Identifier
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00114: Permutations —connectivity set⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Images
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Cc0009;cc-rep-0
{{1}}=>[1]=>=> {{1,2}}=>[2,1]=>0=>0 {{1},{2}}=>[1,2]=>1=>1 {{1,2,3}}=>[2,3,1]=>00=>00 {{1,2},{3}}=>[2,1,3]=>01=>10 {{1,3},{2}}=>[3,2,1]=>00=>00 {{1},{2,3}}=>[1,3,2]=>10=>01 {{1},{2},{3}}=>[1,2,3]=>11=>11 {{1,2,3,4}}=>[2,3,4,1]=>000=>000 {{1,2,3},{4}}=>[2,3,1,4]=>001=>100 {{1,2,4},{3}}=>[2,4,3,1]=>000=>000 {{1,2},{3,4}}=>[2,1,4,3]=>010=>010 {{1,2},{3},{4}}=>[2,1,3,4]=>011=>110 {{1,3,4},{2}}=>[3,2,4,1]=>000=>000 {{1,3},{2,4}}=>[3,4,1,2]=>000=>000 {{1,3},{2},{4}}=>[3,2,1,4]=>001=>100 {{1,4},{2,3}}=>[4,3,2,1]=>000=>000 {{1},{2,3,4}}=>[1,3,4,2]=>100=>001 {{1},{2,3},{4}}=>[1,3,2,4]=>101=>101 {{1,4},{2},{3}}=>[4,2,3,1]=>000=>000 {{1},{2,4},{3}}=>[1,4,3,2]=>100=>001 {{1},{2},{3,4}}=>[1,2,4,3]=>110=>011 {{1},{2},{3},{4}}=>[1,2,3,4]=>111=>111 {{1,2,3,4,5}}=>[2,3,4,5,1]=>0000=>0000 {{1,2,3,4},{5}}=>[2,3,4,1,5]=>0001=>1000 {{1,2,3,5},{4}}=>[2,3,5,4,1]=>0000=>0000 {{1,2,3},{4,5}}=>[2,3,1,5,4]=>0010=>0100 {{1,2,3},{4},{5}}=>[2,3,1,4,5]=>0011=>1100 {{1,2,4,5},{3}}=>[2,4,3,5,1]=>0000=>0000 {{1,2,4},{3,5}}=>[2,4,5,1,3]=>0000=>0000 {{1,2,4},{3},{5}}=>[2,4,3,1,5]=>0001=>1000 {{1,2,5},{3,4}}=>[2,5,4,3,1]=>0000=>0000 {{1,2},{3,4,5}}=>[2,1,4,5,3]=>0100=>0010 {{1,2},{3,4},{5}}=>[2,1,4,3,5]=>0101=>1010 {{1,2,5},{3},{4}}=>[2,5,3,4,1]=>0000=>0000 {{1,2},{3,5},{4}}=>[2,1,5,4,3]=>0100=>0010 {{1,2},{3},{4,5}}=>[2,1,3,5,4]=>0110=>0110 {{1,2},{3},{4},{5}}=>[2,1,3,4,5]=>0111=>1110 {{1,3,4,5},{2}}=>[3,2,4,5,1]=>0000=>0000 {{1,3,4},{2,5}}=>[3,5,4,1,2]=>0000=>0000 {{1,3,4},{2},{5}}=>[3,2,4,1,5]=>0001=>1000 {{1,3,5},{2,4}}=>[3,4,5,2,1]=>0000=>0000 {{1,3},{2,4,5}}=>[3,4,1,5,2]=>0000=>0000 {{1,3},{2,4},{5}}=>[3,4,1,2,5]=>0001=>1000 {{1,3,5},{2},{4}}=>[3,2,5,4,1]=>0000=>0000 {{1,3},{2,5},{4}}=>[3,5,1,4,2]=>0000=>0000 {{1,3},{2},{4,5}}=>[3,2,1,5,4]=>0010=>0100 {{1,3},{2},{4},{5}}=>[3,2,1,4,5]=>0011=>1100 {{1,4,5},{2,3}}=>[4,3,2,5,1]=>0000=>0000 {{1,4},{2,3,5}}=>[4,3,5,1,2]=>0000=>0000 {{1,4},{2,3},{5}}=>[4,3,2,1,5]=>0001=>1000 {{1,5},{2,3,4}}=>[5,3,4,2,1]=>0000=>0000 {{1},{2,3,4,5}}=>[1,3,4,5,2]=>1000=>0001 {{1},{2,3,4},{5}}=>[1,3,4,2,5]=>1001=>1001 {{1,5},{2,3},{4}}=>[5,3,2,4,1]=>0000=>0000 {{1},{2,3,5},{4}}=>[1,3,5,4,2]=>1000=>0001 {{1},{2,3},{4,5}}=>[1,3,2,5,4]=>1010=>0101 {{1},{2,3},{4},{5}}=>[1,3,2,4,5]=>1011=>1101 {{1,4,5},{2},{3}}=>[4,2,3,5,1]=>0000=>0000 {{1,4},{2,5},{3}}=>[4,5,3,1,2]=>0000=>0000 {{1,4},{2},{3,5}}=>[4,2,5,1,3]=>0000=>0000 {{1,4},{2},{3},{5}}=>[4,2,3,1,5]=>0001=>1000 {{1,5},{2,4},{3}}=>[5,4,3,2,1]=>0000=>0000 {{1},{2,4,5},{3}}=>[1,4,3,5,2]=>1000=>0001 {{1},{2,4},{3,5}}=>[1,4,5,2,3]=>1000=>0001 {{1},{2,4},{3},{5}}=>[1,4,3,2,5]=>1001=>1001 {{1,5},{2},{3,4}}=>[5,2,4,3,1]=>0000=>0000 {{1},{2,5},{3,4}}=>[1,5,4,3,2]=>1000=>0001 {{1},{2},{3,4,5}}=>[1,2,4,5,3]=>1100=>0011 {{1},{2},{3,4},{5}}=>[1,2,4,3,5]=>1101=>1011 {{1,5},{2},{3},{4}}=>[5,2,3,4,1]=>0000=>0000 {{1},{2,5},{3},{4}}=>[1,5,3,4,2]=>1000=>0001 {{1},{2},{3,5},{4}}=>[1,2,5,4,3]=>1100=>0011 {{1},{2},{3},{4,5}}=>[1,2,3,5,4]=>1110=>0111 {{1},{2},{3},{4},{5}}=>[1,2,3,4,5]=>1111=>1111 {{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>00000=>00000 {{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>00001=>10000 {{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>00000=>00000 {{1,2,3,4},{5,6}}=>[2,3,4,1,6,5]=>00010=>01000 {{1,2,3,4},{5},{6}}=>[2,3,4,1,5,6]=>00011=>11000 {{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>00000=>00000 {{1,2,3,5},{4,6}}=>[2,3,5,6,1,4]=>00000=>00000 {{1,2,3,5},{4},{6}}=>[2,3,5,4,1,6]=>00001=>10000 {{1,2,3,6},{4,5}}=>[2,3,6,5,4,1]=>00000=>00000 {{1,2,3},{4,5,6}}=>[2,3,1,5,6,4]=>00100=>00100 {{1,2,3},{4,5},{6}}=>[2,3,1,5,4,6]=>00101=>10100 {{1,2,3,6},{4},{5}}=>[2,3,6,4,5,1]=>00000=>00000 {{1,2,3},{4,6},{5}}=>[2,3,1,6,5,4]=>00100=>00100 {{1,2,3},{4},{5,6}}=>[2,3,1,4,6,5]=>00110=>01100 {{1,2,3},{4},{5},{6}}=>[2,3,1,4,5,6]=>00111=>11100 {{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>00000=>00000 {{1,2,4,5},{3,6}}=>[2,4,6,5,1,3]=>00000=>00000 {{1,2,4,5},{3},{6}}=>[2,4,3,5,1,6]=>00001=>10000 {{1,2,4,6},{3,5}}=>[2,4,5,6,3,1]=>00000=>00000 {{1,2,4},{3,5,6}}=>[2,4,5,1,6,3]=>00000=>00000 {{1,2,4},{3,5},{6}}=>[2,4,5,1,3,6]=>00001=>10000 {{1,2,4,6},{3},{5}}=>[2,4,3,6,5,1]=>00000=>00000 {{1,2,4},{3,6},{5}}=>[2,4,6,1,5,3]=>00000=>00000 {{1,2,4},{3},{5,6}}=>[2,4,3,1,6,5]=>00010=>01000 {{1,2,4},{3},{5},{6}}=>[2,4,3,1,5,6]=>00011=>11000 {{1,2,5,6},{3,4}}=>[2,5,4,3,6,1]=>00000=>00000 {{1,2,5},{3,4,6}}=>[2,5,4,6,1,3]=>00000=>00000 {{1,2,5},{3,4},{6}}=>[2,5,4,3,1,6]=>00001=>10000 {{1,2,6},{3,4,5}}=>[2,6,4,5,3,1]=>00000=>00000 {{1,2},{3,4,5,6}}=>[2,1,4,5,6,3]=>01000=>00010 {{1,2},{3,4,5},{6}}=>[2,1,4,5,3,6]=>01001=>10010 {{1,2,6},{3,4},{5}}=>[2,6,4,3,5,1]=>00000=>00000 {{1,2},{3,4,6},{5}}=>[2,1,4,6,5,3]=>01000=>00010 {{1,2},{3,4},{5,6}}=>[2,1,4,3,6,5]=>01010=>01010 {{1,2},{3,4},{5},{6}}=>[2,1,4,3,5,6]=>01011=>11010 {{1,2,5,6},{3},{4}}=>[2,5,3,4,6,1]=>00000=>00000 {{1,2,5},{3,6},{4}}=>[2,5,6,4,1,3]=>00000=>00000 {{1,2,5},{3},{4,6}}=>[2,5,3,6,1,4]=>00000=>00000 {{1,2,5},{3},{4},{6}}=>[2,5,3,4,1,6]=>00001=>10000 {{1,2,6},{3,5},{4}}=>[2,6,5,4,3,1]=>00000=>00000 {{1,2},{3,5,6},{4}}=>[2,1,5,4,6,3]=>01000=>00010 {{1,2},{3,5},{4,6}}=>[2,1,5,6,3,4]=>01000=>00010 {{1,2},{3,5},{4},{6}}=>[2,1,5,4,3,6]=>01001=>10010 {{1,2,6},{3},{4,5}}=>[2,6,3,5,4,1]=>00000=>00000 {{1,2},{3,6},{4,5}}=>[2,1,6,5,4,3]=>01000=>00010 {{1,2},{3},{4,5,6}}=>[2,1,3,5,6,4]=>01100=>00110 {{1,2},{3},{4,5},{6}}=>[2,1,3,5,4,6]=>01101=>10110 {{1,2,6},{3},{4},{5}}=>[2,6,3,4,5,1]=>00000=>00000 {{1,2},{3,6},{4},{5}}=>[2,1,6,4,5,3]=>01000=>00010 {{1,2},{3},{4,6},{5}}=>[2,1,3,6,5,4]=>01100=>00110 {{1,2},{3},{4},{5,6}}=>[2,1,3,4,6,5]=>01110=>01110 {{1,2},{3},{4},{5},{6}}=>[2,1,3,4,5,6]=>01111=>11110 {{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>00000=>00000 {{1,3,4,5},{2,6}}=>[3,6,4,5,1,2]=>00000=>00000 {{1,3,4,5},{2},{6}}=>[3,2,4,5,1,6]=>00001=>10000 {{1,3,4,6},{2,5}}=>[3,5,4,6,2,1]=>00000=>00000 {{1,3,4},{2,5,6}}=>[3,5,4,1,6,2]=>00000=>00000 {{1,3,4},{2,5},{6}}=>[3,5,4,1,2,6]=>00001=>10000 {{1,3,4,6},{2},{5}}=>[3,2,4,6,5,1]=>00000=>00000 {{1,3,4},{2,6},{5}}=>[3,6,4,1,5,2]=>00000=>00000 {{1,3,4},{2},{5,6}}=>[3,2,4,1,6,5]=>00010=>01000 {{1,3,4},{2},{5},{6}}=>[3,2,4,1,5,6]=>00011=>11000 {{1,3,5,6},{2,4}}=>[3,4,5,2,6,1]=>00000=>00000 {{1,3,5},{2,4,6}}=>[3,4,5,6,1,2]=>00000=>00000 {{1,3,5},{2,4},{6}}=>[3,4,5,2,1,6]=>00001=>10000 {{1,3,6},{2,4,5}}=>[3,4,6,5,2,1]=>00000=>00000 {{1,3},{2,4,5,6}}=>[3,4,1,5,6,2]=>00000=>00000 {{1,3},{2,4,5},{6}}=>[3,4,1,5,2,6]=>00001=>10000 {{1,3,6},{2,4},{5}}=>[3,4,6,2,5,1]=>00000=>00000 {{1,3},{2,4,6},{5}}=>[3,4,1,6,5,2]=>00000=>00000 {{1,3},{2,4},{5,6}}=>[3,4,1,2,6,5]=>00010=>01000 {{1,3},{2,4},{5},{6}}=>[3,4,1,2,5,6]=>00011=>11000 {{1,3,5,6},{2},{4}}=>[3,2,5,4,6,1]=>00000=>00000 {{1,3,5},{2,6},{4}}=>[3,6,5,4,1,2]=>00000=>00000 {{1,3,5},{2},{4,6}}=>[3,2,5,6,1,4]=>00000=>00000 {{1,3,5},{2},{4},{6}}=>[3,2,5,4,1,6]=>00001=>10000 {{1,3,6},{2,5},{4}}=>[3,5,6,4,2,1]=>00000=>00000 {{1,3},{2,5,6},{4}}=>[3,5,1,4,6,2]=>00000=>00000 {{1,3},{2,5},{4,6}}=>[3,5,1,6,2,4]=>00000=>00000 {{1,3},{2,5},{4},{6}}=>[3,5,1,4,2,6]=>00001=>10000 {{1,3,6},{2},{4,5}}=>[3,2,6,5,4,1]=>00000=>00000 {{1,3},{2,6},{4,5}}=>[3,6,1,5,4,2]=>00000=>00000 {{1,3},{2},{4,5,6}}=>[3,2,1,5,6,4]=>00100=>00100 {{1,3},{2},{4,5},{6}}=>[3,2,1,5,4,6]=>00101=>10100 {{1,3,6},{2},{4},{5}}=>[3,2,6,4,5,1]=>00000=>00000 {{1,3},{2,6},{4},{5}}=>[3,6,1,4,5,2]=>00000=>00000 {{1,3},{2},{4,6},{5}}=>[3,2,1,6,5,4]=>00100=>00100 {{1,3},{2},{4},{5,6}}=>[3,2,1,4,6,5]=>00110=>01100 {{1,3},{2},{4},{5},{6}}=>[3,2,1,4,5,6]=>00111=>11100 {{1,4,5,6},{2,3}}=>[4,3,2,5,6,1]=>00000=>00000 {{1,4,5},{2,3,6}}=>[4,3,6,5,1,2]=>00000=>00000 {{1,4,5},{2,3},{6}}=>[4,3,2,5,1,6]=>00001=>10000 {{1,4,6},{2,3,5}}=>[4,3,5,6,2,1]=>00000=>00000 {{1,4},{2,3,5,6}}=>[4,3,5,1,6,2]=>00000=>00000 {{1,4},{2,3,5},{6}}=>[4,3,5,1,2,6]=>00001=>10000 {{1,4,6},{2,3},{5}}=>[4,3,2,6,5,1]=>00000=>00000 {{1,4},{2,3,6},{5}}=>[4,3,6,1,5,2]=>00000=>00000 {{1,4},{2,3},{5,6}}=>[4,3,2,1,6,5]=>00010=>01000 {{1,4},{2,3},{5},{6}}=>[4,3,2,1,5,6]=>00011=>11000 {{1,5,6},{2,3,4}}=>[5,3,4,2,6,1]=>00000=>00000 {{1,5},{2,3,4,6}}=>[5,3,4,6,1,2]=>00000=>00000 {{1,5},{2,3,4},{6}}=>[5,3,4,2,1,6]=>00001=>10000 {{1,6},{2,3,4,5}}=>[6,3,4,5,2,1]=>00000=>00000 {{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>10000=>00001 {{1},{2,3,4,5},{6}}=>[1,3,4,5,2,6]=>10001=>10001 {{1,6},{2,3,4},{5}}=>[6,3,4,2,5,1]=>00000=>00000 {{1},{2,3,4,6},{5}}=>[1,3,4,6,5,2]=>10000=>00001 {{1},{2,3,4},{5,6}}=>[1,3,4,2,6,5]=>10010=>01001 {{1},{2,3,4},{5},{6}}=>[1,3,4,2,5,6]=>10011=>11001 {{1,5,6},{2,3},{4}}=>[5,3,2,4,6,1]=>00000=>00000 {{1,5},{2,3,6},{4}}=>[5,3,6,4,1,2]=>00000=>00000 {{1,5},{2,3},{4,6}}=>[5,3,2,6,1,4]=>00000=>00000 {{1,5},{2,3},{4},{6}}=>[5,3,2,4,1,6]=>00001=>10000 {{1,6},{2,3,5},{4}}=>[6,3,5,4,2,1]=>00000=>00000 {{1},{2,3,5,6},{4}}=>[1,3,5,4,6,2]=>10000=>00001 {{1},{2,3,5},{4,6}}=>[1,3,5,6,2,4]=>10000=>00001 {{1},{2,3,5},{4},{6}}=>[1,3,5,4,2,6]=>10001=>10001 {{1,6},{2,3},{4,5}}=>[6,3,2,5,4,1]=>00000=>00000 {{1},{2,3,6},{4,5}}=>[1,3,6,5,4,2]=>10000=>00001 {{1},{2,3},{4,5,6}}=>[1,3,2,5,6,4]=>10100=>00101 {{1},{2,3},{4,5},{6}}=>[1,3,2,5,4,6]=>10101=>10101 {{1,6},{2,3},{4},{5}}=>[6,3,2,4,5,1]=>00000=>00000 {{1},{2,3,6},{4},{5}}=>[1,3,6,4,5,2]=>10000=>00001 {{1},{2,3},{4,6},{5}}=>[1,3,2,6,5,4]=>10100=>00101 {{1},{2,3},{4},{5,6}}=>[1,3,2,4,6,5]=>10110=>01101 {{1},{2,3},{4},{5},{6}}=>[1,3,2,4,5,6]=>10111=>11101 {{1,4,5,6},{2},{3}}=>[4,2,3,5,6,1]=>00000=>00000 {{1,4,5},{2,6},{3}}=>[4,6,3,5,1,2]=>00000=>00000 {{1,4,5},{2},{3,6}}=>[4,2,6,5,1,3]=>00000=>00000 {{1,4,5},{2},{3},{6}}=>[4,2,3,5,1,6]=>00001=>10000 {{1,4,6},{2,5},{3}}=>[4,5,3,6,2,1]=>00000=>00000 {{1,4},{2,5,6},{3}}=>[4,5,3,1,6,2]=>00000=>00000 {{1,4},{2,5},{3,6}}=>[4,5,6,1,2,3]=>00000=>00000 {{1,4},{2,5},{3},{6}}=>[4,5,3,1,2,6]=>00001=>10000 {{1,4,6},{2},{3,5}}=>[4,2,5,6,3,1]=>00000=>00000 {{1,4},{2,6},{3,5}}=>[4,6,5,1,3,2]=>00000=>00000 {{1,4},{2},{3,5,6}}=>[4,2,5,1,6,3]=>00000=>00000 {{1,4},{2},{3,5},{6}}=>[4,2,5,1,3,6]=>00001=>10000 {{1,4,6},{2},{3},{5}}=>[4,2,3,6,5,1]=>00000=>00000 {{1,4},{2,6},{3},{5}}=>[4,6,3,1,5,2]=>00000=>00000 {{1,4},{2},{3,6},{5}}=>[4,2,6,1,5,3]=>00000=>00000 {{1,4},{2},{3},{5,6}}=>[4,2,3,1,6,5]=>00010=>01000 {{1,4},{2},{3},{5},{6}}=>[4,2,3,1,5,6]=>00011=>11000 {{1,5,6},{2,4},{3}}=>[5,4,3,2,6,1]=>00000=>00000 {{1,5},{2,4,6},{3}}=>[5,4,3,6,1,2]=>00000=>00000 {{1,5},{2,4},{3,6}}=>[5,4,6,2,1,3]=>00000=>00000 {{1,5},{2,4},{3},{6}}=>[5,4,3,2,1,6]=>00001=>10000 {{1,6},{2,4,5},{3}}=>[6,4,3,5,2,1]=>00000=>00000 {{1},{2,4,5,6},{3}}=>[1,4,3,5,6,2]=>10000=>00001 {{1},{2,4,5},{3,6}}=>[1,4,6,5,2,3]=>10000=>00001 {{1},{2,4,5},{3},{6}}=>[1,4,3,5,2,6]=>10001=>10001 {{1,6},{2,4},{3,5}}=>[6,4,5,2,3,1]=>00000=>00000 {{1},{2,4,6},{3,5}}=>[1,4,5,6,3,2]=>10000=>00001 {{1},{2,4},{3,5,6}}=>[1,4,5,2,6,3]=>10000=>00001 {{1},{2,4},{3,5},{6}}=>[1,4,5,2,3,6]=>10001=>10001 {{1,6},{2,4},{3},{5}}=>[6,4,3,2,5,1]=>00000=>00000 {{1},{2,4,6},{3},{5}}=>[1,4,3,6,5,2]=>10000=>00001 {{1},{2,4},{3,6},{5}}=>[1,4,6,2,5,3]=>10000=>00001 {{1},{2,4},{3},{5,6}}=>[1,4,3,2,6,5]=>10010=>01001 {{1},{2,4},{3},{5},{6}}=>[1,4,3,2,5,6]=>10011=>11001 {{1,5,6},{2},{3,4}}=>[5,2,4,3,6,1]=>00000=>00000 {{1,5},{2,6},{3,4}}=>[5,6,4,3,1,2]=>00000=>00000 {{1,5},{2},{3,4,6}}=>[5,2,4,6,1,3]=>00000=>00000 {{1,5},{2},{3,4},{6}}=>[5,2,4,3,1,6]=>00001=>10000 {{1,6},{2,5},{3,4}}=>[6,5,4,3,2,1]=>00000=>00000 {{1},{2,5,6},{3,4}}=>[1,5,4,3,6,2]=>10000=>00001 {{1},{2,5},{3,4,6}}=>[1,5,4,6,2,3]=>10000=>00001 {{1},{2,5},{3,4},{6}}=>[1,5,4,3,2,6]=>10001=>10001 {{1,6},{2},{3,4,5}}=>[6,2,4,5,3,1]=>00000=>00000 {{1},{2,6},{3,4,5}}=>[1,6,4,5,3,2]=>10000=>00001 {{1},{2},{3,4,5,6}}=>[1,2,4,5,6,3]=>11000=>00011 {{1},{2},{3,4,5},{6}}=>[1,2,4,5,3,6]=>11001=>10011 {{1,6},{2},{3,4},{5}}=>[6,2,4,3,5,1]=>00000=>00000 {{1},{2,6},{3,4},{5}}=>[1,6,4,3,5,2]=>10000=>00001 {{1},{2},{3,4,6},{5}}=>[1,2,4,6,5,3]=>11000=>00011 {{1},{2},{3,4},{5,6}}=>[1,2,4,3,6,5]=>11010=>01011 {{1},{2},{3,4},{5},{6}}=>[1,2,4,3,5,6]=>11011=>11011 {{1,5,6},{2},{3},{4}}=>[5,2,3,4,6,1]=>00000=>00000 {{1,5},{2,6},{3},{4}}=>[5,6,3,4,1,2]=>00000=>00000 {{1,5},{2},{3,6},{4}}=>[5,2,6,4,1,3]=>00000=>00000 {{1,5},{2},{3},{4,6}}=>[5,2,3,6,1,4]=>00000=>00000 {{1,5},{2},{3},{4},{6}}=>[5,2,3,4,1,6]=>00001=>10000 {{1,6},{2,5},{3},{4}}=>[6,5,3,4,2,1]=>00000=>00000 {{1},{2,5,6},{3},{4}}=>[1,5,3,4,6,2]=>10000=>00001 {{1},{2,5},{3,6},{4}}=>[1,5,6,4,2,3]=>10000=>00001 {{1},{2,5},{3},{4,6}}=>[1,5,3,6,2,4]=>10000=>00001 {{1},{2,5},{3},{4},{6}}=>[1,5,3,4,2,6]=>10001=>10001 {{1,6},{2},{3,5},{4}}=>[6,2,5,4,3,1]=>00000=>00000 {{1},{2,6},{3,5},{4}}=>[1,6,5,4,3,2]=>10000=>00001 {{1},{2},{3,5,6},{4}}=>[1,2,5,4,6,3]=>11000=>00011 {{1},{2},{3,5},{4,6}}=>[1,2,5,6,3,4]=>11000=>00011 {{1},{2},{3,5},{4},{6}}=>[1,2,5,4,3,6]=>11001=>10011 {{1,6},{2},{3},{4,5}}=>[6,2,3,5,4,1]=>00000=>00000 {{1},{2,6},{3},{4,5}}=>[1,6,3,5,4,2]=>10000=>00001 {{1},{2},{3,6},{4,5}}=>[1,2,6,5,4,3]=>11000=>00011 {{1},{2},{3},{4,5,6}}=>[1,2,3,5,6,4]=>11100=>00111 {{1},{2},{3},{4,5},{6}}=>[1,2,3,5,4,6]=>11101=>10111 {{1,6},{2},{3},{4},{5}}=>[6,2,3,4,5,1]=>00000=>00000 {{1},{2,6},{3},{4},{5}}=>[1,6,3,4,5,2]=>10000=>00001 {{1},{2},{3,6},{4},{5}}=>[1,2,6,4,5,3]=>11000=>00011 {{1},{2},{3},{4,6},{5}}=>[1,2,3,6,5,4]=>11100=>00111 {{1},{2},{3},{4},{5,6}}=>[1,2,3,4,6,5]=>11110=>01111 {{1},{2},{3},{4},{5},{6}}=>[1,2,3,4,5,6]=>11111=>11111 {{1,2,3,4,5,6,7}}=>[2,3,4,5,6,7,1]=>000000=>000000 {{1,2,3,4,5,6},{7}}=>[2,3,4,5,6,1,7]=>000001=>100000 {{1,2,3,4,5,7},{6}}=>[2,3,4,5,7,6,1]=>000000=>000000 {{1,2,3,4,5},{6,7}}=>[2,3,4,5,1,7,6]=>000010=>010000 {{1,2,3,4,5},{6},{7}}=>[2,3,4,5,1,6,7]=>000011=>110000 {{1,2,3,4,6,7},{5}}=>[2,3,4,6,5,7,1]=>000000=>000000 {{1,2,3,4,6},{5,7}}=>[2,3,4,6,7,1,5]=>000000=>000000 {{1,2,3,4,6},{5},{7}}=>[2,3,4,6,5,1,7]=>000001=>100000 {{1,2,3,4,7},{5,6}}=>[2,3,4,7,6,5,1]=>000000=>000000 {{1,2,3,4},{5,6,7}}=>[2,3,4,1,6,7,5]=>000100=>001000 {{1,2,3,4},{5,6},{7}}=>[2,3,4,1,6,5,7]=>000101=>101000 {{1,2,3,4,7},{5},{6}}=>[2,3,4,7,5,6,1]=>000000=>000000 {{1,2,3,4},{5,7},{6}}=>[2,3,4,1,7,6,5]=>000100=>001000 {{1,2,3,4},{5},{6,7}}=>[2,3,4,1,5,7,6]=>000110=>011000 {{1,2,3,4},{5},{6},{7}}=>[2,3,4,1,5,6,7]=>000111=>111000 {{1,2,3,5,6,7},{4}}=>[2,3,5,4,6,7,1]=>000000=>000000 {{1,2,3,5,6},{4,7}}=>[2,3,5,7,6,1,4]=>000000=>000000 {{1,2,3,5,6},{4},{7}}=>[2,3,5,4,6,1,7]=>000001=>100000 {{1,2,3,5,7},{4,6}}=>[2,3,5,6,7,4,1]=>000000=>000000 {{1,2,3,5},{4,6,7}}=>[2,3,5,6,1,7,4]=>000000=>000000 {{1,2,3,5},{4,6},{7}}=>[2,3,5,6,1,4,7]=>000001=>100000 {{1,2,3,5,7},{4},{6}}=>[2,3,5,4,7,6,1]=>000000=>000000 {{1,2,3,5},{4,7},{6}}=>[2,3,5,7,1,6,4]=>000000=>000000 {{1,2,3,5},{4},{6,7}}=>[2,3,5,4,1,7,6]=>000010=>010000 {{1,2,3,5},{4},{6},{7}}=>[2,3,5,4,1,6,7]=>000011=>110000 {{1,2,3,6,7},{4,5}}=>[2,3,6,5,4,7,1]=>000000=>000000 {{1,2,3,6},{4,5,7}}=>[2,3,6,5,7,1,4]=>000000=>000000 {{1,2,3,6},{4,5},{7}}=>[2,3,6,5,4,1,7]=>000001=>100000 {{1,2,3,7},{4,5,6}}=>[2,3,7,5,6,4,1]=>000000=>000000 {{1,2,3},{4,5,6,7}}=>[2,3,1,5,6,7,4]=>001000=>000100 {{1,2,3},{4,5,6},{7}}=>[2,3,1,5,6,4,7]=>001001=>100100 {{1,2,3,7},{4,5},{6}}=>[2,3,7,5,4,6,1]=>000000=>000000 {{1,2,3},{4,5,7},{6}}=>[2,3,1,5,7,6,4]=>001000=>000100 {{1,2,3},{4,5},{6,7}}=>[2,3,1,5,4,7,6]=>001010=>010100 {{1,2,3},{4,5},{6},{7}}=>[2,3,1,5,4,6,7]=>001011=>110100 {{1,2,3,6,7},{4},{5}}=>[2,3,6,4,5,7,1]=>000000=>000000 {{1,2,3,6},{4,7},{5}}=>[2,3,6,7,5,1,4]=>000000=>000000 {{1,2,3,6},{4},{5,7}}=>[2,3,6,4,7,1,5]=>000000=>000000 {{1,2,3,6},{4},{5},{7}}=>[2,3,6,4,5,1,7]=>000001=>100000 {{1,2,3,7},{4,6},{5}}=>[2,3,7,6,5,4,1]=>000000=>000000 {{1,2,3},{4,6,7},{5}}=>[2,3,1,6,5,7,4]=>001000=>000100 {{1,2,3},{4,6},{5,7}}=>[2,3,1,6,7,4,5]=>001000=>000100 {{1,2,3},{4,6},{5},{7}}=>[2,3,1,6,5,4,7]=>001001=>100100 {{1,2,3,7},{4},{5,6}}=>[2,3,7,4,6,5,1]=>000000=>000000 {{1,2,3},{4,7},{5,6}}=>[2,3,1,7,6,5,4]=>001000=>000100 {{1,2,3},{4},{5,6,7}}=>[2,3,1,4,6,7,5]=>001100=>001100 {{1,2,3},{4},{5,6},{7}}=>[2,3,1,4,6,5,7]=>001101=>101100 {{1,2,3,7},{4},{5},{6}}=>[2,3,7,4,5,6,1]=>000000=>000000 {{1,2,3},{4,7},{5},{6}}=>[2,3,1,7,5,6,4]=>001000=>000100 {{1,2,3},{4},{5,7},{6}}=>[2,3,1,4,7,6,5]=>001100=>001100 {{1,2,3},{4},{5},{6,7}}=>[2,3,1,4,5,7,6]=>001110=>011100 {{1,2,3},{4},{5},{6},{7}}=>[2,3,1,4,5,6,7]=>001111=>111100 {{1,2,4,5,6,7},{3}}=>[2,4,3,5,6,7,1]=>000000=>000000 {{1,2,4,5,6},{3,7}}=>[2,4,7,5,6,1,3]=>000000=>000000 {{1,2,4,5,6},{3},{7}}=>[2,4,3,5,6,1,7]=>000001=>100000 {{1,2,4,5,7},{3,6}}=>[2,4,6,5,7,3,1]=>000000=>000000 {{1,2,4,5},{3,6,7}}=>[2,4,6,5,1,7,3]=>000000=>000000 {{1,2,4,5},{3,6},{7}}=>[2,4,6,5,1,3,7]=>000001=>100000 {{1,2,4,5,7},{3},{6}}=>[2,4,3,5,7,6,1]=>000000=>000000 {{1,2,4,5},{3,7},{6}}=>[2,4,7,5,1,6,3]=>000000=>000000 {{1,2,4,5},{3},{6,7}}=>[2,4,3,5,1,7,6]=>000010=>010000 {{1,2,4,5},{3},{6},{7}}=>[2,4,3,5,1,6,7]=>000011=>110000 {{1,2,4,6,7},{3,5}}=>[2,4,5,6,3,7,1]=>000000=>000000 {{1,2,4,6},{3,5,7}}=>[2,4,5,6,7,1,3]=>000000=>000000 {{1,2,4,6},{3,5},{7}}=>[2,4,5,6,3,1,7]=>000001=>100000 {{1,2,4,7},{3,5,6}}=>[2,4,5,7,6,3,1]=>000000=>000000 {{1,2,4},{3,5,6,7}}=>[2,4,5,1,6,7,3]=>000000=>000000 {{1,2,4},{3,5,6},{7}}=>[2,4,5,1,6,3,7]=>000001=>100000 {{1,2,4,7},{3,5},{6}}=>[2,4,5,7,3,6,1]=>000000=>000000 {{1,2,4},{3,5,7},{6}}=>[2,4,5,1,7,6,3]=>000000=>000000 {{1,2,4},{3,5},{6,7}}=>[2,4,5,1,3,7,6]=>000010=>010000 {{1,2,4},{3,5},{6},{7}}=>[2,4,5,1,3,6,7]=>000011=>110000 {{1,2,4,6,7},{3},{5}}=>[2,4,3,6,5,7,1]=>000000=>000000 {{1,2,4,6},{3,7},{5}}=>[2,4,7,6,5,1,3]=>000000=>000000 {{1,2,4,6},{3},{5,7}}=>[2,4,3,6,7,1,5]=>000000=>000000 {{1,2,4,6},{3},{5},{7}}=>[2,4,3,6,5,1,7]=>000001=>100000 {{1,2,4,7},{3,6},{5}}=>[2,4,6,7,5,3,1]=>000000=>000000 {{1,2,4},{3,6,7},{5}}=>[2,4,6,1,5,7,3]=>000000=>000000 {{1,2,4},{3,6},{5,7}}=>[2,4,6,1,7,3,5]=>000000=>000000 {{1,2,4},{3,6},{5},{7}}=>[2,4,6,1,5,3,7]=>000001=>100000 {{1,2,4,7},{3},{5,6}}=>[2,4,3,7,6,5,1]=>000000=>000000 {{1,2,4},{3,7},{5,6}}=>[2,4,7,1,6,5,3]=>000000=>000000 {{1,2,4},{3},{5,6,7}}=>[2,4,3,1,6,7,5]=>000100=>001000 {{1,2,4},{3},{5,6},{7}}=>[2,4,3,1,6,5,7]=>000101=>101000 {{1,2,4,7},{3},{5},{6}}=>[2,4,3,7,5,6,1]=>000000=>000000 {{1,2,4},{3,7},{5},{6}}=>[2,4,7,1,5,6,3]=>000000=>000000 {{1,2,4},{3},{5,7},{6}}=>[2,4,3,1,7,6,5]=>000100=>001000 {{1,2,4},{3},{5},{6,7}}=>[2,4,3,1,5,7,6]=>000110=>011000 {{1,2,4},{3},{5},{6},{7}}=>[2,4,3,1,5,6,7]=>000111=>111000 {{1,2,5,6,7},{3,4}}=>[2,5,4,3,6,7,1]=>000000=>000000 {{1,2,5,6},{3,4,7}}=>[2,5,4,7,6,1,3]=>000000=>000000 {{1,2,5,6},{3,4},{7}}=>[2,5,4,3,6,1,7]=>000001=>100000 {{1,2,5,7},{3,4,6}}=>[2,5,4,6,7,3,1]=>000000=>000000 {{1,2,5},{3,4,6,7}}=>[2,5,4,6,1,7,3]=>000000=>000000 {{1,2,5},{3,4,6},{7}}=>[2,5,4,6,1,3,7]=>000001=>100000 {{1,2,5,7},{3,4},{6}}=>[2,5,4,3,7,6,1]=>000000=>000000 {{1,2,5},{3,4,7},{6}}=>[2,5,4,7,1,6,3]=>000000=>000000 {{1,2,5},{3,4},{6,7}}=>[2,5,4,3,1,7,6]=>000010=>010000 {{1,2,5},{3,4},{6},{7}}=>[2,5,4,3,1,6,7]=>000011=>110000 {{1,2,6,7},{3,4,5}}=>[2,6,4,5,3,7,1]=>000000=>000000 {{1,2,6},{3,4,5,7}}=>[2,6,4,5,7,1,3]=>000000=>000000 {{1,2,6},{3,4,5},{7}}=>[2,6,4,5,3,1,7]=>000001=>100000 {{1,2,7},{3,4,5,6}}=>[2,7,4,5,6,3,1]=>000000=>000000 {{1,2},{3,4,5,6,7}}=>[2,1,4,5,6,7,3]=>010000=>000010 {{1,2},{3,4,5,6},{7}}=>[2,1,4,5,6,3,7]=>010001=>100010 {{1,2,7},{3,4,5},{6}}=>[2,7,4,5,3,6,1]=>000000=>000000 {{1,2},{3,4,5,7},{6}}=>[2,1,4,5,7,6,3]=>010000=>000010 {{1,2},{3,4,5},{6,7}}=>[2,1,4,5,3,7,6]=>010010=>010010 {{1,2},{3,4,5},{6},{7}}=>[2,1,4,5,3,6,7]=>010011=>110010 {{1,2,6,7},{3,4},{5}}=>[2,6,4,3,5,7,1]=>000000=>000000 {{1,2,6},{3,4,7},{5}}=>[2,6,4,7,5,1,3]=>000000=>000000 {{1,2,6},{3,4},{5,7}}=>[2,6,4,3,7,1,5]=>000000=>000000 {{1,2,6},{3,4},{5},{7}}=>[2,6,4,3,5,1,7]=>000001=>100000 {{1,2,7},{3,4,6},{5}}=>[2,7,4,6,5,3,1]=>000000=>000000 {{1,2},{3,4,6,7},{5}}=>[2,1,4,6,5,7,3]=>010000=>000010 {{1,2},{3,4,6},{5,7}}=>[2,1,4,6,7,3,5]=>010000=>000010 {{1,2},{3,4,6},{5},{7}}=>[2,1,4,6,5,3,7]=>010001=>100010 {{1,2,7},{3,4},{5,6}}=>[2,7,4,3,6,5,1]=>000000=>000000 {{1,2},{3,4,7},{5,6}}=>[2,1,4,7,6,5,3]=>010000=>000010 {{1,2},{3,4},{5,6,7}}=>[2,1,4,3,6,7,5]=>010100=>001010 {{1,2},{3,4},{5,6},{7}}=>[2,1,4,3,6,5,7]=>010101=>101010 {{1,2,7},{3,4},{5},{6}}=>[2,7,4,3,5,6,1]=>000000=>000000 {{1,2},{3,4,7},{5},{6}}=>[2,1,4,7,5,6,3]=>010000=>000010 {{1,2},{3,4},{5,7},{6}}=>[2,1,4,3,7,6,5]=>010100=>001010 {{1,2},{3,4},{5},{6,7}}=>[2,1,4,3,5,7,6]=>010110=>011010 {{1,2},{3,4},{5},{6},{7}}=>[2,1,4,3,5,6,7]=>010111=>111010 {{1,2,5,6,7},{3},{4}}=>[2,5,3,4,6,7,1]=>000000=>000000 {{1,2,5,6},{3,7},{4}}=>[2,5,7,4,6,1,3]=>000000=>000000 {{1,2,5,6},{3},{4,7}}=>[2,5,3,7,6,1,4]=>000000=>000000 {{1,2,5,6},{3},{4},{7}}=>[2,5,3,4,6,1,7]=>000001=>100000 {{1,2,5,7},{3,6},{4}}=>[2,5,6,4,7,3,1]=>000000=>000000 {{1,2,5},{3,6,7},{4}}=>[2,5,6,4,1,7,3]=>000000=>000000 {{1,2,5},{3,6},{4,7}}=>[2,5,6,7,1,3,4]=>000000=>000000 {{1,2,5},{3,6},{4},{7}}=>[2,5,6,4,1,3,7]=>000001=>100000 {{1,2,5,7},{3},{4,6}}=>[2,5,3,6,7,4,1]=>000000=>000000 {{1,2,5},{3,7},{4,6}}=>[2,5,7,6,1,4,3]=>000000=>000000 {{1,2,5},{3},{4,6,7}}=>[2,5,3,6,1,7,4]=>000000=>000000 {{1,2,5},{3},{4,6},{7}}=>[2,5,3,6,1,4,7]=>000001=>100000 {{1,2,5,7},{3},{4},{6}}=>[2,5,3,4,7,6,1]=>000000=>000000 {{1,2,5},{3,7},{4},{6}}=>[2,5,7,4,1,6,3]=>000000=>000000 {{1,2,5},{3},{4,7},{6}}=>[2,5,3,7,1,6,4]=>000000=>000000 {{1,2,5},{3},{4},{6,7}}=>[2,5,3,4,1,7,6]=>000010=>010000 {{1,2,5},{3},{4},{6},{7}}=>[2,5,3,4,1,6,7]=>000011=>110000 {{1,2,6,7},{3,5},{4}}=>[2,6,5,4,3,7,1]=>000000=>000000 {{1,2,6},{3,5,7},{4}}=>[2,6,5,4,7,1,3]=>000000=>000000 {{1,2,6},{3,5},{4,7}}=>[2,6,5,7,3,1,4]=>000000=>000000 {{1,2,6},{3,5},{4},{7}}=>[2,6,5,4,3,1,7]=>000001=>100000 {{1,2,7},{3,5,6},{4}}=>[2,7,5,4,6,3,1]=>000000=>000000 {{1,2},{3,5,6,7},{4}}=>[2,1,5,4,6,7,3]=>010000=>000010 {{1,2},{3,5,6},{4,7}}=>[2,1,5,7,6,3,4]=>010000=>000010 {{1,2},{3,5,6},{4},{7}}=>[2,1,5,4,6,3,7]=>010001=>100010 {{1,2,7},{3,5},{4,6}}=>[2,7,5,6,3,4,1]=>000000=>000000 {{1,2},{3,5,7},{4,6}}=>[2,1,5,6,7,4,3]=>010000=>000010 {{1,2},{3,5},{4,6,7}}=>[2,1,5,6,3,7,4]=>010000=>000010 {{1,2},{3,5},{4,6},{7}}=>[2,1,5,6,3,4,7]=>010001=>100010 {{1,2,7},{3,5},{4},{6}}=>[2,7,5,4,3,6,1]=>000000=>000000 {{1,2},{3,5,7},{4},{6}}=>[2,1,5,4,7,6,3]=>010000=>000010 {{1,2},{3,5},{4,7},{6}}=>[2,1,5,7,3,6,4]=>010000=>000010 {{1,2},{3,5},{4},{6,7}}=>[2,1,5,4,3,7,6]=>010010=>010010 {{1,2},{3,5},{4},{6},{7}}=>[2,1,5,4,3,6,7]=>010011=>110010 {{1,2,6,7},{3},{4,5}}=>[2,6,3,5,4,7,1]=>000000=>000000 {{1,2,6},{3,7},{4,5}}=>[2,6,7,5,4,1,3]=>000000=>000000 {{1,2,6},{3},{4,5,7}}=>[2,6,3,5,7,1,4]=>000000=>000000 {{1,2,6},{3},{4,5},{7}}=>[2,6,3,5,4,1,7]=>000001=>100000 {{1,2,7},{3,6},{4,5}}=>[2,7,6,5,4,3,1]=>000000=>000000 {{1,2},{3,6,7},{4,5}}=>[2,1,6,5,4,7,3]=>010000=>000010 {{1,2},{3,6},{4,5,7}}=>[2,1,6,5,7,3,4]=>010000=>000010 {{1,2},{3,6},{4,5},{7}}=>[2,1,6,5,4,3,7]=>010001=>100010 {{1,2,7},{3},{4,5,6}}=>[2,7,3,5,6,4,1]=>000000=>000000 {{1,2},{3,7},{4,5,6}}=>[2,1,7,5,6,4,3]=>010000=>000010 {{1,2},{3},{4,5,6,7}}=>[2,1,3,5,6,7,4]=>011000=>000110 {{1,2},{3},{4,5,6},{7}}=>[2,1,3,5,6,4,7]=>011001=>100110 {{1,2,7},{3},{4,5},{6}}=>[2,7,3,5,4,6,1]=>000000=>000000 {{1,2},{3,7},{4,5},{6}}=>[2,1,7,5,4,6,3]=>010000=>000010 {{1,2},{3},{4,5,7},{6}}=>[2,1,3,5,7,6,4]=>011000=>000110 {{1,2},{3},{4,5},{6,7}}=>[2,1,3,5,4,7,6]=>011010=>010110 {{1,2},{3},{4,5},{6},{7}}=>[2,1,3,5,4,6,7]=>011011=>110110 {{1,2,6,7},{3},{4},{5}}=>[2,6,3,4,5,7,1]=>000000=>000000 {{1,2,6},{3,7},{4},{5}}=>[2,6,7,4,5,1,3]=>000000=>000000 {{1,2,6},{3},{4,7},{5}}=>[2,6,3,7,5,1,4]=>000000=>000000 {{1,2,6},{3},{4},{5,7}}=>[2,6,3,4,7,1,5]=>000000=>000000 {{1,2,6},{3},{4},{5},{7}}=>[2,6,3,4,5,1,7]=>000001=>100000 {{1,2,7},{3,6},{4},{5}}=>[2,7,6,4,5,3,1]=>000000=>000000 {{1,2},{3,6,7},{4},{5}}=>[2,1,6,4,5,7,3]=>010000=>000010 {{1,2},{3,6},{4,7},{5}}=>[2,1,6,7,5,3,4]=>010000=>000010 {{1,2},{3,6},{4},{5,7}}=>[2,1,6,4,7,3,5]=>010000=>000010 {{1,2},{3,6},{4},{5},{7}}=>[2,1,6,4,5,3,7]=>010001=>100010 {{1,2,7},{3},{4,6},{5}}=>[2,7,3,6,5,4,1]=>000000=>000000 {{1,2},{3,7},{4,6},{5}}=>[2,1,7,6,5,4,3]=>010000=>000010 {{1,2},{3},{4,6,7},{5}}=>[2,1,3,6,5,7,4]=>011000=>000110 {{1,2},{3},{4,6},{5,7}}=>[2,1,3,6,7,4,5]=>011000=>000110 {{1,2},{3},{4,6},{5},{7}}=>[2,1,3,6,5,4,7]=>011001=>100110 {{1,2,7},{3},{4},{5,6}}=>[2,7,3,4,6,5,1]=>000000=>000000 {{1,2},{3,7},{4},{5,6}}=>[2,1,7,4,6,5,3]=>010000=>000010 {{1,2},{3},{4,7},{5,6}}=>[2,1,3,7,6,5,4]=>011000=>000110 {{1,2},{3},{4},{5,6,7}}=>[2,1,3,4,6,7,5]=>011100=>001110 {{1,2},{3},{4},{5,6},{7}}=>[2,1,3,4,6,5,7]=>011101=>101110 {{1,2,7},{3},{4},{5},{6}}=>[2,7,3,4,5,6,1]=>000000=>000000 {{1,2},{3,7},{4},{5},{6}}=>[2,1,7,4,5,6,3]=>010000=>000010 {{1,2},{3},{4,7},{5},{6}}=>[2,1,3,7,5,6,4]=>011000=>000110 {{1,2},{3},{4},{5,7},{6}}=>[2,1,3,4,7,6,5]=>011100=>001110 {{1,2},{3},{4},{5},{6,7}}=>[2,1,3,4,5,7,6]=>011110=>011110 {{1,2},{3},{4},{5},{6},{7}}=>[2,1,3,4,5,6,7]=>011111=>111110 {{1,3,4,5,6,7},{2}}=>[3,2,4,5,6,7,1]=>000000=>000000 {{1,3,4,5,6},{2,7}}=>[3,7,4,5,6,1,2]=>000000=>000000 {{1,3,4,5,6},{2},{7}}=>[3,2,4,5,6,1,7]=>000001=>100000 {{1,3,4,5,7},{2,6}}=>[3,6,4,5,7,2,1]=>000000=>000000 {{1,3,4,5},{2,6,7}}=>[3,6,4,5,1,7,2]=>000000=>000000 {{1,3,4,5},{2,6},{7}}=>[3,6,4,5,1,2,7]=>000001=>100000 {{1,3,4,5,7},{2},{6}}=>[3,2,4,5,7,6,1]=>000000=>000000 {{1,3,4,5},{2,7},{6}}=>[3,7,4,5,1,6,2]=>000000=>000000 {{1,3,4,5},{2},{6,7}}=>[3,2,4,5,1,7,6]=>000010=>010000 {{1,3,4,5},{2},{6},{7}}=>[3,2,4,5,1,6,7]=>000011=>110000 {{1,3,4,6,7},{2,5}}=>[3,5,4,6,2,7,1]=>000000=>000000 {{1,3,4,6},{2,5,7}}=>[3,5,4,6,7,1,2]=>000000=>000000 {{1,3,4,6},{2,5},{7}}=>[3,5,4,6,2,1,7]=>000001=>100000 {{1,3,4,7},{2,5,6}}=>[3,5,4,7,6,2,1]=>000000=>000000 {{1,3,4},{2,5,6,7}}=>[3,5,4,1,6,7,2]=>000000=>000000 {{1,3,4},{2,5,6},{7}}=>[3,5,4,1,6,2,7]=>000001=>100000 {{1,3,4,7},{2,5},{6}}=>[3,5,4,7,2,6,1]=>000000=>000000 {{1,3,4},{2,5,7},{6}}=>[3,5,4,1,7,6,2]=>000000=>000000 {{1,3,4},{2,5},{6,7}}=>[3,5,4,1,2,7,6]=>000010=>010000 {{1,3,4},{2,5},{6},{7}}=>[3,5,4,1,2,6,7]=>000011=>110000 {{1,3,4,6,7},{2},{5}}=>[3,2,4,6,5,7,1]=>000000=>000000 {{1,3,4,6},{2,7},{5}}=>[3,7,4,6,5,1,2]=>000000=>000000 {{1,3,4,6},{2},{5,7}}=>[3,2,4,6,7,1,5]=>000000=>000000 {{1,3,4,6},{2},{5},{7}}=>[3,2,4,6,5,1,7]=>000001=>100000 {{1,3,4,7},{2,6},{5}}=>[3,6,4,7,5,2,1]=>000000=>000000 {{1,3,4},{2,6,7},{5}}=>[3,6,4,1,5,7,2]=>000000=>000000 {{1,3,4},{2,6},{5,7}}=>[3,6,4,1,7,2,5]=>000000=>000000 {{1,3,4},{2,6},{5},{7}}=>[3,6,4,1,5,2,7]=>000001=>100000 {{1,3,4,7},{2},{5,6}}=>[3,2,4,7,6,5,1]=>000000=>000000 {{1,3,4},{2,7},{5,6}}=>[3,7,4,1,6,5,2]=>000000=>000000 {{1,3,4},{2},{5,6,7}}=>[3,2,4,1,6,7,5]=>000100=>001000 {{1,3,4},{2},{5,6},{7}}=>[3,2,4,1,6,5,7]=>000101=>101000 {{1,3,4,7},{2},{5},{6}}=>[3,2,4,7,5,6,1]=>000000=>000000 {{1,3,4},{2,7},{5},{6}}=>[3,7,4,1,5,6,2]=>000000=>000000 {{1,3,4},{2},{5,7},{6}}=>[3,2,4,1,7,6,5]=>000100=>001000 {{1,3,4},{2},{5},{6,7}}=>[3,2,4,1,5,7,6]=>000110=>011000 {{1,3,4},{2},{5},{6},{7}}=>[3,2,4,1,5,6,7]=>000111=>111000 {{1,3,5,6,7},{2,4}}=>[3,4,5,2,6,7,1]=>000000=>000000 {{1,3,5,6},{2,4,7}}=>[3,4,5,7,6,1,2]=>000000=>000000 {{1,3,5,6},{2,4},{7}}=>[3,4,5,2,6,1,7]=>000001=>100000 {{1,3,5,7},{2,4,6}}=>[3,4,5,6,7,2,1]=>000000=>000000 {{1,3,5},{2,4,6,7}}=>[3,4,5,6,1,7,2]=>000000=>000000 {{1,3,5},{2,4,6},{7}}=>[3,4,5,6,1,2,7]=>000001=>100000 {{1,3,5,7},{2,4},{6}}=>[3,4,5,2,7,6,1]=>000000=>000000 {{1,3,5},{2,4,7},{6}}=>[3,4,5,7,1,6,2]=>000000=>000000 {{1,3,5},{2,4},{6,7}}=>[3,4,5,2,1,7,6]=>000010=>010000 {{1,3,5},{2,4},{6},{7}}=>[3,4,5,2,1,6,7]=>000011=>110000 {{1,3,6,7},{2,4,5}}=>[3,4,6,5,2,7,1]=>000000=>000000 {{1,3,6},{2,4,5,7}}=>[3,4,6,5,7,1,2]=>000000=>000000 {{1,3,6},{2,4,5},{7}}=>[3,4,6,5,2,1,7]=>000001=>100000 {{1,3,7},{2,4,5,6}}=>[3,4,7,5,6,2,1]=>000000=>000000 {{1,3},{2,4,5,6,7}}=>[3,4,1,5,6,7,2]=>000000=>000000 {{1,3},{2,4,5,6},{7}}=>[3,4,1,5,6,2,7]=>000001=>100000 {{1,3,7},{2,4,5},{6}}=>[3,4,7,5,2,6,1]=>000000=>000000 {{1,3},{2,4,5,7},{6}}=>[3,4,1,5,7,6,2]=>000000=>000000 {{1,3},{2,4,5},{6,7}}=>[3,4,1,5,2,7,6]=>000010=>010000 {{1,3},{2,4,5},{6},{7}}=>[3,4,1,5,2,6,7]=>000011=>110000 {{1,3,6,7},{2,4},{5}}=>[3,4,6,2,5,7,1]=>000000=>000000 {{1,3,6},{2,4,7},{5}}=>[3,4,6,7,5,1,2]=>000000=>000000 {{1,3,6},{2,4},{5,7}}=>[3,4,6,2,7,1,5]=>000000=>000000 {{1,3,6},{2,4},{5},{7}}=>[3,4,6,2,5,1,7]=>000001=>100000 {{1,3,7},{2,4,6},{5}}=>[3,4,7,6,5,2,1]=>000000=>000000 {{1,3},{2,4,6,7},{5}}=>[3,4,1,6,5,7,2]=>000000=>000000 {{1,3},{2,4,6},{5,7}}=>[3,4,1,6,7,2,5]=>000000=>000000 {{1,3},{2,4,6},{5},{7}}=>[3,4,1,6,5,2,7]=>000001=>100000 {{1,3,7},{2,4},{5,6}}=>[3,4,7,2,6,5,1]=>000000=>000000 {{1,3},{2,4,7},{5,6}}=>[3,4,1,7,6,5,2]=>000000=>000000 {{1,3},{2,4},{5,6,7}}=>[3,4,1,2,6,7,5]=>000100=>001000 {{1,3},{2,4},{5,6},{7}}=>[3,4,1,2,6,5,7]=>000101=>101000 {{1,3,7},{2,4},{5},{6}}=>[3,4,7,2,5,6,1]=>000000=>000000 {{1,3},{2,4,7},{5},{6}}=>[3,4,1,7,5,6,2]=>000000=>000000 {{1,3},{2,4},{5,7},{6}}=>[3,4,1,2,7,6,5]=>000100=>001000 {{1,3},{2,4},{5},{6,7}}=>[3,4,1,2,5,7,6]=>000110=>011000 {{1,3},{2,4},{5},{6},{7}}=>[3,4,1,2,5,6,7]=>000111=>111000 {{1,3,5,6,7},{2},{4}}=>[3,2,5,4,6,7,1]=>000000=>000000 {{1,3,5,6},{2,7},{4}}=>[3,7,5,4,6,1,2]=>000000=>000000 {{1,3,5,6},{2},{4,7}}=>[3,2,5,7,6,1,4]=>000000=>000000 {{1,3,5,6},{2},{4},{7}}=>[3,2,5,4,6,1,7]=>000001=>100000 {{1,3,5,7},{2,6},{4}}=>[3,6,5,4,7,2,1]=>000000=>000000 {{1,3,5},{2,6,7},{4}}=>[3,6,5,4,1,7,2]=>000000=>000000 {{1,3,5},{2,6},{4,7}}=>[3,6,5,7,1,2,4]=>000000=>000000 {{1,3,5},{2,6},{4},{7}}=>[3,6,5,4,1,2,7]=>000001=>100000 {{1,3,5,7},{2},{4,6}}=>[3,2,5,6,7,4,1]=>000000=>000000 {{1,3,5},{2,7},{4,6}}=>[3,7,5,6,1,4,2]=>000000=>000000 {{1,3,5},{2},{4,6,7}}=>[3,2,5,6,1,7,4]=>000000=>000000 {{1,3,5},{2},{4,6},{7}}=>[3,2,5,6,1,4,7]=>000001=>100000 {{1,3,5,7},{2},{4},{6}}=>[3,2,5,4,7,6,1]=>000000=>000000 {{1,3,5},{2,7},{4},{6}}=>[3,7,5,4,1,6,2]=>000000=>000000 {{1,3,5},{2},{4,7},{6}}=>[3,2,5,7,1,6,4]=>000000=>000000 {{1,3,5},{2},{4},{6,7}}=>[3,2,5,4,1,7,6]=>000010=>010000 {{1,3,5},{2},{4},{6},{7}}=>[3,2,5,4,1,6,7]=>000011=>110000 {{1,3,6,7},{2,5},{4}}=>[3,5,6,4,2,7,1]=>000000=>000000 {{1,3,6},{2,5,7},{4}}=>[3,5,6,4,7,1,2]=>000000=>000000 {{1,3,6},{2,5},{4,7}}=>[3,5,6,7,2,1,4]=>000000=>000000 {{1,3,6},{2,5},{4},{7}}=>[3,5,6,4,2,1,7]=>000001=>100000 {{1,3,7},{2,5,6},{4}}=>[3,5,7,4,6,2,1]=>000000=>000000 {{1,3},{2,5,6,7},{4}}=>[3,5,1,4,6,7,2]=>000000=>000000 {{1,3},{2,5,6},{4,7}}=>[3,5,1,7,6,2,4]=>000000=>000000 {{1,3},{2,5,6},{4},{7}}=>[3,5,1,4,6,2,7]=>000001=>100000 {{1,3,7},{2,5},{4,6}}=>[3,5,7,6,2,4,1]=>000000=>000000 {{1,3},{2,5,7},{4,6}}=>[3,5,1,6,7,4,2]=>000000=>000000 {{1,3},{2,5},{4,6,7}}=>[3,5,1,6,2,7,4]=>000000=>000000 {{1,3},{2,5},{4,6},{7}}=>[3,5,1,6,2,4,7]=>000001=>100000 {{1,3,7},{2,5},{4},{6}}=>[3,5,7,4,2,6,1]=>000000=>000000 {{1,3},{2,5,7},{4},{6}}=>[3,5,1,4,7,6,2]=>000000=>000000 {{1,3},{2,5},{4,7},{6}}=>[3,5,1,7,2,6,4]=>000000=>000000 {{1,3},{2,5},{4},{6,7}}=>[3,5,1,4,2,7,6]=>000010=>010000 {{1,3},{2,5},{4},{6},{7}}=>[3,5,1,4,2,6,7]=>000011=>110000 {{1,3,6,7},{2},{4,5}}=>[3,2,6,5,4,7,1]=>000000=>000000 {{1,3,6},{2,7},{4,5}}=>[3,7,6,5,4,1,2]=>000000=>000000 {{1,3,6},{2},{4,5,7}}=>[3,2,6,5,7,1,4]=>000000=>000000 {{1,3,6},{2},{4,5},{7}}=>[3,2,6,5,4,1,7]=>000001=>100000 {{1,3,7},{2,6},{4,5}}=>[3,6,7,5,4,2,1]=>000000=>000000 {{1,3},{2,6,7},{4,5}}=>[3,6,1,5,4,7,2]=>000000=>000000 {{1,3},{2,6},{4,5,7}}=>[3,6,1,5,7,2,4]=>000000=>000000 {{1,3},{2,6},{4,5},{7}}=>[3,6,1,5,4,2,7]=>000001=>100000 {{1,3,7},{2},{4,5,6}}=>[3,2,7,5,6,4,1]=>000000=>000000 {{1,3},{2,7},{4,5,6}}=>[3,7,1,5,6,4,2]=>000000=>000000 {{1,3},{2},{4,5,6,7}}=>[3,2,1,5,6,7,4]=>001000=>000100 {{1,3},{2},{4,5,6},{7}}=>[3,2,1,5,6,4,7]=>001001=>100100 {{1,3,7},{2},{4,5},{6}}=>[3,2,7,5,4,6,1]=>000000=>000000 {{1,3},{2,7},{4,5},{6}}=>[3,7,1,5,4,6,2]=>000000=>000000 {{1,3},{2},{4,5,7},{6}}=>[3,2,1,5,7,6,4]=>001000=>000100 {{1,3},{2},{4,5},{6,7}}=>[3,2,1,5,4,7,6]=>001010=>010100 {{1,3},{2},{4,5},{6},{7}}=>[3,2,1,5,4,6,7]=>001011=>110100 {{1,3,6,7},{2},{4},{5}}=>[3,2,6,4,5,7,1]=>000000=>000000 {{1,3,6},{2,7},{4},{5}}=>[3,7,6,4,5,1,2]=>000000=>000000 {{1,3,6},{2},{4,7},{5}}=>[3,2,6,7,5,1,4]=>000000=>000000 {{1,3,6},{2},{4},{5,7}}=>[3,2,6,4,7,1,5]=>000000=>000000 {{1,3,6},{2},{4},{5},{7}}=>[3,2,6,4,5,1,7]=>000001=>100000 {{1,3,7},{2,6},{4},{5}}=>[3,6,7,4,5,2,1]=>000000=>000000 {{1,3},{2,6,7},{4},{5}}=>[3,6,1,4,5,7,2]=>000000=>000000 {{1,3},{2,6},{4,7},{5}}=>[3,6,1,7,5,2,4]=>000000=>000000 {{1,3},{2,6},{4},{5,7}}=>[3,6,1,4,7,2,5]=>000000=>000000 {{1,3},{2,6},{4},{5},{7}}=>[3,6,1,4,5,2,7]=>000001=>100000 {{1,3,7},{2},{4,6},{5}}=>[3,2,7,6,5,4,1]=>000000=>000000 {{1,3},{2,7},{4,6},{5}}=>[3,7,1,6,5,4,2]=>000000=>000000 {{1,3},{2},{4,6,7},{5}}=>[3,2,1,6,5,7,4]=>001000=>000100 {{1,3},{2},{4,6},{5,7}}=>[3,2,1,6,7,4,5]=>001000=>000100 {{1,3},{2},{4,6},{5},{7}}=>[3,2,1,6,5,4,7]=>001001=>100100 {{1,3,7},{2},{4},{5,6}}=>[3,2,7,4,6,5,1]=>000000=>000000 {{1,3},{2,7},{4},{5,6}}=>[3,7,1,4,6,5,2]=>000000=>000000 {{1,3},{2},{4,7},{5,6}}=>[3,2,1,7,6,5,4]=>001000=>000100 {{1,3},{2},{4},{5,6,7}}=>[3,2,1,4,6,7,5]=>001100=>001100 {{1,3},{2},{4},{5,6},{7}}=>[3,2,1,4,6,5,7]=>001101=>101100 {{1,3,7},{2},{4},{5},{6}}=>[3,2,7,4,5,6,1]=>000000=>000000 {{1,3},{2,7},{4},{5},{6}}=>[3,7,1,4,5,6,2]=>000000=>000000 {{1,3},{2},{4,7},{5},{6}}=>[3,2,1,7,5,6,4]=>001000=>000100 {{1,3},{2},{4},{5,7},{6}}=>[3,2,1,4,7,6,5]=>001100=>001100 {{1,3},{2},{4},{5},{6,7}}=>[3,2,1,4,5,7,6]=>001110=>011100 {{1,3},{2},{4},{5},{6},{7}}=>[3,2,1,4,5,6,7]=>001111=>111100 {{1,4,5,6,7},{2,3}}=>[4,3,2,5,6,7,1]=>000000=>000000 {{1,4,5,6},{2,3,7}}=>[4,3,7,5,6,1,2]=>000000=>000000 {{1,4,5,6},{2,3},{7}}=>[4,3,2,5,6,1,7]=>000001=>100000 {{1,4,5,7},{2,3,6}}=>[4,3,6,5,7,2,1]=>000000=>000000 {{1,4,5},{2,3,6,7}}=>[4,3,6,5,1,7,2]=>000000=>000000 {{1,4,5},{2,3,6},{7}}=>[4,3,6,5,1,2,7]=>000001=>100000 {{1,4,5,7},{2,3},{6}}=>[4,3,2,5,7,6,1]=>000000=>000000 {{1,4,5},{2,3,7},{6}}=>[4,3,7,5,1,6,2]=>000000=>000000 {{1,4,5},{2,3},{6,7}}=>[4,3,2,5,1,7,6]=>000010=>010000 {{1,4,5},{2,3},{6},{7}}=>[4,3,2,5,1,6,7]=>000011=>110000 {{1,4,6,7},{2,3,5}}=>[4,3,5,6,2,7,1]=>000000=>000000 {{1,4,6},{2,3,5,7}}=>[4,3,5,6,7,1,2]=>000000=>000000 {{1,4,6},{2,3,5},{7}}=>[4,3,5,6,2,1,7]=>000001=>100000 {{1,4,7},{2,3,5,6}}=>[4,3,5,7,6,2,1]=>000000=>000000 {{1,4},{2,3,5,6,7}}=>[4,3,5,1,6,7,2]=>000000=>000000 {{1,4},{2,3,5,6},{7}}=>[4,3,5,1,6,2,7]=>000001=>100000 {{1,4,7},{2,3,5},{6}}=>[4,3,5,7,2,6,1]=>000000=>000000 {{1,4},{2,3,5,7},{6}}=>[4,3,5,1,7,6,2]=>000000=>000000 {{1,4},{2,3,5},{6,7}}=>[4,3,5,1,2,7,6]=>000010=>010000 {{1,4},{2,3,5},{6},{7}}=>[4,3,5,1,2,6,7]=>000011=>110000 {{1,4,6,7},{2,3},{5}}=>[4,3,2,6,5,7,1]=>000000=>000000 {{1,4,6},{2,3,7},{5}}=>[4,3,7,6,5,1,2]=>000000=>000000 {{1,4,6},{2,3},{5,7}}=>[4,3,2,6,7,1,5]=>000000=>000000 {{1,4,6},{2,3},{5},{7}}=>[4,3,2,6,5,1,7]=>000001=>100000 {{1,4,7},{2,3,6},{5}}=>[4,3,6,7,5,2,1]=>000000=>000000 {{1,4},{2,3,6,7},{5}}=>[4,3,6,1,5,7,2]=>000000=>000000 {{1,4},{2,3,6},{5,7}}=>[4,3,6,1,7,2,5]=>000000=>000000 {{1,4},{2,3,6},{5},{7}}=>[4,3,6,1,5,2,7]=>000001=>100000 {{1,4,7},{2,3},{5,6}}=>[4,3,2,7,6,5,1]=>000000=>000000 {{1,4},{2,3,7},{5,6}}=>[4,3,7,1,6,5,2]=>000000=>000000 {{1,4},{2,3},{5,6,7}}=>[4,3,2,1,6,7,5]=>000100=>001000 {{1,4},{2,3},{5,6},{7}}=>[4,3,2,1,6,5,7]=>000101=>101000 {{1,4,7},{2,3},{5},{6}}=>[4,3,2,7,5,6,1]=>000000=>000000 {{1,4},{2,3,7},{5},{6}}=>[4,3,7,1,5,6,2]=>000000=>000000 {{1,4},{2,3},{5,7},{6}}=>[4,3,2,1,7,6,5]=>000100=>001000 {{1,4},{2,3},{5},{6,7}}=>[4,3,2,1,5,7,6]=>000110=>011000 {{1,4},{2,3},{5},{6},{7}}=>[4,3,2,1,5,6,7]=>000111=>111000 {{1,5,6,7},{2,3,4}}=>[5,3,4,2,6,7,1]=>000000=>000000 {{1,5,6},{2,3,4,7}}=>[5,3,4,7,6,1,2]=>000000=>000000 {{1,5,6},{2,3,4},{7}}=>[5,3,4,2,6,1,7]=>000001=>100000 {{1,5,7},{2,3,4,6}}=>[5,3,4,6,7,2,1]=>000000=>000000 {{1,5},{2,3,4,6,7}}=>[5,3,4,6,1,7,2]=>000000=>000000 {{1,5},{2,3,4,6},{7}}=>[5,3,4,6,1,2,7]=>000001=>100000 {{1,5,7},{2,3,4},{6}}=>[5,3,4,2,7,6,1]=>000000=>000000 {{1,5},{2,3,4,7},{6}}=>[5,3,4,7,1,6,2]=>000000=>000000 {{1,5},{2,3,4},{6,7}}=>[5,3,4,2,1,7,6]=>000010=>010000 {{1,5},{2,3,4},{6},{7}}=>[5,3,4,2,1,6,7]=>000011=>110000 {{1,6,7},{2,3,4,5}}=>[6,3,4,5,2,7,1]=>000000=>000000 {{1,6},{2,3,4,5,7}}=>[6,3,4,5,7,1,2]=>000000=>000000 {{1,6},{2,3,4,5},{7}}=>[6,3,4,5,2,1,7]=>000001=>100000 {{1,7},{2,3,4,5,6}}=>[7,3,4,5,6,2,1]=>000000=>000000 {{1},{2,3,4,5,6,7}}=>[1,3,4,5,6,7,2]=>100000=>000001 {{1},{2,3,4,5,6},{7}}=>[1,3,4,5,6,2,7]=>100001=>100001 {{1,7},{2,3,4,5},{6}}=>[7,3,4,5,2,6,1]=>000000=>000000 {{1},{2,3,4,5,7},{6}}=>[1,3,4,5,7,6,2]=>100000=>000001 {{1},{2,3,4,5},{6,7}}=>[1,3,4,5,2,7,6]=>100010=>010001 {{1},{2,3,4,5},{6},{7}}=>[1,3,4,5,2,6,7]=>100011=>110001 {{1,6,7},{2,3,4},{5}}=>[6,3,4,2,5,7,1]=>000000=>000000 {{1,6},{2,3,4,7},{5}}=>[6,3,4,7,5,1,2]=>000000=>000000 {{1,6},{2,3,4},{5,7}}=>[6,3,4,2,7,1,5]=>000000=>000000 {{1,6},{2,3,4},{5},{7}}=>[6,3,4,2,5,1,7]=>000001=>100000 {{1,7},{2,3,4,6},{5}}=>[7,3,4,6,5,2,1]=>000000=>000000 {{1},{2,3,4,6,7},{5}}=>[1,3,4,6,5,7,2]=>100000=>000001 {{1},{2,3,4,6},{5,7}}=>[1,3,4,6,7,2,5]=>100000=>000001 {{1},{2,3,4,6},{5},{7}}=>[1,3,4,6,5,2,7]=>100001=>100001 {{1,7},{2,3,4},{5,6}}=>[7,3,4,2,6,5,1]=>000000=>000000 {{1},{2,3,4,7},{5,6}}=>[1,3,4,7,6,5,2]=>100000=>000001 {{1},{2,3,4},{5,6,7}}=>[1,3,4,2,6,7,5]=>100100=>001001 {{1},{2,3,4},{5,6},{7}}=>[1,3,4,2,6,5,7]=>100101=>101001 {{1,7},{2,3,4},{5},{6}}=>[7,3,4,2,5,6,1]=>000000=>000000 {{1},{2,3,4,7},{5},{6}}=>[1,3,4,7,5,6,2]=>100000=>000001 {{1},{2,3,4},{5,7},{6}}=>[1,3,4,2,7,6,5]=>100100=>001001 {{1},{2,3,4},{5},{6,7}}=>[1,3,4,2,5,7,6]=>100110=>011001 {{1},{2,3,4},{5},{6},{7}}=>[1,3,4,2,5,6,7]=>100111=>111001 {{1,5,6,7},{2,3},{4}}=>[5,3,2,4,6,7,1]=>000000=>000000 {{1,5,6},{2,3,7},{4}}=>[5,3,7,4,6,1,2]=>000000=>000000 {{1,5,6},{2,3},{4,7}}=>[5,3,2,7,6,1,4]=>000000=>000000 {{1,5,6},{2,3},{4},{7}}=>[5,3,2,4,6,1,7]=>000001=>100000 {{1,5,7},{2,3,6},{4}}=>[5,3,6,4,7,2,1]=>000000=>000000 {{1,5},{2,3,6,7},{4}}=>[5,3,6,4,1,7,2]=>000000=>000000 {{1,5},{2,3,6},{4,7}}=>[5,3,6,7,1,2,4]=>000000=>000000 {{1,5},{2,3,6},{4},{7}}=>[5,3,6,4,1,2,7]=>000001=>100000 {{1,5,7},{2,3},{4,6}}=>[5,3,2,6,7,4,1]=>000000=>000000 {{1,5},{2,3,7},{4,6}}=>[5,3,7,6,1,4,2]=>000000=>000000 {{1,5},{2,3},{4,6,7}}=>[5,3,2,6,1,7,4]=>000000=>000000 {{1,5},{2,3},{4,6},{7}}=>[5,3,2,6,1,4,7]=>000001=>100000 {{1,5,7},{2,3},{4},{6}}=>[5,3,2,4,7,6,1]=>000000=>000000 {{1,5},{2,3,7},{4},{6}}=>[5,3,7,4,1,6,2]=>000000=>000000 {{1,5},{2,3},{4,7},{6}}=>[5,3,2,7,1,6,4]=>000000=>000000 {{1,5},{2,3},{4},{6,7}}=>[5,3,2,4,1,7,6]=>000010=>010000 {{1,5},{2,3},{4},{6},{7}}=>[5,3,2,4,1,6,7]=>000011=>110000 {{1,6,7},{2,3,5},{4}}=>[6,3,5,4,2,7,1]=>000000=>000000 {{1,6},{2,3,5,7},{4}}=>[6,3,5,4,7,1,2]=>000000=>000000 {{1,6},{2,3,5},{4,7}}=>[6,3,5,7,2,1,4]=>000000=>000000 {{1,6},{2,3,5},{4},{7}}=>[6,3,5,4,2,1,7]=>000001=>100000 {{1,7},{2,3,5,6},{4}}=>[7,3,5,4,6,2,1]=>000000=>000000 {{1},{2,3,5,6,7},{4}}=>[1,3,5,4,6,7,2]=>100000=>000001 {{1},{2,3,5,6},{4,7}}=>[1,3,5,7,6,2,4]=>100000=>000001 {{1},{2,3,5,6},{4},{7}}=>[1,3,5,4,6,2,7]=>100001=>100001 {{1,7},{2,3,5},{4,6}}=>[7,3,5,6,2,4,1]=>000000=>000000 {{1},{2,3,5,7},{4,6}}=>[1,3,5,6,7,4,2]=>100000=>000001 {{1},{2,3,5},{4,6,7}}=>[1,3,5,6,2,7,4]=>100000=>000001 {{1},{2,3,5},{4,6},{7}}=>[1,3,5,6,2,4,7]=>100001=>100001 {{1,7},{2,3,5},{4},{6}}=>[7,3,5,4,2,6,1]=>000000=>000000 {{1},{2,3,5,7},{4},{6}}=>[1,3,5,4,7,6,2]=>100000=>000001 {{1},{2,3,5},{4,7},{6}}=>[1,3,5,7,2,6,4]=>100000=>000001 {{1},{2,3,5},{4},{6,7}}=>[1,3,5,4,2,7,6]=>100010=>010001 {{1},{2,3,5},{4},{6},{7}}=>[1,3,5,4,2,6,7]=>100011=>110001 {{1,6,7},{2,3},{4,5}}=>[6,3,2,5,4,7,1]=>000000=>000000 {{1,6},{2,3,7},{4,5}}=>[6,3,7,5,4,1,2]=>000000=>000000 {{1,6},{2,3},{4,5,7}}=>[6,3,2,5,7,1,4]=>000000=>000000 {{1,6},{2,3},{4,5},{7}}=>[6,3,2,5,4,1,7]=>000001=>100000 {{1,7},{2,3,6},{4,5}}=>[7,3,6,5,4,2,1]=>000000=>000000 {{1},{2,3,6,7},{4,5}}=>[1,3,6,5,4,7,2]=>100000=>000001 {{1},{2,3,6},{4,5,7}}=>[1,3,6,5,7,2,4]=>100000=>000001 {{1},{2,3,6},{4,5},{7}}=>[1,3,6,5,4,2,7]=>100001=>100001 {{1,7},{2,3},{4,5,6}}=>[7,3,2,5,6,4,1]=>000000=>000000 {{1},{2,3,7},{4,5,6}}=>[1,3,7,5,6,4,2]=>100000=>000001 {{1},{2,3},{4,5,6,7}}=>[1,3,2,5,6,7,4]=>101000=>000101 {{1},{2,3},{4,5,6},{7}}=>[1,3,2,5,6,4,7]=>101001=>100101 {{1,7},{2,3},{4,5},{6}}=>[7,3,2,5,4,6,1]=>000000=>000000 {{1},{2,3,7},{4,5},{6}}=>[1,3,7,5,4,6,2]=>100000=>000001 {{1},{2,3},{4,5,7},{6}}=>[1,3,2,5,7,6,4]=>101000=>000101 {{1},{2,3},{4,5},{6,7}}=>[1,3,2,5,4,7,6]=>101010=>010101 {{1},{2,3},{4,5},{6},{7}}=>[1,3,2,5,4,6,7]=>101011=>110101 {{1,6,7},{2,3},{4},{5}}=>[6,3,2,4,5,7,1]=>000000=>000000 {{1,6},{2,3,7},{4},{5}}=>[6,3,7,4,5,1,2]=>000000=>000000 {{1,6},{2,3},{4,7},{5}}=>[6,3,2,7,5,1,4]=>000000=>000000 {{1,6},{2,3},{4},{5,7}}=>[6,3,2,4,7,1,5]=>000000=>000000 {{1,6},{2,3},{4},{5},{7}}=>[6,3,2,4,5,1,7]=>000001=>100000 {{1,7},{2,3,6},{4},{5}}=>[7,3,6,4,5,2,1]=>000000=>000000 {{1},{2,3,6,7},{4},{5}}=>[1,3,6,4,5,7,2]=>100000=>000001 {{1},{2,3,6},{4,7},{5}}=>[1,3,6,7,5,2,4]=>100000=>000001 {{1},{2,3,6},{4},{5,7}}=>[1,3,6,4,7,2,5]=>100000=>000001 {{1},{2,3,6},{4},{5},{7}}=>[1,3,6,4,5,2,7]=>100001=>100001 {{1,7},{2,3},{4,6},{5}}=>[7,3,2,6,5,4,1]=>000000=>000000 {{1},{2,3,7},{4,6},{5}}=>[1,3,7,6,5,4,2]=>100000=>000001 {{1},{2,3},{4,6,7},{5}}=>[1,3,2,6,5,7,4]=>101000=>000101 {{1},{2,3},{4,6},{5,7}}=>[1,3,2,6,7,4,5]=>101000=>000101 {{1},{2,3},{4,6},{5},{7}}=>[1,3,2,6,5,4,7]=>101001=>100101 {{1,7},{2,3},{4},{5,6}}=>[7,3,2,4,6,5,1]=>000000=>000000 {{1},{2,3,7},{4},{5,6}}=>[1,3,7,4,6,5,2]=>100000=>000001 {{1},{2,3},{4,7},{5,6}}=>[1,3,2,7,6,5,4]=>101000=>000101 {{1},{2,3},{4},{5,6,7}}=>[1,3,2,4,6,7,5]=>101100=>001101 {{1},{2,3},{4},{5,6},{7}}=>[1,3,2,4,6,5,7]=>101101=>101101 {{1,7},{2,3},{4},{5},{6}}=>[7,3,2,4,5,6,1]=>000000=>000000 {{1},{2,3,7},{4},{5},{6}}=>[1,3,7,4,5,6,2]=>100000=>000001 {{1},{2,3},{4,7},{5},{6}}=>[1,3,2,7,5,6,4]=>101000=>000101 {{1},{2,3},{4},{5,7},{6}}=>[1,3,2,4,7,6,5]=>101100=>001101 {{1},{2,3},{4},{5},{6,7}}=>[1,3,2,4,5,7,6]=>101110=>011101 {{1},{2,3},{4},{5},{6},{7}}=>[1,3,2,4,5,6,7]=>101111=>111101 {{1,4,5,6,7},{2},{3}}=>[4,2,3,5,6,7,1]=>000000=>000000 {{1,4,5,6},{2,7},{3}}=>[4,7,3,5,6,1,2]=>000000=>000000 {{1,4,5,6},{2},{3,7}}=>[4,2,7,5,6,1,3]=>000000=>000000 {{1,4,5,6},{2},{3},{7}}=>[4,2,3,5,6,1,7]=>000001=>100000 {{1,4,5,7},{2,6},{3}}=>[4,6,3,5,7,2,1]=>000000=>000000 {{1,4,5},{2,6,7},{3}}=>[4,6,3,5,1,7,2]=>000000=>000000 {{1,4,5},{2,6},{3,7}}=>[4,6,7,5,1,2,3]=>000000=>000000 {{1,4,5},{2,6},{3},{7}}=>[4,6,3,5,1,2,7]=>000001=>100000 {{1,4,5,7},{2},{3,6}}=>[4,2,6,5,7,3,1]=>000000=>000000 {{1,4,5},{2,7},{3,6}}=>[4,7,6,5,1,3,2]=>000000=>000000 {{1,4,5},{2},{3,6,7}}=>[4,2,6,5,1,7,3]=>000000=>000000 {{1,4,5},{2},{3,6},{7}}=>[4,2,6,5,1,3,7]=>000001=>100000 {{1,4,5,7},{2},{3},{6}}=>[4,2,3,5,7,6,1]=>000000=>000000 {{1,4,5},{2,7},{3},{6}}=>[4,7,3,5,1,6,2]=>000000=>000000 {{1,4,5},{2},{3,7},{6}}=>[4,2,7,5,1,6,3]=>000000=>000000 {{1,4,5},{2},{3},{6,7}}=>[4,2,3,5,1,7,6]=>000010=>010000 {{1,4,5},{2},{3},{6},{7}}=>[4,2,3,5,1,6,7]=>000011=>110000 {{1,4,6,7},{2,5},{3}}=>[4,5,3,6,2,7,1]=>000000=>000000 {{1,4,6},{2,5,7},{3}}=>[4,5,3,6,7,1,2]=>000000=>000000 {{1,4,6},{2,5},{3,7}}=>[4,5,7,6,2,1,3]=>000000=>000000 {{1,4,6},{2,5},{3},{7}}=>[4,5,3,6,2,1,7]=>000001=>100000 {{1,4,7},{2,5,6},{3}}=>[4,5,3,7,6,2,1]=>000000=>000000 {{1,4},{2,5,6,7},{3}}=>[4,5,3,1,6,7,2]=>000000=>000000 {{1,4},{2,5,6},{3,7}}=>[4,5,7,1,6,2,3]=>000000=>000000 {{1,4},{2,5,6},{3},{7}}=>[4,5,3,1,6,2,7]=>000001=>100000 {{1,4,7},{2,5},{3,6}}=>[4,5,6,7,2,3,1]=>000000=>000000 {{1,4},{2,5,7},{3,6}}=>[4,5,6,1,7,3,2]=>000000=>000000 {{1,4},{2,5},{3,6,7}}=>[4,5,6,1,2,7,3]=>000000=>000000 {{1,4},{2,5},{3,6},{7}}=>[4,5,6,1,2,3,7]=>000001=>100000 {{1,4,7},{2,5},{3},{6}}=>[4,5,3,7,2,6,1]=>000000=>000000 {{1,4},{2,5,7},{3},{6}}=>[4,5,3,1,7,6,2]=>000000=>000000 {{1,4},{2,5},{3,7},{6}}=>[4,5,7,1,2,6,3]=>000000=>000000 {{1,4},{2,5},{3},{6,7}}=>[4,5,3,1,2,7,6]=>000010=>010000 {{1,4},{2,5},{3},{6},{7}}=>[4,5,3,1,2,6,7]=>000011=>110000 {{1,4,6,7},{2},{3,5}}=>[4,2,5,6,3,7,1]=>000000=>000000 {{1,4,6},{2,7},{3,5}}=>[4,7,5,6,3,1,2]=>000000=>000000 {{1,4,6},{2},{3,5,7}}=>[4,2,5,6,7,1,3]=>000000=>000000 {{1,4,6},{2},{3,5},{7}}=>[4,2,5,6,3,1,7]=>000001=>100000 {{1,4,7},{2,6},{3,5}}=>[4,6,5,7,3,2,1]=>000000=>000000 {{1,4},{2,6,7},{3,5}}=>[4,6,5,1,3,7,2]=>000000=>000000 {{1,4},{2,6},{3,5,7}}=>[4,6,5,1,7,2,3]=>000000=>000000 {{1,4},{2,6},{3,5},{7}}=>[4,6,5,1,3,2,7]=>000001=>100000 {{1,4,7},{2},{3,5,6}}=>[4,2,5,7,6,3,1]=>000000=>000000 {{1,4},{2,7},{3,5,6}}=>[4,7,5,1,6,3,2]=>000000=>000000 {{1,4},{2},{3,5,6,7}}=>[4,2,5,1,6,7,3]=>000000=>000000 {{1,4},{2},{3,5,6},{7}}=>[4,2,5,1,6,3,7]=>000001=>100000 {{1,4,7},{2},{3,5},{6}}=>[4,2,5,7,3,6,1]=>000000=>000000 {{1,4},{2,7},{3,5},{6}}=>[4,7,5,1,3,6,2]=>000000=>000000 {{1,4},{2},{3,5,7},{6}}=>[4,2,5,1,7,6,3]=>000000=>000000 {{1,4},{2},{3,5},{6,7}}=>[4,2,5,1,3,7,6]=>000010=>010000 {{1,4},{2},{3,5},{6},{7}}=>[4,2,5,1,3,6,7]=>000011=>110000 {{1,4,6,7},{2},{3},{5}}=>[4,2,3,6,5,7,1]=>000000=>000000 {{1,4,6},{2,7},{3},{5}}=>[4,7,3,6,5,1,2]=>000000=>000000 {{1,4,6},{2},{3,7},{5}}=>[4,2,7,6,5,1,3]=>000000=>000000 {{1,4,6},{2},{3},{5,7}}=>[4,2,3,6,7,1,5]=>000000=>000000 {{1,4,6},{2},{3},{5},{7}}=>[4,2,3,6,5,1,7]=>000001=>100000 {{1,4,7},{2,6},{3},{5}}=>[4,6,3,7,5,2,1]=>000000=>000000 {{1,4},{2,6,7},{3},{5}}=>[4,6,3,1,5,7,2]=>000000=>000000 {{1,4},{2,6},{3,7},{5}}=>[4,6,7,1,5,2,3]=>000000=>000000 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{{1,4},{2},{3},{5},{6},{7}}=>[4,2,3,1,5,6,7]=>000111=>111000 {{1,5,6,7},{2,4},{3}}=>[5,4,3,2,6,7,1]=>000000=>000000 {{1,5,6},{2,4,7},{3}}=>[5,4,3,7,6,1,2]=>000000=>000000 {{1,5,6},{2,4},{3,7}}=>[5,4,7,2,6,1,3]=>000000=>000000 {{1,5,6},{2,4},{3},{7}}=>[5,4,3,2,6,1,7]=>000001=>100000 {{1,5,7},{2,4,6},{3}}=>[5,4,3,6,7,2,1]=>000000=>000000 {{1,5},{2,4,6,7},{3}}=>[5,4,3,6,1,7,2]=>000000=>000000 {{1,5},{2,4,6},{3,7}}=>[5,4,7,6,1,2,3]=>000000=>000000 {{1,5},{2,4,6},{3},{7}}=>[5,4,3,6,1,2,7]=>000001=>100000 {{1,5,7},{2,4},{3,6}}=>[5,4,6,2,7,3,1]=>000000=>000000 {{1,5},{2,4,7},{3,6}}=>[5,4,6,7,1,3,2]=>000000=>000000 {{1,5},{2,4},{3,6,7}}=>[5,4,6,2,1,7,3]=>000000=>000000 {{1,5},{2,4},{3,6},{7}}=>[5,4,6,2,1,3,7]=>000001=>100000 {{1,5,7},{2,4},{3},{6}}=>[5,4,3,2,7,6,1]=>000000=>000000 {{1,5},{2,4,7},{3},{6}}=>[5,4,3,7,1,6,2]=>000000=>000000 {{1,5},{2,4},{3,7},{6}}=>[5,4,7,2,1,6,3]=>000000=>000000 {{1,5},{2,4},{3},{6,7}}=>[5,4,3,2,1,7,6]=>000010=>010000 {{1,5},{2,4},{3},{6},{7}}=>[5,4,3,2,1,6,7]=>000011=>110000 {{1,6,7},{2,4,5},{3}}=>[6,4,3,5,2,7,1]=>000000=>000000 {{1,6},{2,4,5,7},{3}}=>[6,4,3,5,7,1,2]=>000000=>000000 {{1,6},{2,4,5},{3,7}}=>[6,4,7,5,2,1,3]=>000000=>000000 {{1,6},{2,4,5},{3},{7}}=>[6,4,3,5,2,1,7]=>000001=>100000 {{1,7},{2,4,5,6},{3}}=>[7,4,3,5,6,2,1]=>000000=>000000 {{1},{2,4,5,6,7},{3}}=>[1,4,3,5,6,7,2]=>100000=>000001 {{1},{2,4,5,6},{3,7}}=>[1,4,7,5,6,2,3]=>100000=>000001 {{1},{2,4,5,6},{3},{7}}=>[1,4,3,5,6,2,7]=>100001=>100001 {{1,7},{2,4,5},{3,6}}=>[7,4,6,5,2,3,1]=>000000=>000000 {{1},{2,4,5,7},{3,6}}=>[1,4,6,5,7,3,2]=>100000=>000001 {{1},{2,4,5},{3,6,7}}=>[1,4,6,5,2,7,3]=>100000=>000001 {{1},{2,4,5},{3,6},{7}}=>[1,4,6,5,2,3,7]=>100001=>100001 {{1,7},{2,4,5},{3},{6}}=>[7,4,3,5,2,6,1]=>000000=>000000 {{1},{2,4,5,7},{3},{6}}=>[1,4,3,5,7,6,2]=>100000=>000001 {{1},{2,4,5},{3,7},{6}}=>[1,4,7,5,2,6,3]=>100000=>000001 {{1},{2,4,5},{3},{6,7}}=>[1,4,3,5,2,7,6]=>100010=>010001 {{1},{2,4,5},{3},{6},{7}}=>[1,4,3,5,2,6,7]=>100011=>110001 {{1,6,7},{2,4},{3,5}}=>[6,4,5,2,3,7,1]=>000000=>000000 {{1,6},{2,4,7},{3,5}}=>[6,4,5,7,3,1,2]=>000000=>000000 {{1,6},{2,4},{3,5,7}}=>[6,4,5,2,7,1,3]=>000000=>000000 {{1,6},{2,4},{3,5},{7}}=>[6,4,5,2,3,1,7]=>000001=>100000 {{1,7},{2,4,6},{3,5}}=>[7,4,5,6,3,2,1]=>000000=>000000 {{1},{2,4,6,7},{3,5}}=>[1,4,5,6,3,7,2]=>100000=>000001 {{1},{2,4,6},{3,5,7}}=>[1,4,5,6,7,2,3]=>100000=>000001 {{1},{2,4,6},{3,5},{7}}=>[1,4,5,6,3,2,7]=>100001=>100001 {{1,7},{2,4},{3,5,6}}=>[7,4,5,2,6,3,1]=>000000=>000000 {{1},{2,4,7},{3,5,6}}=>[1,4,5,7,6,3,2]=>100000=>000001 {{1},{2,4},{3,5,6,7}}=>[1,4,5,2,6,7,3]=>100000=>000001 {{1},{2,4},{3,5,6},{7}}=>[1,4,5,2,6,3,7]=>100001=>100001 {{1,7},{2,4},{3,5},{6}}=>[7,4,5,2,3,6,1]=>000000=>000000 {{1},{2,4,7},{3,5},{6}}=>[1,4,5,7,3,6,2]=>100000=>000001 {{1},{2,4},{3,5,7},{6}}=>[1,4,5,2,7,6,3]=>100000=>000001 {{1},{2,4},{3,5},{6,7}}=>[1,4,5,2,3,7,6]=>100010=>010001 {{1},{2,4},{3,5},{6},{7}}=>[1,4,5,2,3,6,7]=>100011=>110001 {{1,6,7},{2,4},{3},{5}}=>[6,4,3,2,5,7,1]=>000000=>000000 {{1,6},{2,4,7},{3},{5}}=>[6,4,3,7,5,1,2]=>000000=>000000 {{1,6},{2,4},{3,7},{5}}=>[6,4,7,2,5,1,3]=>000000=>000000 {{1,6},{2,4},{3},{5,7}}=>[6,4,3,2,7,1,5]=>000000=>000000 {{1,6},{2,4},{3},{5},{7}}=>[6,4,3,2,5,1,7]=>000001=>100000 {{1,7},{2,4,6},{3},{5}}=>[7,4,3,6,5,2,1]=>000000=>000000 {{1},{2,4,6,7},{3},{5}}=>[1,4,3,6,5,7,2]=>100000=>000001 {{1},{2,4,6},{3,7},{5}}=>[1,4,7,6,5,2,3]=>100000=>000001 {{1},{2,4,6},{3},{5,7}}=>[1,4,3,6,7,2,5]=>100000=>000001 {{1},{2,4,6},{3},{5},{7}}=>[1,4,3,6,5,2,7]=>100001=>100001 {{1,7},{2,4},{3,6},{5}}=>[7,4,6,2,5,3,1]=>000000=>000000 {{1},{2,4,7},{3,6},{5}}=>[1,4,6,7,5,3,2]=>100000=>000001 {{1},{2,4},{3,6,7},{5}}=>[1,4,6,2,5,7,3]=>100000=>000001 {{1},{2,4},{3,6},{5,7}}=>[1,4,6,2,7,3,5]=>100000=>000001 {{1},{2,4},{3,6},{5},{7}}=>[1,4,6,2,5,3,7]=>100001=>100001 {{1,7},{2,4},{3},{5,6}}=>[7,4,3,2,6,5,1]=>000000=>000000 {{1},{2,4,7},{3},{5,6}}=>[1,4,3,7,6,5,2]=>100000=>000001 {{1},{2,4},{3,7},{5,6}}=>[1,4,7,2,6,5,3]=>100000=>000001 {{1},{2,4},{3},{5,6,7}}=>[1,4,3,2,6,7,5]=>100100=>001001 {{1},{2,4},{3},{5,6},{7}}=>[1,4,3,2,6,5,7]=>100101=>101001 {{1,7},{2,4},{3},{5},{6}}=>[7,4,3,2,5,6,1]=>000000=>000000 {{1},{2,4,7},{3},{5},{6}}=>[1,4,3,7,5,6,2]=>100000=>000001 {{1},{2,4},{3,7},{5},{6}}=>[1,4,7,2,5,6,3]=>100000=>000001 {{1},{2,4},{3},{5,7},{6}}=>[1,4,3,2,7,6,5]=>100100=>001001 {{1},{2,4},{3},{5},{6,7}}=>[1,4,3,2,5,7,6]=>100110=>011001 {{1},{2,4},{3},{5},{6},{7}}=>[1,4,3,2,5,6,7]=>100111=>111001 {{1,5,6,7},{2},{3,4}}=>[5,2,4,3,6,7,1]=>000000=>000000 {{1,5,6},{2,7},{3,4}}=>[5,7,4,3,6,1,2]=>000000=>000000 {{1,5,6},{2},{3,4,7}}=>[5,2,4,7,6,1,3]=>000000=>000000 {{1,5,6},{2},{3,4},{7}}=>[5,2,4,3,6,1,7]=>000001=>100000 {{1,5,7},{2,6},{3,4}}=>[5,6,4,3,7,2,1]=>000000=>000000 {{1,5},{2,6,7},{3,4}}=>[5,6,4,3,1,7,2]=>000000=>000000 {{1,5},{2,6},{3,4,7}}=>[5,6,4,7,1,2,3]=>000000=>000000 {{1,5},{2,6},{3,4},{7}}=>[5,6,4,3,1,2,7]=>000001=>100000 {{1,5,7},{2},{3,4,6}}=>[5,2,4,6,7,3,1]=>000000=>000000 {{1,5},{2,7},{3,4,6}}=>[5,7,4,6,1,3,2]=>000000=>000000 {{1,5},{2},{3,4,6,7}}=>[5,2,4,6,1,7,3]=>000000=>000000 {{1,5},{2},{3,4,6},{7}}=>[5,2,4,6,1,3,7]=>000001=>100000 {{1,5,7},{2},{3,4},{6}}=>[5,2,4,3,7,6,1]=>000000=>000000 {{1,5},{2,7},{3,4},{6}}=>[5,7,4,3,1,6,2]=>000000=>000000 {{1,5},{2},{3,4,7},{6}}=>[5,2,4,7,1,6,3]=>000000=>000000 {{1,5},{2},{3,4},{6,7}}=>[5,2,4,3,1,7,6]=>000010=>010000 {{1,5},{2},{3,4},{6},{7}}=>[5,2,4,3,1,6,7]=>000011=>110000 {{1,6,7},{2,5},{3,4}}=>[6,5,4,3,2,7,1]=>000000=>000000 {{1,6},{2,5,7},{3,4}}=>[6,5,4,3,7,1,2]=>000000=>000000 {{1,6},{2,5},{3,4,7}}=>[6,5,4,7,2,1,3]=>000000=>000000 {{1,6},{2,5},{3,4},{7}}=>[6,5,4,3,2,1,7]=>000001=>100000 {{1,7},{2,5,6},{3,4}}=>[7,5,4,3,6,2,1]=>000000=>000000 {{1},{2,5,6,7},{3,4}}=>[1,5,4,3,6,7,2]=>100000=>000001 {{1},{2,5,6},{3,4,7}}=>[1,5,4,7,6,2,3]=>100000=>000001 {{1},{2,5,6},{3,4},{7}}=>[1,5,4,3,6,2,7]=>100001=>100001 {{1,7},{2,5},{3,4,6}}=>[7,5,4,6,2,3,1]=>000000=>000000 {{1},{2,5,7},{3,4,6}}=>[1,5,4,6,7,3,2]=>100000=>000001 {{1},{2,5},{3,4,6,7}}=>[1,5,4,6,2,7,3]=>100000=>000001 {{1},{2,5},{3,4,6},{7}}=>[1,5,4,6,2,3,7]=>100001=>100001 {{1,7},{2,5},{3,4},{6}}=>[7,5,4,3,2,6,1]=>000000=>000000 {{1},{2,5,7},{3,4},{6}}=>[1,5,4,3,7,6,2]=>100000=>000001 {{1},{2,5},{3,4,7},{6}}=>[1,5,4,7,2,6,3]=>100000=>000001 {{1},{2,5},{3,4},{6,7}}=>[1,5,4,3,2,7,6]=>100010=>010001 {{1},{2,5},{3,4},{6},{7}}=>[1,5,4,3,2,6,7]=>100011=>110001 {{1,6,7},{2},{3,4,5}}=>[6,2,4,5,3,7,1]=>000000=>000000 {{1,6},{2,7},{3,4,5}}=>[6,7,4,5,3,1,2]=>000000=>000000 {{1,6},{2},{3,4,5,7}}=>[6,2,4,5,7,1,3]=>000000=>000000 {{1,6},{2},{3,4,5},{7}}=>[6,2,4,5,3,1,7]=>000001=>100000 {{1,7},{2,6},{3,4,5}}=>[7,6,4,5,3,2,1]=>000000=>000000 {{1},{2,6,7},{3,4,5}}=>[1,6,4,5,3,7,2]=>100000=>000001 {{1},{2,6},{3,4,5,7}}=>[1,6,4,5,7,2,3]=>100000=>000001 {{1},{2,6},{3,4,5},{7}}=>[1,6,4,5,3,2,7]=>100001=>100001 {{1,7},{2},{3,4,5,6}}=>[7,2,4,5,6,3,1]=>000000=>000000 {{1},{2,7},{3,4,5,6}}=>[1,7,4,5,6,3,2]=>100000=>000001 {{1},{2},{3,4,5,6,7}}=>[1,2,4,5,6,7,3]=>110000=>000011 {{1},{2},{3,4,5,6},{7}}=>[1,2,4,5,6,3,7]=>110001=>100011 {{1,7},{2},{3,4,5},{6}}=>[7,2,4,5,3,6,1]=>000000=>000000 {{1},{2,7},{3,4,5},{6}}=>[1,7,4,5,3,6,2]=>100000=>000001 {{1},{2},{3,4,5,7},{6}}=>[1,2,4,5,7,6,3]=>110000=>000011 {{1},{2},{3,4,5},{6,7}}=>[1,2,4,5,3,7,6]=>110010=>010011 {{1},{2},{3,4,5},{6},{7}}=>[1,2,4,5,3,6,7]=>110011=>110011 {{1,6,7},{2},{3,4},{5}}=>[6,2,4,3,5,7,1]=>000000=>000000 {{1,6},{2,7},{3,4},{5}}=>[6,7,4,3,5,1,2]=>000000=>000000 {{1,6},{2},{3,4,7},{5}}=>[6,2,4,7,5,1,3]=>000000=>000000 {{1,6},{2},{3,4},{5,7}}=>[6,2,4,3,7,1,5]=>000000=>000000 {{1,6},{2},{3,4},{5},{7}}=>[6,2,4,3,5,1,7]=>000001=>100000 {{1,7},{2,6},{3,4},{5}}=>[7,6,4,3,5,2,1]=>000000=>000000 {{1},{2,6,7},{3,4},{5}}=>[1,6,4,3,5,7,2]=>100000=>000001 {{1},{2,6},{3,4,7},{5}}=>[1,6,4,7,5,2,3]=>100000=>000001 {{1},{2,6},{3,4},{5,7}}=>[1,6,4,3,7,2,5]=>100000=>000001 {{1},{2,6},{3,4},{5},{7}}=>[1,6,4,3,5,2,7]=>100001=>100001 {{1,7},{2},{3,4,6},{5}}=>[7,2,4,6,5,3,1]=>000000=>000000 {{1},{2,7},{3,4,6},{5}}=>[1,7,4,6,5,3,2]=>100000=>000001 {{1},{2},{3,4,6,7},{5}}=>[1,2,4,6,5,7,3]=>110000=>000011 {{1},{2},{3,4,6},{5,7}}=>[1,2,4,6,7,3,5]=>110000=>000011 {{1},{2},{3,4,6},{5},{7}}=>[1,2,4,6,5,3,7]=>110001=>100011 {{1,7},{2},{3,4},{5,6}}=>[7,2,4,3,6,5,1]=>000000=>000000 {{1},{2,7},{3,4},{5,6}}=>[1,7,4,3,6,5,2]=>100000=>000001 {{1},{2},{3,4,7},{5,6}}=>[1,2,4,7,6,5,3]=>110000=>000011 {{1},{2},{3,4},{5,6,7}}=>[1,2,4,3,6,7,5]=>110100=>001011 {{1},{2},{3,4},{5,6},{7}}=>[1,2,4,3,6,5,7]=>110101=>101011 {{1,7},{2},{3,4},{5},{6}}=>[7,2,4,3,5,6,1]=>000000=>000000 {{1},{2,7},{3,4},{5},{6}}=>[1,7,4,3,5,6,2]=>100000=>000001 {{1},{2},{3,4,7},{5},{6}}=>[1,2,4,7,5,6,3]=>110000=>000011 {{1},{2},{3,4},{5,7},{6}}=>[1,2,4,3,7,6,5]=>110100=>001011 {{1},{2},{3,4},{5},{6,7}}=>[1,2,4,3,5,7,6]=>110110=>011011 {{1},{2},{3,4},{5},{6},{7}}=>[1,2,4,3,5,6,7]=>110111=>111011 {{1,5,6,7},{2},{3},{4}}=>[5,2,3,4,6,7,1]=>000000=>000000 {{1,5,6},{2,7},{3},{4}}=>[5,7,3,4,6,1,2]=>000000=>000000 {{1,5,6},{2},{3,7},{4}}=>[5,2,7,4,6,1,3]=>000000=>000000 {{1,5,6},{2},{3},{4,7}}=>[5,2,3,7,6,1,4]=>000000=>000000 {{1,5,6},{2},{3},{4},{7}}=>[5,2,3,4,6,1,7]=>000001=>100000 {{1,5,7},{2,6},{3},{4}}=>[5,6,3,4,7,2,1]=>000000=>000000 {{1,5},{2,6,7},{3},{4}}=>[5,6,3,4,1,7,2]=>000000=>000000 {{1,5},{2,6},{3,7},{4}}=>[5,6,7,4,1,2,3]=>000000=>000000 {{1,5},{2,6},{3},{4,7}}=>[5,6,3,7,1,2,4]=>000000=>000000 {{1,5},{2,6},{3},{4},{7}}=>[5,6,3,4,1,2,7]=>000001=>100000 {{1,5,7},{2},{3,6},{4}}=>[5,2,6,4,7,3,1]=>000000=>000000 {{1,5},{2,7},{3,6},{4}}=>[5,7,6,4,1,3,2]=>000000=>000000 {{1,5},{2},{3,6,7},{4}}=>[5,2,6,4,1,7,3]=>000000=>000000 {{1,5},{2},{3,6},{4,7}}=>[5,2,6,7,1,3,4]=>000000=>000000 {{1,5},{2},{3,6},{4},{7}}=>[5,2,6,4,1,3,7]=>000001=>100000 {{1,5,7},{2},{3},{4,6}}=>[5,2,3,6,7,4,1]=>000000=>000000 {{1,5},{2,7},{3},{4,6}}=>[5,7,3,6,1,4,2]=>000000=>000000 {{1,5},{2},{3,7},{4,6}}=>[5,2,7,6,1,4,3]=>000000=>000000 {{1,5},{2},{3},{4,6,7}}=>[5,2,3,6,1,7,4]=>000000=>000000 {{1,5},{2},{3},{4,6},{7}}=>[5,2,3,6,1,4,7]=>000001=>100000 {{1,5,7},{2},{3},{4},{6}}=>[5,2,3,4,7,6,1]=>000000=>000000 {{1,5},{2,7},{3},{4},{6}}=>[5,7,3,4,1,6,2]=>000000=>000000 {{1,5},{2},{3,7},{4},{6}}=>[5,2,7,4,1,6,3]=>000000=>000000 {{1,5},{2},{3},{4,7},{6}}=>[5,2,3,7,1,6,4]=>000000=>000000 {{1,5},{2},{3},{4},{6,7}}=>[5,2,3,4,1,7,6]=>000010=>010000 {{1,5},{2},{3},{4},{6},{7}}=>[5,2,3,4,1,6,7]=>000011=>110000 {{1,6,7},{2,5},{3},{4}}=>[6,5,3,4,2,7,1]=>000000=>000000 {{1,6},{2,5,7},{3},{4}}=>[6,5,3,4,7,1,2]=>000000=>000000 {{1,6},{2,5},{3,7},{4}}=>[6,5,7,4,2,1,3]=>000000=>000000 {{1,6},{2,5},{3},{4,7}}=>[6,5,3,7,2,1,4]=>000000=>000000 {{1,6},{2,5},{3},{4},{7}}=>[6,5,3,4,2,1,7]=>000001=>100000 {{1,7},{2,5,6},{3},{4}}=>[7,5,3,4,6,2,1]=>000000=>000000 {{1},{2,5,6,7},{3},{4}}=>[1,5,3,4,6,7,2]=>100000=>000001 {{1},{2,5,6},{3,7},{4}}=>[1,5,7,4,6,2,3]=>100000=>000001 {{1},{2,5,6},{3},{4,7}}=>[1,5,3,7,6,2,4]=>100000=>000001 {{1},{2,5,6},{3},{4},{7}}=>[1,5,3,4,6,2,7]=>100001=>100001 {{1,7},{2,5},{3,6},{4}}=>[7,5,6,4,2,3,1]=>000000=>000000 {{1},{2,5,7},{3,6},{4}}=>[1,5,6,4,7,3,2]=>100000=>000001 {{1},{2,5},{3,6,7},{4}}=>[1,5,6,4,2,7,3]=>100000=>000001 {{1},{2,5},{3,6},{4,7}}=>[1,5,6,7,2,3,4]=>100000=>000001 {{1},{2,5},{3,6},{4},{7}}=>[1,5,6,4,2,3,7]=>100001=>100001 {{1,7},{2,5},{3},{4,6}}=>[7,5,3,6,2,4,1]=>000000=>000000 {{1},{2,5,7},{3},{4,6}}=>[1,5,3,6,7,4,2]=>100000=>000001 {{1},{2,5},{3,7},{4,6}}=>[1,5,7,6,2,4,3]=>100000=>000001 {{1},{2,5},{3},{4,6,7}}=>[1,5,3,6,2,7,4]=>100000=>000001 {{1},{2,5},{3},{4,6},{7}}=>[1,5,3,6,2,4,7]=>100001=>100001 {{1,7},{2,5},{3},{4},{6}}=>[7,5,3,4,2,6,1]=>000000=>000000 {{1},{2,5,7},{3},{4},{6}}=>[1,5,3,4,7,6,2]=>100000=>000001 {{1},{2,5},{3,7},{4},{6}}=>[1,5,7,4,2,6,3]=>100000=>000001 {{1},{2,5},{3},{4,7},{6}}=>[1,5,3,7,2,6,4]=>100000=>000001 {{1},{2,5},{3},{4},{6,7}}=>[1,5,3,4,2,7,6]=>100010=>010001 {{1},{2,5},{3},{4},{6},{7}}=>[1,5,3,4,2,6,7]=>100011=>110001 {{1,6,7},{2},{3,5},{4}}=>[6,2,5,4,3,7,1]=>000000=>000000 {{1,6},{2,7},{3,5},{4}}=>[6,7,5,4,3,1,2]=>000000=>000000 {{1,6},{2},{3,5,7},{4}}=>[6,2,5,4,7,1,3]=>000000=>000000 {{1,6},{2},{3,5},{4,7}}=>[6,2,5,7,3,1,4]=>000000=>000000 {{1,6},{2},{3,5},{4},{7}}=>[6,2,5,4,3,1,7]=>000001=>100000 {{1,7},{2,6},{3,5},{4}}=>[7,6,5,4,3,2,1]=>000000=>000000 {{1},{2,6,7},{3,5},{4}}=>[1,6,5,4,3,7,2]=>100000=>000001 {{1},{2,6},{3,5,7},{4}}=>[1,6,5,4,7,2,3]=>100000=>000001 {{1},{2,6},{3,5},{4,7}}=>[1,6,5,7,3,2,4]=>100000=>000001 {{1},{2,6},{3,5},{4},{7}}=>[1,6,5,4,3,2,7]=>100001=>100001 {{1,7},{2},{3,5,6},{4}}=>[7,2,5,4,6,3,1]=>000000=>000000 {{1},{2,7},{3,5,6},{4}}=>[1,7,5,4,6,3,2]=>100000=>000001 {{1},{2},{3,5,6,7},{4}}=>[1,2,5,4,6,7,3]=>110000=>000011 {{1},{2},{3,5,6},{4,7}}=>[1,2,5,7,6,3,4]=>110000=>000011 {{1},{2},{3,5,6},{4},{7}}=>[1,2,5,4,6,3,7]=>110001=>100011 {{1,7},{2},{3,5},{4,6}}=>[7,2,5,6,3,4,1]=>000000=>000000 {{1},{2,7},{3,5},{4,6}}=>[1,7,5,6,3,4,2]=>100000=>000001 {{1},{2},{3,5,7},{4,6}}=>[1,2,5,6,7,4,3]=>110000=>000011 {{1},{2},{3,5},{4,6,7}}=>[1,2,5,6,3,7,4]=>110000=>000011 {{1},{2},{3,5},{4,6},{7}}=>[1,2,5,6,3,4,7]=>110001=>100011 {{1,7},{2},{3,5},{4},{6}}=>[7,2,5,4,3,6,1]=>000000=>000000 {{1},{2,7},{3,5},{4},{6}}=>[1,7,5,4,3,6,2]=>100000=>000001 {{1},{2},{3,5,7},{4},{6}}=>[1,2,5,4,7,6,3]=>110000=>000011 {{1},{2},{3,5},{4,7},{6}}=>[1,2,5,7,3,6,4]=>110000=>000011 {{1},{2},{3,5},{4},{6,7}}=>[1,2,5,4,3,7,6]=>110010=>010011 {{1},{2},{3,5},{4},{6},{7}}=>[1,2,5,4,3,6,7]=>110011=>110011 {{1,6,7},{2},{3},{4,5}}=>[6,2,3,5,4,7,1]=>000000=>000000 {{1,6},{2,7},{3},{4,5}}=>[6,7,3,5,4,1,2]=>000000=>000000 {{1,6},{2},{3,7},{4,5}}=>[6,2,7,5,4,1,3]=>000000=>000000 {{1,6},{2},{3},{4,5,7}}=>[6,2,3,5,7,1,4]=>000000=>000000 {{1,6},{2},{3},{4,5},{7}}=>[6,2,3,5,4,1,7]=>000001=>100000 {{1,7},{2,6},{3},{4,5}}=>[7,6,3,5,4,2,1]=>000000=>000000 {{1},{2,6,7},{3},{4,5}}=>[1,6,3,5,4,7,2]=>100000=>000001 {{1},{2,6},{3,7},{4,5}}=>[1,6,7,5,4,2,3]=>100000=>000001 {{1},{2,6},{3},{4,5,7}}=>[1,6,3,5,7,2,4]=>100000=>000001 {{1},{2,6},{3},{4,5},{7}}=>[1,6,3,5,4,2,7]=>100001=>100001 {{1,7},{2},{3,6},{4,5}}=>[7,2,6,5,4,3,1]=>000000=>000000 {{1},{2,7},{3,6},{4,5}}=>[1,7,6,5,4,3,2]=>100000=>000001 {{1},{2},{3,6,7},{4,5}}=>[1,2,6,5,4,7,3]=>110000=>000011 {{1},{2},{3,6},{4,5,7}}=>[1,2,6,5,7,3,4]=>110000=>000011 {{1},{2},{3,6},{4,5},{7}}=>[1,2,6,5,4,3,7]=>110001=>100011 {{1,7},{2},{3},{4,5,6}}=>[7,2,3,5,6,4,1]=>000000=>000000 {{1},{2,7},{3},{4,5,6}}=>[1,7,3,5,6,4,2]=>100000=>000001 {{1},{2},{3,7},{4,5,6}}=>[1,2,7,5,6,4,3]=>110000=>000011 {{1},{2},{3},{4,5,6,7}}=>[1,2,3,5,6,7,4]=>111000=>000111 {{1},{2},{3},{4,5,6},{7}}=>[1,2,3,5,6,4,7]=>111001=>100111 {{1,7},{2},{3},{4,5},{6}}=>[7,2,3,5,4,6,1]=>000000=>000000 {{1},{2,7},{3},{4,5},{6}}=>[1,7,3,5,4,6,2]=>100000=>000001 {{1},{2},{3,7},{4,5},{6}}=>[1,2,7,5,4,6,3]=>110000=>000011 {{1},{2},{3},{4,5,7},{6}}=>[1,2,3,5,7,6,4]=>111000=>000111 {{1},{2},{3},{4,5},{6,7}}=>[1,2,3,5,4,7,6]=>111010=>010111 {{1},{2},{3},{4,5},{6},{7}}=>[1,2,3,5,4,6,7]=>111011=>110111 {{1,6,7},{2},{3},{4},{5}}=>[6,2,3,4,5,7,1]=>000000=>000000 {{1,6},{2,7},{3},{4},{5}}=>[6,7,3,4,5,1,2]=>000000=>000000 {{1,6},{2},{3,7},{4},{5}}=>[6,2,7,4,5,1,3]=>000000=>000000 {{1,6},{2},{3},{4,7},{5}}=>[6,2,3,7,5,1,4]=>000000=>000000 {{1,6},{2},{3},{4},{5,7}}=>[6,2,3,4,7,1,5]=>000000=>000000 {{1,6},{2},{3},{4},{5},{7}}=>[6,2,3,4,5,1,7]=>000001=>100000 {{1,7},{2,6},{3},{4},{5}}=>[7,6,3,4,5,2,1]=>000000=>000000 {{1},{2,6,7},{3},{4},{5}}=>[1,6,3,4,5,7,2]=>100000=>000001 {{1},{2,6},{3,7},{4},{5}}=>[1,6,7,4,5,2,3]=>100000=>000001 {{1},{2,6},{3},{4,7},{5}}=>[1,6,3,7,5,2,4]=>100000=>000001 {{1},{2,6},{3},{4},{5,7}}=>[1,6,3,4,7,2,5]=>100000=>000001 {{1},{2,6},{3},{4},{5},{7}}=>[1,6,3,4,5,2,7]=>100001=>100001 {{1,7},{2},{3,6},{4},{5}}=>[7,2,6,4,5,3,1]=>000000=>000000 {{1},{2,7},{3,6},{4},{5}}=>[1,7,6,4,5,3,2]=>100000=>000001 {{1},{2},{3,6,7},{4},{5}}=>[1,2,6,4,5,7,3]=>110000=>000011 {{1},{2},{3,6},{4,7},{5}}=>[1,2,6,7,5,3,4]=>110000=>000011 {{1},{2},{3,6},{4},{5,7}}=>[1,2,6,4,7,3,5]=>110000=>000011 {{1},{2},{3,6},{4},{5},{7}}=>[1,2,6,4,5,3,7]=>110001=>100011 {{1,7},{2},{3},{4,6},{5}}=>[7,2,3,6,5,4,1]=>000000=>000000 {{1},{2,7},{3},{4,6},{5}}=>[1,7,3,6,5,4,2]=>100000=>000001 {{1},{2},{3,7},{4,6},{5}}=>[1,2,7,6,5,4,3]=>110000=>000011 {{1},{2},{3},{4,6,7},{5}}=>[1,2,3,6,5,7,4]=>111000=>000111 {{1},{2},{3},{4,6},{5,7}}=>[1,2,3,6,7,4,5]=>111000=>000111 {{1},{2},{3},{4,6},{5},{7}}=>[1,2,3,6,5,4,7]=>111001=>100111 {{1,7},{2},{3},{4},{5,6}}=>[7,2,3,4,6,5,1]=>000000=>000000 {{1},{2,7},{3},{4},{5,6}}=>[1,7,3,4,6,5,2]=>100000=>000001 {{1},{2},{3,7},{4},{5,6}}=>[1,2,7,4,6,5,3]=>110000=>000011 {{1},{2},{3},{4,7},{5,6}}=>[1,2,3,7,6,5,4]=>111000=>000111 {{1},{2},{3},{4},{5,6,7}}=>[1,2,3,4,6,7,5]=>111100=>001111 {{1},{2},{3},{4},{5,6},{7}}=>[1,2,3,4,6,5,7]=>111101=>101111 {{1,7},{2},{3},{4},{5},{6}}=>[7,2,3,4,5,6,1]=>000000=>000000 {{1},{2,7},{3},{4},{5},{6}}=>[1,7,3,4,5,6,2]=>100000=>000001 {{1},{2},{3,7},{4},{5},{6}}=>[1,2,7,4,5,6,3]=>110000=>000011 {{1},{2},{3},{4,7},{5},{6}}=>[1,2,3,7,5,6,4]=>111000=>000111 {{1},{2},{3},{4},{5,7},{6}}=>[1,2,3,4,7,6,5]=>111100=>001111 {{1},{2},{3},{4},{5},{6,7}}=>[1,2,3,4,5,7,6]=>111110=>011111 {{1},{2},{3},{4},{5},{6},{7}}=>[1,2,3,4,5,6,7]=>111111=>111111 {{1,2},{3,4},{5,6},{7,8}}=>[2,1,4,3,6,5,8,7]=>0101010=>0101010 {{1,3},{2,4},{5,6},{7,8}}=>[3,4,1,2,6,5,8,7]=>0001010=>0101000 {{1,4},{2,3},{5,6},{7,8}}=>[4,3,2,1,6,5,8,7]=>0001010=>0101000 {{1,5},{2,3},{4,6},{7,8}}=>[5,3,2,6,1,4,8,7]=>0000010=>0100000 {{1,6},{2,3},{4,5},{7,8}}=>[6,3,2,5,4,1,8,7]=>0000010=>0100000 {{1,7},{2,3},{4,5},{6,8}}=>[7,3,2,5,4,8,1,6]=>0000000=>0000000 {{1,8},{2,3},{4,5},{6,7}}=>[8,3,2,5,4,7,6,1]=>0000000=>0000000 {{1,8},{2,4},{3,5},{6,7}}=>[8,4,5,2,3,7,6,1]=>0000000=>0000000 {{1,7},{2,4},{3,5},{6,8}}=>[7,4,5,2,3,8,1,6]=>0000000=>0000000 {{1,6},{2,4},{3,5},{7,8}}=>[6,4,5,2,3,1,8,7]=>0000010=>0100000 {{1,5},{2,4},{3,6},{7,8}}=>[5,4,6,2,1,3,8,7]=>0000010=>0100000 {{1,4},{2,5},{3,6},{7,8}}=>[4,5,6,1,2,3,8,7]=>0000010=>0100000 {{1,3},{2,5},{4,6},{7,8}}=>[3,5,1,6,2,4,8,7]=>0000010=>0100000 {{1,2},{3,5},{4,6},{7,8}}=>[2,1,5,6,3,4,8,7]=>0100010=>0100010 {{1,2},{3,6},{4,5},{7,8}}=>[2,1,6,5,4,3,8,7]=>0100010=>0100010 {{1,3},{2,6},{4,5},{7,8}}=>[3,6,1,5,4,2,8,7]=>0000010=>0100000 {{1,4},{2,6},{3,5},{7,8}}=>[4,6,5,1,3,2,8,7]=>0000010=>0100000 {{1,5},{2,6},{3,4},{7,8}}=>[5,6,4,3,1,2,8,7]=>0000010=>0100000 {{1,6},{2,5},{3,4},{7,8}}=>[6,5,4,3,2,1,8,7]=>0000010=>0100000 {{1,7},{2,5},{3,4},{6,8}}=>[7,5,4,3,2,8,1,6]=>0000000=>0000000 {{1,8},{2,5},{3,4},{6,7}}=>[8,5,4,3,2,7,6,1]=>0000000=>0000000 {{1,8},{2,6},{3,4},{5,7}}=>[8,6,4,3,7,2,5,1]=>0000000=>0000000 {{1,7},{2,6},{3,4},{5,8}}=>[7,6,4,3,8,2,1,5]=>0000000=>0000000 {{1,6},{2,7},{3,4},{5,8}}=>[6,7,4,3,8,1,2,5]=>0000000=>0000000 {{1,5},{2,7},{3,4},{6,8}}=>[5,7,4,3,1,8,2,6]=>0000000=>0000000 {{1,4},{2,7},{3,5},{6,8}}=>[4,7,5,1,3,8,2,6]=>0000000=>0000000 {{1,3},{2,7},{4,5},{6,8}}=>[3,7,1,5,4,8,2,6]=>0000000=>0000000 {{1,2},{3,7},{4,5},{6,8}}=>[2,1,7,5,4,8,3,6]=>0100000=>0000010 {{1,2},{3,8},{4,5},{6,7}}=>[2,1,8,5,4,7,6,3]=>0100000=>0000010 {{1,3},{2,8},{4,5},{6,7}}=>[3,8,1,5,4,7,6,2]=>0000000=>0000000 {{1,4},{2,8},{3,5},{6,7}}=>[4,8,5,1,3,7,6,2]=>0000000=>0000000 {{1,5},{2,8},{3,4},{6,7}}=>[5,8,4,3,1,7,6,2]=>0000000=>0000000 {{1,6},{2,8},{3,4},{5,7}}=>[6,8,4,3,7,1,5,2]=>0000000=>0000000 {{1,7},{2,8},{3,4},{5,6}}=>[7,8,4,3,6,5,1,2]=>0000000=>0000000 {{1,8},{2,7},{3,4},{5,6}}=>[8,7,4,3,6,5,2,1]=>0000000=>0000000 {{1,8},{2,7},{3,5},{4,6}}=>[8,7,5,6,3,4,2,1]=>0000000=>0000000 {{1,7},{2,8},{3,5},{4,6}}=>[7,8,5,6,3,4,1,2]=>0000000=>0000000 {{1,6},{2,8},{3,5},{4,7}}=>[6,8,5,7,3,1,4,2]=>0000000=>0000000 {{1,5},{2,8},{3,6},{4,7}}=>[5,8,6,7,1,3,4,2]=>0000000=>0000000 {{1,4},{2,8},{3,6},{5,7}}=>[4,8,6,1,7,3,5,2]=>0000000=>0000000 {{1,3},{2,8},{4,6},{5,7}}=>[3,8,1,6,7,4,5,2]=>0000000=>0000000 {{1,2},{3,8},{4,6},{5,7}}=>[2,1,8,6,7,4,5,3]=>0100000=>0000010 {{1,2},{3,7},{4,6},{5,8}}=>[2,1,7,6,8,4,3,5]=>0100000=>0000010 {{1,3},{2,7},{4,6},{5,8}}=>[3,7,1,6,8,4,2,5]=>0000000=>0000000 {{1,4},{2,7},{3,6},{5,8}}=>[4,7,6,1,8,3,2,5]=>0000000=>0000000 {{1,5},{2,7},{3,6},{4,8}}=>[5,7,6,8,1,3,2,4]=>0000000=>0000000 {{1,6},{2,7},{3,5},{4,8}}=>[6,7,5,8,3,1,2,4]=>0000000=>0000000 {{1,7},{2,6},{3,5},{4,8}}=>[7,6,5,8,3,2,1,4]=>0000000=>0000000 {{1,8},{2,6},{3,5},{4,7}}=>[8,6,5,7,3,2,4,1]=>0000000=>0000000 {{1,8},{2,5},{3,6},{4,7}}=>[8,5,6,7,2,3,4,1]=>0000000=>0000000 {{1,7},{2,5},{3,6},{4,8}}=>[7,5,6,8,2,3,1,4]=>0000000=>0000000 {{1,6},{2,5},{3,7},{4,8}}=>[6,5,7,8,2,1,3,4]=>0000000=>0000000 {{1,5},{2,6},{3,7},{4,8}}=>[5,6,7,8,1,2,3,4]=>0000000=>0000000 {{1,4},{2,6},{3,7},{5,8}}=>[4,6,7,1,8,2,3,5]=>0000000=>0000000 {{1,3},{2,6},{4,7},{5,8}}=>[3,6,1,7,8,2,4,5]=>0000000=>0000000 {{1,2},{3,6},{4,7},{5,8}}=>[2,1,6,7,8,3,4,5]=>0100000=>0000010 {{1,2},{3,5},{4,7},{6,8}}=>[2,1,5,7,3,8,4,6]=>0100000=>0000010 {{1,3},{2,5},{4,7},{6,8}}=>[3,5,1,7,2,8,4,6]=>0000000=>0000000 {{1,4},{2,5},{3,7},{6,8}}=>[4,5,7,1,2,8,3,6]=>0000000=>0000000 {{1,5},{2,4},{3,7},{6,8}}=>[5,4,7,2,1,8,3,6]=>0000000=>0000000 {{1,6},{2,4},{3,7},{5,8}}=>[6,4,7,2,8,1,3,5]=>0000000=>0000000 {{1,7},{2,4},{3,6},{5,8}}=>[7,4,6,2,8,3,1,5]=>0000000=>0000000 {{1,8},{2,4},{3,6},{5,7}}=>[8,4,6,2,7,3,5,1]=>0000000=>0000000 {{1,8},{2,3},{4,6},{5,7}}=>[8,3,2,6,7,4,5,1]=>0000000=>0000000 {{1,7},{2,3},{4,6},{5,8}}=>[7,3,2,6,8,4,1,5]=>0000000=>0000000 {{1,6},{2,3},{4,7},{5,8}}=>[6,3,2,7,8,1,4,5]=>0000000=>0000000 {{1,5},{2,3},{4,7},{6,8}}=>[5,3,2,7,1,8,4,6]=>0000000=>0000000 {{1,4},{2,3},{5,7},{6,8}}=>[4,3,2,1,7,8,5,6]=>0001000=>0001000 {{1,3},{2,4},{5,7},{6,8}}=>[3,4,1,2,7,8,5,6]=>0001000=>0001000 {{1,2},{3,4},{5,7},{6,8}}=>[2,1,4,3,7,8,5,6]=>0101000=>0001010 {{1,2},{3,4},{5,8},{6,7}}=>[2,1,4,3,8,7,6,5]=>0101000=>0001010 {{1,3},{2,4},{5,8},{6,7}}=>[3,4,1,2,8,7,6,5]=>0001000=>0001000 {{1,4},{2,3},{5,8},{6,7}}=>[4,3,2,1,8,7,6,5]=>0001000=>0001000 {{1,5},{2,3},{4,8},{6,7}}=>[5,3,2,8,1,7,6,4]=>0000000=>0000000 {{1,6},{2,3},{4,8},{5,7}}=>[6,3,2,8,7,1,5,4]=>0000000=>0000000 {{1,7},{2,3},{4,8},{5,6}}=>[7,3,2,8,6,5,1,4]=>0000000=>0000000 {{1,8},{2,3},{4,7},{5,6}}=>[8,3,2,7,6,5,4,1]=>0000000=>0000000 {{1,8},{2,4},{3,7},{5,6}}=>[8,4,7,2,6,5,3,1]=>0000000=>0000000 {{1,7},{2,4},{3,8},{5,6}}=>[7,4,8,2,6,5,1,3]=>0000000=>0000000 {{1,6},{2,4},{3,8},{5,7}}=>[6,4,8,2,7,1,5,3]=>0000000=>0000000 {{1,5},{2,4},{3,8},{6,7}}=>[5,4,8,2,1,7,6,3]=>0000000=>0000000 {{1,4},{2,5},{3,8},{6,7}}=>[4,5,8,1,2,7,6,3]=>0000000=>0000000 {{1,3},{2,5},{4,8},{6,7}}=>[3,5,1,8,2,7,6,4]=>0000000=>0000000 {{1,2},{3,5},{4,8},{6,7}}=>[2,1,5,8,3,7,6,4]=>0100000=>0000010 {{1,2},{3,6},{4,8},{5,7}}=>[2,1,6,8,7,3,5,4]=>0100000=>0000010 {{1,3},{2,6},{4,8},{5,7}}=>[3,6,1,8,7,2,5,4]=>0000000=>0000000 {{1,4},{2,6},{3,8},{5,7}}=>[4,6,8,1,7,2,5,3]=>0000000=>0000000 {{1,5},{2,6},{3,8},{4,7}}=>[5,6,8,7,1,2,4,3]=>0000000=>0000000 {{1,6},{2,5},{3,8},{4,7}}=>[6,5,8,7,2,1,4,3]=>0000000=>0000000 {{1,7},{2,5},{3,8},{4,6}}=>[7,5,8,6,2,4,1,3]=>0000000=>0000000 {{1,8},{2,5},{3,7},{4,6}}=>[8,5,7,6,2,4,3,1]=>0000000=>0000000 {{1,8},{2,6},{3,7},{4,5}}=>[8,6,7,5,4,2,3,1]=>0000000=>0000000 {{1,7},{2,6},{3,8},{4,5}}=>[7,6,8,5,4,2,1,3]=>0000000=>0000000 {{1,6},{2,7},{3,8},{4,5}}=>[6,7,8,5,4,1,2,3]=>0000000=>0000000 {{1,5},{2,7},{3,8},{4,6}}=>[5,7,8,6,1,4,2,3]=>0000000=>0000000 {{1,4},{2,7},{3,8},{5,6}}=>[4,7,8,1,6,5,2,3]=>0000000=>0000000 {{1,3},{2,7},{4,8},{5,6}}=>[3,7,1,8,6,5,2,4]=>0000000=>0000000 {{1,2},{3,7},{4,8},{5,6}}=>[2,1,7,8,6,5,3,4]=>0100000=>0000010 {{1,2},{3,8},{4,7},{5,6}}=>[2,1,8,7,6,5,4,3]=>0100000=>0000010 {{1,3},{2,8},{4,7},{5,6}}=>[3,8,1,7,6,5,4,2]=>0000000=>0000000 {{1,4},{2,8},{3,7},{5,6}}=>[4,8,7,1,6,5,3,2]=>0000000=>0000000 {{1,5},{2,8},{3,7},{4,6}}=>[5,8,7,6,1,4,3,2]=>0000000=>0000000 {{1,6},{2,8},{3,7},{4,5}}=>[6,8,7,5,4,1,3,2]=>0000000=>0000000 {{1,7},{2,8},{3,6},{4,5}}=>[7,8,6,5,4,3,1,2]=>0000000=>0000000 {{1,8},{2,7},{3,6},{4,5}}=>[8,7,6,5,4,3,2,1]=>0000000=>0000000 {{1},{2},{3},{4},{5},{6},{7},{8}}=>[1,2,3,4,5,6,7,8]=>1111111=>1111111 {{1},{2},{3},{4},{5,8},{6,7}}=>[1,2,3,4,8,7,6,5]=>1111000=>0001111 {{1},{2},{3},{4,5,6,7,8}}=>[1,2,3,5,6,7,8,4]=>1110000=>0000111 {{1},{2},{3,4},{5,8},{6,7}}=>[1,2,4,3,8,7,6,5]=>1101000=>0001011 {{1},{2,3},{4},{5,8},{6,7}}=>[1,3,2,4,8,7,6,5]=>1011000=>0001101 {{1},{2,4},{3},{5,8},{6,7}}=>[1,4,3,2,8,7,6,5]=>1001000=>0001001 {{1},{2,4,6,8},{3},{5},{7}}=>[1,4,3,6,5,8,7,2]=>1000000=>0000001 {{1},{2,4,8},{3},{5,6,7}}=>[1,4,3,8,6,7,5,2]=>1000000=>0000001 {{1},{2,3,4},{5,8},{6,7}}=>[1,3,4,2,8,7,6,5]=>1001000=>0001001 {{1},{2,6,8},{3,4,5},{7}}=>[1,6,4,5,3,8,7,2]=>1000000=>0000001 {{1},{2,8},{3,4,5,6,7}}=>[1,8,4,5,6,7,3,2]=>1000000=>0000001 {{1,2},{3},{4},{5},{6},{7},{8}}=>[2,1,3,4,5,6,7,8]=>0111111=>1111110 {{1,2},{3},{4},{5,8},{6,7}}=>[2,1,3,4,8,7,6,5]=>0111000=>0001110 {{1,2},{3,4},{5},{6},{7},{8}}=>[2,1,4,3,5,6,7,8]=>0101111=>1111010 {{1,2},{3,4},{5,6},{7},{8}}=>[2,1,4,3,6,5,7,8]=>0101011=>1101010 {{1,2},{3,4},{5,6,8},{7}}=>[2,1,4,3,6,8,7,5]=>0101000=>0001010 {{1,2},{3,4,6,8},{5},{7}}=>[2,1,4,6,5,8,7,3]=>0100000=>0000010 {{1,2},{3,4,5,6},{7,8}}=>[2,1,4,5,6,3,8,7]=>0100010=>0100010 {{1,2},{3,4,5,6,8},{7}}=>[2,1,4,5,6,8,7,3]=>0100000=>0000010 {{1,3},{2},{4},{5},{6},{7},{8}}=>[3,2,1,4,5,6,7,8]=>0011111=>1111100 {{1,3},{2},{4},{5,8},{6,7}}=>[3,2,1,4,8,7,6,5]=>0011000=>0001100 {{1,3},{2},{4,5,6,7,8}}=>[3,2,1,5,6,7,8,4]=>0010000=>0000100 {{1,4},{2},{3},{5,8},{6,7}}=>[4,2,3,1,8,7,6,5]=>0001000=>0001000 {{1,5},{2},{3},{4},{6},{7},{8}}=>[5,2,3,4,1,6,7,8]=>0000111=>1110000 {{1,3,4},{2},{5,6},{7,8}}=>[3,2,4,1,6,5,8,7]=>0001010=>0101000 {{1,3,4},{2},{5,8},{6,7}}=>[3,2,4,1,8,7,6,5]=>0001000=>0001000 {{1,3,5},{2},{4},{6},{7},{8}}=>[3,2,5,4,1,6,7,8]=>0000111=>1110000 {{1,3,5},{2},{4},{6,7,8}}=>[3,2,5,4,1,7,8,6]=>0000100=>0010000 {{1,3,5,7},{2},{4},{6},{8}}=>[3,2,5,4,7,6,1,8]=>0000001=>1000000 {{1,3,7},{2},{4,5,6},{8}}=>[3,2,7,5,6,4,1,8]=>0000001=>1000000 {{1,2,3},{4},{5},{6},{7},{8}}=>[2,3,1,4,5,6,7,8]=>0011111=>1111100 {{1,2,3},{4},{5,8},{6,7}}=>[2,3,1,4,8,7,6,5]=>0011000=>0001100 {{1,2,3},{4,5},{6,7},{8}}=>[2,3,1,5,4,7,6,8]=>0010101=>1010100 {{1,2,3},{4,6,8},{5},{7}}=>[2,3,1,6,5,8,7,4]=>0010000=>0000100 {{1,2,3},{4,8},{5,6,7}}=>[2,3,1,8,6,7,5,4]=>0010000=>0000100 {{1,2,3},{4,5,6,7,8}}=>[2,3,1,5,6,7,8,4]=>0010000=>0000100 {{1,4},{2,3},{5},{6},{7},{8}}=>[4,3,2,1,5,6,7,8]=>0001111=>1111000 {{1,4},{2,3},{5},{6},{7,8}}=>[4,3,2,1,5,6,8,7]=>0001110=>0111000 {{1,4},{2,3},{5},{6,7},{8}}=>[4,3,2,1,5,7,6,8]=>0001101=>1011000 {{1,4},{2,3},{5},{6,8},{7}}=>[4,3,2,1,5,8,7,6]=>0001100=>0011000 {{1,4},{2,3},{5},{6,7,8}}=>[4,3,2,1,5,7,8,6]=>0001100=>0011000 {{1,4},{2,3},{5,6},{7},{8}}=>[4,3,2,1,6,5,7,8]=>0001011=>1101000 {{1,4},{2,3},{5,7},{6},{8}}=>[4,3,2,1,7,6,5,8]=>0001001=>1001000 {{1,4},{2,3},{5,8},{6},{7}}=>[4,3,2,1,8,6,7,5]=>0001000=>0001000 {{1,4},{2,3},{5,7,8},{6}}=>[4,3,2,1,7,6,8,5]=>0001000=>0001000 {{1,4},{2,3},{5,6,7},{8}}=>[4,3,2,1,6,7,5,8]=>0001001=>1001000 {{1,4},{2,3},{5,6,8},{7}}=>[4,3,2,1,6,8,7,5]=>0001000=>0001000 {{1,4},{2,3},{5,6,7,8}}=>[4,3,2,1,6,7,8,5]=>0001000=>0001000 {{1,4,6,8},{2,3},{5},{7}}=>[4,3,2,6,5,8,7,1]=>0000000=>0000000 {{1,4,6,7,8},{2,3},{5}}=>[4,3,2,6,5,7,8,1]=>0000000=>0000000 {{1,4,8},{2,3},{5,6,7}}=>[4,3,2,8,6,7,5,1]=>0000000=>0000000 {{1,4,5,8},{2,3},{6,7}}=>[4,3,2,5,8,7,6,1]=>0000000=>0000000 {{1,4,5,6,8},{2,3},{7}}=>[4,3,2,5,6,8,7,1]=>0000000=>0000000 {{1,2,4},{3},{5,8},{6,7}}=>[2,4,3,1,8,7,6,5]=>0001000=>0001000 {{1,2,4,6,8},{3},{5},{7}}=>[2,4,3,6,5,8,7,1]=>0000000=>0000000 {{1,2,4,6,7,8},{3},{5}}=>[2,4,3,6,5,7,8,1]=>0000000=>0000000 {{1,2,4,5,7,8},{3},{6}}=>[2,4,3,5,7,6,8,1]=>0000000=>0000000 {{1,2,4,5,6,8},{3},{7}}=>[2,4,3,5,6,8,7,1]=>0000000=>0000000 {{1,2,4,5,6,7,8},{3}}=>[2,4,3,5,6,7,8,1]=>0000000=>0000000 {{1,2,3,4},{5},{6},{7},{8}}=>[2,3,4,1,5,6,7,8]=>0001111=>1111000 {{1,2,3,4},{5,8},{6,7}}=>[2,3,4,1,8,7,6,5]=>0001000=>0001000 {{1,2,3,4},{5,6,7,8}}=>[2,3,4,1,6,7,8,5]=>0001000=>0001000 {{1,5},{2,3,4},{6,7,8}}=>[5,3,4,2,1,7,8,6]=>0000100=>0010000 {{1,5,7},{2,3,4},{6},{8}}=>[5,3,4,2,7,6,1,8]=>0000001=>1000000 {{1,6,8},{2,5},{3,4},{7}}=>[6,5,4,3,2,8,7,1]=>0000000=>0000000 {{1,6,7,8},{2,5},{3,4}}=>[6,5,4,3,2,7,8,1]=>0000000=>0000000 {{1,2,5,6,7,8},{3,4}}=>[2,5,4,3,6,7,8,1]=>0000000=>0000000 {{1,2,3,7,8},{4},{5},{6}}=>[2,3,7,4,5,6,8,1]=>0000000=>0000000 {{1,2,3,6,7,8},{4},{5}}=>[2,3,6,4,5,7,8,1]=>0000000=>0000000 {{1,2,3,4,5},{6},{7},{8}}=>[2,3,4,5,1,6,7,8]=>0000111=>1110000 {{1,2,3,4,5},{6,8},{7}}=>[2,3,4,5,1,8,7,6]=>0000100=>0010000 {{1,2,6,7,8},{3,4,5}}=>[2,6,4,5,3,7,8,1]=>0000000=>0000000 {{1,2,3,6,7,8},{4,5}}=>[2,3,6,5,4,7,8,1]=>0000000=>0000000 {{1,2,8},{3,7},{4,6},{5}}=>[2,8,7,6,5,4,3,1]=>0000000=>0000000 {{1,2,3,4,6,8},{5},{7}}=>[2,3,4,6,5,8,7,1]=>0000000=>0000000 {{1,2,3,4,6,7,8},{5}}=>[2,3,4,6,5,7,8,1]=>0000000=>0000000 {{1,7},{2,3,4,5,6},{8}}=>[7,3,4,5,6,2,1,8]=>0000001=>1000000 {{1,2,8},{3,7},{4,5,6}}=>[2,8,7,5,6,4,3,1]=>0000000=>0000000 {{1,2,3,7,8},{4,5,6}}=>[2,3,7,5,6,4,8,1]=>0000000=>0000000 {{1,2,3,8},{4,7},{5,6}}=>[2,3,8,7,6,5,4,1]=>0000000=>0000000 {{1,2,3,4,8},{5,7},{6}}=>[2,3,4,8,7,6,5,1]=>0000000=>0000000 {{1,2,3,4,5,6,8},{7}}=>[2,3,4,5,6,8,7,1]=>0000000=>0000000 {{1,2,3,4,5,6,7,8}}=>[2,3,4,5,6,7,8,1]=>0000000=>0000000 {{1,3,5,7},{2},{4},{6,8}}=>[3,2,5,4,7,8,1,6]=>0000000=>0000000 {{1,2,5,7},{3},{4,8},{6}}=>[2,5,3,8,7,6,1,4]=>0000000=>0000000 {{1,7},{2,3,8},{4,5},{6}}=>[7,3,8,5,4,6,1,2]=>0000000=>0000000 {{1},{2,5},{3,4,8},{6,7}}=>[1,5,4,8,2,7,6,3]=>1000000=>0000001 {{1,4,8},{2,3,7},{5},{6}}=>[4,3,7,8,5,6,2,1]=>0000000=>0000000 {{1,2,4},{3,7,8},{5},{6}}=>[2,4,7,1,5,6,8,3]=>0000000=>0000000 {{1,7},{2,4,5},{3,8},{6}}=>[7,4,8,5,2,6,1,3]=>0000000=>0000000 {{1,3,5},{2,7},{4,8},{6}}=>[3,7,5,8,1,6,2,4]=>0000000=>0000000 {{1,5},{2,3,7},{4,8},{6}}=>[5,3,7,8,1,6,2,4]=>0000000=>0000000 {{1,4,8},{2,3,6},{5},{7}}=>[4,3,6,8,5,2,7,1]=>0000000=>0000000 {{1,6},{2,3,5},{4,8},{7}}=>[6,3,5,8,2,1,7,4]=>0000000=>0000000 {{1,2,6},{3,5},{4,8},{7}}=>[2,6,5,8,3,1,7,4]=>0000000=>0000000 {{1,3,7},{2,6},{4,8},{5}}=>[3,6,7,8,5,2,1,4]=>0000000=>0000000 {{1,7},{2,4,8},{3,5},{6}}=>[7,4,5,8,3,6,1,2]=>0000000=>0000000 {{1,3},{2},{4,6,8},{5,7}}=>[3,2,1,6,7,8,5,4]=>0010000=>0000100 {{1,3,6},{2},{4,7},{5,8}}=>[3,2,6,7,8,1,4,5]=>0000000=>0000000 {{1,3,5},{2},{4,7},{6,8}}=>[3,2,5,7,1,8,4,6]=>0000000=>0000000 {{1,5,7},{2,4,8},{3},{6}}=>[5,4,3,8,7,6,1,2]=>0000000=>0000000 {{1,3,7},{2,5},{4,6},{8}}=>[3,5,7,6,2,4,1,8]=>0000001=>1000000 {{1,3,5},{2,4},{6,8},{7}}=>[3,4,5,2,1,8,7,6]=>0000100=>0010000 {{1,5,7},{2,3,8},{4},{6}}=>[5,3,8,4,7,6,1,2]=>0000000=>0000000 {{1,2,5,7},{3,8},{4},{6}}=>[2,5,8,4,7,6,1,3]=>0000000=>0000000 {{1,6,7},{2,5,8},{3},{4}}=>[6,5,3,4,8,7,1,2]=>0000000=>0000000 {{1,7,8},{2,5},{3},{4,6}}=>[7,5,3,6,2,4,8,1]=>0000000=>0000000 {{1,6},{2,4,7,8},{3},{5}}=>[6,4,3,7,5,1,8,2]=>0000000=>0000000 {{1,6},{2},{3,4,8},{5,7}}=>[6,2,4,8,7,1,5,3]=>0000000=>0000000 {{1,4,7,8},{2},{3,6},{5}}=>[4,2,6,7,5,3,8,1]=>0000000=>0000000 {{1,3},{2,5,8},{4,7},{6}}=>[3,5,1,7,8,6,4,2]=>0000000=>0000000 {{1,4},{2,6},{3,5,7},{8}}=>[4,6,5,1,7,2,3,8]=>0000001=>1000000 {{1,3,7},{2,5,8},{4},{6}}=>[3,5,7,4,8,6,1,2]=>0000000=>0000000 {{1,6},{2,4,5,8},{3},{7}}=>[6,4,3,5,8,1,7,2]=>0000000=>0000000 {{1,5},{2,7},{3},{4,6,8}}=>[5,7,3,6,1,8,2,4]=>0000000=>0000000 {{1,5},{2,6,7},{3},{4,8}}=>[5,6,3,8,1,7,2,4]=>0000000=>0000000 {{1,3,7},{2,5},{4},{6,8}}=>[3,5,7,4,2,8,1,6]=>0000000=>0000000 {{1,4},{2,5,7},{3},{6,8}}=>[4,5,3,1,7,8,2,6]=>0000000=>0000000 {{1,5},{2,6},{3,7},{4},{8}}=>[5,6,7,4,1,2,3,8]=>0000001=>1000000 {{1},{2,6},{3,7},{4,8},{5}}=>[1,6,7,8,5,2,3,4]=>1000000=>0000001 {{1,4,6,7},{2,3,5,8}}=>[4,3,5,6,8,7,1,2]=>0000000=>0000000 {{1,3,5,7},{2,4,6,8}}=>[3,4,5,6,7,8,1,2]=>0000000=>0000000 {{1,3,4,7},{2,5,6,8}}=>[3,5,4,7,6,8,1,2]=>0000000=>0000000 {{1,3,7},{2,6,8},{4},{5}}=>[3,6,7,4,5,8,1,2]=>0000000=>0000000 {{1},{2,6},{3,7},{4},{5},{8}}=>[1,6,7,4,5,2,3,8]=>1000001=>1000001 {{1,2,5,6},{3,4,7,8}}=>[2,5,4,7,6,1,8,3]=>0000000=>0000000 {{1,5,6,7},{2,3,4,8}}=>[5,3,4,8,6,7,1,2]=>0000000=>0000000 {{1,6,7},{2,3,8},{4},{5}}=>[6,3,8,4,5,7,1,2]=>0000000=>0000000 {{1,2,4,6},{3,5,7,8}}=>[2,4,5,6,7,1,8,3]=>0000000=>0000000 {{1,2,3,5},{4,6,7,8}}=>[2,3,5,6,1,7,8,4]=>0000000=>0000000 {{1,5},{2},{3},{4,8},{6},{7}}=>[5,2,3,8,1,6,7,4]=>0000000=>0000000 {{1,5},{2,3},{4,7,8},{6}}=>[5,3,2,7,1,6,8,4]=>0000000=>0000000 {{1},{2,5},{3},{4,8},{6,7}}=>[1,5,3,8,2,7,6,4]=>1000000=>0000001 {{1,4,7,8},{2,6},{3},{5}}=>[4,6,3,7,5,2,8,1]=>0000000=>0000000 {{1,3,5},{2},{4,8},{6,7}}=>[3,2,5,8,1,7,6,4]=>0000000=>0000000 {{1,3,6,8},{2,7},{4},{5}}=>[3,7,6,4,5,8,2,1]=>0000000=>0000000 {{1,6},{2,4},{3,7,8},{5}}=>[6,4,7,2,5,1,8,3]=>0000000=>0000000 {{1},{2,3,5},{4,8},{6,7}}=>[1,3,5,8,2,7,6,4]=>1000000=>0000001 {{1,4,7},{2},{3,6},{5,8}}=>[4,2,6,7,8,3,1,5]=>0000000=>0000000 {{1,4,5,7},{2,3,6,8}}=>[4,3,6,5,7,8,1,2]=>0000000=>0000000 {{1,7},{2,5},{3},{4,8},{6}}=>[7,5,3,8,2,6,1,4]=>0000000=>0000000 {{1,5},{2,3},{4,6},{7},{8}}=>[5,3,2,6,1,4,7,8]=>0000011=>1100000 {{1,2,3,4,6,7},{5,8}}=>[2,3,4,6,8,7,1,5]=>0000000=>0000000 {{1,2},{3,4,6,8},{5,7}}=>[2,1,4,6,7,8,5,3]=>0100000=>0000010 {{1,3,4,5,7,8},{2,6}}=>[3,6,4,5,7,2,8,1]=>0000000=>0000000 {{1,4},{2,3,5,7},{6,8}}=>[4,3,5,1,7,8,2,6]=>0000000=>0000000 {{1,3},{2,4,5,7},{6,8}}=>[3,4,1,5,7,8,2,6]=>0000000=>0000000 {{1,2,3,5,6,7},{4,8}}=>[2,3,5,8,6,7,1,4]=>0000000=>0000000 {{1,3,5,7},{2,6},{4,8}}=>[3,6,5,8,7,2,1,4]=>0000000=>0000000 {{1,2,3,6},{4,7},{5,8}}=>[2,3,6,7,8,1,4,5]=>0000000=>0000000 {{1,3},{2,4},{5,6,7,8}}=>[3,4,1,2,6,7,8,5]=>0001000=>0001000 {{1,2,4,5,6,8},{3,7}}=>[2,4,7,5,6,8,3,1]=>0000000=>0000000 {{1,3},{2,5},{4,6,7,8}}=>[3,5,1,6,2,7,8,4]=>0000000=>0000000 {{1,2},{3,5},{4,6,7,8}}=>[2,1,5,6,3,7,8,4]=>0100000=>0000010 {{1,5},{2,4,6,8},{3,7}}=>[5,4,7,6,1,8,3,2]=>0000000=>0000000 {{1,4,5,8},{2,3,6,7}}=>[4,3,6,5,8,7,2,1]=>0000000=>0000000 {{1,6},{2,4},{3,7},{5},{8}}=>[6,4,7,2,5,1,3,8]=>0000001=>1000000 {{1,5,6},{2,3,4,7,8}}=>[5,3,4,7,6,1,8,2]=>0000000=>0000000 {{1,7},{2,8},{3,4},{5},{6}}=>[7,8,4,3,5,6,1,2]=>0000000=>0000000 {{1,5,6,7},{2,4,8},{3}}=>[5,4,3,8,6,7,1,2]=>0000000=>0000000 {{1,5,7},{2,4,6,8},{3}}=>[5,4,3,6,7,8,1,2]=>0000000=>0000000 {{1,5},{2,3},{4,6,7},{8}}=>[5,3,2,6,1,7,4,8]=>0000001=>1000000 {{1,5},{2,3},{4,6,7,8}}=>[5,3,2,6,1,7,8,4]=>0000000=>0000000 {{1,5},{2,3},{4,6,8},{7}}=>[5,3,2,6,1,8,7,4]=>0000000=>0000000 {{1,6},{2,4},{3,8},{5},{7}}=>[6,4,8,2,5,1,7,3]=>0000000=>0000000 {{1,5},{2,3},{4,8},{6},{7}}=>[5,3,2,8,1,6,7,4]=>0000000=>0000000 {{1,5},{2,3},{4,7},{6},{8}}=>[5,3,2,7,1,6,4,8]=>0000001=>1000000 {{1,2,6},{3,8},{4},{5,7}}=>[2,6,8,4,7,1,5,3]=>0000000=>0000000 {{1},{2,6},{3,8},{4},{5,7}}=>[1,6,8,4,7,2,5,3]=>1000000=>0000001 {{1},{2,5,6,7},{3,4,8}}=>[1,5,4,8,6,7,2,3]=>1000000=>0000001 {{1,7},{2,8},{3},{4},{5,6}}=>[7,8,3,4,6,5,1,2]=>0000000=>0000000 {{1,5,7},{2,3,4,8},{6}}=>[5,3,4,8,7,6,1,2]=>0000000=>0000000 {{1,3,5,7},{2,4,8},{6}}=>[3,4,5,8,7,6,1,2]=>0000000=>0000000 {{1,2,3,5},{4,8},{6,7}}=>[2,3,5,8,1,7,6,4]=>0000000=>0000000 {{1,6},{2},{3,8},{4},{5,7}}=>[6,2,8,4,7,1,5,3]=>0000000=>0000000 {{1},{2},{3,5},{4,8},{6,7}}=>[1,2,5,8,3,7,6,4]=>1100000=>0000011 {{1,2,5},{3},{4,8},{6,7}}=>[2,5,3,8,1,7,6,4]=>0000000=>0000000 {{1,5},{2},{3},{4,8},{6,7}}=>[5,2,3,8,1,7,6,4]=>0000000=>0000000 {{1,2,4,5,7,8},{3,6}}=>[2,4,6,5,7,3,8,1]=>0000000=>0000000 {{1,2,3,6,7},{4,5,8}}=>[2,3,6,5,8,7,1,4]=>0000000=>0000000 {{1,2,3,7},{4,5,6,8}}=>[2,3,7,5,6,8,1,4]=>0000000=>0000000 {{1,2,6},{3,4,5,8},{7}}=>[2,6,4,5,8,1,7,3]=>0000000=>0000000 {{1,3,5,6},{2,4,8},{7}}=>[3,4,5,8,6,1,7,2]=>0000000=>0000000 {{1,2,4,8},{3,5},{6,7}}=>[2,4,5,8,3,7,6,1]=>0000000=>0000000 {{1,3,4},{2,5,6,7,8}}=>[3,5,4,1,6,7,8,2]=>0000000=>0000000 {{1,3,8},{2,4,6,7},{5}}=>[3,4,8,6,5,7,2,1]=>0000000=>0000000 {{1,3,5},{2,8},{4,6,7}}=>[3,8,5,6,1,7,4,2]=>0000000=>0000000 {{1,4,7,8},{2,3,6},{5}}=>[4,3,6,7,5,2,8,1]=>0000000=>0000000 {{1,2,6},{3,5},{4,7,8}}=>[2,6,5,7,3,1,8,4]=>0000000=>0000000 {{1,4,7,8},{2,6},{3,5}}=>[4,6,5,7,3,2,8,1]=>0000000=>0000000 {{1,3,6,8},{2,4,5,7}}=>[3,4,6,5,7,8,2,1]=>0000000=>0000000 {{1,6},{2,5,7,8},{3,4}}=>[6,5,4,3,7,1,8,2]=>0000000=>0000000 {{1,5,7},{2,3,6,8},{4}}=>[5,3,6,4,7,8,1,2]=>0000000=>0000000 {{1,3,7},{2,4,5,8},{6}}=>[3,4,7,5,8,6,1,2]=>0000000=>0000000 {{1,6,7},{2,3,4,5,8}}=>[6,3,4,5,8,7,1,2]=>0000000=>0000000 {{1,7},{2,3,4},{5,6,8}}=>[7,3,4,2,6,8,1,5]=>0000000=>0000000 {{1,2,4,5},{3,7,8},{6}}=>[2,4,7,5,1,6,8,3]=>0000000=>0000000 {{1,4,8},{2,3,6,7},{5}}=>[4,3,6,8,5,7,2,1]=>0000000=>0000000 {{1,2,3},{4,7},{5,6,8}}=>[2,3,1,7,6,8,4,5]=>0010000=>0000100 {{1,2,5,8},{3,6,7},{4}}=>[2,5,6,4,8,7,3,1]=>0000000=>0000000 {{1,3,5},{2},{4,6},{7},{8}}=>[3,2,5,6,1,4,7,8]=>0000011=>1100000 {{1,3},{2,4},{5},{6},{7},{8}}=>[3,4,1,2,5,6,7,8]=>0001111=>1111000 {{1,3,7},{2},{4},{5},{6,8}}=>[3,2,7,4,5,8,1,6]=>0000000=>0000000 {{1,3,6},{2},{4},{5,8},{7}}=>[3,2,6,4,8,1,7,5]=>0000000=>0000000 {{1},{2},{3},{4,7},{5,8},{6}}=>[1,2,3,7,8,6,4,5]=>1110000=>0000111 {{1},{2},{3,7},{4,8},{5},{6}}=>[1,2,7,8,5,6,3,4]=>1100000=>0000011 {{1,4,7},{2,5},{3},{6},{8}}=>[4,5,3,7,2,6,1,8]=>0000001=>1000000 {{1,5},{2,6},{3},{4},{7},{8}}=>[5,6,3,4,1,2,7,8]=>0000011=>1100000 {{1,3},{2,6},{4,7},{5},{8}}=>[3,6,1,7,5,2,4,8]=>0000001=>1000000 {{1,3},{2,5},{4,6},{7},{8}}=>[3,5,1,6,2,4,7,8]=>0000011=>1100000 {{1,3,5},{2,4},{6},{7},{8}}=>[3,4,5,2,1,6,7,8]=>0000111=>1110000 {{1,5},{2},{3},{4,6},{7},{8}}=>[5,2,3,6,1,4,7,8]=>0000011=>1100000 {{1,4},{2},{3,6},{5},{7},{8}}=>[4,2,6,1,5,3,7,8]=>0000011=>1100000 {{1},{2,5},{3,6},{4},{7},{8}}=>[1,5,6,4,2,3,7,8]=>1000011=>1100001 {{1,4,6},{2},{3,5,7},{8}}=>[4,2,5,6,7,1,3,8]=>0000001=>1000000 {{1,6},{2},{3},{4,7},{5},{8}}=>[6,2,3,7,5,1,4,8]=>0000001=>1000000 {{1,6},{2},{3},{4,7},{5,8}}=>[6,2,3,7,8,1,4,5]=>0000000=>0000000 {{1,4,7},{2},{3,6},{5},{8}}=>[4,2,6,7,5,3,1,8]=>0000001=>1000000 {{1},{2,6},{3},{4,8},{5},{7}}=>[1,6,3,8,5,2,7,4]=>1000000=>0000001 {{1,4,7},{2,3,5,6},{8}}=>[4,3,5,7,6,2,1,8]=>0000001=>1000000 {{1,3,5,7},{2},{4,6,8}}=>[3,2,5,6,7,8,1,4]=>0000000=>0000000 {{1,7},{2,3,5,6},{4,8}}=>[7,3,5,8,6,2,1,4]=>0000000=>0000000 {{1,5,6,8},{2,3},{4,7}}=>[5,3,2,7,6,8,4,1]=>0000000=>0000000 {{1,4,7,8},{2},{3,5},{6}}=>[4,2,5,7,3,6,8,1]=>0000000=>0000000 {{1,4,7},{2,3,5,6,8}}=>[4,3,5,7,6,8,1,2]=>0000000=>0000000 {{1},{2,4,6},{3},{5,7,8}}=>[1,4,3,6,7,2,8,5]=>1000000=>0000001 {{1,2,4,5,7},{3},{6,8}}=>[2,4,3,5,7,8,1,6]=>0000000=>0000000 {{1,6,7},{2,4,5,8},{3}}=>[6,4,3,5,8,7,1,2]=>0000000=>0000000 {{1},{2,5,7},{3},{4,6,8}}=>[1,5,3,6,7,8,2,4]=>1000000=>0000001 {{1},{2,3,5,7},{4,6,8}}=>[1,3,5,6,7,8,2,4]=>1000000=>0000001 {{1,2,3,5,7},{4,6,8}}=>[2,3,5,6,7,8,1,4]=>0000000=>0000000 {{1,2},{3,5,7},{4,6,8}}=>[2,1,5,6,7,8,3,4]=>0100000=>0000010 {{1,3,4,5,7},{2},{6,8}}=>[3,2,4,5,7,8,1,6]=>0000000=>0000000 {{1,2,4,6,8},{3,7},{5}}=>[2,4,7,6,5,8,3,1]=>0000000=>0000000 {{1,5,6},{2,4,7},{3,8}}=>[5,4,8,7,6,1,2,3]=>0000000=>0000000 {{1,3,6,7},{2,4,8},{5}}=>[3,4,6,8,5,7,1,2]=>0000000=>0000000 {{1,3,7},{2,4},{5,6,8}}=>[3,4,7,2,6,8,1,5]=>0000000=>0000000 {{1,2,5},{3,4,6,7,8}}=>[2,5,4,6,1,7,8,3]=>0000000=>0000000 {{1,2},{3,5,7,8},{4,6}}=>[2,1,5,6,7,4,8,3]=>0100000=>0000010 {{1,5,8},{2,7},{3,4,6}}=>[5,7,4,6,8,3,2,1]=>0000000=>0000000 {{1,6,8},{2,5,7},{3,4}}=>[6,5,4,3,7,8,2,1]=>0000000=>0000000 {{1,3,4},{2,8},{5,6,7}}=>[3,8,4,1,6,7,5,2]=>0000000=>0000000 {{1,4,5},{2,7,8},{3,6}}=>[4,7,6,5,1,3,8,2]=>0000000=>0000000 {{1,7},{2,6},{3,4,5,8}}=>[7,6,4,5,8,2,1,3]=>0000000=>0000000 {{1,4,5,8},{2,6},{3},{7}}=>[4,6,3,5,8,2,7,1]=>0000000=>0000000 {{1,4},{2,3,6,8},{5,7}}=>[4,3,6,1,7,8,5,2]=>0000000=>0000000 {{1,4,5},{2,3,6,7,8}}=>[4,3,6,5,1,7,8,2]=>0000000=>0000000 {{1,4,7},{2,3,8},{5,6}}=>[4,3,8,7,6,5,1,2]=>0000000=>0000000 {{1,2,6},{3,4,8},{5,7}}=>[2,6,4,8,7,1,5,3]=>0000000=>0000000 {{1,5,6},{2,4},{3,7,8}}=>[5,4,7,2,6,1,8,3]=>0000000=>0000000 {{1,6,7},{2,3},{4,5,8}}=>[6,3,2,5,8,7,1,4]=>0000000=>0000000 {{1,6,7},{2,5,8},{3,4}}=>[6,5,4,3,8,7,1,2]=>0000000=>0000000 {{1,4,5},{2},{3,6,8},{7}}=>[4,2,6,5,1,8,7,3]=>0000000=>0000000 {{1,4,8},{2},{3,6},{5},{7}}=>[4,2,6,8,5,3,7,1]=>0000000=>0000000 {{1,2,4},{3,6},{5,7,8}}=>[2,4,6,1,7,3,8,5]=>0000000=>0000000 {{1,3,5},{2,7,8},{4,6}}=>[3,7,5,6,1,4,8,2]=>0000000=>0000000 {{1,3,4},{2,6,8},{5,7}}=>[3,6,4,1,7,8,5,2]=>0000000=>0000000 {{1,4,5,6},{2},{3,7,8}}=>[4,2,7,5,6,1,8,3]=>0000000=>0000000 {{1,4,7},{2,5,8},{3,6}}=>[4,5,6,7,8,3,1,2]=>0000000=>0000000 {{1,5,7},{2,3,4,6,8}}=>[5,3,4,6,7,8,1,2]=>0000000=>0000000 {{1},{2,3,4,6,8},{5,7}}=>[1,3,4,6,7,8,5,2]=>1000000=>0000001 {{1,3,5},{2,4,6,7,8}}=>[3,4,5,6,1,7,8,2]=>0000000=>0000000 {{1,3,6},{2,5,8},{4,7}}=>[3,5,6,7,8,1,4,2]=>0000000=>0000000 {{1,2,6,8},{3,5,7},{4}}=>[2,6,5,4,7,8,3,1]=>0000000=>0000000 {{1,3,4,6,7},{2,5},{8}}=>[3,5,4,6,2,7,1,8]=>0000001=>1000000 {{1,2,3,5,7},{4,6},{8}}=>[2,3,5,6,7,4,1,8]=>0000001=>1000000 {{1,3,5,6,7},{2,4,8}}=>[3,4,5,8,6,7,1,2]=>0000000=>0000000 {{1,3,4,5},{2,6,7,8}}=>[3,6,4,5,1,7,8,2]=>0000000=>0000000 {{1,3,4,8},{2,6,7},{5}}=>[3,6,4,8,5,7,2,1]=>0000000=>0000000 {{1,6},{2,8},{3},{4},{5},{7}}=>[6,8,3,4,5,1,7,2]=>0000000=>0000000
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.
Map
reverse
Description
Return the reversal of a binary word.