Identifier
Mp00284: Standard tableaux —rows⟶ Set partitions
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Images
=>
Cc0007;cc-rep-0Cc0009;cc-rep-1
[[1]]=>{{1}}=>[1]=> [[1,2]]=>{{1,2}}=>[2,1]=>0 [[1],[2]]=>{{1},{2}}=>[1,2]=>1 [[1,2,3]]=>{{1,2,3}}=>[2,3,1]=>00 [[1,3],[2]]=>{{1,3},{2}}=>[3,2,1]=>00 [[1,2],[3]]=>{{1,2},{3}}=>[2,1,3]=>01 [[1],[2],[3]]=>{{1},{2},{3}}=>[1,2,3]=>11 [[1,2,3,4]]=>{{1,2,3,4}}=>[2,3,4,1]=>000 [[1,3,4],[2]]=>{{1,3,4},{2}}=>[3,2,4,1]=>000 [[1,2,4],[3]]=>{{1,2,4},{3}}=>[2,4,3,1]=>000 [[1,2,3],[4]]=>{{1,2,3},{4}}=>[2,3,1,4]=>001 [[1,3],[2,4]]=>{{1,3},{2,4}}=>[3,4,1,2]=>000 [[1,2],[3,4]]=>{{1,2},{3,4}}=>[2,1,4,3]=>010 [[1,4],[2],[3]]=>{{1,4},{2},{3}}=>[4,2,3,1]=>000 [[1,3],[2],[4]]=>{{1,3},{2},{4}}=>[3,2,1,4]=>001 [[1,2],[3],[4]]=>{{1,2},{3},{4}}=>[2,1,3,4]=>011 [[1],[2],[3],[4]]=>{{1},{2},{3},{4}}=>[1,2,3,4]=>111 [[1,2,3,4,5]]=>{{1,2,3,4,5}}=>[2,3,4,5,1]=>0000 [[1,3,4,5],[2]]=>{{1,3,4,5},{2}}=>[3,2,4,5,1]=>0000 [[1,2,4,5],[3]]=>{{1,2,4,5},{3}}=>[2,4,3,5,1]=>0000 [[1,2,3,5],[4]]=>{{1,2,3,5},{4}}=>[2,3,5,4,1]=>0000 [[1,2,3,4],[5]]=>{{1,2,3,4},{5}}=>[2,3,4,1,5]=>0001 [[1,3,5],[2,4]]=>{{1,3,5},{2,4}}=>[3,4,5,2,1]=>0000 [[1,2,5],[3,4]]=>{{1,2,5},{3,4}}=>[2,5,4,3,1]=>0000 [[1,3,4],[2,5]]=>{{1,3,4},{2,5}}=>[3,5,4,1,2]=>0000 [[1,2,4],[3,5]]=>{{1,2,4},{3,5}}=>[2,4,5,1,3]=>0000 [[1,2,3],[4,5]]=>{{1,2,3},{4,5}}=>[2,3,1,5,4]=>0010 [[1,4,5],[2],[3]]=>{{1,4,5},{2},{3}}=>[4,2,3,5,1]=>0000 [[1,3,5],[2],[4]]=>{{1,3,5},{2},{4}}=>[3,2,5,4,1]=>0000 [[1,2,5],[3],[4]]=>{{1,2,5},{3},{4}}=>[2,5,3,4,1]=>0000 [[1,3,4],[2],[5]]=>{{1,3,4},{2},{5}}=>[3,2,4,1,5]=>0001 [[1,2,4],[3],[5]]=>{{1,2,4},{3},{5}}=>[2,4,3,1,5]=>0001 [[1,2,3],[4],[5]]=>{{1,2,3},{4},{5}}=>[2,3,1,4,5]=>0011 [[1,4],[2,5],[3]]=>{{1,4},{2,5},{3}}=>[4,5,3,1,2]=>0000 [[1,3],[2,5],[4]]=>{{1,3},{2,5},{4}}=>[3,5,1,4,2]=>0000 [[1,2],[3,5],[4]]=>{{1,2},{3,5},{4}}=>[2,1,5,4,3]=>0100 [[1,3],[2,4],[5]]=>{{1,3},{2,4},{5}}=>[3,4,1,2,5]=>0001 [[1,2],[3,4],[5]]=>{{1,2},{3,4},{5}}=>[2,1,4,3,5]=>0101 [[1,5],[2],[3],[4]]=>{{1,5},{2},{3},{4}}=>[5,2,3,4,1]=>0000 [[1,4],[2],[3],[5]]=>{{1,4},{2},{3},{5}}=>[4,2,3,1,5]=>0001 [[1,3],[2],[4],[5]]=>{{1,3},{2},{4},{5}}=>[3,2,1,4,5]=>0011 [[1,2],[3],[4],[5]]=>{{1,2},{3},{4},{5}}=>[2,1,3,4,5]=>0111 [[1],[2],[3],[4],[5]]=>{{1},{2},{3},{4},{5}}=>[1,2,3,4,5]=>1111 [[1,2,3,4,5,6]]=>{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000 [[1,3,4,5,6],[2]]=>{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>00000 [[1,2,4,5,6],[3]]=>{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>00000 [[1,2,3,5,6],[4]]=>{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>00000 [[1,2,3,4,6],[5]]=>{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>00000 [[1,2,3,4,5],[6]]=>{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>00001 [[1,3,5,6],[2,4]]=>{{1,3,5,6},{2,4}}=>[3,4,5,2,6,1]=>00000 [[1,2,5,6],[3,4]]=>{{1,2,5,6},{3,4}}=>[2,5,4,3,6,1]=>00000 [[1,3,4,6],[2,5]]=>{{1,3,4,6},{2,5}}=>[3,5,4,6,2,1]=>00000 [[1,2,4,6],[3,5]]=>{{1,2,4,6},{3,5}}=>[2,4,5,6,3,1]=>00000 [[1,2,3,6],[4,5]]=>{{1,2,3,6},{4,5}}=>[2,3,6,5,4,1]=>00000 [[1,3,4,5],[2,6]]=>{{1,3,4,5},{2,6}}=>[3,6,4,5,1,2]=>00000 [[1,2,4,5],[3,6]]=>{{1,2,4,5},{3,6}}=>[2,4,6,5,1,3]=>00000 [[1,2,3,5],[4,6]]=>{{1,2,3,5},{4,6}}=>[2,3,5,6,1,4]=>00000 [[1,2,3,4],[5,6]]=>{{1,2,3,4},{5,6}}=>[2,3,4,1,6,5]=>00010 [[1,4,5,6],[2],[3]]=>{{1,4,5,6},{2},{3}}=>[4,2,3,5,6,1]=>00000 [[1,3,5,6],[2],[4]]=>{{1,3,5,6},{2},{4}}=>[3,2,5,4,6,1]=>00000 [[1,2,5,6],[3],[4]]=>{{1,2,5,6},{3},{4}}=>[2,5,3,4,6,1]=>00000 [[1,3,4,6],[2],[5]]=>{{1,3,4,6},{2},{5}}=>[3,2,4,6,5,1]=>00000 [[1,2,4,6],[3],[5]]=>{{1,2,4,6},{3},{5}}=>[2,4,3,6,5,1]=>00000 [[1,2,3,6],[4],[5]]=>{{1,2,3,6},{4},{5}}=>[2,3,6,4,5,1]=>00000 [[1,3,4,5],[2],[6]]=>{{1,3,4,5},{2},{6}}=>[3,2,4,5,1,6]=>00001 [[1,2,4,5],[3],[6]]=>{{1,2,4,5},{3},{6}}=>[2,4,3,5,1,6]=>00001 [[1,2,3,5],[4],[6]]=>{{1,2,3,5},{4},{6}}=>[2,3,5,4,1,6]=>00001 [[1,2,3,4],[5],[6]]=>{{1,2,3,4},{5},{6}}=>[2,3,4,1,5,6]=>00011 [[1,3,5],[2,4,6]]=>{{1,3,5},{2,4,6}}=>[3,4,5,6,1,2]=>00000 [[1,2,5],[3,4,6]]=>{{1,2,5},{3,4,6}}=>[2,5,4,6,1,3]=>00000 [[1,3,4],[2,5,6]]=>{{1,3,4},{2,5,6}}=>[3,5,4,1,6,2]=>00000 [[1,2,4],[3,5,6]]=>{{1,2,4},{3,5,6}}=>[2,4,5,1,6,3]=>00000 [[1,2,3],[4,5,6]]=>{{1,2,3},{4,5,6}}=>[2,3,1,5,6,4]=>00100 [[1,4,6],[2,5],[3]]=>{{1,4,6},{2,5},{3}}=>[4,5,3,6,2,1]=>00000 [[1,3,6],[2,5],[4]]=>{{1,3,6},{2,5},{4}}=>[3,5,6,4,2,1]=>00000 [[1,2,6],[3,5],[4]]=>{{1,2,6},{3,5},{4}}=>[2,6,5,4,3,1]=>00000 [[1,3,6],[2,4],[5]]=>{{1,3,6},{2,4},{5}}=>[3,4,6,2,5,1]=>00000 [[1,2,6],[3,4],[5]]=>{{1,2,6},{3,4},{5}}=>[2,6,4,3,5,1]=>00000 [[1,4,5],[2,6],[3]]=>{{1,4,5},{2,6},{3}}=>[4,6,3,5,1,2]=>00000 [[1,3,5],[2,6],[4]]=>{{1,3,5},{2,6},{4}}=>[3,6,5,4,1,2]=>00000 [[1,2,5],[3,6],[4]]=>{{1,2,5},{3,6},{4}}=>[2,5,6,4,1,3]=>00000 [[1,3,4],[2,6],[5]]=>{{1,3,4},{2,6},{5}}=>[3,6,4,1,5,2]=>00000 [[1,2,4],[3,6],[5]]=>{{1,2,4},{3,6},{5}}=>[2,4,6,1,5,3]=>00000 [[1,2,3],[4,6],[5]]=>{{1,2,3},{4,6},{5}}=>[2,3,1,6,5,4]=>00100 [[1,3,5],[2,4],[6]]=>{{1,3,5},{2,4},{6}}=>[3,4,5,2,1,6]=>00001 [[1,2,5],[3,4],[6]]=>{{1,2,5},{3,4},{6}}=>[2,5,4,3,1,6]=>00001 [[1,3,4],[2,5],[6]]=>{{1,3,4},{2,5},{6}}=>[3,5,4,1,2,6]=>00001 [[1,2,4],[3,5],[6]]=>{{1,2,4},{3,5},{6}}=>[2,4,5,1,3,6]=>00001 [[1,2,3],[4,5],[6]]=>{{1,2,3},{4,5},{6}}=>[2,3,1,5,4,6]=>00101 [[1,5,6],[2],[3],[4]]=>{{1,5,6},{2},{3},{4}}=>[5,2,3,4,6,1]=>00000 [[1,4,6],[2],[3],[5]]=>{{1,4,6},{2},{3},{5}}=>[4,2,3,6,5,1]=>00000 [[1,3,6],[2],[4],[5]]=>{{1,3,6},{2},{4},{5}}=>[3,2,6,4,5,1]=>00000 [[1,2,6],[3],[4],[5]]=>{{1,2,6},{3},{4},{5}}=>[2,6,3,4,5,1]=>00000 [[1,4,5],[2],[3],[6]]=>{{1,4,5},{2},{3},{6}}=>[4,2,3,5,1,6]=>00001 [[1,3,5],[2],[4],[6]]=>{{1,3,5},{2},{4},{6}}=>[3,2,5,4,1,6]=>00001 [[1,2,5],[3],[4],[6]]=>{{1,2,5},{3},{4},{6}}=>[2,5,3,4,1,6]=>00001 [[1,3,4],[2],[5],[6]]=>{{1,3,4},{2},{5},{6}}=>[3,2,4,1,5,6]=>00011 [[1,2,4],[3],[5],[6]]=>{{1,2,4},{3},{5},{6}}=>[2,4,3,1,5,6]=>00011 [[1,2,3],[4],[5],[6]]=>{{1,2,3},{4},{5},{6}}=>[2,3,1,4,5,6]=>00111 [[1,4],[2,5],[3,6]]=>{{1,4},{2,5},{3,6}}=>[4,5,6,1,2,3]=>00000 [[1,3],[2,5],[4,6]]=>{{1,3},{2,5},{4,6}}=>[3,5,1,6,2,4]=>00000 [[1,2],[3,5],[4,6]]=>{{1,2},{3,5},{4,6}}=>[2,1,5,6,3,4]=>01000 [[1,3],[2,4],[5,6]]=>{{1,3},{2,4},{5,6}}=>[3,4,1,2,6,5]=>00010 [[1,2],[3,4],[5,6]]=>{{1,2},{3,4},{5,6}}=>[2,1,4,3,6,5]=>01010 [[1,5],[2,6],[3],[4]]=>{{1,5},{2,6},{3},{4}}=>[5,6,3,4,1,2]=>00000 [[1,4],[2,6],[3],[5]]=>{{1,4},{2,6},{3},{5}}=>[4,6,3,1,5,2]=>00000 [[1,3],[2,6],[4],[5]]=>{{1,3},{2,6},{4},{5}}=>[3,6,1,4,5,2]=>00000 [[1,2],[3,6],[4],[5]]=>{{1,2},{3,6},{4},{5}}=>[2,1,6,4,5,3]=>01000 [[1,4],[2,5],[3],[6]]=>{{1,4},{2,5},{3},{6}}=>[4,5,3,1,2,6]=>00001 [[1,3],[2,5],[4],[6]]=>{{1,3},{2,5},{4},{6}}=>[3,5,1,4,2,6]=>00001 [[1,2],[3,5],[4],[6]]=>{{1,2},{3,5},{4},{6}}=>[2,1,5,4,3,6]=>01001 [[1,3],[2,4],[5],[6]]=>{{1,3},{2,4},{5},{6}}=>[3,4,1,2,5,6]=>00011 [[1,2],[3,4],[5],[6]]=>{{1,2},{3,4},{5},{6}}=>[2,1,4,3,5,6]=>01011 [[1,6],[2],[3],[4],[5]]=>{{1,6},{2},{3},{4},{5}}=>[6,2,3,4,5,1]=>00000 [[1,5],[2],[3],[4],[6]]=>{{1,5},{2},{3},{4},{6}}=>[5,2,3,4,1,6]=>00001 [[1,4],[2],[3],[5],[6]]=>{{1,4},{2},{3},{5},{6}}=>[4,2,3,1,5,6]=>00011 [[1,3],[2],[4],[5],[6]]=>{{1,3},{2},{4},{5},{6}}=>[3,2,1,4,5,6]=>00111 [[1,2],[3],[4],[5],[6]]=>{{1,2},{3},{4},{5},{6}}=>[2,1,3,4,5,6]=>01111 [[1],[2],[3],[4],[5],[6]]=>{{1},{2},{3},{4},{5},{6}}=>[1,2,3,4,5,6]=>11111 [[1,2,3,4,5,6,7]]=>{{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000 [[1,3,4,5,6,7],[2]]=>{{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000 [[1,2,4,5,6,7],[3]]=>{{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000 [[1,2,3,5,6,7],[4]]=>{{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000 [[1,2,3,4,6,7],[5]]=>{{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000 [[1,2,3,4,5,7],[6]]=>{{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000 [[1,2,3,4,5,6],[7]]=>{{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001 [[1,3,5,6,7],[2,4]]=>{{1,3,5,6,7},{2,4}}=>[3,4,5,2,6,7,1]=>000000 [[1,2,5,6,7],[3,4]]=>{{1,2,5,6,7},{3,4}}=>[2,5,4,3,6,7,1]=>000000 [[1,3,4,6,7],[2,5]]=>{{1,3,4,6,7},{2,5}}=>[3,5,4,6,2,7,1]=>000000 [[1,2,4,6,7],[3,5]]=>{{1,2,4,6,7},{3,5}}=>[2,4,5,6,3,7,1]=>000000 [[1,2,3,6,7],[4,5]]=>{{1,2,3,6,7},{4,5}}=>[2,3,6,5,4,7,1]=>000000 [[1,3,4,5,7],[2,6]]=>{{1,3,4,5,7},{2,6}}=>[3,6,4,5,7,2,1]=>000000 [[1,2,4,5,7],[3,6]]=>{{1,2,4,5,7},{3,6}}=>[2,4,6,5,7,3,1]=>000000 [[1,2,3,5,7],[4,6]]=>{{1,2,3,5,7},{4,6}}=>[2,3,5,6,7,4,1]=>000000 [[1,2,3,4,7],[5,6]]=>{{1,2,3,4,7},{5,6}}=>[2,3,4,7,6,5,1]=>000000 [[1,3,4,5,6],[2,7]]=>{{1,3,4,5,6},{2,7}}=>[3,7,4,5,6,1,2]=>000000 [[1,2,4,5,6],[3,7]]=>{{1,2,4,5,6},{3,7}}=>[2,4,7,5,6,1,3]=>000000 [[1,2,3,5,6],[4,7]]=>{{1,2,3,5,6},{4,7}}=>[2,3,5,7,6,1,4]=>000000 [[1,2,3,4,6],[5,7]]=>{{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>000000 [[1,2,3,4,5],[6,7]]=>{{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>000010 [[1,4,5,6,7],[2],[3]]=>{{1,4,5,6,7},{2},{3}}=>[4,2,3,5,6,7,1]=>000000 [[1,3,5,6,7],[2],[4]]=>{{1,3,5,6,7},{2},{4}}=>[3,2,5,4,6,7,1]=>000000 [[1,2,5,6,7],[3],[4]]=>{{1,2,5,6,7},{3},{4}}=>[2,5,3,4,6,7,1]=>000000 [[1,3,4,6,7],[2],[5]]=>{{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>000000 [[1,2,4,6,7],[3],[5]]=>{{1,2,4,6,7},{3},{5}}=>[2,4,3,6,5,7,1]=>000000 [[1,2,3,6,7],[4],[5]]=>{{1,2,3,6,7},{4},{5}}=>[2,3,6,4,5,7,1]=>000000 [[1,3,4,5,7],[2],[6]]=>{{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>000000 [[1,2,4,5,7],[3],[6]]=>{{1,2,4,5,7},{3},{6}}=>[2,4,3,5,7,6,1]=>000000 [[1,2,3,5,7],[4],[6]]=>{{1,2,3,5,7},{4},{6}}=>[2,3,5,4,7,6,1]=>000000 [[1,2,3,4,7],[5],[6]]=>{{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>000000 [[1,3,4,5,6],[2],[7]]=>{{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>000001 [[1,2,4,5,6],[3],[7]]=>{{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>000001 [[1,2,3,5,6],[4],[7]]=>{{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>000001 [[1,2,3,4,6],[5],[7]]=>{{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>000001 [[1,2,3,4,5],[6],[7]]=>{{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>000011 [[1,3,5,7],[2,4,6]]=>{{1,3,5,7},{2,4,6}}=>[3,4,5,6,7,2,1]=>000000 [[1,2,5,7],[3,4,6]]=>{{1,2,5,7},{3,4,6}}=>[2,5,4,6,7,3,1]=>000000 [[1,3,4,7],[2,5,6]]=>{{1,3,4,7},{2,5,6}}=>[3,5,4,7,6,2,1]=>000000 [[1,2,4,7],[3,5,6]]=>{{1,2,4,7},{3,5,6}}=>[2,4,5,7,6,3,1]=>000000 [[1,2,3,7],[4,5,6]]=>{{1,2,3,7},{4,5,6}}=>[2,3,7,5,6,4,1]=>000000 [[1,3,5,6],[2,4,7]]=>{{1,3,5,6},{2,4,7}}=>[3,4,5,7,6,1,2]=>000000 [[1,2,5,6],[3,4,7]]=>{{1,2,5,6},{3,4,7}}=>[2,5,4,7,6,1,3]=>000000 [[1,3,4,6],[2,5,7]]=>{{1,3,4,6},{2,5,7}}=>[3,5,4,6,7,1,2]=>000000 [[1,2,4,6],[3,5,7]]=>{{1,2,4,6},{3,5,7}}=>[2,4,5,6,7,1,3]=>000000 [[1,2,3,6],[4,5,7]]=>{{1,2,3,6},{4,5,7}}=>[2,3,6,5,7,1,4]=>000000 [[1,3,4,5],[2,6,7]]=>{{1,3,4,5},{2,6,7}}=>[3,6,4,5,1,7,2]=>000000 [[1,2,4,5],[3,6,7]]=>{{1,2,4,5},{3,6,7}}=>[2,4,6,5,1,7,3]=>000000 [[1,2,3,5],[4,6,7]]=>{{1,2,3,5},{4,6,7}}=>[2,3,5,6,1,7,4]=>000000 [[1,2,3,4],[5,6,7]]=>{{1,2,3,4},{5,6,7}}=>[2,3,4,1,6,7,5]=>000100 [[1,4,6,7],[2,5],[3]]=>{{1,4,6,7},{2,5},{3}}=>[4,5,3,6,2,7,1]=>000000 [[1,3,6,7],[2,5],[4]]=>{{1,3,6,7},{2,5},{4}}=>[3,5,6,4,2,7,1]=>000000 [[1,2,6,7],[3,5],[4]]=>{{1,2,6,7},{3,5},{4}}=>[2,6,5,4,3,7,1]=>000000 [[1,3,6,7],[2,4],[5]]=>{{1,3,6,7},{2,4},{5}}=>[3,4,6,2,5,7,1]=>000000 [[1,2,6,7],[3,4],[5]]=>{{1,2,6,7},{3,4},{5}}=>[2,6,4,3,5,7,1]=>000000 [[1,4,5,7],[2,6],[3]]=>{{1,4,5,7},{2,6},{3}}=>[4,6,3,5,7,2,1]=>000000 [[1,3,5,7],[2,6],[4]]=>{{1,3,5,7},{2,6},{4}}=>[3,6,5,4,7,2,1]=>000000 [[1,2,5,7],[3,6],[4]]=>{{1,2,5,7},{3,6},{4}}=>[2,5,6,4,7,3,1]=>000000 [[1,3,4,7],[2,6],[5]]=>{{1,3,4,7},{2,6},{5}}=>[3,6,4,7,5,2,1]=>000000 [[1,2,4,7],[3,6],[5]]=>{{1,2,4,7},{3,6},{5}}=>[2,4,6,7,5,3,1]=>000000 [[1,2,3,7],[4,6],[5]]=>{{1,2,3,7},{4,6},{5}}=>[2,3,7,6,5,4,1]=>000000 [[1,3,5,7],[2,4],[6]]=>{{1,3,5,7},{2,4},{6}}=>[3,4,5,2,7,6,1]=>000000 [[1,2,5,7],[3,4],[6]]=>{{1,2,5,7},{3,4},{6}}=>[2,5,4,3,7,6,1]=>000000 [[1,3,4,7],[2,5],[6]]=>{{1,3,4,7},{2,5},{6}}=>[3,5,4,7,2,6,1]=>000000 [[1,2,4,7],[3,5],[6]]=>{{1,2,4,7},{3,5},{6}}=>[2,4,5,7,3,6,1]=>000000 [[1,2,3,7],[4,5],[6]]=>{{1,2,3,7},{4,5},{6}}=>[2,3,7,5,4,6,1]=>000000 [[1,4,5,6],[2,7],[3]]=>{{1,4,5,6},{2,7},{3}}=>[4,7,3,5,6,1,2]=>000000 [[1,3,5,6],[2,7],[4]]=>{{1,3,5,6},{2,7},{4}}=>[3,7,5,4,6,1,2]=>000000 [[1,2,5,6],[3,7],[4]]=>{{1,2,5,6},{3,7},{4}}=>[2,5,7,4,6,1,3]=>000000 [[1,3,4,6],[2,7],[5]]=>{{1,3,4,6},{2,7},{5}}=>[3,7,4,6,5,1,2]=>000000 [[1,2,4,6],[3,7],[5]]=>{{1,2,4,6},{3,7},{5}}=>[2,4,7,6,5,1,3]=>000000 [[1,2,3,6],[4,7],[5]]=>{{1,2,3,6},{4,7},{5}}=>[2,3,6,7,5,1,4]=>000000 [[1,3,4,5],[2,7],[6]]=>{{1,3,4,5},{2,7},{6}}=>[3,7,4,5,1,6,2]=>000000 [[1,2,4,5],[3,7],[6]]=>{{1,2,4,5},{3,7},{6}}=>[2,4,7,5,1,6,3]=>000000 [[1,2,3,5],[4,7],[6]]=>{{1,2,3,5},{4,7},{6}}=>[2,3,5,7,1,6,4]=>000000 [[1,2,3,4],[5,7],[6]]=>{{1,2,3,4},{5,7},{6}}=>[2,3,4,1,7,6,5]=>000100 [[1,3,5,6],[2,4],[7]]=>{{1,3,5,6},{2,4},{7}}=>[3,4,5,2,6,1,7]=>000001 [[1,2,5,6],[3,4],[7]]=>{{1,2,5,6},{3,4},{7}}=>[2,5,4,3,6,1,7]=>000001 [[1,3,4,6],[2,5],[7]]=>{{1,3,4,6},{2,5},{7}}=>[3,5,4,6,2,1,7]=>000001 [[1,2,4,6],[3,5],[7]]=>{{1,2,4,6},{3,5},{7}}=>[2,4,5,6,3,1,7]=>000001 [[1,2,3,6],[4,5],[7]]=>{{1,2,3,6},{4,5},{7}}=>[2,3,6,5,4,1,7]=>000001 [[1,3,4,5],[2,6],[7]]=>{{1,3,4,5},{2,6},{7}}=>[3,6,4,5,1,2,7]=>000001 [[1,2,4,5],[3,6],[7]]=>{{1,2,4,5},{3,6},{7}}=>[2,4,6,5,1,3,7]=>000001 [[1,2,3,5],[4,6],[7]]=>{{1,2,3,5},{4,6},{7}}=>[2,3,5,6,1,4,7]=>000001 [[1,2,3,4],[5,6],[7]]=>{{1,2,3,4},{5,6},{7}}=>[2,3,4,1,6,5,7]=>000101 [[1,5,6,7],[2],[3],[4]]=>{{1,5,6,7},{2},{3},{4}}=>[5,2,3,4,6,7,1]=>000000 [[1,4,6,7],[2],[3],[5]]=>{{1,4,6,7},{2},{3},{5}}=>[4,2,3,6,5,7,1]=>000000 [[1,3,6,7],[2],[4],[5]]=>{{1,3,6,7},{2},{4},{5}}=>[3,2,6,4,5,7,1]=>000000 [[1,2,6,7],[3],[4],[5]]=>{{1,2,6,7},{3},{4},{5}}=>[2,6,3,4,5,7,1]=>000000 [[1,4,5,7],[2],[3],[6]]=>{{1,4,5,7},{2},{3},{6}}=>[4,2,3,5,7,6,1]=>000000 [[1,3,5,7],[2],[4],[6]]=>{{1,3,5,7},{2},{4},{6}}=>[3,2,5,4,7,6,1]=>000000 [[1,2,5,7],[3],[4],[6]]=>{{1,2,5,7},{3},{4},{6}}=>[2,5,3,4,7,6,1]=>000000 [[1,3,4,7],[2],[5],[6]]=>{{1,3,4,7},{2},{5},{6}}=>[3,2,4,7,5,6,1]=>000000 [[1,2,4,7],[3],[5],[6]]=>{{1,2,4,7},{3},{5},{6}}=>[2,4,3,7,5,6,1]=>000000 [[1,2,3,7],[4],[5],[6]]=>{{1,2,3,7},{4},{5},{6}}=>[2,3,7,4,5,6,1]=>000000 [[1,4,5,6],[2],[3],[7]]=>{{1,4,5,6},{2},{3},{7}}=>[4,2,3,5,6,1,7]=>000001 [[1,3,5,6],[2],[4],[7]]=>{{1,3,5,6},{2},{4},{7}}=>[3,2,5,4,6,1,7]=>000001 [[1,2,5,6],[3],[4],[7]]=>{{1,2,5,6},{3},{4},{7}}=>[2,5,3,4,6,1,7]=>000001 [[1,3,4,6],[2],[5],[7]]=>{{1,3,4,6},{2},{5},{7}}=>[3,2,4,6,5,1,7]=>000001 [[1,2,4,6],[3],[5],[7]]=>{{1,2,4,6},{3},{5},{7}}=>[2,4,3,6,5,1,7]=>000001 [[1,2,3,6],[4],[5],[7]]=>{{1,2,3,6},{4},{5},{7}}=>[2,3,6,4,5,1,7]=>000001 [[1,3,4,5],[2],[6],[7]]=>{{1,3,4,5},{2},{6},{7}}=>[3,2,4,5,1,6,7]=>000011 [[1,2,4,5],[3],[6],[7]]=>{{1,2,4,5},{3},{6},{7}}=>[2,4,3,5,1,6,7]=>000011 [[1,2,3,5],[4],[6],[7]]=>{{1,2,3,5},{4},{6},{7}}=>[2,3,5,4,1,6,7]=>000011 [[1,2,3,4],[5],[6],[7]]=>{{1,2,3,4},{5},{6},{7}}=>[2,3,4,1,5,6,7]=>000111 [[1,4,6],[2,5,7],[3]]=>{{1,4,6},{2,5,7},{3}}=>[4,5,3,6,7,1,2]=>000000 [[1,3,6],[2,5,7],[4]]=>{{1,3,6},{2,5,7},{4}}=>[3,5,6,4,7,1,2]=>000000 [[1,2,6],[3,5,7],[4]]=>{{1,2,6},{3,5,7},{4}}=>[2,6,5,4,7,1,3]=>000000 [[1,3,6],[2,4,7],[5]]=>{{1,3,6},{2,4,7},{5}}=>[3,4,6,7,5,1,2]=>000000 [[1,2,6],[3,4,7],[5]]=>{{1,2,6},{3,4,7},{5}}=>[2,6,4,7,5,1,3]=>000000 [[1,4,5],[2,6,7],[3]]=>{{1,4,5},{2,6,7},{3}}=>[4,6,3,5,1,7,2]=>000000 [[1,3,5],[2,6,7],[4]]=>{{1,3,5},{2,6,7},{4}}=>[3,6,5,4,1,7,2]=>000000 [[1,2,5],[3,6,7],[4]]=>{{1,2,5},{3,6,7},{4}}=>[2,5,6,4,1,7,3]=>000000 [[1,3,4],[2,6,7],[5]]=>{{1,3,4},{2,6,7},{5}}=>[3,6,4,1,5,7,2]=>000000 [[1,2,4],[3,6,7],[5]]=>{{1,2,4},{3,6,7},{5}}=>[2,4,6,1,5,7,3]=>000000 [[1,2,3],[4,6,7],[5]]=>{{1,2,3},{4,6,7},{5}}=>[2,3,1,6,5,7,4]=>001000 [[1,3,5],[2,4,7],[6]]=>{{1,3,5},{2,4,7},{6}}=>[3,4,5,7,1,6,2]=>000000 [[1,2,5],[3,4,7],[6]]=>{{1,2,5},{3,4,7},{6}}=>[2,5,4,7,1,6,3]=>000000 [[1,3,4],[2,5,7],[6]]=>{{1,3,4},{2,5,7},{6}}=>[3,5,4,1,7,6,2]=>000000 [[1,2,4],[3,5,7],[6]]=>{{1,2,4},{3,5,7},{6}}=>[2,4,5,1,7,6,3]=>000000 [[1,2,3],[4,5,7],[6]]=>{{1,2,3},{4,5,7},{6}}=>[2,3,1,5,7,6,4]=>001000 [[1,3,5],[2,4,6],[7]]=>{{1,3,5},{2,4,6},{7}}=>[3,4,5,6,1,2,7]=>000001 [[1,2,5],[3,4,6],[7]]=>{{1,2,5},{3,4,6},{7}}=>[2,5,4,6,1,3,7]=>000001 [[1,3,4],[2,5,6],[7]]=>{{1,3,4},{2,5,6},{7}}=>[3,5,4,1,6,2,7]=>000001 [[1,2,4],[3,5,6],[7]]=>{{1,2,4},{3,5,6},{7}}=>[2,4,5,1,6,3,7]=>000001 [[1,2,3],[4,5,6],[7]]=>{{1,2,3},{4,5,6},{7}}=>[2,3,1,5,6,4,7]=>001001 [[1,4,7],[2,5],[3,6]]=>{{1,4,7},{2,5},{3,6}}=>[4,5,6,7,2,3,1]=>000000 [[1,3,7],[2,5],[4,6]]=>{{1,3,7},{2,5},{4,6}}=>[3,5,7,6,2,4,1]=>000000 [[1,2,7],[3,5],[4,6]]=>{{1,2,7},{3,5},{4,6}}=>[2,7,5,6,3,4,1]=>000000 [[1,3,7],[2,4],[5,6]]=>{{1,3,7},{2,4},{5,6}}=>[3,4,7,2,6,5,1]=>000000 [[1,2,7],[3,4],[5,6]]=>{{1,2,7},{3,4},{5,6}}=>[2,7,4,3,6,5,1]=>000000 [[1,4,6],[2,5],[3,7]]=>{{1,4,6},{2,5},{3,7}}=>[4,5,7,6,2,1,3]=>000000 [[1,3,6],[2,5],[4,7]]=>{{1,3,6},{2,5},{4,7}}=>[3,5,6,7,2,1,4]=>000000 [[1,2,6],[3,5],[4,7]]=>{{1,2,6},{3,5},{4,7}}=>[2,6,5,7,3,1,4]=>000000 [[1,3,6],[2,4],[5,7]]=>{{1,3,6},{2,4},{5,7}}=>[3,4,6,2,7,1,5]=>000000 [[1,2,6],[3,4],[5,7]]=>{{1,2,6},{3,4},{5,7}}=>[2,6,4,3,7,1,5]=>000000 [[1,4,5],[2,6],[3,7]]=>{{1,4,5},{2,6},{3,7}}=>[4,6,7,5,1,2,3]=>000000 [[1,3,5],[2,6],[4,7]]=>{{1,3,5},{2,6},{4,7}}=>[3,6,5,7,1,2,4]=>000000 [[1,2,5],[3,6],[4,7]]=>{{1,2,5},{3,6},{4,7}}=>[2,5,6,7,1,3,4]=>000000 [[1,3,4],[2,6],[5,7]]=>{{1,3,4},{2,6},{5,7}}=>[3,6,4,1,7,2,5]=>000000 [[1,2,4],[3,6],[5,7]]=>{{1,2,4},{3,6},{5,7}}=>[2,4,6,1,7,3,5]=>000000 [[1,2,3],[4,6],[5,7]]=>{{1,2,3},{4,6},{5,7}}=>[2,3,1,6,7,4,5]=>001000 [[1,3,5],[2,4],[6,7]]=>{{1,3,5},{2,4},{6,7}}=>[3,4,5,2,1,7,6]=>000010 [[1,2,5],[3,4],[6,7]]=>{{1,2,5},{3,4},{6,7}}=>[2,5,4,3,1,7,6]=>000010 [[1,3,4],[2,5],[6,7]]=>{{1,3,4},{2,5},{6,7}}=>[3,5,4,1,2,7,6]=>000010 [[1,2,4],[3,5],[6,7]]=>{{1,2,4},{3,5},{6,7}}=>[2,4,5,1,3,7,6]=>000010 [[1,2,3],[4,5],[6,7]]=>{{1,2,3},{4,5},{6,7}}=>[2,3,1,5,4,7,6]=>001010 [[1,5,7],[2,6],[3],[4]]=>{{1,5,7},{2,6},{3},{4}}=>[5,6,3,4,7,2,1]=>000000 [[1,4,7],[2,6],[3],[5]]=>{{1,4,7},{2,6},{3},{5}}=>[4,6,3,7,5,2,1]=>000000 [[1,3,7],[2,6],[4],[5]]=>{{1,3,7},{2,6},{4},{5}}=>[3,6,7,4,5,2,1]=>000000 [[1,2,7],[3,6],[4],[5]]=>{{1,2,7},{3,6},{4},{5}}=>[2,7,6,4,5,3,1]=>000000 [[1,4,7],[2,5],[3],[6]]=>{{1,4,7},{2,5},{3},{6}}=>[4,5,3,7,2,6,1]=>000000 [[1,3,7],[2,5],[4],[6]]=>{{1,3,7},{2,5},{4},{6}}=>[3,5,7,4,2,6,1]=>000000 [[1,2,7],[3,5],[4],[6]]=>{{1,2,7},{3,5},{4},{6}}=>[2,7,5,4,3,6,1]=>000000 [[1,3,7],[2,4],[5],[6]]=>{{1,3,7},{2,4},{5},{6}}=>[3,4,7,2,5,6,1]=>000000 [[1,2,7],[3,4],[5],[6]]=>{{1,2,7},{3,4},{5},{6}}=>[2,7,4,3,5,6,1]=>000000 [[1,5,6],[2,7],[3],[4]]=>{{1,5,6},{2,7},{3},{4}}=>[5,7,3,4,6,1,2]=>000000 [[1,4,6],[2,7],[3],[5]]=>{{1,4,6},{2,7},{3},{5}}=>[4,7,3,6,5,1,2]=>000000 [[1,3,6],[2,7],[4],[5]]=>{{1,3,6},{2,7},{4},{5}}=>[3,7,6,4,5,1,2]=>000000 [[1,2,6],[3,7],[4],[5]]=>{{1,2,6},{3,7},{4},{5}}=>[2,6,7,4,5,1,3]=>000000 [[1,4,5],[2,7],[3],[6]]=>{{1,4,5},{2,7},{3},{6}}=>[4,7,3,5,1,6,2]=>000000 [[1,3,5],[2,7],[4],[6]]=>{{1,3,5},{2,7},{4},{6}}=>[3,7,5,4,1,6,2]=>000000 [[1,2,5],[3,7],[4],[6]]=>{{1,2,5},{3,7},{4},{6}}=>[2,5,7,4,1,6,3]=>000000 [[1,3,4],[2,7],[5],[6]]=>{{1,3,4},{2,7},{5},{6}}=>[3,7,4,1,5,6,2]=>000000 [[1,2,4],[3,7],[5],[6]]=>{{1,2,4},{3,7},{5},{6}}=>[2,4,7,1,5,6,3]=>000000 [[1,2,3],[4,7],[5],[6]]=>{{1,2,3},{4,7},{5},{6}}=>[2,3,1,7,5,6,4]=>001000 [[1,4,6],[2,5],[3],[7]]=>{{1,4,6},{2,5},{3},{7}}=>[4,5,3,6,2,1,7]=>000001 [[1,3,6],[2,5],[4],[7]]=>{{1,3,6},{2,5},{4},{7}}=>[3,5,6,4,2,1,7]=>000001 [[1,2,6],[3,5],[4],[7]]=>{{1,2,6},{3,5},{4},{7}}=>[2,6,5,4,3,1,7]=>000001 [[1,3,6],[2,4],[5],[7]]=>{{1,3,6},{2,4},{5},{7}}=>[3,4,6,2,5,1,7]=>000001 [[1,2,6],[3,4],[5],[7]]=>{{1,2,6},{3,4},{5},{7}}=>[2,6,4,3,5,1,7]=>000001 [[1,4,5],[2,6],[3],[7]]=>{{1,4,5},{2,6},{3},{7}}=>[4,6,3,5,1,2,7]=>000001 [[1,3,5],[2,6],[4],[7]]=>{{1,3,5},{2,6},{4},{7}}=>[3,6,5,4,1,2,7]=>000001 [[1,2,5],[3,6],[4],[7]]=>{{1,2,5},{3,6},{4},{7}}=>[2,5,6,4,1,3,7]=>000001 [[1,3,4],[2,6],[5],[7]]=>{{1,3,4},{2,6},{5},{7}}=>[3,6,4,1,5,2,7]=>000001 [[1,2,4],[3,6],[5],[7]]=>{{1,2,4},{3,6},{5},{7}}=>[2,4,6,1,5,3,7]=>000001 [[1,2,3],[4,6],[5],[7]]=>{{1,2,3},{4,6},{5},{7}}=>[2,3,1,6,5,4,7]=>001001 [[1,3,5],[2,4],[6],[7]]=>{{1,3,5},{2,4},{6},{7}}=>[3,4,5,2,1,6,7]=>000011 [[1,2,5],[3,4],[6],[7]]=>{{1,2,5},{3,4},{6},{7}}=>[2,5,4,3,1,6,7]=>000011 [[1,3,4],[2,5],[6],[7]]=>{{1,3,4},{2,5},{6},{7}}=>[3,5,4,1,2,6,7]=>000011 [[1,2,4],[3,5],[6],[7]]=>{{1,2,4},{3,5},{6},{7}}=>[2,4,5,1,3,6,7]=>000011 [[1,2,3],[4,5],[6],[7]]=>{{1,2,3},{4,5},{6},{7}}=>[2,3,1,5,4,6,7]=>001011 [[1,6,7],[2],[3],[4],[5]]=>{{1,6,7},{2},{3},{4},{5}}=>[6,2,3,4,5,7,1]=>000000 [[1,5,7],[2],[3],[4],[6]]=>{{1,5,7},{2},{3},{4},{6}}=>[5,2,3,4,7,6,1]=>000000 [[1,4,7],[2],[3],[5],[6]]=>{{1,4,7},{2},{3},{5},{6}}=>[4,2,3,7,5,6,1]=>000000 [[1,3,7],[2],[4],[5],[6]]=>{{1,3,7},{2},{4},{5},{6}}=>[3,2,7,4,5,6,1]=>000000 [[1,2,7],[3],[4],[5],[6]]=>{{1,2,7},{3},{4},{5},{6}}=>[2,7,3,4,5,6,1]=>000000 [[1,5,6],[2],[3],[4],[7]]=>{{1,5,6},{2},{3},{4},{7}}=>[5,2,3,4,6,1,7]=>000001 [[1,4,6],[2],[3],[5],[7]]=>{{1,4,6},{2},{3},{5},{7}}=>[4,2,3,6,5,1,7]=>000001 [[1,3,6],[2],[4],[5],[7]]=>{{1,3,6},{2},{4},{5},{7}}=>[3,2,6,4,5,1,7]=>000001 [[1,2,6],[3],[4],[5],[7]]=>{{1,2,6},{3},{4},{5},{7}}=>[2,6,3,4,5,1,7]=>000001 [[1,4,5],[2],[3],[6],[7]]=>{{1,4,5},{2},{3},{6},{7}}=>[4,2,3,5,1,6,7]=>000011 [[1,3,5],[2],[4],[6],[7]]=>{{1,3,5},{2},{4},{6},{7}}=>[3,2,5,4,1,6,7]=>000011 [[1,2,5],[3],[4],[6],[7]]=>{{1,2,5},{3},{4},{6},{7}}=>[2,5,3,4,1,6,7]=>000011 [[1,3,4],[2],[5],[6],[7]]=>{{1,3,4},{2},{5},{6},{7}}=>[3,2,4,1,5,6,7]=>000111 [[1,2,4],[3],[5],[6],[7]]=>{{1,2,4},{3},{5},{6},{7}}=>[2,4,3,1,5,6,7]=>000111 [[1,2,3],[4],[5],[6],[7]]=>{{1,2,3},{4},{5},{6},{7}}=>[2,3,1,4,5,6,7]=>001111 [[1,5],[2,6],[3,7],[4]]=>{{1,5},{2,6},{3,7},{4}}=>[5,6,7,4,1,2,3]=>000000 [[1,4],[2,6],[3,7],[5]]=>{{1,4},{2,6},{3,7},{5}}=>[4,6,7,1,5,2,3]=>000000 [[1,3],[2,6],[4,7],[5]]=>{{1,3},{2,6},{4,7},{5}}=>[3,6,1,7,5,2,4]=>000000 [[1,2],[3,6],[4,7],[5]]=>{{1,2},{3,6},{4,7},{5}}=>[2,1,6,7,5,3,4]=>010000 [[1,4],[2,5],[3,7],[6]]=>{{1,4},{2,5},{3,7},{6}}=>[4,5,7,1,2,6,3]=>000000 [[1,3],[2,5],[4,7],[6]]=>{{1,3},{2,5},{4,7},{6}}=>[3,5,1,7,2,6,4]=>000000 [[1,2],[3,5],[4,7],[6]]=>{{1,2},{3,5},{4,7},{6}}=>[2,1,5,7,3,6,4]=>010000 [[1,3],[2,4],[5,7],[6]]=>{{1,3},{2,4},{5,7},{6}}=>[3,4,1,2,7,6,5]=>000100 [[1,2],[3,4],[5,7],[6]]=>{{1,2},{3,4},{5,7},{6}}=>[2,1,4,3,7,6,5]=>010100 [[1,4],[2,5],[3,6],[7]]=>{{1,4},{2,5},{3,6},{7}}=>[4,5,6,1,2,3,7]=>000001 [[1,3],[2,5],[4,6],[7]]=>{{1,3},{2,5},{4,6},{7}}=>[3,5,1,6,2,4,7]=>000001 [[1,2],[3,5],[4,6],[7]]=>{{1,2},{3,5},{4,6},{7}}=>[2,1,5,6,3,4,7]=>010001 [[1,3],[2,4],[5,6],[7]]=>{{1,3},{2,4},{5,6},{7}}=>[3,4,1,2,6,5,7]=>000101 [[1,2],[3,4],[5,6],[7]]=>{{1,2},{3,4},{5,6},{7}}=>[2,1,4,3,6,5,7]=>010101 [[1,6],[2,7],[3],[4],[5]]=>{{1,6},{2,7},{3},{4},{5}}=>[6,7,3,4,5,1,2]=>000000 [[1,5],[2,7],[3],[4],[6]]=>{{1,5},{2,7},{3},{4},{6}}=>[5,7,3,4,1,6,2]=>000000 [[1,4],[2,7],[3],[5],[6]]=>{{1,4},{2,7},{3},{5},{6}}=>[4,7,3,1,5,6,2]=>000000 [[1,3],[2,7],[4],[5],[6]]=>{{1,3},{2,7},{4},{5},{6}}=>[3,7,1,4,5,6,2]=>000000 [[1,2],[3,7],[4],[5],[6]]=>{{1,2},{3,7},{4},{5},{6}}=>[2,1,7,4,5,6,3]=>010000 [[1,5],[2,6],[3],[4],[7]]=>{{1,5},{2,6},{3},{4},{7}}=>[5,6,3,4,1,2,7]=>000001 [[1,4],[2,6],[3],[5],[7]]=>{{1,4},{2,6},{3},{5},{7}}=>[4,6,3,1,5,2,7]=>000001 [[1,3],[2,6],[4],[5],[7]]=>{{1,3},{2,6},{4},{5},{7}}=>[3,6,1,4,5,2,7]=>000001 [[1,2],[3,6],[4],[5],[7]]=>{{1,2},{3,6},{4},{5},{7}}=>[2,1,6,4,5,3,7]=>010001 [[1,4],[2,5],[3],[6],[7]]=>{{1,4},{2,5},{3},{6},{7}}=>[4,5,3,1,2,6,7]=>000011 [[1,3],[2,5],[4],[6],[7]]=>{{1,3},{2,5},{4},{6},{7}}=>[3,5,1,4,2,6,7]=>000011 [[1,2],[3,5],[4],[6],[7]]=>{{1,2},{3,5},{4},{6},{7}}=>[2,1,5,4,3,6,7]=>010011 [[1,3],[2,4],[5],[6],[7]]=>{{1,3},{2,4},{5},{6},{7}}=>[3,4,1,2,5,6,7]=>000111 [[1,2],[3,4],[5],[6],[7]]=>{{1,2},{3,4},{5},{6},{7}}=>[2,1,4,3,5,6,7]=>010111 [[1,7],[2],[3],[4],[5],[6]]=>{{1,7},{2},{3},{4},{5},{6}}=>[7,2,3,4,5,6,1]=>000000 [[1,6],[2],[3],[4],[5],[7]]=>{{1,6},{2},{3},{4},{5},{7}}=>[6,2,3,4,5,1,7]=>000001 [[1,5],[2],[3],[4],[6],[7]]=>{{1,5},{2},{3},{4},{6},{7}}=>[5,2,3,4,1,6,7]=>000011 [[1,4],[2],[3],[5],[6],[7]]=>{{1,4},{2},{3},{5},{6},{7}}=>[4,2,3,1,5,6,7]=>000111 [[1,3],[2],[4],[5],[6],[7]]=>{{1,3},{2},{4},{5},{6},{7}}=>[3,2,1,4,5,6,7]=>001111 [[1,2],[3],[4],[5],[6],[7]]=>{{1,2},{3},{4},{5},{6},{7}}=>[2,1,3,4,5,6,7]=>011111 [[1],[2],[3],[4],[5],[6],[7]]=>{{1},{2},{3},{4},{5},{6},{7}}=>[1,2,3,4,5,6,7]=>111111 [[1,2,3,4,5,6,7,8]]=>{{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000 [[1,3,4,5,6,7,8],[2]]=>{{1,3,4,5,6,7,8},{2}}=>[3,2,4,5,6,7,8,1]=>0000000 [[1,2,4,5,6,7,8],[3]]=>{{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000 [[1,2,3,5,6,7,8],[4]]=>{{1,2,3,5,6,7,8},{4}}=>[2,3,5,4,6,7,8,1]=>0000000 [[1,2,3,4,6,7,8],[5]]=>{{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000 [[1,2,3,4,5,7,8],[6]]=>{{1,2,3,4,5,7,8},{6}}=>[2,3,4,5,7,6,8,1]=>0000000 [[1,2,3,4,5,6,8],[7]]=>{{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000 [[1,2,3,4,5,6,7],[8]]=>{{1,2,3,4,5,6,7},{8}}=>[2,3,4,5,6,7,1,8]=>0000001 [[1,3,5,6,7,8],[2,4]]=>{{1,3,5,6,7,8},{2,4}}=>[3,4,5,2,6,7,8,1]=>0000000 [[1,2,5,6,7,8],[3,4]]=>{{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000 [[1,2,4,6,7,8],[3,5]]=>{{1,2,4,6,7,8},{3,5}}=>[2,4,5,6,3,7,8,1]=>0000000 [[1,2,3,6,7,8],[4,5]]=>{{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000 [[1,3,4,5,7,8],[2,6]]=>{{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000 [[1,2,4,5,7,8],[3,6]]=>{{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000 [[1,2,3,5,7,8],[4,6]]=>{{1,2,3,5,7,8},{4,6}}=>[2,3,5,6,7,4,8,1]=>0000000 [[1,2,3,4,7,8],[5,6]]=>{{1,2,3,4,7,8},{5,6}}=>[2,3,4,7,6,5,8,1]=>0000000 [[1,2,4,5,6,8],[3,7]]=>{{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000 [[1,2,3,4,6,8],[5,7]]=>{{1,2,3,4,6,8},{5,7}}=>[2,3,4,6,7,8,5,1]=>0000000 [[1,2,3,4,5,8],[6,7]]=>{{1,2,3,4,5,8},{6,7}}=>[2,3,4,5,8,7,6,1]=>0000000 [[1,2,3,5,6,7],[4,8]]=>{{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000 [[1,2,3,4,6,7],[5,8]]=>{{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000 [[1,2,3,4,5,7],[6,8]]=>{{1,2,3,4,5,7},{6,8}}=>[2,3,4,5,7,8,1,6]=>0000000 [[1,2,3,4,5,6],[7,8]]=>{{1,2,3,4,5,6},{7,8}}=>[2,3,4,5,6,1,8,7]=>0000010 [[1,4,5,6,7,8],[2],[3]]=>{{1,4,5,6,7,8},{2},{3}}=>[4,2,3,5,6,7,8,1]=>0000000 [[1,3,5,6,7,8],[2],[4]]=>{{1,3,5,6,7,8},{2},{4}}=>[3,2,5,4,6,7,8,1]=>0000000 [[1,2,5,6,7,8],[3],[4]]=>{{1,2,5,6,7,8},{3},{4}}=>[2,5,3,4,6,7,8,1]=>0000000 [[1,2,4,6,7,8],[3],[5]]=>{{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000 [[1,2,3,6,7,8],[4],[5]]=>{{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000 [[1,3,4,5,7,8],[2],[6]]=>{{1,3,4,5,7,8},{2},{6}}=>[3,2,4,5,7,6,8,1]=>0000000 [[1,2,4,5,7,8],[3],[6]]=>{{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000 [[1,2,3,5,7,8],[4],[6]]=>{{1,2,3,5,7,8},{4},{6}}=>[2,3,5,4,7,6,8,1]=>0000000 [[1,2,4,5,6,8],[3],[7]]=>{{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000 [[1,2,3,4,6,8],[5],[7]]=>{{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000 [[1,2,3,4,5,8],[6],[7]]=>{{1,2,3,4,5,8},{6},{7}}=>[2,3,4,5,8,6,7,1]=>0000000 [[1,3,4,5,6,7],[2],[8]]=>{{1,3,4,5,6,7},{2},{8}}=>[3,2,4,5,6,7,1,8]=>0000001 [[1,2,3,4,6,7],[5],[8]]=>{{1,2,3,4,6,7},{5},{8}}=>[2,3,4,6,5,7,1,8]=>0000001 [[1,2,3,4,5,7],[6],[8]]=>{{1,2,3,4,5,7},{6},{8}}=>[2,3,4,5,7,6,1,8]=>0000001 [[1,2,3,4,5,6],[7],[8]]=>{{1,2,3,4,5,6},{7},{8}}=>[2,3,4,5,6,1,7,8]=>0000011 [[1,3,5,7,8],[2,4,6]]=>{{1,3,5,7,8},{2,4,6}}=>[3,4,5,6,7,2,8,1]=>0000000 [[1,3,4,7,8],[2,5,6]]=>{{1,3,4,7,8},{2,5,6}}=>[3,5,4,7,6,2,8,1]=>0000000 [[1,2,3,7,8],[4,5,6]]=>{{1,2,3,7,8},{4,5,6}}=>[2,3,7,5,6,4,8,1]=>0000000 [[1,2,4,6,8],[3,5,7]]=>{{1,2,4,6,8},{3,5,7}}=>[2,4,5,6,7,8,3,1]=>0000000 [[1,2,4,5,8],[3,6,7]]=>{{1,2,4,5,8},{3,6,7}}=>[2,4,6,5,8,7,3,1]=>0000000 [[1,2,3,5,8],[4,6,7]]=>{{1,2,3,5,8},{4,6,7}}=>[2,3,5,6,8,7,4,1]=>0000000 [[1,2,3,4,8],[5,6,7]]=>{{1,2,3,4,8},{5,6,7}}=>[2,3,4,8,6,7,5,1]=>0000000 [[1,3,5,6,7],[2,4,8]]=>{{1,3,5,6,7},{2,4,8}}=>[3,4,5,8,6,7,1,2]=>0000000 [[1,3,4,6,7],[2,5,8]]=>{{1,3,4,6,7},{2,5,8}}=>[3,5,4,6,8,7,1,2]=>0000000 [[1,2,4,6,7],[3,5,8]]=>{{1,2,4,6,7},{3,5,8}}=>[2,4,5,6,8,7,1,3]=>0000000 [[1,2,3,6,7],[4,5,8]]=>{{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000 [[1,2,4,5,7],[3,6,8]]=>{{1,2,4,5,7},{3,6,8}}=>[2,4,6,5,7,8,1,3]=>0000000 [[1,2,3,5,7],[4,6,8]]=>{{1,2,3,5,7},{4,6,8}}=>[2,3,5,6,7,8,1,4]=>0000000 [[1,2,3,4,5],[6,7,8]]=>{{1,2,3,4,5},{6,7,8}}=>[2,3,4,5,1,7,8,6]=>0000100 [[1,2,6,7,8],[3,5],[4]]=>{{1,2,6,7,8},{3,5},{4}}=>[2,6,5,4,3,7,8,1]=>0000000 [[1,2,4,7,8],[3,6],[5]]=>{{1,2,4,7,8},{3,6},{5}}=>[2,4,6,7,5,3,8,1]=>0000000 [[1,2,3,7,8],[4,6],[5]]=>{{1,2,3,7,8},{4,6},{5}}=>[2,3,7,6,5,4,8,1]=>0000000 [[1,2,4,6,8],[3,7],[5]]=>{{1,2,4,6,8},{3,7},{5}}=>[2,4,7,6,5,8,3,1]=>0000000 [[1,2,3,4,8],[5,7],[6]]=>{{1,2,3,4,8},{5,7},{6}}=>[2,3,4,8,7,6,5,1]=>0000000 [[1,2,4,5,8],[3,6],[7]]=>{{1,2,4,5,8},{3,6},{7}}=>[2,4,6,5,8,3,7,1]=>0000000 [[1,2,3,4,8],[5,6],[7]]=>{{1,2,3,4,8},{5,6},{7}}=>[2,3,4,8,6,5,7,1]=>0000000 [[1,3,4,6,7],[2,8],[5]]=>{{1,3,4,6,7},{2,8},{5}}=>[3,8,4,6,5,7,1,2]=>0000000 [[1,2,4,6,7],[3,8],[5]]=>{{1,2,4,6,7},{3,8},{5}}=>[2,4,8,6,5,7,1,3]=>0000000 [[1,3,4,5,6],[2,8],[7]]=>{{1,3,4,5,6},{2,8},{7}}=>[3,8,4,5,6,1,7,2]=>0000000 [[1,2,3,5,6],[4,8],[7]]=>{{1,2,3,5,6},{4,8},{7}}=>[2,3,5,8,6,1,7,4]=>0000000 [[1,2,3,4,6],[5,8],[7]]=>{{1,2,3,4,6},{5,8},{7}}=>[2,3,4,6,8,1,7,5]=>0000000 [[1,2,3,4,5],[6,8],[7]]=>{{1,2,3,4,5},{6,8},{7}}=>[2,3,4,5,1,8,7,6]=>0000100 [[1,3,4,6,7],[2,5],[8]]=>{{1,3,4,6,7},{2,5},{8}}=>[3,5,4,6,2,7,1,8]=>0000001 [[1,2,3,5,7],[4,6],[8]]=>{{1,2,3,5,7},{4,6},{8}}=>[2,3,5,6,7,4,1,8]=>0000001 [[1,2,3,4,7],[5,6],[8]]=>{{1,2,3,4,7},{5,6},{8}}=>[2,3,4,7,6,5,1,8]=>0000001 [[1,2,3,4,6],[5,7],[8]]=>{{1,2,3,4,6},{5,7},{8}}=>[2,3,4,6,7,1,5,8]=>0000001 [[1,2,3,4,5],[6,7],[8]]=>{{1,2,3,4,5},{6,7},{8}}=>[2,3,4,5,1,7,6,8]=>0000101 [[1,5,6,7,8],[2],[3],[4]]=>{{1,5,6,7,8},{2},{3},{4}}=>[5,2,3,4,6,7,8,1]=>0000000 [[1,2,6,7,8],[3],[4],[5]]=>{{1,2,6,7,8},{3},{4},{5}}=>[2,6,3,4,5,7,8,1]=>0000000 [[1,3,5,7,8],[2],[4],[6]]=>{{1,3,5,7,8},{2},{4},{6}}=>[3,2,5,4,7,6,8,1]=>0000000 [[1,2,3,7,8],[4],[5],[6]]=>{{1,2,3,7,8},{4},{5},{6}}=>[2,3,7,4,5,6,8,1]=>0000000 [[1,4,5,6,8],[2],[3],[7]]=>{{1,4,5,6,8},{2},{3},{7}}=>[4,2,3,5,6,8,7,1]=>0000000 [[1,2,4,6,8],[3],[5],[7]]=>{{1,2,4,6,8},{3},{5},{7}}=>[2,4,3,6,5,8,7,1]=>0000000 [[1,2,3,4,8],[5],[6],[7]]=>{{1,2,3,4,8},{5},{6},{7}}=>[2,3,4,8,5,6,7,1]=>0000000 [[1,4,5,6,7],[2],[3],[8]]=>{{1,4,5,6,7},{2},{3},{8}}=>[4,2,3,5,6,7,1,8]=>0000001 [[1,2,5,6,7],[3],[4],[8]]=>{{1,2,5,6,7},{3},{4},{8}}=>[2,5,3,4,6,7,1,8]=>0000001 [[1,3,4,5,6],[2],[7],[8]]=>{{1,3,4,5,6},{2},{7},{8}}=>[3,2,4,5,6,1,7,8]=>0000011 [[1,2,3,5,6],[4],[7],[8]]=>{{1,2,3,5,6},{4},{7},{8}}=>[2,3,5,4,6,1,7,8]=>0000011 [[1,2,3,4,6],[5],[7],[8]]=>{{1,2,3,4,6},{5},{7},{8}}=>[2,3,4,6,5,1,7,8]=>0000011 [[1,2,3,4,5],[6],[7],[8]]=>{{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>0000111 [[1,3,5,7],[2,4,6,8]]=>{{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>0000000 [[1,3,4,7],[2,5,6,8]]=>{{1,3,4,7},{2,5,6,8}}=>[3,5,4,7,6,8,1,2]=>0000000 [[1,2,3,7],[4,5,6,8]]=>{{1,2,3,7},{4,5,6,8}}=>[2,3,7,5,6,8,1,4]=>0000000 [[1,2,5,6],[3,4,7,8]]=>{{1,2,5,6},{3,4,7,8}}=>[2,5,4,7,6,1,8,3]=>0000000 [[1,2,4,6],[3,5,7,8]]=>{{1,2,4,6},{3,5,7,8}}=>[2,4,5,6,7,1,8,3]=>0000000 [[1,3,4,5],[2,6,7,8]]=>{{1,3,4,5},{2,6,7,8}}=>[3,6,4,5,1,7,8,2]=>0000000 [[1,2,3,5],[4,6,7,8]]=>{{1,2,3,5},{4,6,7,8}}=>[2,3,5,6,1,7,8,4]=>0000000 [[1,2,3,4],[5,6,7,8]]=>{{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000 [[1,2,6,8],[3,5,7],[4]]=>{{1,2,6,8},{3,5,7},{4}}=>[2,6,5,4,7,8,3,1]=>0000000 [[1,2,5,8],[3,6,7],[4]]=>{{1,2,5,8},{3,6,7},{4}}=>[2,5,6,4,8,7,3,1]=>0000000 [[1,3,4,8],[2,6,7],[5]]=>{{1,3,4,8},{2,6,7},{5}}=>[3,6,4,8,5,7,2,1]=>0000000 [[1,2,3,8],[4,5,6],[7]]=>{{1,2,3,8},{4,5,6},{7}}=>[2,3,8,5,6,4,7,1]=>0000000 [[1,2,6,7],[3,5,8],[4]]=>{{1,2,6,7},{3,5,8},{4}}=>[2,6,5,4,8,7,1,3]=>0000000 [[1,3,6,7],[2,4,8],[5]]=>{{1,3,6,7},{2,4,8},{5}}=>[3,4,6,8,5,7,1,2]=>0000000 [[1,3,4,7],[2,6,8],[5]]=>{{1,3,4,7},{2,6,8},{5}}=>[3,6,4,7,5,8,1,2]=>0000000 [[1,2,4,7],[3,6,8],[5]]=>{{1,2,4,7},{3,6,8},{5}}=>[2,4,6,7,5,8,1,3]=>0000000 [[1,3,5,7],[2,4,8],[6]]=>{{1,3,5,7},{2,4,8},{6}}=>[3,4,5,8,7,6,1,2]=>0000000 [[1,2,5,7],[3,4,8],[6]]=>{{1,2,5,7},{3,4,8},{6}}=>[2,5,4,8,7,6,1,3]=>0000000 [[1,2,4,5],[3,7,8],[6]]=>{{1,2,4,5},{3,7,8},{6}}=>[2,4,7,5,1,6,8,3]=>0000000 [[1,3,5,6],[2,4,8],[7]]=>{{1,3,5,6},{2,4,8},{7}}=>[3,4,5,8,6,1,7,2]=>0000000 [[1,3,5,7],[2,4,6],[8]]=>{{1,3,5,7},{2,4,6},{8}}=>[3,4,5,6,7,2,1,8]=>0000001 [[1,2,3,4],[5,6,7],[8]]=>{{1,2,3,4},{5,6,7},{8}}=>[2,3,4,1,6,7,5,8]=>0001001 [[1,4,7,8],[2,5],[3,6]]=>{{1,4,7,8},{2,5},{3,6}}=>[4,5,6,7,2,3,8,1]=>0000000 [[1,3,6,8],[2,4],[5,7]]=>{{1,3,6,8},{2,4},{5,7}}=>[3,4,6,2,7,8,5,1]=>0000000 [[1,3,5,8],[2,6],[4,7]]=>{{1,3,5,8},{2,6},{4,7}}=>[3,6,5,7,8,2,4,1]=>0000000 [[1,2,5,8],[3,6],[4,7]]=>{{1,2,5,8},{3,6},{4,7}}=>[2,5,6,7,8,3,4,1]=>0000000 [[1,3,4,8],[2,6],[5,7]]=>{{1,3,4,8},{2,6},{5,7}}=>[3,6,4,8,7,2,5,1]=>0000000 [[1,2,4,8],[3,5],[6,7]]=>{{1,2,4,8},{3,5},{6,7}}=>[2,4,5,8,3,7,6,1]=>0000000 [[1,3,5,7],[2,6],[4,8]]=>{{1,3,5,7},{2,6},{4,8}}=>[3,6,5,8,7,2,1,4]=>0000000 [[1,2,3,6],[4,7],[5,8]]=>{{1,2,3,6},{4,7},{5,8}}=>[2,3,6,7,8,1,4,5]=>0000000 [[1,2,4,5],[3,7],[6,8]]=>{{1,2,4,5},{3,7},{6,8}}=>[2,4,7,5,1,8,3,6]=>0000000 [[1,2,3,4],[5,7],[6,8]]=>{{1,2,3,4},{5,7},{6,8}}=>[2,3,4,1,7,8,5,6]=>0001000 [[1,2,3,4],[5,6],[7,8]]=>{{1,2,3,4},{5,6},{7,8}}=>[2,3,4,1,6,5,8,7]=>0001010 [[1,5,7,8],[2,6],[3],[4]]=>{{1,5,7,8},{2,6},{3},{4}}=>[5,6,3,4,7,2,8,1]=>0000000 [[1,4,7,8],[2,6],[3],[5]]=>{{1,4,7,8},{2,6},{3},{5}}=>[4,6,3,7,5,2,8,1]=>0000000 [[1,2,7,8],[3,5],[4],[6]]=>{{1,2,7,8},{3,5},{4},{6}}=>[2,7,5,4,3,6,8,1]=>0000000 [[1,2,7,8],[3,4],[5],[6]]=>{{1,2,7,8},{3,4},{5},{6}}=>[2,7,4,3,5,6,8,1]=>0000000 [[1,3,6,8],[2,7],[4],[5]]=>{{1,3,6,8},{2,7},{4},{5}}=>[3,7,6,4,5,8,2,1]=>0000000 [[1,4,5,8],[2,7],[3],[6]]=>{{1,4,5,8},{2,7},{3},{6}}=>[4,7,3,5,8,6,2,1]=>0000000 [[1,2,4,8],[3,7],[5],[6]]=>{{1,2,4,8},{3,7},{5},{6}}=>[2,4,7,8,5,6,3,1]=>0000000 [[1,2,6,8],[3,5],[4],[7]]=>{{1,2,6,8},{3,5},{4},{7}}=>[2,6,5,4,3,8,7,1]=>0000000 [[1,3,6,8],[2,4],[5],[7]]=>{{1,3,6,8},{2,4},{5},{7}}=>[3,4,6,2,5,8,7,1]=>0000000 [[1,4,5,8],[2,6],[3],[7]]=>{{1,4,5,8},{2,6},{3},{7}}=>[4,6,3,5,8,2,7,1]=>0000000 [[1,3,5,8],[2,6],[4],[7]]=>{{1,3,5,8},{2,6},{4},{7}}=>[3,6,5,4,8,2,7,1]=>0000000 [[1,2,5,8],[3,6],[4],[7]]=>{{1,2,5,8},{3,6},{4},{7}}=>[2,5,6,4,8,3,7,1]=>0000000 [[1,2,4,8],[3,6],[5],[7]]=>{{1,2,4,8},{3,6},{5},{7}}=>[2,4,6,8,5,3,7,1]=>0000000 [[1,2,3,8],[4,6],[5],[7]]=>{{1,2,3,8},{4,6},{5},{7}}=>[2,3,8,6,5,4,7,1]=>0000000 [[1,2,5,8],[3,4],[6],[7]]=>{{1,2,5,8},{3,4},{6},{7}}=>[2,5,4,3,8,6,7,1]=>0000000 [[1,2,4,8],[3,5],[6],[7]]=>{{1,2,4,8},{3,5},{6},{7}}=>[2,4,5,8,3,6,7,1]=>0000000 [[1,2,3,8],[4,5],[6],[7]]=>{{1,2,3,8},{4,5},{6},{7}}=>[2,3,8,5,4,6,7,1]=>0000000 [[1,4,6,7],[2,8],[3],[5]]=>{{1,4,6,7},{2,8},{3},{5}}=>[4,8,3,6,5,7,1,2]=>0000000 [[1,3,5,7],[2,8],[4],[6]]=>{{1,3,5,7},{2,8},{4},{6}}=>[3,8,5,4,7,6,1,2]=>0000000 [[1,2,5,7],[3,8],[4],[6]]=>{{1,2,5,7},{3,8},{4},{6}}=>[2,5,8,4,7,6,1,3]=>0000000 [[1,3,4,7],[2,8],[5],[6]]=>{{1,3,4,7},{2,8},{5},{6}}=>[3,8,4,7,5,6,1,2]=>0000000 [[1,2,4,7],[3,8],[5],[6]]=>{{1,2,4,7},{3,8},{5},{6}}=>[2,4,8,7,5,6,1,3]=>0000000 [[1,4,5,6],[2,8],[3],[7]]=>{{1,4,5,6},{2,8},{3},{7}}=>[4,8,3,5,6,1,7,2]=>0000000 [[1,2,5,6],[3,8],[4],[7]]=>{{1,2,5,6},{3,8},{4},{7}}=>[2,5,8,4,6,1,7,3]=>0000000 [[1,2,3,6],[4,8],[5],[7]]=>{{1,2,3,6},{4,8},{5},{7}}=>[2,3,6,8,5,1,7,4]=>0000000 [[1,2,4,5],[3,8],[6],[7]]=>{{1,2,4,5},{3,8},{6},{7}}=>[2,4,8,5,1,6,7,3]=>0000000 [[1,4,6,7],[2,5],[3],[8]]=>{{1,4,6,7},{2,5},{3},{8}}=>[4,5,3,6,2,7,1,8]=>0000001 [[1,3,5,7],[2,6],[4],[8]]=>{{1,3,5,7},{2,6},{4},{8}}=>[3,6,5,4,7,2,1,8]=>0000001 [[1,2,5,7],[3,6],[4],[8]]=>{{1,2,5,7},{3,6},{4},{8}}=>[2,5,6,4,7,3,1,8]=>0000001 [[1,2,4,7],[3,6],[5],[8]]=>{{1,2,4,7},{3,6},{5},{8}}=>[2,4,6,7,5,3,1,8]=>0000001 [[1,2,3,7],[4,6],[5],[8]]=>{{1,2,3,7},{4,6},{5},{8}}=>[2,3,7,6,5,4,1,8]=>0000001 [[1,3,5,7],[2,4],[6],[8]]=>{{1,3,5,7},{2,4},{6},{8}}=>[3,4,5,2,7,6,1,8]=>0000001 [[1,3,4,7],[2,5],[6],[8]]=>{{1,3,4,7},{2,5},{6},{8}}=>[3,5,4,7,2,6,1,8]=>0000001 [[1,2,4,7],[3,5],[6],[8]]=>{{1,2,4,7},{3,5},{6},{8}}=>[2,4,5,7,3,6,1,8]=>0000001 [[1,3,4,5],[2,7],[6],[8]]=>{{1,3,4,5},{2,7},{6},{8}}=>[3,7,4,5,1,6,2,8]=>0000001 [[1,2,4,5],[3,7],[6],[8]]=>{{1,2,4,5},{3,7},{6},{8}}=>[2,4,7,5,1,6,3,8]=>0000001 [[1,3,5,6],[2,4],[7],[8]]=>{{1,3,5,6},{2,4},{7},{8}}=>[3,4,5,2,6,1,7,8]=>0000011 [[1,2,4,6],[3,5],[7],[8]]=>{{1,2,4,6},{3,5},{7},{8}}=>[2,4,5,6,3,1,7,8]=>0000011 [[1,2,3,5],[4,6],[7],[8]]=>{{1,2,3,5},{4,6},{7},{8}}=>[2,3,5,6,1,4,7,8]=>0000011 [[1,2,3,4],[5,6],[7],[8]]=>{{1,2,3,4},{5,6},{7},{8}}=>[2,3,4,1,6,5,7,8]=>0001011 [[1,6,7,8],[2],[3],[4],[5]]=>{{1,6,7,8},{2},{3},{4},{5}}=>[6,2,3,4,5,7,8,1]=>0000000 [[1,2,3,8],[4],[5],[6],[7]]=>{{1,2,3,8},{4},{5},{6},{7}}=>[2,3,8,4,5,6,7,1]=>0000000 [[1,3,5,7],[2],[4],[6],[8]]=>{{1,3,5,7},{2},{4},{6},{8}}=>[3,2,5,4,7,6,1,8]=>0000001 [[1,2,3,4],[5],[6],[7],[8]]=>{{1,2,3,4},{5},{6},{7},{8}}=>[2,3,4,1,5,6,7,8]=>0001111 [[1,4,7],[2,5,8],[3,6]]=>{{1,4,7},{2,5,8},{3,6}}=>[4,5,6,7,8,3,1,2]=>0000000 [[1,4,6],[2,5,8],[3,7]]=>{{1,4,6},{2,5,8},{3,7}}=>[4,5,7,6,8,1,3,2]=>0000000 [[1,3,6],[2,5,8],[4,7]]=>{{1,3,6},{2,5,8},{4,7}}=>[3,5,6,7,8,1,4,2]=>0000000 [[1,2,6],[3,4,8],[5,7]]=>{{1,2,6},{3,4,8},{5,7}}=>[2,6,4,8,7,1,5,3]=>0000000 [[1,3,5],[2,6,8],[4,7]]=>{{1,3,5},{2,6,8},{4,7}}=>[3,6,5,7,1,8,4,2]=>0000000 [[1,3,4],[2,6,8],[5,7]]=>{{1,3,4},{2,6,8},{5,7}}=>[3,6,4,1,7,8,5,2]=>0000000 [[1,2,5],[3,4,8],[6,7]]=>{{1,2,5},{3,4,8},{6,7}}=>[2,5,4,8,1,7,6,3]=>0000000 [[1,3,6],[2,5,7],[4,8]]=>{{1,3,6},{2,5,7},{4,8}}=>[3,5,6,8,7,1,2,4]=>0000000 [[1,2,4],[3,5,7],[6,8]]=>{{1,2,4},{3,5,7},{6,8}}=>[2,4,5,1,7,8,3,6]=>0000000 [[1,2,5],[3,4,6],[7,8]]=>{{1,2,5},{3,4,6},{7,8}}=>[2,5,4,6,1,3,8,7]=>0000010 [[1,2,4],[3,5,6],[7,8]]=>{{1,2,4},{3,5,6},{7,8}}=>[2,4,5,1,6,3,8,7]=>0000010 [[1,5,7],[2,6,8],[3],[4]]=>{{1,5,7},{2,6,8},{3},{4}}=>[5,6,3,4,7,8,1,2]=>0000000 [[1,4,7],[2,6,8],[3],[5]]=>{{1,4,7},{2,6,8},{3},{5}}=>[4,6,3,7,5,8,1,2]=>0000000 [[1,3,7],[2,6,8],[4],[5]]=>{{1,3,7},{2,6,8},{4},{5}}=>[3,6,7,4,5,8,1,2]=>0000000 [[1,4,7],[2,5,8],[3],[6]]=>{{1,4,7},{2,5,8},{3},{6}}=>[4,5,3,7,8,6,1,2]=>0000000 [[1,3,7],[2,5,8],[4],[6]]=>{{1,3,7},{2,5,8},{4},{6}}=>[3,5,7,4,8,6,1,2]=>0000000 [[1,2,7],[3,5,8],[4],[6]]=>{{1,2,7},{3,5,8},{4},{6}}=>[2,7,5,4,8,6,1,3]=>0000000 [[1,3,7],[2,4,8],[5],[6]]=>{{1,3,7},{2,4,8},{5},{6}}=>[3,4,7,8,5,6,1,2]=>0000000 [[1,2,7],[3,4,8],[5],[6]]=>{{1,2,7},{3,4,8},{5},{6}}=>[2,7,4,8,5,6,1,3]=>0000000 [[1,5,6],[2,7,8],[3],[4]]=>{{1,5,6},{2,7,8},{3},{4}}=>[5,7,3,4,6,1,8,2]=>0000000 [[1,4,6],[2,7,8],[3],[5]]=>{{1,4,6},{2,7,8},{3},{5}}=>[4,7,3,6,5,1,8,2]=>0000000 [[1,2,6],[3,7,8],[4],[5]]=>{{1,2,6},{3,7,8},{4},{5}}=>[2,6,7,4,5,1,8,3]=>0000000 [[1,2,5],[3,7,8],[4],[6]]=>{{1,2,5},{3,7,8},{4},{6}}=>[2,5,7,4,1,6,8,3]=>0000000 [[1,2,4],[3,7,8],[5],[6]]=>{{1,2,4},{3,7,8},{5},{6}}=>[2,4,7,1,5,6,8,3]=>0000000 [[1,4,6],[2,5,8],[3],[7]]=>{{1,4,6},{2,5,8},{3},{7}}=>[4,5,3,6,8,1,7,2]=>0000000 [[1,3,6],[2,4,8],[5],[7]]=>{{1,3,6},{2,4,8},{5},{7}}=>[3,4,6,8,5,1,7,2]=>0000000 [[1,2,6],[3,4,8],[5],[7]]=>{{1,2,6},{3,4,8},{5},{7}}=>[2,6,4,8,5,1,7,3]=>0000000 [[1,4,5],[2,6,8],[3],[7]]=>{{1,4,5},{2,6,8},{3},{7}}=>[4,6,3,5,1,8,7,2]=>0000000 [[1,3,5],[2,6,8],[4],[7]]=>{{1,3,5},{2,6,8},{4},{7}}=>[3,6,5,4,1,8,7,2]=>0000000 [[1,3,4],[2,6,8],[5],[7]]=>{{1,3,4},{2,6,8},{5},{7}}=>[3,6,4,1,5,8,7,2]=>0000000 [[1,2,3],[4,6,8],[5],[7]]=>{{1,2,3},{4,6,8},{5},{7}}=>[2,3,1,6,5,8,7,4]=>0010000 [[1,3,5],[2,4,8],[6],[7]]=>{{1,3,5},{2,4,8},{6},{7}}=>[3,4,5,8,1,6,7,2]=>0000000 [[1,3,5],[2,6,7],[4],[8]]=>{{1,3,5},{2,6,7},{4},{8}}=>[3,6,5,4,1,7,2,8]=>0000001 [[1,2,5],[3,6,7],[4],[8]]=>{{1,2,5},{3,6,7},{4},{8}}=>[2,5,6,4,1,7,3,8]=>0000001 [[1,2,3],[4,6,7],[5],[8]]=>{{1,2,3},{4,6,7},{5},{8}}=>[2,3,1,6,5,7,4,8]=>0010001 [[1,2,4],[3,5,7],[6],[8]]=>{{1,2,4},{3,5,7},{6},{8}}=>[2,4,5,1,7,6,3,8]=>0000001 [[1,3,5],[2,4,6],[7],[8]]=>{{1,3,5},{2,4,6},{7},{8}}=>[3,4,5,6,1,2,7,8]=>0000011 [[1,2,5],[3,4,6],[7],[8]]=>{{1,2,5},{3,4,6},{7},{8}}=>[2,5,4,6,1,3,7,8]=>0000011 [[1,2,3],[4,5,6],[7],[8]]=>{{1,2,3},{4,5,6},{7},{8}}=>[2,3,1,5,6,4,7,8]=>0010011 [[1,4,8],[2,6],[3,7],[5]]=>{{1,4,8},{2,6},{3,7},{5}}=>[4,6,7,8,5,2,3,1]=>0000000 [[1,3,8],[2,6],[4,7],[5]]=>{{1,3,8},{2,6},{4,7},{5}}=>[3,6,8,7,5,2,4,1]=>0000000 [[1,2,8],[3,6],[4,7],[5]]=>{{1,2,8},{3,6},{4,7},{5}}=>[2,8,6,7,5,3,4,1]=>0000000 [[1,4,8],[2,5],[3,7],[6]]=>{{1,4,8},{2,5},{3,7},{6}}=>[4,5,7,8,2,6,3,1]=>0000000 [[1,3,8],[2,5],[4,7],[6]]=>{{1,3,8},{2,5},{4,7},{6}}=>[3,5,8,7,2,6,4,1]=>0000000 [[1,2,8],[3,5],[4,7],[6]]=>{{1,2,8},{3,5},{4,7},{6}}=>[2,8,5,7,3,6,4,1]=>0000000 [[1,3,8],[2,4],[5,7],[6]]=>{{1,3,8},{2,4},{5,7},{6}}=>[3,4,8,2,7,6,5,1]=>0000000 [[1,2,8],[3,4],[5,7],[6]]=>{{1,2,8},{3,4},{5,7},{6}}=>[2,8,4,3,7,6,5,1]=>0000000 [[1,4,8],[2,5],[3,6],[7]]=>{{1,4,8},{2,5},{3,6},{7}}=>[4,5,6,8,2,3,7,1]=>0000000 [[1,3,8],[2,5],[4,6],[7]]=>{{1,3,8},{2,5},{4,6},{7}}=>[3,5,8,6,2,4,7,1]=>0000000 [[1,4,7],[2,6],[3,8],[5]]=>{{1,4,7},{2,6},{3,8},{5}}=>[4,6,8,7,5,2,1,3]=>0000000 [[1,3,7],[2,6],[4,8],[5]]=>{{1,3,7},{2,6},{4,8},{5}}=>[3,6,7,8,5,2,1,4]=>0000000 [[1,2,7],[3,6],[4,8],[5]]=>{{1,2,7},{3,6},{4,8},{5}}=>[2,7,6,8,5,3,1,4]=>0000000 [[1,4,7],[2,5],[3,8],[6]]=>{{1,4,7},{2,5},{3,8},{6}}=>[4,5,8,7,2,6,1,3]=>0000000 [[1,3,7],[2,5],[4,8],[6]]=>{{1,3,7},{2,5},{4,8},{6}}=>[3,5,7,8,2,6,1,4]=>0000000 [[1,2,7],[3,5],[4,8],[6]]=>{{1,2,7},{3,5},{4,8},{6}}=>[2,7,5,8,3,6,1,4]=>0000000 [[1,3,7],[2,4],[5,8],[6]]=>{{1,3,7},{2,4},{5,8},{6}}=>[3,4,7,2,8,6,1,5]=>0000000 [[1,4,6],[2,7],[3,8],[5]]=>{{1,4,6},{2,7},{3,8},{5}}=>[4,7,8,6,5,1,2,3]=>0000000 [[1,3,6],[2,7],[4,8],[5]]=>{{1,3,6},{2,7},{4,8},{5}}=>[3,7,6,8,5,1,2,4]=>0000000 [[1,2,6],[3,7],[4,8],[5]]=>{{1,2,6},{3,7},{4,8},{5}}=>[2,6,7,8,5,1,3,4]=>0000000 [[1,3,5],[2,7],[4,8],[6]]=>{{1,3,5},{2,7},{4,8},{6}}=>[3,7,5,8,1,6,2,4]=>0000000 [[1,2,5],[3,7],[4,8],[6]]=>{{1,2,5},{3,7},{4,8},{6}}=>[2,5,7,8,1,6,3,4]=>0000000 [[1,3,4],[2,7],[5,8],[6]]=>{{1,3,4},{2,7},{5,8},{6}}=>[3,7,4,1,8,6,2,5]=>0000000 [[1,2,3],[4,7],[5,8],[6]]=>{{1,2,3},{4,7},{5,8},{6}}=>[2,3,1,7,8,6,4,5]=>0010000 [[1,3,6],[2,5],[4,8],[7]]=>{{1,3,6},{2,5},{4,8},{7}}=>[3,5,6,8,2,1,7,4]=>0000000 [[1,2,6],[3,5],[4,8],[7]]=>{{1,2,6},{3,5},{4,8},{7}}=>[2,6,5,8,3,1,7,4]=>0000000 [[1,2,6],[3,4],[5,8],[7]]=>{{1,2,6},{3,4},{5,8},{7}}=>[2,6,4,3,8,1,7,5]=>0000000 [[1,3,5],[2,6],[4,8],[7]]=>{{1,3,5},{2,6},{4,8},{7}}=>[3,6,5,8,1,2,7,4]=>0000000 [[1,2,5],[3,6],[4,8],[7]]=>{{1,2,5},{3,6},{4,8},{7}}=>[2,5,6,8,1,3,7,4]=>0000000 [[1,3,4],[2,6],[5,8],[7]]=>{{1,3,4},{2,6},{5,8},{7}}=>[3,6,4,1,8,2,7,5]=>0000000 [[1,3,5],[2,4],[6,8],[7]]=>{{1,3,5},{2,4},{6,8},{7}}=>[3,4,5,2,1,8,7,6]=>0000100 [[1,2,5],[3,4],[6,8],[7]]=>{{1,2,5},{3,4},{6,8},{7}}=>[2,5,4,3,1,8,7,6]=>0000100 [[1,4,7],[2,5],[3,6],[8]]=>{{1,4,7},{2,5},{3,6},{8}}=>[4,5,6,7,2,3,1,8]=>0000001 [[1,3,7],[2,5],[4,6],[8]]=>{{1,3,7},{2,5},{4,6},{8}}=>[3,5,7,6,2,4,1,8]=>0000001 [[1,2,7],[3,5],[4,6],[8]]=>{{1,2,7},{3,5},{4,6},{8}}=>[2,7,5,6,3,4,1,8]=>0000001 [[1,3,7],[2,4],[5,6],[8]]=>{{1,3,7},{2,4},{5,6},{8}}=>[3,4,7,2,6,5,1,8]=>0000001 [[1,3,6],[2,4],[5,7],[8]]=>{{1,3,6},{2,4},{5,7},{8}}=>[3,4,6,2,7,1,5,8]=>0000001 [[1,3,4],[2,6],[5,7],[8]]=>{{1,3,4},{2,6},{5,7},{8}}=>[3,6,4,1,7,2,5,8]=>0000001 [[1,2,3],[4,5],[6,7],[8]]=>{{1,2,3},{4,5},{6,7},{8}}=>[2,3,1,5,4,7,6,8]=>0010101 [[1,3,8],[2,4],[5],[6],[7]]=>{{1,3,8},{2,4},{5},{6},{7}}=>[3,4,8,2,5,6,7,1]=>0000000 [[1,6,7],[2,8],[3],[4],[5]]=>{{1,6,7},{2,8},{3},{4},{5}}=>[6,8,3,4,5,7,1,2]=>0000000 [[1,3,4],[2,8],[5],[6],[7]]=>{{1,3,4},{2,8},{5},{6},{7}}=>[3,8,4,1,5,6,7,2]=>0000000 [[1,4,7],[2,6],[3],[5],[8]]=>{{1,4,7},{2,6},{3},{5},{8}}=>[4,6,3,7,5,2,1,8]=>0000001 [[1,4,7],[2,5],[3],[6],[8]]=>{{1,4,7},{2,5},{3},{6},{8}}=>[4,5,3,7,2,6,1,8]=>0000001 [[1,4,6],[2,7],[3],[5],[8]]=>{{1,4,6},{2,7},{3},{5},{8}}=>[4,7,3,6,5,1,2,8]=>0000001 [[1,3,5],[2,4],[6],[7],[8]]=>{{1,3,5},{2,4},{6},{7},{8}}=>[3,4,5,2,1,6,7,8]=>0000111 [[1,2,3],[4,5],[6],[7],[8]]=>{{1,2,3},{4,5},{6},{7},{8}}=>[2,3,1,5,4,6,7,8]=>0010111 [[1,7,8],[2],[3],[4],[5],[6]]=>{{1,7,8},{2},{3},{4},{5},{6}}=>[7,2,3,4,5,6,8,1]=>0000000 [[1,3,8],[2],[4],[5],[6],[7]]=>{{1,3,8},{2},{4},{5},{6},{7}}=>[3,2,8,4,5,6,7,1]=>0000000 [[1,2,8],[3],[4],[5],[6],[7]]=>{{1,2,8},{3},{4},{5},{6},{7}}=>[2,8,3,4,5,6,7,1]=>0000000 [[1,5,7],[2],[3],[4],[6],[8]]=>{{1,5,7},{2},{3},{4},{6},{8}}=>[5,2,3,4,7,6,1,8]=>0000001 [[1,3,7],[2],[4],[5],[6],[8]]=>{{1,3,7},{2},{4},{5},{6},{8}}=>[3,2,7,4,5,6,1,8]=>0000001 [[1,3,5],[2],[4],[6],[7],[8]]=>{{1,3,5},{2},{4},{6},{7},{8}}=>[3,2,5,4,1,6,7,8]=>0000111 [[1,3,4],[2],[5],[6],[7],[8]]=>{{1,3,4},{2},{5},{6},{7},{8}}=>[3,2,4,1,5,6,7,8]=>0001111 [[1,2,3],[4],[5],[6],[7],[8]]=>{{1,2,3},{4},{5},{6},{7},{8}}=>[2,3,1,4,5,6,7,8]=>0011111 [[1,5],[2,6],[3,7],[4,8]]=>{{1,5},{2,6},{3,7},{4,8}}=>[5,6,7,8,1,2,3,4]=>0000000 [[1,4],[2,6],[3,7],[5,8]]=>{{1,4},{2,6},{3,7},{5,8}}=>[4,6,7,1,8,2,3,5]=>0000000 [[1,3],[2,6],[4,7],[5,8]]=>{{1,3},{2,6},{4,7},{5,8}}=>[3,6,1,7,8,2,4,5]=>0000000 [[1,2],[3,6],[4,7],[5,8]]=>{{1,2},{3,6},{4,7},{5,8}}=>[2,1,6,7,8,3,4,5]=>0100000 [[1,4],[2,5],[3,7],[6,8]]=>{{1,4},{2,5},{3,7},{6,8}}=>[4,5,7,1,2,8,3,6]=>0000000 [[1,3],[2,5],[4,7],[6,8]]=>{{1,3},{2,5},{4,7},{6,8}}=>[3,5,1,7,2,8,4,6]=>0000000 [[1,2],[3,5],[4,7],[6,8]]=>{{1,2},{3,5},{4,7},{6,8}}=>[2,1,5,7,3,8,4,6]=>0100000 [[1,3],[2,4],[5,7],[6,8]]=>{{1,3},{2,4},{5,7},{6,8}}=>[3,4,1,2,7,8,5,6]=>0001000 [[1,2],[3,4],[5,7],[6,8]]=>{{1,2},{3,4},{5,7},{6,8}}=>[2,1,4,3,7,8,5,6]=>0101000 [[1,4],[2,5],[3,6],[7,8]]=>{{1,4},{2,5},{3,6},{7,8}}=>[4,5,6,1,2,3,8,7]=>0000010 [[1,3],[2,5],[4,6],[7,8]]=>{{1,3},{2,5},{4,6},{7,8}}=>[3,5,1,6,2,4,8,7]=>0000010 [[1,2],[3,5],[4,6],[7,8]]=>{{1,2},{3,5},{4,6},{7,8}}=>[2,1,5,6,3,4,8,7]=>0100010 [[1,3],[2,4],[5,6],[7,8]]=>{{1,3},{2,4},{5,6},{7,8}}=>[3,4,1,2,6,5,8,7]=>0001010 [[1,2],[3,4],[5,6],[7,8]]=>{{1,2},{3,4},{5,6},{7,8}}=>[2,1,4,3,6,5,8,7]=>0101010 [[1,4],[2,6],[3,8],[5],[7]]=>{{1,4},{2,6},{3,8},{5},{7}}=>[4,6,8,1,5,2,7,3]=>0000000 [[1,5],[2,6],[3,7],[4],[8]]=>{{1,5},{2,6},{3,7},{4},{8}}=>[5,6,7,4,1,2,3,8]=>0000001 [[1,3],[2,6],[4,7],[5],[8]]=>{{1,3},{2,6},{4,7},{5},{8}}=>[3,6,1,7,5,2,4,8]=>0000001 [[1,4],[2,5],[3,6],[7],[8]]=>{{1,4},{2,5},{3,6},{7},{8}}=>[4,5,6,1,2,3,7,8]=>0000011 [[1,3],[2,5],[4,6],[7],[8]]=>{{1,3},{2,5},{4,6},{7},{8}}=>[3,5,1,6,2,4,7,8]=>0000011 [[1,2],[3,4],[5,6],[7],[8]]=>{{1,2},{3,4},{5,6},{7},{8}}=>[2,1,4,3,6,5,7,8]=>0101011 [[1,7],[2,8],[3],[4],[5],[6]]=>{{1,7},{2,8},{3},{4},{5},{6}}=>[7,8,3,4,5,6,1,2]=>0000000 [[1,6],[2,8],[3],[4],[5],[7]]=>{{1,6},{2,8},{3},{4},{5},{7}}=>[6,8,3,4,5,1,7,2]=>0000000 [[1,4],[2,8],[3],[5],[6],[7]]=>{{1,4},{2,8},{3},{5},{6},{7}}=>[4,8,3,1,5,6,7,2]=>0000000 [[1,3],[2,8],[4],[5],[6],[7]]=>{{1,3},{2,8},{4},{5},{6},{7}}=>[3,8,1,4,5,6,7,2]=>0000000 [[1,5],[2,6],[3],[4],[7],[8]]=>{{1,5},{2,6},{3},{4},{7},{8}}=>[5,6,3,4,1,2,7,8]=>0000011 [[1,2],[3,5],[4],[6],[7],[8]]=>{{1,2},{3,5},{4},{6},{7},{8}}=>[2,1,5,4,3,6,7,8]=>0100111 [[1,3],[2,4],[5],[6],[7],[8]]=>{{1,3},{2,4},{5},{6},{7},{8}}=>[3,4,1,2,5,6,7,8]=>0001111 [[1,2],[3,4],[5],[6],[7],[8]]=>{{1,2},{3,4},{5},{6},{7},{8}}=>[2,1,4,3,5,6,7,8]=>0101111 [[1,8],[2],[3],[4],[5],[6],[7]]=>{{1,8},{2},{3},{4},{5},{6},{7}}=>[8,2,3,4,5,6,7,1]=>0000000 [[1,7],[2],[3],[4],[5],[6],[8]]=>{{1,7},{2},{3},{4},{5},{6},{8}}=>[7,2,3,4,5,6,1,8]=>0000001 [[1,6],[2],[3],[4],[5],[7],[8]]=>{{1,6},{2},{3},{4},{5},{7},{8}}=>[6,2,3,4,5,1,7,8]=>0000011 [[1,5],[2],[3],[4],[6],[7],[8]]=>{{1,5},{2},{3},{4},{6},{7},{8}}=>[5,2,3,4,1,6,7,8]=>0000111 [[1,4],[2],[3],[5],[6],[7],[8]]=>{{1,4},{2},{3},{5},{6},{7},{8}}=>[4,2,3,1,5,6,7,8]=>0001111 [[1,3],[2],[4],[5],[6],[7],[8]]=>{{1,3},{2},{4},{5},{6},{7},{8}}=>[3,2,1,4,5,6,7,8]=>0011111 [[1,2],[3],[4],[5],[6],[7],[8]]=>{{1,2},{3},{4},{5},{6},{7},{8}}=>[2,1,3,4,5,6,7,8]=>0111111 [[1],[2],[3],[4],[5],[6],[7],[8]]=>{{1},{2},{3},{4},{5},{6},{7},{8}}=>[1,2,3,4,5,6,7,8]=>1111111 [[1,3,5,7,9],[2,4,6,8,10]]=>{{1,3,5,7,9},{2,4,6,8,10}}=>[3,4,5,6,7,8,9,10,1,2]=>000000000 [[1,2,4,6,8],[3,5,7,9,10]]=>{{1,2,4,6,8},{3,5,7,9,10}}=>[2,4,5,6,7,8,9,1,10,3]=>000000000 [[1,2,3,4,5],[6,7,8,9,10]]=>{{1,2,3,4,5},{6,7,8,9,10}}=>[2,3,4,5,1,7,8,9,10,6]=>000010000 [[1,3,5,7,9,11],[2,4,6,8,10,12]]=>{{1,3,5,7,9,11},{2,4,6,8,10,12}}=>[3,4,5,6,7,8,9,10,11,12,1,2]=>00000000000 [[1,2,3,4,5,6,7,8,9]]=>{{1,2,3,4,5,6,7,8,9}}=>[2,3,4,5,6,7,8,9,1]=>00000000 [[1,2,3,4,5,6,7,8],[9]]=>{{1,2,3,4,5,6,7,8},{9}}=>[2,3,4,5,6,7,8,1,9]=>00000001 [[1,2,3,4,5,6,7],[8,9]]=>{{1,2,3,4,5,6,7},{8,9}}=>[2,3,4,5,6,7,1,9,8]=>00000010 [[1,2,3,4,5,6,7],[8],[9]]=>{{1,2,3,4,5,6,7},{8},{9}}=>[2,3,4,5,6,7,1,8,9]=>00000011 [[1,2,3,4,5,6],[7,8,9]]=>{{1,2,3,4,5,6},{7,8,9}}=>[2,3,4,5,6,1,8,9,7]=>00000100 [[1,2,3,4,5,6],[7,8],[9]]=>{{1,2,3,4,5,6},{7,8},{9}}=>[2,3,4,5,6,1,8,7,9]=>00000101 [[1,2,3,4,5,6],[7],[8],[9]]=>{{1,2,3,4,5,6},{7},{8},{9}}=>[2,3,4,5,6,1,7,8,9]=>00000111 [[1,2,3,4,5],[6,7,8,9]]=>{{1,2,3,4,5},{6,7,8,9}}=>[2,3,4,5,1,7,8,9,6]=>00001000 [[1,2,3,4,5],[6,7],[8,9]]=>{{1,2,3,4,5},{6,7},{8,9}}=>[2,3,4,5,1,7,6,9,8]=>00001010 [[1,2,3,4,5],[6,7],[8],[9]]=>{{1,2,3,4,5},{6,7},{8},{9}}=>[2,3,4,5,1,7,6,8,9]=>00001011 [[1,2,3,4,5],[6],[7],[8],[9]]=>{{1,2,3,4,5},{6},{7},{8},{9}}=>[2,3,4,5,1,6,7,8,9]=>00001111 [[1,2,3,4],[5,6],[7,8],[9]]=>{{1,2,3,4},{5,6},{7,8},{9}}=>[2,3,4,1,6,5,8,7,9]=>00010101 [[1,2,3,4],[5,6],[7],[8],[9]]=>{{1,2,3,4},{5,6},{7},{8},{9}}=>[2,3,4,1,6,5,7,8,9]=>00010111 [[1,2,3,4],[5],[6],[7],[8],[9]]=>{{1,2,3,4},{5},{6},{7},{8},{9}}=>[2,3,4,1,5,6,7,8,9]=>00011111 [[1,2,3],[4,5],[6,7],[8,9]]=>{{1,2,3},{4,5},{6,7},{8,9}}=>[2,3,1,5,4,7,6,9,8]=>00101010 [[1,2,3],[4,5],[6],[7],[8],[9]]=>{{1,2,3},{4,5},{6},{7},{8},{9}}=>[2,3,1,5,4,6,7,8,9]=>00101111 [[1,2,3],[4],[5],[6],[7],[8],[9]]=>{{1,2,3},{4},{5},{6},{7},{8},{9}}=>[2,3,1,4,5,6,7,8,9]=>00111111 [[1,2],[3,4],[5,6],[7,8],[9]]=>{{1,2},{3,4},{5,6},{7,8},{9}}=>[2,1,4,3,6,5,8,7,9]=>01010101 [[1,2],[3,4],[5,6],[7],[8],[9]]=>{{1,2},{3,4},{5,6},{7},{8},{9}}=>[2,1,4,3,6,5,7,8,9]=>01010111 [[1,2],[3,4],[5],[6],[7],[8],[9]]=>{{1,2},{3,4},{5},{6},{7},{8},{9}}=>[2,1,4,3,5,6,7,8,9]=>01011111 [[1,2],[3],[4],[5],[6],[7],[8],[9]]=>{{1,2},{3},{4},{5},{6},{7},{8},{9}}=>[2,1,3,4,5,6,7,8,9]=>01111111 [[1],[2],[3],[4],[5],[6],[7],[8],[9]]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}=>[1,2,3,4,5,6,7,8,9]=>11111111 [[1,2,3,4,5,6,7,8,9,10]]=>{{1,2,3,4,5,6,7,8,9,10}}=>[2,3,4,5,6,7,8,9,10,1]=>000000000 [[1,2,3,4,5,6,7,8,9],[10]]=>{{1,2,3,4,5,6,7,8,9},{10}}=>[2,3,4,5,6,7,8,9,1,10]=>000000001 [[1,2,3,4,5,6,7,8],[9,10]]=>{{1,2,3,4,5,6,7,8},{9,10}}=>[2,3,4,5,6,7,8,1,10,9]=>000000010 [[1,2,3,4,5,6,7,8],[9],[10]]=>{{1,2,3,4,5,6,7,8},{9},{10}}=>[2,3,4,5,6,7,8,1,9,10]=>000000011 [[1,2,3,4,5,6,7],[8,9,10]]=>{{1,2,3,4,5,6,7},{8,9,10}}=>[2,3,4,5,6,7,1,9,10,8]=>000000100 [[1,2,3,4,5,6,7],[8,9],[10]]=>{{1,2,3,4,5,6,7},{8,9},{10}}=>[2,3,4,5,6,7,1,9,8,10]=>000000101 [[1,2,3,4,5,6,7],[8],[9],[10]]=>{{1,2,3,4,5,6,7},{8},{9},{10}}=>[2,3,4,5,6,7,1,8,9,10]=>000000111 [[1,2,3,4,5,6],[7,8,9,10]]=>{{1,2,3,4,5,6},{7,8,9,10}}=>[2,3,4,5,6,1,8,9,10,7]=>000001000 [[1,2,3,4,5,6],[7,8],[9,10]]=>{{1,2,3,4,5,6},{7,8},{9,10}}=>[2,3,4,5,6,1,8,7,10,9]=>000001010 [[1,2,3,4,5,6],[7],[8],[9],[10]]=>{{1,2,3,4,5,6},{7},{8},{9},{10}}=>[2,3,4,5,6,1,7,8,9,10]=>000001111 [[1,2,3,4,5],[6,7],[8,9],[10]]=>{{1,2,3,4,5},{6,7},{8,9},{10}}=>[2,3,4,5,1,7,6,9,8,10]=>000010101 [[1,2,3,4,5],[6],[7],[8],[9],[10]]=>{{1,2,3,4,5},{6},{7},{8},{9},{10}}=>[2,3,4,5,1,6,7,8,9,10]=>000011111 [[1,2,3,4],[5,6],[7,8],[9,10]]=>{{1,2,3,4},{5,6},{7,8},{9,10}}=>[2,3,4,1,6,5,8,7,10,9]=>000101010 [[1,2,3,4],[5],[6],[7],[8],[9],[10]]=>{{1,2,3,4},{5},{6},{7},{8},{9},{10}}=>[2,3,4,1,5,6,7,8,9,10]=>000111111 [[1,2,3],[4,5],[6,7],[8,9],[10]]=>{{1,2,3},{4,5},{6,7},{8,9},{10}}=>[2,3,1,5,4,7,6,9,8,10]=>001010101 [[1,2,3],[4],[5],[6],[7],[8],[9],[10]]=>{{1,2,3},{4},{5},{6},{7},{8},{9},{10}}=>[2,3,1,4,5,6,7,8,9,10]=>001111111 [[1,2],[3,4],[5,6],[7,8],[9,10]]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}=>[2,1,4,3,6,5,8,7,10,9]=>010101010 [[1,2],[3,4],[5,6],[7,8],[9],[10]]=>{{1,2},{3,4},{5,6},{7,8},{9},{10}}=>[2,1,4,3,6,5,8,7,9,10]=>010101011 [[1,2],[3,4],[5,6],[7],[8],[9],[10]]=>{{1,2},{3,4},{5,6},{7},{8},{9},{10}}=>[2,1,4,3,6,5,7,8,9,10]=>010101111 [[1,2],[3,4],[5],[6],[7],[8],[9],[10]]=>{{1,2},{3,4},{5},{6},{7},{8},{9},{10}}=>[2,1,4,3,5,6,7,8,9,10]=>010111111 [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]]=>{{1,2},{3},{4},{5},{6},{7},{8},{9},{10}}=>[2,1,3,4,5,6,7,8,9,10]=>011111111 [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}=>[1,2,3,4,5,6,7,8,9,10]=>111111111 [[1,3,4,5,6,7,8,9],[2]]=>{{1,3,4,5,6,7,8,9},{2}}=>[3,2,4,5,6,7,8,9,1]=>00000000 [[1,4,5,6,7,8,9],[2],[3]]=>{{1,4,5,6,7,8,9},{2},{3}}=>[4,2,3,5,6,7,8,9,1]=>00000000 [[1,8,9],[2],[3],[4],[5],[6],[7]]=>{{1,8,9},{2},{3},{4},{5},{6},{7}}=>[8,2,3,4,5,6,7,9,1]=>00000000 [[1,7],[2,9],[3],[4],[5],[6],[8]]=>{{1,7},{2,9},{3},{4},{5},{6},{8}}=>[7,9,3,4,5,6,1,8,2]=>00000000 [[1,9],[2],[3],[4],[5],[6],[7],[8]]=>{{1,9},{2},{3},{4},{5},{6},{7},{8}}=>[9,2,3,4,5,6,7,8,1]=>00000000 [[1,3,4,5,6,7,8,9,10],[2]]=>{{1,3,4,5,6,7,8,9,10},{2}}=>[3,2,4,5,6,7,8,9,10,1]=>000000000 [[1,4,5,6,7,8,9,10],[2],[3]]=>{{1,4,5,6,7,8,9,10},{2},{3}}=>[4,2,3,5,6,7,8,9,10,1]=>000000000 [[1,6,7,8,9,10],[2],[3],[4],[5]]=>{{1,6,7,8,9,10},{2},{3},{4},{5}}=>[6,2,3,4,5,7,8,9,10,1]=>000000000 [[1,8],[2,10],[3],[4],[5],[6],[7],[9]]=>{{1,8},{2,10},{3},{4},{5},{6},{7},{9}}=>[8,10,3,4,5,6,7,1,9,2]=>000000000 [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]]=>{{1,10},{2},{3},{4},{5},{6},{7},{8},{9}}=>[10,2,3,4,5,6,7,8,9,1]=>000000000 [[1,8],[2,9],[3],[4],[5],[6],[7]]=>{{1,8},{2,9},{3},{4},{5},{6},{7}}=>[8,9,3,4,5,6,7,1,2]=>00000000 [[1,6],[2,7],[3,8],[4,9],[5,10]]=>{{1,6},{2,7},{3,8},{4,9},{5,10}}=>[6,7,8,9,10,1,2,3,4,5]=>000000000 [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]]=>{{1,7},{2,8},{3,9},{4,10},{5,11},{6,12}}=>[7,8,9,10,11,12,1,2,3,4,5,6]=>00000000000 [[1,2,9],[3],[4],[5],[6],[7],[8]]=>{{1,2,9},{3},{4},{5},{6},{7},{8}}=>[2,9,3,4,5,6,7,8,1]=>00000000 [[1,3],[2,9],[4],[5],[6],[7],[8]]=>{{1,3},{2,9},{4},{5},{6},{7},{8}}=>[3,9,1,4,5,6,7,8,2]=>00000000 [[1,8],[2],[3],[4],[5],[6],[7],[9]]=>{{1,8},{2},{3},{4},{5},{6},{7},{9}}=>[8,2,3,4,5,6,7,1,9]=>00000001 [[1,3,4,5,6,7,8],[2],[9]]=>{{1,3,4,5,6,7,8},{2},{9}}=>[3,2,4,5,6,7,8,1,9]=>00000001 [[1,3],[2],[4],[5],[6],[7],[8],[9]]=>{{1,3},{2},{4},{5},{6},{7},{8},{9}}=>[3,2,1,4,5,6,7,8,9]=>00111111 [[1,3],[2],[4],[5],[6],[7],[8],[9],[10]]=>{{1,3},{2},{4},{5},{6},{7},{8},{9},{10}}=>[3,2,1,4,5,6,7,8,9,10]=>001111111
Map
rows
Description
The set partition whose blocks are the rows of the tableau.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
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.