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Identifier
Values
=>
Cc0009;cc-rep
{{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}}=>0 {{1,2,3,4}}=>0 {{1,2,3},{4}}=>0 {{1,2,4},{3}}=>0 {{1,2},{3,4}}=>0 {{1,2},{3},{4}}=>0 {{1,3,4},{2}}=>0 {{1,3},{2,4}}=>1 {{1,3},{2},{4}}=>1 {{1,4},{2,3}}=>0 {{1},{2,3,4}}=>0 {{1},{2,3},{4}}=>0 {{1,4},{2},{3}}=>0 {{1},{2,4},{3}}=>0 {{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}}=>0 {{1,2,3},{4,5}}=>0 {{1,2,3},{4},{5}}=>0 {{1,2,4,5},{3}}=>0 {{1,2,4},{3,5}}=>1 {{1,2,4},{3},{5}}=>1 {{1,2,5},{3,4}}=>0 {{1,2},{3,4,5}}=>0 {{1,2},{3,4},{5}}=>0 {{1,2,5},{3},{4}}=>0 {{1,2},{3,5},{4}}=>0 {{1,2},{3},{4,5}}=>0 {{1,2},{3},{4},{5}}=>0 {{1,3,4,5},{2}}=>0 {{1,3,4},{2,5}}=>2 {{1,3,4},{2},{5}}=>2 {{1,3,5},{2,4}}=>1 {{1,3},{2,4,5}}=>1 {{1,3},{2,4},{5}}=>1 {{1,3,5},{2},{4}}=>1 {{1,3},{2,5},{4}}=>1 {{1,3},{2},{4,5}}=>1 {{1,3},{2},{4},{5}}=>1 {{1,4,5},{2,3}}=>0 {{1,4},{2,3,5}}=>1 {{1,4},{2,3},{5}}=>1 {{1,5},{2,3,4}}=>0 {{1},{2,3,4,5}}=>0 {{1},{2,3,4},{5}}=>0 {{1,5},{2,3},{4}}=>0 {{1},{2,3,5},{4}}=>0 {{1},{2,3},{4,5}}=>0 {{1},{2,3},{4},{5}}=>0 {{1,4,5},{2},{3}}=>0 {{1,4},{2,5},{3}}=>1 {{1,4},{2},{3,5}}=>1 {{1,4},{2},{3},{5}}=>1 {{1,5},{2,4},{3}}=>0 {{1},{2,4,5},{3}}=>0 {{1},{2,4},{3,5}}=>1 {{1},{2,4},{3},{5}}=>1 {{1,5},{2},{3,4}}=>0 {{1},{2,5},{3,4}}=>0 {{1},{2},{3,4,5}}=>0 {{1},{2},{3,4},{5}}=>0 {{1,5},{2},{3},{4}}=>0 {{1},{2,5},{3},{4}}=>0 {{1},{2},{3,5},{4}}=>0 {{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}}=>0 {{1,2,3,4},{5,6}}=>0 {{1,2,3,4},{5},{6}}=>0 {{1,2,3,5,6},{4}}=>0 {{1,2,3,5},{4,6}}=>1 {{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}}=>0 {{1,2,3,6},{4},{5}}=>0 {{1,2,3},{4,6},{5}}=>0 {{1,2,3},{4},{5,6}}=>0 {{1,2,3},{4},{5},{6}}=>0 {{1,2,4,5,6},{3}}=>0 {{1,2,4,5},{3,6}}=>2 {{1,2,4,5},{3},{6}}=>2 {{1,2,4,6},{3,5}}=>1 {{1,2,4},{3,5,6}}=>1 {{1,2,4},{3,5},{6}}=>1 {{1,2,4,6},{3},{5}}=>1 {{1,2,4},{3,6},{5}}=>1 {{1,2,4},{3},{5,6}}=>1 {{1,2,4},{3},{5},{6}}=>1 {{1,2,5,6},{3,4}}=>0 {{1,2,5},{3,4,6}}=>1 {{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}}=>0 {{1,2,6},{3,4},{5}}=>0 {{1,2},{3,4,6},{5}}=>0 {{1,2},{3,4},{5,6}}=>0 {{1,2},{3,4},{5},{6}}=>0 {{1,2,5,6},{3},{4}}=>0 {{1,2,5},{3,6},{4}}=>1 {{1,2,5},{3},{4,6}}=>1 {{1,2,5},{3},{4},{6}}=>1 {{1,2,6},{3,5},{4}}=>0 {{1,2},{3,5,6},{4}}=>0 {{1,2},{3,5},{4,6}}=>1 {{1,2},{3,5},{4},{6}}=>1 {{1,2,6},{3},{4,5}}=>0 {{1,2},{3,6},{4,5}}=>0 {{1,2},{3},{4,5,6}}=>0 {{1,2},{3},{4,5},{6}}=>0 {{1,2,6},{3},{4},{5}}=>0 {{1,2},{3,6},{4},{5}}=>0 {{1,2},{3},{4,6},{5}}=>0 {{1,2},{3},{4},{5,6}}=>0 {{1,2},{3},{4},{5},{6}}=>0 {{1,3,4,5,6},{2}}=>0 {{1,3,4,5},{2,6}}=>3 {{1,3,4,5},{2},{6}}=>3 {{1,3,4,6},{2,5}}=>2 {{1,3,4},{2,5,6}}=>2 {{1,3,4},{2,5},{6}}=>2 {{1,3,4,6},{2},{5}}=>2 {{1,3,4},{2,6},{5}}=>2 {{1,3,4},{2},{5,6}}=>2 {{1,3,4},{2},{5},{6}}=>2 {{1,3,5,6},{2,4}}=>1 {{1,3,5},{2,4,6}}=>2 {{1,3,5},{2,4},{6}}=>2 {{1,3,6},{2,4,5}}=>1 {{1,3},{2,4,5,6}}=>1 {{1,3},{2,4,5},{6}}=>1 {{1,3,6},{2,4},{5}}=>1 {{1,3},{2,4,6},{5}}=>1 {{1,3},{2,4},{5,6}}=>1 {{1,3},{2,4},{5},{6}}=>1 {{1,3,5,6},{2},{4}}=>1 {{1,3,5},{2,6},{4}}=>2 {{1,3,5},{2},{4,6}}=>2 {{1,3,5},{2},{4},{6}}=>2 {{1,3,6},{2,5},{4}}=>1 {{1,3},{2,5,6},{4}}=>1 {{1,3},{2,5},{4,6}}=>2 {{1,3},{2,5},{4},{6}}=>2 {{1,3,6},{2},{4,5}}=>1 {{1,3},{2,6},{4,5}}=>1 {{1,3},{2},{4,5,6}}=>1 {{1,3},{2},{4,5},{6}}=>1 {{1,3,6},{2},{4},{5}}=>1 {{1,3},{2,6},{4},{5}}=>1 {{1,3},{2},{4,6},{5}}=>1 {{1,3},{2},{4},{5,6}}=>1 {{1,3},{2},{4},{5},{6}}=>1 {{1,4,5,6},{2,3}}=>0 {{1,4,5},{2,3,6}}=>2 {{1,4,5},{2,3},{6}}=>2 {{1,4,6},{2,3,5}}=>1 {{1,4},{2,3,5,6}}=>1 {{1,4},{2,3,5},{6}}=>1 {{1,4,6},{2,3},{5}}=>1 {{1,4},{2,3,6},{5}}=>1 {{1,4},{2,3},{5,6}}=>1 {{1,4},{2,3},{5},{6}}=>1 {{1,5,6},{2,3,4}}=>0 {{1,5},{2,3,4,6}}=>1 {{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}}=>0 {{1,6},{2,3,4},{5}}=>0 {{1},{2,3,4,6},{5}}=>0 {{1},{2,3,4},{5,6}}=>0 {{1},{2,3,4},{5},{6}}=>0 {{1,5,6},{2,3},{4}}=>0 {{1,5},{2,3,6},{4}}=>1 {{1,5},{2,3},{4,6}}=>1 {{1,5},{2,3},{4},{6}}=>1 {{1,6},{2,3,5},{4}}=>0 {{1},{2,3,5,6},{4}}=>0 {{1},{2,3,5},{4,6}}=>1 {{1},{2,3,5},{4},{6}}=>1 {{1,6},{2,3},{4,5}}=>0 {{1},{2,3,6},{4,5}}=>0 {{1},{2,3},{4,5,6}}=>0 {{1},{2,3},{4,5},{6}}=>0 {{1,6},{2,3},{4},{5}}=>0 {{1},{2,3,6},{4},{5}}=>0 {{1},{2,3},{4,6},{5}}=>0 {{1},{2,3},{4},{5,6}}=>0 {{1},{2,3},{4},{5},{6}}=>0 {{1,4,5,6},{2},{3}}=>0 {{1,4,5},{2,6},{3}}=>2 {{1,4,5},{2},{3,6}}=>2 {{1,4,5},{2},{3},{6}}=>2 {{1,4,6},{2,5},{3}}=>1 {{1,4},{2,5,6},{3}}=>1 {{1,4},{2,5},{3,6}}=>2 {{1,4},{2,5},{3},{6}}=>2 {{1,4,6},{2},{3,5}}=>1 {{1,4},{2,6},{3,5}}=>1 {{1,4},{2},{3,5,6}}=>1 {{1,4},{2},{3,5},{6}}=>1 {{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}}=>1 {{1,4},{2},{3},{5},{6}}=>1 {{1,5,6},{2,4},{3}}=>0 {{1,5},{2,4,6},{3}}=>1 {{1,5},{2,4},{3,6}}=>2 {{1,5},{2,4},{3},{6}}=>2 {{1,6},{2,4,5},{3}}=>0 {{1},{2,4,5,6},{3}}=>0 {{1},{2,4,5},{3,6}}=>2 {{1},{2,4,5},{3},{6}}=>2 {{1,6},{2,4},{3,5}}=>1 {{1},{2,4,6},{3,5}}=>1 {{1},{2,4},{3,5,6}}=>1 {{1},{2,4},{3,5},{6}}=>1 {{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}}=>1 {{1},{2,4},{3},{5},{6}}=>1 {{1,5,6},{2},{3,4}}=>0 {{1,5},{2,6},{3,4}}=>1 {{1,5},{2},{3,4,6}}=>1 {{1,5},{2},{3,4},{6}}=>1 {{1,6},{2,5},{3,4}}=>0 {{1},{2,5,6},{3,4}}=>0 {{1},{2,5},{3,4,6}}=>1 {{1},{2,5},{3,4},{6}}=>1 {{1,6},{2},{3,4,5}}=>0 {{1},{2,6},{3,4,5}}=>0 {{1},{2},{3,4,5,6}}=>0 {{1},{2},{3,4,5},{6}}=>0 {{1,6},{2},{3,4},{5}}=>0 {{1},{2,6},{3,4},{5}}=>0 {{1},{2},{3,4,6},{5}}=>0 {{1},{2},{3,4},{5,6}}=>0 {{1},{2},{3,4},{5},{6}}=>0 {{1,5,6},{2},{3},{4}}=>0 {{1,5},{2,6},{3},{4}}=>1 {{1,5},{2},{3,6},{4}}=>1 {{1,5},{2},{3},{4,6}}=>1 {{1,5},{2},{3},{4},{6}}=>1 {{1,6},{2,5},{3},{4}}=>0 {{1},{2,5,6},{3},{4}}=>0 {{1},{2,5},{3,6},{4}}=>1 {{1},{2,5},{3},{4,6}}=>1 {{1},{2,5},{3},{4},{6}}=>1 {{1,6},{2},{3,5},{4}}=>0 {{1},{2,6},{3,5},{4}}=>0 {{1},{2},{3,5,6},{4}}=>0 {{1},{2},{3,5},{4,6}}=>1 {{1},{2},{3,5},{4},{6}}=>1 {{1,6},{2},{3},{4,5}}=>0 {{1},{2,6},{3},{4,5}}=>0 {{1},{2},{3,6},{4,5}}=>0 {{1},{2},{3},{4,5,6}}=>0 {{1},{2},{3},{4,5},{6}}=>0 {{1,6},{2},{3},{4},{5}}=>0 {{1},{2,6},{3},{4},{5}}=>0 {{1},{2},{3,6},{4},{5}}=>0 {{1},{2},{3},{4,6},{5}}=>0 {{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}}=>0 {{1,2,3,4,5},{6,7}}=>0 {{1,2,3,4,5},{6},{7}}=>0 {{1,2,3,4,6,7},{5}}=>0 {{1,2,3,4,6},{5,7}}=>1 {{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}}=>0 {{1,2,3,4,7},{5},{6}}=>0 {{1,2,3,4},{5,7},{6}}=>0 {{1,2,3,4},{5},{6,7}}=>0 {{1,2,3,4},{5},{6},{7}}=>0 {{1,2,3,5,6,7},{4}}=>0 {{1,2,3,5,6},{4,7}}=>2 {{1,2,3,5,6},{4},{7}}=>2 {{1,2,3,5,7},{4,6}}=>1 {{1,2,3,5},{4,6,7}}=>1 {{1,2,3,5},{4,6},{7}}=>1 {{1,2,3,5,7},{4},{6}}=>1 {{1,2,3,5},{4,7},{6}}=>1 {{1,2,3,5},{4},{6,7}}=>1 {{1,2,3,5},{4},{6},{7}}=>1 {{1,2,3,6,7},{4,5}}=>0 {{1,2,3,6},{4,5,7}}=>1 {{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}}=>0 {{1,2,3,7},{4,5},{6}}=>0 {{1,2,3},{4,5,7},{6}}=>0 {{1,2,3},{4,5},{6,7}}=>0 {{1,2,3},{4,5},{6},{7}}=>0 {{1,2,3,6,7},{4},{5}}=>0 {{1,2,3,6},{4,7},{5}}=>1 {{1,2,3,6},{4},{5,7}}=>1 {{1,2,3,6},{4},{5},{7}}=>1 {{1,2,3,7},{4,6},{5}}=>0 {{1,2,3},{4,6,7},{5}}=>0 {{1,2,3},{4,6},{5,7}}=>1 {{1,2,3},{4,6},{5},{7}}=>1 {{1,2,3,7},{4},{5,6}}=>0 {{1,2,3},{4,7},{5,6}}=>0 {{1,2,3},{4},{5,6,7}}=>0 {{1,2,3},{4},{5,6},{7}}=>0 {{1,2,3,7},{4},{5},{6}}=>0 {{1,2,3},{4,7},{5},{6}}=>0 {{1,2,3},{4},{5,7},{6}}=>0 {{1,2,3},{4},{5},{6,7}}=>0 {{1,2,3},{4},{5},{6},{7}}=>0 {{1,2,4,5,6,7},{3}}=>0 {{1,2,4,5,6},{3,7}}=>3 {{1,2,4,5,6},{3},{7}}=>3 {{1,2,4,5,7},{3,6}}=>2 {{1,2,4,5},{3,6,7}}=>2 {{1,2,4,5},{3,6},{7}}=>2 {{1,2,4,5,7},{3},{6}}=>2 {{1,2,4,5},{3,7},{6}}=>2 {{1,2,4,5},{3},{6,7}}=>2 {{1,2,4,5},{3},{6},{7}}=>2 {{1,2,4,6,7},{3,5}}=>1 {{1,2,4,6},{3,5,7}}=>2 {{1,2,4,6},{3,5},{7}}=>2 {{1,2,4,7},{3,5,6}}=>1 {{1,2,4},{3,5,6,7}}=>1 {{1,2,4},{3,5,6},{7}}=>1 {{1,2,4,7},{3,5},{6}}=>1 {{1,2,4},{3,5,7},{6}}=>1 {{1,2,4},{3,5},{6,7}}=>1 {{1,2,4},{3,5},{6},{7}}=>1 {{1,2,4,6,7},{3},{5}}=>1 {{1,2,4,6},{3,7},{5}}=>2 {{1,2,4,6},{3},{5,7}}=>2 {{1,2,4,6},{3},{5},{7}}=>2 {{1,2,4,7},{3,6},{5}}=>1 {{1,2,4},{3,6,7},{5}}=>1 {{1,2,4},{3,6},{5,7}}=>2 {{1,2,4},{3,6},{5},{7}}=>2 {{1,2,4,7},{3},{5,6}}=>1 {{1,2,4},{3,7},{5,6}}=>1 {{1,2,4},{3},{5,6,7}}=>1 {{1,2,4},{3},{5,6},{7}}=>1 {{1,2,4,7},{3},{5},{6}}=>1 {{1,2,4},{3,7},{5},{6}}=>1 {{1,2,4},{3},{5,7},{6}}=>1 {{1,2,4},{3},{5},{6,7}}=>1 {{1,2,4},{3},{5},{6},{7}}=>1 {{1,2,5,6,7},{3,4}}=>0 {{1,2,5,6},{3,4,7}}=>2 {{1,2,5,6},{3,4},{7}}=>2 {{1,2,5,7},{3,4,6}}=>1 {{1,2,5},{3,4,6,7}}=>1 {{1,2,5},{3,4,6},{7}}=>1 {{1,2,5,7},{3,4},{6}}=>1 {{1,2,5},{3,4,7},{6}}=>1 {{1,2,5},{3,4},{6,7}}=>1 {{1,2,5},{3,4},{6},{7}}=>1 {{1,2,6,7},{3,4,5}}=>0 {{1,2,6},{3,4,5,7}}=>1 {{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}}=>0 {{1,2,7},{3,4,5},{6}}=>0 {{1,2},{3,4,5,7},{6}}=>0 {{1,2},{3,4,5},{6,7}}=>0 {{1,2},{3,4,5},{6},{7}}=>0 {{1,2,6,7},{3,4},{5}}=>0 {{1,2,6},{3,4,7},{5}}=>1 {{1,2,6},{3,4},{5,7}}=>1 {{1,2,6},{3,4},{5},{7}}=>1 {{1,2,7},{3,4,6},{5}}=>0 {{1,2},{3,4,6,7},{5}}=>0 {{1,2},{3,4,6},{5,7}}=>1 {{1,2},{3,4,6},{5},{7}}=>1 {{1,2,7},{3,4},{5,6}}=>0 {{1,2},{3,4,7},{5,6}}=>0 {{1,2},{3,4},{5,6,7}}=>0 {{1,2},{3,4},{5,6},{7}}=>0 {{1,2,7},{3,4},{5},{6}}=>0 {{1,2},{3,4,7},{5},{6}}=>0 {{1,2},{3,4},{5,7},{6}}=>0 {{1,2},{3,4},{5},{6,7}}=>0 {{1,2},{3,4},{5},{6},{7}}=>0 {{1,2,5,6,7},{3},{4}}=>0 {{1,2,5,6},{3,7},{4}}=>2 {{1,2,5,6},{3},{4,7}}=>2 {{1,2,5,6},{3},{4},{7}}=>2 {{1,2,5,7},{3,6},{4}}=>1 {{1,2,5},{3,6,7},{4}}=>1 {{1,2,5},{3,6},{4,7}}=>2 {{1,2,5},{3,6},{4},{7}}=>2 {{1,2,5,7},{3},{4,6}}=>1 {{1,2,5},{3,7},{4,6}}=>1 {{1,2,5},{3},{4,6,7}}=>1 {{1,2,5},{3},{4,6},{7}}=>1 {{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}}=>1 {{1,2,5},{3},{4},{6},{7}}=>1 {{1,2,6,7},{3,5},{4}}=>0 {{1,2,6},{3,5,7},{4}}=>1 {{1,2,6},{3,5},{4,7}}=>2 {{1,2,6},{3,5},{4},{7}}=>2 {{1,2,7},{3,5,6},{4}}=>0 {{1,2},{3,5,6,7},{4}}=>0 {{1,2},{3,5,6},{4,7}}=>2 {{1,2},{3,5,6},{4},{7}}=>2 {{1,2,7},{3,5},{4,6}}=>1 {{1,2},{3,5,7},{4,6}}=>1 {{1,2},{3,5},{4,6,7}}=>1 {{1,2},{3,5},{4,6},{7}}=>1 {{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}}=>1 {{1,2},{3,5},{4},{6},{7}}=>1 {{1,2,6,7},{3},{4,5}}=>0 {{1,2,6},{3,7},{4,5}}=>1 {{1,2,6},{3},{4,5,7}}=>1 {{1,2,6},{3},{4,5},{7}}=>1 {{1,2,7},{3,6},{4,5}}=>0 {{1,2},{3,6,7},{4,5}}=>0 {{1,2},{3,6},{4,5,7}}=>1 {{1,2},{3,6},{4,5},{7}}=>1 {{1,2,7},{3},{4,5,6}}=>0 {{1,2},{3,7},{4,5,6}}=>0 {{1,2},{3},{4,5,6,7}}=>0 {{1,2},{3},{4,5,6},{7}}=>0 {{1,2,7},{3},{4,5},{6}}=>0 {{1,2},{3,7},{4,5},{6}}=>0 {{1,2},{3},{4,5,7},{6}}=>0 {{1,2},{3},{4,5},{6,7}}=>0 {{1,2},{3},{4,5},{6},{7}}=>0 {{1,2,6,7},{3},{4},{5}}=>0 {{1,2,6},{3,7},{4},{5}}=>1 {{1,2,6},{3},{4,7},{5}}=>1 {{1,2,6},{3},{4},{5,7}}=>1 {{1,2,6},{3},{4},{5},{7}}=>1 {{1,2,7},{3,6},{4},{5}}=>0 {{1,2},{3,6,7},{4},{5}}=>0 {{1,2},{3,6},{4,7},{5}}=>1 {{1,2},{3,6},{4},{5,7}}=>1 {{1,2},{3,6},{4},{5},{7}}=>1 {{1,2,7},{3},{4,6},{5}}=>0 {{1,2},{3,7},{4,6},{5}}=>0 {{1,2},{3},{4,6,7},{5}}=>0 {{1,2},{3},{4,6},{5,7}}=>1 {{1,2},{3},{4,6},{5},{7}}=>1 {{1,2,7},{3},{4},{5,6}}=>0 {{1,2},{3,7},{4},{5,6}}=>0 {{1,2},{3},{4,7},{5,6}}=>0 {{1,2},{3},{4},{5,6,7}}=>0 {{1,2},{3},{4},{5,6},{7}}=>0 {{1,2,7},{3},{4},{5},{6}}=>0 {{1,2},{3,7},{4},{5},{6}}=>0 {{1,2},{3},{4,7},{5},{6}}=>0 {{1,2},{3},{4},{5,7},{6}}=>0 {{1,2},{3},{4},{5},{6,7}}=>0 {{1,2},{3},{4},{5},{6},{7}}=>0 {{1,3,4,5,6,7},{2}}=>0 {{1,3,4,5,6},{2,7}}=>4 {{1,3,4,5,6},{2},{7}}=>4 {{1,3,4,5,7},{2,6}}=>3 {{1,3,4,5},{2,6,7}}=>3 {{1,3,4,5},{2,6},{7}}=>3 {{1,3,4,5,7},{2},{6}}=>3 {{1,3,4,5},{2,7},{6}}=>3 {{1,3,4,5},{2},{6,7}}=>3 {{1,3,4,5},{2},{6},{7}}=>3 {{1,3,4,6,7},{2,5}}=>2 {{1,3,4,6},{2,5,7}}=>3 {{1,3,4,6},{2,5},{7}}=>3 {{1,3,4,7},{2,5,6}}=>2 {{1,3,4},{2,5,6,7}}=>2 {{1,3,4},{2,5,6},{7}}=>2 {{1,3,4,7},{2,5},{6}}=>2 {{1,3,4},{2,5,7},{6}}=>2 {{1,3,4},{2,5},{6,7}}=>2 {{1,3,4},{2,5},{6},{7}}=>2 {{1,3,4,6,7},{2},{5}}=>2 {{1,3,4,6},{2,7},{5}}=>3 {{1,3,4,6},{2},{5,7}}=>3 {{1,3,4,6},{2},{5},{7}}=>3 {{1,3,4,7},{2,6},{5}}=>2 {{1,3,4},{2,6,7},{5}}=>2 {{1,3,4},{2,6},{5,7}}=>3 {{1,3,4},{2,6},{5},{7}}=>3 {{1,3,4,7},{2},{5,6}}=>2 {{1,3,4},{2,7},{5,6}}=>2 {{1,3,4},{2},{5,6,7}}=>2 {{1,3,4},{2},{5,6},{7}}=>2 {{1,3,4,7},{2},{5},{6}}=>2 {{1,3,4},{2,7},{5},{6}}=>2 {{1,3,4},{2},{5,7},{6}}=>2 {{1,3,4},{2},{5},{6,7}}=>2 {{1,3,4},{2},{5},{6},{7}}=>2 {{1,3,5,6,7},{2,4}}=>1 {{1,3,5,6},{2,4,7}}=>3 {{1,3,5,6},{2,4},{7}}=>3 {{1,3,5,7},{2,4,6}}=>2 {{1,3,5},{2,4,6,7}}=>2 {{1,3,5},{2,4,6},{7}}=>2 {{1,3,5,7},{2,4},{6}}=>2 {{1,3,5},{2,4,7},{6}}=>2 {{1,3,5},{2,4},{6,7}}=>2 {{1,3,5},{2,4},{6},{7}}=>2 {{1,3,6,7},{2,4,5}}=>1 {{1,3,6},{2,4,5,7}}=>2 {{1,3,6},{2,4,5},{7}}=>2 {{1,3,7},{2,4,5,6}}=>1 {{1,3},{2,4,5,6,7}}=>1 {{1,3},{2,4,5,6},{7}}=>1 {{1,3,7},{2,4,5},{6}}=>1 {{1,3},{2,4,5,7},{6}}=>1 {{1,3},{2,4,5},{6,7}}=>1 {{1,3},{2,4,5},{6},{7}}=>1 {{1,3,6,7},{2,4},{5}}=>1 {{1,3,6},{2,4,7},{5}}=>2 {{1,3,6},{2,4},{5,7}}=>2 {{1,3,6},{2,4},{5},{7}}=>2 {{1,3,7},{2,4,6},{5}}=>1 {{1,3},{2,4,6,7},{5}}=>1 {{1,3},{2,4,6},{5,7}}=>2 {{1,3},{2,4,6},{5},{7}}=>2 {{1,3,7},{2,4},{5,6}}=>1 {{1,3},{2,4,7},{5,6}}=>1 {{1,3},{2,4},{5,6,7}}=>1 {{1,3},{2,4},{5,6},{7}}=>1 {{1,3,7},{2,4},{5},{6}}=>1 {{1,3},{2,4,7},{5},{6}}=>1 {{1,3},{2,4},{5,7},{6}}=>1 {{1,3},{2,4},{5},{6,7}}=>1 {{1,3},{2,4},{5},{6},{7}}=>1 {{1,3,5,6,7},{2},{4}}=>1 {{1,3,5,6},{2,7},{4}}=>3 {{1,3,5,6},{2},{4,7}}=>3 {{1,3,5,6},{2},{4},{7}}=>3 {{1,3,5,7},{2,6},{4}}=>2 {{1,3,5},{2,6,7},{4}}=>2 {{1,3,5},{2,6},{4,7}}=>3 {{1,3,5},{2,6},{4},{7}}=>3 {{1,3,5,7},{2},{4,6}}=>2 {{1,3,5},{2,7},{4,6}}=>2 {{1,3,5},{2},{4,6,7}}=>2 {{1,3,5},{2},{4,6},{7}}=>2 {{1,3,5,7},{2},{4},{6}}=>2 {{1,3,5},{2,7},{4},{6}}=>2 {{1,3,5},{2},{4,7},{6}}=>2 {{1,3,5},{2},{4},{6,7}}=>2 {{1,3,5},{2},{4},{6},{7}}=>2 {{1,3,6,7},{2,5},{4}}=>1 {{1,3,6},{2,5,7},{4}}=>2 {{1,3,6},{2,5},{4,7}}=>3 {{1,3,6},{2,5},{4},{7}}=>3 {{1,3,7},{2,5,6},{4}}=>1 {{1,3},{2,5,6,7},{4}}=>1 {{1,3},{2,5,6},{4,7}}=>3 {{1,3},{2,5,6},{4},{7}}=>3 {{1,3,7},{2,5},{4,6}}=>2 {{1,3},{2,5,7},{4,6}}=>2 {{1,3},{2,5},{4,6,7}}=>2 {{1,3},{2,5},{4,6},{7}}=>2 {{1,3,7},{2,5},{4},{6}}=>2 {{1,3},{2,5,7},{4},{6}}=>2 {{1,3},{2,5},{4,7},{6}}=>2 {{1,3},{2,5},{4},{6,7}}=>2 {{1,3},{2,5},{4},{6},{7}}=>2 {{1,3,6,7},{2},{4,5}}=>1 {{1,3,6},{2,7},{4,5}}=>2 {{1,3,6},{2},{4,5,7}}=>2 {{1,3,6},{2},{4,5},{7}}=>2 {{1,3,7},{2,6},{4,5}}=>1 {{1,3},{2,6,7},{4,5}}=>1 {{1,3},{2,6},{4,5,7}}=>2 {{1,3},{2,6},{4,5},{7}}=>2 {{1,3,7},{2},{4,5,6}}=>1 {{1,3},{2,7},{4,5,6}}=>1 {{1,3},{2},{4,5,6,7}}=>1 {{1,3},{2},{4,5,6},{7}}=>1 {{1,3,7},{2},{4,5},{6}}=>1 {{1,3},{2,7},{4,5},{6}}=>1 {{1,3},{2},{4,5,7},{6}}=>1 {{1,3},{2},{4,5},{6,7}}=>1 {{1,3},{2},{4,5},{6},{7}}=>1 {{1,3,6,7},{2},{4},{5}}=>1 {{1,3,6},{2,7},{4},{5}}=>2 {{1,3,6},{2},{4,7},{5}}=>2 {{1,3,6},{2},{4},{5,7}}=>2 {{1,3,6},{2},{4},{5},{7}}=>2 {{1,3,7},{2,6},{4},{5}}=>1 {{1,3},{2,6,7},{4},{5}}=>1 {{1,3},{2,6},{4,7},{5}}=>2 {{1,3},{2,6},{4},{5,7}}=>2 {{1,3},{2,6},{4},{5},{7}}=>2 {{1,3,7},{2},{4,6},{5}}=>1 {{1,3},{2,7},{4,6},{5}}=>1 {{1,3},{2},{4,6,7},{5}}=>1 {{1,3},{2},{4,6},{5,7}}=>2 {{1,3},{2},{4,6},{5},{7}}=>2 {{1,3,7},{2},{4},{5,6}}=>1 {{1,3},{2,7},{4},{5,6}}=>1 {{1,3},{2},{4,7},{5,6}}=>1 {{1,3},{2},{4},{5,6,7}}=>1 {{1,3},{2},{4},{5,6},{7}}=>1 {{1,3,7},{2},{4},{5},{6}}=>1 {{1,3},{2,7},{4},{5},{6}}=>1 {{1,3},{2},{4,7},{5},{6}}=>1 {{1,3},{2},{4},{5,7},{6}}=>1 {{1,3},{2},{4},{5},{6,7}}=>1 {{1,3},{2},{4},{5},{6},{7}}=>1 {{1,4,5,6,7},{2,3}}=>0 {{1,4,5,6},{2,3,7}}=>3 {{1,4,5,6},{2,3},{7}}=>3 {{1,4,5,7},{2,3,6}}=>2 {{1,4,5},{2,3,6,7}}=>2 {{1,4,5},{2,3,6},{7}}=>2 {{1,4,5,7},{2,3},{6}}=>2 {{1,4,5},{2,3,7},{6}}=>2 {{1,4,5},{2,3},{6,7}}=>2 {{1,4,5},{2,3},{6},{7}}=>2 {{1,4,6,7},{2,3,5}}=>1 {{1,4,6},{2,3,5,7}}=>2 {{1,4,6},{2,3,5},{7}}=>2 {{1,4,7},{2,3,5,6}}=>1 {{1,4},{2,3,5,6,7}}=>1 {{1,4},{2,3,5,6},{7}}=>1 {{1,4,7},{2,3,5},{6}}=>1 {{1,4},{2,3,5,7},{6}}=>1 {{1,4},{2,3,5},{6,7}}=>1 {{1,4},{2,3,5},{6},{7}}=>1 {{1,4,6,7},{2,3},{5}}=>1 {{1,4,6},{2,3,7},{5}}=>2 {{1,4,6},{2,3},{5,7}}=>2 {{1,4,6},{2,3},{5},{7}}=>2 {{1,4,7},{2,3,6},{5}}=>1 {{1,4},{2,3,6,7},{5}}=>1 {{1,4},{2,3,6},{5,7}}=>2 {{1,4},{2,3,6},{5},{7}}=>2 {{1,4,7},{2,3},{5,6}}=>1 {{1,4},{2,3,7},{5,6}}=>1 {{1,4},{2,3},{5,6,7}}=>1 {{1,4},{2,3},{5,6},{7}}=>1 {{1,4,7},{2,3},{5},{6}}=>1 {{1,4},{2,3,7},{5},{6}}=>1 {{1,4},{2,3},{5,7},{6}}=>1 {{1,4},{2,3},{5},{6,7}}=>1 {{1,4},{2,3},{5},{6},{7}}=>1 {{1,5,6,7},{2,3,4}}=>0 {{1,5,6},{2,3,4,7}}=>2 {{1,5,6},{2,3,4},{7}}=>2 {{1,5,7},{2,3,4,6}}=>1 {{1,5},{2,3,4,6,7}}=>1 {{1,5},{2,3,4,6},{7}}=>1 {{1,5,7},{2,3,4},{6}}=>1 {{1,5},{2,3,4,7},{6}}=>1 {{1,5},{2,3,4},{6,7}}=>1 {{1,5},{2,3,4},{6},{7}}=>1 {{1,6,7},{2,3,4,5}}=>0 {{1,6},{2,3,4,5,7}}=>1 {{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}}=>0 {{1,7},{2,3,4,5},{6}}=>0 {{1},{2,3,4,5,7},{6}}=>0 {{1},{2,3,4,5},{6,7}}=>0 {{1},{2,3,4,5},{6},{7}}=>0 {{1,6,7},{2,3,4},{5}}=>0 {{1,6},{2,3,4,7},{5}}=>1 {{1,6},{2,3,4},{5,7}}=>1 {{1,6},{2,3,4},{5},{7}}=>1 {{1,7},{2,3,4,6},{5}}=>0 {{1},{2,3,4,6,7},{5}}=>0 {{1},{2,3,4,6},{5,7}}=>1 {{1},{2,3,4,6},{5},{7}}=>1 {{1,7},{2,3,4},{5,6}}=>0 {{1},{2,3,4,7},{5,6}}=>0 {{1},{2,3,4},{5,6,7}}=>0 {{1},{2,3,4},{5,6},{7}}=>0 {{1,7},{2,3,4},{5},{6}}=>0 {{1},{2,3,4,7},{5},{6}}=>0 {{1},{2,3,4},{5,7},{6}}=>0 {{1},{2,3,4},{5},{6,7}}=>0 {{1},{2,3,4},{5},{6},{7}}=>0 {{1,5,6,7},{2,3},{4}}=>0 {{1,5,6},{2,3,7},{4}}=>2 {{1,5,6},{2,3},{4,7}}=>2 {{1,5,6},{2,3},{4},{7}}=>2 {{1,5,7},{2,3,6},{4}}=>1 {{1,5},{2,3,6,7},{4}}=>1 {{1,5},{2,3,6},{4,7}}=>2 {{1,5},{2,3,6},{4},{7}}=>2 {{1,5,7},{2,3},{4,6}}=>1 {{1,5},{2,3,7},{4,6}}=>1 {{1,5},{2,3},{4,6,7}}=>1 {{1,5},{2,3},{4,6},{7}}=>1 {{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}}=>1 {{1,5},{2,3},{4},{6},{7}}=>1 {{1,6,7},{2,3,5},{4}}=>0 {{1,6},{2,3,5,7},{4}}=>1 {{1,6},{2,3,5},{4,7}}=>2 {{1,6},{2,3,5},{4},{7}}=>2 {{1,7},{2,3,5,6},{4}}=>0 {{1},{2,3,5,6,7},{4}}=>0 {{1},{2,3,5,6},{4,7}}=>2 {{1},{2,3,5,6},{4},{7}}=>2 {{1,7},{2,3,5},{4,6}}=>1 {{1},{2,3,5,7},{4,6}}=>1 {{1},{2,3,5},{4,6,7}}=>1 {{1},{2,3,5},{4,6},{7}}=>1 {{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}}=>1 {{1},{2,3,5},{4},{6},{7}}=>1 {{1,6,7},{2,3},{4,5}}=>0 {{1,6},{2,3,7},{4,5}}=>1 {{1,6},{2,3},{4,5,7}}=>1 {{1,6},{2,3},{4,5},{7}}=>1 {{1,7},{2,3,6},{4,5}}=>0 {{1},{2,3,6,7},{4,5}}=>0 {{1},{2,3,6},{4,5,7}}=>1 {{1},{2,3,6},{4,5},{7}}=>1 {{1,7},{2,3},{4,5,6}}=>0 {{1},{2,3,7},{4,5,6}}=>0 {{1},{2,3},{4,5,6,7}}=>0 {{1},{2,3},{4,5,6},{7}}=>0 {{1,7},{2,3},{4,5},{6}}=>0 {{1},{2,3,7},{4,5},{6}}=>0 {{1},{2,3},{4,5,7},{6}}=>0 {{1},{2,3},{4,5},{6,7}}=>0 {{1},{2,3},{4,5},{6},{7}}=>0 {{1,6,7},{2,3},{4},{5}}=>0 {{1,6},{2,3,7},{4},{5}}=>1 {{1,6},{2,3},{4,7},{5}}=>1 {{1,6},{2,3},{4},{5,7}}=>1 {{1,6},{2,3},{4},{5},{7}}=>1 {{1,7},{2,3,6},{4},{5}}=>0 {{1},{2,3,6,7},{4},{5}}=>0 {{1},{2,3,6},{4,7},{5}}=>1 {{1},{2,3,6},{4},{5,7}}=>1 {{1},{2,3,6},{4},{5},{7}}=>1 {{1,7},{2,3},{4,6},{5}}=>0 {{1},{2,3,7},{4,6},{5}}=>0 {{1},{2,3},{4,6,7},{5}}=>0 {{1},{2,3},{4,6},{5,7}}=>1 {{1},{2,3},{4,6},{5},{7}}=>1 {{1,7},{2,3},{4},{5,6}}=>0 {{1},{2,3,7},{4},{5,6}}=>0 {{1},{2,3},{4,7},{5,6}}=>0 {{1},{2,3},{4},{5,6,7}}=>0 {{1},{2,3},{4},{5,6},{7}}=>0 {{1,7},{2,3},{4},{5},{6}}=>0 {{1},{2,3,7},{4},{5},{6}}=>0 {{1},{2,3},{4,7},{5},{6}}=>0 {{1},{2,3},{4},{5,7},{6}}=>0 {{1},{2,3},{4},{5},{6,7}}=>0 {{1},{2,3},{4},{5},{6},{7}}=>0 {{1,4,5,6,7},{2},{3}}=>0 {{1,4,5,6},{2,7},{3}}=>3 {{1,4,5,6},{2},{3,7}}=>3 {{1,4,5,6},{2},{3},{7}}=>3 {{1,4,5,7},{2,6},{3}}=>2 {{1,4,5},{2,6,7},{3}}=>2 {{1,4,5},{2,6},{3,7}}=>3 {{1,4,5},{2,6},{3},{7}}=>3 {{1,4,5,7},{2},{3,6}}=>2 {{1,4,5},{2,7},{3,6}}=>2 {{1,4,5},{2},{3,6,7}}=>2 {{1,4,5},{2},{3,6},{7}}=>2 {{1,4,5,7},{2},{3},{6}}=>2 {{1,4,5},{2,7},{3},{6}}=>2 {{1,4,5},{2},{3,7},{6}}=>2 {{1,4,5},{2},{3},{6,7}}=>2 {{1,4,5},{2},{3},{6},{7}}=>2 {{1,4,6,7},{2,5},{3}}=>1 {{1,4,6},{2,5,7},{3}}=>2 {{1,4,6},{2,5},{3,7}}=>3 {{1,4,6},{2,5},{3},{7}}=>3 {{1,4,7},{2,5,6},{3}}=>1 {{1,4},{2,5,6,7},{3}}=>1 {{1,4},{2,5,6},{3,7}}=>3 {{1,4},{2,5,6},{3},{7}}=>3 {{1,4,7},{2,5},{3,6}}=>2 {{1,4},{2,5,7},{3,6}}=>2 {{1,4},{2,5},{3,6,7}}=>2 {{1,4},{2,5},{3,6},{7}}=>2 {{1,4,7},{2,5},{3},{6}}=>2 {{1,4},{2,5,7},{3},{6}}=>2 {{1,4},{2,5},{3,7},{6}}=>2 {{1,4},{2,5},{3},{6,7}}=>2 {{1,4},{2,5},{3},{6},{7}}=>2 {{1,4,6,7},{2},{3,5}}=>1 {{1,4,6},{2,7},{3,5}}=>2 {{1,4,6},{2},{3,5,7}}=>2 {{1,4,6},{2},{3,5},{7}}=>2 {{1,4,7},{2,6},{3,5}}=>1 {{1,4},{2,6,7},{3,5}}=>1 {{1,4},{2,6},{3,5,7}}=>2 {{1,4},{2,6},{3,5},{7}}=>2 {{1,4,7},{2},{3,5,6}}=>1 {{1,4},{2,7},{3,5,6}}=>1 {{1,4},{2},{3,5,6,7}}=>1 {{1,4},{2},{3,5,6},{7}}=>1 {{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}}=>1 {{1,4},{2},{3,5},{6},{7}}=>1 {{1,4,6,7},{2},{3},{5}}=>1 {{1,4,6},{2,7},{3},{5}}=>2 {{1,4,6},{2},{3,7},{5}}=>2 {{1,4,6},{2},{3},{5,7}}=>2 {{1,4,6},{2},{3},{5},{7}}=>2 {{1,4,7},{2,6},{3},{5}}=>1 {{1,4},{2,6,7},{3},{5}}=>1 {{1,4},{2,6},{3,7},{5}}=>2 {{1,4},{2,6},{3},{5,7}}=>2 {{1,4},{2,6},{3},{5},{7}}=>2 {{1,4,7},{2},{3,6},{5}}=>1 {{1,4},{2,7},{3,6},{5}}=>1 {{1,4},{2},{3,6,7},{5}}=>1 {{1,4},{2},{3,6},{5,7}}=>2 {{1,4},{2},{3,6},{5},{7}}=>2 {{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}}=>1 {{1,4},{2},{3},{5,6},{7}}=>1 {{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},{5,7},{6}}=>1 {{1,4},{2},{3},{5},{6,7}}=>1 {{1,4},{2},{3},{5},{6},{7}}=>1 {{1,5,6,7},{2,4},{3}}=>0 {{1,5,6},{2,4,7},{3}}=>2 {{1,5,6},{2,4},{3,7}}=>3 {{1,5,6},{2,4},{3},{7}}=>3 {{1,5,7},{2,4,6},{3}}=>1 {{1,5},{2,4,6,7},{3}}=>1 {{1,5},{2,4,6},{3,7}}=>3 {{1,5},{2,4,6},{3},{7}}=>3 {{1,5,7},{2,4},{3,6}}=>2 {{1,5},{2,4,7},{3,6}}=>2 {{1,5},{2,4},{3,6,7}}=>2 {{1,5},{2,4},{3,6},{7}}=>2 {{1,5,7},{2,4},{3},{6}}=>2 {{1,5},{2,4,7},{3},{6}}=>2 {{1,5},{2,4},{3,7},{6}}=>2 {{1,5},{2,4},{3},{6,7}}=>2 {{1,5},{2,4},{3},{6},{7}}=>2 {{1,6,7},{2,4,5},{3}}=>0 {{1,6},{2,4,5,7},{3}}=>1 {{1,6},{2,4,5},{3,7}}=>3 {{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}}=>3 {{1},{2,4,5,6},{3},{7}}=>3 {{1,7},{2,4,5},{3,6}}=>2 {{1},{2,4,5,7},{3,6}}=>2 {{1},{2,4,5},{3,6,7}}=>2 {{1},{2,4,5},{3,6},{7}}=>2 {{1,7},{2,4,5},{3},{6}}=>2 {{1},{2,4,5,7},{3},{6}}=>2 {{1},{2,4,5},{3,7},{6}}=>2 {{1},{2,4,5},{3},{6,7}}=>2 {{1},{2,4,5},{3},{6},{7}}=>2 {{1,6,7},{2,4},{3,5}}=>1 {{1,6},{2,4,7},{3,5}}=>2 {{1,6},{2,4},{3,5,7}}=>2 {{1,6},{2,4},{3,5},{7}}=>2 {{1,7},{2,4,6},{3,5}}=>1 {{1},{2,4,6,7},{3,5}}=>1 {{1},{2,4,6},{3,5,7}}=>2 {{1},{2,4,6},{3,5},{7}}=>2 {{1,7},{2,4},{3,5,6}}=>1 {{1},{2,4,7},{3,5,6}}=>1 {{1},{2,4},{3,5,6,7}}=>1 {{1},{2,4},{3,5,6},{7}}=>1 {{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}}=>1 {{1},{2,4},{3,5},{6},{7}}=>1 {{1,6,7},{2,4},{3},{5}}=>1 {{1,6},{2,4,7},{3},{5}}=>2 {{1,6},{2,4},{3,7},{5}}=>2 {{1,6},{2,4},{3},{5,7}}=>2 {{1,6},{2,4},{3},{5},{7}}=>2 {{1,7},{2,4,6},{3},{5}}=>1 {{1},{2,4,6,7},{3},{5}}=>1 {{1},{2,4,6},{3,7},{5}}=>2 {{1},{2,4,6},{3},{5,7}}=>2 {{1},{2,4,6},{3},{5},{7}}=>2 {{1,7},{2,4},{3,6},{5}}=>1 {{1},{2,4,7},{3,6},{5}}=>1 {{1},{2,4},{3,6,7},{5}}=>1 {{1},{2,4},{3,6},{5,7}}=>2 {{1},{2,4},{3,6},{5},{7}}=>2 {{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}}=>1 {{1},{2,4},{3},{5,6},{7}}=>1 {{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},{5,7},{6}}=>1 {{1},{2,4},{3},{5},{6,7}}=>1 {{1},{2,4},{3},{5},{6},{7}}=>1 {{1,5,6,7},{2},{3,4}}=>0 {{1,5,6},{2,7},{3,4}}=>2 {{1,5,6},{2},{3,4,7}}=>2 {{1,5,6},{2},{3,4},{7}}=>2 {{1,5,7},{2,6},{3,4}}=>1 {{1,5},{2,6,7},{3,4}}=>1 {{1,5},{2,6},{3,4,7}}=>2 {{1,5},{2,6},{3,4},{7}}=>2 {{1,5,7},{2},{3,4,6}}=>1 {{1,5},{2,7},{3,4,6}}=>1 {{1,5},{2},{3,4,6,7}}=>1 {{1,5},{2},{3,4,6},{7}}=>1 {{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}}=>1 {{1,5},{2},{3,4},{6},{7}}=>1 {{1,6,7},{2,5},{3,4}}=>0 {{1,6},{2,5,7},{3,4}}=>1 {{1,6},{2,5},{3,4,7}}=>2 {{1,6},{2,5},{3,4},{7}}=>2 {{1,7},{2,5,6},{3,4}}=>0 {{1},{2,5,6,7},{3,4}}=>0 {{1},{2,5,6},{3,4,7}}=>2 {{1},{2,5,6},{3,4},{7}}=>2 {{1,7},{2,5},{3,4,6}}=>1 {{1},{2,5,7},{3,4,6}}=>1 {{1},{2,5},{3,4,6,7}}=>1 {{1},{2,5},{3,4,6},{7}}=>1 {{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}}=>1 {{1},{2,5},{3,4},{6},{7}}=>1 {{1,6,7},{2},{3,4,5}}=>0 {{1,6},{2,7},{3,4,5}}=>1 {{1,6},{2},{3,4,5,7}}=>1 {{1,6},{2},{3,4,5},{7}}=>1 {{1,7},{2,6},{3,4,5}}=>0 {{1},{2,6,7},{3,4,5}}=>0 {{1},{2,6},{3,4,5,7}}=>1 {{1},{2,6},{3,4,5},{7}}=>1 {{1,7},{2},{3,4,5,6}}=>0 {{1},{2,7},{3,4,5,6}}=>0 {{1},{2},{3,4,5,6,7}}=>0 {{1},{2},{3,4,5,6},{7}}=>0 {{1,7},{2},{3,4,5},{6}}=>0 {{1},{2,7},{3,4,5},{6}}=>0 {{1},{2},{3,4,5,7},{6}}=>0 {{1},{2},{3,4,5},{6,7}}=>0 {{1},{2},{3,4,5},{6},{7}}=>0 {{1,6,7},{2},{3,4},{5}}=>0 {{1,6},{2,7},{3,4},{5}}=>1 {{1,6},{2},{3,4,7},{5}}=>1 {{1,6},{2},{3,4},{5,7}}=>1 {{1,6},{2},{3,4},{5},{7}}=>1 {{1,7},{2,6},{3,4},{5}}=>0 {{1},{2,6,7},{3,4},{5}}=>0 {{1},{2,6},{3,4,7},{5}}=>1 {{1},{2,6},{3,4},{5,7}}=>1 {{1},{2,6},{3,4},{5},{7}}=>1 {{1,7},{2},{3,4,6},{5}}=>0 {{1},{2,7},{3,4,6},{5}}=>0 {{1},{2},{3,4,6,7},{5}}=>0 {{1},{2},{3,4,6},{5,7}}=>1 {{1},{2},{3,4,6},{5},{7}}=>1 {{1,7},{2},{3,4},{5,6}}=>0 {{1},{2,7},{3,4},{5,6}}=>0 {{1},{2},{3,4,7},{5,6}}=>0 {{1},{2},{3,4},{5,6,7}}=>0 {{1},{2},{3,4},{5,6},{7}}=>0 {{1,7},{2},{3,4},{5},{6}}=>0 {{1},{2,7},{3,4},{5},{6}}=>0 {{1},{2},{3,4,7},{5},{6}}=>0 {{1},{2},{3,4},{5,7},{6}}=>0 {{1},{2},{3,4},{5},{6,7}}=>0 {{1},{2},{3,4},{5},{6},{7}}=>0 {{1,5,6,7},{2},{3},{4}}=>0 {{1,5,6},{2,7},{3},{4}}=>2 {{1,5,6},{2},{3,7},{4}}=>2 {{1,5,6},{2},{3},{4,7}}=>2 {{1,5,6},{2},{3},{4},{7}}=>2 {{1,5,7},{2,6},{3},{4}}=>1 {{1,5},{2,6,7},{3},{4}}=>1 {{1,5},{2,6},{3,7},{4}}=>2 {{1,5},{2,6},{3},{4,7}}=>2 {{1,5},{2,6},{3},{4},{7}}=>2 {{1,5,7},{2},{3,6},{4}}=>1 {{1,5},{2,7},{3,6},{4}}=>1 {{1,5},{2},{3,6,7},{4}}=>1 {{1,5},{2},{3,6},{4,7}}=>2 {{1,5},{2},{3,6},{4},{7}}=>2 {{1,5,7},{2},{3},{4,6}}=>1 {{1,5},{2,7},{3},{4,6}}=>1 {{1,5},{2},{3,7},{4,6}}=>1 {{1,5},{2},{3},{4,6,7}}=>1 {{1,5},{2},{3},{4,6},{7}}=>1 {{1,5,7},{2},{3},{4},{6}}=>1 {{1,5},{2,7},{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}}=>1 {{1,5},{2},{3},{4},{6},{7}}=>1 {{1,6,7},{2,5},{3},{4}}=>0 {{1,6},{2,5,7},{3},{4}}=>1 {{1,6},{2,5},{3,7},{4}}=>2 {{1,6},{2,5},{3},{4,7}}=>2 {{1,6},{2,5},{3},{4},{7}}=>2 {{1,7},{2,5,6},{3},{4}}=>0 {{1},{2,5,6,7},{3},{4}}=>0 {{1},{2,5,6},{3,7},{4}}=>2 {{1},{2,5,6},{3},{4,7}}=>2 {{1},{2,5,6},{3},{4},{7}}=>2 {{1,7},{2,5},{3,6},{4}}=>1 {{1},{2,5,7},{3,6},{4}}=>1 {{1},{2,5},{3,6,7},{4}}=>1 {{1},{2,5},{3,6},{4,7}}=>2 {{1},{2,5},{3,6},{4},{7}}=>2 {{1,7},{2,5},{3},{4,6}}=>1 {{1},{2,5,7},{3},{4,6}}=>1 {{1},{2,5},{3,7},{4,6}}=>1 {{1},{2,5},{3},{4,6,7}}=>1 {{1},{2,5},{3},{4,6},{7}}=>1 {{1,7},{2,5},{3},{4},{6}}=>1 {{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}}=>1 {{1},{2,5},{3},{4},{6},{7}}=>1 {{1,6,7},{2},{3,5},{4}}=>0 {{1,6},{2,7},{3,5},{4}}=>1 {{1,6},{2},{3,5,7},{4}}=>1 {{1,6},{2},{3,5},{4,7}}=>2 {{1,6},{2},{3,5},{4},{7}}=>2 {{1,7},{2,6},{3,5},{4}}=>0 {{1},{2,6,7},{3,5},{4}}=>0 {{1},{2,6},{3,5,7},{4}}=>1 {{1},{2,6},{3,5},{4,7}}=>2 {{1},{2,6},{3,5},{4},{7}}=>2 {{1,7},{2},{3,5,6},{4}}=>0 {{1},{2,7},{3,5,6},{4}}=>0 {{1},{2},{3,5,6,7},{4}}=>0 {{1},{2},{3,5,6},{4,7}}=>2 {{1},{2},{3,5,6},{4},{7}}=>2 {{1,7},{2},{3,5},{4,6}}=>1 {{1},{2,7},{3,5},{4,6}}=>1 {{1},{2},{3,5,7},{4,6}}=>1 {{1},{2},{3,5},{4,6,7}}=>1 {{1},{2},{3,5},{4,6},{7}}=>1 {{1,7},{2},{3,5},{4},{6}}=>1 {{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}}=>1 {{1},{2},{3,5},{4},{6},{7}}=>1 {{1,6,7},{2},{3},{4,5}}=>0 {{1,6},{2,7},{3},{4,5}}=>1 {{1,6},{2},{3,7},{4,5}}=>1 {{1,6},{2},{3},{4,5,7}}=>1 {{1,6},{2},{3},{4,5},{7}}=>1 {{1,7},{2,6},{3},{4,5}}=>0 {{1},{2,6,7},{3},{4,5}}=>0 {{1},{2,6},{3,7},{4,5}}=>1 {{1},{2,6},{3},{4,5,7}}=>1 {{1},{2,6},{3},{4,5},{7}}=>1 {{1,7},{2},{3,6},{4,5}}=>0 {{1},{2,7},{3,6},{4,5}}=>0 {{1},{2},{3,6,7},{4,5}}=>0 {{1},{2},{3,6},{4,5,7}}=>1 {{1},{2},{3,6},{4,5},{7}}=>1 {{1,7},{2},{3},{4,5,6}}=>0 {{1},{2,7},{3},{4,5,6}}=>0 {{1},{2},{3,7},{4,5,6}}=>0 {{1},{2},{3},{4,5,6,7}}=>0 {{1},{2},{3},{4,5,6},{7}}=>0 {{1,7},{2},{3},{4,5},{6}}=>0 {{1},{2,7},{3},{4,5},{6}}=>0 {{1},{2},{3,7},{4,5},{6}}=>0 {{1},{2},{3},{4,5,7},{6}}=>0 {{1},{2},{3},{4,5},{6,7}}=>0 {{1},{2},{3},{4,5},{6},{7}}=>0 {{1,6,7},{2},{3},{4},{5}}=>0 {{1,6},{2,7},{3},{4},{5}}=>1 {{1,6},{2},{3,7},{4},{5}}=>1 {{1,6},{2},{3},{4,7},{5}}=>1 {{1,6},{2},{3},{4},{5,7}}=>1 {{1,6},{2},{3},{4},{5},{7}}=>1 {{1,7},{2,6},{3},{4},{5}}=>0 {{1},{2,6,7},{3},{4},{5}}=>0 {{1},{2,6},{3,7},{4},{5}}=>1 {{1},{2,6},{3},{4,7},{5}}=>1 {{1},{2,6},{3},{4},{5,7}}=>1 {{1},{2,6},{3},{4},{5},{7}}=>1 {{1,7},{2},{3,6},{4},{5}}=>0 {{1},{2,7},{3,6},{4},{5}}=>0 {{1},{2},{3,6,7},{4},{5}}=>0 {{1},{2},{3,6},{4,7},{5}}=>1 {{1},{2},{3,6},{4},{5,7}}=>1 {{1},{2},{3,6},{4},{5},{7}}=>1 {{1,7},{2},{3},{4,6},{5}}=>0 {{1},{2,7},{3},{4,6},{5}}=>0 {{1},{2},{3,7},{4,6},{5}}=>0 {{1},{2},{3},{4,6,7},{5}}=>0 {{1},{2},{3},{4,6},{5,7}}=>1 {{1},{2},{3},{4,6},{5},{7}}=>1 {{1,7},{2},{3},{4},{5,6}}=>0 {{1},{2,7},{3},{4},{5,6}}=>0 {{1},{2},{3,7},{4},{5,6}}=>0 {{1},{2},{3},{4,7},{5,6}}=>0 {{1},{2},{3},{4},{5,6,7}}=>0 {{1},{2},{3},{4},{5,6},{7}}=>0 {{1,7},{2},{3},{4},{5},{6}}=>0 {{1},{2,7},{3},{4},{5},{6}}=>0 {{1},{2},{3,7},{4},{5},{6}}=>0 {{1},{2},{3},{4,7},{5},{6}}=>0 {{1},{2},{3},{4},{5,7},{6}}=>0 {{1},{2},{3},{4},{5},{6,7}}=>0 {{1},{2},{3},{4},{5},{6},{7}}=>0 {{1},{2},{3,4,5,6,7,8}}=>0 {{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},{2,3,4,5,7,8},{6}}=>0 {{1},{2,3,4,5,6,7},{8}}=>0 {{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}}=>1 {{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 {{1,2,3,5,6,7,8},{4}}=>0 {{1,2,3,6,7,8},{4,5}}=>0 {{1,2,3,4,6,7,8},{5}}=>0 {{1,2,3,4,5,6},{7,8}}=>0 {{1,2,3,4,7,8},{5,6}}=>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}}=>1 {{1,3,4,6,7,8},{2,5}}=>2 {{1,2,4,6,7,8},{3,5}}=>1 {{1,3,4,5,7,8},{2,6}}=>3 {{1,2,4,5,7,8},{3,6}}=>2 {{1,2,3,5,7,8},{4,6}}=>1 {{1,3,4,5,6,8},{2,7}}=>4 {{1,2,4,5,6,8},{3,7}}=>3 {{1,2,3,5,6,8},{4,7}}=>2 {{1,2,3,4,6,8},{5,7}}=>1 {{1,3,4,5,6,7},{2,8}}=>5 {{1,2,4,5,6,7},{3,8}}=>4 {{1,2,3,5,6,7},{4,8}}=>3 {{1,2,3,4,6,7},{5,8}}=>2 {{1,2,3,4,5,7},{6,8}}=>1 {{1,3},{2,4,5,6,7,8}}=>1 {{1,4},{2,3,5,6,7,8}}=>1 {{1,5},{2,3,4,6,7,8}}=>1 {{1,6},{2,3,4,5,7,8}}=>1 {{1,7},{2,3,4,5,6,8}}=>1
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Description
The number of internal points of a set partition.
An element $e$ is internal, if there are $f < e < g$ such that the blocks of $f$ and $g$ have larger minimal element than the block of $e$. See Section 5.5 of [1]
References
[1] Mansour, T. Combinatorics of set partitions MathSciNet:2953184
Code
def canonical_word(pi):
    """

    Return the word with w_i being the index of the block of i, when
    pi is sorted according to minimal elements.

    EXAMPLES:

    sage: canonical_word([[1,3],[2,4,7],[5,6]])
    1212332

    """
    pi = SetPartition(pi).standardization()
    w = [None]*pi.size()
    for i, block in enumerate(sorted([sorted(b) for b in pi]), 1):
        for e in block:
            w[e-1] = i
    return Word(w)

def statistic(pi):
    """e is internal, if there are f < e < g such that the blocks of f
    and g have larger minimal element than the block of e.

    sage: statistic([[1,4],[2,5,7],[3],[6]])
    2
    sage: canonical_word([[1,5,9,12],[2,4,8],[3,7,11],[6,10]])
    word: 123214321431
    sage: statistic([[1,5,9,12],[2,4,8],[3,7,11],[6,10]])
    5
    """
    w = canonical_word(pi)
    count = 0
    for (i, b) in enumerate(w):
        has_smaller = any(b < w[j] for j in range(i))
        has_bigger = any(b < w[j] for j in range(i+1, len(w)))
        if has_smaller and has_bigger:
            count += 1
    return count
Created
Aug 06, 2016 at 09:27 by Martin Rubey
Updated
Aug 06, 2016 at 09:27 by Martin Rubey