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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}}=>0 {{1},{2,3}}=>0 {{1},{2},{3}}=>1 {{1,2,3,4}}=>0 {{1,2,3},{4}}=>0 {{1,2,4},{3}}=>0 {{1,2},{3,4}}=>0 {{1,2},{3},{4}}=>1 {{1,3,4},{2}}=>0 {{1,3},{2,4}}=>0 {{1,3},{2},{4}}=>1 {{1,4},{2,3}}=>0 {{1},{2,3,4}}=>0 {{1},{2,3},{4}}=>1 {{1,4},{2},{3}}=>0 {{1},{2,4},{3}}=>0 {{1},{2},{3,4}}=>1 {{1},{2},{3},{4}}=>4 {{1,2,3,4,5}}=>0 {{1,2,3,4},{5}}=>0 {{1,2,3,5},{4}}=>0 {{1,2,3},{4,5}}=>0 {{1,2,3},{4},{5}}=>1 {{1,2,4,5},{3}}=>0 {{1,2,4},{3,5}}=>0 {{1,2,4},{3},{5}}=>1 {{1,2,5},{3,4}}=>0 {{1,2},{3,4,5}}=>0 {{1,2},{3,4},{5}}=>1 {{1,2,5},{3},{4}}=>0 {{1,2},{3,5},{4}}=>0 {{1,2},{3},{4,5}}=>1 {{1,2},{3},{4},{5}}=>4 {{1,3,4,5},{2}}=>0 {{1,3,4},{2,5}}=>0 {{1,3,4},{2},{5}}=>1 {{1,3,5},{2,4}}=>0 {{1,3},{2,4,5}}=>0 {{1,3},{2,4},{5}}=>1 {{1,3,5},{2},{4}}=>0 {{1,3},{2,5},{4}}=>0 {{1,3},{2},{4,5}}=>1 {{1,3},{2},{4},{5}}=>4 {{1,4,5},{2,3}}=>0 {{1,4},{2,3,5}}=>0 {{1,4},{2,3},{5}}=>1 {{1,5},{2,3,4}}=>0 {{1},{2,3,4,5}}=>0 {{1},{2,3,4},{5}}=>1 {{1,5},{2,3},{4}}=>0 {{1},{2,3,5},{4}}=>0 {{1},{2,3},{4,5}}=>1 {{1},{2,3},{4},{5}}=>4 {{1,4,5},{2},{3}}=>0 {{1,4},{2,5},{3}}=>0 {{1,4},{2},{3,5}}=>0 {{1,4},{2},{3},{5}}=>3 {{1,5},{2,4},{3}}=>0 {{1},{2,4,5},{3}}=>0 {{1},{2,4},{3,5}}=>0 {{1},{2,4},{3},{5}}=>3 {{1,5},{2},{3,4}}=>0 {{1},{2,5},{3,4}}=>0 {{1},{2},{3,4,5}}=>1 {{1},{2},{3,4},{5}}=>4 {{1,5},{2},{3},{4}}=>1 {{1},{2,5},{3},{4}}=>1 {{1},{2},{3,5},{4}}=>2 {{1},{2},{3},{4,5}}=>4 {{1},{2},{3},{4},{5}}=>10 {{1,2,3,4,5,6}}=>0 {{1,2,3,4,5},{6}}=>0 {{1,2,3,4,6},{5}}=>0 {{1,2,3,4},{5,6}}=>0 {{1,2,3,4},{5},{6}}=>1 {{1,2,3,5,6},{4}}=>0 {{1,2,3,5},{4,6}}=>0 {{1,2,3,5},{4},{6}}=>1 {{1,2,3,6},{4,5}}=>0 {{1,2,3},{4,5,6}}=>0 {{1,2,3},{4,5},{6}}=>1 {{1,2,3,6},{4},{5}}=>0 {{1,2,3},{4,6},{5}}=>0 {{1,2,3},{4},{5,6}}=>1 {{1,2,3},{4},{5},{6}}=>4 {{1,2,4,5,6},{3}}=>0 {{1,2,4,5},{3,6}}=>0 {{1,2,4,5},{3},{6}}=>1 {{1,2,4,6},{3,5}}=>0 {{1,2,4},{3,5,6}}=>0 {{1,2,4},{3,5},{6}}=>1 {{1,2,4,6},{3},{5}}=>0 {{1,2,4},{3,6},{5}}=>0 {{1,2,4},{3},{5,6}}=>1 {{1,2,4},{3},{5},{6}}=>4 {{1,2,5,6},{3,4}}=>0 {{1,2,5},{3,4,6}}=>0 {{1,2,5},{3,4},{6}}=>1 {{1,2,6},{3,4,5}}=>0 {{1,2},{3,4,5,6}}=>0 {{1,2},{3,4,5},{6}}=>1 {{1,2,6},{3,4},{5}}=>0 {{1,2},{3,4,6},{5}}=>0 {{1,2},{3,4},{5,6}}=>1 {{1,2},{3,4},{5},{6}}=>4 {{1,2,5,6},{3},{4}}=>0 {{1,2,5},{3,6},{4}}=>0 {{1,2,5},{3},{4,6}}=>0 {{1,2,5},{3},{4},{6}}=>3 {{1,2,6},{3,5},{4}}=>0 {{1,2},{3,5,6},{4}}=>0 {{1,2},{3,5},{4,6}}=>0 {{1,2},{3,5},{4},{6}}=>3 {{1,2,6},{3},{4,5}}=>0 {{1,2},{3,6},{4,5}}=>0 {{1,2},{3},{4,5,6}}=>1 {{1,2},{3},{4,5},{6}}=>4 {{1,2,6},{3},{4},{5}}=>1 {{1,2},{3,6},{4},{5}}=>1 {{1,2},{3},{4,6},{5}}=>2 {{1,2},{3},{4},{5,6}}=>4 {{1,2},{3},{4},{5},{6}}=>10 {{1,3,4,5,6},{2}}=>0 {{1,3,4,5},{2,6}}=>0 {{1,3,4,5},{2},{6}}=>1 {{1,3,4,6},{2,5}}=>0 {{1,3,4},{2,5,6}}=>0 {{1,3,4},{2,5},{6}}=>1 {{1,3,4,6},{2},{5}}=>0 {{1,3,4},{2,6},{5}}=>0 {{1,3,4},{2},{5,6}}=>1 {{1,3,4},{2},{5},{6}}=>4 {{1,3,5,6},{2,4}}=>0 {{1,3,5},{2,4,6}}=>0 {{1,3,5},{2,4},{6}}=>1 {{1,3,6},{2,4,5}}=>0 {{1,3},{2,4,5,6}}=>0 {{1,3},{2,4,5},{6}}=>1 {{1,3,6},{2,4},{5}}=>0 {{1,3},{2,4,6},{5}}=>0 {{1,3},{2,4},{5,6}}=>1 {{1,3},{2,4},{5},{6}}=>4 {{1,3,5,6},{2},{4}}=>0 {{1,3,5},{2,6},{4}}=>0 {{1,3,5},{2},{4,6}}=>0 {{1,3,5},{2},{4},{6}}=>3 {{1,3,6},{2,5},{4}}=>0 {{1,3},{2,5,6},{4}}=>0 {{1,3},{2,5},{4,6}}=>0 {{1,3},{2,5},{4},{6}}=>3 {{1,3,6},{2},{4,5}}=>0 {{1,3},{2,6},{4,5}}=>0 {{1,3},{2},{4,5,6}}=>1 {{1,3},{2},{4,5},{6}}=>4 {{1,3,6},{2},{4},{5}}=>1 {{1,3},{2,6},{4},{5}}=>1 {{1,3},{2},{4,6},{5}}=>2 {{1,3},{2},{4},{5,6}}=>4 {{1,3},{2},{4},{5},{6}}=>10 {{1,4,5,6},{2,3}}=>0 {{1,4,5},{2,3,6}}=>0 {{1,4,5},{2,3},{6}}=>1 {{1,4,6},{2,3,5}}=>0 {{1,4},{2,3,5,6}}=>0 {{1,4},{2,3,5},{6}}=>1 {{1,4,6},{2,3},{5}}=>0 {{1,4},{2,3,6},{5}}=>0 {{1,4},{2,3},{5,6}}=>1 {{1,4},{2,3},{5},{6}}=>4 {{1,5,6},{2,3,4}}=>0 {{1,5},{2,3,4,6}}=>0 {{1,5},{2,3,4},{6}}=>1 {{1,6},{2,3,4,5}}=>0 {{1},{2,3,4,5,6}}=>0 {{1},{2,3,4,5},{6}}=>1 {{1,6},{2,3,4},{5}}=>0 {{1},{2,3,4,6},{5}}=>0 {{1},{2,3,4},{5,6}}=>1 {{1},{2,3,4},{5},{6}}=>4 {{1,5,6},{2,3},{4}}=>0 {{1,5},{2,3,6},{4}}=>0 {{1,5},{2,3},{4,6}}=>0 {{1,5},{2,3},{4},{6}}=>3 {{1,6},{2,3,5},{4}}=>0 {{1},{2,3,5,6},{4}}=>0 {{1},{2,3,5},{4,6}}=>0 {{1},{2,3,5},{4},{6}}=>3 {{1,6},{2,3},{4,5}}=>0 {{1},{2,3,6},{4,5}}=>0 {{1},{2,3},{4,5,6}}=>1 {{1},{2,3},{4,5},{6}}=>4 {{1,6},{2,3},{4},{5}}=>1 {{1},{2,3,6},{4},{5}}=>1 {{1},{2,3},{4,6},{5}}=>2 {{1},{2,3},{4},{5,6}}=>4 {{1},{2,3},{4},{5},{6}}=>10 {{1,4,5,6},{2},{3}}=>0 {{1,4,5},{2,6},{3}}=>0 {{1,4,5},{2},{3,6}}=>0 {{1,4,5},{2},{3},{6}}=>3 {{1,4,6},{2,5},{3}}=>0 {{1,4},{2,5,6},{3}}=>0 {{1,4},{2,5},{3,6}}=>0 {{1,4},{2,5},{3},{6}}=>3 {{1,4,6},{2},{3,5}}=>0 {{1,4},{2,6},{3,5}}=>0 {{1,4},{2},{3,5,6}}=>0 {{1,4},{2},{3,5},{6}}=>3 {{1,4,6},{2},{3},{5}}=>1 {{1,4},{2,6},{3},{5}}=>1 {{1,4},{2},{3,6},{5}}=>1 {{1,4},{2},{3},{5,6}}=>3 {{1,4},{2},{3},{5},{6}}=>9 {{1,5,6},{2,4},{3}}=>0 {{1,5},{2,4,6},{3}}=>0 {{1,5},{2,4},{3,6}}=>0 {{1,5},{2,4},{3},{6}}=>3 {{1,6},{2,4,5},{3}}=>0 {{1},{2,4,5,6},{3}}=>0 {{1},{2,4,5},{3,6}}=>0 {{1},{2,4,5},{3},{6}}=>3 {{1,6},{2,4},{3,5}}=>0 {{1},{2,4,6},{3,5}}=>0 {{1},{2,4},{3,5,6}}=>0 {{1},{2,4},{3,5},{6}}=>3 {{1,6},{2,4},{3},{5}}=>1 {{1},{2,4,6},{3},{5}}=>1 {{1},{2,4},{3,6},{5}}=>1 {{1},{2,4},{3},{5,6}}=>3 {{1},{2,4},{3},{5},{6}}=>9 {{1,5,6},{2},{3,4}}=>0 {{1,5},{2,6},{3,4}}=>0 {{1,5},{2},{3,4,6}}=>0 {{1,5},{2},{3,4},{6}}=>3 {{1,6},{2,5},{3,4}}=>0 {{1},{2,5,6},{3,4}}=>0 {{1},{2,5},{3,4,6}}=>0 {{1},{2,5},{3,4},{6}}=>3 {{1,6},{2},{3,4,5}}=>0 {{1},{2,6},{3,4,5}}=>0 {{1},{2},{3,4,5,6}}=>1 {{1},{2},{3,4,5},{6}}=>4 {{1,6},{2},{3,4},{5}}=>1 {{1},{2,6},{3,4},{5}}=>1 {{1},{2},{3,4,6},{5}}=>2 {{1},{2},{3,4},{5,6}}=>4 {{1},{2},{3,4},{5},{6}}=>10 {{1,5,6},{2},{3},{4}}=>1 {{1,5},{2,6},{3},{4}}=>0 {{1,5},{2},{3,6},{4}}=>0 {{1,5},{2},{3},{4,6}}=>1 {{1,5},{2},{3},{4},{6}}=>7 {{1,6},{2,5},{3},{4}}=>0 {{1},{2,5,6},{3},{4}}=>1 {{1},{2,5},{3,6},{4}}=>0 {{1},{2,5},{3},{4,6}}=>1 {{1},{2,5},{3},{4},{6}}=>7 {{1,6},{2},{3,5},{4}}=>0 {{1},{2,6},{3,5},{4}}=>0 {{1},{2},{3,5,6},{4}}=>2 {{1},{2},{3,5},{4,6}}=>2 {{1},{2},{3,5},{4},{6}}=>8 {{1,6},{2},{3},{4,5}}=>1 {{1},{2,6},{3},{4,5}}=>1 {{1},{2},{3,6},{4,5}}=>2 {{1},{2},{3},{4,5,6}}=>4 {{1},{2},{3},{4,5},{6}}=>10 {{1,6},{2},{3},{4},{5}}=>4 {{1},{2,6},{3},{4},{5}}=>4 {{1},{2},{3,6},{4},{5}}=>5 {{1},{2},{3},{4,6},{5}}=>7 {{1},{2},{3},{4},{5,6}}=>10 {{1},{2},{3},{4},{5},{6}}=>20 {{1,2,3,4,5,6,7}}=>0 {{1,2,3,4,5,6},{7}}=>0 {{1,2,3,4,5,7},{6}}=>0 {{1,2,3,4,5},{6,7}}=>0 {{1,2,3,4,5},{6},{7}}=>1 {{1,2,3,4,6,7},{5}}=>0 {{1,2,3,4,6},{5,7}}=>0 {{1,2,3,4,6},{5},{7}}=>1 {{1,2,3,4,7},{5,6}}=>0 {{1,2,3,4},{5,6,7}}=>0 {{1,2,3,4},{5,6},{7}}=>1 {{1,2,3,4,7},{5},{6}}=>0 {{1,2,3,4},{5,7},{6}}=>0 {{1,2,3,4},{5},{6,7}}=>1 {{1,2,3,4},{5},{6},{7}}=>4 {{1,2,3,5,6,7},{4}}=>0 {{1,2,3,5,6},{4,7}}=>0 {{1,2,3,5,6},{4},{7}}=>1 {{1,2,3,5,7},{4,6}}=>0 {{1,2,3,5},{4,6,7}}=>0 {{1,2,3,5},{4,6},{7}}=>1 {{1,2,3,5,7},{4},{6}}=>0 {{1,2,3,5},{4,7},{6}}=>0 {{1,2,3,5},{4},{6,7}}=>1 {{1,2,3,5},{4},{6},{7}}=>4 {{1,2,3,6,7},{4,5}}=>0 {{1,2,3,6},{4,5,7}}=>0 {{1,2,3,6},{4,5},{7}}=>1 {{1,2,3,7},{4,5,6}}=>0 {{1,2,3},{4,5,6,7}}=>0 {{1,2,3},{4,5,6},{7}}=>1 {{1,2,3,7},{4,5},{6}}=>0 {{1,2,3},{4,5,7},{6}}=>0 {{1,2,3},{4,5},{6,7}}=>1 {{1,2,3},{4,5},{6},{7}}=>4 {{1,2,3,6,7},{4},{5}}=>0 {{1,2,3,6},{4,7},{5}}=>0 {{1,2,3,6},{4},{5,7}}=>0 {{1,2,3,6},{4},{5},{7}}=>3 {{1,2,3,7},{4,6},{5}}=>0 {{1,2,3},{4,6,7},{5}}=>0 {{1,2,3},{4,6},{5,7}}=>0 {{1,2,3},{4,6},{5},{7}}=>3 {{1,2,3,7},{4},{5,6}}=>0 {{1,2,3},{4,7},{5,6}}=>0 {{1,2,3},{4},{5,6,7}}=>1 {{1,2,3},{4},{5,6},{7}}=>4 {{1,2,3,7},{4},{5},{6}}=>1 {{1,2,3},{4,7},{5},{6}}=>1 {{1,2,3},{4},{5,7},{6}}=>2 {{1,2,3},{4},{5},{6,7}}=>4 {{1,2,3},{4},{5},{6},{7}}=>10 {{1,2,4,5,6,7},{3}}=>0 {{1,2,4,5,6},{3,7}}=>0 {{1,2,4,5,6},{3},{7}}=>1 {{1,2,4,5,7},{3,6}}=>0 {{1,2,4,5},{3,6,7}}=>0 {{1,2,4,5},{3,6},{7}}=>1 {{1,2,4,5,7},{3},{6}}=>0 {{1,2,4,5},{3,7},{6}}=>0 {{1,2,4,5},{3},{6,7}}=>1 {{1,2,4,5},{3},{6},{7}}=>4 {{1,2,4,6,7},{3,5}}=>0 {{1,2,4,6},{3,5,7}}=>0 {{1,2,4,6},{3,5},{7}}=>1 {{1,2,4,7},{3,5,6}}=>0 {{1,2,4},{3,5,6,7}}=>0 {{1,2,4},{3,5,6},{7}}=>1 {{1,2,4,7},{3,5},{6}}=>0 {{1,2,4},{3,5,7},{6}}=>0 {{1,2,4},{3,5},{6,7}}=>1 {{1,2,4},{3,5},{6},{7}}=>4 {{1,2,4,6,7},{3},{5}}=>0 {{1,2,4,6},{3,7},{5}}=>0 {{1,2,4,6},{3},{5,7}}=>0 {{1,2,4,6},{3},{5},{7}}=>3 {{1,2,4,7},{3,6},{5}}=>0 {{1,2,4},{3,6,7},{5}}=>0 {{1,2,4},{3,6},{5,7}}=>0 {{1,2,4},{3,6},{5},{7}}=>3 {{1,2,4,7},{3},{5,6}}=>0 {{1,2,4},{3,7},{5,6}}=>0 {{1,2,4},{3},{5,6,7}}=>1 {{1,2,4},{3},{5,6},{7}}=>4 {{1,2,4,7},{3},{5},{6}}=>1 {{1,2,4},{3,7},{5},{6}}=>1 {{1,2,4},{3},{5,7},{6}}=>2 {{1,2,4},{3},{5},{6,7}}=>4 {{1,2,4},{3},{5},{6},{7}}=>10 {{1,2,5,6,7},{3,4}}=>0 {{1,2,5,6},{3,4,7}}=>0 {{1,2,5,6},{3,4},{7}}=>1 {{1,2,5,7},{3,4,6}}=>0 {{1,2,5},{3,4,6,7}}=>0 {{1,2,5},{3,4,6},{7}}=>1 {{1,2,5,7},{3,4},{6}}=>0 {{1,2,5},{3,4,7},{6}}=>0 {{1,2,5},{3,4},{6,7}}=>1 {{1,2,5},{3,4},{6},{7}}=>4 {{1,2,6,7},{3,4,5}}=>0 {{1,2,6},{3,4,5,7}}=>0 {{1,2,6},{3,4,5},{7}}=>1 {{1,2,7},{3,4,5,6}}=>0 {{1,2},{3,4,5,6,7}}=>0 {{1,2},{3,4,5,6},{7}}=>1 {{1,2,7},{3,4,5},{6}}=>0 {{1,2},{3,4,5,7},{6}}=>0 {{1,2},{3,4,5},{6,7}}=>1 {{1,2},{3,4,5},{6},{7}}=>4 {{1,2,6,7},{3,4},{5}}=>0 {{1,2,6},{3,4,7},{5}}=>0 {{1,2,6},{3,4},{5,7}}=>0 {{1,2,6},{3,4},{5},{7}}=>3 {{1,2,7},{3,4,6},{5}}=>0 {{1,2},{3,4,6,7},{5}}=>0 {{1,2},{3,4,6},{5,7}}=>0 {{1,2},{3,4,6},{5},{7}}=>3 {{1,2,7},{3,4},{5,6}}=>0 {{1,2},{3,4,7},{5,6}}=>0 {{1,2},{3,4},{5,6,7}}=>1 {{1,2},{3,4},{5,6},{7}}=>4 {{1,2,7},{3,4},{5},{6}}=>1 {{1,2},{3,4,7},{5},{6}}=>1 {{1,2},{3,4},{5,7},{6}}=>2 {{1,2},{3,4},{5},{6,7}}=>4 {{1,2},{3,4},{5},{6},{7}}=>10 {{1,2,5,6,7},{3},{4}}=>0 {{1,2,5,6},{3,7},{4}}=>0 {{1,2,5,6},{3},{4,7}}=>0 {{1,2,5,6},{3},{4},{7}}=>3 {{1,2,5,7},{3,6},{4}}=>0 {{1,2,5},{3,6,7},{4}}=>0 {{1,2,5},{3,6},{4,7}}=>0 {{1,2,5},{3,6},{4},{7}}=>3 {{1,2,5,7},{3},{4,6}}=>0 {{1,2,5},{3,7},{4,6}}=>0 {{1,2,5},{3},{4,6,7}}=>0 {{1,2,5},{3},{4,6},{7}}=>3 {{1,2,5,7},{3},{4},{6}}=>1 {{1,2,5},{3,7},{4},{6}}=>1 {{1,2,5},{3},{4,7},{6}}=>1 {{1,2,5},{3},{4},{6,7}}=>3 {{1,2,5},{3},{4},{6},{7}}=>9 {{1,2,6,7},{3,5},{4}}=>0 {{1,2,6},{3,5,7},{4}}=>0 {{1,2,6},{3,5},{4,7}}=>0 {{1,2,6},{3,5},{4},{7}}=>3 {{1,2,7},{3,5,6},{4}}=>0 {{1,2},{3,5,6,7},{4}}=>0 {{1,2},{3,5,6},{4,7}}=>0 {{1,2},{3,5,6},{4},{7}}=>3 {{1,2,7},{3,5},{4,6}}=>0 {{1,2},{3,5,7},{4,6}}=>0 {{1,2},{3,5},{4,6,7}}=>0 {{1,2},{3,5},{4,6},{7}}=>3 {{1,2,7},{3,5},{4},{6}}=>1 {{1,2},{3,5,7},{4},{6}}=>1 {{1,2},{3,5},{4,7},{6}}=>1 {{1,2},{3,5},{4},{6,7}}=>3 {{1,2},{3,5},{4},{6},{7}}=>9 {{1,2,6,7},{3},{4,5}}=>0 {{1,2,6},{3,7},{4,5}}=>0 {{1,2,6},{3},{4,5,7}}=>0 {{1,2,6},{3},{4,5},{7}}=>3 {{1,2,7},{3,6},{4,5}}=>0 {{1,2},{3,6,7},{4,5}}=>0 {{1,2},{3,6},{4,5,7}}=>0 {{1,2},{3,6},{4,5},{7}}=>3 {{1,2,7},{3},{4,5,6}}=>0 {{1,2},{3,7},{4,5,6}}=>0 {{1,2},{3},{4,5,6,7}}=>1 {{1,2},{3},{4,5,6},{7}}=>4 {{1,2,7},{3},{4,5},{6}}=>1 {{1,2},{3,7},{4,5},{6}}=>1 {{1,2},{3},{4,5,7},{6}}=>2 {{1,2},{3},{4,5},{6,7}}=>4 {{1,2},{3},{4,5},{6},{7}}=>10 {{1,2,6,7},{3},{4},{5}}=>1 {{1,2,6},{3,7},{4},{5}}=>0 {{1,2,6},{3},{4,7},{5}}=>0 {{1,2,6},{3},{4},{5,7}}=>1 {{1,2,6},{3},{4},{5},{7}}=>7 {{1,2,7},{3,6},{4},{5}}=>0 {{1,2},{3,6,7},{4},{5}}=>1 {{1,2},{3,6},{4,7},{5}}=>0 {{1,2},{3,6},{4},{5,7}}=>1 {{1,2},{3,6},{4},{5},{7}}=>7 {{1,2,7},{3},{4,6},{5}}=>0 {{1,2},{3,7},{4,6},{5}}=>0 {{1,2},{3},{4,6,7},{5}}=>2 {{1,2},{3},{4,6},{5,7}}=>2 {{1,2},{3},{4,6},{5},{7}}=>8 {{1,2,7},{3},{4},{5,6}}=>1 {{1,2},{3,7},{4},{5,6}}=>1 {{1,2},{3},{4,7},{5,6}}=>2 {{1,2},{3},{4},{5,6,7}}=>4 {{1,2},{3},{4},{5,6},{7}}=>10 {{1,2,7},{3},{4},{5},{6}}=>4 {{1,2},{3,7},{4},{5},{6}}=>4 {{1,2},{3},{4,7},{5},{6}}=>5 {{1,2},{3},{4},{5,7},{6}}=>7 {{1,2},{3},{4},{5},{6,7}}=>10 {{1,2},{3},{4},{5},{6},{7}}=>20 {{1,3,4,5,6,7},{2}}=>0 {{1,3,4,5,6},{2,7}}=>0 {{1,3,4,5,6},{2},{7}}=>1 {{1,3,4,5,7},{2,6}}=>0 {{1,3,4,5},{2,6,7}}=>0 {{1,3,4,5},{2,6},{7}}=>1 {{1,3,4,5,7},{2},{6}}=>0 {{1,3,4,5},{2,7},{6}}=>0 {{1,3,4,5},{2},{6,7}}=>1 {{1,3,4,5},{2},{6},{7}}=>4 {{1,3,4,6,7},{2,5}}=>0 {{1,3,4,6},{2,5,7}}=>0 {{1,3,4,6},{2,5},{7}}=>1 {{1,3,4,7},{2,5,6}}=>0 {{1,3,4},{2,5,6,7}}=>0 {{1,3,4},{2,5,6},{7}}=>1 {{1,3,4,7},{2,5},{6}}=>0 {{1,3,4},{2,5,7},{6}}=>0 {{1,3,4},{2,5},{6,7}}=>1 {{1,3,4},{2,5},{6},{7}}=>4 {{1,3,4,6,7},{2},{5}}=>0 {{1,3,4,6},{2,7},{5}}=>0 {{1,3,4,6},{2},{5,7}}=>0 {{1,3,4,6},{2},{5},{7}}=>3 {{1,3,4,7},{2,6},{5}}=>0 {{1,3,4},{2,6,7},{5}}=>0 {{1,3,4},{2,6},{5,7}}=>0 {{1,3,4},{2,6},{5},{7}}=>3 {{1,3,4,7},{2},{5,6}}=>0 {{1,3,4},{2,7},{5,6}}=>0 {{1,3,4},{2},{5,6,7}}=>1 {{1,3,4},{2},{5,6},{7}}=>4 {{1,3,4,7},{2},{5},{6}}=>1 {{1,3,4},{2,7},{5},{6}}=>1 {{1,3,4},{2},{5,7},{6}}=>2 {{1,3,4},{2},{5},{6,7}}=>4 {{1,3,4},{2},{5},{6},{7}}=>10 {{1,3,5,6,7},{2,4}}=>0 {{1,3,5,6},{2,4,7}}=>0 {{1,3,5,6},{2,4},{7}}=>1 {{1,3,5,7},{2,4,6}}=>0 {{1,3,5},{2,4,6,7}}=>0 {{1,3,5},{2,4,6},{7}}=>1 {{1,3,5,7},{2,4},{6}}=>0 {{1,3,5},{2,4,7},{6}}=>0 {{1,3,5},{2,4},{6,7}}=>1 {{1,3,5},{2,4},{6},{7}}=>4 {{1,3,6,7},{2,4,5}}=>0 {{1,3,6},{2,4,5,7}}=>0 {{1,3,6},{2,4,5},{7}}=>1 {{1,3,7},{2,4,5,6}}=>0 {{1,3},{2,4,5,6,7}}=>0 {{1,3},{2,4,5,6},{7}}=>1 {{1,3,7},{2,4,5},{6}}=>0 {{1,3},{2,4,5,7},{6}}=>0 {{1,3},{2,4,5},{6,7}}=>1 {{1,3},{2,4,5},{6},{7}}=>4 {{1,3,6,7},{2,4},{5}}=>0 {{1,3,6},{2,4,7},{5}}=>0 {{1,3,6},{2,4},{5,7}}=>0 {{1,3,6},{2,4},{5},{7}}=>3 {{1,3,7},{2,4,6},{5}}=>0 {{1,3},{2,4,6,7},{5}}=>0 {{1,3},{2,4,6},{5,7}}=>0 {{1,3},{2,4,6},{5},{7}}=>3 {{1,3,7},{2,4},{5,6}}=>0 {{1,3},{2,4,7},{5,6}}=>0 {{1,3},{2,4},{5,6,7}}=>1 {{1,3},{2,4},{5,6},{7}}=>4 {{1,3,7},{2,4},{5},{6}}=>1 {{1,3},{2,4,7},{5},{6}}=>1 {{1,3},{2,4},{5,7},{6}}=>2 {{1,3},{2,4},{5},{6,7}}=>4 {{1,3},{2,4},{5},{6},{7}}=>10 {{1,3,5,6,7},{2},{4}}=>0 {{1,3,5,6},{2,7},{4}}=>0 {{1,3,5,6},{2},{4,7}}=>0 {{1,3,5,6},{2},{4},{7}}=>3 {{1,3,5,7},{2,6},{4}}=>0 {{1,3,5},{2,6,7},{4}}=>0 {{1,3,5},{2,6},{4,7}}=>0 {{1,3,5},{2,6},{4},{7}}=>3 {{1,3,5,7},{2},{4,6}}=>0 {{1,3,5},{2,7},{4,6}}=>0 {{1,3,5},{2},{4,6,7}}=>0 {{1,3,5},{2},{4,6},{7}}=>3 {{1,3,5,7},{2},{4},{6}}=>1 {{1,3,5},{2,7},{4},{6}}=>1 {{1,3,5},{2},{4,7},{6}}=>1 {{1,3,5},{2},{4},{6,7}}=>3 {{1,3,5},{2},{4},{6},{7}}=>9 {{1,3,6,7},{2,5},{4}}=>0 {{1,3,6},{2,5,7},{4}}=>0 {{1,3,6},{2,5},{4,7}}=>0 {{1,3,6},{2,5},{4},{7}}=>3 {{1,3,7},{2,5,6},{4}}=>0 {{1,3},{2,5,6,7},{4}}=>0 {{1,3},{2,5,6},{4,7}}=>0 {{1,3},{2,5,6},{4},{7}}=>3 {{1,3,7},{2,5},{4,6}}=>0 {{1,3},{2,5,7},{4,6}}=>0 {{1,3},{2,5},{4,6,7}}=>0 {{1,3},{2,5},{4,6},{7}}=>3 {{1,3,7},{2,5},{4},{6}}=>1 {{1,3},{2,5,7},{4},{6}}=>1 {{1,3},{2,5},{4,7},{6}}=>1 {{1,3},{2,5},{4},{6,7}}=>3 {{1,3},{2,5},{4},{6},{7}}=>9 {{1,3,6,7},{2},{4,5}}=>0 {{1,3,6},{2,7},{4,5}}=>0 {{1,3,6},{2},{4,5,7}}=>0 {{1,3,6},{2},{4,5},{7}}=>3 {{1,3,7},{2,6},{4,5}}=>0 {{1,3},{2,6,7},{4,5}}=>0 {{1,3},{2,6},{4,5,7}}=>0 {{1,3},{2,6},{4,5},{7}}=>3 {{1,3,7},{2},{4,5,6}}=>0 {{1,3},{2,7},{4,5,6}}=>0 {{1,3},{2},{4,5,6,7}}=>1 {{1,3},{2},{4,5,6},{7}}=>4 {{1,3,7},{2},{4,5},{6}}=>1 {{1,3},{2,7},{4,5},{6}}=>1 {{1,3},{2},{4,5,7},{6}}=>2 {{1,3},{2},{4,5},{6,7}}=>4 {{1,3},{2},{4,5},{6},{7}}=>10 {{1,3,6,7},{2},{4},{5}}=>1 {{1,3,6},{2,7},{4},{5}}=>0 {{1,3,6},{2},{4,7},{5}}=>0 {{1,3,6},{2},{4},{5,7}}=>1 {{1,3,6},{2},{4},{5},{7}}=>7 {{1,3,7},{2,6},{4},{5}}=>0 {{1,3},{2,6,7},{4},{5}}=>1 {{1,3},{2,6},{4,7},{5}}=>0 {{1,3},{2,6},{4},{5,7}}=>1 {{1,3},{2,6},{4},{5},{7}}=>7 {{1,3,7},{2},{4,6},{5}}=>0 {{1,3},{2,7},{4,6},{5}}=>0 {{1,3},{2},{4,6,7},{5}}=>2 {{1,3},{2},{4,6},{5,7}}=>2 {{1,3},{2},{4,6},{5},{7}}=>8 {{1,3,7},{2},{4},{5,6}}=>1 {{1,3},{2,7},{4},{5,6}}=>1 {{1,3},{2},{4,7},{5,6}}=>2 {{1,3},{2},{4},{5,6,7}}=>4 {{1,3},{2},{4},{5,6},{7}}=>10 {{1,3,7},{2},{4},{5},{6}}=>4 {{1,3},{2,7},{4},{5},{6}}=>4 {{1,3},{2},{4,7},{5},{6}}=>5 {{1,3},{2},{4},{5,7},{6}}=>7 {{1,3},{2},{4},{5},{6,7}}=>10 {{1,3},{2},{4},{5},{6},{7}}=>20 {{1,4,5,6,7},{2,3}}=>0 {{1,4,5,6},{2,3,7}}=>0 {{1,4,5,6},{2,3},{7}}=>1 {{1,4,5,7},{2,3,6}}=>0 {{1,4,5},{2,3,6,7}}=>0 {{1,4,5},{2,3,6},{7}}=>1 {{1,4,5,7},{2,3},{6}}=>0 {{1,4,5},{2,3,7},{6}}=>0 {{1,4,5},{2,3},{6,7}}=>1 {{1,4,5},{2,3},{6},{7}}=>4 {{1,4,6,7},{2,3,5}}=>0 {{1,4,6},{2,3,5,7}}=>0 {{1,4,6},{2,3,5},{7}}=>1 {{1,4,7},{2,3,5,6}}=>0 {{1,4},{2,3,5,6,7}}=>0 {{1,4},{2,3,5,6},{7}}=>1 {{1,4,7},{2,3,5},{6}}=>0 {{1,4},{2,3,5,7},{6}}=>0 {{1,4},{2,3,5},{6,7}}=>1 {{1,4},{2,3,5},{6},{7}}=>4 {{1,4,6,7},{2,3},{5}}=>0 {{1,4,6},{2,3,7},{5}}=>0 {{1,4,6},{2,3},{5,7}}=>0 {{1,4,6},{2,3},{5},{7}}=>3 {{1,4,7},{2,3,6},{5}}=>0 {{1,4},{2,3,6,7},{5}}=>0 {{1,4},{2,3,6},{5,7}}=>0 {{1,4},{2,3,6},{5},{7}}=>3 {{1,4,7},{2,3},{5,6}}=>0 {{1,4},{2,3,7},{5,6}}=>0 {{1,4},{2,3},{5,6,7}}=>1 {{1,4},{2,3},{5,6},{7}}=>4 {{1,4,7},{2,3},{5},{6}}=>1 {{1,4},{2,3,7},{5},{6}}=>1 {{1,4},{2,3},{5,7},{6}}=>2 {{1,4},{2,3},{5},{6,7}}=>4 {{1,4},{2,3},{5},{6},{7}}=>10 {{1,5,6,7},{2,3,4}}=>0 {{1,5,6},{2,3,4,7}}=>0 {{1,5,6},{2,3,4},{7}}=>1 {{1,5,7},{2,3,4,6}}=>0 {{1,5},{2,3,4,6,7}}=>0 {{1,5},{2,3,4,6},{7}}=>1 {{1,5,7},{2,3,4},{6}}=>0 {{1,5},{2,3,4,7},{6}}=>0 {{1,5},{2,3,4},{6,7}}=>1 {{1,5},{2,3,4},{6},{7}}=>4 {{1,6,7},{2,3,4,5}}=>0 {{1,6},{2,3,4,5,7}}=>0 {{1,6},{2,3,4,5},{7}}=>1 {{1,7},{2,3,4,5,6}}=>0 {{1},{2,3,4,5,6,7}}=>0 {{1},{2,3,4,5,6},{7}}=>1 {{1,7},{2,3,4,5},{6}}=>0 {{1},{2,3,4,5,7},{6}}=>0 {{1},{2,3,4,5},{6,7}}=>1 {{1},{2,3,4,5},{6},{7}}=>4 {{1,6,7},{2,3,4},{5}}=>0 {{1,6},{2,3,4,7},{5}}=>0 {{1,6},{2,3,4},{5,7}}=>0 {{1,6},{2,3,4},{5},{7}}=>3 {{1,7},{2,3,4,6},{5}}=>0 {{1},{2,3,4,6,7},{5}}=>0 {{1},{2,3,4,6},{5,7}}=>0 {{1},{2,3,4,6},{5},{7}}=>3 {{1,7},{2,3,4},{5,6}}=>0 {{1},{2,3,4,7},{5,6}}=>0 {{1},{2,3,4},{5,6,7}}=>1 {{1},{2,3,4},{5,6},{7}}=>4 {{1,7},{2,3,4},{5},{6}}=>1 {{1},{2,3,4,7},{5},{6}}=>1 {{1},{2,3,4},{5,7},{6}}=>2 {{1},{2,3,4},{5},{6,7}}=>4 {{1},{2,3,4},{5},{6},{7}}=>10 {{1,5,6,7},{2,3},{4}}=>0 {{1,5,6},{2,3,7},{4}}=>0 {{1,5,6},{2,3},{4,7}}=>0 {{1,5,6},{2,3},{4},{7}}=>3 {{1,5,7},{2,3,6},{4}}=>0 {{1,5},{2,3,6,7},{4}}=>0 {{1,5},{2,3,6},{4,7}}=>0 {{1,5},{2,3,6},{4},{7}}=>3 {{1,5,7},{2,3},{4,6}}=>0 {{1,5},{2,3,7},{4,6}}=>0 {{1,5},{2,3},{4,6,7}}=>0 {{1,5},{2,3},{4,6},{7}}=>3 {{1,5,7},{2,3},{4},{6}}=>1 {{1,5},{2,3,7},{4},{6}}=>1 {{1,5},{2,3},{4,7},{6}}=>1 {{1,5},{2,3},{4},{6,7}}=>3 {{1,5},{2,3},{4},{6},{7}}=>9 {{1,6,7},{2,3,5},{4}}=>0 {{1,6},{2,3,5,7},{4}}=>0 {{1,6},{2,3,5},{4,7}}=>0 {{1,6},{2,3,5},{4},{7}}=>3 {{1,7},{2,3,5,6},{4}}=>0 {{1},{2,3,5,6,7},{4}}=>0 {{1},{2,3,5,6},{4,7}}=>0 {{1},{2,3,5,6},{4},{7}}=>3 {{1,7},{2,3,5},{4,6}}=>0 {{1},{2,3,5,7},{4,6}}=>0 {{1},{2,3,5},{4,6,7}}=>0 {{1},{2,3,5},{4,6},{7}}=>3 {{1,7},{2,3,5},{4},{6}}=>1 {{1},{2,3,5,7},{4},{6}}=>1 {{1},{2,3,5},{4,7},{6}}=>1 {{1},{2,3,5},{4},{6,7}}=>3 {{1},{2,3,5},{4},{6},{7}}=>9 {{1,6,7},{2,3},{4,5}}=>0 {{1,6},{2,3,7},{4,5}}=>0 {{1,6},{2,3},{4,5,7}}=>0 {{1,6},{2,3},{4,5},{7}}=>3 {{1,7},{2,3,6},{4,5}}=>0 {{1},{2,3,6,7},{4,5}}=>0 {{1},{2,3,6},{4,5,7}}=>0 {{1},{2,3,6},{4,5},{7}}=>3 {{1,7},{2,3},{4,5,6}}=>0 {{1},{2,3,7},{4,5,6}}=>0 {{1},{2,3},{4,5,6,7}}=>1 {{1},{2,3},{4,5,6},{7}}=>4 {{1,7},{2,3},{4,5},{6}}=>1 {{1},{2,3,7},{4,5},{6}}=>1 {{1},{2,3},{4,5,7},{6}}=>2 {{1},{2,3},{4,5},{6,7}}=>4 {{1},{2,3},{4,5},{6},{7}}=>10 {{1,6,7},{2,3},{4},{5}}=>1 {{1,6},{2,3,7},{4},{5}}=>0 {{1,6},{2,3},{4,7},{5}}=>0 {{1,6},{2,3},{4},{5,7}}=>1 {{1,6},{2,3},{4},{5},{7}}=>7 {{1,7},{2,3,6},{4},{5}}=>0 {{1},{2,3,6,7},{4},{5}}=>1 {{1},{2,3,6},{4,7},{5}}=>0 {{1},{2,3,6},{4},{5,7}}=>1 {{1},{2,3,6},{4},{5},{7}}=>7 {{1,7},{2,3},{4,6},{5}}=>0 {{1},{2,3,7},{4,6},{5}}=>0 {{1},{2,3},{4,6,7},{5}}=>2 {{1},{2,3},{4,6},{5,7}}=>2 {{1},{2,3},{4,6},{5},{7}}=>8 {{1,7},{2,3},{4},{5,6}}=>1 {{1},{2,3,7},{4},{5,6}}=>1 {{1},{2,3},{4,7},{5,6}}=>2 {{1},{2,3},{4},{5,6,7}}=>4 {{1},{2,3},{4},{5,6},{7}}=>10 {{1,7},{2,3},{4},{5},{6}}=>4 {{1},{2,3,7},{4},{5},{6}}=>4 {{1},{2,3},{4,7},{5},{6}}=>5 {{1},{2,3},{4},{5,7},{6}}=>7 {{1},{2,3},{4},{5},{6,7}}=>10 {{1},{2,3},{4},{5},{6},{7}}=>20 {{1,4,5,6,7},{2},{3}}=>0 {{1,4,5,6},{2,7},{3}}=>0 {{1,4,5,6},{2},{3,7}}=>0 {{1,4,5,6},{2},{3},{7}}=>3 {{1,4,5,7},{2,6},{3}}=>0 {{1,4,5},{2,6,7},{3}}=>0 {{1,4,5},{2,6},{3,7}}=>0 {{1,4,5},{2,6},{3},{7}}=>3 {{1,4,5,7},{2},{3,6}}=>0 {{1,4,5},{2,7},{3,6}}=>0 {{1,4,5},{2},{3,6,7}}=>0 {{1,4,5},{2},{3,6},{7}}=>3 {{1,4,5,7},{2},{3},{6}}=>1 {{1,4,5},{2,7},{3},{6}}=>1 {{1,4,5},{2},{3,7},{6}}=>1 {{1,4,5},{2},{3},{6,7}}=>3 {{1,4,5},{2},{3},{6},{7}}=>9 {{1,4,6,7},{2,5},{3}}=>0 {{1,4,6},{2,5,7},{3}}=>0 {{1,4,6},{2,5},{3,7}}=>0 {{1,4,6},{2,5},{3},{7}}=>3 {{1,4,7},{2,5,6},{3}}=>0 {{1,4},{2,5,6,7},{3}}=>0 {{1,4},{2,5,6},{3,7}}=>0 {{1,4},{2,5,6},{3},{7}}=>3 {{1,4,7},{2,5},{3,6}}=>0 {{1,4},{2,5,7},{3,6}}=>0 {{1,4},{2,5},{3,6,7}}=>0 {{1,4},{2,5},{3,6},{7}}=>3 {{1,4,7},{2,5},{3},{6}}=>1 {{1,4},{2,5,7},{3},{6}}=>1 {{1,4},{2,5},{3,7},{6}}=>1 {{1,4},{2,5},{3},{6,7}}=>3 {{1,4},{2,5},{3},{6},{7}}=>9 {{1,4,6,7},{2},{3,5}}=>0 {{1,4,6},{2,7},{3,5}}=>0 {{1,4,6},{2},{3,5,7}}=>0 {{1,4,6},{2},{3,5},{7}}=>3 {{1,4,7},{2,6},{3,5}}=>0 {{1,4},{2,6,7},{3,5}}=>0 {{1,4},{2,6},{3,5,7}}=>0 {{1,4},{2,6},{3,5},{7}}=>3 {{1,4,7},{2},{3,5,6}}=>0 {{1,4},{2,7},{3,5,6}}=>0 {{1,4},{2},{3,5,6,7}}=>0 {{1,4},{2},{3,5,6},{7}}=>3 {{1,4,7},{2},{3,5},{6}}=>1 {{1,4},{2,7},{3,5},{6}}=>1 {{1,4},{2},{3,5,7},{6}}=>1 {{1,4},{2},{3,5},{6,7}}=>3 {{1,4},{2},{3,5},{6},{7}}=>9 {{1,4,6,7},{2},{3},{5}}=>1 {{1,4,6},{2,7},{3},{5}}=>0 {{1,4,6},{2},{3,7},{5}}=>0 {{1,4,6},{2},{3},{5,7}}=>1 {{1,4,6},{2},{3},{5},{7}}=>7 {{1,4,7},{2,6},{3},{5}}=>0 {{1,4},{2,6,7},{3},{5}}=>1 {{1,4},{2,6},{3,7},{5}}=>0 {{1,4},{2,6},{3},{5,7}}=>1 {{1,4},{2,6},{3},{5},{7}}=>7 {{1,4,7},{2},{3,6},{5}}=>0 {{1,4},{2,7},{3,6},{5}}=>0 {{1,4},{2},{3,6,7},{5}}=>1 {{1,4},{2},{3,6},{5,7}}=>1 {{1,4},{2},{3,6},{5},{7}}=>7 {{1,4,7},{2},{3},{5,6}}=>1 {{1,4},{2,7},{3},{5,6}}=>1 {{1,4},{2},{3,7},{5,6}}=>1 {{1,4},{2},{3},{5,6,7}}=>3 {{1,4},{2},{3},{5,6},{7}}=>9 {{1,4,7},{2},{3},{5},{6}}=>4 {{1,4},{2,7},{3},{5},{6}}=>4 {{1,4},{2},{3,7},{5},{6}}=>4 {{1,4},{2},{3},{5,7},{6}}=>6 {{1,4},{2},{3},{5},{6,7}}=>9 {{1,4},{2},{3},{5},{6},{7}}=>19 {{1,5,6,7},{2,4},{3}}=>0 {{1,5,6},{2,4,7},{3}}=>0 {{1,5,6},{2,4},{3,7}}=>0 {{1,5,6},{2,4},{3},{7}}=>3 {{1,5,7},{2,4,6},{3}}=>0 {{1,5},{2,4,6,7},{3}}=>0 {{1,5},{2,4,6},{3,7}}=>0 {{1,5},{2,4,6},{3},{7}}=>3 {{1,5,7},{2,4},{3,6}}=>0 {{1,5},{2,4,7},{3,6}}=>0 {{1,5},{2,4},{3,6,7}}=>0 {{1,5},{2,4},{3,6},{7}}=>3 {{1,5,7},{2,4},{3},{6}}=>1 {{1,5},{2,4,7},{3},{6}}=>1 {{1,5},{2,4},{3,7},{6}}=>1 {{1,5},{2,4},{3},{6,7}}=>3 {{1,5},{2,4},{3},{6},{7}}=>9 {{1,6,7},{2,4,5},{3}}=>0 {{1,6},{2,4,5,7},{3}}=>0 {{1,6},{2,4,5},{3,7}}=>0 {{1,6},{2,4,5},{3},{7}}=>3 {{1,7},{2,4,5,6},{3}}=>0 {{1},{2,4,5,6,7},{3}}=>0 {{1},{2,4,5,6},{3,7}}=>0 {{1},{2,4,5,6},{3},{7}}=>3 {{1,7},{2,4,5},{3,6}}=>0 {{1},{2,4,5,7},{3,6}}=>0 {{1},{2,4,5},{3,6,7}}=>0 {{1},{2,4,5},{3,6},{7}}=>3 {{1,7},{2,4,5},{3},{6}}=>1 {{1},{2,4,5,7},{3},{6}}=>1 {{1},{2,4,5},{3,7},{6}}=>1 {{1},{2,4,5},{3},{6,7}}=>3 {{1},{2,4,5},{3},{6},{7}}=>9 {{1,6,7},{2,4},{3,5}}=>0 {{1,6},{2,4,7},{3,5}}=>0 {{1,6},{2,4},{3,5,7}}=>0 {{1,6},{2,4},{3,5},{7}}=>3 {{1,7},{2,4,6},{3,5}}=>0 {{1},{2,4,6,7},{3,5}}=>0 {{1},{2,4,6},{3,5,7}}=>0 {{1},{2,4,6},{3,5},{7}}=>3 {{1,7},{2,4},{3,5,6}}=>0 {{1},{2,4,7},{3,5,6}}=>0 {{1},{2,4},{3,5,6,7}}=>0 {{1},{2,4},{3,5,6},{7}}=>3 {{1,7},{2,4},{3,5},{6}}=>1 {{1},{2,4,7},{3,5},{6}}=>1 {{1},{2,4},{3,5,7},{6}}=>1 {{1},{2,4},{3,5},{6,7}}=>3 {{1},{2,4},{3,5},{6},{7}}=>9 {{1,6,7},{2,4},{3},{5}}=>1 {{1,6},{2,4,7},{3},{5}}=>0 {{1,6},{2,4},{3,7},{5}}=>0 {{1,6},{2,4},{3},{5,7}}=>1 {{1,6},{2,4},{3},{5},{7}}=>7 {{1,7},{2,4,6},{3},{5}}=>0 {{1},{2,4,6,7},{3},{5}}=>1 {{1},{2,4,6},{3,7},{5}}=>0 {{1},{2,4,6},{3},{5,7}}=>1 {{1},{2,4,6},{3},{5},{7}}=>7 {{1,7},{2,4},{3,6},{5}}=>0 {{1},{2,4,7},{3,6},{5}}=>0 {{1},{2,4},{3,6,7},{5}}=>1 {{1},{2,4},{3,6},{5,7}}=>1 {{1},{2,4},{3,6},{5},{7}}=>7 {{1,7},{2,4},{3},{5,6}}=>1 {{1},{2,4,7},{3},{5,6}}=>1 {{1},{2,4},{3,7},{5,6}}=>1 {{1},{2,4},{3},{5,6,7}}=>3 {{1},{2,4},{3},{5,6},{7}}=>9 {{1,7},{2,4},{3},{5},{6}}=>4 {{1},{2,4,7},{3},{5},{6}}=>4 {{1},{2,4},{3,7},{5},{6}}=>4 {{1},{2,4},{3},{5,7},{6}}=>6 {{1},{2,4},{3},{5},{6,7}}=>9 {{1},{2,4},{3},{5},{6},{7}}=>19 {{1,5,6,7},{2},{3,4}}=>0 {{1,5,6},{2,7},{3,4}}=>0 {{1,5,6},{2},{3,4,7}}=>0 {{1,5,6},{2},{3,4},{7}}=>3 {{1,5,7},{2,6},{3,4}}=>0 {{1,5},{2,6,7},{3,4}}=>0 {{1,5},{2,6},{3,4,7}}=>0 {{1,5},{2,6},{3,4},{7}}=>3 {{1,5,7},{2},{3,4,6}}=>0 {{1,5},{2,7},{3,4,6}}=>0 {{1,5},{2},{3,4,6,7}}=>0 {{1,5},{2},{3,4,6},{7}}=>3 {{1,5,7},{2},{3,4},{6}}=>1 {{1,5},{2,7},{3,4},{6}}=>1 {{1,5},{2},{3,4,7},{6}}=>1 {{1,5},{2},{3,4},{6,7}}=>3 {{1,5},{2},{3,4},{6},{7}}=>9 {{1,6,7},{2,5},{3,4}}=>0 {{1,6},{2,5,7},{3,4}}=>0 {{1,6},{2,5},{3,4,7}}=>0 {{1,6},{2,5},{3,4},{7}}=>3 {{1,7},{2,5,6},{3,4}}=>0 {{1},{2,5,6,7},{3,4}}=>0 {{1},{2,5,6},{3,4,7}}=>0 {{1},{2,5,6},{3,4},{7}}=>3 {{1,7},{2,5},{3,4,6}}=>0 {{1},{2,5,7},{3,4,6}}=>0 {{1},{2,5},{3,4,6,7}}=>0 {{1},{2,5},{3,4,6},{7}}=>3 {{1,7},{2,5},{3,4},{6}}=>1 {{1},{2,5,7},{3,4},{6}}=>1 {{1},{2,5},{3,4,7},{6}}=>1 {{1},{2,5},{3,4},{6,7}}=>3 {{1},{2,5},{3,4},{6},{7}}=>9 {{1,6,7},{2},{3,4,5}}=>0 {{1,6},{2,7},{3,4,5}}=>0 {{1,6},{2},{3,4,5,7}}=>0 {{1,6},{2},{3,4,5},{7}}=>3 {{1,7},{2,6},{3,4,5}}=>0 {{1},{2,6,7},{3,4,5}}=>0 {{1},{2,6},{3,4,5,7}}=>0 {{1},{2,6},{3,4,5},{7}}=>3 {{1,7},{2},{3,4,5,6}}=>0 {{1},{2,7},{3,4,5,6}}=>0 {{1},{2},{3,4,5,6,7}}=>1 {{1},{2},{3,4,5,6},{7}}=>4 {{1,7},{2},{3,4,5},{6}}=>1 {{1},{2,7},{3,4,5},{6}}=>1 {{1},{2},{3,4,5,7},{6}}=>2 {{1},{2},{3,4,5},{6,7}}=>4 {{1},{2},{3,4,5},{6},{7}}=>10 {{1,6,7},{2},{3,4},{5}}=>1 {{1,6},{2,7},{3,4},{5}}=>0 {{1,6},{2},{3,4,7},{5}}=>0 {{1,6},{2},{3,4},{5,7}}=>1 {{1,6},{2},{3,4},{5},{7}}=>7 {{1,7},{2,6},{3,4},{5}}=>0 {{1},{2,6,7},{3,4},{5}}=>1 {{1},{2,6},{3,4,7},{5}}=>0 {{1},{2,6},{3,4},{5,7}}=>1 {{1},{2,6},{3,4},{5},{7}}=>7 {{1,7},{2},{3,4,6},{5}}=>0 {{1},{2,7},{3,4,6},{5}}=>0 {{1},{2},{3,4,6,7},{5}}=>2 {{1},{2},{3,4,6},{5,7}}=>2 {{1},{2},{3,4,6},{5},{7}}=>8 {{1,7},{2},{3,4},{5,6}}=>1 {{1},{2,7},{3,4},{5,6}}=>1 {{1},{2},{3,4,7},{5,6}}=>2 {{1},{2},{3,4},{5,6,7}}=>4 {{1},{2},{3,4},{5,6},{7}}=>10 {{1,7},{2},{3,4},{5},{6}}=>4 {{1},{2,7},{3,4},{5},{6}}=>4 {{1},{2},{3,4,7},{5},{6}}=>5 {{1},{2},{3,4},{5,7},{6}}=>7 {{1},{2},{3,4},{5},{6,7}}=>10 {{1},{2},{3,4},{5},{6},{7}}=>20 {{1,5,6,7},{2},{3},{4}}=>1 {{1,5,6},{2,7},{3},{4}}=>0 {{1,5,6},{2},{3,7},{4}}=>0 {{1,5,6},{2},{3},{4,7}}=>1 {{1,5,6},{2},{3},{4},{7}}=>7 {{1,5,7},{2,6},{3},{4}}=>0 {{1,5},{2,6,7},{3},{4}}=>0 {{1,5},{2,6},{3,7},{4}}=>0 {{1,5},{2,6},{3},{4,7}}=>0 {{1,5},{2,6},{3},{4},{7}}=>6 {{1,5,7},{2},{3,6},{4}}=>0 {{1,5},{2,7},{3,6},{4}}=>0 {{1,5},{2},{3,6,7},{4}}=>0 {{1,5},{2},{3,6},{4,7}}=>0 {{1,5},{2},{3,6},{4},{7}}=>6 {{1,5,7},{2},{3},{4,6}}=>1 {{1,5},{2,7},{3},{4,6}}=>0 {{1,5},{2},{3,7},{4,6}}=>0 {{1,5},{2},{3},{4,6,7}}=>1 {{1,5},{2},{3},{4,6},{7}}=>7 {{1,5,7},{2},{3},{4},{6}}=>4 {{1,5},{2,7},{3},{4},{6}}=>3 {{1,5},{2},{3,7},{4},{6}}=>3 {{1,5},{2},{3},{4,7},{6}}=>4 {{1,5},{2},{3},{4},{6,7}}=>7 {{1,5},{2},{3},{4},{6},{7}}=>17 {{1,6,7},{2,5},{3},{4}}=>0 {{1,6},{2,5,7},{3},{4}}=>0 {{1,6},{2,5},{3,7},{4}}=>0 {{1,6},{2,5},{3},{4,7}}=>0 {{1,6},{2,5},{3},{4},{7}}=>6 {{1,7},{2,5,6},{3},{4}}=>0 {{1},{2,5,6,7},{3},{4}}=>1 {{1},{2,5,6},{3,7},{4}}=>0 {{1},{2,5,6},{3},{4,7}}=>1 {{1},{2,5,6},{3},{4},{7}}=>7 {{1,7},{2,5},{3,6},{4}}=>0 {{1},{2,5,7},{3,6},{4}}=>0 {{1},{2,5},{3,6,7},{4}}=>0 {{1},{2,5},{3,6},{4,7}}=>0 {{1},{2,5},{3,6},{4},{7}}=>6 {{1,7},{2,5},{3},{4,6}}=>0 {{1},{2,5,7},{3},{4,6}}=>1 {{1},{2,5},{3,7},{4,6}}=>0 {{1},{2,5},{3},{4,6,7}}=>1 {{1},{2,5},{3},{4,6},{7}}=>7 {{1,7},{2,5},{3},{4},{6}}=>3 {{1},{2,5,7},{3},{4},{6}}=>4 {{1},{2,5},{3,7},{4},{6}}=>3 {{1},{2,5},{3},{4,7},{6}}=>4 {{1},{2,5},{3},{4},{6,7}}=>7 {{1},{2,5},{3},{4},{6},{7}}=>17 {{1,6,7},{2},{3,5},{4}}=>0 {{1,6},{2,7},{3,5},{4}}=>0 {{1,6},{2},{3,5,7},{4}}=>0 {{1,6},{2},{3,5},{4,7}}=>0 {{1,6},{2},{3,5},{4},{7}}=>6 {{1,7},{2,6},{3,5},{4}}=>0 {{1},{2,6,7},{3,5},{4}}=>0 {{1},{2,6},{3,5,7},{4}}=>0 {{1},{2,6},{3,5},{4,7}}=>0 {{1},{2,6},{3,5},{4},{7}}=>6 {{1,7},{2},{3,5,6},{4}}=>0 {{1},{2,7},{3,5,6},{4}}=>0 {{1},{2},{3,5,6,7},{4}}=>2 {{1},{2},{3,5,6},{4,7}}=>2 {{1},{2},{3,5,6},{4},{7}}=>8 {{1,7},{2},{3,5},{4,6}}=>0 {{1},{2,7},{3,5},{4,6}}=>0 {{1},{2},{3,5,7},{4,6}}=>2 {{1},{2},{3,5},{4,6,7}}=>2 {{1},{2},{3,5},{4,6},{7}}=>8 {{1,7},{2},{3,5},{4},{6}}=>3 {{1},{2,7},{3,5},{4},{6}}=>3 {{1},{2},{3,5,7},{4},{6}}=>5 {{1},{2},{3,5},{4,7},{6}}=>5 {{1},{2},{3,5},{4},{6,7}}=>8 {{1},{2},{3,5},{4},{6},{7}}=>18 {{1,6,7},{2},{3},{4,5}}=>1 {{1,6},{2,7},{3},{4,5}}=>0 {{1,6},{2},{3,7},{4,5}}=>0 {{1,6},{2},{3},{4,5,7}}=>1 {{1,6},{2},{3},{4,5},{7}}=>7 {{1,7},{2,6},{3},{4,5}}=>0 {{1},{2,6,7},{3},{4,5}}=>1 {{1},{2,6},{3,7},{4,5}}=>0 {{1},{2,6},{3},{4,5,7}}=>1 {{1},{2,6},{3},{4,5},{7}}=>7 {{1,7},{2},{3,6},{4,5}}=>0 {{1},{2,7},{3,6},{4,5}}=>0 {{1},{2},{3,6,7},{4,5}}=>2 {{1},{2},{3,6},{4,5,7}}=>2 {{1},{2},{3,6},{4,5},{7}}=>8 {{1,7},{2},{3},{4,5,6}}=>1 {{1},{2,7},{3},{4,5,6}}=>1 {{1},{2},{3,7},{4,5,6}}=>2 {{1},{2},{3},{4,5,6,7}}=>4 {{1},{2},{3},{4,5,6},{7}}=>10 {{1,7},{2},{3},{4,5},{6}}=>4 {{1},{2,7},{3},{4,5},{6}}=>4 {{1},{2},{3,7},{4,5},{6}}=>5 {{1},{2},{3},{4,5,7},{6}}=>7 {{1},{2},{3},{4,5},{6,7}}=>10 {{1},{2},{3},{4,5},{6},{7}}=>20 {{1,6,7},{2},{3},{4},{5}}=>4 {{1,6},{2,7},{3},{4},{5}}=>1 {{1,6},{2},{3,7},{4},{5}}=>1 {{1,6},{2},{3},{4,7},{5}}=>2 {{1,6},{2},{3},{4},{5,7}}=>4 {{1,6},{2},{3},{4},{5},{7}}=>14 {{1,7},{2,6},{3},{4},{5}}=>1 {{1},{2,6,7},{3},{4},{5}}=>4 {{1},{2,6},{3,7},{4},{5}}=>1 {{1},{2,6},{3},{4,7},{5}}=>2 {{1},{2,6},{3},{4},{5,7}}=>4 {{1},{2,6},{3},{4},{5},{7}}=>14 {{1,7},{2},{3,6},{4},{5}}=>1 {{1},{2,7},{3,6},{4},{5}}=>1 {{1},{2},{3,6,7},{4},{5}}=>5 {{1},{2},{3,6},{4,7},{5}}=>3 {{1},{2},{3,6},{4},{5,7}}=>5 {{1},{2},{3,6},{4},{5},{7}}=>15 {{1,7},{2},{3},{4,6},{5}}=>2 {{1},{2,7},{3},{4,6},{5}}=>2 {{1},{2},{3,7},{4,6},{5}}=>3 {{1},{2},{3},{4,6,7},{5}}=>7 {{1},{2},{3},{4,6},{5,7}}=>7 {{1},{2},{3},{4,6},{5},{7}}=>17 {{1,7},{2},{3},{4},{5,6}}=>4 {{1},{2,7},{3},{4},{5,6}}=>4 {{1},{2},{3,7},{4},{5,6}}=>5 {{1},{2},{3},{4,7},{5,6}}=>7 {{1},{2},{3},{4},{5,6,7}}=>10 {{1},{2},{3},{4},{5,6},{7}}=>20 {{1,7},{2},{3},{4},{5},{6}}=>10 {{1},{2,7},{3},{4},{5},{6}}=>10 {{1},{2},{3,7},{4},{5},{6}}=>11 {{1},{2},{3},{4,7},{5},{6}}=>13 {{1},{2},{3},{4},{5,7},{6}}=>16 {{1},{2},{3},{4},{5},{6,7}}=>20 {{1},{2},{3},{4},{5},{6},{7}}=>35 {{1,2},{3,4},{5,6},{7,8}}=>7 {{1,3},{2,4},{5,6},{7,8}}=>6 {{1,4},{2,3},{5,6},{7,8}}=>6 {{1,5},{2,3},{4,6},{7,8}}=>4 {{1,6},{2,3},{4,5},{7,8}}=>4 {{1,7},{2,3},{4,5},{6,8}}=>2 {{1,8},{2,3},{4,5},{6,7}}=>4 {{1,8},{2,4},{3,5},{6,7}}=>3 {{1,7},{2,4},{3,5},{6,8}}=>1 {{1,6},{2,4},{3,5},{7,8}}=>3 {{1,5},{2,4},{3,6},{7,8}}=>3 {{1,4},{2,5},{3,6},{7,8}}=>3 {{1,3},{2,5},{4,6},{7,8}}=>4 {{1,2},{3,5},{4,6},{7,8}}=>5 {{1,2},{3,6},{4,5},{7,8}}=>5 {{1,3},{2,6},{4,5},{7,8}}=>4 {{1,4},{2,6},{3,5},{7,8}}=>3 {{1,5},{2,6},{3,4},{7,8}}=>3 {{1,6},{2,5},{3,4},{7,8}}=>3 {{1,7},{2,5},{3,4},{6,8}}=>1 {{1,8},{2,5},{3,4},{6,7}}=>3 {{1,8},{2,6},{3,4},{5,7}}=>1 {{1,7},{2,6},{3,4},{5,8}}=>0 {{1,6},{2,7},{3,4},{5,8}}=>0 {{1,5},{2,7},{3,4},{6,8}}=>1 {{1,4},{2,7},{3,5},{6,8}}=>1 {{1,3},{2,7},{4,5},{6,8}}=>2 {{1,2},{3,7},{4,5},{6,8}}=>3 {{1,2},{3,8},{4,5},{6,7}}=>4 {{1,3},{2,8},{4,5},{6,7}}=>4 {{1,4},{2,8},{3,5},{6,7}}=>3 {{1,5},{2,8},{3,4},{6,7}}=>3 {{1,6},{2,8},{3,4},{5,7}}=>1 {{1,7},{2,8},{3,4},{5,6}}=>1 {{1,8},{2,7},{3,4},{5,6}}=>1 {{1,8},{2,7},{3,5},{4,6}}=>0 {{1,7},{2,8},{3,5},{4,6}}=>0 {{1,6},{2,8},{3,5},{4,7}}=>0 {{1,5},{2,8},{3,6},{4,7}}=>0 {{1,4},{2,8},{3,6},{5,7}}=>1 {{1,3},{2,8},{4,6},{5,7}}=>2 {{1,2},{3,8},{4,6},{5,7}}=>2 {{1,2},{3,7},{4,6},{5,8}}=>2 {{1,3},{2,7},{4,6},{5,8}}=>1 {{1,4},{2,7},{3,6},{5,8}}=>0 {{1,5},{2,7},{3,6},{4,8}}=>0 {{1,6},{2,7},{3,5},{4,8}}=>0 {{1,7},{2,6},{3,5},{4,8}}=>0 {{1,8},{2,6},{3,5},{4,7}}=>0 {{1,8},{2,5},{3,6},{4,7}}=>0 {{1,7},{2,5},{3,6},{4,8}}=>0 {{1,6},{2,5},{3,7},{4,8}}=>0 {{1,5},{2,6},{3,7},{4,8}}=>0 {{1,4},{2,6},{3,7},{5,8}}=>0 {{1,3},{2,6},{4,7},{5,8}}=>1 {{1,2},{3,6},{4,7},{5,8}}=>2 {{1,2},{3,5},{4,7},{6,8}}=>3 {{1,3},{2,5},{4,7},{6,8}}=>2 {{1,4},{2,5},{3,7},{6,8}}=>1 {{1,5},{2,4},{3,7},{6,8}}=>1 {{1,6},{2,4},{3,7},{5,8}}=>0 {{1,7},{2,4},{3,6},{5,8}}=>0 {{1,8},{2,4},{3,6},{5,7}}=>1 {{1,8},{2,3},{4,6},{5,7}}=>2 {{1,7},{2,3},{4,6},{5,8}}=>1 {{1,6},{2,3},{4,7},{5,8}}=>1 {{1,5},{2,3},{4,7},{6,8}}=>2 {{1,4},{2,3},{5,7},{6,8}}=>4 {{1,3},{2,4},{5,7},{6,8}}=>4 {{1,2},{3,4},{5,7},{6,8}}=>5 {{1,2},{3,4},{5,8},{6,7}}=>5 {{1,3},{2,4},{5,8},{6,7}}=>4 {{1,4},{2,3},{5,8},{6,7}}=>4 {{1,5},{2,3},{4,8},{6,7}}=>3 {{1,6},{2,3},{4,8},{5,7}}=>1 {{1,7},{2,3},{4,8},{5,6}}=>1 {{1,8},{2,3},{4,7},{5,6}}=>2 {{1,8},{2,4},{3,7},{5,6}}=>1 {{1,7},{2,4},{3,8},{5,6}}=>1 {{1,6},{2,4},{3,8},{5,7}}=>1 {{1,5},{2,4},{3,8},{6,7}}=>3 {{1,4},{2,5},{3,8},{6,7}}=>3 {{1,3},{2,5},{4,8},{6,7}}=>3 {{1,2},{3,5},{4,8},{6,7}}=>4 {{1,2},{3,6},{4,8},{5,7}}=>2 {{1,3},{2,6},{4,8},{5,7}}=>1 {{1,4},{2,6},{3,8},{5,7}}=>1 {{1,5},{2,6},{3,8},{4,7}}=>0 {{1,6},{2,5},{3,8},{4,7}}=>0 {{1,7},{2,5},{3,8},{4,6}}=>0 {{1,8},{2,5},{3,7},{4,6}}=>0 {{1,8},{2,6},{3,7},{4,5}}=>0 {{1,7},{2,6},{3,8},{4,5}}=>0 {{1,6},{2,7},{3,8},{4,5}}=>0 {{1,5},{2,7},{3,8},{4,6}}=>0 {{1,4},{2,7},{3,8},{5,6}}=>1 {{1,3},{2,7},{4,8},{5,6}}=>1 {{1,2},{3,7},{4,8},{5,6}}=>2 {{1,2},{3,8},{4,7},{5,6}}=>2 {{1,3},{2,8},{4,7},{5,6}}=>2 {{1,4},{2,8},{3,7},{5,6}}=>1 {{1,5},{2,8},{3,7},{4,6}}=>0 {{1,6},{2,8},{3,7},{4,5}}=>0 {{1,7},{2,8},{3,6},{4,5}}=>0 {{1,8},{2,7},{3,6},{4,5}}=>0 {{1},{2},{3,4,5,6,7,8}}=>1 {{1},{2,4,5,6,7,8},{3}}=>0 {{1},{2,3,5,6,7,8},{4}}=>0 {{1},{2,3,4,6,7,8},{5}}=>0 {{1},{2,3,4,5,8},{6},{7}}=>4 {{1},{2,3,4,5,7,8},{6}}=>0 {{1},{2,3,4,5,6,7},{8}}=>1 {{1},{2,3,4,8},{5,6,7}}=>1 {{1},{2,3,4,5,8},{6,7}}=>1 {{1},{2,3,4,5,6,8},{7}}=>0 {{1},{2,3,4,5,6,7,8}}=>0 {{1,2},{3,4,5,6,7,8}}=>0 {{1,4,5,6,7,8},{2},{3}}=>0 {{1,3,5,6,7,8},{2},{4}}=>0 {{1,3,4,5,6,7,8},{2}}=>0 {{1,4,5,6,7,8},{2,3}}=>0 {{1,2,4,5,6,7,8},{3}}=>0 {{1,2,5,6,7,8},{3,4}}=>0 {{1,2,3,5,6,7},{4},{8}}=>0 {{1,2,3,5,6,7,8},{4}}=>0 {{1,2,3,6,7,8},{4,5}}=>0 {{1,2,3,4,7},{5},{6},{8}}=>1 {{1,2,3,4,6,7},{5},{8}}=>0 {{1,2,3,4,6,7,8},{5}}=>0 {{1,2,3,4,5,6},{7,8}}=>0 {{1,2,3,7},{4,5,6},{8}}=>0 {{1,2,3,4,7},{5,6},{8}}=>0 {{1,2,3,4,7,8},{5,6}}=>0 {{1,2,3,4,5,7},{6},{8}}=>0 {{1,2,3,4,5,7,8},{6}}=>0 {{1,2,3,4,5,6,7},{8}}=>0 {{1,8},{2,3,4,5,6,7}}=>0 {{1,2,3,4,5,8},{6,7}}=>0 {{1,2,3,4,5,6,8},{7}}=>0 {{1,2,3,4,5,6,7,8}}=>0 {{1,3,5,6,7,8},{2,4}}=>0 {{1,3,4,6,7,8},{2,5}}=>0 {{1,2,4,6,7,8},{3,5}}=>0 {{1,3,4,5,7,8},{2,6}}=>0 {{1,2,4,5,7,8},{3,6}}=>0 {{1,2,3,5,7,8},{4,6}}=>0 {{1,3,4,5,6,8},{2,7}}=>0 {{1,2,4,5,6,8},{3,7}}=>0 {{1,2,3,5,6,8},{4,7}}=>0 {{1,2,3,4,6,8},{5,7}}=>0 {{1,3,4,5,6,7},{2,8}}=>0 {{1,2,4,5,6,7},{3,8}}=>0 {{1,2,3,5,6,7},{4,8}}=>0 {{1,2,3,4,6,7},{5,8}}=>0 {{1,2,3,4,5,7},{6,8}}=>0 {{1,3},{2,4,5,6,7,8}}=>0 {{1,4},{2,3,5,6,7,8}}=>0 {{1,5},{2,3,4,6,7,8}}=>0 {{1,6},{2,3,4,5,7,8}}=>0 {{1,7},{2,3,4,5,6,8}}=>0 {{1,2,3,4,5,6,7,8},{9}}=>0 {{1},{2,3,4,5,6,7,8,9}}=>0 {{1,2,3,4,5,6,8},{7},{9}}=>1 {{1},{2,3,4,5,6,7,9},{8}}=>1 {{1,2,3,4,5,8},{6,7},{9}}=>1 {{1,2,3,4,5,7,8},{6},{9}}=>1 {{1},{2,3,4,5,6,9},{7,8}}=>1 {{1},{2,3,4,5,6,8,9},{7}}=>0 {{1,2},{3,4},{5,6},{7,8},{9,10}}=>14 {{1,4},{2,3},{5,6},{7,8},{9,10}}=>12 {{1,6},{2,3},{4,5},{7,8},{9,10}}=>9 {{1,8},{2,3},{4,5},{6,7},{9,10}}=>9 {{1,10},{2,3},{4,5},{6,7},{8,9}}=>9 {{1,2},{3,6},{4,5},{7,8},{9,10}}=>10 {{1,6},{2,5},{3,4},{7,8},{9,10}}=>7 {{1,8},{2,5},{3,4},{6,7},{9,10}}=>7 {{1,10},{2,5},{3,4},{6,7},{8,9}}=>7 {{1,2},{3,8},{4,5},{6,7},{9,10}}=>8 {{1,8},{2,7},{3,4},{5,6},{9,10}}=>4 {{1,10},{2,7},{3,4},{5,6},{8,9}}=>4 {{1,2},{3,10},{4,5},{6,7},{8,9}}=>9 {{1,10},{2,9},{3,4},{5,6},{7,8}}=>15 {{1,2},{3,4},{5,8},{6,7},{9,10}}=>11 {{1,4},{2,3},{5,8},{6,7},{9,10}}=>9 {{1,8},{2,3},{4,7},{5,6},{9,10}}=>6 {{1,10},{2,3},{4,7},{5,6},{8,9}}=>6 {{1,2},{3,8},{4,7},{5,6},{9,10}}=>5 {{1,8},{2,7},{3,6},{4,5},{9,10}}=>2 {{1,10},{2,7},{3,6},{4,5},{8,9}}=>2 {{1,2},{3,10},{4,7},{5,6},{8,9}}=>6 {{1,10},{2,9},{3,6},{4,5},{7,8}}=>12 {{1,2},{3,4},{5,10},{6,7},{8,9}}=>11 {{1,4},{2,3},{5,10},{6,7},{8,9}}=>9 {{1,10},{2,3},{4,9},{5,6},{7,8}}=>16 {{1,2},{3,10},{4,9},{5,6},{7,8}}=>17 {{1,10},{2,9},{3,8},{4,5},{6,7}}=>10 {{1,2},{3,4},{5,6},{7,10},{8,9}}=>14 {{1,4},{2,3},{5,6},{7,10},{8,9}}=>12 {{1,6},{2,3},{4,5},{7,10},{8,9}}=>9 {{1,10},{2,3},{4,5},{6,9},{7,8}}=>19 {{1,2},{3,6},{4,5},{7,10},{8,9}}=>10 {{1,6},{2,5},{3,4},{7,10},{8,9}}=>7 {{1,10},{2,5},{3,4},{6,9},{7,8}}=>16 {{1,2},{3,10},{4,5},{6,9},{7,8}}=>20 {{1,10},{2,9},{3,4},{5,8},{6,7}}=>12 {{1,2},{3,4},{5,10},{6,9},{7,8}}=>23 {{1,4},{2,3},{5,10},{6,9},{7,8}}=>19 {{1,10},{2,3},{4,9},{5,8},{6,7}}=>13 {{1,2},{3,10},{4,9},{5,8},{6,7}}=>14 {{1,10},{2,9},{3,8},{4,7},{5,6}}=>7 {{1,2,3,4,5,6,7,8,9},{10}}=>0 {{1},{2,3,4,5,6,7,8,9,10}}=>0 {{1,2,3,4,5,6,7,9},{8},{10}}=>1 {{1},{2,3,4,5,6,7,8,10},{9}}=>1 {{1,2,3,4,5,6,7,8,9,10},{11}}=>0 {{1},{2,3,4,5,6,7,8,9,10,11}}=>0 {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>24 {{1,2},{3,4},{5,6},{7,8},{9,12},{10,11}}=>24 {{1,2},{3,4},{5,6},{7,10},{8,9},{11,12}}=>24 {{1,2},{3,4},{5,6},{7,12},{8,9},{10,11}}=>24 {{1,2},{3,4},{5,6},{7,12},{8,11},{9,10}}=>20 {{1,2},{3,4},{5,8},{6,7},{9,10},{11,12}}=>20 {{1,2},{3,4},{5,8},{6,7},{9,12},{10,11}}=>20 {{1,2},{3,4},{5,10},{6,7},{8,9},{11,12}}=>20 {{1,2},{3,4},{5,12},{6,7},{8,9},{10,11}}=>20 {{1,2},{3,4},{5,12},{6,7},{8,11},{9,10}}=>16 {{1,2},{3,4},{5,10},{6,9},{7,8},{11,12}}=>40 {{1,2},{3,4},{5,12},{6,9},{7,8},{10,11}}=>38 {{1,2},{3,4},{5,12},{6,11},{7,8},{9,10}}=>32 {{1,2},{3,4},{5,12},{6,11},{7,10},{8,9}}=>32 {{1,2},{3,6},{4,5},{7,8},{9,10},{11,12}}=>16 {{1,2},{3,6},{4,5},{7,8},{9,12},{10,11}}=>16 {{1,2},{3,6},{4,5},{7,10},{8,9},{11,12}}=>16 {{1,2},{3,6},{4,5},{7,12},{8,9},{10,11}}=>16 {{1,2},{3,6},{4,5},{7,12},{8,11},{9,10}}=>12 {{1,2},{3,8},{4,5},{6,7},{9,10},{11,12}}=>14 {{1,2},{3,8},{4,5},{6,7},{9,12},{10,11}}=>15 {{1,2},{3,10},{4,5},{6,7},{8,9},{11,12}}=>15 {{1,2},{3,12},{4,5},{6,7},{8,9},{10,11}}=>16 {{1,2},{3,12},{4,5},{6,7},{8,11},{9,10}}=>12 {{1,2},{3,10},{4,5},{6,9},{7,8},{11,12}}=>33 {{1,2},{3,12},{4,5},{6,9},{7,8},{10,11}}=>33 {{1,2},{3,12},{4,5},{6,11},{7,8},{9,10}}=>27 {{1,2},{3,12},{4,5},{6,11},{7,10},{8,9}}=>27 {{1,2},{3,8},{4,7},{5,6},{9,10},{11,12}}=>10 {{1,2},{3,8},{4,7},{5,6},{9,12},{10,11}}=>11 {{1,2},{3,10},{4,7},{5,6},{8,9},{11,12}}=>11 {{1,2},{3,12},{4,7},{5,6},{8,9},{10,11}}=>12 {{1,2},{3,12},{4,7},{5,6},{8,11},{9,10}}=>8 {{1,2},{3,10},{4,9},{5,6},{7,8},{11,12}}=>30 {{1,2},{3,12},{4,9},{5,6},{7,8},{10,11}}=>30 {{1,2},{3,12},{4,11},{5,6},{7,8},{9,10}}=>24 {{1,2},{3,12},{4,11},{5,6},{7,10},{8,9}}=>24 {{1,2},{3,10},{4,9},{5,8},{6,7},{11,12}}=>26 {{1,2},{3,12},{4,9},{5,8},{6,7},{10,11}}=>26 {{1,2},{3,12},{4,11},{5,8},{6,7},{9,10}}=>20 {{1,2},{3,12},{4,11},{5,10},{6,7},{8,9}}=>20 {{1,2},{3,12},{4,11},{5,10},{6,9},{7,8}}=>40 {{1,4},{2,3},{5,6},{7,8},{9,10},{11,12}}=>23 {{1,4},{2,3},{5,6},{7,8},{9,12},{10,11}}=>20 {{1,4},{2,3},{5,6},{7,10},{8,9},{11,12}}=>23 {{1,4},{2,3},{5,6},{7,12},{8,9},{10,11}}=>20 {{1,4},{2,3},{5,6},{7,12},{8,11},{9,10}}=>20 {{1,4},{2,3},{5,8},{6,7},{9,10},{11,12}}=>19 {{1,4},{2,3},{5,8},{6,7},{9,12},{10,11}}=>16 {{1,4},{2,3},{5,10},{6,7},{8,9},{11,12}}=>19 {{1,4},{2,3},{5,12},{6,7},{8,9},{10,11}}=>16 {{1,4},{2,3},{5,12},{6,7},{8,11},{9,10}}=>16 {{1,4},{2,3},{5,10},{6,9},{7,8},{11,12}}=>37 {{1,4},{2,3},{5,12},{6,9},{7,8},{10,11}}=>32 {{1,4},{2,3},{5,12},{6,11},{7,8},{9,10}}=>30 {{1,4},{2,3},{5,12},{6,11},{7,10},{8,9}}=>30 {{1,6},{2,3},{4,5},{7,8},{9,10},{11,12}}=>16 {{1,6},{2,3},{4,5},{7,8},{9,12},{10,11}}=>13 {{1,6},{2,3},{4,5},{7,10},{8,9},{11,12}}=>16 {{1,6},{2,3},{4,5},{7,12},{8,9},{10,11}}=>13 {{1,6},{2,3},{4,5},{7,12},{8,11},{9,10}}=>13 {{1,8},{2,3},{4,5},{6,7},{9,10},{11,12}}=>16 {{1,8},{2,3},{4,5},{6,7},{9,12},{10,11}}=>13 {{1,10},{2,3},{4,5},{6,7},{8,9},{11,12}}=>16 {{1,12},{2,3},{4,5},{6,7},{8,9},{10,11}}=>13 {{1,12},{2,3},{4,5},{6,7},{8,11},{9,10}}=>13 {{1,10},{2,3},{4,5},{6,9},{7,8},{11,12}}=>33 {{1,12},{2,3},{4,5},{6,9},{7,8},{10,11}}=>28 {{1,12},{2,3},{4,5},{6,11},{7,8},{9,10}}=>26 {{1,12},{2,3},{4,5},{6,11},{7,10},{8,9}}=>26 {{1,8},{2,3},{4,7},{5,6},{9,10},{11,12}}=>12 {{1,8},{2,3},{4,7},{5,6},{9,12},{10,11}}=>9 {{1,10},{2,3},{4,7},{5,6},{8,9},{11,12}}=>12 {{1,12},{2,3},{4,7},{5,6},{8,9},{10,11}}=>9 {{1,12},{2,3},{4,7},{5,6},{8,11},{9,10}}=>9 {{1,10},{2,3},{4,9},{5,6},{7,8},{11,12}}=>30 {{1,12},{2,3},{4,9},{5,6},{7,8},{10,11}}=>25 {{1,12},{2,3},{4,11},{5,6},{7,8},{9,10}}=>23 {{1,12},{2,3},{4,11},{5,6},{7,10},{8,9}}=>23 {{1,10},{2,3},{4,9},{5,8},{6,7},{11,12}}=>26 {{1,12},{2,3},{4,9},{5,8},{6,7},{10,11}}=>21 {{1,12},{2,3},{4,11},{5,8},{6,7},{9,10}}=>19 {{1,12},{2,3},{4,11},{5,10},{6,7},{8,9}}=>19 {{1,12},{2,3},{4,11},{5,10},{6,9},{7,8}}=>37 {{1,6},{2,5},{3,4},{7,8},{9,10},{11,12}}=>12 {{1,6},{2,5},{3,4},{7,8},{9,12},{10,11}}=>10 {{1,6},{2,5},{3,4},{7,10},{8,9},{11,12}}=>12 {{1,6},{2,5},{3,4},{7,12},{8,9},{10,11}}=>10 {{1,6},{2,5},{3,4},{7,12},{8,11},{9,10}}=>10 {{1,8},{2,5},{3,4},{6,7},{9,10},{11,12}}=>12 {{1,8},{2,5},{3,4},{6,7},{9,12},{10,11}}=>10 {{1,10},{2,5},{3,4},{6,7},{8,9},{11,12}}=>12 {{1,12},{2,5},{3,4},{6,7},{8,9},{10,11}}=>10 {{1,12},{2,5},{3,4},{6,7},{8,11},{9,10}}=>10 {{1,10},{2,5},{3,4},{6,9},{7,8},{11,12}}=>27 {{1,12},{2,5},{3,4},{6,9},{7,8},{10,11}}=>23 {{1,12},{2,5},{3,4},{6,11},{7,8},{9,10}}=>21 {{1,12},{2,5},{3,4},{6,11},{7,10},{8,9}}=>21 {{1,8},{2,7},{3,4},{5,6},{9,10},{11,12}}=>8 {{1,8},{2,7},{3,4},{5,6},{9,12},{10,11}}=>6 {{1,10},{2,7},{3,4},{5,6},{8,9},{11,12}}=>8 {{1,12},{2,7},{3,4},{5,6},{8,9},{10,11}}=>6 {{1,12},{2,7},{3,4},{5,6},{8,11},{9,10}}=>6 {{1,10},{2,9},{3,4},{5,6},{7,8},{11,12}}=>26 {{1,12},{2,9},{3,4},{5,6},{7,8},{10,11}}=>22 {{1,12},{2,11},{3,4},{5,6},{7,8},{9,10}}=>21 {{1,12},{2,11},{3,4},{5,6},{7,10},{8,9}}=>21 {{1,10},{2,9},{3,4},{5,8},{6,7},{11,12}}=>22 {{1,12},{2,9},{3,4},{5,8},{6,7},{10,11}}=>18 {{1,12},{2,11},{3,4},{5,8},{6,7},{9,10}}=>17 {{1,12},{2,11},{3,4},{5,10},{6,7},{8,9}}=>17 {{1,12},{2,11},{3,4},{5,10},{6,9},{7,8}}=>34 {{1,8},{2,7},{3,6},{4,5},{9,10},{11,12}}=>3 {{1,8},{2,7},{3,6},{4,5},{9,12},{10,11}}=>1 {{1,10},{2,7},{3,6},{4,5},{8,9},{11,12}}=>3 {{1,12},{2,7},{3,6},{4,5},{8,9},{10,11}}=>1 {{1,12},{2,7},{3,6},{4,5},{8,11},{9,10}}=>1 {{1,10},{2,9},{3,6},{4,5},{7,8},{11,12}}=>19 {{1,12},{2,9},{3,6},{4,5},{7,8},{10,11}}=>15 {{1,12},{2,11},{3,6},{4,5},{7,8},{9,10}}=>14 {{1,12},{2,11},{3,6},{4,5},{7,10},{8,9}}=>14 {{1,10},{2,9},{3,8},{4,5},{6,7},{11,12}}=>17 {{1,12},{2,9},{3,8},{4,5},{6,7},{10,11}}=>14 {{1,12},{2,11},{3,8},{4,5},{6,7},{9,10}}=>13 {{1,12},{2,11},{3,10},{4,5},{6,7},{8,9}}=>13 {{1,12},{2,11},{3,10},{4,5},{6,9},{7,8}}=>28 {{1,10},{2,9},{3,8},{4,7},{5,6},{11,12}}=>13 {{1,12},{2,9},{3,8},{4,7},{5,6},{10,11}}=>10 {{1,12},{2,11},{3,8},{4,7},{5,6},{9,10}}=>9 {{1,12},{2,11},{3,10},{4,7},{5,6},{8,9}}=>9 {{1,12},{2,11},{3,10},{4,9},{5,6},{7,8}}=>25 {{1,12},{2,11},{3,10},{4,9},{5,8},{6,7}}=>21
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Description
The number of occurrences of the pattern {{1},{2},{3}} such that 3 is minimal, 1, 2 are maximal.
References
[1] Chern, B., Diaconis, P., Kane, D. M., Rhoades, R. C. Closed expressions for averages of set partition statistics MathSciNet:3338726 arXiv:1304.4309
Code
def statistic(pi):
    return len(pattern_occurrences(pi, [[1], [2], [3]], [3], [1, 2], [], []))

def pattern_occurrences(pi, P, First, Last, Arcs, Consecutives):
    """We assume that pi is a SetPartition of {1,2,...,n} and P is a
    SetPartition of {1,2,...,k}.
    """
    occurrences = []
    pi = SetPartition(pi)
    P = SetPartition(P)

    openers = [min(B) for B in pi]
    closers = [max(B) for B in pi]
    pi_sorted = sorted([sorted(b) for b in pi])
    edges = [(a,b) for B in pi_sorted for (a,b) in zip(B, B[1:])]

    for s in Subsets(pi.base_set(), P.size()):
        s = sorted(s)
        pi_r = pi.restriction(s)
        if pi_r.standardization() != P:
            continue

        X = pi_r.base_set()

        if any(X[i-1] not in openers for i in First):
            continue

        if any(X[i-1] not in closers for i in Last):
            continue

        if any((X[i-1], X[j-1]) not in edges for (i,j) in Arcs):
            continue

        if any(abs(X[i-1]-X[j-1]) != 1 for (i,j) in Consecutives):
            continue

        occurrences += [s]
    return occurrences
Created
Aug 11, 2016 at 14:50 by Martin Rubey
Updated
Apr 01, 2018 at 21:29 by Martin Rubey