [[1,2,3,5,8],[4,6],[7]]=>[7,4,6,1,2,3,5,8]=>[8,5,3,2,1,6,4,7]=>0000000 [[1,2,3,4,8],[5,6],[7]]=>[7,5,6,1,2,3,4,8]=>[8,4,3,2,1,6,5,7]=>0000000 [[1,4,5,6,7],[2,8],[3]]=>[3,2,8,1,4,5,6,7]=>[7,6,5,4,1,8,2,3]=>0000000 [[1,3,5,6,7],[2,8],[4]]=>[4,2,8,1,3,5,6,7]=>[7,6,5,3,1,8,2,4]=>0000000 [[1,3,4,6,7],[2,8],[5]]=>[5,2,8,1,3,4,6,7]=>[7,6,4,3,1,8,2,5]=>0000000 [[1,2,4,6,7],[3,8],[5]]=>[5,3,8,1,2,4,6,7]=>[7,6,4,2,1,8,3,5]=>0000000 [[1,2,3,6,7],[4,8],[5]]=>[5,4,8,1,2,3,6,7]=>[7,6,3,2,1,8,4,5]=>0000000 [[1,3,4,5,7],[2,8],[6]]=>[6,2,8,1,3,4,5,7]=>[7,5,4,3,1,8,2,6]=>0000000 [[1,2,4,5,7],[3,8],[6]]=>[6,3,8,1,2,4,5,7]=>[7,5,4,2,1,8,3,6]=>0000000 [[1,2,3,5,7],[4,8],[6]]=>[6,4,8,1,2,3,5,7]=>[7,5,3,2,1,8,4,6]=>0000000 [[1,2,3,4,7],[5,8],[6]]=>[6,5,8,1,2,3,4,7]=>[7,4,3,2,1,8,5,6]=>0000000 [[1,3,4,5,6],[2,8],[7]]=>[7,2,8,1,3,4,5,6]=>[6,5,4,3,1,8,2,7]=>0000000 [[1,2,3,4,6],[5,8],[7]]=>[7,5,8,1,2,3,4,6]=>[6,4,3,2,1,8,5,7]=>0000000 [[1,2,3,4,5],[6,8],[7]]=>[7,6,8,1,2,3,4,5]=>[5,4,3,2,1,8,6,7]=>0000100 [[1,2,5,6,7],[3,4],[8]]=>[8,3,4,1,2,5,6,7]=>[7,6,5,2,1,4,3,8]=>0000001 [[1,3,4,6,7],[2,5],[8]]=>[8,2,5,1,3,4,6,7]=>[7,6,4,3,1,5,2,8]=>0000001 [[1,2,4,6,7],[3,5],[8]]=>[8,3,5,1,2,4,6,7]=>[7,6,4,2,1,5,3,8]=>0000001 [[1,2,3,6,7],[4,5],[8]]=>[8,4,5,1,2,3,6,7]=>[7,6,3,2,1,5,4,8]=>0000001 [[1,2,4,5,7],[3,6],[8]]=>[8,3,6,1,2,4,5,7]=>[7,5,4,2,1,6,3,8]=>0000001 [[1,2,3,4,7],[5,6],[8]]=>[8,5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5,8]=>0000001 [[1,2,4,5,6],[3,7],[8]]=>[8,3,7,1,2,4,5,6]=>[6,5,4,2,1,7,3,8]=>0000001 [[1,2,3,4,6],[5,7],[8]]=>[8,5,7,1,2,3,4,6]=>[6,4,3,2,1,7,5,8]=>0000001 [[1,2,3,4,5],[6,7],[8]]=>[8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8]=>0000101 [[1,5,6,7,8],[2],[3],[4]]=>[4,3,2,1,5,6,7,8]=>[8,7,6,5,1,2,3,4]=>0000000 [[1,4,6,7,8],[2],[3],[5]]=>[5,3,2,1,4,6,7,8]=>[8,7,6,4,1,2,3,5]=>0000000 [[1,3,6,7,8],[2],[4],[5]]=>[5,4,2,1,3,6,7,8]=>[8,7,6,3,1,2,4,5]=>0000000 [[1,2,6,7,8],[3],[4],[5]]=>[5,4,3,1,2,6,7,8]=>[8,7,6,2,1,3,4,5]=>0000000 [[1,4,5,7,8],[2],[3],[6]]=>[6,3,2,1,4,5,7,8]=>[8,7,5,4,1,2,3,6]=>0000000 [[1,2,5,7,8],[3],[4],[6]]=>[6,4,3,1,2,5,7,8]=>[8,7,5,2,1,3,4,6]=>0000000 [[1,2,4,7,8],[3],[5],[6]]=>[6,5,3,1,2,4,7,8]=>[8,7,4,2,1,3,5,6]=>0000000 [[1,2,3,7,8],[4],[5],[6]]=>[6,5,4,1,2,3,7,8]=>[8,7,3,2,1,4,5,6]=>0000000 [[1,4,5,6,8],[2],[3],[7]]=>[7,3,2,1,4,5,6,8]=>[8,6,5,4,1,2,3,7]=>0000000 [[1,2,4,6,8],[3],[5],[7]]=>[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>0000000 [[1,2,3,6,8],[4],[5],[7]]=>[7,5,4,1,2,3,6,8]=>[8,6,3,2,1,4,5,7]=>0000000 [[1,2,4,5,8],[3],[6],[7]]=>[7,6,3,1,2,4,5,8]=>[8,5,4,2,1,3,6,7]=>0000000 [[1,2,3,4,8],[5],[6],[7]]=>[7,6,5,1,2,3,4,8]=>[8,4,3,2,1,5,6,7]=>0000000 [[1,4,5,6,7],[2],[3],[8]]=>[8,3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3,8]=>0000001 [[1,2,5,6,7],[3],[4],[8]]=>[8,4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4,8]=>0000001 [[1,3,4,6,7],[2],[5],[8]]=>[8,5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5,8]=>0000001 [[1,2,4,6,7],[3],[5],[8]]=>[8,5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5,8]=>0000001 [[1,2,3,6,7],[4],[5],[8]]=>[8,5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5,8]=>0000001 [[1,3,4,5,7],[2],[6],[8]]=>[8,6,2,1,3,4,5,7]=>[7,5,4,3,1,2,6,8]=>0000001 [[1,2,3,5,7],[4],[6],[8]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>0000001 [[1,2,3,4,7],[5],[6],[8]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>0000001 [[1,3,4,5,6],[2],[7],[8]]=>[8,7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7,8]=>0000011 [[1,2,4,5,6],[3],[7],[8]]=>[8,7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7,8]=>0000011 [[1,2,3,5,6],[4],[7],[8]]=>[8,7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7,8]=>0000011 [[1,2,3,4,6],[5],[7],[8]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>0000011 [[1,2,3,4,5],[6],[7],[8]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>0000111 [[1,3,5,7],[2,4,6,8]]=>[2,4,6,8,1,3,5,7]=>[7,5,3,1,8,6,4,2]=>0000000 [[1,2,5,7],[3,4,6,8]]=>[3,4,6,8,1,2,5,7]=>[7,5,2,1,8,6,4,3]=>0000000 [[1,3,4,7],[2,5,6,8]]=>[2,5,6,8,1,3,4,7]=>[7,4,3,1,8,6,5,2]=>0000000 [[1,2,4,7],[3,5,6,8]]=>[3,5,6,8,1,2,4,7]=>[7,4,2,1,8,6,5,3]=>0000000 [[1,2,3,7],[4,5,6,8]]=>[4,5,6,8,1,2,3,7]=>[7,3,2,1,8,6,5,4]=>0000000 [[1,3,5,6],[2,4,7,8]]=>[2,4,7,8,1,3,5,6]=>[6,5,3,1,8,7,4,2]=>0000000 [[1,2,5,6],[3,4,7,8]]=>[3,4,7,8,1,2,5,6]=>[6,5,2,1,8,7,4,3]=>0000000 [[1,3,4,6],[2,5,7,8]]=>[2,5,7,8,1,3,4,6]=>[6,4,3,1,8,7,5,2]=>0000000 [[1,2,4,6],[3,5,7,8]]=>[3,5,7,8,1,2,4,6]=>[6,4,2,1,8,7,5,3]=>0000000 [[1,2,3,6],[4,5,7,8]]=>[4,5,7,8,1,2,3,6]=>[6,3,2,1,8,7,5,4]=>0000000 [[1,3,4,5],[2,6,7,8]]=>[2,6,7,8,1,3,4,5]=>[5,4,3,1,8,7,6,2]=>0000000 [[1,2,4,5],[3,6,7,8]]=>[3,6,7,8,1,2,4,5]=>[5,4,2,1,8,7,6,3]=>0000000 [[1,2,3,5],[4,6,7,8]]=>[4,6,7,8,1,2,3,5]=>[5,3,2,1,8,7,6,4]=>0000000 [[1,2,3,4],[5,6,7,8]]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>0001000 [[1,4,6,8],[2,5,7],[3]]=>[3,2,5,7,1,4,6,8]=>[8,6,4,1,7,5,2,3]=>0000000 [[1,3,6,8],[2,4,7],[5]]=>[5,2,4,7,1,3,6,8]=>[8,6,3,1,7,4,2,5]=>0000000 [[1,2,5,8],[3,6,7],[4]]=>[4,3,6,7,1,2,5,8]=>[8,5,2,1,7,6,3,4]=>0000000 [[1,3,4,8],[2,6,7],[5]]=>[5,2,6,7,1,3,4,8]=>[8,4,3,1,7,6,2,5]=>0000000 [[1,2,4,8],[3,6,7],[5]]=>[5,3,6,7,1,2,4,8]=>[8,4,2,1,7,6,3,5]=>0000000 [[1,2,3,8],[4,6,7],[5]]=>[5,4,6,7,1,2,3,8]=>[8,3,2,1,7,6,4,5]=>0000000 [[1,3,5,8],[2,4,7],[6]]=>[6,2,4,7,1,3,5,8]=>[8,5,3,1,7,4,2,6]=>0000000 [[1,2,5,8],[3,4,7],[6]]=>[6,3,4,7,1,2,5,8]=>[8,5,2,1,7,4,3,6]=>0000000 [[1,3,4,8],[2,5,7],[6]]=>[6,2,5,7,1,3,4,8]=>[8,4,3,1,7,5,2,6]=>0000000 [[1,2,4,8],[3,5,7],[6]]=>[6,3,5,7,1,2,4,8]=>[8,4,2,1,7,5,3,6]=>0000000 [[1,3,5,8],[2,4,6],[7]]=>[7,2,4,6,1,3,5,8]=>[8,5,3,1,6,4,2,7]=>0000000 [[1,2,5,8],[3,4,6],[7]]=>[7,3,4,6,1,2,5,8]=>[8,5,2,1,6,4,3,7]=>0000000 [[1,2,4,8],[3,5,6],[7]]=>[7,3,5,6,1,2,4,8]=>[8,4,2,1,6,5,3,7]=>0000000 [[1,2,3,8],[4,5,6],[7]]=>[7,4,5,6,1,2,3,8]=>[8,3,2,1,6,5,4,7]=>0000000 [[1,4,6,7],[2,5,8],[3]]=>[3,2,5,8,1,4,6,7]=>[7,6,4,1,8,5,2,3]=>0000000 [[1,3,6,7],[2,5,8],[4]]=>[4,2,5,8,1,3,6,7]=>[7,6,3,1,8,5,2,4]=>0000000 [[1,2,6,7],[3,5,8],[4]]=>[4,3,5,8,1,2,6,7]=>[7,6,2,1,8,5,3,4]=>0000000 [[1,3,6,7],[2,4,8],[5]]=>[5,2,4,8,1,3,6,7]=>[7,6,3,1,8,4,2,5]=>0000000 [[1,2,6,7],[3,4,8],[5]]=>[5,3,4,8,1,2,6,7]=>[7,6,2,1,8,4,3,5]=>0000000 [[1,3,5,7],[2,6,8],[4]]=>[4,2,6,8,1,3,5,7]=>[7,5,3,1,8,6,2,4]=>0000000 [[1,2,3,7],[4,6,8],[5]]=>[5,4,6,8,1,2,3,7]=>[7,3,2,1,8,6,4,5]=>0000000 [[1,3,4,7],[2,5,8],[6]]=>[6,2,5,8,1,3,4,7]=>[7,4,3,1,8,5,2,6]=>0000000 [[1,2,4,7],[3,5,8],[6]]=>[6,3,5,8,1,2,4,7]=>[7,4,2,1,8,5,3,6]=>0000000 [[1,2,3,7],[4,5,8],[6]]=>[6,4,5,8,1,2,3,7]=>[7,3,2,1,8,5,4,6]=>0000000 [[1,4,5,6],[2,7,8],[3]]=>[3,2,7,8,1,4,5,6]=>[6,5,4,1,8,7,2,3]=>0000000 [[1,2,5,6],[3,7,8],[4]]=>[4,3,7,8,1,2,5,6]=>[6,5,2,1,8,7,3,4]=>0000000 [[1,2,3,6],[4,7,8],[5]]=>[5,4,7,8,1,2,3,6]=>[6,3,2,1,8,7,4,5]=>0000000 [[1,2,3,4],[5,7,8],[6]]=>[6,5,7,8,1,2,3,4]=>[4,3,2,1,8,7,5,6]=>0001000 [[1,3,5,6],[2,4,8],[7]]=>[7,2,4,8,1,3,5,6]=>[6,5,3,1,8,4,2,7]=>0000000 [[1,2,5,6],[3,4,8],[7]]=>[7,3,4,8,1,2,5,6]=>[6,5,2,1,8,4,3,7]=>0000000 [[1,2,4,6],[3,5,8],[7]]=>[7,3,5,8,1,2,4,6]=>[6,4,2,1,8,5,3,7]=>0000000 [[1,2,3,6],[4,5,8],[7]]=>[7,4,5,8,1,2,3,6]=>[6,3,2,1,8,5,4,7]=>0000000 [[1,2,3,4],[5,6,8],[7]]=>[7,5,6,8,1,2,3,4]=>[4,3,2,1,8,6,5,7]=>0001000 [[1,3,4,7],[2,5,6],[8]]=>[8,2,5,6,1,3,4,7]=>[7,4,3,1,6,5,2,8]=>0000001 [[1,2,4,7],[3,5,6],[8]]=>[8,3,5,6,1,2,4,7]=>[7,4,2,1,6,5,3,8]=>0000001 [[1,2,4,6],[3,5,7],[8]]=>[8,3,5,7,1,2,4,6]=>[6,4,2,1,7,5,3,8]=>0000001 [[1,3,4,5],[2,6,7],[8]]=>[8,2,6,7,1,3,4,5]=>[5,4,3,1,7,6,2,8]=>0000001 [[1,2,4,5],[3,6,7],[8]]=>[8,3,6,7,1,2,4,5]=>[5,4,2,1,7,6,3,8]=>0000001 [[1,2,3,5],[4,6,7],[8]]=>[8,4,6,7,1,2,3,5]=>[5,3,2,1,7,6,4,8]=>0000001 [[1,2,3,4],[5,6,7],[8]]=>[8,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,8]=>0001001 [[1,4,7,8],[2,5],[3,6]]=>[3,6,2,5,1,4,7,8]=>[8,7,4,1,5,2,6,3]=>0000000 [[1,2,7,8],[3,5],[4,6]]=>[4,6,3,5,1,2,7,8]=>[8,7,2,1,5,3,6,4]=>0000000 [[1,3,7,8],[2,4],[5,6]]=>[5,6,2,4,1,3,7,8]=>[8,7,3,1,4,2,6,5]=>0000000 [[1,2,7,8],[3,4],[5,6]]=>[5,6,3,4,1,2,7,8]=>[8,7,2,1,4,3,6,5]=>0000000 [[1,4,6,8],[2,5],[3,7]]=>[3,7,2,5,1,4,6,8]=>[8,6,4,1,5,2,7,3]=>0000000 [[1,2,5,8],[3,6],[4,7]]=>[4,7,3,6,1,2,5,8]=>[8,5,2,1,6,3,7,4]=>0000000 [[1,2,5,8],[3,4],[6,7]]=>[6,7,3,4,1,2,5,8]=>[8,5,2,1,4,3,7,6]=>0000000 [[1,2,4,8],[3,5],[6,7]]=>[6,7,3,5,1,2,4,8]=>[8,4,2,1,5,3,7,6]=>0000000 [[1,2,3,8],[4,5],[6,7]]=>[6,7,4,5,1,2,3,8]=>[8,3,2,1,5,4,7,6]=>0000000 [[1,4,6,7],[2,5],[3,8]]=>[3,8,2,5,1,4,6,7]=>[7,6,4,1,5,2,8,3]=>0000000 [[1,2,6,7],[3,4],[5,8]]=>[5,8,3,4,1,2,6,7]=>[7,6,2,1,4,3,8,5]=>0000000 [[1,3,4,7],[2,6],[5,8]]=>[5,8,2,6,1,3,4,7]=>[7,4,3,1,6,2,8,5]=>0000000 [[1,2,3,7],[4,6],[5,8]]=>[5,8,4,6,1,2,3,7]=>[7,3,2,1,6,4,8,5]=>0000000 [[1,2,5,7],[3,4],[6,8]]=>[6,8,3,4,1,2,5,7]=>[7,5,2,1,4,3,8,6]=>0000000 [[1,2,3,7],[4,5],[6,8]]=>[6,8,4,5,1,2,3,7]=>[7,3,2,1,5,4,8,6]=>0000000 [[1,4,5,6],[2,7],[3,8]]=>[3,8,2,7,1,4,5,6]=>[6,5,4,1,7,2,8,3]=>0000000 [[1,3,5,6],[2,7],[4,8]]=>[4,8,2,7,1,3,5,6]=>[6,5,3,1,7,2,8,4]=>0000000 [[1,2,5,6],[3,7],[4,8]]=>[4,8,3,7,1,2,5,6]=>[6,5,2,1,7,3,8,4]=>0000000 [[1,3,4,6],[2,7],[5,8]]=>[5,8,2,7,1,3,4,6]=>[6,4,3,1,7,2,8,5]=>0000000 [[1,2,4,6],[3,7],[5,8]]=>[5,8,3,7,1,2,4,6]=>[6,4,2,1,7,3,8,5]=>0000000 [[1,2,3,6],[4,7],[5,8]]=>[5,8,4,7,1,2,3,6]=>[6,3,2,1,7,4,8,5]=>0000000 [[1,3,4,5],[2,7],[6,8]]=>[6,8,2,7,1,3,4,5]=>[5,4,3,1,7,2,8,6]=>0000000 [[1,2,3,4],[5,7],[6,8]]=>[6,8,5,7,1,2,3,4]=>[4,3,2,1,7,5,8,6]=>0001000 [[1,3,5,6],[2,4],[7,8]]=>[7,8,2,4,1,3,5,6]=>[6,5,3,1,4,2,8,7]=>0000010 [[1,3,4,6],[2,5],[7,8]]=>[7,8,2,5,1,3,4,6]=>[6,4,3,1,5,2,8,7]=>0000010 [[1,2,4,6],[3,5],[7,8]]=>[7,8,3,5,1,2,4,6]=>[6,4,2,1,5,3,8,7]=>0000010 [[1,2,3,6],[4,5],[7,8]]=>[7,8,4,5,1,2,3,6]=>[6,3,2,1,5,4,8,7]=>0000010 [[1,2,3,5],[4,6],[7,8]]=>[7,8,4,6,1,2,3,5]=>[5,3,2,1,6,4,8,7]=>0000010 [[1,2,3,4],[5,6],[7,8]]=>[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>0001010 [[1,5,7,8],[2,6],[3],[4]]=>[4,3,2,6,1,5,7,8]=>[8,7,5,1,6,2,3,4]=>0000000 [[1,4,7,8],[2,6],[3],[5]]=>[5,3,2,6,1,4,7,8]=>[8,7,4,1,6,2,3,5]=>0000000 [[1,3,7,8],[2,6],[4],[5]]=>[5,4,2,6,1,3,7,8]=>[8,7,3,1,6,2,4,5]=>0000000 [[1,2,7,8],[3,6],[4],[5]]=>[5,4,3,6,1,2,7,8]=>[8,7,2,1,6,3,4,5]=>0000000 [[1,3,7,8],[2,5],[4],[6]]=>[6,4,2,5,1,3,7,8]=>[8,7,3,1,5,2,4,6]=>0000000 [[1,2,7,8],[3,5],[4],[6]]=>[6,4,3,5,1,2,7,8]=>[8,7,2,1,5,3,4,6]=>0000000 [[1,3,7,8],[2,4],[5],[6]]=>[6,5,2,4,1,3,7,8]=>[8,7,3,1,4,2,5,6]=>0000000 [[1,2,7,8],[3,4],[5],[6]]=>[6,5,3,4,1,2,7,8]=>[8,7,2,1,4,3,5,6]=>0000000 [[1,4,6,8],[2,7],[3],[5]]=>[5,3,2,7,1,4,6,8]=>[8,6,4,1,7,2,3,5]=>0000000 [[1,3,6,8],[2,7],[4],[5]]=>[5,4,2,7,1,3,6,8]=>[8,6,3,1,7,2,4,5]=>0000000 [[1,2,6,8],[3,7],[4],[5]]=>[5,4,3,7,1,2,6,8]=>[8,6,2,1,7,3,4,5]=>0000000 [[1,4,5,8],[2,7],[3],[6]]=>[6,3,2,7,1,4,5,8]=>[8,5,4,1,7,2,3,6]=>0000000 [[1,3,5,8],[2,7],[4],[6]]=>[6,4,2,7,1,3,5,8]=>[8,5,3,1,7,2,4,6]=>0000000 [[1,2,5,8],[3,7],[4],[6]]=>[6,4,3,7,1,2,5,8]=>[8,5,2,1,7,3,4,6]=>0000000 [[1,2,4,8],[3,7],[5],[6]]=>[6,5,3,7,1,2,4,8]=>[8,4,2,1,7,3,5,6]=>0000000 [[1,2,3,8],[4,7],[5],[6]]=>[6,5,4,7,1,2,3,8]=>[8,3,2,1,7,4,5,6]=>0000000 [[1,4,6,8],[2,5],[3],[7]]=>[7,3,2,5,1,4,6,8]=>[8,6,4,1,5,2,3,7]=>0000000 [[1,3,6,8],[2,5],[4],[7]]=>[7,4,2,5,1,3,6,8]=>[8,6,3,1,5,2,4,7]=>0000000 [[1,2,6,8],[3,5],[4],[7]]=>[7,4,3,5,1,2,6,8]=>[8,6,2,1,5,3,4,7]=>0000000 [[1,3,6,8],[2,4],[5],[7]]=>[7,5,2,4,1,3,6,8]=>[8,6,3,1,4,2,5,7]=>0000000 [[1,2,6,8],[3,4],[5],[7]]=>[7,5,3,4,1,2,6,8]=>[8,6,2,1,4,3,5,7]=>0000000 [[1,4,5,8],[2,6],[3],[7]]=>[7,3,2,6,1,4,5,8]=>[8,5,4,1,6,2,3,7]=>0000000 [[1,3,5,8],[2,6],[4],[7]]=>[7,4,2,6,1,3,5,8]=>[8,5,3,1,6,2,4,7]=>0000000 [[1,2,5,8],[3,6],[4],[7]]=>[7,4,3,6,1,2,5,8]=>[8,5,2,1,6,3,4,7]=>0000000 [[1,3,4,8],[2,6],[5],[7]]=>[7,5,2,6,1,3,4,8]=>[8,4,3,1,6,2,5,7]=>0000000 [[1,2,4,8],[3,6],[5],[7]]=>[7,5,3,6,1,2,4,8]=>[8,4,2,1,6,3,5,7]=>0000000 [[1,2,3,8],[4,6],[5],[7]]=>[7,5,4,6,1,2,3,8]=>[8,3,2,1,6,4,5,7]=>0000000 [[1,2,4,8],[3,5],[6],[7]]=>[7,6,3,5,1,2,4,8]=>[8,4,2,1,5,3,6,7]=>0000000 [[1,2,3,8],[4,5],[6],[7]]=>[7,6,4,5,1,2,3,8]=>[8,3,2,1,5,4,6,7]=>0000000 [[1,5,6,7],[2,8],[3],[4]]=>[4,3,2,8,1,5,6,7]=>[7,6,5,1,8,2,3,4]=>0000000 [[1,4,6,7],[2,8],[3],[5]]=>[5,3,2,8,1,4,6,7]=>[7,6,4,1,8,2,3,5]=>0000000 [[1,3,6,7],[2,8],[4],[5]]=>[5,4,2,8,1,3,6,7]=>[7,6,3,1,8,2,4,5]=>0000000 [[1,2,6,7],[3,8],[4],[5]]=>[5,4,3,8,1,2,6,7]=>[7,6,2,1,8,3,4,5]=>0000000 [[1,4,5,7],[2,8],[3],[6]]=>[6,3,2,8,1,4,5,7]=>[7,5,4,1,8,2,3,6]=>0000000 [[1,2,5,7],[3,8],[4],[6]]=>[6,4,3,8,1,2,5,7]=>[7,5,2,1,8,3,4,6]=>0000000 [[1,3,4,7],[2,8],[5],[6]]=>[6,5,2,8,1,3,4,7]=>[7,4,3,1,8,2,5,6]=>0000000 [[1,2,4,7],[3,8],[5],[6]]=>[6,5,3,8,1,2,4,7]=>[7,4,2,1,8,3,5,6]=>0000000 [[1,2,3,7],[4,8],[5],[6]]=>[6,5,4,8,1,2,3,7]=>[7,3,2,1,8,4,5,6]=>0000000 [[1,3,5,6],[2,8],[4],[7]]=>[7,4,2,8,1,3,5,6]=>[6,5,3,1,8,2,4,7]=>0000000 [[1,2,5,6],[3,8],[4],[7]]=>[7,4,3,8,1,2,5,6]=>[6,5,2,1,8,3,4,7]=>0000000 [[1,3,4,6],[2,8],[5],[7]]=>[7,5,2,8,1,3,4,6]=>[6,4,3,1,8,2,5,7]=>0000000 [[1,2,4,6],[3,8],[5],[7]]=>[7,5,3,8,1,2,4,6]=>[6,4,2,1,8,3,5,7]=>0000000 [[1,2,4,5],[3,8],[6],[7]]=>[7,6,3,8,1,2,4,5]=>[5,4,2,1,8,3,6,7]=>0000000 [[1,2,3,5],[4,8],[6],[7]]=>[7,6,4,8,1,2,3,5]=>[5,3,2,1,8,4,6,7]=>0000000 [[1,2,3,4],[5,8],[6],[7]]=>[7,6,5,8,1,2,3,4]=>[4,3,2,1,8,5,6,7]=>0001000 [[1,4,6,7],[2,5],[3],[8]]=>[8,3,2,5,1,4,6,7]=>[7,6,4,1,5,2,3,8]=>0000001 [[1,3,6,7],[2,4],[5],[8]]=>[8,5,2,4,1,3,6,7]=>[7,6,3,1,4,2,5,8]=>0000001 [[1,4,5,7],[2,6],[3],[8]]=>[8,3,2,6,1,4,5,7]=>[7,5,4,1,6,2,3,8]=>0000001 [[1,2,5,7],[3,6],[4],[8]]=>[8,4,3,6,1,2,5,7]=>[7,5,2,1,6,3,4,8]=>0000001 [[1,2,3,7],[4,6],[5],[8]]=>[8,5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5,8]=>0000001 [[1,3,5,7],[2,4],[6],[8]]=>[8,6,2,4,1,3,5,7]=>[7,5,3,1,4,2,6,8]=>0000001 [[1,2,3,7],[4,5],[6],[8]]=>[8,6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6,8]=>0000001 [[1,4,5,6],[2,7],[3],[8]]=>[8,3,2,7,1,4,5,6]=>[6,5,4,1,7,2,3,8]=>0000001 [[1,3,5,6],[2,7],[4],[8]]=>[8,4,2,7,1,3,5,6]=>[6,5,3,1,7,2,4,8]=>0000001 [[1,3,4,6],[2,7],[5],[8]]=>[8,5,2,7,1,3,4,6]=>[6,4,3,1,7,2,5,8]=>0000001 [[1,2,4,6],[3,7],[5],[8]]=>[8,5,3,7,1,2,4,6]=>[6,4,2,1,7,3,5,8]=>0000001 [[1,2,3,6],[4,7],[5],[8]]=>[8,5,4,7,1,2,3,6]=>[6,3,2,1,7,4,5,8]=>0000001 [[1,2,4,5],[3,7],[6],[8]]=>[8,6,3,7,1,2,4,5]=>[5,4,2,1,7,3,6,8]=>0000001 [[1,2,3,5],[4,7],[6],[8]]=>[8,6,4,7,1,2,3,5]=>[5,3,2,1,7,4,6,8]=>0000001 [[1,2,3,4],[5,7],[6],[8]]=>[8,6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6,8]=>0001001 [[1,3,5,6],[2,4],[7],[8]]=>[8,7,2,4,1,3,5,6]=>[6,5,3,1,4,2,7,8]=>0000011 [[1,3,4,6],[2,5],[7],[8]]=>[8,7,2,5,1,3,4,6]=>[6,4,3,1,5,2,7,8]=>0000011 [[1,2,4,6],[3,5],[7],[8]]=>[8,7,3,5,1,2,4,6]=>[6,4,2,1,5,3,7,8]=>0000011 [[1,2,3,6],[4,5],[7],[8]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>0000011 [[1,3,4,5],[2,6],[7],[8]]=>[8,7,2,6,1,3,4,5]=>[5,4,3,1,6,2,7,8]=>0000011 [[1,2,4,5],[3,6],[7],[8]]=>[8,7,3,6,1,2,4,5]=>[5,4,2,1,6,3,7,8]=>0000011 [[1,2,3,5],[4,6],[7],[8]]=>[8,7,4,6,1,2,3,5]=>[5,3,2,1,6,4,7,8]=>0000011 [[1,2,3,4],[5,6],[7],[8]]=>[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>0001011 [[1,6,7,8],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8]=>[8,7,6,1,2,3,4,5]=>0000000 [[1,5,7,8],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7,8]=>[8,7,5,1,2,3,4,6]=>0000000 [[1,4,7,8],[2],[3],[5],[6]]=>[6,5,3,2,1,4,7,8]=>[8,7,4,1,2,3,5,6]=>0000000 [[1,2,7,8],[3],[4],[5],[6]]=>[6,5,4,3,1,2,7,8]=>[8,7,2,1,3,4,5,6]=>0000000 [[1,5,6,8],[2],[3],[4],[7]]=>[7,4,3,2,1,5,6,8]=>[8,6,5,1,2,3,4,7]=>0000000 [[1,2,5,8],[3],[4],[6],[7]]=>[7,6,4,3,1,2,5,8]=>[8,5,2,1,3,4,6,7]=>0000000 [[1,2,3,8],[4],[5],[6],[7]]=>[7,6,5,4,1,2,3,8]=>[8,3,2,1,4,5,6,7]=>0000000 [[1,5,6,7],[2],[3],[4],[8]]=>[8,4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4,8]=>0000001 [[1,3,5,7],[2],[4],[6],[8]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0000001 [[1,3,4,7],[2],[5],[6],[8]]=>[8,6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6,8]=>0000001 [[1,2,3,7],[4],[5],[6],[8]]=>[8,6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6,8]=>0000001 [[1,4,5,6],[2],[3],[7],[8]]=>[8,7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7,8]=>0000011 [[1,3,4,6],[2],[5],[7],[8]]=>[8,7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7,8]=>0000011 [[1,2,4,6],[3],[5],[7],[8]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>0000011 [[1,3,4,5],[2],[6],[7],[8]]=>[8,7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7,8]=>0000111 [[1,2,4,5],[3],[6],[7],[8]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>0000111 [[1,2,3,5],[4],[6],[7],[8]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>0000111 [[1,2,3,4],[5],[6],[7],[8]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>0001111 [[1,4,7],[2,5,8],[3,6]]=>[3,6,2,5,8,1,4,7]=>[7,4,1,8,5,2,6,3]=>0000000 [[1,3,7],[2,4,8],[5,6]]=>[5,6,2,4,8,1,3,7]=>[7,3,1,8,4,2,6,5]=>0000000 [[1,4,6],[2,5,8],[3,7]]=>[3,7,2,5,8,1,4,6]=>[6,4,1,8,5,2,7,3]=>0000000 [[1,2,6],[3,5,8],[4,7]]=>[4,7,3,5,8,1,2,6]=>[6,2,1,8,5,3,7,4]=>0000000 [[1,3,6],[2,4,8],[5,7]]=>[5,7,2,4,8,1,3,6]=>[6,3,1,8,4,2,7,5]=>0000000 [[1,2,6],[3,4,8],[5,7]]=>[5,7,3,4,8,1,2,6]=>[6,2,1,8,4,3,7,5]=>0000000 [[1,4,5],[2,6,8],[3,7]]=>[3,7,2,6,8,1,4,5]=>[5,4,1,8,6,2,7,3]=>0000000 [[1,2,5],[3,6,8],[4,7]]=>[4,7,3,6,8,1,2,5]=>[5,2,1,8,6,3,7,4]=>0000000 [[1,3,4],[2,6,8],[5,7]]=>[5,7,2,6,8,1,3,4]=>[4,3,1,8,6,2,7,5]=>0000000 [[1,2,4],[3,6,8],[5,7]]=>[5,7,3,6,8,1,2,4]=>[4,2,1,8,6,3,7,5]=>0000000 [[1,2,3],[4,6,8],[5,7]]=>[5,7,4,6,8,1,2,3]=>[3,2,1,8,6,4,7,5]=>0010000 [[1,2,5],[3,4,8],[6,7]]=>[6,7,3,4,8,1,2,5]=>[5,2,1,8,4,3,7,6]=>0000000 [[1,2,3],[4,5,8],[6,7]]=>[6,7,4,5,8,1,2,3]=>[3,2,1,8,5,4,7,6]=>0010000 [[1,4,6],[2,5,7],[3,8]]=>[3,8,2,5,7,1,4,6]=>[6,4,1,7,5,2,8,3]=>0000000 [[1,3,6],[2,5,7],[4,8]]=>[4,8,2,5,7,1,3,6]=>[6,3,1,7,5,2,8,4]=>0000000 [[1,2,6],[3,5,7],[4,8]]=>[4,8,3,5,7,1,2,6]=>[6,2,1,7,5,3,8,4]=>0000000 [[1,3,6],[2,4,7],[5,8]]=>[5,8,2,4,7,1,3,6]=>[6,3,1,7,4,2,8,5]=>0000000 [[1,2,6],[3,4,7],[5,8]]=>[5,8,3,4,7,1,2,6]=>[6,2,1,7,4,3,8,5]=>0000000 [[1,4,5],[2,6,7],[3,8]]=>[3,8,2,6,7,1,4,5]=>[5,4,1,7,6,2,8,3]=>0000000 [[1,3,4],[2,5,7],[6,8]]=>[6,8,2,5,7,1,3,4]=>[4,3,1,7,5,2,8,6]=>0000000 [[1,2,3],[4,5,7],[6,8]]=>[6,8,4,5,7,1,2,3]=>[3,2,1,7,5,4,8,6]=>0010000 [[1,3,5],[2,4,6],[7,8]]=>[7,8,2,4,6,1,3,5]=>[5,3,1,6,4,2,8,7]=>0000010 [[1,2,4],[3,5,6],[7,8]]=>[7,8,3,5,6,1,2,4]=>[4,2,1,6,5,3,8,7]=>0000010 [[1,2,3],[4,5,6],[7,8]]=>[7,8,4,5,6,1,2,3]=>[3,2,1,6,5,4,8,7]=>0010010 [[1,5,7],[2,6,8],[3],[4]]=>[4,3,2,6,8,1,5,7]=>[7,5,1,8,6,2,3,4]=>0000000 [[1,2,7],[3,6,8],[4],[5]]=>[5,4,3,6,8,1,2,7]=>[7,2,1,8,6,3,4,5]=>0000000 [[1,2,7],[3,5,8],[4],[6]]=>[6,4,3,5,8,1,2,7]=>[7,2,1,8,5,3,4,6]=>0000000 [[1,3,7],[2,4,8],[5],[6]]=>[6,5,2,4,8,1,3,7]=>[7,3,1,8,4,2,5,6]=>0000000 [[1,5,6],[2,7,8],[3],[4]]=>[4,3,2,7,8,1,5,6]=>[6,5,1,8,7,2,3,4]=>0000000 [[1,3,6],[2,7,8],[4],[5]]=>[5,4,2,7,8,1,3,6]=>[6,3,1,8,7,2,4,5]=>0000000 [[1,2,6],[3,7,8],[4],[5]]=>[5,4,3,7,8,1,2,6]=>[6,2,1,8,7,3,4,5]=>0000000 [[1,4,5],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5]=>[5,4,1,8,7,2,3,6]=>0000000 [[1,3,5],[2,7,8],[4],[6]]=>[6,4,2,7,8,1,3,5]=>[5,3,1,8,7,2,4,6]=>0000000 [[1,3,4],[2,7,8],[5],[6]]=>[6,5,2,7,8,1,3,4]=>[4,3,1,8,7,2,5,6]=>0000000 [[1,2,4],[3,7,8],[5],[6]]=>[6,5,3,7,8,1,2,4]=>[4,2,1,8,7,3,5,6]=>0000000 [[1,2,3],[4,7,8],[5],[6]]=>[6,5,4,7,8,1,2,3]=>[3,2,1,8,7,4,5,6]=>0010000 [[1,3,5],[2,6,8],[4],[7]]=>[7,4,2,6,8,1,3,5]=>[5,3,1,8,6,2,4,7]=>0000000 [[1,3,4],[2,6,8],[5],[7]]=>[7,5,2,6,8,1,3,4]=>[4,3,1,8,6,2,5,7]=>0000000 [[1,2,3],[4,6,8],[5],[7]]=>[7,5,4,6,8,1,2,3]=>[3,2,1,8,6,4,5,7]=>0010000 [[1,3,4],[2,5,8],[6],[7]]=>[7,6,2,5,8,1,3,4]=>[4,3,1,8,5,2,6,7]=>0000000 [[1,2,4],[3,5,8],[6],[7]]=>[7,6,3,5,8,1,2,4]=>[4,2,1,8,5,3,6,7]=>0000000 [[1,2,3],[4,5,8],[6],[7]]=>[7,6,4,5,8,1,2,3]=>[3,2,1,8,5,4,6,7]=>0010000 [[1,4,6],[2,5,7],[3],[8]]=>[8,3,2,5,7,1,4,6]=>[6,4,1,7,5,2,3,8]=>0000001 [[1,3,6],[2,4,7],[5],[8]]=>[8,5,2,4,7,1,3,6]=>[6,3,1,7,4,2,5,8]=>0000001 [[1,2,3],[4,6,7],[5],[8]]=>[8,5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5,8]=>0010001 [[1,3,4],[2,5,7],[6],[8]]=>[8,6,2,5,7,1,3,4]=>[4,3,1,7,5,2,6,8]=>0000001 [[1,2,4],[3,5,7],[6],[8]]=>[8,6,3,5,7,1,2,4]=>[4,2,1,7,5,3,6,8]=>0000001 [[1,2,3],[4,5,7],[6],[8]]=>[8,6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6,8]=>0010001 [[1,3,5],[2,4,6],[7],[8]]=>[8,7,2,4,6,1,3,5]=>[5,3,1,6,4,2,7,8]=>0000011 [[1,2,5],[3,4,6],[7],[8]]=>[8,7,3,4,6,1,2,5]=>[5,2,1,6,4,3,7,8]=>0000011 [[1,2,4],[3,5,6],[7],[8]]=>[8,7,3,5,6,1,2,4]=>[4,2,1,6,5,3,7,8]=>0000011 [[1,2,3],[4,5,6],[7],[8]]=>[8,7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7,8]=>0010011 [[1,5,8],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5,8]=>[8,5,1,6,2,7,3,4]=>0000000 [[1,3,8],[2,6],[4,7],[5]]=>[5,4,7,2,6,1,3,8]=>[8,3,1,6,2,7,4,5]=>0000000 [[1,3,8],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3,8]=>[8,3,1,5,2,7,4,6]=>0000000 [[1,2,8],[3,5],[4,7],[6]]=>[6,4,7,3,5,1,2,8]=>[8,2,1,5,3,7,4,6]=>0000000 [[1,2,8],[3,4],[5,7],[6]]=>[6,5,7,3,4,1,2,8]=>[8,2,1,4,3,7,5,6]=>0000000 [[1,4,8],[2,5],[3,6],[7]]=>[7,3,6,2,5,1,4,8]=>[8,4,1,5,2,6,3,7]=>0000000 [[1,2,8],[3,4],[5,6],[7]]=>[7,5,6,3,4,1,2,8]=>[8,2,1,4,3,6,5,7]=>0000000 [[1,3,7],[2,6],[4,8],[5]]=>[5,4,8,2,6,1,3,7]=>[7,3,1,6,2,8,4,5]=>0000000 [[1,2,7],[3,5],[4,8],[6]]=>[6,4,8,3,5,1,2,7]=>[7,2,1,5,3,8,4,6]=>0000000 [[1,5,6],[2,7],[3,8],[4]]=>[4,3,8,2,7,1,5,6]=>[6,5,1,7,2,8,3,4]=>0000000 [[1,2,6],[3,7],[4,8],[5]]=>[5,4,8,3,7,1,2,6]=>[6,2,1,7,3,8,4,5]=>0000000 [[1,2,5],[3,7],[4,8],[6]]=>[6,4,8,3,7,1,2,5]=>[5,2,1,7,3,8,4,6]=>0000000 [[1,2,4],[3,7],[5,8],[6]]=>[6,5,8,3,7,1,2,4]=>[4,2,1,7,3,8,5,6]=>0000000 [[1,2,3],[4,7],[5,8],[6]]=>[6,5,8,4,7,1,2,3]=>[3,2,1,7,4,8,5,6]=>0010000 [[1,2,6],[3,5],[4,8],[7]]=>[7,4,8,3,5,1,2,6]=>[6,2,1,5,3,8,4,7]=>0000000 [[1,3,6],[2,4],[5,8],[7]]=>[7,5,8,2,4,1,3,6]=>[6,3,1,4,2,8,5,7]=>0000000 [[1,2,6],[3,4],[5,8],[7]]=>[7,5,8,3,4,1,2,6]=>[6,2,1,4,3,8,5,7]=>0000000 [[1,4,5],[2,6],[3,8],[7]]=>[7,3,8,2,6,1,4,5]=>[5,4,1,6,2,8,3,7]=>0000000 [[1,2,5],[3,6],[4,8],[7]]=>[7,4,8,3,6,1,2,5]=>[5,2,1,6,3,8,4,7]=>0000000 [[1,3,4],[2,6],[5,8],[7]]=>[7,5,8,2,6,1,3,4]=>[4,3,1,6,2,8,5,7]=>0000000 [[1,2,4],[3,6],[5,8],[7]]=>[7,5,8,3,6,1,2,4]=>[4,2,1,6,3,8,5,7]=>0000000 [[1,2,3],[4,6],[5,8],[7]]=>[7,5,8,4,6,1,2,3]=>[3,2,1,6,4,8,5,7]=>0010000 [[1,3,4],[2,5],[6,8],[7]]=>[7,6,8,2,5,1,3,4]=>[4,3,1,5,2,8,6,7]=>0000100 [[1,3,7],[2,5],[4,6],[8]]=>[8,4,6,2,5,1,3,7]=>[7,3,1,5,2,6,4,8]=>0000001 [[1,2,7],[3,4],[5,6],[8]]=>[8,5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5,8]=>0000001 [[1,2,6],[3,5],[4,7],[8]]=>[8,4,7,3,5,1,2,6]=>[6,2,1,5,3,7,4,8]=>0000001 [[1,3,6],[2,4],[5,7],[8]]=>[8,5,7,2,4,1,3,6]=>[6,3,1,4,2,7,5,8]=>0000001 [[1,4,5],[2,6],[3,7],[8]]=>[8,3,7,2,6,1,4,5]=>[5,4,1,6,2,7,3,8]=>0000001 [[1,3,5],[2,6],[4,7],[8]]=>[8,4,7,2,6,1,3,5]=>[5,3,1,6,2,7,4,8]=>0000001 [[1,2,5],[3,6],[4,7],[8]]=>[8,4,7,3,6,1,2,5]=>[5,2,1,6,3,7,4,8]=>0000001 [[1,3,4],[2,6],[5,7],[8]]=>[8,5,7,2,6,1,3,4]=>[4,3,1,6,2,7,5,8]=>0000001 [[1,2,4],[3,6],[5,7],[8]]=>[8,5,7,3,6,1,2,4]=>[4,2,1,6,3,7,5,8]=>0000001 [[1,2,3],[4,6],[5,7],[8]]=>[8,5,7,4,6,1,2,3]=>[3,2,1,6,4,7,5,8]=>0010001 [[1,3,5],[2,4],[6,7],[8]]=>[8,6,7,2,4,1,3,5]=>[5,3,1,4,2,7,6,8]=>0000101 [[1,3,4],[2,5],[6,7],[8]]=>[8,6,7,2,5,1,3,4]=>[4,3,1,5,2,7,6,8]=>0000101 [[1,2,4],[3,5],[6,7],[8]]=>[8,6,7,3,5,1,2,4]=>[4,2,1,5,3,7,6,8]=>0000101 [[1,2,3],[4,5],[6,7],[8]]=>[8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8]=>0010101 [[1,6,8],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6,8]=>[8,6,1,7,2,3,4,5]=>0000000 [[1,5,8],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5,8]=>[8,5,1,7,2,3,4,6]=>0000000 [[1,4,8],[2,7],[3],[5],[6]]=>[6,5,3,2,7,1,4,8]=>[8,4,1,7,2,3,5,6]=>0000000 [[1,3,8],[2,7],[4],[5],[6]]=>[6,5,4,2,7,1,3,8]=>[8,3,1,7,2,4,5,6]=>0000000 [[1,2,8],[3,7],[4],[5],[6]]=>[6,5,4,3,7,1,2,8]=>[8,2,1,7,3,4,5,6]=>0000000 [[1,4,8],[2,6],[3],[5],[7]]=>[7,5,3,2,6,1,4,8]=>[8,4,1,6,2,3,5,7]=>0000000 [[1,3,8],[2,6],[4],[5],[7]]=>[7,5,4,2,6,1,3,8]=>[8,3,1,6,2,4,5,7]=>0000000 [[1,2,8],[3,6],[4],[5],[7]]=>[7,5,4,3,6,1,2,8]=>[8,2,1,6,3,4,5,7]=>0000000 [[1,3,8],[2,5],[4],[6],[7]]=>[7,6,4,2,5,1,3,8]=>[8,3,1,5,2,4,6,7]=>0000000 [[1,6,7],[2,8],[3],[4],[5]]=>[5,4,3,2,8,1,6,7]=>[7,6,1,8,2,3,4,5]=>0000000 [[1,4,7],[2,8],[3],[5],[6]]=>[6,5,3,2,8,1,4,7]=>[7,4,1,8,2,3,5,6]=>0000000 [[1,2,7],[3,8],[4],[5],[6]]=>[6,5,4,3,8,1,2,7]=>[7,2,1,8,3,4,5,6]=>0000000 [[1,5,6],[2,8],[3],[4],[7]]=>[7,4,3,2,8,1,5,6]=>[6,5,1,8,2,3,4,7]=>0000000 [[1,4,6],[2,8],[3],[5],[7]]=>[7,5,3,2,8,1,4,6]=>[6,4,1,8,2,3,5,7]=>0000000 [[1,3,6],[2,8],[4],[5],[7]]=>[7,5,4,2,8,1,3,6]=>[6,3,1,8,2,4,5,7]=>0000000 [[1,4,5],[2,8],[3],[6],[7]]=>[7,6,3,2,8,1,4,5]=>[5,4,1,8,2,3,6,7]=>0000000 [[1,3,5],[2,8],[4],[6],[7]]=>[7,6,4,2,8,1,3,5]=>[5,3,1,8,2,4,6,7]=>0000000 [[1,2,5],[3,8],[4],[6],[7]]=>[7,6,4,3,8,1,2,5]=>[5,2,1,8,3,4,6,7]=>0000000 [[1,2,3],[4,8],[5],[6],[7]]=>[7,6,5,4,8,1,2,3]=>[3,2,1,8,4,5,6,7]=>0010000 [[1,4,7],[2,6],[3],[5],[8]]=>[8,5,3,2,6,1,4,7]=>[7,4,1,6,2,3,5,8]=>0000001 [[1,4,7],[2,5],[3],[6],[8]]=>[8,6,3,2,5,1,4,7]=>[7,4,1,5,2,3,6,8]=>0000001 [[1,3,7],[2,5],[4],[6],[8]]=>[8,6,4,2,5,1,3,7]=>[7,3,1,5,2,4,6,8]=>0000001 [[1,2,7],[3,4],[5],[6],[8]]=>[8,6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6,8]=>0000001 [[1,5,6],[2,7],[3],[4],[8]]=>[8,4,3,2,7,1,5,6]=>[6,5,1,7,2,3,4,8]=>0000001 [[1,4,6],[2,7],[3],[5],[8]]=>[8,5,3,2,7,1,4,6]=>[6,4,1,7,2,3,5,8]=>0000001 [[1,3,5],[2,7],[4],[6],[8]]=>[8,6,4,2,7,1,3,5]=>[5,3,1,7,2,4,6,8]=>0000001 [[1,2,5],[3,7],[4],[6],[8]]=>[8,6,4,3,7,1,2,5]=>[5,2,1,7,3,4,6,8]=>0000001 [[1,2,3],[4,7],[5],[6],[8]]=>[8,6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6,8]=>0010001 [[1,4,6],[2,5],[3],[7],[8]]=>[8,7,3,2,5,1,4,6]=>[6,4,1,5,2,3,7,8]=>0000011 [[1,2,6],[3,4],[5],[7],[8]]=>[8,7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7,8]=>0000011 [[1,4,5],[2,6],[3],[7],[8]]=>[8,7,3,2,6,1,4,5]=>[5,4,1,6,2,3,7,8]=>0000011 [[1,3,5],[2,6],[4],[7],[8]]=>[8,7,4,2,6,1,3,5]=>[5,3,1,6,2,4,7,8]=>0000011 [[1,2,5],[3,6],[4],[7],[8]]=>[8,7,4,3,6,1,2,5]=>[5,2,1,6,3,4,7,8]=>0000011 [[1,3,4],[2,6],[5],[7],[8]]=>[8,7,5,2,6,1,3,4]=>[4,3,1,6,2,5,7,8]=>0000011 [[1,2,4],[3,6],[5],[7],[8]]=>[8,7,5,3,6,1,2,4]=>[4,2,1,6,3,5,7,8]=>0000011 [[1,2,3],[4,6],[5],[7],[8]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>0010011 [[1,3,5],[2,4],[6],[7],[8]]=>[8,7,6,2,4,1,3,5]=>[5,3,1,4,2,6,7,8]=>0000111 [[1,2,5],[3,4],[6],[7],[8]]=>[8,7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7,8]=>0000111 [[1,2,4],[3,5],[6],[7],[8]]=>[8,7,6,3,5,1,2,4]=>[4,2,1,5,3,6,7,8]=>0000111 [[1,2,3],[4,5],[6],[7],[8]]=>[8,7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7,8]=>0010111 [[1,7,8],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7,8]=>[8,7,1,2,3,4,5,6]=>0000000 [[1,6,8],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6,8]=>[8,6,1,2,3,4,5,7]=>0000000 [[1,5,8],[2],[3],[4],[6],[7]]=>[7,6,4,3,2,1,5,8]=>[8,5,1,2,3,4,6,7]=>0000000 [[1,4,8],[2],[3],[5],[6],[7]]=>[7,6,5,3,2,1,4,8]=>[8,4,1,2,3,5,6,7]=>0000000 [[1,3,8],[2],[4],[5],[6],[7]]=>[7,6,5,4,2,1,3,8]=>[8,3,1,2,4,5,6,7]=>0000000 [[1,2,8],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,1,2,8]=>[8,2,1,3,4,5,6,7]=>0000000 [[1,6,7],[2],[3],[4],[5],[8]]=>[8,5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5,8]=>0000001 [[1,5,7],[2],[3],[4],[6],[8]]=>[8,6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6,8]=>0000001 [[1,4,7],[2],[3],[5],[6],[8]]=>[8,6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6,8]=>0000001 [[1,3,7],[2],[4],[5],[6],[8]]=>[8,6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6,8]=>0000001 [[1,2,7],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6,8]=>0000001 [[1,4,6],[2],[3],[5],[7],[8]]=>[8,7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7,8]=>0000011 [[1,3,6],[2],[4],[5],[7],[8]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0000011 [[1,4,5],[2],[3],[6],[7],[8]]=>[8,7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7,8]=>0000111 [[1,3,5],[2],[4],[6],[7],[8]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0000111 [[1,2,5],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>0000111 [[1,3,4],[2],[5],[6],[7],[8]]=>[8,7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7,8]=>0001111 [[1,2,4],[3],[5],[6],[7],[8]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>0001111 [[1,2,3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>0011111 [[1,5],[2,6],[3,7],[4,8]]=>[4,8,3,7,2,6,1,5]=>[5,1,6,2,7,3,8,4]=>0000000 [[1,4],[2,6],[3,7],[5,8]]=>[5,8,3,7,2,6,1,4]=>[4,1,6,2,7,3,8,5]=>0000000 [[1,3],[2,6],[4,7],[5,8]]=>[5,8,4,7,2,6,1,3]=>[3,1,6,2,7,4,8,5]=>0000000 [[1,2],[3,6],[4,7],[5,8]]=>[5,8,4,7,3,6,1,2]=>[2,1,6,3,7,4,8,5]=>0100000 [[1,4],[2,5],[3,7],[6,8]]=>[6,8,3,7,2,5,1,4]=>[4,1,5,2,7,3,8,6]=>0000000 [[1,3],[2,5],[4,7],[6,8]]=>[6,8,4,7,2,5,1,3]=>[3,1,5,2,7,4,8,6]=>0000000 [[1,2],[3,5],[4,7],[6,8]]=>[6,8,4,7,3,5,1,2]=>[2,1,5,3,7,4,8,6]=>0100000 [[1,3],[2,4],[5,7],[6,8]]=>[6,8,5,7,2,4,1,3]=>[3,1,4,2,7,5,8,6]=>0001000 [[1,2],[3,4],[5,7],[6,8]]=>[6,8,5,7,3,4,1,2]=>[2,1,4,3,7,5,8,6]=>0101000 [[1,4],[2,5],[3,6],[7,8]]=>[7,8,3,6,2,5,1,4]=>[4,1,5,2,6,3,8,7]=>0000010 [[1,3],[2,5],[4,6],[7,8]]=>[7,8,4,6,2,5,1,3]=>[3,1,5,2,6,4,8,7]=>0000010 [[1,2],[3,5],[4,6],[7,8]]=>[7,8,4,6,3,5,1,2]=>[2,1,5,3,6,4,8,7]=>0100010 [[1,3],[2,4],[5,6],[7,8]]=>[7,8,5,6,2,4,1,3]=>[3,1,4,2,6,5,8,7]=>0001010 [[1,2],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>0101010 [[1,6],[2,7],[3,8],[4],[5]]=>[5,4,3,8,2,7,1,6]=>[6,1,7,2,8,3,4,5]=>0000000 [[1,5],[2,7],[3,8],[4],[6]]=>[6,4,3,8,2,7,1,5]=>[5,1,7,2,8,3,4,6]=>0000000 [[1,4],[2,7],[3,8],[5],[6]]=>[6,5,3,8,2,7,1,4]=>[4,1,7,2,8,3,5,6]=>0000000 [[1,5],[2,6],[3,8],[4],[7]]=>[7,4,3,8,2,6,1,5]=>[5,1,6,2,8,3,4,7]=>0000000 [[1,4],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4]=>[4,1,6,2,8,3,5,7]=>0000000 [[1,3],[2,6],[4,8],[5],[7]]=>[7,5,4,8,2,6,1,3]=>[3,1,6,2,8,4,5,7]=>0000000 [[1,2],[3,6],[4,8],[5],[7]]=>[7,5,4,8,3,6,1,2]=>[2,1,6,3,8,4,5,7]=>0100000 [[1,4],[2,5],[3,8],[6],[7]]=>[7,6,3,8,2,5,1,4]=>[4,1,5,2,8,3,6,7]=>0000000 [[1,3],[2,5],[4,8],[6],[7]]=>[7,6,4,8,2,5,1,3]=>[3,1,5,2,8,4,6,7]=>0000000 [[1,2],[3,5],[4,8],[6],[7]]=>[7,6,4,8,3,5,1,2]=>[2,1,5,3,8,4,6,7]=>0100000 [[1,3],[2,4],[5,8],[6],[7]]=>[7,6,5,8,2,4,1,3]=>[3,1,4,2,8,5,6,7]=>0001000 [[1,2],[3,4],[5,8],[6],[7]]=>[7,6,5,8,3,4,1,2]=>[2,1,4,3,8,5,6,7]=>0101000 [[1,5],[2,6],[3,7],[4],[8]]=>[8,4,3,7,2,6,1,5]=>[5,1,6,2,7,3,4,8]=>0000001 [[1,4],[2,6],[3,7],[5],[8]]=>[8,5,3,7,2,6,1,4]=>[4,1,6,2,7,3,5,8]=>0000001 [[1,3],[2,6],[4,7],[5],[8]]=>[8,5,4,7,2,6,1,3]=>[3,1,6,2,7,4,5,8]=>0000001 [[1,2],[3,6],[4,7],[5],[8]]=>[8,5,4,7,3,6,1,2]=>[2,1,6,3,7,4,5,8]=>0100001 [[1,4],[2,5],[3,7],[6],[8]]=>[8,6,3,7,2,5,1,4]=>[4,1,5,2,7,3,6,8]=>0000001 [[1,3],[2,5],[4,7],[6],[8]]=>[8,6,4,7,2,5,1,3]=>[3,1,5,2,7,4,6,8]=>0000001 [[1,3],[2,4],[5,7],[6],[8]]=>[8,6,5,7,2,4,1,3]=>[3,1,4,2,7,5,6,8]=>0001001 [[1,4],[2,5],[3,6],[7],[8]]=>[8,7,3,6,2,5,1,4]=>[4,1,5,2,6,3,7,8]=>0000011 [[1,3],[2,4],[5,6],[7],[8]]=>[8,7,5,6,2,4,1,3]=>[3,1,4,2,6,5,7,8]=>0001011 [[1,2],[3,4],[5,6],[7],[8]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>0101011 [[1,7],[2,8],[3],[4],[5],[6]]=>[6,5,4,3,2,8,1,7]=>[7,1,8,2,3,4,5,6]=>0000000 [[1,6],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6]=>[6,1,8,2,3,4,5,7]=>0000000 [[1,4],[2,8],[3],[5],[6],[7]]=>[7,6,5,3,2,8,1,4]=>[4,1,8,2,3,5,6,7]=>0000000 [[1,3],[2,8],[4],[5],[6],[7]]=>[7,6,5,4,2,8,1,3]=>[3,1,8,2,4,5,6,7]=>0000000 [[1,2],[3,8],[4],[5],[6],[7]]=>[7,6,5,4,3,8,1,2]=>[2,1,8,3,4,5,6,7]=>0100000 [[1,6],[2,7],[3],[4],[5],[8]]=>[8,5,4,3,2,7,1,6]=>[6,1,7,2,3,4,5,8]=>0000001 [[1,5],[2,7],[3],[4],[6],[8]]=>[8,6,4,3,2,7,1,5]=>[5,1,7,2,3,4,6,8]=>0000001 [[1,4],[2,7],[3],[5],[6],[8]]=>[8,6,5,3,2,7,1,4]=>[4,1,7,2,3,5,6,8]=>0000001 [[1,3],[2,7],[4],[5],[6],[8]]=>[8,6,5,4,2,7,1,3]=>[3,1,7,2,4,5,6,8]=>0000001 [[1,2],[3,7],[4],[5],[6],[8]]=>[8,6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6,8]=>0100001 [[1,5],[2,6],[3],[4],[7],[8]]=>[8,7,4,3,2,6,1,5]=>[5,1,6,2,3,4,7,8]=>0000011 [[1,4],[2,6],[3],[5],[7],[8]]=>[8,7,5,3,2,6,1,4]=>[4,1,6,2,3,5,7,8]=>0000011 [[1,3],[2,6],[4],[5],[7],[8]]=>[8,7,5,4,2,6,1,3]=>[3,1,6,2,4,5,7,8]=>0000011 [[1,3],[2,4],[5],[6],[7],[8]]=>[8,7,6,5,2,4,1,3]=>[3,1,4,2,5,6,7,8]=>0001111 [[1,2],[3,4],[5],[6],[7],[8]]=>[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>0101111 [[1,8],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7]=>0000000 [[1,7],[2],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,8]=>0000001 [[1,6],[2],[3],[4],[5],[7],[8]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8]=>0000011 [[1,5],[2],[3],[4],[6],[7],[8]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0000111 [[1,4],[2],[3],[5],[6],[7],[8]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>0001111 [[1,3],[2],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>0011111 [[1,2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8]=>0111111 [[1],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>1111111 [[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]=>000000000 [[1,3,5,7,8],[2,4,6,9,10]]=>[2,4,6,9,10,1,3,5,7,8]=>[8,7,5,3,1,10,9,6,4,2]=>000000000 [[1,3,5,6,9],[2,4,7,8,10]]=>[2,4,7,8,10,1,3,5,6,9]=>[9,6,5,3,1,10,8,7,4,2]=>000000000 [[1,3,5,6,8],[2,4,7,9,10]]=>[2,4,7,9,10,1,3,5,6,8]=>[8,6,5,3,1,10,9,7,4,2]=>000000000 [[1,3,5,6,7],[2,4,8,9,10]]=>[2,4,8,9,10,1,3,5,6,7]=>[7,6,5,3,1,10,9,8,4,2]=>000000000 [[1,3,4,7,9],[2,5,6,8,10]]=>[2,5,6,8,10,1,3,4,7,9]=>[9,7,4,3,1,10,8,6,5,2]=>000000000 [[1,3,4,7,8],[2,5,6,9,10]]=>[2,5,6,9,10,1,3,4,7,8]=>[8,7,4,3,1,10,9,6,5,2]=>000000000 [[1,3,4,6,9],[2,5,7,8,10]]=>[2,5,7,8,10,1,3,4,6,9]=>[9,6,4,3,1,10,8,7,5,2]=>000000000 [[1,3,4,6,8],[2,5,7,9,10]]=>[2,5,7,9,10,1,3,4,6,8]=>[8,6,4,3,1,10,9,7,5,2]=>000000000 [[1,3,4,6,7],[2,5,8,9,10]]=>[2,5,8,9,10,1,3,4,6,7]=>[7,6,4,3,1,10,9,8,5,2]=>000000000 [[1,3,4,5,9],[2,6,7,8,10]]=>[2,6,7,8,10,1,3,4,5,9]=>[9,5,4,3,1,10,8,7,6,2]=>000000000 [[1,3,4,5,8],[2,6,7,9,10]]=>[2,6,7,9,10,1,3,4,5,8]=>[8,5,4,3,1,10,9,7,6,2]=>000000000 [[1,3,4,5,7],[2,6,8,9,10]]=>[2,6,8,9,10,1,3,4,5,7]=>[7,5,4,3,1,10,9,8,6,2]=>000000000 [[1,3,4,5,6],[2,7,8,9,10]]=>[2,7,8,9,10,1,3,4,5,6]=>[6,5,4,3,1,10,9,8,7,2]=>000000000 [[1,2,5,7,9],[3,4,6,8,10]]=>[3,4,6,8,10,1,2,5,7,9]=>[9,7,5,2,1,10,8,6,4,3]=>000000000 [[1,2,5,7,8],[3,4,6,9,10]]=>[3,4,6,9,10,1,2,5,7,8]=>[8,7,5,2,1,10,9,6,4,3]=>000000000 [[1,2,5,6,9],[3,4,7,8,10]]=>[3,4,7,8,10,1,2,5,6,9]=>[9,6,5,2,1,10,8,7,4,3]=>000000000 [[1,2,5,6,8],[3,4,7,9,10]]=>[3,4,7,9,10,1,2,5,6,8]=>[8,6,5,2,1,10,9,7,4,3]=>000000000 [[1,2,5,6,7],[3,4,8,9,10]]=>[3,4,8,9,10,1,2,5,6,7]=>[7,6,5,2,1,10,9,8,4,3]=>000000000 [[1,2,4,7,9],[3,5,6,8,10]]=>[3,5,6,8,10,1,2,4,7,9]=>[9,7,4,2,1,10,8,6,5,3]=>000000000 [[1,2,4,7,8],[3,5,6,9,10]]=>[3,5,6,9,10,1,2,4,7,8]=>[8,7,4,2,1,10,9,6,5,3]=>000000000 [[1,2,4,6,9],[3,5,7,8,10]]=>[3,5,7,8,10,1,2,4,6,9]=>[9,6,4,2,1,10,8,7,5,3]=>000000000 [[1,2,4,6,8],[3,5,7,9,10]]=>[3,5,7,9,10,1,2,4,6,8]=>[8,6,4,2,1,10,9,7,5,3]=>000000000 [[1,2,4,6,7],[3,5,8,9,10]]=>[3,5,8,9,10,1,2,4,6,7]=>[7,6,4,2,1,10,9,8,5,3]=>000000000 [[1,2,4,5,9],[3,6,7,8,10]]=>[3,6,7,8,10,1,2,4,5,9]=>[9,5,4,2,1,10,8,7,6,3]=>000000000 [[1,2,4,5,8],[3,6,7,9,10]]=>[3,6,7,9,10,1,2,4,5,8]=>[8,5,4,2,1,10,9,7,6,3]=>000000000 [[1,2,4,5,7],[3,6,8,9,10]]=>[3,6,8,9,10,1,2,4,5,7]=>[7,5,4,2,1,10,9,8,6,3]=>000000000 [[1,2,4,5,6],[3,7,8,9,10]]=>[3,7,8,9,10,1,2,4,5,6]=>[6,5,4,2,1,10,9,8,7,3]=>000000000 [[1,2,3,7,9],[4,5,6,8,10]]=>[4,5,6,8,10,1,2,3,7,9]=>[9,7,3,2,1,10,8,6,5,4]=>000000000 [[1,2,3,7,8],[4,5,6,9,10]]=>[4,5,6,9,10,1,2,3,7,8]=>[8,7,3,2,1,10,9,6,5,4]=>000000000 [[1,2,3,6,9],[4,5,7,8,10]]=>[4,5,7,8,10,1,2,3,6,9]=>[9,6,3,2,1,10,8,7,5,4]=>000000000 [[1,2,3,6,8],[4,5,7,9,10]]=>[4,5,7,9,10,1,2,3,6,8]=>[8,6,3,2,1,10,9,7,5,4]=>000000000 [[1,2,3,6,7],[4,5,8,9,10]]=>[4,5,8,9,10,1,2,3,6,7]=>[7,6,3,2,1,10,9,8,5,4]=>000000000 [[1,2,3,5,9],[4,6,7,8,10]]=>[4,6,7,8,10,1,2,3,5,9]=>[9,5,3,2,1,10,8,7,6,4]=>000000000 [[1,2,3,5,8],[4,6,7,9,10]]=>[4,6,7,9,10,1,2,3,5,8]=>[8,5,3,2,1,10,9,7,6,4]=>000000000 [[1,2,3,5,7],[4,6,8,9,10]]=>[4,6,8,9,10,1,2,3,5,7]=>[7,5,3,2,1,10,9,8,6,4]=>000000000 [[1,2,3,5,6],[4,7,8,9,10]]=>[4,7,8,9,10,1,2,3,5,6]=>[6,5,3,2,1,10,9,8,7,4]=>000000000 [[1,2,3,4,9],[5,6,7,8,10]]=>[5,6,7,8,10,1,2,3,4,9]=>[9,4,3,2,1,10,8,7,6,5]=>000000000 [[1,2,3,4,8],[5,6,7,9,10]]=>[5,6,7,9,10,1,2,3,4,8]=>[8,4,3,2,1,10,9,7,6,5]=>000000000 [[1,2,3,4,7],[5,6,8,9,10]]=>[5,6,8,9,10,1,2,3,4,7]=>[7,4,3,2,1,10,9,8,6,5]=>000000000 [[1,2,3,4,6],[5,7,8,9,10]]=>[5,7,8,9,10,1,2,3,4,6]=>[6,4,3,2,1,10,9,8,7,5]=>000000000 [[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]=>000010000 [[1,3,5,7,9,11],[2,4,6,8,10,12]]=>[2,4,6,8,10,12,1,3,5,7,9,11]=>[11,9,7,5,3,1,12,10,8,6,4,2]=>00000000000 [[1,3,5,7,9,10],[2,4,6,8,11,12]]=>[2,4,6,8,11,12,1,3,5,7,9,10]=>[10,9,7,5,3,1,12,11,8,6,4,2]=>00000000000 [[1,3,5,7,8,11],[2,4,6,9,10,12]]=>[2,4,6,9,10,12,1,3,5,7,8,11]=>[11,8,7,5,3,1,12,10,9,6,4,2]=>00000000000 [[1,3,5,7,8,10],[2,4,6,9,11,12]]=>[2,4,6,9,11,12,1,3,5,7,8,10]=>[10,8,7,5,3,1,12,11,9,6,4,2]=>00000000000 [[1,3,5,7,8,9],[2,4,6,10,11,12]]=>[2,4,6,10,11,12,1,3,5,7,8,9]=>[9,8,7,5,3,1,12,11,10,6,4,2]=>00000000000 [[1,3,5,6,9,11],[2,4,7,8,10,12]]=>[2,4,7,8,10,12,1,3,5,6,9,11]=>[11,9,6,5,3,1,12,10,8,7,4,2]=>00000000000 [[1,3,5,6,9,10],[2,4,7,8,11,12]]=>[2,4,7,8,11,12,1,3,5,6,9,10]=>[10,9,6,5,3,1,12,11,8,7,4,2]=>00000000000 [[1,3,5,6,8,11],[2,4,7,9,10,12]]=>[2,4,7,9,10,12,1,3,5,6,8,11]=>[11,8,6,5,3,1,12,10,9,7,4,2]=>00000000000 [[1,3,5,6,8,10],[2,4,7,9,11,12]]=>[2,4,7,9,11,12,1,3,5,6,8,10]=>[10,8,6,5,3,1,12,11,9,7,4,2]=>00000000000 [[1,3,5,6,8,9],[2,4,7,10,11,12]]=>[2,4,7,10,11,12,1,3,5,6,8,9]=>[9,8,6,5,3,1,12,11,10,7,4,2]=>00000000000 [[1,3,5,6,7,11],[2,4,8,9,10,12]]=>[2,4,8,9,10,12,1,3,5,6,7,11]=>[11,7,6,5,3,1,12,10,9,8,4,2]=>00000000000 [[1,3,5,6,7,10],[2,4,8,9,11,12]]=>[2,4,8,9,11,12,1,3,5,6,7,10]=>[10,7,6,5,3,1,12,11,9,8,4,2]=>00000000000 [[1,3,5,6,7,9],[2,4,8,10,11,12]]=>[2,4,8,10,11,12,1,3,5,6,7,9]=>[9,7,6,5,3,1,12,11,10,8,4,2]=>00000000000 [[1,3,5,6,7,8],[2,4,9,10,11,12]]=>[2,4,9,10,11,12,1,3,5,6,7,8]=>[8,7,6,5,3,1,12,11,10,9,4,2]=>00000000000 [[1,3,4,7,9,11],[2,5,6,8,10,12]]=>[2,5,6,8,10,12,1,3,4,7,9,11]=>[11,9,7,4,3,1,12,10,8,6,5,2]=>00000000000 [[1,3,4,7,9,10],[2,5,6,8,11,12]]=>[2,5,6,8,11,12,1,3,4,7,9,10]=>[10,9,7,4,3,1,12,11,8,6,5,2]=>00000000000 [[1,3,4,7,8,11],[2,5,6,9,10,12]]=>[2,5,6,9,10,12,1,3,4,7,8,11]=>[11,8,7,4,3,1,12,10,9,6,5,2]=>00000000000 [[1,3,4,7,8,10],[2,5,6,9,11,12]]=>[2,5,6,9,11,12,1,3,4,7,8,10]=>[10,8,7,4,3,1,12,11,9,6,5,2]=>00000000000 [[1,3,4,7,8,9],[2,5,6,10,11,12]]=>[2,5,6,10,11,12,1,3,4,7,8,9]=>[9,8,7,4,3,1,12,11,10,6,5,2]=>00000000000 [[1,3,4,6,9,11],[2,5,7,8,10,12]]=>[2,5,7,8,10,12,1,3,4,6,9,11]=>[11,9,6,4,3,1,12,10,8,7,5,2]=>00000000000 [[1,3,4,6,9,10],[2,5,7,8,11,12]]=>[2,5,7,8,11,12,1,3,4,6,9,10]=>[10,9,6,4,3,1,12,11,8,7,5,2]=>00000000000 [[1,3,4,6,8,11],[2,5,7,9,10,12]]=>[2,5,7,9,10,12,1,3,4,6,8,11]=>[11,8,6,4,3,1,12,10,9,7,5,2]=>00000000000 [[1,3,4,6,8,10],[2,5,7,9,11,12]]=>[2,5,7,9,11,12,1,3,4,6,8,10]=>[10,8,6,4,3,1,12,11,9,7,5,2]=>00000000000 [[1,3,4,6,8,9],[2,5,7,10,11,12]]=>[2,5,7,10,11,12,1,3,4,6,8,9]=>[9,8,6,4,3,1,12,11,10,7,5,2]=>00000000000 [[1,3,4,6,7,11],[2,5,8,9,10,12]]=>[2,5,8,9,10,12,1,3,4,6,7,11]=>[11,7,6,4,3,1,12,10,9,8,5,2]=>00000000000 [[1,3,4,6,7,10],[2,5,8,9,11,12]]=>[2,5,8,9,11,12,1,3,4,6,7,10]=>[10,7,6,4,3,1,12,11,9,8,5,2]=>00000000000 [[1,3,4,6,7,9],[2,5,8,10,11,12]]=>[2,5,8,10,11,12,1,3,4,6,7,9]=>[9,7,6,4,3,1,12,11,10,8,5,2]=>00000000000 [[1,3,4,6,7,8],[2,5,9,10,11,12]]=>[2,5,9,10,11,12,1,3,4,6,7,8]=>[8,7,6,4,3,1,12,11,10,9,5,2]=>00000000000 [[1,3,4,5,9,11],[2,6,7,8,10,12]]=>[2,6,7,8,10,12,1,3,4,5,9,11]=>[11,9,5,4,3,1,12,10,8,7,6,2]=>00000000000 [[1,3,4,5,9,10],[2,6,7,8,11,12]]=>[2,6,7,8,11,12,1,3,4,5,9,10]=>[10,9,5,4,3,1,12,11,8,7,6,2]=>00000000000 [[1,3,4,5,8,11],[2,6,7,9,10,12]]=>[2,6,7,9,10,12,1,3,4,5,8,11]=>[11,8,5,4,3,1,12,10,9,7,6,2]=>00000000000 [[1,3,4,5,8,10],[2,6,7,9,11,12]]=>[2,6,7,9,11,12,1,3,4,5,8,10]=>[10,8,5,4,3,1,12,11,9,7,6,2]=>00000000000 [[1,3,4,5,8,9],[2,6,7,10,11,12]]=>[2,6,7,10,11,12,1,3,4,5,8,9]=>[9,8,5,4,3,1,12,11,10,7,6,2]=>00000000000 [[1,3,4,5,7,11],[2,6,8,9,10,12]]=>[2,6,8,9,10,12,1,3,4,5,7,11]=>[11,7,5,4,3,1,12,10,9,8,6,2]=>00000000000 [[1,3,4,5,7,10],[2,6,8,9,11,12]]=>[2,6,8,9,11,12,1,3,4,5,7,10]=>[10,7,5,4,3,1,12,11,9,8,6,2]=>00000000000 [[1,3,4,5,7,9],[2,6,8,10,11,12]]=>[2,6,8,10,11,12,1,3,4,5,7,9]=>[9,7,5,4,3,1,12,11,10,8,6,2]=>00000000000 [[1,3,4,5,7,8],[2,6,9,10,11,12]]=>[2,6,9,10,11,12,1,3,4,5,7,8]=>[8,7,5,4,3,1,12,11,10,9,6,2]=>00000000000 [[1,3,4,5,6,11],[2,7,8,9,10,12]]=>[2,7,8,9,10,12,1,3,4,5,6,11]=>[11,6,5,4,3,1,12,10,9,8,7,2]=>00000000000 [[1,3,4,5,6,10],[2,7,8,9,11,12]]=>[2,7,8,9,11,12,1,3,4,5,6,10]=>[10,6,5,4,3,1,12,11,9,8,7,2]=>00000000000 [[1,3,4,5,6,9],[2,7,8,10,11,12]]=>[2,7,8,10,11,12,1,3,4,5,6,9]=>[9,6,5,4,3,1,12,11,10,8,7,2]=>00000000000 [[1,3,4,5,6,8],[2,7,9,10,11,12]]=>[2,7,9,10,11,12,1,3,4,5,6,8]=>[8,6,5,4,3,1,12,11,10,9,7,2]=>00000000000 [[1,3,4,5,6,7],[2,8,9,10,11,12]]=>[2,8,9,10,11,12,1,3,4,5,6,7]=>[7,6,5,4,3,1,12,11,10,9,8,2]=>00000000000 [[1,2,5,7,9,11],[3,4,6,8,10,12]]=>[3,4,6,8,10,12,1,2,5,7,9,11]=>[11,9,7,5,2,1,12,10,8,6,4,3]=>00000000000 [[1,2,5,7,9,10],[3,4,6,8,11,12]]=>[3,4,6,8,11,12,1,2,5,7,9,10]=>[10,9,7,5,2,1,12,11,8,6,4,3]=>00000000000 [[1,2,5,7,8,11],[3,4,6,9,10,12]]=>[3,4,6,9,10,12,1,2,5,7,8,11]=>[11,8,7,5,2,1,12,10,9,6,4,3]=>00000000000 [[1,2,5,7,8,10],[3,4,6,9,11,12]]=>[3,4,6,9,11,12,1,2,5,7,8,10]=>[10,8,7,5,2,1,12,11,9,6,4,3]=>00000000000 [[1,2,5,7,8,9],[3,4,6,10,11,12]]=>[3,4,6,10,11,12,1,2,5,7,8,9]=>[9,8,7,5,2,1,12,11,10,6,4,3]=>00000000000 [[1,2,5,6,9,11],[3,4,7,8,10,12]]=>[3,4,7,8,10,12,1,2,5,6,9,11]=>[11,9,6,5,2,1,12,10,8,7,4,3]=>00000000000 [[1,2,5,6,9,10],[3,4,7,8,11,12]]=>[3,4,7,8,11,12,1,2,5,6,9,10]=>[10,9,6,5,2,1,12,11,8,7,4,3]=>00000000000 [[1,2,5,6,8,11],[3,4,7,9,10,12]]=>[3,4,7,9,10,12,1,2,5,6,8,11]=>[11,8,6,5,2,1,12,10,9,7,4,3]=>00000000000 [[1,2,5,6,8,10],[3,4,7,9,11,12]]=>[3,4,7,9,11,12,1,2,5,6,8,10]=>[10,8,6,5,2,1,12,11,9,7,4,3]=>00000000000 [[1,2,5,6,8,9],[3,4,7,10,11,12]]=>[3,4,7,10,11,12,1,2,5,6,8,9]=>[9,8,6,5,2,1,12,11,10,7,4,3]=>00000000000 [[1,2,5,6,7,11],[3,4,8,9,10,12]]=>[3,4,8,9,10,12,1,2,5,6,7,11]=>[11,7,6,5,2,1,12,10,9,8,4,3]=>00000000000 [[1,2,5,6,7,10],[3,4,8,9,11,12]]=>[3,4,8,9,11,12,1,2,5,6,7,10]=>[10,7,6,5,2,1,12,11,9,8,4,3]=>00000000000 [[1,2,5,6,7,9],[3,4,8,10,11,12]]=>[3,4,8,10,11,12,1,2,5,6,7,9]=>[9,7,6,5,2,1,12,11,10,8,4,3]=>00000000000 [[1,2,5,6,7,8],[3,4,9,10,11,12]]=>[3,4,9,10,11,12,1,2,5,6,7,8]=>[8,7,6,5,2,1,12,11,10,9,4,3]=>00000000000 [[1,2,4,7,9,11],[3,5,6,8,10,12]]=>[3,5,6,8,10,12,1,2,4,7,9,11]=>[11,9,7,4,2,1,12,10,8,6,5,3]=>00000000000 [[1,2,4,7,9,10],[3,5,6,8,11,12]]=>[3,5,6,8,11,12,1,2,4,7,9,10]=>[10,9,7,4,2,1,12,11,8,6,5,3]=>00000000000 [[1,2,4,7,8,11],[3,5,6,9,10,12]]=>[3,5,6,9,10,12,1,2,4,7,8,11]=>[11,8,7,4,2,1,12,10,9,6,5,3]=>00000000000 [[1,2,4,7,8,10],[3,5,6,9,11,12]]=>[3,5,6,9,11,12,1,2,4,7,8,10]=>[10,8,7,4,2,1,12,11,9,6,5,3]=>00000000000 [[1,2,4,7,8,9],[3,5,6,10,11,12]]=>[3,5,6,10,11,12,1,2,4,7,8,9]=>[9,8,7,4,2,1,12,11,10,6,5,3]=>00000000000 [[1,2,4,6,9,11],[3,5,7,8,10,12]]=>[3,5,7,8,10,12,1,2,4,6,9,11]=>[11,9,6,4,2,1,12,10,8,7,5,3]=>00000000000 [[1,2,4,6,9,10],[3,5,7,8,11,12]]=>[3,5,7,8,11,12,1,2,4,6,9,10]=>[10,9,6,4,2,1,12,11,8,7,5,3]=>00000000000 [[1,2,4,6,8,11],[3,5,7,9,10,12]]=>[3,5,7,9,10,12,1,2,4,6,8,11]=>[11,8,6,4,2,1,12,10,9,7,5,3]=>00000000000 [[1,2,4,6,8,10],[3,5,7,9,11,12]]=>[3,5,7,9,11,12,1,2,4,6,8,10]=>[10,8,6,4,2,1,12,11,9,7,5,3]=>00000000000 [[1,2,4,6,8,9],[3,5,7,10,11,12]]=>[3,5,7,10,11,12,1,2,4,6,8,9]=>[9,8,6,4,2,1,12,11,10,7,5,3]=>00000000000 [[1,2,4,6,7,11],[3,5,8,9,10,12]]=>[3,5,8,9,10,12,1,2,4,6,7,11]=>[11,7,6,4,2,1,12,10,9,8,5,3]=>00000000000 [[1,2,4,6,7,10],[3,5,8,9,11,12]]=>[3,5,8,9,11,12,1,2,4,6,7,10]=>[10,7,6,4,2,1,12,11,9,8,5,3]=>00000000000 [[1,2,4,6,7,9],[3,5,8,10,11,12]]=>[3,5,8,10,11,12,1,2,4,6,7,9]=>[9,7,6,4,2,1,12,11,10,8,5,3]=>00000000000 [[1,2,4,6,7,8],[3,5,9,10,11,12]]=>[3,5,9,10,11,12,1,2,4,6,7,8]=>[8,7,6,4,2,1,12,11,10,9,5,3]=>00000000000 [[1,2,4,5,9,11],[3,6,7,8,10,12]]=>[3,6,7,8,10,12,1,2,4,5,9,11]=>[11,9,5,4,2,1,12,10,8,7,6,3]=>00000000000 [[1,2,4,5,9,10],[3,6,7,8,11,12]]=>[3,6,7,8,11,12,1,2,4,5,9,10]=>[10,9,5,4,2,1,12,11,8,7,6,3]=>00000000000 [[1,2,4,5,8,11],[3,6,7,9,10,12]]=>[3,6,7,9,10,12,1,2,4,5,8,11]=>[11,8,5,4,2,1,12,10,9,7,6,3]=>00000000000 [[1,2,4,5,8,10],[3,6,7,9,11,12]]=>[3,6,7,9,11,12,1,2,4,5,8,10]=>[10,8,5,4,2,1,12,11,9,7,6,3]=>00000000000 [[1,2,4,5,8,9],[3,6,7,10,11,12]]=>[3,6,7,10,11,12,1,2,4,5,8,9]=>[9,8,5,4,2,1,12,11,10,7,6,3]=>00000000000 [[1,2,4,5,7,11],[3,6,8,9,10,12]]=>[3,6,8,9,10,12,1,2,4,5,7,11]=>[11,7,5,4,2,1,12,10,9,8,6,3]=>00000000000 [[1,2,4,5,7,10],[3,6,8,9,11,12]]=>[3,6,8,9,11,12,1,2,4,5,7,10]=>[10,7,5,4,2,1,12,11,9,8,6,3]=>00000000000 [[1,2,4,5,7,9],[3,6,8,10,11,12]]=>[3,6,8,10,11,12,1,2,4,5,7,9]=>[9,7,5,4,2,1,12,11,10,8,6,3]=>00000000000 [[1,2,4,5,7,8],[3,6,9,10,11,12]]=>[3,6,9,10,11,12,1,2,4,5,7,8]=>[8,7,5,4,2,1,12,11,10,9,6,3]=>00000000000 [[1,2,4,5,6,11],[3,7,8,9,10,12]]=>[3,7,8,9,10,12,1,2,4,5,6,11]=>[11,6,5,4,2,1,12,10,9,8,7,3]=>00000000000 [[1,2,4,5,6,10],[3,7,8,9,11,12]]=>[3,7,8,9,11,12,1,2,4,5,6,10]=>[10,6,5,4,2,1,12,11,9,8,7,3]=>00000000000 [[1,2,4,5,6,9],[3,7,8,10,11,12]]=>[3,7,8,10,11,12,1,2,4,5,6,9]=>[9,6,5,4,2,1,12,11,10,8,7,3]=>00000000000 [[1,2,4,5,6,8],[3,7,9,10,11,12]]=>[3,7,9,10,11,12,1,2,4,5,6,8]=>[8,6,5,4,2,1,12,11,10,9,7,3]=>00000000000 [[1,2,4,5,6,7],[3,8,9,10,11,12]]=>[3,8,9,10,11,12,1,2,4,5,6,7]=>[7,6,5,4,2,1,12,11,10,9,8,3]=>00000000000 [[1,2,3,7,9,11],[4,5,6,8,10,12]]=>[4,5,6,8,10,12,1,2,3,7,9,11]=>[11,9,7,3,2,1,12,10,8,6,5,4]=>00000000000 [[1,2,3,7,9,10],[4,5,6,8,11,12]]=>[4,5,6,8,11,12,1,2,3,7,9,10]=>[10,9,7,3,2,1,12,11,8,6,5,4]=>00000000000 [[1,2,3,7,8,11],[4,5,6,9,10,12]]=>[4,5,6,9,10,12,1,2,3,7,8,11]=>[11,8,7,3,2,1,12,10,9,6,5,4]=>00000000000 [[1,2,3,7,8,10],[4,5,6,9,11,12]]=>[4,5,6,9,11,12,1,2,3,7,8,10]=>[10,8,7,3,2,1,12,11,9,6,5,4]=>00000000000 [[1,2,3,7,8,9],[4,5,6,10,11,12]]=>[4,5,6,10,11,12,1,2,3,7,8,9]=>[9,8,7,3,2,1,12,11,10,6,5,4]=>00000000000 [[1,2,3,6,9,11],[4,5,7,8,10,12]]=>[4,5,7,8,10,12,1,2,3,6,9,11]=>[11,9,6,3,2,1,12,10,8,7,5,4]=>00000000000 [[1,2,3,6,9,10],[4,5,7,8,11,12]]=>[4,5,7,8,11,12,1,2,3,6,9,10]=>[10,9,6,3,2,1,12,11,8,7,5,4]=>00000000000 [[1,2,3,6,8,11],[4,5,7,9,10,12]]=>[4,5,7,9,10,12,1,2,3,6,8,11]=>[11,8,6,3,2,1,12,10,9,7,5,4]=>00000000000 [[1,2,3,6,8,10],[4,5,7,9,11,12]]=>[4,5,7,9,11,12,1,2,3,6,8,10]=>[10,8,6,3,2,1,12,11,9,7,5,4]=>00000000000 [[1,2,3,6,8,9],[4,5,7,10,11,12]]=>[4,5,7,10,11,12,1,2,3,6,8,9]=>[9,8,6,3,2,1,12,11,10,7,5,4]=>00000000000 [[1,2,3,6,7,11],[4,5,8,9,10,12]]=>[4,5,8,9,10,12,1,2,3,6,7,11]=>[11,7,6,3,2,1,12,10,9,8,5,4]=>00000000000 [[1,2,3,6,7,10],[4,5,8,9,11,12]]=>[4,5,8,9,11,12,1,2,3,6,7,10]=>[10,7,6,3,2,1,12,11,9,8,5,4]=>00000000000 [[1,2,3,6,7,9],[4,5,8,10,11,12]]=>[4,5,8,10,11,12,1,2,3,6,7,9]=>[9,7,6,3,2,1,12,11,10,8,5,4]=>00000000000 [[1,2,3,6,7,8],[4,5,9,10,11,12]]=>[4,5,9,10,11,12,1,2,3,6,7,8]=>[8,7,6,3,2,1,12,11,10,9,5,4]=>00000000000 [[1,2,3,5,9,11],[4,6,7,8,10,12]]=>[4,6,7,8,10,12,1,2,3,5,9,11]=>[11,9,5,3,2,1,12,10,8,7,6,4]=>00000000000 [[1,2,3,5,9,10],[4,6,7,8,11,12]]=>[4,6,7,8,11,12,1,2,3,5,9,10]=>[10,9,5,3,2,1,12,11,8,7,6,4]=>00000000000 [[1,2,3,5,8,11],[4,6,7,9,10,12]]=>[4,6,7,9,10,12,1,2,3,5,8,11]=>[11,8,5,3,2,1,12,10,9,7,6,4]=>00000000000 [[1,2,3,5,8,10],[4,6,7,9,11,12]]=>[4,6,7,9,11,12,1,2,3,5,8,10]=>[10,8,5,3,2,1,12,11,9,7,6,4]=>00000000000 [[1,2,3,5,8,9],[4,6,7,10,11,12]]=>[4,6,7,10,11,12,1,2,3,5,8,9]=>[9,8,5,3,2,1,12,11,10,7,6,4]=>00000000000 [[1,2,3,5,7,11],[4,6,8,9,10,12]]=>[4,6,8,9,10,12,1,2,3,5,7,11]=>[11,7,5,3,2,1,12,10,9,8,6,4]=>00000000000 [[1,2,3,5,7,10],[4,6,8,9,11,12]]=>[4,6,8,9,11,12,1,2,3,5,7,10]=>[10,7,5,3,2,1,12,11,9,8,6,4]=>00000000000 [[1,2,3,5,7,9],[4,6,8,10,11,12]]=>[4,6,8,10,11,12,1,2,3,5,7,9]=>[9,7,5,3,2,1,12,11,10,8,6,4]=>00000000000 [[1,2,3,5,7,8],[4,6,9,10,11,12]]=>[4,6,9,10,11,12,1,2,3,5,7,8]=>[8,7,5,3,2,1,12,11,10,9,6,4]=>00000000000 [[1,2,3,5,6,11],[4,7,8,9,10,12]]=>[4,7,8,9,10,12,1,2,3,5,6,11]=>[11,6,5,3,2,1,12,10,9,8,7,4]=>00000000000 [[1,2,3,5,6,10],[4,7,8,9,11,12]]=>[4,7,8,9,11,12,1,2,3,5,6,10]=>[10,6,5,3,2,1,12,11,9,8,7,4]=>00000000000 [[1,2,3,5,6,9],[4,7,8,10,11,12]]=>[4,7,8,10,11,12,1,2,3,5,6,9]=>[9,6,5,3,2,1,12,11,10,8,7,4]=>00000000000 [[1,2,3,5,6,8],[4,7,9,10,11,12]]=>[4,7,9,10,11,12,1,2,3,5,6,8]=>[8,6,5,3,2,1,12,11,10,9,7,4]=>00000000000 [[1,2,3,5,6,7],[4,8,9,10,11,12]]=>[4,8,9,10,11,12,1,2,3,5,6,7]=>[7,6,5,3,2,1,12,11,10,9,8,4]=>00000000000 [[1,2,3,4,9,11],[5,6,7,8,10,12]]=>[5,6,7,8,10,12,1,2,3,4,9,11]=>[11,9,4,3,2,1,12,10,8,7,6,5]=>00000000000 [[1,2,3,4,9,10],[5,6,7,8,11,12]]=>[5,6,7,8,11,12,1,2,3,4,9,10]=>[10,9,4,3,2,1,12,11,8,7,6,5]=>00000000000 [[1,2,3,4,8,11],[5,6,7,9,10,12]]=>[5,6,7,9,10,12,1,2,3,4,8,11]=>[11,8,4,3,2,1,12,10,9,7,6,5]=>00000000000 [[1,2,3,4,8,10],[5,6,7,9,11,12]]=>[5,6,7,9,11,12,1,2,3,4,8,10]=>[10,8,4,3,2,1,12,11,9,7,6,5]=>00000000000 [[1,2,3,4,8,9],[5,6,7,10,11,12]]=>[5,6,7,10,11,12,1,2,3,4,8,9]=>[9,8,4,3,2,1,12,11,10,7,6,5]=>00000000000 [[1,2,3,4,7,11],[5,6,8,9,10,12]]=>[5,6,8,9,10,12,1,2,3,4,7,11]=>[11,7,4,3,2,1,12,10,9,8,6,5]=>00000000000 [[1,2,3,4,7,10],[5,6,8,9,11,12]]=>[5,6,8,9,11,12,1,2,3,4,7,10]=>[10,7,4,3,2,1,12,11,9,8,6,5]=>00000000000 [[1,2,3,4,7,9],[5,6,8,10,11,12]]=>[5,6,8,10,11,12,1,2,3,4,7,9]=>[9,7,4,3,2,1,12,11,10,8,6,5]=>00000000000 [[1,2,3,4,7,8],[5,6,9,10,11,12]]=>[5,6,9,10,11,12,1,2,3,4,7,8]=>[8,7,4,3,2,1,12,11,10,9,6,5]=>00000000000 [[1,2,3,4,6,11],[5,7,8,9,10,12]]=>[5,7,8,9,10,12,1,2,3,4,6,11]=>[11,6,4,3,2,1,12,10,9,8,7,5]=>00000000000 [[1,2,3,4,6,10],[5,7,8,9,11,12]]=>[5,7,8,9,11,12,1,2,3,4,6,10]=>[10,6,4,3,2,1,12,11,9,8,7,5]=>00000000000 [[1,2,3,4,6,9],[5,7,8,10,11,12]]=>[5,7,8,10,11,12,1,2,3,4,6,9]=>[9,6,4,3,2,1,12,11,10,8,7,5]=>00000000000 [[1,2,3,4,6,8],[5,7,9,10,11,12]]=>[5,7,9,10,11,12,1,2,3,4,6,8]=>[8,6,4,3,2,1,12,11,10,9,7,5]=>00000000000 [[1,2,3,4,6,7],[5,8,9,10,11,12]]=>[5,8,9,10,11,12,1,2,3,4,6,7]=>[7,6,4,3,2,1,12,11,10,9,8,5]=>00000000000 [[1,2,3,4,5,11],[6,7,8,9,10,12]]=>[6,7,8,9,10,12,1,2,3,4,5,11]=>[11,5,4,3,2,1,12,10,9,8,7,6]=>00000000000 [[1,2,3,4,5,10],[6,7,8,9,11,12]]=>[6,7,8,9,11,12,1,2,3,4,5,10]=>[10,5,4,3,2,1,12,11,9,8,7,6]=>00000000000 [[1,2,3,4,5,9],[6,7,8,10,11,12]]=>[6,7,8,10,11,12,1,2,3,4,5,9]=>[9,5,4,3,2,1,12,11,10,8,7,6]=>00000000000 [[1,2,3,4,5,8],[6,7,9,10,11,12]]=>[6,7,9,10,11,12,1,2,3,4,5,8]=>[8,5,4,3,2,1,12,11,10,9,7,6]=>00000000000 [[1,2,3,4,5,7],[6,8,9,10,11,12]]=>[6,8,9,10,11,12,1,2,3,4,5,7]=>[7,5,4,3,2,1,12,11,10,9,8,6]=>00000000000 [[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]=>00000100000 [[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]=>00000000 [[1,2,3,4,5,6,7,8],[9]]=>[9,1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1,9]=>00000001 [[1,2,3,4,5,6,7],[8,9]]=>[8,9,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,9,8]=>00000010 [[1,2,3,4,5,6,7],[8],[9]]=>[9,8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8,9]=>00000011 [[1,2,3,4,5,6],[7,8,9]]=>[7,8,9,1,2,3,4,5,6]=>[6,5,4,3,2,1,9,8,7]=>00000100 [[1,2,3,4,5,6],[7,8],[9]]=>[9,7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7,9]=>00000101 [[1,2,3,4,5,6],[7],[8],[9]]=>[9,8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8,9]=>00000111 [[1,2,3,4,5],[6,7,8,9]]=>[6,7,8,9,1,2,3,4,5]=>[5,4,3,2,1,9,8,7,6]=>00001000 [[1,2,3,4,5],[6,7,8],[9]]=>[9,6,7,8,1,2,3,4,5]=>[5,4,3,2,1,8,7,6,9]=>00001001 [[1,2,3,4,5],[6,7],[8,9]]=>[8,9,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,9,8]=>00001010 [[1,2,3,4,5],[6,7],[8],[9]]=>[9,8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8,9]=>00001011 [[1,2,3,4,5],[6],[7],[8],[9]]=>[9,8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8,9]=>00001111 [[1,2,3,4],[5,6,7,8],[9]]=>[9,5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5,9]=>00010001 [[1,2,3,4],[5,6,7],[8,9]]=>[8,9,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,9,8]=>00010010 [[1,2,3,4],[5,6,7],[8],[9]]=>[9,8,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,8,9]=>00010011 [[1,2,3,4],[5,6],[7,8],[9]]=>[9,7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7,9]=>00010101 [[1,2,3,4],[5,6],[7],[8],[9]]=>[9,8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8,9]=>00010111 [[1,2,3,4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8,9]=>00011111 [[1,2,3],[4,5,6],[7,8,9]]=>[7,8,9,4,5,6,1,2,3]=>[3,2,1,6,5,4,9,8,7]=>00100100 [[1,2,3],[4,5,6],[7,8],[9]]=>[9,7,8,4,5,6,1,2,3]=>[3,2,1,6,5,4,8,7,9]=>00100101 [[1,2,3],[4,5,6],[7],[8],[9]]=>[9,8,7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7,8,9]=>00100111 [[1,2,3],[4,5],[6,7],[8,9]]=>[8,9,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,9,8]=>00101010 [[1,2,3],[4,5],[6,7],[8],[9]]=>[9,8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8,9]=>00101011 [[1,2,3],[4,5],[6],[7],[8],[9]]=>[9,8,7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7,8,9]=>00101111 [[1,2,3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8,9]=>00111111 [[1,2],[3,4],[5,6],[7,8],[9]]=>[9,7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7,9]=>01010101 [[1,2],[3,4],[5,6],[7],[8],[9]]=>[9,8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8,9]=>01010111 [[1,2],[3,4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8,9]=>01011111 [[1,2],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8,9]=>01111111 [[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]=>11111111 [[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]=>000000000 [[1,2,3,4,5,6,7,8,9],[10]]=>[10,1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1,10]=>000000001 [[1,2,3,4,5,6,7,8],[9,10]]=>[9,10,1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1,10,9]=>000000010 [[1,2,3,4,5,6,7,8],[9],[10]]=>[10,9,1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1,9,10]=>000000011 [[1,2,3,4,5,6,7],[8,9,10]]=>[8,9,10,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,10,9,8]=>000000100 [[1,2,3,4,5,6,7],[8,9],[10]]=>[10,8,9,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,9,8,10]=>000000101 [[1,2,3,4,5,6,7],[8],[9],[10]]=>[10,9,8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8,9,10]=>000000111 [[1,2,3,4,5,6],[7,8,9,10]]=>[7,8,9,10,1,2,3,4,5,6]=>[6,5,4,3,2,1,10,9,8,7]=>000001000 [[1,2,3,4,5,6],[7,8,9],[10]]=>[10,7,8,9,1,2,3,4,5,6]=>[6,5,4,3,2,1,9,8,7,10]=>000001001 [[1,2,3,4,5,6],[7,8],[9,10]]=>[9,10,7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7,10,9]=>000001010 [[1,2,3,4,5,6],[7,8],[9],[10]]=>[10,9,7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7,9,10]=>000001011 [[1,2,3,4,5,6],[7],[8],[9],[10]]=>[10,9,8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8,9,10]=>000001111 [[1,2,3,4,5],[6,7,8,9],[10]]=>[10,6,7,8,9,1,2,3,4,5]=>[5,4,3,2,1,9,8,7,6,10]=>000010001 [[1,2,3,4,5],[6,7,8],[9,10]]=>[9,10,6,7,8,1,2,3,4,5]=>[5,4,3,2,1,8,7,6,10,9]=>000010010 [[1,2,3,4,5],[6,7,8],[9],[10]]=>[10,9,6,7,8,1,2,3,4,5]=>[5,4,3,2,1,8,7,6,9,10]=>000010011 [[1,2,3,4,5],[6,7],[8,9],[10]]=>[10,8,9,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,9,8,10]=>000010101 [[1,2,3,4,5],[6,7],[8],[9],[10]]=>[10,9,8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8,9,10]=>000010111 [[1,2,3,4,5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8,9,10]=>000011111 [[1,2,3,4],[5,6,7,8],[9,10]]=>[9,10,5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5,10,9]=>000100010 [[1,2,3,4],[5,6,7,8],[9],[10]]=>[10,9,5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5,9,10]=>000100011 [[1,2,3,4],[5,6,7],[8,9,10]]=>[8,9,10,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,10,9,8]=>000100100 [[1,2,3,4],[5,6,7],[8,9],[10]]=>[10,8,9,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,9,8,10]=>000100101 [[1,2,3,4],[5,6,7],[8],[9],[10]]=>[10,9,8,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,8,9,10]=>000100111 [[1,2,3,4],[5,6],[7,8],[9,10]]=>[9,10,7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7,10,9]=>000101010 [[1,2,3,4],[5,6],[7,8],[9],[10]]=>[10,9,7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7,9,10]=>000101011 [[1,2,3,4],[5,6],[7],[8],[9],[10]]=>[10,9,8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8,9,10]=>000101111 [[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8,9,10]=>000111111 [[1,2,3],[4,5,6],[7,8,9],[10]]=>[10,7,8,9,4,5,6,1,2,3]=>[3,2,1,6,5,4,9,8,7,10]=>001001001 [[1,2,3],[4,5,6],[7,8],[9,10]]=>[9,10,7,8,4,5,6,1,2,3]=>[3,2,1,6,5,4,8,7,10,9]=>001001010 [[1,2,3],[4,5,6],[7,8],[9],[10]]=>[10,9,7,8,4,5,6,1,2,3]=>[3,2,1,6,5,4,8,7,9,10]=>001001011 [[1,2,3],[4,5,6],[7],[8],[9],[10]]=>[10,9,8,7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7,8,9,10]=>001001111 [[1,2,3],[4,5],[6,7],[8,9],[10]]=>[10,8,9,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,9,8,10]=>001010101 [[1,2,3],[4,5],[6,7],[8],[9],[10]]=>[10,9,8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8,9,10]=>001010111 [[1,2,3],[4,5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7,8,9,10]=>001011111 [[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8,9,10]=>001111111 [[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]=>010101010 [[1,2],[3,4],[5,6],[7,8],[9],[10]]=>[10,9,7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7,9,10]=>010101011 [[1,2],[3,4],[5,6],[7],[8],[9],[10]]=>[10,9,8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8,9,10]=>010101111 [[1,2],[3,4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8,9,10]=>010111111 [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8,9,10]=>011111111 [[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]=>111111111 [[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]=>00000000000 [[1,2,3,4,5,6],[7,8,9,10],[11,12]]=>[11,12,7,8,9,10,1,2,3,4,5,6]=>[6,5,4,3,2,1,10,9,8,7,12,11]=>00000100010 [[1,2,3,4],[5,6,7,8],[9,10],[11,12]]=>[11,12,9,10,5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5,10,9,12,11]=>00010001010 [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]]=>[11,12,9,10,7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7,10,9,12,11]=>00010101010 [[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]=>01010101010 [[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]=>11111111111 [[1,3,4,5,6,7,8,9],[2]]=>[2,1,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,1,2]=>00000000 [[1,2,5,6,7,8,9],[3,4]]=>[3,4,1,2,5,6,7,8,9]=>[9,8,7,6,5,2,1,4,3]=>00000000 [[1,4,5,6,7,8,9],[2],[3]]=>[3,2,1,4,5,6,7,8,9]=>[9,8,7,6,5,4,1,2,3]=>00000000 [[1,2,3,7,8,9],[4,5,6]]=>[4,5,6,1,2,3,7,8,9]=>[9,8,7,3,2,1,6,5,4]=>00000000 [[1,3,6,7,8,9],[2,5],[4]]=>[4,2,5,1,3,6,7,8,9]=>[9,8,7,6,3,1,5,2,4]=>00000000 [[1,5,6,7,8,9],[2],[3],[4]]=>[4,3,2,1,5,6,7,8,9]=>[9,8,7,6,5,1,2,3,4]=>00000000 [[1,2,3,4,9],[5,6,7,8]]=>[5,6,7,8,1,2,3,4,9]=>[9,4,3,2,1,8,7,6,5]=>00000000 [[1,3,4,8,9],[2,6,7],[5]]=>[5,2,6,7,1,3,4,8,9]=>[9,8,4,3,1,7,6,2,5]=>00000000 [[1,2,7,8,9],[3,4],[5,6]]=>[5,6,3,4,1,2,7,8,9]=>[9,8,7,2,1,4,3,6,5]=>00000000 [[1,4,7,8,9],[2,6],[3],[5]]=>[5,3,2,6,1,4,7,8,9]=>[9,8,7,4,1,6,2,3,5]=>00000000 [[1,6,7,8,9],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8,9]=>[9,8,7,6,1,2,3,4,5]=>00000000 [[1,3,4,5],[2,7,8,9],[6]]=>[6,2,7,8,9,1,3,4,5]=>[5,4,3,1,9,8,7,2,6]=>00000000 [[1,2,5,9],[3,4,8],[6,7]]=>[6,7,3,4,8,1,2,5,9]=>[9,5,2,1,8,4,3,7,6]=>00000000 [[1,4,5,9],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5,9]=>[9,5,4,1,8,7,2,3,6]=>00000000 [[1,3,8,9],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3,8,9]=>[9,8,3,1,5,2,7,4,6]=>00000000 [[1,5,8,9],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5,8,9]=>[9,8,5,1,7,2,3,4,6]=>00000000 [[1,7,8,9],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7,8,9]=>[9,8,7,1,2,3,4,5,6]=>00000000 [[1,3,6],[2,5,9],[4,8],[7]]=>[7,4,8,2,5,9,1,3,6]=>[6,3,1,9,5,2,8,4,7]=>00000000 [[1,5,6],[2,8,9],[3],[4],[7]]=>[7,4,3,2,8,9,1,5,6]=>[6,5,1,9,8,2,3,4,7]=>00000000 [[1,2,9],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2,9]=>[9,2,1,4,3,6,5,8,7]=>00000000 [[1,4,9],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4,9]=>[9,4,1,6,2,8,3,5,7]=>00000000 [[1,6,9],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6,9]=>[9,6,1,8,2,3,4,5,7]=>00000000 [[1,8,9],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8,9]=>[9,8,1,2,3,4,5,6,7]=>00000000 [[1,3],[2,5],[4,7],[6,9],[8]]=>[8,6,9,4,7,2,5,1,3]=>[3,1,5,2,7,4,9,6,8]=>00000000 [[1,5],[2,7],[3,9],[4],[6],[8]]=>[8,6,4,3,9,2,7,1,5]=>[5,1,7,2,9,3,4,6,8]=>00000000 [[1,7],[2,9],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,9,1,7]=>[7,1,9,2,3,4,5,6,8]=>00000000 [[1,9],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1,9]=>[9,1,2,3,4,5,6,7,8]=>00000000 [[1,3,4,5,6,7,8,9,10],[2]]=>[2,1,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,1,2]=>000000000 [[1,2,5,6,7,8,9,10],[3,4]]=>[3,4,1,2,5,6,7,8,9,10]=>[10,9,8,7,6,5,2,1,4,3]=>000000000 [[1,4,5,6,7,8,9,10],[2],[3]]=>[3,2,1,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,1,2,3]=>000000000 [[1,2,3,7,8,9,10],[4,5,6]]=>[4,5,6,1,2,3,7,8,9,10]=>[10,9,8,7,3,2,1,6,5,4]=>000000000 [[1,3,6,7,8,9,10],[2,5],[4]]=>[4,2,5,1,3,6,7,8,9,10]=>[10,9,8,7,6,3,1,5,2,4]=>000000000 [[1,5,6,7,8,9,10],[2],[3],[4]]=>[4,3,2,1,5,6,7,8,9,10]=>[10,9,8,7,6,5,1,2,3,4]=>000000000 [[1,2,3,4,9,10],[5,6,7,8]]=>[5,6,7,8,1,2,3,4,9,10]=>[10,9,4,3,2,1,8,7,6,5]=>000000000 [[1,3,4,8,9,10],[2,6,7],[5]]=>[5,2,6,7,1,3,4,8,9,10]=>[10,9,8,4,3,1,7,6,2,5]=>000000000 [[1,2,7,8,9,10],[3,4],[5,6]]=>[5,6,3,4,1,2,7,8,9,10]=>[10,9,8,7,2,1,4,3,6,5]=>000000000 [[1,4,7,8,9,10],[2,6],[3],[5]]=>[5,3,2,6,1,4,7,8,9,10]=>[10,9,8,7,4,1,6,2,3,5]=>000000000 [[1,6,7,8,9,10],[2],[3],[4],[5]]=>[5,4,3,2,1,6,7,8,9,10]=>[10,9,8,7,6,1,2,3,4,5]=>000000000 [[1,3,4,5,10],[2,7,8,9],[6]]=>[6,2,7,8,9,1,3,4,5,10]=>[10,5,4,3,1,9,8,7,2,6]=>000000000 [[1,2,5,9,10],[3,4,8],[6,7]]=>[6,7,3,4,8,1,2,5,9,10]=>[10,9,5,2,1,8,4,3,7,6]=>000000000 [[1,4,5,9,10],[2,7,8],[3],[6]]=>[6,3,2,7,8,1,4,5,9,10]=>[10,9,5,4,1,8,7,2,3,6]=>000000000 [[1,3,8,9,10],[2,5],[4,7],[6]]=>[6,4,7,2,5,1,3,8,9,10]=>[10,9,8,3,1,5,2,7,4,6]=>000000000 [[1,5,8,9,10],[2,7],[3],[4],[6]]=>[6,4,3,2,7,1,5,8,9,10]=>[10,9,8,5,1,7,2,3,4,6]=>000000000 [[1,7,8,9,10],[2],[3],[4],[5],[6]]=>[6,5,4,3,2,1,7,8,9,10]=>[10,9,8,7,1,2,3,4,5,6]=>000000000 [[1,2,5,6],[3,4,9,10],[7,8]]=>[7,8,3,4,9,10,1,2,5,6]=>[6,5,2,1,10,9,4,3,8,7]=>000000000 [[1,4,5,6],[2,8,9,10],[3],[7]]=>[7,3,2,8,9,10,1,4,5,6]=>[6,5,4,1,10,9,8,2,3,7]=>000000000 [[1,2,3,10],[4,5,6],[7,8,9]]=>[7,8,9,4,5,6,1,2,3,10]=>[10,3,2,1,6,5,4,9,8,7]=>000000000 [[1,3,6,10],[2,5,9],[4,8],[7]]=>[7,4,8,2,5,9,1,3,6,10]=>[10,6,3,1,9,5,2,8,4,7]=>000000000 [[1,5,6,10],[2,8,9],[3],[4],[7]]=>[7,4,3,2,8,9,1,5,6,10]=>[10,6,5,1,9,8,2,3,4,7]=>000000000 [[1,2,9,10],[3,4],[5,6],[7,8]]=>[7,8,5,6,3,4,1,2,9,10]=>[10,9,2,1,4,3,6,5,8,7]=>000000000 [[1,4,9,10],[2,6],[3,8],[5],[7]]=>[7,5,3,8,2,6,1,4,9,10]=>[10,9,4,1,6,2,8,3,5,7]=>000000000 [[1,6,9,10],[2,8],[3],[4],[5],[7]]=>[7,5,4,3,2,8,1,6,9,10]=>[10,9,6,1,8,2,3,4,5,7]=>000000000 [[1,8,9,10],[2],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,1,8,9,10]=>[10,9,8,1,2,3,4,5,6,7]=>000000000 [[1,3,4],[2,6,7],[5,9,10],[8]]=>[8,5,9,10,2,6,7,1,3,4]=>[4,3,1,7,6,2,10,9,5,8]=>000000000 [[1,2,7],[3,4,10],[5,6],[8,9]]=>[8,9,5,6,3,4,10,1,2,7]=>[7,2,1,10,4,3,6,5,9,8]=>000000000 [[1,4,7],[2,6,10],[3,9],[5],[8]]=>[8,5,3,9,2,6,10,1,4,7]=>[7,4,1,10,6,2,9,3,5,8]=>000000000 [[1,6,7],[2,9,10],[3],[4],[5],[8]]=>[8,5,4,3,2,9,10,1,6,7]=>[7,6,1,10,9,2,3,4,5,8]=>000000000 [[1,3,10],[2,5],[4,7],[6,9],[8]]=>[8,6,9,4,7,2,5,1,3,10]=>[10,3,1,5,2,7,4,9,6,8]=>000000000 [[1,5,10],[2,7],[3,9],[4],[6],[8]]=>[8,6,4,3,9,2,7,1,5,10]=>[10,5,1,7,2,9,3,4,6,8]=>000000000 [[1,7,10],[2,9],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,9,1,7,10]=>[10,7,1,9,2,3,4,5,6,8]=>000000000 [[1,9,10],[2],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,1,9,10]=>[10,9,1,2,3,4,5,6,7,8]=>000000000 [[1,4],[2,6],[3,8],[5,10],[7],[9]]=>[9,7,5,10,3,8,2,6,1,4]=>[4,1,6,2,8,3,10,5,7,9]=>000000000 [[1,6],[2,8],[3,10],[4],[5],[7],[9]]=>[9,7,5,4,3,10,2,8,1,6]=>[6,1,8,2,10,3,4,5,7,9]=>000000000 [[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>[9,7,6,5,4,3,2,10,1,8]=>[8,1,10,2,3,4,5,6,7,9]=>000000000 [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,2,1,10]=>[10,1,2,3,4,5,6,7,8,9]=>000000000 [[1,8],[2,9],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,9,1,8]=>[8,1,9,2,3,4,5,6,7]=>00000000 [[1,7],[2,8],[3,9],[4],[5],[6]]=>[6,5,4,3,9,2,8,1,7]=>[7,1,8,2,9,3,4,5,6]=>00000000 [[1,7,9],[2,8],[3],[4],[5],[6]]=>[6,5,4,3,2,8,1,7,9]=>[9,7,1,8,2,3,4,5,6]=>00000000 [[1,6],[2,7],[3,8],[4,9],[5]]=>[5,4,9,3,8,2,7,1,6]=>[6,1,7,2,8,3,9,4,5]=>00000000 [[1,6,9],[2,7],[3,8],[4],[5]]=>[5,4,3,8,2,7,1,6,9]=>[9,6,1,7,2,8,3,4,5]=>00000000 [[1,6,8],[2,7,9],[3],[4],[5]]=>[5,4,3,2,7,9,1,6,8]=>[8,6,1,9,7,2,3,4,5]=>00000000 [[1,6,8,9],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6,8,9]=>[9,8,6,1,7,2,3,4,5]=>00000000 [[1,5,9],[2,6],[3,7],[4,8]]=>[4,8,3,7,2,6,1,5,9]=>[9,5,1,6,2,7,3,8,4]=>00000000 [[1,5,8],[2,6,9],[3,7],[4]]=>[4,3,7,2,6,9,1,5,8]=>[8,5,1,9,6,2,7,3,4]=>00000000 [[1,5,8,9],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5,8,9]=>[9,8,5,1,6,2,7,3,4]=>00000000 [[1,5,7,9],[2,6,8],[3],[4]]=>[4,3,2,6,8,1,5,7,9]=>[9,7,5,1,8,6,2,3,4]=>00000000 [[1,5,7,8,9],[2,6],[3],[4]]=>[4,3,2,6,1,5,7,8,9]=>[9,8,7,5,1,6,2,3,4]=>00000000 [[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]=>00000000 [[1,4,7,9],[2,5,8],[3,6]]=>[3,6,2,5,8,1,4,7,9]=>[9,7,4,1,8,5,2,6,3]=>00000000 [[1,4,7,8,9],[2,5],[3,6]]=>[3,6,2,5,1,4,7,8,9]=>[9,8,7,4,1,5,2,6,3]=>00000000 [[1,4,6,8],[2,5,7,9],[3]]=>[3,2,5,7,9,1,4,6,8]=>[8,6,4,1,9,7,5,2,3]=>00000000 [[1,4,6,8,9],[2,5,7],[3]]=>[3,2,5,7,1,4,6,8,9]=>[9,8,6,4,1,7,5,2,3]=>00000000 [[1,4,6,7,8,9],[2,5],[3]]=>[3,2,5,1,4,6,7,8,9]=>[9,8,7,6,4,1,5,2,3]=>00000000 [[1,3,5,7,9],[2,4,6,8]]=>[2,4,6,8,1,3,5,7,9]=>[9,7,5,3,1,8,6,4,2]=>00000000 [[1,3,5,7,8,9],[2,4,6]]=>[2,4,6,1,3,5,7,8,9]=>[9,8,7,5,3,1,6,4,2]=>00000000 [[1,3,5,6,7,8,9],[2,4]]=>[2,4,1,3,5,6,7,8,9]=>[9,8,7,6,5,3,1,4,2]=>00000000 [[1,9],[2,10],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,2,10,1,9]=>[9,1,10,2,3,4,5,6,7,8]=>000000000 [[1,8],[2,9],[3,10],[4],[5],[6],[7]]=>[7,6,5,4,3,10,2,9,1,8]=>[8,1,9,2,10,3,4,5,6,7]=>000000000 [[1,8,10],[2,9],[3],[4],[5],[6],[7]]=>[7,6,5,4,3,2,9,1,8,10]=>[10,8,1,9,2,3,4,5,6,7]=>000000000 [[1,7],[2,8],[3,9],[4,10],[5],[6]]=>[6,5,4,10,3,9,2,8,1,7]=>[7,1,8,2,9,3,10,4,5,6]=>000000000 [[1,7,10],[2,8],[3,9],[4],[5],[6]]=>[6,5,4,3,9,2,8,1,7,10]=>[10,7,1,8,2,9,3,4,5,6]=>000000000 [[1,7,9],[2,8,10],[3],[4],[5],[6]]=>[6,5,4,3,2,8,10,1,7,9]=>[9,7,1,10,8,2,3,4,5,6]=>000000000 [[1,7,9,10],[2,8],[3],[4],[5],[6]]=>[6,5,4,3,2,8,1,7,9,10]=>[10,9,7,1,8,2,3,4,5,6]=>000000000 [[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]=>000000000 [[1,6,10],[2,7],[3,8],[4,9],[5]]=>[5,4,9,3,8,2,7,1,6,10]=>[10,6,1,7,2,8,3,9,4,5]=>000000000 [[1,6,9],[2,7,10],[3,8],[4],[5]]=>[5,4,3,8,2,7,10,1,6,9]=>[9,6,1,10,7,2,8,3,4,5]=>000000000 [[1,6,9,10],[2,7],[3,8],[4],[5]]=>[5,4,3,8,2,7,1,6,9,10]=>[10,9,6,1,7,2,8,3,4,5]=>000000000 [[1,6,8,10],[2,7,9],[3],[4],[5]]=>[5,4,3,2,7,9,1,6,8,10]=>[10,8,6,1,9,7,2,3,4,5]=>000000000 [[1,6,8,9,10],[2,7],[3],[4],[5]]=>[5,4,3,2,7,1,6,8,9,10]=>[10,9,8,6,1,7,2,3,4,5]=>000000000 [[1,5,9],[2,6,10],[3,7],[4,8]]=>[4,8,3,7,2,6,10,1,5,9]=>[9,5,1,10,6,2,7,3,8,4]=>000000000 [[1,5,9,10],[2,6],[3,7],[4,8]]=>[4,8,3,7,2,6,1,5,9,10]=>[10,9,5,1,6,2,7,3,8,4]=>000000000 [[1,5,8],[2,6,9],[3,7,10],[4]]=>[4,3,7,10,2,6,9,1,5,8]=>[8,5,1,9,6,2,10,7,3,4]=>000000000 [[1,5,8,10],[2,6,9],[3,7],[4]]=>[4,3,7,2,6,9,1,5,8,10]=>[10,8,5,1,9,6,2,7,3,4]=>000000000 [[1,5,8,9,10],[2,6],[3,7],[4]]=>[4,3,7,2,6,1,5,8,9,10]=>[10,9,8,5,1,6,2,7,3,4]=>000000000 [[1,5,7,9],[2,6,8,10],[3],[4]]=>[4,3,2,6,8,10,1,5,7,9]=>[9,7,5,1,10,8,6,2,3,4]=>000000000 [[1,5,7,9,10],[2,6,8],[3],[4]]=>[4,3,2,6,8,1,5,7,9,10]=>[10,9,7,5,1,8,6,2,3,4]=>000000000 [[1,5,7,8,9,10],[2,6],[3],[4]]=>[4,3,2,6,1,5,7,8,9,10]=>[10,9,8,7,5,1,6,2,3,4]=>000000000 [[1,4,7,10],[2,5,8],[3,6,9]]=>[3,6,9,2,5,8,1,4,7,10]=>[10,7,4,1,8,5,2,9,6,3]=>000000000 [[1,4,7,9],[2,5,8,10],[3,6]]=>[3,6,2,5,8,10,1,4,7,9]=>[9,7,4,1,10,8,5,2,6,3]=>000000000 [[1,4,7,9,10],[2,5,8],[3,6]]=>[3,6,2,5,8,1,4,7,9,10]=>[10,9,7,4,1,8,5,2,6,3]=>000000000 [[1,4,7,8,9,10],[2,5],[3,6]]=>[3,6,2,5,1,4,7,8,9,10]=>[10,9,8,7,4,1,5,2,6,3]=>000000000 [[1,4,6,8,10],[2,5,7,9],[3]]=>[3,2,5,7,9,1,4,6,8,10]=>[10,8,6,4,1,9,7,5,2,3]=>000000000 [[1,4,6,8,9,10],[2,5,7],[3]]=>[3,2,5,7,1,4,6,8,9,10]=>[10,9,8,6,4,1,7,5,2,3]=>000000000 [[1,4,6,7,8,9,10],[2,5],[3]]=>[3,2,5,1,4,6,7,8,9,10]=>[10,9,8,7,6,4,1,5,2,3]=>000000000 [[1,3,5,7,9,10],[2,4,6,8]]=>[2,4,6,8,1,3,5,7,9,10]=>[10,9,7,5,3,1,8,6,4,2]=>000000000 [[1,3,5,7,8,9,10],[2,4,6]]=>[2,4,6,1,3,5,7,8,9,10]=>[10,9,8,7,5,3,1,6,4,2]=>000000000 [[1,3,5,6,7,8,9,10],[2,4]]=>[2,4,1,3,5,6,7,8,9,10]=>[10,9,8,7,6,5,3,1,4,2]=>000000000 [[1,3],[2,4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,2,4,1,3]=>[3,1,4,2,5,6,7,8,9]=>00011111 [[1,4],[2,5],[3,6],[7],[8],[9]]=>[9,8,7,3,6,2,5,1,4]=>[4,1,5,2,6,3,7,8,9]=>00000111 [[1,2,4],[3,5],[6],[7],[8],[9]]=>[9,8,7,6,3,5,1,2,4]=>[4,2,1,5,3,6,7,8,9]=>00001111 [[1,5],[2,6],[3,7],[4,8],[9]]=>[9,4,8,3,7,2,6,1,5]=>[5,1,6,2,7,3,8,4,9]=>00000001 [[1,2,5],[3,6],[4,7],[8],[9]]=>[9,8,4,7,3,6,1,2,5]=>[5,2,1,6,3,7,4,8,9]=>00000011 [[1,3,5],[2,4,6],[7],[8],[9]]=>[9,8,7,2,4,6,1,3,5]=>[5,3,1,6,4,2,7,8,9]=>00000111 [[1,2,3,5],[4,6],[7],[8],[9]]=>[9,8,7,4,6,1,2,3,5]=>[5,3,2,1,6,4,7,8,9]=>00000111 [[1,2,6],[3,7],[4,8],[5,9]]=>[5,9,4,8,3,7,1,2,6]=>[6,2,1,7,3,8,4,9,5]=>00000000 [[1,3,6],[2,4,7],[5,8],[9]]=>[9,5,8,2,4,7,1,3,6]=>[6,3,1,7,4,2,8,5,9]=>00000001 [[1,2,3,6],[4,7],[5,8],[9]]=>[9,5,8,4,7,1,2,3,6]=>[6,3,2,1,7,4,8,5,9]=>00000001 [[1,2,4,6],[3,5,7],[8],[9]]=>[9,8,3,5,7,1,2,4,6]=>[6,4,2,1,7,5,3,8,9]=>00000011 [[1,2,3,4,6],[5,7],[8],[9]]=>[9,8,5,7,1,2,3,4,6]=>[6,4,3,2,1,7,5,8,9]=>00000011 [[1,2,4,7],[3,5,8],[6,9]]=>[6,9,3,5,8,1,2,4,7]=>[7,4,2,1,8,5,3,9,6]=>00000000 [[1,2,3,4,7],[5,8],[6,9]]=>[6,9,5,8,1,2,3,4,7]=>[7,4,3,2,1,8,5,9,6]=>00000000 [[1,3,5,7],[2,4,6,8],[9]]=>[9,2,4,6,8,1,3,5,7]=>[7,5,3,1,8,6,4,2,9]=>00000001 [[1,2,3,5,7],[4,6,8],[9]]=>[9,4,6,8,1,2,3,5,7]=>[7,5,3,2,1,8,6,4,9]=>00000001 [[1,2,3,4,5,7],[6,8],[9]]=>[9,6,8,1,2,3,4,5,7]=>[7,5,4,3,2,1,8,6,9]=>00000001 [[1,2,4,6,8],[3,5,7,9]]=>[3,5,7,9,1,2,4,6,8]=>[8,6,4,2,1,9,7,5,3]=>00000000 [[1,2,3,4,6,8],[5,7,9]]=>[5,7,9,1,2,3,4,6,8]=>[8,6,4,3,2,1,9,7,5]=>00000000 [[1,2,3,4,5,6,8],[7,9]]=>[7,9,1,2,3,4,5,6,8]=>[8,6,5,4,3,2,1,9,7]=>00000000 [[1,3],[2,4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,2,4,1,3]=>[3,1,4,2,5,6,7,8,9,10]=>000111111 [[1,4],[2,5],[3,6],[7],[8],[9],[10]]=>[10,9,8,7,3,6,2,5,1,4]=>[4,1,5,2,6,3,7,8,9,10]=>000001111 [[1,2,4],[3,5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,3,5,1,2,4]=>[4,2,1,5,3,6,7,8,9,10]=>000011111 [[1,5],[2,6],[3,7],[4,8],[9],[10]]=>[10,9,4,8,3,7,2,6,1,5]=>[5,1,6,2,7,3,8,4,9,10]=>000000011 [[1,2,5],[3,6],[4,7],[8],[9],[10]]=>[10,9,8,4,7,3,6,1,2,5]=>[5,2,1,6,3,7,4,8,9,10]=>000000111 [[1,3,5],[2,4,6],[7],[8],[9],[10]]=>[10,9,8,7,2,4,6,1,3,5]=>[5,3,1,6,4,2,7,8,9,10]=>000001111 [[1,2,3,5],[4,6],[7],[8],[9],[10]]=>[10,9,8,7,4,6,1,2,3,5]=>[5,3,2,1,6,4,7,8,9,10]=>000001111 [[1,2,6],[3,7],[4,8],[5,9],[10]]=>[10,5,9,4,8,3,7,1,2,6]=>[6,2,1,7,3,8,4,9,5,10]=>000000001 [[1,3,6],[2,4,7],[5,8],[9],[10]]=>[10,9,5,8,2,4,7,1,3,6]=>[6,3,1,7,4,2,8,5,9,10]=>000000011 [[1,2,3,6],[4,7],[5,8],[9],[10]]=>[10,9,5,8,4,7,1,2,3,6]=>[6,3,2,1,7,4,8,5,9,10]=>000000011 [[1,2,4,6],[3,5,7],[8],[9],[10]]=>[10,9,8,3,5,7,1,2,4,6]=>[6,4,2,1,7,5,3,8,9,10]=>000000111 [[1,2,3,4,6],[5,7],[8],[9],[10]]=>[10,9,8,5,7,1,2,3,4,6]=>[6,4,3,2,1,7,5,8,9,10]=>000000111 [[1,3,7],[2,4,8],[5,9],[6,10]]=>[6,10,5,9,2,4,8,1,3,7]=>[7,3,1,8,4,2,9,5,10,6]=>000000000 [[1,2,3,7],[4,8],[5,9],[6,10]]=>[6,10,5,9,4,8,1,2,3,7]=>[7,3,2,1,8,4,9,5,10,6]=>000000000 [[1,4,7],[2,5,8],[3,6,9],[10]]=>[10,3,6,9,2,5,8,1,4,7]=>[7,4,1,8,5,2,9,6,3,10]=>000000001 [[1,2,4,7],[3,5,8],[6,9],[10]]=>[10,6,9,3,5,8,1,2,4,7]=>[7,4,2,1,8,5,3,9,6,10]=>000000001 [[1,2,3,4,7],[5,8],[6,9],[10]]=>[10,6,9,5,8,1,2,3,4,7]=>[7,4,3,2,1,8,5,9,6,10]=>000000001 [[1,3,5,7],[2,4,6,8],[9],[10]]=>[10,9,2,4,6,8,1,3,5,7]=>[7,5,3,1,8,6,4,2,9,10]=>000000011 [[1,2,3,5,7],[4,6,8],[9],[10]]=>[10,9,4,6,8,1,2,3,5,7]=>[7,5,3,2,1,8,6,4,9,10]=>000000011 [[1,2,3,4,5,7],[6,8],[9],[10]]=>[10,9,6,8,1,2,3,4,5,7]=>[7,5,4,3,2,1,8,6,9,10]=>000000011 [[1,2,5,8],[3,6,9],[4,7,10]]=>[4,7,10,3,6,9,1,2,5,8]=>[8,5,2,1,9,6,3,10,7,4]=>000000000 [[1,3,5,8],[2,4,6,9],[7,10]]=>[7,10,2,4,6,9,1,3,5,8]=>[8,5,3,1,9,6,4,2,10,7]=>000000000 [[1,2,3,5,8],[4,6,9],[7,10]]=>[7,10,4,6,9,1,2,3,5,8]=>[8,5,3,2,1,9,6,4,10,7]=>000000000 [[1,2,3,4,5,8],[6,9],[7,10]]=>[7,10,6,9,1,2,3,4,5,8]=>[8,5,4,3,2,1,9,6,10,7]=>000000000 [[1,2,4,6,8],[3,5,7,9],[10]]=>[10,3,5,7,9,1,2,4,6,8]=>[8,6,4,2,1,9,7,5,3,10]=>000000001 [[1,2,3,4,6,8],[5,7,9],[10]]=>[10,5,7,9,1,2,3,4,6,8]=>[8,6,4,3,2,1,9,7,5,10]=>000000001 [[1,2,3,4,5,6,8],[7,9],[10]]=>[10,7,9,1,2,3,4,5,6,8]=>[8,6,5,4,3,2,1,9,7,10]=>000000001 [[1,2,3,5,7,9],[4,6,8,10]]=>[4,6,8,10,1,2,3,5,7,9]=>[9,7,5,3,2,1,10,8,6,4]=>000000000 [[1,2,3,4,5,7,9],[6,8,10]]=>[6,8,10,1,2,3,4,5,7,9]=>[9,7,5,4,3,2,1,10,8,6]=>000000000 [[1,2,3,4,5,6,7,9],[8,10]]=>[8,10,1,2,3,4,5,6,7,9]=>[9,7,6,5,4,3,2,1,10,8]=>000000000 [[1,2],[3,4],[5,6],[7,9],[8,10]]=>[8,10,7,9,5,6,3,4,1,2]=>[2,1,4,3,6,5,9,7,10,8]=>010101000 [[1,2],[3,4],[5,7],[6,8],[9,10]]=>[9,10,6,8,5,7,3,4,1,2]=>[2,1,4,3,7,5,8,6,10,9]=>010100010 [[1,2],[3,4],[5,7],[6,9],[8,10]]=>[8,10,6,9,5,7,3,4,1,2]=>[2,1,4,3,7,5,9,6,10,8]=>010100000 [[1,2],[3,4],[5,8],[6,9],[7,10]]=>[7,10,6,9,5,8,3,4,1,2]=>[2,1,4,3,8,5,9,6,10,7]=>010100000 [[1,2],[3,5],[4,6],[7,8],[9,10]]=>[9,10,7,8,4,6,3,5,1,2]=>[2,1,5,3,6,4,8,7,10,9]=>010001010 [[1,2],[3,5],[4,6],[7,9],[8,10]]=>[8,10,7,9,4,6,3,5,1,2]=>[2,1,5,3,6,4,9,7,10,8]=>010001000 [[1,2],[3,5],[4,7],[6,8],[9,10]]=>[9,10,6,8,4,7,3,5,1,2]=>[2,1,5,3,7,4,8,6,10,9]=>010000010 [[1,2],[3,5],[4,7],[6,9],[8,10]]=>[8,10,6,9,4,7,3,5,1,2]=>[2,1,5,3,7,4,9,6,10,8]=>010000000 [[1,2],[3,5],[4,8],[6,9],[7,10]]=>[7,10,6,9,4,8,3,5,1,2]=>[2,1,5,3,8,4,9,6,10,7]=>010000000 [[1,2],[3,6],[4,7],[5,8],[9,10]]=>[9,10,5,8,4,7,3,6,1,2]=>[2,1,6,3,7,4,8,5,10,9]=>010000010 [[1,2],[3,6],[4,7],[5,9],[8,10]]=>[8,10,5,9,4,7,3,6,1,2]=>[2,1,6,3,7,4,9,5,10,8]=>010000000 [[1,2],[3,6],[4,8],[5,9],[7,10]]=>[7,10,5,9,4,8,3,6,1,2]=>[2,1,6,3,8,4,9,5,10,7]=>010000000 [[1,2],[3,7],[4,8],[5,9],[6,10]]=>[6,10,5,9,4,8,3,7,1,2]=>[2,1,7,3,8,4,9,5,10,6]=>010000000 [[1,3],[2,4],[5,6],[7,8],[9,10]]=>[9,10,7,8,5,6,2,4,1,3]=>[3,1,4,2,6,5,8,7,10,9]=>000101010 [[1,3],[2,4],[5,6],[7,9],[8,10]]=>[8,10,7,9,5,6,2,4,1,3]=>[3,1,4,2,6,5,9,7,10,8]=>000101000 [[1,3],[2,4],[5,7],[6,8],[9,10]]=>[9,10,6,8,5,7,2,4,1,3]=>[3,1,4,2,7,5,8,6,10,9]=>000100010 [[1,3],[2,4],[5,7],[6,9],[8,10]]=>[8,10,6,9,5,7,2,4,1,3]=>[3,1,4,2,7,5,9,6,10,8]=>000100000 [[1,3],[2,4],[5,8],[6,9],[7,10]]=>[7,10,6,9,5,8,2,4,1,3]=>[3,1,4,2,8,5,9,6,10,7]=>000100000 [[1,3],[2,5],[4,6],[7,8],[9,10]]=>[9,10,7,8,4,6,2,5,1,3]=>[3,1,5,2,6,4,8,7,10,9]=>000001010 [[1,3],[2,5],[4,6],[7,9],[8,10]]=>[8,10,7,9,4,6,2,5,1,3]=>[3,1,5,2,6,4,9,7,10,8]=>000001000 [[1,3],[2,5],[4,7],[6,8],[9,10]]=>[9,10,6,8,4,7,2,5,1,3]=>[3,1,5,2,7,4,8,6,10,9]=>000000010 [[1,3],[2,5],[4,7],[6,9],[8,10]]=>[8,10,6,9,4,7,2,5,1,3]=>[3,1,5,2,7,4,9,6,10,8]=>000000000 [[1,3],[2,5],[4,8],[6,9],[7,10]]=>[7,10,6,9,4,8,2,5,1,3]=>[3,1,5,2,8,4,9,6,10,7]=>000000000 [[1,3],[2,6],[4,7],[5,8],[9,10]]=>[9,10,5,8,4,7,2,6,1,3]=>[3,1,6,2,7,4,8,5,10,9]=>000000010 [[1,3],[2,6],[4,7],[5,9],[8,10]]=>[8,10,5,9,4,7,2,6,1,3]=>[3,1,6,2,7,4,9,5,10,8]=>000000000 [[1,3],[2,6],[4,8],[5,9],[7,10]]=>[7,10,5,9,4,8,2,6,1,3]=>[3,1,6,2,8,4,9,5,10,7]=>000000000 [[1,3],[2,7],[4,8],[5,9],[6,10]]=>[6,10,5,9,4,8,2,7,1,3]=>[3,1,7,2,8,4,9,5,10,6]=>000000000 [[1,4],[2,5],[3,6],[7,8],[9,10]]=>[9,10,7,8,3,6,2,5,1,4]=>[4,1,5,2,6,3,8,7,10,9]=>000001010 [[1,4],[2,5],[3,6],[7,9],[8,10]]=>[8,10,7,9,3,6,2,5,1,4]=>[4,1,5,2,6,3,9,7,10,8]=>000001000 [[1,4],[2,5],[3,7],[6,8],[9,10]]=>[9,10,6,8,3,7,2,5,1,4]=>[4,1,5,2,7,3,8,6,10,9]=>000000010 [[1,4],[2,5],[3,7],[6,9],[8,10]]=>[8,10,6,9,3,7,2,5,1,4]=>[4,1,5,2,7,3,9,6,10,8]=>000000000 [[1,4],[2,5],[3,8],[6,9],[7,10]]=>[7,10,6,9,3,8,2,5,1,4]=>[4,1,5,2,8,3,9,6,10,7]=>000000000 [[1,4],[2,6],[3,7],[5,8],[9,10]]=>[9,10,5,8,3,7,2,6,1,4]=>[4,1,6,2,7,3,8,5,10,9]=>000000010 [[1,4],[2,6],[3,7],[5,9],[8,10]]=>[8,10,5,9,3,7,2,6,1,4]=>[4,1,6,2,7,3,9,5,10,8]=>000000000 [[1,4],[2,6],[3,8],[5,9],[7,10]]=>[7,10,5,9,3,8,2,6,1,4]=>[4,1,6,2,8,3,9,5,10,7]=>000000000 [[1,4],[2,7],[3,8],[5,9],[6,10]]=>[6,10,5,9,3,8,2,7,1,4]=>[4,1,7,2,8,3,9,5,10,6]=>000000000 [[1,5],[2,6],[3,7],[4,8],[9,10]]=>[9,10,4,8,3,7,2,6,1,5]=>[5,1,6,2,7,3,8,4,10,9]=>000000010 [[1,5],[2,6],[3,7],[4,9],[8,10]]=>[8,10,4,9,3,7,2,6,1,5]=>[5,1,6,2,7,3,9,4,10,8]=>000000000 [[1,5],[2,6],[3,8],[4,9],[7,10]]=>[7,10,4,9,3,8,2,6,1,5]=>[5,1,6,2,8,3,9,4,10,7]=>000000000 [[1,5],[2,7],[3,8],[4,9],[6,10]]=>[6,10,4,9,3,8,2,7,1,5]=>[5,1,7,2,8,3,9,4,10,6]=>000000000 [[1,2],[3,4],[5,6],[7,8],[9,11],[10,12]]=>[10,12,9,11,7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7,11,9,12,10]=>01010101000 [[1,2],[3,4],[5,6],[7,9],[8,10],[11,12]]=>[11,12,8,10,7,9,5,6,3,4,1,2]=>[2,1,4,3,6,5,9,7,10,8,12,11]=>01010100010 [[1,2],[3,4],[5,6],[7,9],[8,11],[10,12]]=>[10,12,8,11,7,9,5,6,3,4,1,2]=>[2,1,4,3,6,5,9,7,11,8,12,10]=>01010100000 [[1,2],[3,4],[5,6],[7,10],[8,11],[9,12]]=>[9,12,8,11,7,10,5,6,3,4,1,2]=>[2,1,4,3,6,5,10,7,11,8,12,9]=>01010100000 [[1,2],[3,4],[5,7],[6,8],[9,10],[11,12]]=>[11,12,9,10,6,8,5,7,3,4,1,2]=>[2,1,4,3,7,5,8,6,10,9,12,11]=>01010001010 [[1,2],[3,4],[5,7],[6,8],[9,11],[10,12]]=>[10,12,9,11,6,8,5,7,3,4,1,2]=>[2,1,4,3,7,5,8,6,11,9,12,10]=>01010001000 [[1,2],[3,4],[5,7],[6,9],[8,10],[11,12]]=>[11,12,8,10,6,9,5,7,3,4,1,2]=>[2,1,4,3,7,5,9,6,10,8,12,11]=>01010000010 [[1,2],[3,4],[5,7],[6,9],[8,11],[10,12]]=>[10,12,8,11,6,9,5,7,3,4,1,2]=>[2,1,4,3,7,5,9,6,11,8,12,10]=>01010000000 [[1,2],[3,4],[5,7],[6,10],[8,11],[9,12]]=>[9,12,8,11,6,10,5,7,3,4,1,2]=>[2,1,4,3,7,5,10,6,11,8,12,9]=>01010000000 [[1,2],[3,4],[5,8],[6,9],[7,10],[11,12]]=>[11,12,7,10,6,9,5,8,3,4,1,2]=>[2,1,4,3,8,5,9,6,10,7,12,11]=>01010000010 [[1,2],[3,4],[5,8],[6,9],[7,11],[10,12]]=>[10,12,7,11,6,9,5,8,3,4,1,2]=>[2,1,4,3,8,5,9,6,11,7,12,10]=>01010000000 [[1,2],[3,4],[5,8],[6,10],[7,11],[9,12]]=>[9,12,7,11,6,10,5,8,3,4,1,2]=>[2,1,4,3,8,5,10,6,11,7,12,9]=>01010000000 [[1,2],[3,4],[5,9],[6,10],[7,11],[8,12]]=>[8,12,7,11,6,10,5,9,3,4,1,2]=>[2,1,4,3,9,5,10,6,11,7,12,8]=>01010000000 [[1,2],[3,5],[4,6],[7,8],[9,10],[11,12]]=>[11,12,9,10,7,8,4,6,3,5,1,2]=>[2,1,5,3,6,4,8,7,10,9,12,11]=>01000101010 [[1,2],[3,5],[4,6],[7,8],[9,11],[10,12]]=>[10,12,9,11,7,8,4,6,3,5,1,2]=>[2,1,5,3,6,4,8,7,11,9,12,10]=>01000101000 [[1,2],[3,5],[4,6],[7,9],[8,10],[11,12]]=>[11,12,8,10,7,9,4,6,3,5,1,2]=>[2,1,5,3,6,4,9,7,10,8,12,11]=>01000100010 [[1,2],[3,5],[4,6],[7,9],[8,11],[10,12]]=>[10,12,8,11,7,9,4,6,3,5,1,2]=>[2,1,5,3,6,4,9,7,11,8,12,10]=>01000100000 [[1,2],[3,5],[4,6],[7,10],[8,11],[9,12]]=>[9,12,8,11,7,10,4,6,3,5,1,2]=>[2,1,5,3,6,4,10,7,11,8,12,9]=>01000100000 [[1,2],[3,5],[4,7],[6,8],[9,10],[11,12]]=>[11,12,9,10,6,8,4,7,3,5,1,2]=>[2,1,5,3,7,4,8,6,10,9,12,11]=>01000001010 [[1,2],[3,5],[4,7],[6,8],[9,11],[10,12]]=>[10,12,9,11,6,8,4,7,3,5,1,2]=>[2,1,5,3,7,4,8,6,11,9,12,10]=>01000001000 [[1,2],[3,5],[4,7],[6,9],[8,10],[11,12]]=>[11,12,8,10,6,9,4,7,3,5,1,2]=>[2,1,5,3,7,4,9,6,10,8,12,11]=>01000000010 [[1,2],[3,5],[4,7],[6,9],[8,11],[10,12]]=>[10,12,8,11,6,9,4,7,3,5,1,2]=>[2,1,5,3,7,4,9,6,11,8,12,10]=>01000000000 [[1,2],[3,5],[4,7],[6,10],[8,11],[9,12]]=>[9,12,8,11,6,10,4,7,3,5,1,2]=>[2,1,5,3,7,4,10,6,11,8,12,9]=>01000000000 [[1,2],[3,5],[4,8],[6,9],[7,10],[11,12]]=>[11,12,7,10,6,9,4,8,3,5,1,2]=>[2,1,5,3,8,4,9,6,10,7,12,11]=>01000000010 [[1,2],[3,5],[4,8],[6,9],[7,11],[10,12]]=>[10,12,7,11,6,9,4,8,3,5,1,2]=>[2,1,5,3,8,4,9,6,11,7,12,10]=>01000000000 [[1,2],[3,5],[4,8],[6,10],[7,11],[9,12]]=>[9,12,7,11,6,10,4,8,3,5,1,2]=>[2,1,5,3,8,4,10,6,11,7,12,9]=>01000000000 [[1,2],[3,5],[4,9],[6,10],[7,11],[8,12]]=>[8,12,7,11,6,10,4,9,3,5,1,2]=>[2,1,5,3,9,4,10,6,11,7,12,8]=>01000000000 [[1,2],[3,6],[4,7],[5,8],[9,10],[11,12]]=>[11,12,9,10,5,8,4,7,3,6,1,2]=>[2,1,6,3,7,4,8,5,10,9,12,11]=>01000001010 [[1,2],[3,6],[4,7],[5,8],[9,11],[10,12]]=>[10,12,9,11,5,8,4,7,3,6,1,2]=>[2,1,6,3,7,4,8,5,11,9,12,10]=>01000001000 [[1,2],[3,6],[4,7],[5,9],[8,10],[11,12]]=>[11,12,8,10,5,9,4,7,3,6,1,2]=>[2,1,6,3,7,4,9,5,10,8,12,11]=>01000000010 [[1,2],[3,6],[4,7],[5,9],[8,11],[10,12]]=>[10,12,8,11,5,9,4,7,3,6,1,2]=>[2,1,6,3,7,4,9,5,11,8,12,10]=>01000000000 [[1,2],[3,6],[4,7],[5,10],[8,11],[9,12]]=>[9,12,8,11,5,10,4,7,3,6,1,2]=>[2,1,6,3,7,4,10,5,11,8,12,9]=>01000000000 [[1,2],[3,6],[4,8],[5,9],[7,10],[11,12]]=>[11,12,7,10,5,9,4,8,3,6,1,2]=>[2,1,6,3,8,4,9,5,10,7,12,11]=>01000000010 [[1,2],[3,6],[4,8],[5,9],[7,11],[10,12]]=>[10,12,7,11,5,9,4,8,3,6,1,2]=>[2,1,6,3,8,4,9,5,11,7,12,10]=>01000000000 [[1,2],[3,6],[4,8],[5,10],[7,11],[9,12]]=>[9,12,7,11,5,10,4,8,3,6,1,2]=>[2,1,6,3,8,4,10,5,11,7,12,9]=>01000000000 [[1,2],[3,6],[4,9],[5,10],[7,11],[8,12]]=>[8,12,7,11,5,10,4,9,3,6,1,2]=>[2,1,6,3,9,4,10,5,11,7,12,8]=>01000000000 [[1,2],[3,7],[4,8],[5,9],[6,10],[11,12]]=>[11,12,6,10,5,9,4,8,3,7,1,2]=>[2,1,7,3,8,4,9,5,10,6,12,11]=>01000000010 [[1,2],[3,7],[4,8],[5,9],[6,11],[10,12]]=>[10,12,6,11,5,9,4,8,3,7,1,2]=>[2,1,7,3,8,4,9,5,11,6,12,10]=>01000000000 [[1,2],[3,7],[4,8],[5,10],[6,11],[9,12]]=>[9,12,6,11,5,10,4,8,3,7,1,2]=>[2,1,7,3,8,4,10,5,11,6,12,9]=>01000000000 [[1,2],[3,7],[4,9],[5,10],[6,11],[8,12]]=>[8,12,6,11,5,10,4,9,3,7,1,2]=>[2,1,7,3,9,4,10,5,11,6,12,8]=>01000000000 [[1,2],[3,8],[4,9],[5,10],[6,11],[7,12]]=>[7,12,6,11,5,10,4,9,3,8,1,2]=>[2,1,8,3,9,4,10,5,11,6,12,7]=>01000000000 [[1,3],[2,4],[5,6],[7,8],[9,10],[11,12]]=>[11,12,9,10,7,8,5,6,2,4,1,3]=>[3,1,4,2,6,5,8,7,10,9,12,11]=>00010101010 [[1,3],[2,4],[5,6],[7,8],[9,11],[10,12]]=>[10,12,9,11,7,8,5,6,2,4,1,3]=>[3,1,4,2,6,5,8,7,11,9,12,10]=>00010101000 [[1,3],[2,4],[5,6],[7,9],[8,10],[11,12]]=>[11,12,8,10,7,9,5,6,2,4,1,3]=>[3,1,4,2,6,5,9,7,10,8,12,11]=>00010100010 [[1,3],[2,4],[5,6],[7,9],[8,11],[10,12]]=>[10,12,8,11,7,9,5,6,2,4,1,3]=>[3,1,4,2,6,5,9,7,11,8,12,10]=>00010100000 [[1,3],[2,4],[5,6],[7,10],[8,11],[9,12]]=>[9,12,8,11,7,10,5,6,2,4,1,3]=>[3,1,4,2,6,5,10,7,11,8,12,9]=>00010100000 [[1,3],[2,4],[5,7],[6,8],[9,10],[11,12]]=>[11,12,9,10,6,8,5,7,2,4,1,3]=>[3,1,4,2,7,5,8,6,10,9,12,11]=>00010001010 [[1,3],[2,4],[5,7],[6,8],[9,11],[10,12]]=>[10,12,9,11,6,8,5,7,2,4,1,3]=>[3,1,4,2,7,5,8,6,11,9,12,10]=>00010001000 [[1,3],[2,4],[5,7],[6,9],[8,10],[11,12]]=>[11,12,8,10,6,9,5,7,2,4,1,3]=>[3,1,4,2,7,5,9,6,10,8,12,11]=>00010000010 [[1,3],[2,4],[5,7],[6,9],[8,11],[10,12]]=>[10,12,8,11,6,9,5,7,2,4,1,3]=>[3,1,4,2,7,5,9,6,11,8,12,10]=>00010000000 [[1,3],[2,4],[5,7],[6,10],[8,11],[9,12]]=>[9,12,8,11,6,10,5,7,2,4,1,3]=>[3,1,4,2,7,5,10,6,11,8,12,9]=>00010000000 [[1,3],[2,4],[5,8],[6,9],[7,10],[11,12]]=>[11,12,7,10,6,9,5,8,2,4,1,3]=>[3,1,4,2,8,5,9,6,10,7,12,11]=>00010000010 [[1,3],[2,4],[5,8],[6,9],[7,11],[10,12]]=>[10,12,7,11,6,9,5,8,2,4,1,3]=>[3,1,4,2,8,5,9,6,11,7,12,10]=>00010000000 [[1,3],[2,4],[5,8],[6,10],[7,11],[9,12]]=>[9,12,7,11,6,10,5,8,2,4,1,3]=>[3,1,4,2,8,5,10,6,11,7,12,9]=>00010000000 [[1,3],[2,4],[5,9],[6,10],[7,11],[8,12]]=>[8,12,7,11,6,10,5,9,2,4,1,3]=>[3,1,4,2,9,5,10,6,11,7,12,8]=>00010000000 [[1,3],[2,5],[4,6],[7,8],[9,10],[11,12]]=>[11,12,9,10,7,8,4,6,2,5,1,3]=>[3,1,5,2,6,4,8,7,10,9,12,11]=>00000101010 [[1,3],[2,5],[4,6],[7,8],[9,11],[10,12]]=>[10,12,9,11,7,8,4,6,2,5,1,3]=>[3,1,5,2,6,4,8,7,11,9,12,10]=>00000101000 [[1,3],[2,5],[4,6],[7,9],[8,10],[11,12]]=>[11,12,8,10,7,9,4,6,2,5,1,3]=>[3,1,5,2,6,4,9,7,10,8,12,11]=>00000100010 [[1,3],[2,5],[4,6],[7,9],[8,11],[10,12]]=>[10,12,8,11,7,9,4,6,2,5,1,3]=>[3,1,5,2,6,4,9,7,11,8,12,10]=>00000100000 [[1,3],[2,5],[4,6],[7,10],[8,11],[9,12]]=>[9,12,8,11,7,10,4,6,2,5,1,3]=>[3,1,5,2,6,4,10,7,11,8,12,9]=>00000100000 [[1,3],[2,5],[4,7],[6,8],[9,10],[11,12]]=>[11,12,9,10,6,8,4,7,2,5,1,3]=>[3,1,5,2,7,4,8,6,10,9,12,11]=>00000001010 [[1,3],[2,5],[4,7],[6,8],[9,11],[10,12]]=>[10,12,9,11,6,8,4,7,2,5,1,3]=>[3,1,5,2,7,4,8,6,11,9,12,10]=>00000001000 [[1,3],[2,5],[4,7],[6,9],[8,10],[11,12]]=>[11,12,8,10,6,9,4,7,2,5,1,3]=>[3,1,5,2,7,4,9,6,10,8,12,11]=>00000000010 [[1,3],[2,5],[4,7],[6,9],[8,11],[10,12]]=>[10,12,8,11,6,9,4,7,2,5,1,3]=>[3,1,5,2,7,4,9,6,11,8,12,10]=>00000000000 [[1,3],[2,5],[4,7],[6,10],[8,11],[9,12]]=>[9,12,8,11,6,10,4,7,2,5,1,3]=>[3,1,5,2,7,4,10,6,11,8,12,9]=>00000000000 [[1,3],[2,5],[4,8],[6,9],[7,10],[11,12]]=>[11,12,7,10,6,9,4,8,2,5,1,3]=>[3,1,5,2,8,4,9,6,10,7,12,11]=>00000000010 [[1,3],[2,5],[4,8],[6,9],[7,11],[10,12]]=>[10,12,7,11,6,9,4,8,2,5,1,3]=>[3,1,5,2,8,4,9,6,11,7,12,10]=>00000000000 [[1,3],[2,5],[4,8],[6,10],[7,11],[9,12]]=>[9,12,7,11,6,10,4,8,2,5,1,3]=>[3,1,5,2,8,4,10,6,11,7,12,9]=>00000000000 [[1,3],[2,5],[4,9],[6,10],[7,11],[8,12]]=>[8,12,7,11,6,10,4,9,2,5,1,3]=>[3,1,5,2,9,4,10,6,11,7,12,8]=>00000000000 [[1,3],[2,6],[4,7],[5,8],[9,10],[11,12]]=>[11,12,9,10,5,8,4,7,2,6,1,3]=>[3,1,6,2,7,4,8,5,10,9,12,11]=>00000001010 [[1,3],[2,6],[4,7],[5,8],[9,11],[10,12]]=>[10,12,9,11,5,8,4,7,2,6,1,3]=>[3,1,6,2,7,4,8,5,11,9,12,10]=>00000001000 [[1,3],[2,6],[4,7],[5,9],[8,10],[11,12]]=>[11,12,8,10,5,9,4,7,2,6,1,3]=>[3,1,6,2,7,4,9,5,10,8,12,11]=>00000000010 [[1,3],[2,6],[4,7],[5,9],[8,11],[10,12]]=>[10,12,8,11,5,9,4,7,2,6,1,3]=>[3,1,6,2,7,4,9,5,11,8,12,10]=>00000000000 [[1,3],[2,6],[4,7],[5,10],[8,11],[9,12]]=>[9,12,8,11,5,10,4,7,2,6,1,3]=>[3,1,6,2,7,4,10,5,11,8,12,9]=>00000000000 [[1,3],[2,6],[4,8],[5,9],[7,10],[11,12]]=>[11,12,7,10,5,9,4,8,2,6,1,3]=>[3,1,6,2,8,4,9,5,10,7,12,11]=>00000000010 [[1,3],[2,6],[4,8],[5,9],[7,11],[10,12]]=>[10,12,7,11,5,9,4,8,2,6,1,3]=>[3,1,6,2,8,4,9,5,11,7,12,10]=>00000000000 [[1,3],[2,6],[4,8],[5,10],[7,11],[9,12]]=>[9,12,7,11,5,10,4,8,2,6,1,3]=>[3,1,6,2,8,4,10,5,11,7,12,9]=>00000000000 [[1,3],[2,6],[4,9],[5,10],[7,11],[8,12]]=>[8,12,7,11,5,10,4,9,2,6,1,3]=>[3,1,6,2,9,4,10,5,11,7,12,8]=>00000000000 [[1,3],[2,7],[4,8],[5,9],[6,10],[11,12]]=>[11,12,6,10,5,9,4,8,2,7,1,3]=>[3,1,7,2,8,4,9,5,10,6,12,11]=>00000000010 [[1,3],[2,7],[4,8],[5,9],[6,11],[10,12]]=>[10,12,6,11,5,9,4,8,2,7,1,3]=>[3,1,7,2,8,4,9,5,11,6,12,10]=>00000000000 [[1,3],[2,7],[4,8],[5,10],[6,11],[9,12]]=>[9,12,6,11,5,10,4,8,2,7,1,3]=>[3,1,7,2,8,4,10,5,11,6,12,9]=>00000000000 [[1,3],[2,7],[4,9],[5,10],[6,11],[8,12]]=>[8,12,6,11,5,10,4,9,2,7,1,3]=>[3,1,7,2,9,4,10,5,11,6,12,8]=>00000000000 [[1,3],[2,8],[4,9],[5,10],[6,11],[7,12]]=>[7,12,6,11,5,10,4,9,2,8,1,3]=>[3,1,8,2,9,4,10,5,11,6,12,7]=>00000000000 [[1,4],[2,5],[3,6],[7,8],[9,10],[11,12]]=>[11,12,9,10,7,8,3,6,2,5,1,4]=>[4,1,5,2,6,3,8,7,10,9,12,11]=>00000101010 [[1,4],[2,5],[3,6],[7,8],[9,11],[10,12]]=>[10,12,9,11,7,8,3,6,2,5,1,4]=>[4,1,5,2,6,3,8,7,11,9,12,10]=>00000101000 [[1,4],[2,5],[3,6],[7,9],[8,10],[11,12]]=>[11,12,8,10,7,9,3,6,2,5,1,4]=>[4,1,5,2,6,3,9,7,10,8,12,11]=>00000100010 [[1,4],[2,5],[3,6],[7,9],[8,11],[10,12]]=>[10,12,8,11,7,9,3,6,2,5,1,4]=>[4,1,5,2,6,3,9,7,11,8,12,10]=>00000100000 [[1,4],[2,5],[3,6],[7,10],[8,11],[9,12]]=>[9,12,8,11,7,10,3,6,2,5,1,4]=>[4,1,5,2,6,3,10,7,11,8,12,9]=>00000100000 [[1,4],[2,5],[3,7],[6,8],[9,10],[11,12]]=>[11,12,9,10,6,8,3,7,2,5,1,4]=>[4,1,5,2,7,3,8,6,10,9,12,11]=>00000001010 [[1,4],[2,5],[3,7],[6,8],[9,11],[10,12]]=>[10,12,9,11,6,8,3,7,2,5,1,4]=>[4,1,5,2,7,3,8,6,11,9,12,10]=>00000001000 [[1,4],[2,5],[3,7],[6,9],[8,10],[11,12]]=>[11,12,8,10,6,9,3,7,2,5,1,4]=>[4,1,5,2,7,3,9,6,10,8,12,11]=>00000000010 [[1,4],[2,5],[3,7],[6,9],[8,11],[10,12]]=>[10,12,8,11,6,9,3,7,2,5,1,4]=>[4,1,5,2,7,3,9,6,11,8,12,10]=>00000000000 [[1,4],[2,5],[3,7],[6,10],[8,11],[9,12]]=>[9,12,8,11,6,10,3,7,2,5,1,4]=>[4,1,5,2,7,3,10,6,11,8,12,9]=>00000000000 [[1,4],[2,5],[3,8],[6,9],[7,10],[11,12]]=>[11,12,7,10,6,9,3,8,2,5,1,4]=>[4,1,5,2,8,3,9,6,10,7,12,11]=>00000000010 [[1,4],[2,5],[3,8],[6,9],[7,11],[10,12]]=>[10,12,7,11,6,9,3,8,2,5,1,4]=>[4,1,5,2,8,3,9,6,11,7,12,10]=>00000000000 [[1,4],[2,5],[3,8],[6,10],[7,11],[9,12]]=>[9,12,7,11,6,10,3,8,2,5,1,4]=>[4,1,5,2,8,3,10,6,11,7,12,9]=>00000000000 [[1,4],[2,5],[3,9],[6,10],[7,11],[8,12]]=>[8,12,7,11,6,10,3,9,2,5,1,4]=>[4,1,5,2,9,3,10,6,11,7,12,8]=>00000000000 [[1,4],[2,6],[3,7],[5,8],[9,10],[11,12]]=>[11,12,9,10,5,8,3,7,2,6,1,4]=>[4,1,6,2,7,3,8,5,10,9,12,11]=>00000001010 [[1,4],[2,6],[3,7],[5,8],[9,11],[10,12]]=>[10,12,9,11,5,8,3,7,2,6,1,4]=>[4,1,6,2,7,3,8,5,11,9,12,10]=>00000001000 [[1,4],[2,6],[3,7],[5,9],[8,10],[11,12]]=>[11,12,8,10,5,9,3,7,2,6,1,4]=>[4,1,6,2,7,3,9,5,10,8,12,11]=>00000000010 [[1,4],[2,6],[3,7],[5,9],[8,11],[10,12]]=>[10,12,8,11,5,9,3,7,2,6,1,4]=>[4,1,6,2,7,3,9,5,11,8,12,10]=>00000000000 [[1,4],[2,6],[3,7],[5,10],[8,11],[9,12]]=>[9,12,8,11,5,10,3,7,2,6,1,4]=>[4,1,6,2,7,3,10,5,11,8,12,9]=>00000000000 [[1,4],[2,6],[3,8],[5,9],[7,10],[11,12]]=>[11,12,7,10,5,9,3,8,2,6,1,4]=>[4,1,6,2,8,3,9,5,10,7,12,11]=>00000000010 [[1,4],[2,6],[3,8],[5,9],[7,11],[10,12]]=>[10,12,7,11,5,9,3,8,2,6,1,4]=>[4,1,6,2,8,3,9,5,11,7,12,10]=>00000000000 [[1,4],[2,6],[3,8],[5,10],[7,11],[9,12]]=>[9,12,7,11,5,10,3,8,2,6,1,4]=>[4,1,6,2,8,3,10,5,11,7,12,9]=>00000000000 [[1,4],[2,6],[3,9],[5,10],[7,11],[8,12]]=>[8,12,7,11,5,10,3,9,2,6,1,4]=>[4,1,6,2,9,3,10,5,11,7,12,8]=>00000000000 [[1,4],[2,7],[3,8],[5,9],[6,10],[11,12]]=>[11,12,6,10,5,9,3,8,2,7,1,4]=>[4,1,7,2,8,3,9,5,10,6,12,11]=>00000000010 [[1,4],[2,7],[3,8],[5,9],[6,11],[10,12]]=>[10,12,6,11,5,9,3,8,2,7,1,4]=>[4,1,7,2,8,3,9,5,11,6,12,10]=>00000000000 [[1,4],[2,7],[3,8],[5,10],[6,11],[9,12]]=>[9,12,6,11,5,10,3,8,2,7,1,4]=>[4,1,7,2,8,3,10,5,11,6,12,9]=>00000000000 [[1,4],[2,7],[3,9],[5,10],[6,11],[8,12]]=>[8,12,6,11,5,10,3,9,2,7,1,4]=>[4,1,7,2,9,3,10,5,11,6,12,8]=>00000000000 [[1,4],[2,8],[3,9],[5,10],[6,11],[7,12]]=>[7,12,6,11,5,10,3,9,2,8,1,4]=>[4,1,8,2,9,3,10,5,11,6,12,7]=>00000000000 [[1,5],[2,6],[3,7],[4,8],[9,10],[11,12]]=>[11,12,9,10,4,8,3,7,2,6,1,5]=>[5,1,6,2,7,3,8,4,10,9,12,11]=>00000001010 [[1,5],[2,6],[3,7],[4,8],[9,11],[10,12]]=>[10,12,9,11,4,8,3,7,2,6,1,5]=>[5,1,6,2,7,3,8,4,11,9,12,10]=>00000001000 [[1,5],[2,6],[3,7],[4,9],[8,10],[11,12]]=>[11,12,8,10,4,9,3,7,2,6,1,5]=>[5,1,6,2,7,3,9,4,10,8,12,11]=>00000000010 [[1,5],[2,6],[3,7],[4,9],[8,11],[10,12]]=>[10,12,8,11,4,9,3,7,2,6,1,5]=>[5,1,6,2,7,3,9,4,11,8,12,10]=>00000000000 [[1,5],[2,6],[3,7],[4,10],[8,11],[9,12]]=>[9,12,8,11,4,10,3,7,2,6,1,5]=>[5,1,6,2,7,3,10,4,11,8,12,9]=>00000000000 [[1,5],[2,6],[3,8],[4,9],[7,10],[11,12]]=>[11,12,7,10,4,9,3,8,2,6,1,5]=>[5,1,6,2,8,3,9,4,10,7,12,11]=>00000000010 [[1,5],[2,6],[3,8],[4,9],[7,11],[10,12]]=>[10,12,7,11,4,9,3,8,2,6,1,5]=>[5,1,6,2,8,3,9,4,11,7,12,10]=>00000000000 [[1,5],[2,6],[3,8],[4,10],[7,11],[9,12]]=>[9,12,7,11,4,10,3,8,2,6,1,5]=>[5,1,6,2,8,3,10,4,11,7,12,9]=>00000000000 [[1,5],[2,6],[3,9],[4,10],[7,11],[8,12]]=>[8,12,7,11,4,10,3,9,2,6,1,5]=>[5,1,6,2,9,3,10,4,11,7,12,8]=>00000000000 [[1,5],[2,7],[3,8],[4,9],[6,10],[11,12]]=>[11,12,6,10,4,9,3,8,2,7,1,5]=>[5,1,7,2,8,3,9,4,10,6,12,11]=>00000000010 [[1,5],[2,7],[3,8],[4,9],[6,11],[10,12]]=>[10,12,6,11,4,9,3,8,2,7,1,5]=>[5,1,7,2,8,3,9,4,11,6,12,10]=>00000000000 [[1,5],[2,7],[3,8],[4,10],[6,11],[9,12]]=>[9,12,6,11,4,10,3,8,2,7,1,5]=>[5,1,7,2,8,3,10,4,11,6,12,9]=>00000000000 [[1,5],[2,7],[3,9],[4,10],[6,11],[8,12]]=>[8,12,6,11,4,10,3,9,2,7,1,5]=>[5,1,7,2,9,3,10,4,11,6,12,8]=>00000000000 [[1,5],[2,8],[3,9],[4,10],[6,11],[7,12]]=>[7,12,6,11,4,10,3,9,2,8,1,5]=>[5,1,8,2,9,3,10,4,11,6,12,7]=>00000000000 [[1,6],[2,7],[3,8],[4,9],[5,10],[11,12]]=>[11,12,5,10,4,9,3,8,2,7,1,6]=>[6,1,7,2,8,3,9,4,10,5,12,11]=>00000000010 [[1,6],[2,7],[3,8],[4,9],[5,11],[10,12]]=>[10,12,5,11,4,9,3,8,2,7,1,6]=>[6,1,7,2,8,3,9,4,11,5,12,10]=>00000000000 [[1,6],[2,7],[3,8],[4,10],[5,11],[9,12]]=>[9,12,5,11,4,10,3,8,2,7,1,6]=>[6,1,7,2,8,3,10,4,11,5,12,9]=>00000000000 [[1,6],[2,7],[3,9],[4,10],[5,11],[8,12]]=>[8,12,5,11,4,10,3,9,2,7,1,6]=>[6,1,7,2,9,3,10,4,11,5,12,8]=>00000000000 [[1,6],[2,8],[3,9],[4,10],[5,11],[7,12]]=>[7,12,5,11,4,10,3,9,2,8,1,6]=>[6,1,8,2,9,3,10,4,11,5,12,7]=>00000000000 [[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]=>00000000000 [[1,2,3,4,5,6,7,9],[8]]=>[8,1,2,3,4,5,6,7,9]=>[9,7,6,5,4,3,2,1,8]=>00000000 [[1,2,3,4,5,6,9],[7,8]]=>[7,8,1,2,3,4,5,6,9]=>[9,6,5,4,3,2,1,8,7]=>00000000 [[1,2,3,4,5,6,9],[7],[8]]=>[8,7,1,2,3,4,5,6,9]=>[9,6,5,4,3,2,1,7,8]=>00000000 [[1,2,9],[3],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,1,2,9]=>[9,2,1,3,4,5,6,7,8]=>00000000 [[1,3],[2,9],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,2,9,1,3]=>[3,1,9,2,4,5,6,7,8]=>00000000 [[1,2,3,4,5,6,7,8,10],[9]]=>[9,1,2,3,4,5,6,7,8,10]=>[10,8,7,6,5,4,3,2,1,9]=>000000000 [[1,2,3,4,5,6,7,10],[8,9]]=>[8,9,1,2,3,4,5,6,7,10]=>[10,7,6,5,4,3,2,1,9,8]=>000000000 [[1,2,10],[3],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,1,2,10]=>[10,2,1,3,4,5,6,7,8,9]=>000000000 []=>[]=>[]=> [[1,2,4,5,6,7,8,9],[3]]=>[3,1,2,4,5,6,7,8,9]=>[9,8,7,6,5,4,2,1,3]=>00000000 [[1,3,5,6,7,8,9],[2],[4]]=>[4,2,1,3,5,6,7,8,9]=>[9,8,7,6,5,3,1,2,4]=>00000000 [[1,4,6,7,8,9],[2],[3],[5]]=>[5,3,2,1,4,6,7,8,9]=>[9,8,7,6,4,1,2,3,5]=>00000000 [[1,5,7,8,9],[2],[3],[4],[6]]=>[6,4,3,2,1,5,7,8,9]=>[9,8,7,5,1,2,3,4,6]=>00000000 [[1,6,8,9],[2],[3],[4],[5],[7]]=>[7,5,4,3,2,1,6,8,9]=>[9,8,6,1,2,3,4,5,7]=>00000000 [[1,7,9],[2],[3],[4],[5],[6],[8]]=>[8,6,5,4,3,2,1,7,9]=>[9,7,1,2,3,4,5,6,8]=>00000000 [[1,4],[2,6],[3,8],[5],[7],[9]]=>[9,7,5,3,8,2,6,1,4]=>[4,1,6,2,8,3,5,7,9]=>00000001 [[1,8],[2],[3],[4],[5],[6],[7],[9]]=>[9,7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7,9]=>00000001 [[1,2,4,5,6,7,8,9,10],[3]]=>[3,1,2,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,2,1,3]=>000000000 [[1,9],[2],[3],[4],[5],[6],[7],[8],[10]]=>[10,8,7,6,5,4,3,2,1,9]=>[9,1,2,3,4,5,6,7,8,10]=>000000001 [[1,3,4,5,6,7,8],[2,9]]=>[2,9,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,9,2]=>00000000 [[1,3,4,5,6,7,8],[2],[9]]=>[9,2,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,2,9]=>00000001 [[1,3,4,5,6],[2],[7],[8],[9]]=>[9,8,7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7,8,9]=>00000111 [[1,3,4,5],[2],[6],[7],[8],[9]]=>[9,8,7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7,8,9]=>00001111 [[1,3,4],[2],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7,8,9]=>00011111 [[1,3],[2],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8,9]=>00111111 [[1,3,4,5,6,7,8,9],[2,10]]=>[2,10,1,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,1,10,2]=>000000000 [[1,3,4,5,6,7,8,9],[2],[10]]=>[10,2,1,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,1,2,10]=>000000001 [[1,3,4,5,6,7,8],[2,9,10]]=>[2,9,10,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,10,9,2]=>000000000 [[1,3,4,5,6,7],[2],[8],[9],[10]]=>[10,9,8,2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2,8,9,10]=>000000111 [[1,3,4,5,6],[2],[7],[8],[9],[10]]=>[10,9,8,7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7,8,9,10]=>000001111 [[1,3,4,5],[2,7,8],[6,10],[9]]=>[9,6,10,2,7,8,1,3,4,5]=>[5,4,3,1,8,7,2,10,6,9]=>000000000 [[1,3,4],[2],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7,8,9,10]=>000111111 [[1,3],[2],[4],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8,9,10]=>001111111 [[1,2,3,5,6,7,8,9,10],[4]]=>[4,1,2,3,5,6,7,8,9,10]=>[10,9,8,7,6,5,3,2,1,4]=>000000000 [[1,2,3,4,6,7,8,9,10],[5]]=>[5,1,2,3,4,6,7,8,9,10]=>[10,9,8,7,6,4,3,2,1,5]=>000000000 [[1,2,3,4,5,6,7,9,10],[8]]=>[8,1,2,3,4,5,6,7,9,10]=>[10,9,7,6,5,4,3,2,1,8]=>000000000 [[1,2,3,4,5,6,8,9,10],[7]]=>[7,1,2,3,4,5,6,8,9,10]=>[10,9,8,6,5,4,3,2,1,7]=>000000000 [[1,2,3,4,5,7,8,9,10],[6]]=>[6,1,2,3,4,5,7,8,9,10]=>[10,9,8,7,5,4,3,2,1,6]=>000000000 [[1,2,4,5,6,7,8,9,10,11,12],[3]]=>[3,1,2,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,2,1,3]=>00000000000 [[1,2,3,4,6,7,8,9,10,11,12],[5]]=>[5,1,2,3,4,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,4,3,2,1,5]=>00000000000 [[1,2,3,4,5,6,7,8,9,10,12],[11]]=>[11,1,2,3,4,5,6,7,8,9,10,12]=>[12,10,9,8,7,6,5,4,3,2,1,11]=>00000000000 [[1,2,3,4,5,6,7,8,10,11,12],[9]]=>[9,1,2,3,4,5,6,7,8,10,11,12]=>[12,11,10,8,7,6,5,4,3,2,1,9]=>00000000000 [[1,2,3,4,5,6,8,9,10,11,12],[7]]=>[7,1,2,3,4,5,6,8,9,10,11,12]=>[12,11,10,9,8,6,5,4,3,2,1,7]=>00000000000 [[1,4,5,6,7,8],[2],[3],[9]]=>[9,3,2,1,4,5,6,7,8]=>[8,7,6,5,4,1,2,3,9]=>00000001 [[1,2,5,9],[3,4,8],[6,7],[10]]=>[10,6,7,3,4,8,1,2,5,9]=>[9,5,2,1,8,4,3,7,6,10]=>000000001 [[1,2,5,6,7,8,9],[3],[4]]=>[4,3,1,2,5,6,7,8,9]=>[9,8,7,6,5,2,1,3,4]=>00000000 [[1,2,4,7],[3,6,10],[5,9],[8]]=>[8,5,9,3,6,10,1,2,4,7]=>[7,4,2,1,10,6,3,9,5,8]=>000000000 [[1,2,4,5,6,7,8,9],[3],[10]]=>[10,3,1,2,4,5,6,7,8,9]=>[9,8,7,6,5,4,2,1,3,10]=>000000001 [[1,4],[2],[3],[5],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8,9,10]=>000111111 [[1,5],[2],[3],[4],[6],[7],[8],[9],[10]]=>[10,9,8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8,9,10]=>000011111 [[1,8],[2],[3],[4],[5],[6],[7],[9],[10]]=>[10,9,7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7,9,10]=>000000011 [[1,7],[2],[3],[4],[5],[6],[8],[9],[10]]=>[10,9,8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,8,9,10]=>000000111 [[1,6],[2],[3],[4],[5],[7],[8],[9],[10]]=>[10,9,8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8,9,10]=>000001111 [[1,3],[2],[4],[5],[6],[7],[8],[9],[10],[11],[12]]=>[12,11,10,9,8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8,9,10,11,12]=>00111111111 [[1,2,3,4,5,6,8],[7],[9]]=>[9,7,1,2,3,4,5,6,8]=>[8,6,5,4,3,2,1,7,9]=>00000001 [[1,2,3,4,5,7,9],[6,8]]=>[6,8,1,2,3,4,5,7,9]=>[9,7,5,4,3,2,1,8,6]=>00000000 [[1,2,3,4,5,6,7,9],[8],[10]]=>[10,8,1,2,3,4,5,6,7,9]=>[9,7,6,5,4,3,2,1,8,10]=>000000001 [[1,2,7],[3,8],[4,9],[5,10],[6]]=>[6,5,10,4,9,3,8,1,2,7]=>[7,2,1,8,3,9,4,10,5,6]=>000000000 [[1,2,8],[3,9],[4,10],[5,11],[6,12],[7]]=>[7,6,12,5,11,4,10,3,9,1,2,8]=>[8,2,1,9,3,10,4,11,5,12,6,7]=>00000000000 [[1,2,4,5,6,7,8],[3,9]]=>[3,9,1,2,4,5,6,7,8]=>[8,7,6,5,4,2,1,9,3]=>00000000 [[1,2,4,5,6,7,8,9],[3,10]]=>[3,10,1,2,4,5,6,7,8,9]=>[9,8,7,6,5,4,2,1,10,3]=>000000000 [[1,2],[3,9],[4],[5],[6],[7],[8]]=>[8,7,6,5,4,3,9,1,2]=>[2,1,9,3,4,5,6,7,8]=>01000000 [[1,2],[3,10],[4],[5],[6],[7],[8],[9]]=>[9,8,7,6,5,4,3,10,1,2]=>[2,1,10,3,4,5,6,7,8,9]=>010000000 [[1,5,10],[2,6],[3,7],[4,8],[9]]=>[9,4,8,3,7,2,6,1,5,10]=>[10,5,1,6,2,7,3,8,4,9]=>000000000 [[1,3,4,5,6,7,9],[2,8]]=>[2,8,1,3,4,5,6,7,9]=>[9,7,6,5,4,3,1,8,2]=>00000000 [[1,2,3,4,5,6,8,9],[7,10]]=>[7,10,1,2,3,4,5,6,8,9]=>[9,8,6,5,4,3,2,1,10,7]=>000000000 [[1,2,3,4,5,7,8],[6,9]]=>[6,9,1,2,3,4,5,7,8]=>[8,7,5,4,3,2,1,9,6]=>00000000 [[1,3,4,5,6,7,8,10],[2],[9]]=>[9,2,1,3,4,5,6,7,8,10]=>[10,8,7,6,5,4,3,1,2,9]=>000000000 [[1,3,6,7],[2,5,10],[4,9],[8]]=>[8,4,9,2,5,10,1,3,6,7]=>[7,6,3,1,10,5,2,9,4,8]=>000000000
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
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
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.