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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}}=>0 {{1,2},{3,4}}=>0 {{1,2},{3},{4}}=>0 {{1,3,4},{2}}=>1 {{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}}=>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}}=>0 {{1,2,3},{4,5}}=>0 {{1,2,3},{4},{5}}=>0 {{1,2,4,5},{3}}=>0 {{1,2,4},{3,5}}=>0 {{1,2,4},{3},{5}}=>0 {{1,2,5},{3,4}}=>1 {{1,2},{3,4,5}}=>0 {{1,2},{3,4},{5}}=>0 {{1,2,5},{3},{4}}=>0 {{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}}=>1 {{1,3,4},{2},{5}}=>1 {{1,3,5},{2,4}}=>2 {{1,3},{2,4,5}}=>1 {{1,3},{2,4},{5}}=>1 {{1,3,5},{2},{4}}=>1 {{1,3},{2,5},{4}}=>2 {{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}}=>0 {{1,5},{2,3,4}}=>0 {{1},{2,3,4,5}}=>0 {{1},{2,3,4},{5}}=>0 {{1,5},{2,3},{4}}=>1 {{1},{2,3,5},{4}}=>0 {{1},{2,3},{4,5}}=>0 {{1},{2,3},{4},{5}}=>0 {{1,4,5},{2},{3}}=>2 {{1,4},{2,5},{3}}=>3 {{1,4},{2},{3,5}}=>2 {{1,4},{2},{3},{5}}=>2 {{1,5},{2,4},{3}}=>2 {{1},{2,4,5},{3}}=>1 {{1},{2,4},{3,5}}=>1 {{1},{2,4},{3},{5}}=>1 {{1,5},{2},{3,4}}=>1 {{1},{2,5},{3,4}}=>0 {{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}}=>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}}=>0 {{1,2,3,5},{4},{6}}=>0 {{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}}=>1 {{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}}=>0 {{1,2,4,5},{3},{6}}=>0 {{1,2,4,6},{3,5}}=>0 {{1,2,4},{3,5,6}}=>0 {{1,2,4},{3,5},{6}}=>0 {{1,2,4,6},{3},{5}}=>0 {{1,2,4},{3,6},{5}}=>1 {{1,2,4},{3},{5,6}}=>0 {{1,2,4},{3},{5},{6}}=>0 {{1,2,5,6},{3,4}}=>1 {{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}}=>1 {{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}}=>0 {{1,2,5},{3},{4},{6}}=>0 {{1,2,6},{3,5},{4}}=>2 {{1,2},{3,5,6},{4}}=>1 {{1,2},{3,5},{4,6}}=>1 {{1,2},{3,5},{4},{6}}=>1 {{1,2,6},{3},{4,5}}=>1 {{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}}=>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}}=>1 {{1,3,4,5},{2},{6}}=>1 {{1,3,4,6},{2,5}}=>1 {{1,3,4},{2,5,6}}=>1 {{1,3,4},{2,5},{6}}=>1 {{1,3,4,6},{2},{5}}=>1 {{1,3,4},{2,6},{5}}=>2 {{1,3,4},{2},{5,6}}=>1 {{1,3,4},{2},{5},{6}}=>1 {{1,3,5,6},{2,4}}=>2 {{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}}=>2 {{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}}=>1 {{1,3,5},{2},{4},{6}}=>1 {{1,3,6},{2,5},{4}}=>3 {{1,3},{2,5,6},{4}}=>2 {{1,3},{2,5},{4,6}}=>2 {{1,3},{2,5},{4},{6}}=>2 {{1,3,6},{2},{4,5}}=>2 {{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}}=>3 {{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}}=>0 {{1,4,5},{2,3,6}}=>0 {{1,4,5},{2,3},{6}}=>0 {{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}}=>0 {{1,4},{2,3,6},{5}}=>1 {{1,4},{2,3},{5,6}}=>0 {{1,4},{2,3},{5},{6}}=>0 {{1,5,6},{2,3,4}}=>0 {{1,5},{2,3,4,6}}=>0 {{1,5},{2,3,4},{6}}=>0 {{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}}=>1 {{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}}=>1 {{1,5},{2,3,6},{4}}=>2 {{1,5},{2,3},{4,6}}=>1 {{1,5},{2,3},{4},{6}}=>1 {{1,6},{2,3,5},{4}}=>1 {{1},{2,3,5,6},{4}}=>0 {{1},{2,3,5},{4,6}}=>0 {{1},{2,3,5},{4},{6}}=>0 {{1,6},{2,3},{4,5}}=>0 {{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}}=>2 {{1},{2,3,6},{4},{5}}=>0 {{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}}=>3 {{1,4,5},{2},{3,6}}=>2 {{1,4,5},{2},{3},{6}}=>2 {{1,4,6},{2,5},{3}}=>4 {{1,4},{2,5,6},{3}}=>3 {{1,4},{2,5},{3,6}}=>3 {{1,4},{2,5},{3},{6}}=>3 {{1,4,6},{2},{3,5}}=>3 {{1,4},{2,6},{3,5}}=>2 {{1,4},{2},{3,5,6}}=>2 {{1,4},{2},{3,5},{6}}=>2 {{1,4,6},{2},{3},{5}}=>2 {{1,4},{2,6},{3},{5}}=>4 {{1,4},{2},{3,6},{5}}=>3 {{1,4},{2},{3},{5,6}}=>2 {{1,4},{2},{3},{5},{6}}=>2 {{1,5,6},{2,4},{3}}=>2 {{1,5},{2,4,6},{3}}=>3 {{1,5},{2,4},{3,6}}=>2 {{1,5},{2,4},{3},{6}}=>2 {{1,6},{2,4,5},{3}}=>2 {{1},{2,4,5,6},{3}}=>1 {{1},{2,4,5},{3,6}}=>1 {{1},{2,4,5},{3},{6}}=>1 {{1,6},{2,4},{3,5}}=>1 {{1},{2,4,6},{3,5}}=>2 {{1},{2,4},{3,5,6}}=>1 {{1},{2,4},{3,5},{6}}=>1 {{1,6},{2,4},{3},{5}}=>3 {{1},{2,4,6},{3},{5}}=>1 {{1},{2,4},{3,6},{5}}=>2 {{1},{2,4},{3},{5,6}}=>1 {{1},{2,4},{3},{5},{6}}=>1 {{1,5,6},{2},{3,4}}=>1 {{1,5},{2,6},{3,4}}=>1 {{1,5},{2},{3,4,6}}=>2 {{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}}=>0 {{1,6},{2},{3,4,5}}=>1 {{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}}=>2 {{1},{2,6},{3,4},{5}}=>1 {{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}}=>3 {{1,5},{2,6},{3},{4}}=>5 {{1,5},{2},{3,6},{4}}=>4 {{1,5},{2},{3},{4,6}}=>3 {{1,5},{2},{3},{4},{6}}=>3 {{1,6},{2,5},{3},{4}}=>4 {{1},{2,5,6},{3},{4}}=>2 {{1},{2,5},{3,6},{4}}=>3 {{1},{2,5},{3},{4,6}}=>2 {{1},{2,5},{3},{4},{6}}=>2 {{1,6},{2},{3,5},{4}}=>3 {{1},{2,6},{3,5},{4}}=>2 {{1},{2},{3,5,6},{4}}=>1 {{1},{2},{3,5},{4,6}}=>1 {{1},{2},{3,5},{4},{6}}=>1 {{1,6},{2},{3},{4,5}}=>2 {{1},{2,6},{3},{4,5}}=>1 {{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}}=>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}}=>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}}=>0 {{1,2,3,4,6},{5},{7}}=>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 {{1,2,3,4,7},{5},{6}}=>0 {{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}}=>0 {{1,2,3,5,6},{4,7}}=>0 {{1,2,3,5,6},{4},{7}}=>0 {{1,2,3,5,7},{4,6}}=>0 {{1,2,3,5},{4,6,7}}=>0 {{1,2,3,5},{4,6},{7}}=>0 {{1,2,3,5,7},{4},{6}}=>0 {{1,2,3,5},{4,7},{6}}=>1 {{1,2,3,5},{4},{6,7}}=>0 {{1,2,3,5},{4},{6},{7}}=>0 {{1,2,3,6,7},{4,5}}=>0 {{1,2,3,6},{4,5,7}}=>0 {{1,2,3,6},{4,5},{7}}=>0 {{1,2,3,7},{4,5,6}}=>1 {{1,2,3},{4,5,6,7}}=>0 {{1,2,3},{4,5,6},{7}}=>0 {{1,2,3,7},{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}}=>0 {{1,2,3,6},{4},{5},{7}}=>0 {{1,2,3,7},{4,6},{5}}=>1 {{1,2,3},{4,6,7},{5}}=>1 {{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}}=>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}}=>0 {{1,2,4,5,6},{3,7}}=>0 {{1,2,4,5,6},{3},{7}}=>0 {{1,2,4,5,7},{3,6}}=>0 {{1,2,4,5},{3,6,7}}=>0 {{1,2,4,5},{3,6},{7}}=>0 {{1,2,4,5,7},{3},{6}}=>0 {{1,2,4,5},{3,7},{6}}=>1 {{1,2,4,5},{3},{6,7}}=>0 {{1,2,4,5},{3},{6},{7}}=>0 {{1,2,4,6,7},{3,5}}=>0 {{1,2,4,6},{3,5,7}}=>0 {{1,2,4,6},{3,5},{7}}=>0 {{1,2,4,7},{3,5,6}}=>1 {{1,2,4},{3,5,6,7}}=>0 {{1,2,4},{3,5,6},{7}}=>0 {{1,2,4,7},{3,5},{6}}=>0 {{1,2,4},{3,5,7},{6}}=>0 {{1,2,4},{3,5},{6,7}}=>0 {{1,2,4},{3,5},{6},{7}}=>0 {{1,2,4,6,7},{3},{5}}=>0 {{1,2,4,6},{3,7},{5}}=>1 {{1,2,4,6},{3},{5,7}}=>0 {{1,2,4,6},{3},{5},{7}}=>0 {{1,2,4,7},{3,6},{5}}=>1 {{1,2,4},{3,6,7},{5}}=>1 {{1,2,4},{3,6},{5,7}}=>1 {{1,2,4},{3,6},{5},{7}}=>1 {{1,2,4,7},{3},{5,6}}=>0 {{1,2,4},{3,7},{5,6}}=>0 {{1,2,4},{3},{5,6,7}}=>0 {{1,2,4},{3},{5,6},{7}}=>0 {{1,2,4,7},{3},{5},{6}}=>0 {{1,2,4},{3,7},{5},{6}}=>2 {{1,2,4},{3},{5,7},{6}}=>1 {{1,2,4},{3},{5},{6,7}}=>0 {{1,2,4},{3},{5},{6},{7}}=>0 {{1,2,5,6,7},{3,4}}=>1 {{1,2,5,6},{3,4,7}}=>1 {{1,2,5,6},{3,4},{7}}=>1 {{1,2,5,7},{3,4,6}}=>2 {{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}}=>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 {{1,2,7},{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}}=>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},{3,4,6},{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}}=>0 {{1,2,7},{3,4},{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}}=>1 {{1,2},{3,4,7},{5},{6}}=>0 {{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}}=>0 {{1,2,5,6},{3,7},{4}}=>1 {{1,2,5,6},{3},{4,7}}=>0 {{1,2,5,6},{3},{4},{7}}=>0 {{1,2,5,7},{3,6},{4}}=>1 {{1,2,5},{3,6,7},{4}}=>1 {{1,2,5},{3,6},{4,7}}=>1 {{1,2,5},{3,6},{4},{7}}=>1 {{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}}=>0 {{1,2,5,7},{3},{4},{6}}=>0 {{1,2,5},{3,7},{4},{6}}=>2 {{1,2,5},{3},{4,7},{6}}=>1 {{1,2,5},{3},{4},{6,7}}=>0 {{1,2,5},{3},{4},{6},{7}}=>0 {{1,2,6,7},{3,5},{4}}=>2 {{1,2,6},{3,5,7},{4}}=>2 {{1,2,6},{3,5},{4,7}}=>2 {{1,2,6},{3,5},{4},{7}}=>2 {{1,2,7},{3,5,6},{4}}=>1 {{1,2},{3,5,6,7},{4}}=>1 {{1,2},{3,5,6},{4,7}}=>1 {{1,2},{3,5,6},{4},{7}}=>1 {{1,2,7},{3,5},{4,6}}=>3 {{1,2},{3,5,7},{4,6}}=>2 {{1,2},{3,5},{4,6,7}}=>1 {{1,2},{3,5},{4,6},{7}}=>1 {{1,2,7},{3,5},{4},{6}}=>2 {{1,2},{3,5,7},{4},{6}}=>1 {{1,2},{3,5},{4,7},{6}}=>2 {{1,2},{3,5},{4},{6,7}}=>1 {{1,2},{3,5},{4},{6},{7}}=>1 {{1,2,6,7},{3},{4,5}}=>1 {{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}}=>2 {{1,2},{3,6,7},{4,5}}=>0 {{1,2},{3,6},{4,5,7}}=>1 {{1,2},{3,6},{4,5},{7}}=>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 {{1,2,7},{3},{4,5},{6}}=>1 {{1,2},{3,7},{4,5},{6}}=>1 {{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}}=>2 {{1,2,6},{3},{4,7},{5}}=>1 {{1,2,6},{3},{4},{5,7}}=>0 {{1,2,6},{3},{4},{5},{7}}=>0 {{1,2,7},{3,6},{4},{5}}=>3 {{1,2},{3,6,7},{4},{5}}=>2 {{1,2},{3,6},{4,7},{5}}=>3 {{1,2},{3,6},{4},{5,7}}=>2 {{1,2},{3,6},{4},{5},{7}}=>2 {{1,2,7},{3},{4,6},{5}}=>2 {{1,2},{3,7},{4,6},{5}}=>2 {{1,2},{3},{4,6,7},{5}}=>1 {{1,2},{3},{4,6},{5,7}}=>1 {{1,2},{3},{4,6},{5},{7}}=>1 {{1,2,7},{3},{4},{5,6}}=>1 {{1,2},{3,7},{4},{5,6}}=>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 {{1,2,7},{3},{4},{5},{6}}=>0 {{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}}=>1 {{1,3,4,5,6},{2},{7}}=>1 {{1,3,4,5,7},{2,6}}=>1 {{1,3,4,5},{2,6,7}}=>1 {{1,3,4,5},{2,6},{7}}=>1 {{1,3,4,5,7},{2},{6}}=>1 {{1,3,4,5},{2,7},{6}}=>2 {{1,3,4,5},{2},{6,7}}=>1 {{1,3,4,5},{2},{6},{7}}=>1 {{1,3,4,6,7},{2,5}}=>1 {{1,3,4,6},{2,5,7}}=>1 {{1,3,4,6},{2,5},{7}}=>1 {{1,3,4,7},{2,5,6}}=>2 {{1,3,4},{2,5,6,7}}=>1 {{1,3,4},{2,5,6},{7}}=>1 {{1,3,4,7},{2,5},{6}}=>1 {{1,3,4},{2,5,7},{6}}=>1 {{1,3,4},{2,5},{6,7}}=>1 {{1,3,4},{2,5},{6},{7}}=>1 {{1,3,4,6,7},{2},{5}}=>1 {{1,3,4,6},{2,7},{5}}=>2 {{1,3,4,6},{2},{5,7}}=>1 {{1,3,4,6},{2},{5},{7}}=>1 {{1,3,4,7},{2,6},{5}}=>2 {{1,3,4},{2,6,7},{5}}=>2 {{1,3,4},{2,6},{5,7}}=>2 {{1,3,4},{2,6},{5},{7}}=>2 {{1,3,4,7},{2},{5,6}}=>1 {{1,3,4},{2,7},{5,6}}=>1 {{1,3,4},{2},{5,6,7}}=>1 {{1,3,4},{2},{5,6},{7}}=>1 {{1,3,4,7},{2},{5},{6}}=>1 {{1,3,4},{2,7},{5},{6}}=>3 {{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}}=>2 {{1,3,5,6},{2,4,7}}=>2 {{1,3,5,6},{2,4},{7}}=>2 {{1,3,5,7},{2,4,6}}=>3 {{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}}=>1 {{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}}=>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},{2,4,6},{5}}=>1 {{1,3},{2,4,6,7},{5}}=>1 {{1,3},{2,4,6},{5,7}}=>1 {{1,3},{2,4,6},{5},{7}}=>1 {{1,3,7},{2,4},{5,6}}=>3 {{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}}=>2 {{1,3},{2,4,7},{5},{6}}=>1 {{1,3},{2,4},{5,7},{6}}=>2 {{1,3},{2,4},{5},{6,7}}=>1 {{1,3},{2,4},{5},{6},{7}}=>1 {{1,3,5,6,7},{2},{4}}=>1 {{1,3,5,6},{2,7},{4}}=>2 {{1,3,5,6},{2},{4,7}}=>1 {{1,3,5,6},{2},{4},{7}}=>1 {{1,3,5,7},{2,6},{4}}=>2 {{1,3,5},{2,6,7},{4}}=>2 {{1,3,5},{2,6},{4,7}}=>2 {{1,3,5},{2,6},{4},{7}}=>2 {{1,3,5,7},{2},{4,6}}=>1 {{1,3,5},{2,7},{4,6}}=>1 {{1,3,5},{2},{4,6,7}}=>1 {{1,3,5},{2},{4,6},{7}}=>1 {{1,3,5,7},{2},{4},{6}}=>1 {{1,3,5},{2,7},{4},{6}}=>3 {{1,3,5},{2},{4,7},{6}}=>2 {{1,3,5},{2},{4},{6,7}}=>1 {{1,3,5},{2},{4},{6},{7}}=>1 {{1,3,6,7},{2,5},{4}}=>3 {{1,3,6},{2,5,7},{4}}=>3 {{1,3,6},{2,5},{4,7}}=>3 {{1,3,6},{2,5},{4},{7}}=>3 {{1,3,7},{2,5,6},{4}}=>2 {{1,3},{2,5,6,7},{4}}=>2 {{1,3},{2,5,6},{4,7}}=>2 {{1,3},{2,5,6},{4},{7}}=>2 {{1,3,7},{2,5},{4,6}}=>4 {{1,3},{2,5,7},{4,6}}=>3 {{1,3},{2,5},{4,6,7}}=>2 {{1,3},{2,5},{4,6},{7}}=>2 {{1,3,7},{2,5},{4},{6}}=>3 {{1,3},{2,5,7},{4},{6}}=>2 {{1,3},{2,5},{4,7},{6}}=>3 {{1,3},{2,5},{4},{6,7}}=>2 {{1,3},{2,5},{4},{6},{7}}=>2 {{1,3,6,7},{2},{4,5}}=>2 {{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}}=>3 {{1,3},{2,6,7},{4,5}}=>1 {{1,3},{2,6},{4,5,7}}=>2 {{1,3},{2,6},{4,5},{7}}=>1 {{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}}=>2 {{1,3},{2,7},{4,5},{6}}=>2 {{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}}=>3 {{1,3,6},{2},{4,7},{5}}=>2 {{1,3,6},{2},{4},{5,7}}=>1 {{1,3,6},{2},{4},{5},{7}}=>1 {{1,3,7},{2,6},{4},{5}}=>4 {{1,3},{2,6,7},{4},{5}}=>3 {{1,3},{2,6},{4,7},{5}}=>4 {{1,3},{2,6},{4},{5,7}}=>3 {{1,3},{2,6},{4},{5},{7}}=>3 {{1,3,7},{2},{4,6},{5}}=>3 {{1,3},{2,7},{4,6},{5}}=>3 {{1,3},{2},{4,6,7},{5}}=>2 {{1,3},{2},{4,6},{5,7}}=>2 {{1,3},{2},{4,6},{5},{7}}=>2 {{1,3,7},{2},{4},{5,6}}=>2 {{1,3},{2,7},{4},{5,6}}=>2 {{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}}=>4 {{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}}=>0 {{1,4,5,6},{2,3,7}}=>0 {{1,4,5,6},{2,3},{7}}=>0 {{1,4,5,7},{2,3,6}}=>1 {{1,4,5},{2,3,6,7}}=>0 {{1,4,5},{2,3,6},{7}}=>0 {{1,4,5,7},{2,3},{6}}=>0 {{1,4,5},{2,3,7},{6}}=>0 {{1,4,5},{2,3},{6,7}}=>0 {{1,4,5},{2,3},{6},{7}}=>0 {{1,4,6,7},{2,3,5}}=>1 {{1,4,6},{2,3,5,7}}=>2 {{1,4,6},{2,3,5},{7}}=>1 {{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}}=>0 {{1,4,6},{2,3,7},{5}}=>0 {{1,4,6},{2,3},{5,7}}=>0 {{1,4,6},{2,3},{5},{7}}=>0 {{1,4,7},{2,3,6},{5}}=>1 {{1,4},{2,3,6,7},{5}}=>1 {{1,4},{2,3,6},{5,7}}=>1 {{1,4},{2,3,6},{5},{7}}=>1 {{1,4,7},{2,3},{5,6}}=>1 {{1,4},{2,3,7},{5,6}}=>2 {{1,4},{2,3},{5,6,7}}=>0 {{1,4},{2,3},{5,6},{7}}=>0 {{1,4,7},{2,3},{5},{6}}=>0 {{1,4},{2,3,7},{5},{6}}=>1 {{1,4},{2,3},{5,7},{6}}=>1 {{1,4},{2,3},{5},{6,7}}=>0 {{1,4},{2,3},{5},{6},{7}}=>0 {{1,5,6,7},{2,3,4}}=>0 {{1,5,6},{2,3,4,7}}=>1 {{1,5,6},{2,3,4},{7}}=>0 {{1,5,7},{2,3,4,6}}=>0 {{1,5},{2,3,4,6,7}}=>0 {{1,5},{2,3,4,6},{7}}=>0 {{1,5,7},{2,3,4},{6}}=>0 {{1,5},{2,3,4,7},{6}}=>0 {{1,5},{2,3,4},{6,7}}=>0 {{1,5},{2,3,4},{6},{7}}=>0 {{1,6,7},{2,3,4,5}}=>0 {{1,6},{2,3,4,5,7}}=>0 {{1,6},{2,3,4,5},{7}}=>0 {{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}}=>1 {{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}}=>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},{2,3,4,6},{5}}=>1 {{1},{2,3,4,6,7},{5}}=>0 {{1},{2,3,4,6},{5,7}}=>0 {{1},{2,3,4,6},{5},{7}}=>0 {{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}}=>2 {{1},{2,3,4,7},{5},{6}}=>0 {{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}}=>1 {{1,5,6},{2,3,7},{4}}=>1 {{1,5,6},{2,3},{4,7}}=>1 {{1,5,6},{2,3},{4},{7}}=>1 {{1,5,7},{2,3,6},{4}}=>2 {{1,5},{2,3,6,7},{4}}=>2 {{1,5},{2,3,6},{4,7}}=>2 {{1,5},{2,3,6},{4},{7}}=>2 {{1,5,7},{2,3},{4,6}}=>2 {{1,5},{2,3,7},{4,6}}=>3 {{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}}=>2 {{1,5},{2,3},{4,7},{6}}=>2 {{1,5},{2,3},{4},{6,7}}=>1 {{1,5},{2,3},{4},{6},{7}}=>1 {{1,6,7},{2,3,5},{4}}=>1 {{1,6},{2,3,5,7},{4}}=>1 {{1,6},{2,3,5},{4,7}}=>1 {{1,6},{2,3,5},{4},{7}}=>1 {{1,7},{2,3,5,6},{4}}=>1 {{1},{2,3,5,6,7},{4}}=>0 {{1},{2,3,5,6},{4,7}}=>0 {{1},{2,3,5,6},{4},{7}}=>0 {{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}}=>0 {{1,7},{2,3,5},{4},{6}}=>2 {{1},{2,3,5,7},{4},{6}}=>0 {{1},{2,3,5},{4,7},{6}}=>1 {{1},{2,3,5},{4},{6,7}}=>0 {{1},{2,3,5},{4},{6},{7}}=>0 {{1,6,7},{2,3},{4,5}}=>0 {{1,6},{2,3,7},{4,5}}=>2 {{1,6},{2,3},{4,5,7}}=>1 {{1,6},{2,3},{4,5},{7}}=>0 {{1,7},{2,3,6},{4,5}}=>1 {{1},{2,3,6,7},{4,5}}=>1 {{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}}=>1 {{1},{2,3,7},{4,5},{6}}=>1 {{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}}=>2 {{1,6},{2,3,7},{4},{5}}=>3 {{1,6},{2,3},{4,7},{5}}=>3 {{1,6},{2,3},{4},{5,7}}=>2 {{1,6},{2,3},{4},{5},{7}}=>2 {{1,7},{2,3,6},{4},{5}}=>2 {{1},{2,3,6,7},{4},{5}}=>0 {{1},{2,3,6},{4,7},{5}}=>1 {{1},{2,3,6},{4},{5,7}}=>0 {{1},{2,3,6},{4},{5},{7}}=>0 {{1,7},{2,3},{4,6},{5}}=>2 {{1},{2,3,7},{4,6},{5}}=>2 {{1},{2,3},{4,6,7},{5}}=>1 {{1},{2,3},{4,6},{5,7}}=>1 {{1},{2,3},{4,6},{5},{7}}=>1 {{1,7},{2,3},{4},{5,6}}=>1 {{1},{2,3,7},{4},{5,6}}=>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 {{1,7},{2,3},{4},{5},{6}}=>3 {{1},{2,3,7},{4},{5},{6}}=>0 {{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}}=>3 {{1,4,5,6},{2},{3,7}}=>2 {{1,4,5,6},{2},{3},{7}}=>2 {{1,4,5,7},{2,6},{3}}=>3 {{1,4,5},{2,6,7},{3}}=>3 {{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}}=>4 {{1,4,5},{2},{3,7},{6}}=>3 {{1,4,5},{2},{3},{6,7}}=>2 {{1,4,5},{2},{3},{6},{7}}=>2 {{1,4,6,7},{2,5},{3}}=>4 {{1,4,6},{2,5,7},{3}}=>4 {{1,4,6},{2,5},{3,7}}=>4 {{1,4,6},{2,5},{3},{7}}=>4 {{1,4,7},{2,5,6},{3}}=>3 {{1,4},{2,5,6,7},{3}}=>3 {{1,4},{2,5,6},{3,7}}=>3 {{1,4},{2,5,6},{3},{7}}=>3 {{1,4,7},{2,5},{3,6}}=>5 {{1,4},{2,5,7},{3,6}}=>4 {{1,4},{2,5},{3,6,7}}=>3 {{1,4},{2,5},{3,6},{7}}=>3 {{1,4,7},{2,5},{3},{6}}=>4 {{1,4},{2,5,7},{3},{6}}=>3 {{1,4},{2,5},{3,7},{6}}=>4 {{1,4},{2,5},{3},{6,7}}=>3 {{1,4},{2,5},{3},{6},{7}}=>3 {{1,4,6,7},{2},{3,5}}=>3 {{1,4,6},{2,7},{3,5}}=>3 {{1,4,6},{2},{3,5,7}}=>3 {{1,4,6},{2},{3,5},{7}}=>3 {{1,4,7},{2,6},{3,5}}=>4 {{1,4},{2,6,7},{3,5}}=>2 {{1,4},{2,6},{3,5,7}}=>3 {{1,4},{2,6},{3,5},{7}}=>2 {{1,4,7},{2},{3,5,6}}=>2 {{1,4},{2,7},{3,5,6}}=>2 {{1,4},{2},{3,5,6,7}}=>2 {{1,4},{2},{3,5,6},{7}}=>2 {{1,4,7},{2},{3,5},{6}}=>3 {{1,4},{2,7},{3,5},{6}}=>3 {{1,4},{2},{3,5,7},{6}}=>2 {{1,4},{2},{3,5},{6,7}}=>2 {{1,4},{2},{3,5},{6},{7}}=>2 {{1,4,6,7},{2},{3},{5}}=>2 {{1,4,6},{2,7},{3},{5}}=>4 {{1,4,6},{2},{3,7},{5}}=>3 {{1,4,6},{2},{3},{5,7}}=>2 {{1,4,6},{2},{3},{5},{7}}=>2 {{1,4,7},{2,6},{3},{5}}=>5 {{1,4},{2,6,7},{3},{5}}=>4 {{1,4},{2,6},{3,7},{5}}=>5 {{1,4},{2,6},{3},{5,7}}=>4 {{1,4},{2,6},{3},{5},{7}}=>4 {{1,4,7},{2},{3,6},{5}}=>4 {{1,4},{2,7},{3,6},{5}}=>4 {{1,4},{2},{3,6,7},{5}}=>3 {{1,4},{2},{3,6},{5,7}}=>3 {{1,4},{2},{3,6},{5},{7}}=>3 {{1,4,7},{2},{3},{5,6}}=>3 {{1,4},{2,7},{3},{5,6}}=>3 {{1,4},{2},{3,7},{5,6}}=>2 {{1,4},{2},{3},{5,6,7}}=>2 {{1,4},{2},{3},{5,6},{7}}=>2 {{1,4,7},{2},{3},{5},{6}}=>2 {{1,4},{2,7},{3},{5},{6}}=>5 {{1,4},{2},{3,7},{5},{6}}=>4 {{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}}=>2 {{1,5,6},{2,4,7},{3}}=>2 {{1,5,6},{2,4},{3,7}}=>2 {{1,5,6},{2,4},{3},{7}}=>2 {{1,5,7},{2,4,6},{3}}=>3 {{1,5},{2,4,6,7},{3}}=>3 {{1,5},{2,4,6},{3,7}}=>3 {{1,5},{2,4,6},{3},{7}}=>3 {{1,5,7},{2,4},{3,6}}=>3 {{1,5},{2,4,7},{3,6}}=>4 {{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}}=>3 {{1,5},{2,4},{3,7},{6}}=>3 {{1,5},{2,4},{3},{6,7}}=>2 {{1,5},{2,4},{3},{6},{7}}=>2 {{1,6,7},{2,4,5},{3}}=>2 {{1,6},{2,4,5,7},{3}}=>2 {{1,6},{2,4,5},{3,7}}=>2 {{1,6},{2,4,5},{3},{7}}=>2 {{1,7},{2,4,5,6},{3}}=>2 {{1},{2,4,5,6,7},{3}}=>1 {{1},{2,4,5,6},{3,7}}=>1 {{1},{2,4,5,6},{3},{7}}=>1 {{1,7},{2,4,5},{3,6}}=>1 {{1},{2,4,5,7},{3,6}}=>1 {{1},{2,4,5},{3,6,7}}=>1 {{1},{2,4,5},{3,6},{7}}=>1 {{1,7},{2,4,5},{3},{6}}=>3 {{1},{2,4,5,7},{3},{6}}=>1 {{1},{2,4,5},{3,7},{6}}=>2 {{1},{2,4,5},{3},{6,7}}=>1 {{1},{2,4,5},{3},{6},{7}}=>1 {{1,6,7},{2,4},{3,5}}=>1 {{1,6},{2,4,7},{3,5}}=>3 {{1,6},{2,4},{3,5,7}}=>2 {{1,6},{2,4},{3,5},{7}}=>1 {{1,7},{2,4,6},{3,5}}=>2 {{1},{2,4,6,7},{3,5}}=>2 {{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}}=>2 {{1},{2,4,7},{3,5},{6}}=>2 {{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}}=>3 {{1,6},{2,4,7},{3},{5}}=>4 {{1,6},{2,4},{3,7},{5}}=>4 {{1,6},{2,4},{3},{5,7}}=>3 {{1,6},{2,4},{3},{5},{7}}=>3 {{1,7},{2,4,6},{3},{5}}=>3 {{1},{2,4,6,7},{3},{5}}=>1 {{1},{2,4,6},{3,7},{5}}=>2 {{1},{2,4,6},{3},{5,7}}=>1 {{1},{2,4,6},{3},{5},{7}}=>1 {{1,7},{2,4},{3,6},{5}}=>3 {{1},{2,4,7},{3,6},{5}}=>3 {{1},{2,4},{3,6,7},{5}}=>2 {{1},{2,4},{3,6},{5,7}}=>2 {{1},{2,4},{3,6},{5},{7}}=>2 {{1,7},{2,4},{3},{5,6}}=>2 {{1},{2,4,7},{3},{5,6}}=>2 {{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}}=>4 {{1},{2,4,7},{3},{5},{6}}=>1 {{1},{2,4},{3,7},{5},{6}}=>3 {{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}}=>1 {{1,5,6},{2,7},{3,4}}=>1 {{1,5,6},{2},{3,4,7}}=>1 {{1,5,6},{2},{3,4},{7}}=>1 {{1,5,7},{2,6},{3,4}}=>2 {{1,5},{2,6,7},{3,4}}=>1 {{1,5},{2,6},{3,4,7}}=>3 {{1,5},{2,6},{3,4},{7}}=>1 {{1,5,7},{2},{3,4,6}}=>2 {{1,5},{2,7},{3,4,6}}=>2 {{1,5},{2},{3,4,6,7}}=>2 {{1,5},{2},{3,4,6},{7}}=>2 {{1,5,7},{2},{3,4},{6}}=>1 {{1,5},{2,7},{3,4},{6}}=>2 {{1,5},{2},{3,4,7},{6}}=>2 {{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}}=>0 {{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}}=>0 {{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}}=>0 {{1},{2,5},{3,4,7},{6}}=>1 {{1},{2,5},{3,4},{6,7}}=>0 {{1},{2,5},{3,4},{6},{7}}=>0 {{1,6,7},{2},{3,4,5}}=>1 {{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}}=>0 {{1},{2,6},{3,4,5},{7}}=>0 {{1,7},{2},{3,4,5,6}}=>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 {{1,7},{2},{3,4,5},{6}}=>2 {{1},{2,7},{3,4,5},{6}}=>1 {{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}}=>2 {{1,6},{2,7},{3,4},{5}}=>3 {{1,6},{2},{3,4,7},{5}}=>3 {{1,6},{2},{3,4},{5,7}}=>2 {{1,6},{2},{3,4},{5},{7}}=>2 {{1,7},{2,6},{3,4},{5}}=>2 {{1},{2,6,7},{3,4},{5}}=>1 {{1},{2,6},{3,4,7},{5}}=>2 {{1},{2,6},{3,4},{5,7}}=>1 {{1},{2,6},{3,4},{5},{7}}=>1 {{1,7},{2},{3,4,6},{5}}=>2 {{1},{2,7},{3,4,6},{5}}=>1 {{1},{2},{3,4,6,7},{5}}=>0 {{1},{2},{3,4,6},{5,7}}=>0 {{1},{2},{3,4,6},{5},{7}}=>0 {{1,7},{2},{3,4},{5,6}}=>1 {{1},{2,7},{3,4},{5,6}}=>0 {{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}}=>3 {{1},{2,7},{3,4},{5},{6}}=>2 {{1},{2},{3,4,7},{5},{6}}=>0 {{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}}=>5 {{1,5,6},{2},{3,7},{4}}=>4 {{1,5,6},{2},{3},{4,7}}=>3 {{1,5,6},{2},{3},{4},{7}}=>3 {{1,5,7},{2,6},{3},{4}}=>6 {{1,5},{2,6,7},{3},{4}}=>5 {{1,5},{2,6},{3,7},{4}}=>6 {{1,5},{2,6},{3},{4,7}}=>5 {{1,5},{2,6},{3},{4},{7}}=>5 {{1,5,7},{2},{3,6},{4}}=>5 {{1,5},{2,7},{3,6},{4}}=>5 {{1,5},{2},{3,6,7},{4}}=>4 {{1,5},{2},{3,6},{4,7}}=>4 {{1,5},{2},{3,6},{4},{7}}=>4 {{1,5,7},{2},{3},{4,6}}=>4 {{1,5},{2,7},{3},{4,6}}=>4 {{1,5},{2},{3,7},{4,6}}=>3 {{1,5},{2},{3},{4,6,7}}=>3 {{1,5},{2},{3},{4,6},{7}}=>3 {{1,5,7},{2},{3},{4},{6}}=>3 {{1,5},{2,7},{3},{4},{6}}=>6 {{1,5},{2},{3,7},{4},{6}}=>5 {{1,5},{2},{3},{4,7},{6}}=>4 {{1,5},{2},{3},{4},{6,7}}=>3 {{1,5},{2},{3},{4},{6},{7}}=>3 {{1,6,7},{2,5},{3},{4}}=>4 {{1,6},{2,5,7},{3},{4}}=>5 {{1,6},{2,5},{3,7},{4}}=>5 {{1,6},{2,5},{3},{4,7}}=>4 {{1,6},{2,5},{3},{4},{7}}=>4 {{1,7},{2,5,6},{3},{4}}=>4 {{1},{2,5,6,7},{3},{4}}=>2 {{1},{2,5,6},{3,7},{4}}=>3 {{1},{2,5,6},{3},{4,7}}=>2 {{1},{2,5,6},{3},{4},{7}}=>2 {{1,7},{2,5},{3,6},{4}}=>4 {{1},{2,5,7},{3,6},{4}}=>4 {{1},{2,5},{3,6,7},{4}}=>3 {{1},{2,5},{3,6},{4,7}}=>3 {{1},{2,5},{3,6},{4},{7}}=>3 {{1,7},{2,5},{3},{4,6}}=>3 {{1},{2,5,7},{3},{4,6}}=>3 {{1},{2,5},{3,7},{4,6}}=>2 {{1},{2,5},{3},{4,6,7}}=>2 {{1},{2,5},{3},{4,6},{7}}=>2 {{1,7},{2,5},{3},{4},{6}}=>5 {{1},{2,5,7},{3},{4},{6}}=>2 {{1},{2,5},{3,7},{4},{6}}=>4 {{1},{2,5},{3},{4,7},{6}}=>3 {{1},{2,5},{3},{4},{6,7}}=>2 {{1},{2,5},{3},{4},{6},{7}}=>2 {{1,6,7},{2},{3,5},{4}}=>3 {{1,6},{2,7},{3,5},{4}}=>4 {{1,6},{2},{3,5,7},{4}}=>4 {{1,6},{2},{3,5},{4,7}}=>3 {{1,6},{2},{3,5},{4},{7}}=>3 {{1,7},{2,6},{3,5},{4}}=>3 {{1},{2,6,7},{3,5},{4}}=>2 {{1},{2,6},{3,5,7},{4}}=>3 {{1},{2,6},{3,5},{4,7}}=>2 {{1},{2,6},{3,5},{4},{7}}=>2 {{1,7},{2},{3,5,6},{4}}=>3 {{1},{2,7},{3,5,6},{4}}=>2 {{1},{2},{3,5,6,7},{4}}=>1 {{1},{2},{3,5,6},{4,7}}=>1 {{1},{2},{3,5,6},{4},{7}}=>1 {{1,7},{2},{3,5},{4,6}}=>2 {{1},{2,7},{3,5},{4,6}}=>1 {{1},{2},{3,5,7},{4,6}}=>2 {{1},{2},{3,5},{4,6,7}}=>1 {{1},{2},{3,5},{4,6},{7}}=>1 {{1,7},{2},{3,5},{4},{6}}=>4 {{1},{2,7},{3,5},{4},{6}}=>3 {{1},{2},{3,5,7},{4},{6}}=>1 {{1},{2},{3,5},{4,7},{6}}=>2 {{1},{2},{3,5},{4},{6,7}}=>1 {{1},{2},{3,5},{4},{6},{7}}=>1 {{1,6,7},{2},{3},{4,5}}=>2 {{1,6},{2,7},{3},{4,5}}=>3 {{1,6},{2},{3,7},{4,5}}=>2 {{1,6},{2},{3},{4,5,7}}=>3 {{1,6},{2},{3},{4,5},{7}}=>2 {{1,7},{2,6},{3},{4,5}}=>2 {{1},{2,6,7},{3},{4,5}}=>1 {{1},{2,6},{3,7},{4,5}}=>1 {{1},{2,6},{3},{4,5,7}}=>2 {{1},{2,6},{3},{4,5},{7}}=>1 {{1,7},{2},{3,6},{4,5}}=>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}}=>0 {{1,7},{2},{3},{4,5,6}}=>2 {{1},{2,7},{3},{4,5,6}}=>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 {{1,7},{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},{4,5,7},{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}}=>4 {{1,6},{2,7},{3},{4},{5}}=>7 {{1,6},{2},{3,7},{4},{5}}=>6 {{1,6},{2},{3},{4,7},{5}}=>5 {{1,6},{2},{3},{4},{5,7}}=>4 {{1,6},{2},{3},{4},{5},{7}}=>4 {{1,7},{2,6},{3},{4},{5}}=>6 {{1},{2,6,7},{3},{4},{5}}=>3 {{1},{2,6},{3,7},{4},{5}}=>5 {{1},{2,6},{3},{4,7},{5}}=>4 {{1},{2,6},{3},{4},{5,7}}=>3 {{1},{2,6},{3},{4},{5},{7}}=>3 {{1,7},{2},{3,6},{4},{5}}=>5 {{1},{2,7},{3,6},{4},{5}}=>4 {{1},{2},{3,6,7},{4},{5}}=>2 {{1},{2},{3,6},{4,7},{5}}=>3 {{1},{2},{3,6},{4},{5,7}}=>2 {{1},{2},{3,6},{4},{5},{7}}=>2 {{1,7},{2},{3},{4,6},{5}}=>4 {{1},{2,7},{3},{4,6},{5}}=>3 {{1},{2},{3,7},{4,6},{5}}=>2 {{1},{2},{3},{4,6,7},{5}}=>1 {{1},{2},{3},{4,6},{5,7}}=>1 {{1},{2},{3},{4,6},{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},{4,7},{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}}=>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 interlacing number of a set partition.
Let $\pi$ be a set partition of $\{1,\dots,n\}$ with $k$ blocks. To each block of $\pi$ we add the element $\infty$, which is larger than $n$. Then, an interlacing of $\pi$ is a pair of blocks $B=(B_1 < \dots < B_b < B_{b+1} = \infty)$ and $C=(C_1 < \dots < C_c < C_{c+1} = \infty)$ together with an index $1\leq i\leq \min(b, c)$, such that $B_i < C_i < B_{i+1} < C_{i+1}$.
References
[1] Prasad, A., Ram, S. Set partitions, tableaux, and subspace profiles under regular split semisimple matrices arXiv:2112.00479
Code
def statistic(self):
    self = SetPartition(self)
    arcs = []
    for j, p in enumerate(sorted(self)):
        p = sorted(p)
        arcs.append([])
        for i in range(len(p)-1):
            arcs[j].append((p[i], p[i+1]))
        arcs[j].append((p[-1], Infinity))

    interlacings = 0
    for i in range(len(arcs)):
        for j in range(i+1, len(arcs)):
            for (a,b), (c,d) in zip(arcs[i], arcs[j]):
                if a < c < b < d or c < a < d < b:
                    interlacings += 1
    return interlacings
Created
Mar 28, 2022 at 11:14 by Martin Rubey
Updated
Mar 28, 2022 at 11:14 by Martin Rubey