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Identifier
Values
=>
Cc0009;cc-rep
{{1}}=>0 {{1,2}}=>0 {{1},{2}}=>0 {{1,2,3}}=>0 {{1,2},{3}}=>0 {{1,3},{2}}=>1 {{1},{2,3}}=>0 {{1},{2},{3}}=>0 {{1,2,3,4}}=>0 {{1,2,3},{4}}=>0 {{1,2,4},{3}}=>2 {{1,2},{3,4}}=>0 {{1,2},{3},{4}}=>0 {{1,3,4},{2}}=>1 {{1,3},{2,4}}=>2 {{1,3},{2},{4}}=>1 {{1,4},{2,3}}=>1 {{1},{2,3,4}}=>0 {{1},{2,3},{4}}=>0 {{1,4},{2},{3}}=>2 {{1},{2,4},{3}}=>1 {{1},{2},{3,4}}=>0 {{1},{2},{3},{4}}=>0 {{1,2,3,4,5}}=>0 {{1,2,3,4},{5}}=>0 {{1,2,3,5},{4}}=>3 {{1,2,3},{4,5}}=>0 {{1,2,3},{4},{5}}=>0 {{1,2,4,5},{3}}=>2 {{1,2,4},{3,5}}=>3 {{1,2,4},{3},{5}}=>2 {{1,2,5},{3,4}}=>2 {{1,2},{3,4,5}}=>0 {{1,2},{3,4},{5}}=>0 {{1,2,5},{3},{4}}=>4 {{1,2},{3,5},{4}}=>1 {{1,2},{3},{4,5}}=>0 {{1,2},{3},{4},{5}}=>0 {{1,3,4,5},{2}}=>1 {{1,3,4},{2,5}}=>2 {{1,3,4},{2},{5}}=>1 {{1,3,5},{2,4}}=>4 {{1,3},{2,4,5}}=>2 {{1,3},{2,4},{5}}=>2 {{1,3,5},{2},{4}}=>3 {{1,3},{2,5},{4}}=>3 {{1,3},{2},{4,5}}=>1 {{1,3},{2},{4},{5}}=>1 {{1,4,5},{2,3}}=>1 {{1,4},{2,3,5}}=>3 {{1,4},{2,3},{5}}=>1 {{1,5},{2,3,4}}=>1 {{1},{2,3,4,5}}=>0 {{1},{2,3,4},{5}}=>0 {{1,5},{2,3},{4}}=>2 {{1},{2,3,5},{4}}=>2 {{1},{2,3},{4,5}}=>0 {{1},{2,3},{4},{5}}=>0 {{1,4,5},{2},{3}}=>2 {{1,4},{2,5},{3}}=>4 {{1,4},{2},{3,5}}=>3 {{1,4},{2},{3},{5}}=>2 {{1,5},{2,4},{3}}=>3 {{1},{2,4,5},{3}}=>1 {{1},{2,4},{3,5}}=>2 {{1},{2,4},{3},{5}}=>1 {{1,5},{2},{3,4}}=>2 {{1},{2,5},{3,4}}=>1 {{1},{2},{3,4,5}}=>0 {{1},{2},{3,4},{5}}=>0 {{1,5},{2},{3},{4}}=>3 {{1},{2,5},{3},{4}}=>2 {{1},{2},{3,5},{4}}=>1 {{1},{2},{3},{4,5}}=>0 {{1},{2},{3},{4},{5}}=>0 {{1,2,3,4,5,6}}=>0 {{1,2,3,4,5},{6}}=>0 {{1,2,3,4,6},{5}}=>4 {{1,2,3,4},{5,6}}=>0 {{1,2,3,4},{5},{6}}=>0 {{1,2,3,5,6},{4}}=>3 {{1,2,3,5},{4,6}}=>4 {{1,2,3,5},{4},{6}}=>3 {{1,2,3,6},{4,5}}=>3 {{1,2,3},{4,5,6}}=>0 {{1,2,3},{4,5},{6}}=>0 {{1,2,3,6},{4},{5}}=>6 {{1,2,3},{4,6},{5}}=>1 {{1,2,3},{4},{5,6}}=>0 {{1,2,3},{4},{5},{6}}=>0 {{1,2,4,5,6},{3}}=>2 {{1,2,4,5},{3,6}}=>3 {{1,2,4,5},{3},{6}}=>2 {{1,2,4,6},{3,5}}=>6 {{1,2,4},{3,5,6}}=>3 {{1,2,4},{3,5},{6}}=>3 {{1,2,4,6},{3},{5}}=>5 {{1,2,4},{3,6},{5}}=>4 {{1,2,4},{3},{5,6}}=>2 {{1,2,4},{3},{5},{6}}=>2 {{1,2,5,6},{3,4}}=>2 {{1,2,5},{3,4,6}}=>4 {{1,2,5},{3,4},{6}}=>2 {{1,2,6},{3,4,5}}=>2 {{1,2},{3,4,5,6}}=>0 {{1,2},{3,4,5},{6}}=>0 {{1,2,6},{3,4},{5}}=>4 {{1,2},{3,4,6},{5}}=>2 {{1,2},{3,4},{5,6}}=>0 {{1,2},{3,4},{5},{6}}=>0 {{1,2,5,6},{3},{4}}=>4 {{1,2,5},{3,6},{4}}=>6 {{1,2,5},{3},{4,6}}=>5 {{1,2,5},{3},{4},{6}}=>4 {{1,2,6},{3,5},{4}}=>5 {{1,2},{3,5,6},{4}}=>1 {{1,2},{3,5},{4,6}}=>2 {{1,2},{3,5},{4},{6}}=>1 {{1,2,6},{3},{4,5}}=>4 {{1,2},{3,6},{4,5}}=>1 {{1,2},{3},{4,5,6}}=>0 {{1,2},{3},{4,5},{6}}=>0 {{1,2,6},{3},{4},{5}}=>6 {{1,2},{3,6},{4},{5}}=>2 {{1,2},{3},{4,6},{5}}=>1 {{1,2},{3},{4},{5,6}}=>0 {{1,2},{3},{4},{5},{6}}=>0 {{1,3,4,5,6},{2}}=>1 {{1,3,4,5},{2,6}}=>2 {{1,3,4,5},{2},{6}}=>1 {{1,3,4,6},{2,5}}=>5 {{1,3,4},{2,5,6}}=>2 {{1,3,4},{2,5},{6}}=>2 {{1,3,4,6},{2},{5}}=>4 {{1,3,4},{2,6},{5}}=>3 {{1,3,4},{2},{5,6}}=>1 {{1,3,4},{2},{5},{6}}=>1 {{1,3,5,6},{2,4}}=>4 {{1,3,5},{2,4,6}}=>6 {{1,3,5},{2,4},{6}}=>4 {{1,3,6},{2,4,5}}=>4 {{1,3},{2,4,5,6}}=>2 {{1,3},{2,4,5},{6}}=>2 {{1,3,6},{2,4},{5}}=>6 {{1,3},{2,4,6},{5}}=>4 {{1,3},{2,4},{5,6}}=>2 {{1,3},{2,4},{5},{6}}=>2 {{1,3,5,6},{2},{4}}=>3 {{1,3,5},{2,6},{4}}=>5 {{1,3,5},{2},{4,6}}=>4 {{1,3,5},{2},{4},{6}}=>3 {{1,3,6},{2,5},{4}}=>7 {{1,3},{2,5,6},{4}}=>3 {{1,3},{2,5},{4,6}}=>4 {{1,3},{2,5},{4},{6}}=>3 {{1,3,6},{2},{4,5}}=>3 {{1,3},{2,6},{4,5}}=>3 {{1,3},{2},{4,5,6}}=>1 {{1,3},{2},{4,5},{6}}=>1 {{1,3,6},{2},{4},{5}}=>5 {{1,3},{2,6},{4},{5}}=>4 {{1,3},{2},{4,6},{5}}=>2 {{1,3},{2},{4},{5,6}}=>1 {{1,3},{2},{4},{5},{6}}=>1 {{1,4,5,6},{2,3}}=>1 {{1,4,5},{2,3,6}}=>3 {{1,4,5},{2,3},{6}}=>1 {{1,4,6},{2,3,5}}=>5 {{1,4},{2,3,5,6}}=>3 {{1,4},{2,3,5},{6}}=>3 {{1,4,6},{2,3},{5}}=>3 {{1,4},{2,3,6},{5}}=>5 {{1,4},{2,3},{5,6}}=>1 {{1,4},{2,3},{5},{6}}=>1 {{1,5,6},{2,3,4}}=>1 {{1,5},{2,3,4,6}}=>4 {{1,5},{2,3,4},{6}}=>1 {{1,6},{2,3,4,5}}=>1 {{1},{2,3,4,5,6}}=>0 {{1},{2,3,4,5},{6}}=>0 {{1,6},{2,3,4},{5}}=>2 {{1},{2,3,4,6},{5}}=>3 {{1},{2,3,4},{5,6}}=>0 {{1},{2,3,4},{5},{6}}=>0 {{1,5,6},{2,3},{4}}=>2 {{1,5},{2,3,6},{4}}=>6 {{1,5},{2,3},{4,6}}=>3 {{1,5},{2,3},{4},{6}}=>2 {{1,6},{2,3,5},{4}}=>4 {{1},{2,3,5,6},{4}}=>2 {{1},{2,3,5},{4,6}}=>3 {{1},{2,3,5},{4},{6}}=>2 {{1,6},{2,3},{4,5}}=>2 {{1},{2,3,6},{4,5}}=>2 {{1},{2,3},{4,5,6}}=>0 {{1},{2,3},{4,5},{6}}=>0 {{1,6},{2,3},{4},{5}}=>3 {{1},{2,3,6},{4},{5}}=>4 {{1},{2,3},{4,6},{5}}=>1 {{1},{2,3},{4},{5,6}}=>0 {{1},{2,3},{4},{5},{6}}=>0 {{1,4,5,6},{2},{3}}=>2 {{1,4,5},{2,6},{3}}=>4 {{1,4,5},{2},{3,6}}=>3 {{1,4,5},{2},{3},{6}}=>2 {{1,4,6},{2,5},{3}}=>6 {{1,4},{2,5,6},{3}}=>4 {{1,4},{2,5},{3,6}}=>6 {{1,4},{2,5},{3},{6}}=>4 {{1,4,6},{2},{3,5}}=>5 {{1,4},{2,6},{3,5}}=>5 {{1,4},{2},{3,5,6}}=>3 {{1,4},{2},{3,5},{6}}=>3 {{1,4,6},{2},{3},{5}}=>4 {{1,4},{2,6},{3},{5}}=>5 {{1,4},{2},{3,6},{5}}=>4 {{1,4},{2},{3},{5,6}}=>2 {{1,4},{2},{3},{5},{6}}=>2 {{1,5,6},{2,4},{3}}=>3 {{1,5},{2,4,6},{3}}=>5 {{1,5},{2,4},{3,6}}=>5 {{1,5},{2,4},{3},{6}}=>3 {{1,6},{2,4,5},{3}}=>3 {{1},{2,4,5,6},{3}}=>1 {{1},{2,4,5},{3,6}}=>2 {{1},{2,4,5},{3},{6}}=>1 {{1,6},{2,4},{3,5}}=>4 {{1},{2,4,6},{3,5}}=>4 {{1},{2,4},{3,5,6}}=>2 {{1},{2,4},{3,5},{6}}=>2 {{1,6},{2,4},{3},{5}}=>4 {{1},{2,4,6},{3},{5}}=>3 {{1},{2,4},{3,6},{5}}=>3 {{1},{2,4},{3},{5,6}}=>1 {{1},{2,4},{3},{5},{6}}=>1 {{1,5,6},{2},{3,4}}=>2 {{1,5},{2,6},{3,4}}=>4 {{1,5},{2},{3,4,6}}=>4 {{1,5},{2},{3,4},{6}}=>2 {{1,6},{2,5},{3,4}}=>3 {{1},{2,5,6},{3,4}}=>1 {{1},{2,5},{3,4,6}}=>3 {{1},{2,5},{3,4},{6}}=>1 {{1,6},{2},{3,4,5}}=>2 {{1},{2,6},{3,4,5}}=>1 {{1},{2},{3,4,5,6}}=>0 {{1},{2},{3,4,5},{6}}=>0 {{1,6},{2},{3,4},{5}}=>3 {{1},{2,6},{3,4},{5}}=>2 {{1},{2},{3,4,6},{5}}=>2 {{1},{2},{3,4},{5,6}}=>0 {{1},{2},{3,4},{5},{6}}=>0 {{1,5,6},{2},{3},{4}}=>3 {{1,5},{2,6},{3},{4}}=>6 {{1,5},{2},{3,6},{4}}=>5 {{1,5},{2},{3},{4,6}}=>4 {{1,5},{2},{3},{4},{6}}=>3 {{1,6},{2,5},{3},{4}}=>5 {{1},{2,5,6},{3},{4}}=>2 {{1},{2,5},{3,6},{4}}=>4 {{1},{2,5},{3},{4,6}}=>3 {{1},{2,5},{3},{4},{6}}=>2 {{1,6},{2},{3,5},{4}}=>4 {{1},{2,6},{3,5},{4}}=>3 {{1},{2},{3,5,6},{4}}=>1 {{1},{2},{3,5},{4,6}}=>2 {{1},{2},{3,5},{4},{6}}=>1 {{1,6},{2},{3},{4,5}}=>3 {{1},{2,6},{3},{4,5}}=>2 {{1},{2},{3,6},{4,5}}=>1 {{1},{2},{3},{4,5,6}}=>0 {{1},{2},{3},{4,5},{6}}=>0 {{1,6},{2},{3},{4},{5}}=>4 {{1},{2,6},{3},{4},{5}}=>3 {{1},{2},{3,6},{4},{5}}=>2 {{1},{2},{3},{4,6},{5}}=>1 {{1},{2},{3},{4},{5,6}}=>0 {{1},{2},{3},{4},{5},{6}}=>0 {{1,2,3,4,5,6,7}}=>0 {{1,2,3,4,5,6},{7}}=>0 {{1,2,3,4,5,7},{6}}=>5 {{1,2,3,4,5},{6,7}}=>0 {{1,2,3,4,5},{6},{7}}=>0 {{1,2,3,4,6,7},{5}}=>4 {{1,2,3,4,6},{5,7}}=>5 {{1,2,3,4,6},{5},{7}}=>4 {{1,2,3,4,7},{5,6}}=>4 {{1,2,3,4},{5,6,7}}=>0 {{1,2,3,4},{5,6},{7}}=>0 {{1,2,3,4,7},{5},{6}}=>8 {{1,2,3,4},{5,7},{6}}=>1 {{1,2,3,4},{5},{6,7}}=>0 {{1,2,3,4},{5},{6},{7}}=>0 {{1,2,3,5,6,7},{4}}=>3 {{1,2,3,5,6},{4,7}}=>4 {{1,2,3,5,6},{4},{7}}=>3 {{1,2,3,5,7},{4,6}}=>8 {{1,2,3,5},{4,6,7}}=>4 {{1,2,3,5},{4,6},{7}}=>4 {{1,2,3,5,7},{4},{6}}=>7 {{1,2,3,5},{4,7},{6}}=>5 {{1,2,3,5},{4},{6,7}}=>3 {{1,2,3,5},{4},{6},{7}}=>3 {{1,2,3,6,7},{4,5}}=>3 {{1,2,3,6},{4,5,7}}=>5 {{1,2,3,6},{4,5},{7}}=>3 {{1,2,3,7},{4,5,6}}=>3 {{1,2,3},{4,5,6,7}}=>0 {{1,2,3},{4,5,6},{7}}=>0 {{1,2,3,7},{4,5},{6}}=>6 {{1,2,3},{4,5,7},{6}}=>2 {{1,2,3},{4,5},{6,7}}=>0 {{1,2,3},{4,5},{6},{7}}=>0 {{1,2,3,6,7},{4},{5}}=>6 {{1,2,3,6},{4,7},{5}}=>8 {{1,2,3,6},{4},{5,7}}=>7 {{1,2,3,6},{4},{5},{7}}=>6 {{1,2,3,7},{4,6},{5}}=>7 {{1,2,3},{4,6,7},{5}}=>1 {{1,2,3},{4,6},{5,7}}=>2 {{1,2,3},{4,6},{5},{7}}=>1 {{1,2,3,7},{4},{5,6}}=>6 {{1,2,3},{4,7},{5,6}}=>1 {{1,2,3},{4},{5,6,7}}=>0 {{1,2,3},{4},{5,6},{7}}=>0 {{1,2,3,7},{4},{5},{6}}=>9 {{1,2,3},{4,7},{5},{6}}=>2 {{1,2,3},{4},{5,7},{6}}=>1 {{1,2,3},{4},{5},{6,7}}=>0 {{1,2,3},{4},{5},{6},{7}}=>0 {{1,2,4,5,6,7},{3}}=>2 {{1,2,4,5,6},{3,7}}=>3 {{1,2,4,5,6},{3},{7}}=>2 {{1,2,4,5,7},{3,6}}=>7 {{1,2,4,5},{3,6,7}}=>3 {{1,2,4,5},{3,6},{7}}=>3 {{1,2,4,5,7},{3},{6}}=>6 {{1,2,4,5},{3,7},{6}}=>4 {{1,2,4,5},{3},{6,7}}=>2 {{1,2,4,5},{3},{6},{7}}=>2 {{1,2,4,6,7},{3,5}}=>6 {{1,2,4,6},{3,5,7}}=>8 {{1,2,4,6},{3,5},{7}}=>6 {{1,2,4,7},{3,5,6}}=>6 {{1,2,4},{3,5,6,7}}=>3 {{1,2,4},{3,5,6},{7}}=>3 {{1,2,4,7},{3,5},{6}}=>9 {{1,2,4},{3,5,7},{6}}=>5 {{1,2,4},{3,5},{6,7}}=>3 {{1,2,4},{3,5},{6},{7}}=>3 {{1,2,4,6,7},{3},{5}}=>5 {{1,2,4,6},{3,7},{5}}=>7 {{1,2,4,6},{3},{5,7}}=>6 {{1,2,4,6},{3},{5},{7}}=>5 {{1,2,4,7},{3,6},{5}}=>10 {{1,2,4},{3,6,7},{5}}=>4 {{1,2,4},{3,6},{5,7}}=>5 {{1,2,4},{3,6},{5},{7}}=>4 {{1,2,4,7},{3},{5,6}}=>5 {{1,2,4},{3,7},{5,6}}=>4 {{1,2,4},{3},{5,6,7}}=>2 {{1,2,4},{3},{5,6},{7}}=>2 {{1,2,4,7},{3},{5},{6}}=>8 {{1,2,4},{3,7},{5},{6}}=>5 {{1,2,4},{3},{5,7},{6}}=>3 {{1,2,4},{3},{5},{6,7}}=>2 {{1,2,4},{3},{5},{6},{7}}=>2 {{1,2,5,6,7},{3,4}}=>2 {{1,2,5,6},{3,4,7}}=>4 {{1,2,5,6},{3,4},{7}}=>2 {{1,2,5,7},{3,4,6}}=>7 {{1,2,5},{3,4,6,7}}=>4 {{1,2,5},{3,4,6},{7}}=>4 {{1,2,5,7},{3,4},{6}}=>5 {{1,2,5},{3,4,7},{6}}=>6 {{1,2,5},{3,4},{6,7}}=>2 {{1,2,5},{3,4},{6},{7}}=>2 {{1,2,6,7},{3,4,5}}=>2 {{1,2,6},{3,4,5,7}}=>5 {{1,2,6},{3,4,5},{7}}=>2 {{1,2,7},{3,4,5,6}}=>2 {{1,2},{3,4,5,6,7}}=>0 {{1,2},{3,4,5,6},{7}}=>0 {{1,2,7},{3,4,5},{6}}=>4 {{1,2},{3,4,5,7},{6}}=>3 {{1,2},{3,4,5},{6,7}}=>0 {{1,2},{3,4,5},{6},{7}}=>0 {{1,2,6,7},{3,4},{5}}=>4 {{1,2,6},{3,4,7},{5}}=>8 {{1,2,6},{3,4},{5,7}}=>5 {{1,2,6},{3,4},{5},{7}}=>4 {{1,2,7},{3,4,6},{5}}=>6 {{1,2},{3,4,6,7},{5}}=>2 {{1,2},{3,4,6},{5,7}}=>3 {{1,2},{3,4,6},{5},{7}}=>2 {{1,2,7},{3,4},{5,6}}=>4 {{1,2},{3,4,7},{5,6}}=>2 {{1,2},{3,4},{5,6,7}}=>0 {{1,2},{3,4},{5,6},{7}}=>0 {{1,2,7},{3,4},{5},{6}}=>6 {{1,2},{3,4,7},{5},{6}}=>4 {{1,2},{3,4},{5,7},{6}}=>1 {{1,2},{3,4},{5},{6,7}}=>0 {{1,2},{3,4},{5},{6},{7}}=>0 {{1,2,5,6,7},{3},{4}}=>4 {{1,2,5,6},{3,7},{4}}=>6 {{1,2,5,6},{3},{4,7}}=>5 {{1,2,5,6},{3},{4},{7}}=>4 {{1,2,5,7},{3,6},{4}}=>9 {{1,2,5},{3,6,7},{4}}=>6 {{1,2,5},{3,6},{4,7}}=>8 {{1,2,5},{3,6},{4},{7}}=>6 {{1,2,5,7},{3},{4,6}}=>8 {{1,2,5},{3,7},{4,6}}=>7 {{1,2,5},{3},{4,6,7}}=>5 {{1,2,5},{3},{4,6},{7}}=>5 {{1,2,5,7},{3},{4},{6}}=>7 {{1,2,5},{3,7},{4},{6}}=>7 {{1,2,5},{3},{4,7},{6}}=>6 {{1,2,5},{3},{4},{6,7}}=>4 {{1,2,5},{3},{4},{6},{7}}=>4 {{1,2,6,7},{3,5},{4}}=>5 {{1,2,6},{3,5,7},{4}}=>7 {{1,2,6},{3,5},{4,7}}=>7 {{1,2,6},{3,5},{4},{7}}=>5 {{1,2,7},{3,5,6},{4}}=>5 {{1,2},{3,5,6,7},{4}}=>1 {{1,2},{3,5,6},{4,7}}=>2 {{1,2},{3,5,6},{4},{7}}=>1 {{1,2,7},{3,5},{4,6}}=>6 {{1,2},{3,5,7},{4,6}}=>4 {{1,2},{3,5},{4,6,7}}=>2 {{1,2},{3,5},{4,6},{7}}=>2 {{1,2,7},{3,5},{4},{6}}=>7 {{1,2},{3,5,7},{4},{6}}=>3 {{1,2},{3,5},{4,7},{6}}=>3 {{1,2},{3,5},{4},{6,7}}=>1 {{1,2},{3,5},{4},{6},{7}}=>1 {{1,2,6,7},{3},{4,5}}=>4 {{1,2,6},{3,7},{4,5}}=>6 {{1,2,6},{3},{4,5,7}}=>6 {{1,2,6},{3},{4,5},{7}}=>4 {{1,2,7},{3,6},{4,5}}=>5 {{1,2},{3,6,7},{4,5}}=>1 {{1,2},{3,6},{4,5,7}}=>3 {{1,2},{3,6},{4,5},{7}}=>1 {{1,2,7},{3},{4,5,6}}=>4 {{1,2},{3,7},{4,5,6}}=>1 {{1,2},{3},{4,5,6,7}}=>0 {{1,2},{3},{4,5,6},{7}}=>0 {{1,2,7},{3},{4,5},{6}}=>6 {{1,2},{3,7},{4,5},{6}}=>2 {{1,2},{3},{4,5,7},{6}}=>2 {{1,2},{3},{4,5},{6,7}}=>0 {{1,2},{3},{4,5},{6},{7}}=>0 {{1,2,6,7},{3},{4},{5}}=>6 {{1,2,6},{3,7},{4},{5}}=>9 {{1,2,6},{3},{4,7},{5}}=>8 {{1,2,6},{3},{4},{5,7}}=>7 {{1,2,6},{3},{4},{5},{7}}=>6 {{1,2,7},{3,6},{4},{5}}=>8 {{1,2},{3,6,7},{4},{5}}=>2 {{1,2},{3,6},{4,7},{5}}=>4 {{1,2},{3,6},{4},{5,7}}=>3 {{1,2},{3,6},{4},{5},{7}}=>2 {{1,2,7},{3},{4,6},{5}}=>7 {{1,2},{3,7},{4,6},{5}}=>3 {{1,2},{3},{4,6,7},{5}}=>1 {{1,2},{3},{4,6},{5,7}}=>2 {{1,2},{3},{4,6},{5},{7}}=>1 {{1,2,7},{3},{4},{5,6}}=>6 {{1,2},{3,7},{4},{5,6}}=>2 {{1,2},{3},{4,7},{5,6}}=>1 {{1,2},{3},{4},{5,6,7}}=>0 {{1,2},{3},{4},{5,6},{7}}=>0 {{1,2,7},{3},{4},{5},{6}}=>8 {{1,2},{3,7},{4},{5},{6}}=>3 {{1,2},{3},{4,7},{5},{6}}=>2 {{1,2},{3},{4},{5,7},{6}}=>1 {{1,2},{3},{4},{5},{6,7}}=>0 {{1,2},{3},{4},{5},{6},{7}}=>0 {{1,3,4,5,6,7},{2}}=>1 {{1,3,4,5,6},{2,7}}=>2 {{1,3,4,5,6},{2},{7}}=>1 {{1,3,4,5,7},{2,6}}=>6 {{1,3,4,5},{2,6,7}}=>2 {{1,3,4,5},{2,6},{7}}=>2 {{1,3,4,5,7},{2},{6}}=>5 {{1,3,4,5},{2,7},{6}}=>3 {{1,3,4,5},{2},{6,7}}=>1 {{1,3,4,5},{2},{6},{7}}=>1 {{1,3,4,6,7},{2,5}}=>5 {{1,3,4,6},{2,5,7}}=>7 {{1,3,4,6},{2,5},{7}}=>5 {{1,3,4,7},{2,5,6}}=>5 {{1,3,4},{2,5,6,7}}=>2 {{1,3,4},{2,5,6},{7}}=>2 {{1,3,4,7},{2,5},{6}}=>8 {{1,3,4},{2,5,7},{6}}=>4 {{1,3,4},{2,5},{6,7}}=>2 {{1,3,4},{2,5},{6},{7}}=>2 {{1,3,4,6,7},{2},{5}}=>4 {{1,3,4,6},{2,7},{5}}=>6 {{1,3,4,6},{2},{5,7}}=>5 {{1,3,4,6},{2},{5},{7}}=>4 {{1,3,4,7},{2,6},{5}}=>9 {{1,3,4},{2,6,7},{5}}=>3 {{1,3,4},{2,6},{5,7}}=>4 {{1,3,4},{2,6},{5},{7}}=>3 {{1,3,4,7},{2},{5,6}}=>4 {{1,3,4},{2,7},{5,6}}=>3 {{1,3,4},{2},{5,6,7}}=>1 {{1,3,4},{2},{5,6},{7}}=>1 {{1,3,4,7},{2},{5},{6}}=>7 {{1,3,4},{2,7},{5},{6}}=>4 {{1,3,4},{2},{5,7},{6}}=>2 {{1,3,4},{2},{5},{6,7}}=>1 {{1,3,4},{2},{5},{6},{7}}=>1 {{1,3,5,6,7},{2,4}}=>4 {{1,3,5,6},{2,4,7}}=>6 {{1,3,5,6},{2,4},{7}}=>4 {{1,3,5,7},{2,4,6}}=>9 {{1,3,5},{2,4,6,7}}=>6 {{1,3,5},{2,4,6},{7}}=>6 {{1,3,5,7},{2,4},{6}}=>7 {{1,3,5},{2,4,7},{6}}=>8 {{1,3,5},{2,4},{6,7}}=>4 {{1,3,5},{2,4},{6},{7}}=>4 {{1,3,6,7},{2,4,5}}=>4 {{1,3,6},{2,4,5,7}}=>7 {{1,3,6},{2,4,5},{7}}=>4 {{1,3,7},{2,4,5,6}}=>4 {{1,3},{2,4,5,6,7}}=>2 {{1,3},{2,4,5,6},{7}}=>2 {{1,3,7},{2,4,5},{6}}=>6 {{1,3},{2,4,5,7},{6}}=>5 {{1,3},{2,4,5},{6,7}}=>2 {{1,3},{2,4,5},{6},{7}}=>2 {{1,3,6,7},{2,4},{5}}=>6 {{1,3,6},{2,4,7},{5}}=>10 {{1,3,6},{2,4},{5,7}}=>7 {{1,3,6},{2,4},{5},{7}}=>6 {{1,3,7},{2,4,6},{5}}=>8 {{1,3},{2,4,6,7},{5}}=>4 {{1,3},{2,4,6},{5,7}}=>5 {{1,3},{2,4,6},{5},{7}}=>4 {{1,3,7},{2,4},{5,6}}=>6 {{1,3},{2,4,7},{5,6}}=>4 {{1,3},{2,4},{5,6,7}}=>2 {{1,3},{2,4},{5,6},{7}}=>2 {{1,3,7},{2,4},{5},{6}}=>8 {{1,3},{2,4,7},{5},{6}}=>6 {{1,3},{2,4},{5,7},{6}}=>3 {{1,3},{2,4},{5},{6,7}}=>2 {{1,3},{2,4},{5},{6},{7}}=>2 {{1,3,5,6,7},{2},{4}}=>3 {{1,3,5,6},{2,7},{4}}=>5 {{1,3,5,6},{2},{4,7}}=>4 {{1,3,5,6},{2},{4},{7}}=>3 {{1,3,5,7},{2,6},{4}}=>8 {{1,3,5},{2,6,7},{4}}=>5 {{1,3,5},{2,6},{4,7}}=>7 {{1,3,5},{2,6},{4},{7}}=>5 {{1,3,5,7},{2},{4,6}}=>7 {{1,3,5},{2,7},{4,6}}=>6 {{1,3,5},{2},{4,6,7}}=>4 {{1,3,5},{2},{4,6},{7}}=>4 {{1,3,5,7},{2},{4},{6}}=>6 {{1,3,5},{2,7},{4},{6}}=>6 {{1,3,5},{2},{4,7},{6}}=>5 {{1,3,5},{2},{4},{6,7}}=>3 {{1,3,5},{2},{4},{6},{7}}=>3 {{1,3,6,7},{2,5},{4}}=>7 {{1,3,6},{2,5,7},{4}}=>9 {{1,3,6},{2,5},{4,7}}=>9 {{1,3,6},{2,5},{4},{7}}=>7 {{1,3,7},{2,5,6},{4}}=>7 {{1,3},{2,5,6,7},{4}}=>3 {{1,3},{2,5,6},{4,7}}=>4 {{1,3},{2,5,6},{4},{7}}=>3 {{1,3,7},{2,5},{4,6}}=>8 {{1,3},{2,5,7},{4,6}}=>6 {{1,3},{2,5},{4,6,7}}=>4 {{1,3},{2,5},{4,6},{7}}=>4 {{1,3,7},{2,5},{4},{6}}=>9 {{1,3},{2,5,7},{4},{6}}=>5 {{1,3},{2,5},{4,7},{6}}=>5 {{1,3},{2,5},{4},{6,7}}=>3 {{1,3},{2,5},{4},{6},{7}}=>3 {{1,3,6,7},{2},{4,5}}=>3 {{1,3,6},{2,7},{4,5}}=>5 {{1,3,6},{2},{4,5,7}}=>5 {{1,3,6},{2},{4,5},{7}}=>3 {{1,3,7},{2,6},{4,5}}=>7 {{1,3},{2,6,7},{4,5}}=>3 {{1,3},{2,6},{4,5,7}}=>5 {{1,3},{2,6},{4,5},{7}}=>3 {{1,3,7},{2},{4,5,6}}=>3 {{1,3},{2,7},{4,5,6}}=>3 {{1,3},{2},{4,5,6,7}}=>1 {{1,3},{2},{4,5,6},{7}}=>1 {{1,3,7},{2},{4,5},{6}}=>5 {{1,3},{2,7},{4,5},{6}}=>4 {{1,3},{2},{4,5,7},{6}}=>3 {{1,3},{2},{4,5},{6,7}}=>1 {{1,3},{2},{4,5},{6},{7}}=>1 {{1,3,6,7},{2},{4},{5}}=>5 {{1,3,6},{2,7},{4},{5}}=>8 {{1,3,6},{2},{4,7},{5}}=>7 {{1,3,6},{2},{4},{5,7}}=>6 {{1,3,6},{2},{4},{5},{7}}=>5 {{1,3,7},{2,6},{4},{5}}=>10 {{1,3},{2,6,7},{4},{5}}=>4 {{1,3},{2,6},{4,7},{5}}=>6 {{1,3},{2,6},{4},{5,7}}=>5 {{1,3},{2,6},{4},{5},{7}}=>4 {{1,3,7},{2},{4,6},{5}}=>6 {{1,3},{2,7},{4,6},{5}}=>5 {{1,3},{2},{4,6,7},{5}}=>2 {{1,3},{2},{4,6},{5,7}}=>3 {{1,3},{2},{4,6},{5},{7}}=>2 {{1,3,7},{2},{4},{5,6}}=>5 {{1,3},{2,7},{4},{5,6}}=>4 {{1,3},{2},{4,7},{5,6}}=>2 {{1,3},{2},{4},{5,6,7}}=>1 {{1,3},{2},{4},{5,6},{7}}=>1 {{1,3,7},{2},{4},{5},{6}}=>7 {{1,3},{2,7},{4},{5},{6}}=>5 {{1,3},{2},{4,7},{5},{6}}=>3 {{1,3},{2},{4},{5,7},{6}}=>2 {{1,3},{2},{4},{5},{6,7}}=>1 {{1,3},{2},{4},{5},{6},{7}}=>1 {{1,4,5,6,7},{2,3}}=>1 {{1,4,5,6},{2,3,7}}=>3 {{1,4,5,6},{2,3},{7}}=>1 {{1,4,5,7},{2,3,6}}=>6 {{1,4,5},{2,3,6,7}}=>3 {{1,4,5},{2,3,6},{7}}=>3 {{1,4,5,7},{2,3},{6}}=>4 {{1,4,5},{2,3,7},{6}}=>5 {{1,4,5},{2,3},{6,7}}=>1 {{1,4,5},{2,3},{6},{7}}=>1 {{1,4,6,7},{2,3,5}}=>5 {{1,4,6},{2,3,5,7}}=>8 {{1,4,6},{2,3,5},{7}}=>5 {{1,4,7},{2,3,5,6}}=>5 {{1,4},{2,3,5,6,7}}=>3 {{1,4},{2,3,5,6},{7}}=>3 {{1,4,7},{2,3,5},{6}}=>7 {{1,4},{2,3,5,7},{6}}=>6 {{1,4},{2,3,5},{6,7}}=>3 {{1,4},{2,3,5},{6},{7}}=>3 {{1,4,6,7},{2,3},{5}}=>3 {{1,4,6},{2,3,7},{5}}=>7 {{1,4,6},{2,3},{5,7}}=>4 {{1,4,6},{2,3},{5},{7}}=>3 {{1,4,7},{2,3,6},{5}}=>9 {{1,4},{2,3,6,7},{5}}=>5 {{1,4},{2,3,6},{5,7}}=>6 {{1,4},{2,3,6},{5},{7}}=>5 {{1,4,7},{2,3},{5,6}}=>3 {{1,4},{2,3,7},{5,6}}=>5 {{1,4},{2,3},{5,6,7}}=>1 {{1,4},{2,3},{5,6},{7}}=>1 {{1,4,7},{2,3},{5},{6}}=>5 {{1,4},{2,3,7},{5},{6}}=>7 {{1,4},{2,3},{5,7},{6}}=>2 {{1,4},{2,3},{5},{6,7}}=>1 {{1,4},{2,3},{5},{6},{7}}=>1 {{1,5,6,7},{2,3,4}}=>1 {{1,5,6},{2,3,4,7}}=>4 {{1,5,6},{2,3,4},{7}}=>1 {{1,5,7},{2,3,4,6}}=>6 {{1,5},{2,3,4,6,7}}=>4 {{1,5},{2,3,4,6},{7}}=>4 {{1,5,7},{2,3,4},{6}}=>3 {{1,5},{2,3,4,7},{6}}=>7 {{1,5},{2,3,4},{6,7}}=>1 {{1,5},{2,3,4},{6},{7}}=>1 {{1,6,7},{2,3,4,5}}=>1 {{1,6},{2,3,4,5,7}}=>5 {{1,6},{2,3,4,5},{7}}=>1 {{1,7},{2,3,4,5,6}}=>1 {{1},{2,3,4,5,6,7}}=>0 {{1},{2,3,4,5,6},{7}}=>0 {{1,7},{2,3,4,5},{6}}=>2 {{1},{2,3,4,5,7},{6}}=>4 {{1},{2,3,4,5},{6,7}}=>0 {{1},{2,3,4,5},{6},{7}}=>0 {{1,6,7},{2,3,4},{5}}=>2 {{1,6},{2,3,4,7},{5}}=>8 {{1,6},{2,3,4},{5,7}}=>3 {{1,6},{2,3,4},{5},{7}}=>2 {{1,7},{2,3,4,6},{5}}=>5 {{1},{2,3,4,6,7},{5}}=>3 {{1},{2,3,4,6},{5,7}}=>4 {{1},{2,3,4,6},{5},{7}}=>3 {{1,7},{2,3,4},{5,6}}=>2 {{1},{2,3,4,7},{5,6}}=>3 {{1},{2,3,4},{5,6,7}}=>0 {{1},{2,3,4},{5,6},{7}}=>0 {{1,7},{2,3,4},{5},{6}}=>3 {{1},{2,3,4,7},{5},{6}}=>6 {{1},{2,3,4},{5,7},{6}}=>1 {{1},{2,3,4},{5},{6,7}}=>0 {{1},{2,3,4},{5},{6},{7}}=>0 {{1,5,6,7},{2,3},{4}}=>2 {{1,5,6},{2,3,7},{4}}=>6 {{1,5,6},{2,3},{4,7}}=>3 {{1,5,6},{2,3},{4},{7}}=>2 {{1,5,7},{2,3,6},{4}}=>8 {{1,5},{2,3,6,7},{4}}=>6 {{1,5},{2,3,6},{4,7}}=>8 {{1,5},{2,3,6},{4},{7}}=>6 {{1,5,7},{2,3},{4,6}}=>5 {{1,5},{2,3,7},{4,6}}=>7 {{1,5},{2,3},{4,6,7}}=>3 {{1,5},{2,3},{4,6},{7}}=>3 {{1,5,7},{2,3},{4},{6}}=>4 {{1,5},{2,3,7},{4},{6}}=>8 {{1,5},{2,3},{4,7},{6}}=>4 {{1,5},{2,3},{4},{6,7}}=>2 {{1,5},{2,3},{4},{6},{7}}=>2 {{1,6,7},{2,3,5},{4}}=>4 {{1,6},{2,3,5,7},{4}}=>7 {{1,6},{2,3,5},{4,7}}=>6 {{1,6},{2,3,5},{4},{7}}=>4 {{1,7},{2,3,5,6},{4}}=>4 {{1},{2,3,5,6,7},{4}}=>2 {{1},{2,3,5,6},{4,7}}=>3 {{1},{2,3,5,6},{4},{7}}=>2 {{1,7},{2,3,5},{4,6}}=>5 {{1},{2,3,5,7},{4,6}}=>6 {{1},{2,3,5},{4,6,7}}=>3 {{1},{2,3,5},{4,6},{7}}=>3 {{1,7},{2,3,5},{4},{6}}=>5 {{1},{2,3,5,7},{4},{6}}=>5 {{1},{2,3,5},{4,7},{6}}=>4 {{1},{2,3,5},{4},{6,7}}=>2 {{1},{2,3,5},{4},{6},{7}}=>2 {{1,6,7},{2,3},{4,5}}=>2 {{1,6},{2,3,7},{4,5}}=>6 {{1,6},{2,3},{4,5,7}}=>4 {{1,6},{2,3},{4,5},{7}}=>2 {{1,7},{2,3,6},{4,5}}=>4 {{1},{2,3,6,7},{4,5}}=>2 {{1},{2,3,6},{4,5,7}}=>4 {{1},{2,3,6},{4,5},{7}}=>2 {{1,7},{2,3},{4,5,6}}=>2 {{1},{2,3,7},{4,5,6}}=>2 {{1},{2,3},{4,5,6,7}}=>0 {{1},{2,3},{4,5,6},{7}}=>0 {{1,7},{2,3},{4,5},{6}}=>3 {{1},{2,3,7},{4,5},{6}}=>4 {{1},{2,3},{4,5,7},{6}}=>2 {{1},{2,3},{4,5},{6,7}}=>0 {{1},{2,3},{4,5},{6},{7}}=>0 {{1,6,7},{2,3},{4},{5}}=>3 {{1,6},{2,3,7},{4},{5}}=>9 {{1,6},{2,3},{4,7},{5}}=>5 {{1,6},{2,3},{4},{5,7}}=>4 {{1,6},{2,3},{4},{5},{7}}=>3 {{1,7},{2,3,6},{4},{5}}=>7 {{1},{2,3,6,7},{4},{5}}=>4 {{1},{2,3,6},{4,7},{5}}=>6 {{1},{2,3,6},{4},{5,7}}=>5 {{1},{2,3,6},{4},{5},{7}}=>4 {{1,7},{2,3},{4,6},{5}}=>4 {{1},{2,3,7},{4,6},{5}}=>5 {{1},{2,3},{4,6,7},{5}}=>1 {{1},{2,3},{4,6},{5,7}}=>2 {{1},{2,3},{4,6},{5},{7}}=>1 {{1,7},{2,3},{4},{5,6}}=>3 {{1},{2,3,7},{4},{5,6}}=>4 {{1},{2,3},{4,7},{5,6}}=>1 {{1},{2,3},{4},{5,6,7}}=>0 {{1},{2,3},{4},{5,6},{7}}=>0 {{1,7},{2,3},{4},{5},{6}}=>4 {{1},{2,3,7},{4},{5},{6}}=>6 {{1},{2,3},{4,7},{5},{6}}=>2 {{1},{2,3},{4},{5,7},{6}}=>1 {{1},{2,3},{4},{5},{6,7}}=>0 {{1},{2,3},{4},{5},{6},{7}}=>0 {{1,4,5,6,7},{2},{3}}=>2 {{1,4,5,6},{2,7},{3}}=>4 {{1,4,5,6},{2},{3,7}}=>3 {{1,4,5,6},{2},{3},{7}}=>2 {{1,4,5,7},{2,6},{3}}=>7 {{1,4,5},{2,6,7},{3}}=>4 {{1,4,5},{2,6},{3,7}}=>6 {{1,4,5},{2,6},{3},{7}}=>4 {{1,4,5,7},{2},{3,6}}=>6 {{1,4,5},{2,7},{3,6}}=>5 {{1,4,5},{2},{3,6,7}}=>3 {{1,4,5},{2},{3,6},{7}}=>3 {{1,4,5,7},{2},{3},{6}}=>5 {{1,4,5},{2,7},{3},{6}}=>5 {{1,4,5},{2},{3,7},{6}}=>4 {{1,4,5},{2},{3},{6,7}}=>2 {{1,4,5},{2},{3},{6},{7}}=>2 {{1,4,6,7},{2,5},{3}}=>6 {{1,4,6},{2,5,7},{3}}=>8 {{1,4,6},{2,5},{3,7}}=>8 {{1,4,6},{2,5},{3},{7}}=>6 {{1,4,7},{2,5,6},{3}}=>6 {{1,4},{2,5,6,7},{3}}=>4 {{1,4},{2,5,6},{3,7}}=>6 {{1,4},{2,5,6},{3},{7}}=>4 {{1,4,7},{2,5},{3,6}}=>10 {{1,4},{2,5,7},{3,6}}=>8 {{1,4},{2,5},{3,6,7}}=>6 {{1,4},{2,5},{3,6},{7}}=>6 {{1,4,7},{2,5},{3},{6}}=>8 {{1,4},{2,5,7},{3},{6}}=>6 {{1,4},{2,5},{3,7},{6}}=>7 {{1,4},{2,5},{3},{6,7}}=>4 {{1,4},{2,5},{3},{6},{7}}=>4 {{1,4,6,7},{2},{3,5}}=>5 {{1,4,6},{2,7},{3,5}}=>7 {{1,4,6},{2},{3,5,7}}=>7 {{1,4,6},{2},{3,5},{7}}=>5 {{1,4,7},{2,6},{3,5}}=>9 {{1,4},{2,6,7},{3,5}}=>5 {{1,4},{2,6},{3,5,7}}=>7 {{1,4},{2,6},{3,5},{7}}=>5 {{1,4,7},{2},{3,5,6}}=>5 {{1,4},{2,7},{3,5,6}}=>5 {{1,4},{2},{3,5,6,7}}=>3 {{1,4},{2},{3,5,6},{7}}=>3 {{1,4,7},{2},{3,5},{6}}=>7 {{1,4},{2,7},{3,5},{6}}=>6 {{1,4},{2},{3,5,7},{6}}=>5 {{1,4},{2},{3,5},{6,7}}=>3 {{1,4},{2},{3,5},{6},{7}}=>3 {{1,4,6,7},{2},{3},{5}}=>4 {{1,4,6},{2,7},{3},{5}}=>7 {{1,4,6},{2},{3,7},{5}}=>6 {{1,4,6},{2},{3},{5,7}}=>5 {{1,4,6},{2},{3},{5},{7}}=>4 {{1,4,7},{2,6},{3},{5}}=>9 {{1,4},{2,6,7},{3},{5}}=>5 {{1,4},{2,6},{3,7},{5}}=>8 {{1,4},{2,6},{3},{5,7}}=>6 {{1,4},{2,6},{3},{5},{7}}=>5 {{1,4,7},{2},{3,6},{5}}=>8 {{1,4},{2,7},{3,6},{5}}=>7 {{1,4},{2},{3,6,7},{5}}=>4 {{1,4},{2},{3,6},{5,7}}=>5 {{1,4},{2},{3,6},{5},{7}}=>4 {{1,4,7},{2},{3},{5,6}}=>4 {{1,4},{2,7},{3},{5,6}}=>5 {{1,4},{2},{3,7},{5,6}}=>4 {{1,4},{2},{3},{5,6,7}}=>2 {{1,4},{2},{3},{5,6},{7}}=>2 {{1,4,7},{2},{3},{5},{6}}=>6 {{1,4},{2,7},{3},{5},{6}}=>6 {{1,4},{2},{3,7},{5},{6}}=>5 {{1,4},{2},{3},{5,7},{6}}=>3 {{1,4},{2},{3},{5},{6,7}}=>2 {{1,4},{2},{3},{5},{6},{7}}=>2 {{1,5,6,7},{2,4},{3}}=>3 {{1,5,6},{2,4,7},{3}}=>5 {{1,5,6},{2,4},{3,7}}=>5 {{1,5,6},{2,4},{3},{7}}=>3 {{1,5,7},{2,4,6},{3}}=>7 {{1,5},{2,4,6,7},{3}}=>5 {{1,5},{2,4,6},{3,7}}=>7 {{1,5},{2,4,6},{3},{7}}=>5 {{1,5,7},{2,4},{3,6}}=>7 {{1,5},{2,4,7},{3,6}}=>9 {{1,5},{2,4},{3,6,7}}=>5 {{1,5},{2,4},{3,6},{7}}=>5 {{1,5,7},{2,4},{3},{6}}=>5 {{1,5},{2,4,7},{3},{6}}=>7 {{1,5},{2,4},{3,7},{6}}=>6 {{1,5},{2,4},{3},{6,7}}=>3 {{1,5},{2,4},{3},{6},{7}}=>3 {{1,6,7},{2,4,5},{3}}=>3 {{1,6},{2,4,5,7},{3}}=>6 {{1,6},{2,4,5},{3,7}}=>5 {{1,6},{2,4,5},{3},{7}}=>3 {{1,7},{2,4,5,6},{3}}=>3 {{1},{2,4,5,6,7},{3}}=>1 {{1},{2,4,5,6},{3,7}}=>2 {{1},{2,4,5,6},{3},{7}}=>1 {{1,7},{2,4,5},{3,6}}=>4 {{1},{2,4,5,7},{3,6}}=>5 {{1},{2,4,5},{3,6,7}}=>2 {{1},{2,4,5},{3,6},{7}}=>2 {{1,7},{2,4,5},{3},{6}}=>4 {{1},{2,4,5,7},{3},{6}}=>4 {{1},{2,4,5},{3,7},{6}}=>3 {{1},{2,4,5},{3},{6,7}}=>1 {{1},{2,4,5},{3},{6},{7}}=>1 {{1,6,7},{2,4},{3,5}}=>4 {{1,6},{2,4,7},{3,5}}=>8 {{1,6},{2,4},{3,5,7}}=>6 {{1,6},{2,4},{3,5},{7}}=>4 {{1,7},{2,4,6},{3,5}}=>6 {{1},{2,4,6,7},{3,5}}=>4 {{1},{2,4,6},{3,5,7}}=>6 {{1},{2,4,6},{3,5},{7}}=>4 {{1,7},{2,4},{3,5,6}}=>4 {{1},{2,4,7},{3,5,6}}=>4 {{1},{2,4},{3,5,6,7}}=>2 {{1},{2,4},{3,5,6},{7}}=>2 {{1,7},{2,4},{3,5},{6}}=>5 {{1},{2,4,7},{3,5},{6}}=>6 {{1},{2,4},{3,5,7},{6}}=>4 {{1},{2,4},{3,5},{6,7}}=>2 {{1},{2,4},{3,5},{6},{7}}=>2 {{1,6,7},{2,4},{3},{5}}=>4 {{1,6},{2,4,7},{3},{5}}=>8 {{1,6},{2,4},{3,7},{5}}=>7 {{1,6},{2,4},{3},{5,7}}=>5 {{1,6},{2,4},{3},{5},{7}}=>4 {{1,7},{2,4,6},{3},{5}}=>6 {{1},{2,4,6,7},{3},{5}}=>3 {{1},{2,4,6},{3,7},{5}}=>5 {{1},{2,4,6},{3},{5,7}}=>4 {{1},{2,4,6},{3},{5},{7}}=>3 {{1,7},{2,4},{3,6},{5}}=>6 {{1},{2,4,7},{3,6},{5}}=>7 {{1},{2,4},{3,6,7},{5}}=>3 {{1},{2,4},{3,6},{5,7}}=>4 {{1},{2,4},{3,6},{5},{7}}=>3 {{1,7},{2,4},{3},{5,6}}=>4 {{1},{2,4,7},{3},{5,6}}=>3 {{1},{2,4},{3,7},{5,6}}=>3 {{1},{2,4},{3},{5,6,7}}=>1 {{1},{2,4},{3},{5,6},{7}}=>1 {{1,7},{2,4},{3},{5},{6}}=>5 {{1},{2,4,7},{3},{5},{6}}=>5 {{1},{2,4},{3,7},{5},{6}}=>4 {{1},{2,4},{3},{5,7},{6}}=>2 {{1},{2,4},{3},{5},{6,7}}=>1 {{1},{2,4},{3},{5},{6},{7}}=>1 {{1,5,6,7},{2},{3,4}}=>2 {{1,5,6},{2,7},{3,4}}=>4 {{1,5,6},{2},{3,4,7}}=>4 {{1,5,6},{2},{3,4},{7}}=>2 {{1,5,7},{2,6},{3,4}}=>6 {{1,5},{2,6,7},{3,4}}=>4 {{1,5},{2,6},{3,4,7}}=>8 {{1,5},{2,6},{3,4},{7}}=>4 {{1,5,7},{2},{3,4,6}}=>6 {{1,5},{2,7},{3,4,6}}=>6 {{1,5},{2},{3,4,6,7}}=>4 {{1,5},{2},{3,4,6},{7}}=>4 {{1,5,7},{2},{3,4},{6}}=>4 {{1,5},{2,7},{3,4},{6}}=>5 {{1,5},{2},{3,4,7},{6}}=>6 {{1,5},{2},{3,4},{6,7}}=>2 {{1,5},{2},{3,4},{6},{7}}=>2 {{1,6,7},{2,5},{3,4}}=>3 {{1,6},{2,5,7},{3,4}}=>5 {{1,6},{2,5},{3,4,7}}=>7 {{1,6},{2,5},{3,4},{7}}=>3 {{1,7},{2,5,6},{3,4}}=>3 {{1},{2,5,6,7},{3,4}}=>1 {{1},{2,5,6},{3,4,7}}=>3 {{1},{2,5,6},{3,4},{7}}=>1 {{1,7},{2,5},{3,4,6}}=>5 {{1},{2,5,7},{3,4,6}}=>5 {{1},{2,5},{3,4,6,7}}=>3 {{1},{2,5},{3,4,6},{7}}=>3 {{1,7},{2,5},{3,4},{6}}=>4 {{1},{2,5,7},{3,4},{6}}=>3 {{1},{2,5},{3,4,7},{6}}=>5 {{1},{2,5},{3,4},{6,7}}=>1 {{1},{2,5},{3,4},{6},{7}}=>1 {{1,6,7},{2},{3,4,5}}=>2 {{1,6},{2,7},{3,4,5}}=>4 {{1,6},{2},{3,4,5,7}}=>5 {{1,6},{2},{3,4,5},{7}}=>2 {{1,7},{2,6},{3,4,5}}=>3 {{1},{2,6,7},{3,4,5}}=>1 {{1},{2,6},{3,4,5,7}}=>4 {{1},{2,6},{3,4,5},{7}}=>1 {{1,7},{2},{3,4,5,6}}=>2 {{1},{2,7},{3,4,5,6}}=>1 {{1},{2},{3,4,5,6,7}}=>0 {{1},{2},{3,4,5,6},{7}}=>0 {{1,7},{2},{3,4,5},{6}}=>3 {{1},{2,7},{3,4,5},{6}}=>2 {{1},{2},{3,4,5,7},{6}}=>3 {{1},{2},{3,4,5},{6,7}}=>0 {{1},{2},{3,4,5},{6},{7}}=>0 {{1,6,7},{2},{3,4},{5}}=>3 {{1,6},{2,7},{3,4},{5}}=>6 {{1,6},{2},{3,4,7},{5}}=>7 {{1,6},{2},{3,4},{5,7}}=>4 {{1,6},{2},{3,4},{5},{7}}=>3 {{1,7},{2,6},{3,4},{5}}=>5 {{1},{2,6,7},{3,4},{5}}=>2 {{1},{2,6},{3,4,7},{5}}=>6 {{1},{2,6},{3,4},{5,7}}=>3 {{1},{2,6},{3,4},{5},{7}}=>2 {{1,7},{2},{3,4,6},{5}}=>5 {{1},{2,7},{3,4,6},{5}}=>4 {{1},{2},{3,4,6,7},{5}}=>2 {{1},{2},{3,4,6},{5,7}}=>3 {{1},{2},{3,4,6},{5},{7}}=>2 {{1,7},{2},{3,4},{5,6}}=>3 {{1},{2,7},{3,4},{5,6}}=>2 {{1},{2},{3,4,7},{5,6}}=>2 {{1},{2},{3,4},{5,6,7}}=>0 {{1},{2},{3,4},{5,6},{7}}=>0 {{1,7},{2},{3,4},{5},{6}}=>4 {{1},{2,7},{3,4},{5},{6}}=>3 {{1},{2},{3,4,7},{5},{6}}=>4 {{1},{2},{3,4},{5,7},{6}}=>1 {{1},{2},{3,4},{5},{6,7}}=>0 {{1},{2},{3,4},{5},{6},{7}}=>0 {{1,5,6,7},{2},{3},{4}}=>3 {{1,5,6},{2,7},{3},{4}}=>6 {{1,5,6},{2},{3,7},{4}}=>5 {{1,5,6},{2},{3},{4,7}}=>4 {{1,5,6},{2},{3},{4},{7}}=>3 {{1,5,7},{2,6},{3},{4}}=>8 {{1,5},{2,6,7},{3},{4}}=>6 {{1,5},{2,6},{3,7},{4}}=>9 {{1,5},{2,6},{3},{4,7}}=>8 {{1,5},{2,6},{3},{4},{7}}=>6 {{1,5,7},{2},{3,6},{4}}=>7 {{1,5},{2,7},{3,6},{4}}=>8 {{1,5},{2},{3,6,7},{4}}=>5 {{1,5},{2},{3,6},{4,7}}=>7 {{1,5},{2},{3,6},{4},{7}}=>5 {{1,5,7},{2},{3},{4,6}}=>6 {{1,5},{2,7},{3},{4,6}}=>7 {{1,5},{2},{3,7},{4,6}}=>6 {{1,5},{2},{3},{4,6,7}}=>4 {{1,5},{2},{3},{4,6},{7}}=>4 {{1,5,7},{2},{3},{4},{6}}=>5 {{1,5},{2,7},{3},{4},{6}}=>7 {{1,5},{2},{3,7},{4},{6}}=>6 {{1,5},{2},{3},{4,7},{6}}=>5 {{1,5},{2},{3},{4},{6,7}}=>3 {{1,5},{2},{3},{4},{6},{7}}=>3 {{1,6,7},{2,5},{3},{4}}=>5 {{1,6},{2,5,7},{3},{4}}=>7 {{1,6},{2,5},{3,7},{4}}=>8 {{1,6},{2,5},{3},{4,7}}=>7 {{1,6},{2,5},{3},{4},{7}}=>5 {{1,7},{2,5,6},{3},{4}}=>5 {{1},{2,5,6,7},{3},{4}}=>2 {{1},{2,5,6},{3,7},{4}}=>4 {{1},{2,5,6},{3},{4,7}}=>3 {{1},{2,5,6},{3},{4},{7}}=>2 {{1,7},{2,5},{3,6},{4}}=>7 {{1},{2,5,7},{3,6},{4}}=>6 {{1},{2,5},{3,6,7},{4}}=>4 {{1},{2,5},{3,6},{4,7}}=>6 {{1},{2,5},{3,6},{4},{7}}=>4 {{1,7},{2,5},{3},{4,6}}=>6 {{1},{2,5,7},{3},{4,6}}=>5 {{1},{2,5},{3,7},{4,6}}=>5 {{1},{2,5},{3},{4,6,7}}=>3 {{1},{2,5},{3},{4,6},{7}}=>3 {{1,7},{2,5},{3},{4},{6}}=>6 {{1},{2,5,7},{3},{4},{6}}=>4 {{1},{2,5},{3,7},{4},{6}}=>5 {{1},{2,5},{3},{4,7},{6}}=>4 {{1},{2,5},{3},{4},{6,7}}=>2 {{1},{2,5},{3},{4},{6},{7}}=>2 {{1,6,7},{2},{3,5},{4}}=>4 {{1,6},{2,7},{3,5},{4}}=>7 {{1,6},{2},{3,5,7},{4}}=>6 {{1,6},{2},{3,5},{4,7}}=>6 {{1,6},{2},{3,5},{4},{7}}=>4 {{1,7},{2,6},{3,5},{4}}=>6 {{1},{2,6,7},{3,5},{4}}=>3 {{1},{2,6},{3,5,7},{4}}=>5 {{1},{2,6},{3,5},{4,7}}=>5 {{1},{2,6},{3,5},{4},{7}}=>3 {{1,7},{2},{3,5,6},{4}}=>4 {{1},{2,7},{3,5,6},{4}}=>3 {{1},{2},{3,5,6,7},{4}}=>1 {{1},{2},{3,5,6},{4,7}}=>2 {{1},{2},{3,5,6},{4},{7}}=>1 {{1,7},{2},{3,5},{4,6}}=>5 {{1},{2,7},{3,5},{4,6}}=>4 {{1},{2},{3,5,7},{4,6}}=>4 {{1},{2},{3,5},{4,6,7}}=>2 {{1},{2},{3,5},{4,6},{7}}=>2 {{1,7},{2},{3,5},{4},{6}}=>5 {{1},{2,7},{3,5},{4},{6}}=>4 {{1},{2},{3,5,7},{4},{6}}=>3 {{1},{2},{3,5},{4,7},{6}}=>3 {{1},{2},{3,5},{4},{6,7}}=>1 {{1},{2},{3,5},{4},{6},{7}}=>1 {{1,6,7},{2},{3},{4,5}}=>3 {{1,6},{2,7},{3},{4,5}}=>6 {{1,6},{2},{3,7},{4,5}}=>5 {{1,6},{2},{3},{4,5,7}}=>5 {{1,6},{2},{3},{4,5},{7}}=>3 {{1,7},{2,6},{3},{4,5}}=>5 {{1},{2,6,7},{3},{4,5}}=>2 {{1},{2,6},{3,7},{4,5}}=>4 {{1},{2,6},{3},{4,5,7}}=>4 {{1},{2,6},{3},{4,5},{7}}=>2 {{1,7},{2},{3,6},{4,5}}=>4 {{1},{2,7},{3,6},{4,5}}=>3 {{1},{2},{3,6,7},{4,5}}=>1 {{1},{2},{3,6},{4,5,7}}=>3 {{1},{2},{3,6},{4,5},{7}}=>1 {{1,7},{2},{3},{4,5,6}}=>3 {{1},{2,7},{3},{4,5,6}}=>2 {{1},{2},{3,7},{4,5,6}}=>1 {{1},{2},{3},{4,5,6,7}}=>0 {{1},{2},{3},{4,5,6},{7}}=>0 {{1,7},{2},{3},{4,5},{6}}=>4 {{1},{2,7},{3},{4,5},{6}}=>3 {{1},{2},{3,7},{4,5},{6}}=>2 {{1},{2},{3},{4,5,7},{6}}=>2 {{1},{2},{3},{4,5},{6,7}}=>0 {{1},{2},{3},{4,5},{6},{7}}=>0 {{1,6,7},{2},{3},{4},{5}}=>4 {{1,6},{2,7},{3},{4},{5}}=>8 {{1,6},{2},{3,7},{4},{5}}=>7 {{1,6},{2},{3},{4,7},{5}}=>6 {{1,6},{2},{3},{4},{5,7}}=>5 {{1,6},{2},{3},{4},{5},{7}}=>4 {{1,7},{2,6},{3},{4},{5}}=>7 {{1},{2,6,7},{3},{4},{5}}=>3 {{1},{2,6},{3,7},{4},{5}}=>6 {{1},{2,6},{3},{4,7},{5}}=>5 {{1},{2,6},{3},{4},{5,7}}=>4 {{1},{2,6},{3},{4},{5},{7}}=>3 {{1,7},{2},{3,6},{4},{5}}=>6 {{1},{2,7},{3,6},{4},{5}}=>5 {{1},{2},{3,6,7},{4},{5}}=>2 {{1},{2},{3,6},{4,7},{5}}=>4 {{1},{2},{3,6},{4},{5,7}}=>3 {{1},{2},{3,6},{4},{5},{7}}=>2 {{1,7},{2},{3},{4,6},{5}}=>5 {{1},{2,7},{3},{4,6},{5}}=>4 {{1},{2},{3,7},{4,6},{5}}=>3 {{1},{2},{3},{4,6,7},{5}}=>1 {{1},{2},{3},{4,6},{5,7}}=>2 {{1},{2},{3},{4,6},{5},{7}}=>1 {{1,7},{2},{3},{4},{5,6}}=>4 {{1},{2,7},{3},{4},{5,6}}=>3 {{1},{2},{3,7},{4},{5,6}}=>2 {{1},{2},{3},{4,7},{5,6}}=>1 {{1},{2},{3},{4},{5,6,7}}=>0 {{1},{2},{3},{4},{5,6},{7}}=>0 {{1,7},{2},{3},{4},{5},{6}}=>5 {{1},{2,7},{3},{4},{5},{6}}=>4 {{1},{2},{3,7},{4},{5},{6}}=>3 {{1},{2},{3},{4,7},{5},{6}}=>2 {{1},{2},{3},{4},{5,7},{6}}=>1 {{1},{2},{3},{4},{5},{6,7}}=>0 {{1},{2},{3},{4},{5},{6},{7}}=>0
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Description
The Z-index of a set partition.
The Mahonian representation of a set partition $\{B_1,\dots,B_k\}$ of $\{1,\dots,n\}$ is the restricted growth word $w_1\dots w_n$ obtained by sorting the blocks of the set partition according to their maximal element, and setting $w_i$ to the index of the block containing $i$.
The Z-index of $w$ equals
$$ \sum_{i < j} w_{i,j}, $$
where $w_{i,j}$ is the word obtained from $w$ by removing all letters different from $i$ and $j$.
References
[1] Liu, S.-H. Mahonian and Euler-Mahonian statistics for set partitions arXiv:2202.02089
Code
def to_restricted_growth_word_blocks_max(self):
    w = [0] * self.size()
    for i, B in enumerate(sorted(self, key=lambda B: max(B))):
        for j in B:
            w[j-1] = i
    return w

def statistic(p):
    w = to_restricted_growth_word_blocks_max(p)
    return sum(Word(e for e in w if e in [i, j]).major_index() for j in range(len(w)) for i in range(j))
Created
Oct 06, 2022 at 15:30 by Martin Rubey
Updated
Oct 06, 2022 at 15:30 by Martin Rubey