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Identifier
Values
=>
Cc0009;cc-rep
{{1,2}}=>1 {{1},{2}}=>0 {{1,2,3}}=>1 {{1,2},{3}}=>1 {{1,3},{2}}=>1 {{1},{2,3}}=>1 {{1},{2},{3}}=>0 {{1,2,3,4}}=>1 {{1,2,3},{4}}=>1 {{1,2,4},{3}}=>1 {{1,2},{3,4}}=>1 {{1,2},{3},{4}}=>1 {{1,3,4},{2}}=>1 {{1,3},{2,4}}=>2 {{1,3},{2},{4}}=>1 {{1,4},{2,3}}=>1 {{1},{2,3,4}}=>1 {{1},{2,3},{4}}=>1 {{1,4},{2},{3}}=>1 {{1},{2,4},{3}}=>1 {{1},{2},{3,4}}=>1 {{1},{2},{3},{4}}=>0 {{1,2,3,4,5}}=>1 {{1,2,3,4},{5}}=>1 {{1,2,3,5},{4}}=>1 {{1,2,3},{4,5}}=>1 {{1,2,3},{4},{5}}=>1 {{1,2,4,5},{3}}=>1 {{1,2,4},{3,5}}=>2 {{1,2,4},{3},{5}}=>1 {{1,2,5},{3,4}}=>1 {{1,2},{3,4,5}}=>1 {{1,2},{3,4},{5}}=>1 {{1,2,5},{3},{4}}=>1 {{1,2},{3,5},{4}}=>1 {{1,2},{3},{4,5}}=>1 {{1,2},{3},{4},{5}}=>1 {{1,3,4,5},{2}}=>1 {{1,3,4},{2,5}}=>2 {{1,3,4},{2},{5}}=>1 {{1,3,5},{2,4}}=>2 {{1,3},{2,4,5}}=>2 {{1,3},{2,4},{5}}=>2 {{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}}=>1 {{1,4},{2,3,5}}=>2 {{1,4},{2,3},{5}}=>1 {{1,5},{2,3,4}}=>1 {{1},{2,3,4,5}}=>1 {{1},{2,3,4},{5}}=>1 {{1,5},{2,3},{4}}=>1 {{1},{2,3,5},{4}}=>1 {{1},{2,3},{4,5}}=>1 {{1},{2,3},{4},{5}}=>1 {{1,4,5},{2},{3}}=>1 {{1,4},{2,5},{3}}=>2 {{1,4},{2},{3,5}}=>2 {{1,4},{2},{3},{5}}=>1 {{1,5},{2,4},{3}}=>1 {{1},{2,4,5},{3}}=>1 {{1},{2,4},{3,5}}=>2 {{1},{2,4},{3},{5}}=>1 {{1,5},{2},{3,4}}=>1 {{1},{2,5},{3,4}}=>1 {{1},{2},{3,4,5}}=>1 {{1},{2},{3,4},{5}}=>1 {{1,5},{2},{3},{4}}=>1 {{1},{2,5},{3},{4}}=>1 {{1},{2},{3,5},{4}}=>1 {{1},{2},{3},{4,5}}=>1 {{1},{2},{3},{4},{5}}=>0 {{1,2,3,4,5,6}}=>1 {{1,2,3,4,5},{6}}=>1 {{1,2,3,4,6},{5}}=>1 {{1,2,3,4},{5,6}}=>1 {{1,2,3,4},{5},{6}}=>1 {{1,2,3,5,6},{4}}=>1 {{1,2,3,5},{4,6}}=>2 {{1,2,3,5},{4},{6}}=>1 {{1,2,3,6},{4,5}}=>1 {{1,2,3},{4,5,6}}=>1 {{1,2,3},{4,5},{6}}=>1 {{1,2,3,6},{4},{5}}=>1 {{1,2,3},{4,6},{5}}=>1 {{1,2,3},{4},{5,6}}=>1 {{1,2,3},{4},{5},{6}}=>1 {{1,2,4,5,6},{3}}=>1 {{1,2,4,5},{3,6}}=>2 {{1,2,4,5},{3},{6}}=>1 {{1,2,4,6},{3,5}}=>2 {{1,2,4},{3,5,6}}=>2 {{1,2,4},{3,5},{6}}=>2 {{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 {{1,2,5,6},{3,4}}=>1 {{1,2,5},{3,4,6}}=>2 {{1,2,5},{3,4},{6}}=>1 {{1,2,6},{3,4,5}}=>1 {{1,2},{3,4,5,6}}=>1 {{1,2},{3,4,5},{6}}=>1 {{1,2,6},{3,4},{5}}=>1 {{1,2},{3,4,6},{5}}=>1 {{1,2},{3,4},{5,6}}=>1 {{1,2},{3,4},{5},{6}}=>1 {{1,2,5,6},{3},{4}}=>1 {{1,2,5},{3,6},{4}}=>2 {{1,2,5},{3},{4,6}}=>2 {{1,2,5},{3},{4},{6}}=>1 {{1,2,6},{3,5},{4}}=>1 {{1,2},{3,5,6},{4}}=>1 {{1,2},{3,5},{4,6}}=>2 {{1,2},{3,5},{4},{6}}=>1 {{1,2,6},{3},{4,5}}=>1 {{1,2},{3,6},{4,5}}=>1 {{1,2},{3},{4,5,6}}=>1 {{1,2},{3},{4,5},{6}}=>1 {{1,2,6},{3},{4},{5}}=>1 {{1,2},{3,6},{4},{5}}=>1 {{1,2},{3},{4,6},{5}}=>1 {{1,2},{3},{4},{5,6}}=>1 {{1,2},{3},{4},{5},{6}}=>1 {{1,3,4,5,6},{2}}=>1 {{1,3,4,5},{2,6}}=>2 {{1,3,4,5},{2},{6}}=>1 {{1,3,4,6},{2,5}}=>2 {{1,3,4},{2,5,6}}=>2 {{1,3,4},{2,5},{6}}=>2 {{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}}=>2 {{1,3},{2,4,5,6}}=>2 {{1,3},{2,4,5},{6}}=>2 {{1,3,6},{2,4},{5}}=>2 {{1,3},{2,4,6},{5}}=>2 {{1,3},{2,4},{5,6}}=>2 {{1,3},{2,4},{5},{6}}=>2 {{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}}=>1 {{1,3,6},{2,5},{4}}=>2 {{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}}=>1 {{1,3},{2,6},{4,5}}=>2 {{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}}=>2 {{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}}=>1 {{1,4,5},{2,3,6}}=>2 {{1,4,5},{2,3},{6}}=>1 {{1,4,6},{2,3,5}}=>2 {{1,4},{2,3,5,6}}=>2 {{1,4},{2,3,5},{6}}=>2 {{1,4,6},{2,3},{5}}=>1 {{1,4},{2,3,6},{5}}=>2 {{1,4},{2,3},{5,6}}=>1 {{1,4},{2,3},{5},{6}}=>1 {{1,5,6},{2,3,4}}=>1 {{1,5},{2,3,4,6}}=>2 {{1,5},{2,3,4},{6}}=>1 {{1,6},{2,3,4,5}}=>1 {{1},{2,3,4,5,6}}=>1 {{1},{2,3,4,5},{6}}=>1 {{1,6},{2,3,4},{5}}=>1 {{1},{2,3,4,6},{5}}=>1 {{1},{2,3,4},{5,6}}=>1 {{1},{2,3,4},{5},{6}}=>1 {{1,5,6},{2,3},{4}}=>1 {{1,5},{2,3,6},{4}}=>2 {{1,5},{2,3},{4,6}}=>2 {{1,5},{2,3},{4},{6}}=>1 {{1,6},{2,3,5},{4}}=>1 {{1},{2,3,5,6},{4}}=>1 {{1},{2,3,5},{4,6}}=>2 {{1},{2,3,5},{4},{6}}=>1 {{1,6},{2,3},{4,5}}=>1 {{1},{2,3,6},{4,5}}=>1 {{1},{2,3},{4,5,6}}=>1 {{1},{2,3},{4,5},{6}}=>1 {{1,6},{2,3},{4},{5}}=>1 {{1},{2,3,6},{4},{5}}=>1 {{1},{2,3},{4,6},{5}}=>1 {{1},{2,3},{4},{5,6}}=>1 {{1},{2,3},{4},{5},{6}}=>1 {{1,4,5,6},{2},{3}}=>1 {{1,4,5},{2,6},{3}}=>2 {{1,4,5},{2},{3,6}}=>2 {{1,4,5},{2},{3},{6}}=>1 {{1,4,6},{2,5},{3}}=>2 {{1,4},{2,5,6},{3}}=>2 {{1,4},{2,5},{3,6}}=>3 {{1,4},{2,5},{3},{6}}=>2 {{1,4,6},{2},{3,5}}=>2 {{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}}=>1 {{1,4},{2,6},{3},{5}}=>2 {{1,4},{2},{3,6},{5}}=>2 {{1,4},{2},{3},{5,6}}=>1 {{1,4},{2},{3},{5},{6}}=>1 {{1,5,6},{2,4},{3}}=>1 {{1,5},{2,4,6},{3}}=>2 {{1,5},{2,4},{3,6}}=>2 {{1,5},{2,4},{3},{6}}=>1 {{1,6},{2,4,5},{3}}=>1 {{1},{2,4,5,6},{3}}=>1 {{1},{2,4,5},{3,6}}=>2 {{1},{2,4,5},{3},{6}}=>1 {{1,6},{2,4},{3,5}}=>2 {{1},{2,4,6},{3,5}}=>2 {{1},{2,4},{3,5,6}}=>2 {{1},{2,4},{3,5},{6}}=>2 {{1,6},{2,4},{3},{5}}=>1 {{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}}=>2 {{1,5},{2},{3,4,6}}=>2 {{1,5},{2},{3,4},{6}}=>1 {{1,6},{2,5},{3,4}}=>1 {{1},{2,5,6},{3,4}}=>1 {{1},{2,5},{3,4,6}}=>2 {{1},{2,5},{3,4},{6}}=>1 {{1,6},{2},{3,4,5}}=>1 {{1},{2,6},{3,4,5}}=>1 {{1},{2},{3,4,5,6}}=>1 {{1},{2},{3,4,5},{6}}=>1 {{1,6},{2},{3,4},{5}}=>1 {{1},{2,6},{3,4},{5}}=>1 {{1},{2},{3,4,6},{5}}=>1 {{1},{2},{3,4},{5,6}}=>1 {{1},{2},{3,4},{5},{6}}=>1 {{1,5,6},{2},{3},{4}}=>1 {{1,5},{2,6},{3},{4}}=>2 {{1,5},{2},{3,6},{4}}=>2 {{1,5},{2},{3},{4,6}}=>2 {{1,5},{2},{3},{4},{6}}=>1 {{1,6},{2,5},{3},{4}}=>1 {{1},{2,5,6},{3},{4}}=>1 {{1},{2,5},{3,6},{4}}=>2 {{1},{2,5},{3},{4,6}}=>2 {{1},{2,5},{3},{4},{6}}=>1 {{1,6},{2},{3,5},{4}}=>1 {{1},{2,6},{3,5},{4}}=>1 {{1},{2},{3,5,6},{4}}=>1 {{1},{2},{3,5},{4,6}}=>2 {{1},{2},{3,5},{4},{6}}=>1 {{1,6},{2},{3},{4,5}}=>1 {{1},{2,6},{3},{4,5}}=>1 {{1},{2},{3,6},{4,5}}=>1 {{1},{2},{3},{4,5,6}}=>1 {{1},{2},{3},{4,5},{6}}=>1 {{1,6},{2},{3},{4},{5}}=>1 {{1},{2,6},{3},{4},{5}}=>1 {{1},{2},{3,6},{4},{5}}=>1 {{1},{2},{3},{4,6},{5}}=>1 {{1},{2},{3},{4},{5,6}}=>1 {{1},{2},{3},{4},{5},{6}}=>0 {{1,2,3,4,5,6,7}}=>1 {{1,2,3,4,5,6},{7}}=>1 {{1,2,3,4,5,7},{6}}=>1 {{1,2,3,4,5},{6,7}}=>1 {{1,2,3,4,5},{6},{7}}=>1 {{1,2,3,4,6,7},{5}}=>1 {{1,2,3,4,6},{5,7}}=>2 {{1,2,3,4,6},{5},{7}}=>1 {{1,2,3,4,7},{5,6}}=>1 {{1,2,3,4},{5,6,7}}=>1 {{1,2,3,4},{5,6},{7}}=>1 {{1,2,3,4,7},{5},{6}}=>1 {{1,2,3,4},{5,7},{6}}=>1 {{1,2,3,4},{5},{6,7}}=>1 {{1,2,3,4},{5},{6},{7}}=>1 {{1,2,3,5,6,7},{4}}=>1 {{1,2,3,5,6},{4,7}}=>2 {{1,2,3,5,6},{4},{7}}=>1 {{1,2,3,5,7},{4,6}}=>2 {{1,2,3,5},{4,6,7}}=>2 {{1,2,3,5},{4,6},{7}}=>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 {{1,2,3,6,7},{4,5}}=>1 {{1,2,3,6},{4,5,7}}=>2 {{1,2,3,6},{4,5},{7}}=>1 {{1,2,3,7},{4,5,6}}=>1 {{1,2,3},{4,5,6,7}}=>1 {{1,2,3},{4,5,6},{7}}=>1 {{1,2,3,7},{4,5},{6}}=>1 {{1,2,3},{4,5,7},{6}}=>1 {{1,2,3},{4,5},{6,7}}=>1 {{1,2,3},{4,5},{6},{7}}=>1 {{1,2,3,6,7},{4},{5}}=>1 {{1,2,3,6},{4,7},{5}}=>2 {{1,2,3,6},{4},{5,7}}=>2 {{1,2,3,6},{4},{5},{7}}=>1 {{1,2,3,7},{4,6},{5}}=>1 {{1,2,3},{4,6,7},{5}}=>1 {{1,2,3},{4,6},{5,7}}=>2 {{1,2,3},{4,6},{5},{7}}=>1 {{1,2,3,7},{4},{5,6}}=>1 {{1,2,3},{4,7},{5,6}}=>1 {{1,2,3},{4},{5,6,7}}=>1 {{1,2,3},{4},{5,6},{7}}=>1 {{1,2,3,7},{4},{5},{6}}=>1 {{1,2,3},{4,7},{5},{6}}=>1 {{1,2,3},{4},{5,7},{6}}=>1 {{1,2,3},{4},{5},{6,7}}=>1 {{1,2,3},{4},{5},{6},{7}}=>1 {{1,2,4,5,6,7},{3}}=>1 {{1,2,4,5,6},{3,7}}=>2 {{1,2,4,5,6},{3},{7}}=>1 {{1,2,4,5,7},{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}}=>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 {{1,2,4,6,7},{3,5}}=>2 {{1,2,4,6},{3,5,7}}=>2 {{1,2,4,6},{3,5},{7}}=>2 {{1,2,4,7},{3,5,6}}=>2 {{1,2,4},{3,5,6,7}}=>2 {{1,2,4},{3,5,6},{7}}=>2 {{1,2,4,7},{3,5},{6}}=>2 {{1,2,4},{3,5,7},{6}}=>2 {{1,2,4},{3,5},{6,7}}=>2 {{1,2,4},{3,5},{6},{7}}=>2 {{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}}=>1 {{1,2,4,7},{3,6},{5}}=>2 {{1,2,4},{3,6,7},{5}}=>2 {{1,2,4},{3,6},{5,7}}=>2 {{1,2,4},{3,6},{5},{7}}=>2 {{1,2,4,7},{3},{5,6}}=>1 {{1,2,4},{3,7},{5,6}}=>2 {{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}}=>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 {{1,2,5,6,7},{3,4}}=>1 {{1,2,5,6},{3,4,7}}=>2 {{1,2,5,6},{3,4},{7}}=>1 {{1,2,5,7},{3,4,6}}=>2 {{1,2,5},{3,4,6,7}}=>2 {{1,2,5},{3,4,6},{7}}=>2 {{1,2,5,7},{3,4},{6}}=>1 {{1,2,5},{3,4,7},{6}}=>2 {{1,2,5},{3,4},{6,7}}=>1 {{1,2,5},{3,4},{6},{7}}=>1 {{1,2,6,7},{3,4,5}}=>1 {{1,2,6},{3,4,5,7}}=>2 {{1,2,6},{3,4,5},{7}}=>1 {{1,2,7},{3,4,5,6}}=>1 {{1,2},{3,4,5,6,7}}=>1 {{1,2},{3,4,5,6},{7}}=>1 {{1,2,7},{3,4,5},{6}}=>1 {{1,2},{3,4,5,7},{6}}=>1 {{1,2},{3,4,5},{6,7}}=>1 {{1,2},{3,4,5},{6},{7}}=>1 {{1,2,6,7},{3,4},{5}}=>1 {{1,2,6},{3,4,7},{5}}=>2 {{1,2,6},{3,4},{5,7}}=>2 {{1,2,6},{3,4},{5},{7}}=>1 {{1,2,7},{3,4,6},{5}}=>1 {{1,2},{3,4,6,7},{5}}=>1 {{1,2},{3,4,6},{5,7}}=>2 {{1,2},{3,4,6},{5},{7}}=>1 {{1,2,7},{3,4},{5,6}}=>1 {{1,2},{3,4,7},{5,6}}=>1 {{1,2},{3,4},{5,6,7}}=>1 {{1,2},{3,4},{5,6},{7}}=>1 {{1,2,7},{3,4},{5},{6}}=>1 {{1,2},{3,4,7},{5},{6}}=>1 {{1,2},{3,4},{5,7},{6}}=>1 {{1,2},{3,4},{5},{6,7}}=>1 {{1,2},{3,4},{5},{6},{7}}=>1 {{1,2,5,6,7},{3},{4}}=>1 {{1,2,5,6},{3,7},{4}}=>2 {{1,2,5,6},{3},{4,7}}=>2 {{1,2,5,6},{3},{4},{7}}=>1 {{1,2,5,7},{3,6},{4}}=>2 {{1,2,5},{3,6,7},{4}}=>2 {{1,2,5},{3,6},{4,7}}=>3 {{1,2,5},{3,6},{4},{7}}=>2 {{1,2,5,7},{3},{4,6}}=>2 {{1,2,5},{3,7},{4,6}}=>2 {{1,2,5},{3},{4,6,7}}=>2 {{1,2,5},{3},{4,6},{7}}=>2 {{1,2,5,7},{3},{4},{6}}=>1 {{1,2,5},{3,7},{4},{6}}=>2 {{1,2,5},{3},{4,7},{6}}=>2 {{1,2,5},{3},{4},{6,7}}=>1 {{1,2,5},{3},{4},{6},{7}}=>1 {{1,2,6,7},{3,5},{4}}=>1 {{1,2,6},{3,5,7},{4}}=>2 {{1,2,6},{3,5},{4,7}}=>2 {{1,2,6},{3,5},{4},{7}}=>1 {{1,2,7},{3,5,6},{4}}=>1 {{1,2},{3,5,6,7},{4}}=>1 {{1,2},{3,5,6},{4,7}}=>2 {{1,2},{3,5,6},{4},{7}}=>1 {{1,2,7},{3,5},{4,6}}=>2 {{1,2},{3,5,7},{4,6}}=>2 {{1,2},{3,5},{4,6,7}}=>2 {{1,2},{3,5},{4,6},{7}}=>2 {{1,2,7},{3,5},{4},{6}}=>1 {{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}}=>2 {{1,2,6},{3},{4,5,7}}=>2 {{1,2,6},{3},{4,5},{7}}=>1 {{1,2,7},{3,6},{4,5}}=>1 {{1,2},{3,6,7},{4,5}}=>1 {{1,2},{3,6},{4,5,7}}=>2 {{1,2},{3,6},{4,5},{7}}=>1 {{1,2,7},{3},{4,5,6}}=>1 {{1,2},{3,7},{4,5,6}}=>1 {{1,2},{3},{4,5,6,7}}=>1 {{1,2},{3},{4,5,6},{7}}=>1 {{1,2,7},{3},{4,5},{6}}=>1 {{1,2},{3,7},{4,5},{6}}=>1 {{1,2},{3},{4,5,7},{6}}=>1 {{1,2},{3},{4,5},{6,7}}=>1 {{1,2},{3},{4,5},{6},{7}}=>1 {{1,2,6,7},{3},{4},{5}}=>1 {{1,2,6},{3,7},{4},{5}}=>2 {{1,2,6},{3},{4,7},{5}}=>2 {{1,2,6},{3},{4},{5,7}}=>2 {{1,2,6},{3},{4},{5},{7}}=>1 {{1,2,7},{3,6},{4},{5}}=>1 {{1,2},{3,6,7},{4},{5}}=>1 {{1,2},{3,6},{4,7},{5}}=>2 {{1,2},{3,6},{4},{5,7}}=>2 {{1,2},{3,6},{4},{5},{7}}=>1 {{1,2,7},{3},{4,6},{5}}=>1 {{1,2},{3,7},{4,6},{5}}=>1 {{1,2},{3},{4,6,7},{5}}=>1 {{1,2},{3},{4,6},{5,7}}=>2 {{1,2},{3},{4,6},{5},{7}}=>1 {{1,2,7},{3},{4},{5,6}}=>1 {{1,2},{3,7},{4},{5,6}}=>1 {{1,2},{3},{4,7},{5,6}}=>1 {{1,2},{3},{4},{5,6,7}}=>1 {{1,2},{3},{4},{5,6},{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}}=>1 {{1,2},{3},{4},{5,7},{6}}=>1 {{1,2},{3},{4},{5},{6,7}}=>1 {{1,2},{3},{4},{5},{6},{7}}=>1 {{1,3,4,5,6,7},{2}}=>1 {{1,3,4,5,6},{2,7}}=>2 {{1,3,4,5,6},{2},{7}}=>1 {{1,3,4,5,7},{2,6}}=>2 {{1,3,4,5},{2,6,7}}=>2 {{1,3,4,5},{2,6},{7}}=>2 {{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}}=>2 {{1,3,4,6},{2,5,7}}=>2 {{1,3,4,6},{2,5},{7}}=>2 {{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}}=>1 {{1,3,4,6},{2,7},{5}}=>2 {{1,3,4,6},{2},{5,7}}=>2 {{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}}=>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},{2,7},{5},{6}}=>2 {{1,3,4},{2},{5,7},{6}}=>1 {{1,3,4},{2},{5},{6,7}}=>1 {{1,3,4},{2},{5},{6},{7}}=>1 {{1,3,5,6,7},{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}}=>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}}=>2 {{1,3,6},{2,4,5,7}}=>2 {{1,3,6},{2,4,5},{7}}=>2 {{1,3,7},{2,4,5,6}}=>2 {{1,3},{2,4,5,6,7}}=>2 {{1,3},{2,4,5,6},{7}}=>2 {{1,3,7},{2,4,5},{6}}=>2 {{1,3},{2,4,5,7},{6}}=>2 {{1,3},{2,4,5},{6,7}}=>2 {{1,3},{2,4,5},{6},{7}}=>2 {{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}}=>2 {{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},{2,4,7},{5,6}}=>2 {{1,3},{2,4},{5,6,7}}=>2 {{1,3},{2,4},{5,6},{7}}=>2 {{1,3,7},{2,4},{5},{6}}=>2 {{1,3},{2,4,7},{5},{6}}=>2 {{1,3},{2,4},{5,7},{6}}=>2 {{1,3},{2,4},{5},{6,7}}=>2 {{1,3},{2,4},{5},{6},{7}}=>2 {{1,3,5,6,7},{2},{4}}=>1 {{1,3,5,6},{2,7},{4}}=>2 {{1,3,5,6},{2},{4,7}}=>2 {{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}}=>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}}=>1 {{1,3,5},{2,7},{4},{6}}=>2 {{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}}=>2 {{1,3,6},{2,5,7},{4}}=>2 {{1,3,6},{2,5},{4,7}}=>3 {{1,3,6},{2,5},{4},{7}}=>2 {{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}}=>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}}=>1 {{1,3,7},{2,6},{4,5}}=>2 {{1,3},{2,6,7},{4,5}}=>2 {{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}}=>2 {{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}}=>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}}=>2 {{1,3,6},{2},{4,7},{5}}=>2 {{1,3,6},{2},{4},{5,7}}=>2 {{1,3,6},{2},{4},{5},{7}}=>1 {{1,3,7},{2,6},{4},{5}}=>2 {{1,3},{2,6,7},{4},{5}}=>2 {{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}}=>2 {{1,3},{2},{4,6,7},{5}}=>1 {{1,3},{2},{4,6},{5,7}}=>2 {{1,3},{2},{4,6},{5},{7}}=>1 {{1,3,7},{2},{4},{5,6}}=>1 {{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}}=>2 {{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}}=>1 {{1,4,5,6},{2,3,7}}=>2 {{1,4,5,6},{2,3},{7}}=>1 {{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}}=>1 {{1,4,5},{2,3,7},{6}}=>2 {{1,4,5},{2,3},{6,7}}=>1 {{1,4,5},{2,3},{6},{7}}=>1 {{1,4,6,7},{2,3,5}}=>2 {{1,4,6},{2,3,5,7}}=>2 {{1,4,6},{2,3,5},{7}}=>2 {{1,4,7},{2,3,5,6}}=>2 {{1,4},{2,3,5,6,7}}=>2 {{1,4},{2,3,5,6},{7}}=>2 {{1,4,7},{2,3,5},{6}}=>2 {{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}}=>1 {{1,4,6},{2,3,7},{5}}=>2 {{1,4,6},{2,3},{5,7}}=>2 {{1,4,6},{2,3},{5},{7}}=>1 {{1,4,7},{2,3,6},{5}}=>2 {{1,4},{2,3,6,7},{5}}=>2 {{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}}=>2 {{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}}=>2 {{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}}=>1 {{1,5,6},{2,3,4,7}}=>2 {{1,5,6},{2,3,4},{7}}=>1 {{1,5,7},{2,3,4,6}}=>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},{2,3,4,7},{6}}=>2 {{1,5},{2,3,4},{6,7}}=>1 {{1,5},{2,3,4},{6},{7}}=>1 {{1,6,7},{2,3,4,5}}=>1 {{1,6},{2,3,4,5,7}}=>2 {{1,6},{2,3,4,5},{7}}=>1 {{1,7},{2,3,4,5,6}}=>1 {{1},{2,3,4,5,6,7}}=>1 {{1},{2,3,4,5,6},{7}}=>1 {{1,7},{2,3,4,5},{6}}=>1 {{1},{2,3,4,5,7},{6}}=>1 {{1},{2,3,4,5},{6,7}}=>1 {{1},{2,3,4,5},{6},{7}}=>1 {{1,6,7},{2,3,4},{5}}=>1 {{1,6},{2,3,4,7},{5}}=>2 {{1,6},{2,3,4},{5,7}}=>2 {{1,6},{2,3,4},{5},{7}}=>1 {{1,7},{2,3,4,6},{5}}=>1 {{1},{2,3,4,6,7},{5}}=>1 {{1},{2,3,4,6},{5,7}}=>2 {{1},{2,3,4,6},{5},{7}}=>1 {{1,7},{2,3,4},{5,6}}=>1 {{1},{2,3,4,7},{5,6}}=>1 {{1},{2,3,4},{5,6,7}}=>1 {{1},{2,3,4},{5,6},{7}}=>1 {{1,7},{2,3,4},{5},{6}}=>1 {{1},{2,3,4,7},{5},{6}}=>1 {{1},{2,3,4},{5,7},{6}}=>1 {{1},{2,3,4},{5},{6,7}}=>1 {{1},{2,3,4},{5},{6},{7}}=>1 {{1,5,6,7},{2,3},{4}}=>1 {{1,5,6},{2,3,7},{4}}=>2 {{1,5,6},{2,3},{4,7}}=>2 {{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}}=>3 {{1,5},{2,3,6},{4},{7}}=>2 {{1,5,7},{2,3},{4,6}}=>2 {{1,5},{2,3,7},{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},{2,3,7},{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}}=>2 {{1,6},{2,3,5},{4,7}}=>2 {{1,6},{2,3,5},{4},{7}}=>1 {{1,7},{2,3,5,6},{4}}=>1 {{1},{2,3,5,6,7},{4}}=>1 {{1},{2,3,5,6},{4,7}}=>2 {{1},{2,3,5,6},{4},{7}}=>1 {{1,7},{2,3,5},{4,6}}=>2 {{1},{2,3,5,7},{4,6}}=>2 {{1},{2,3,5},{4,6,7}}=>2 {{1},{2,3,5},{4,6},{7}}=>2 {{1,7},{2,3,5},{4},{6}}=>1 {{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}}=>1 {{1,6},{2,3,7},{4,5}}=>2 {{1,6},{2,3},{4,5,7}}=>2 {{1,6},{2,3},{4,5},{7}}=>1 {{1,7},{2,3,6},{4,5}}=>1 {{1},{2,3,6,7},{4,5}}=>1 {{1},{2,3,6},{4,5,7}}=>2 {{1},{2,3,6},{4,5},{7}}=>1 {{1,7},{2,3},{4,5,6}}=>1 {{1},{2,3,7},{4,5,6}}=>1 {{1},{2,3},{4,5,6,7}}=>1 {{1},{2,3},{4,5,6},{7}}=>1 {{1,7},{2,3},{4,5},{6}}=>1 {{1},{2,3,7},{4,5},{6}}=>1 {{1},{2,3},{4,5,7},{6}}=>1 {{1},{2,3},{4,5},{6,7}}=>1 {{1},{2,3},{4,5},{6},{7}}=>1 {{1,6,7},{2,3},{4},{5}}=>1 {{1,6},{2,3,7},{4},{5}}=>2 {{1,6},{2,3},{4,7},{5}}=>2 {{1,6},{2,3},{4},{5,7}}=>2 {{1,6},{2,3},{4},{5},{7}}=>1 {{1,7},{2,3,6},{4},{5}}=>1 {{1},{2,3,6,7},{4},{5}}=>1 {{1},{2,3,6},{4,7},{5}}=>2 {{1},{2,3,6},{4},{5,7}}=>2 {{1},{2,3,6},{4},{5},{7}}=>1 {{1,7},{2,3},{4,6},{5}}=>1 {{1},{2,3,7},{4,6},{5}}=>1 {{1},{2,3},{4,6,7},{5}}=>1 {{1},{2,3},{4,6},{5,7}}=>2 {{1},{2,3},{4,6},{5},{7}}=>1 {{1,7},{2,3},{4},{5,6}}=>1 {{1},{2,3,7},{4},{5,6}}=>1 {{1},{2,3},{4,7},{5,6}}=>1 {{1},{2,3},{4},{5,6,7}}=>1 {{1},{2,3},{4},{5,6},{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}}=>1 {{1},{2,3},{4},{5,7},{6}}=>1 {{1},{2,3},{4},{5},{6,7}}=>1 {{1},{2,3},{4},{5},{6},{7}}=>1 {{1,4,5,6,7},{2},{3}}=>1 {{1,4,5,6},{2,7},{3}}=>2 {{1,4,5,6},{2},{3,7}}=>2 {{1,4,5,6},{2},{3},{7}}=>1 {{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}}=>2 {{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}}=>1 {{1,4,5},{2,7},{3},{6}}=>2 {{1,4,5},{2},{3,7},{6}}=>2 {{1,4,5},{2},{3},{6,7}}=>1 {{1,4,5},{2},{3},{6},{7}}=>1 {{1,4,6,7},{2,5},{3}}=>2 {{1,4,6},{2,5,7},{3}}=>2 {{1,4,6},{2,5},{3,7}}=>3 {{1,4,6},{2,5},{3},{7}}=>2 {{1,4,7},{2,5,6},{3}}=>2 {{1,4},{2,5,6,7},{3}}=>2 {{1,4},{2,5,6},{3,7}}=>3 {{1,4},{2,5,6},{3},{7}}=>2 {{1,4,7},{2,5},{3,6}}=>3 {{1,4},{2,5,7},{3,6}}=>3 {{1,4},{2,5},{3,6,7}}=>3 {{1,4},{2,5},{3,6},{7}}=>3 {{1,4,7},{2,5},{3},{6}}=>2 {{1,4},{2,5,7},{3},{6}}=>2 {{1,4},{2,5},{3,7},{6}}=>3 {{1,4},{2,5},{3},{6,7}}=>2 {{1,4},{2,5},{3},{6},{7}}=>2 {{1,4,6,7},{2},{3,5}}=>2 {{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}}=>2 {{1,4},{2,6,7},{3,5}}=>2 {{1,4},{2,6},{3,5,7}}=>2 {{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}}=>2 {{1,4},{2,7},{3,5},{6}}=>2 {{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}}=>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}}=>1 {{1,4,7},{2,6},{3},{5}}=>2 {{1,4},{2,6,7},{3},{5}}=>2 {{1,4},{2,6},{3,7},{5}}=>3 {{1,4},{2,6},{3},{5,7}}=>2 {{1,4},{2,6},{3},{5},{7}}=>2 {{1,4,7},{2},{3,6},{5}}=>2 {{1,4},{2,7},{3,6},{5}}=>2 {{1,4},{2},{3,6,7},{5}}=>2 {{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}}=>2 {{1,4},{2},{3,7},{5,6}}=>2 {{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}}=>2 {{1,4},{2},{3,7},{5},{6}}=>2 {{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}}=>1 {{1,5,6},{2,4,7},{3}}=>2 {{1,5,6},{2,4},{3,7}}=>2 {{1,5,6},{2,4},{3},{7}}=>1 {{1,5,7},{2,4,6},{3}}=>2 {{1,5},{2,4,6,7},{3}}=>2 {{1,5},{2,4,6},{3,7}}=>2 {{1,5},{2,4,6},{3},{7}}=>2 {{1,5,7},{2,4},{3,6}}=>2 {{1,5},{2,4,7},{3,6}}=>3 {{1,5},{2,4},{3,6,7}}=>2 {{1,5},{2,4},{3,6},{7}}=>2 {{1,5,7},{2,4},{3},{6}}=>1 {{1,5},{2,4,7},{3},{6}}=>2 {{1,5},{2,4},{3,7},{6}}=>2 {{1,5},{2,4},{3},{6,7}}=>1 {{1,5},{2,4},{3},{6},{7}}=>1 {{1,6,7},{2,4,5},{3}}=>1 {{1,6},{2,4,5,7},{3}}=>2 {{1,6},{2,4,5},{3,7}}=>2 {{1,6},{2,4,5},{3},{7}}=>1 {{1,7},{2,4,5,6},{3}}=>1 {{1},{2,4,5,6,7},{3}}=>1 {{1},{2,4,5,6},{3,7}}=>2 {{1},{2,4,5,6},{3},{7}}=>1 {{1,7},{2,4,5},{3,6}}=>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}}=>1 {{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}}=>2 {{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}}=>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}}=>2 {{1},{2,4,7},{3,5,6}}=>2 {{1},{2,4},{3,5,6,7}}=>2 {{1},{2,4},{3,5,6},{7}}=>2 {{1,7},{2,4},{3,5},{6}}=>2 {{1},{2,4,7},{3,5},{6}}=>2 {{1},{2,4},{3,5,7},{6}}=>2 {{1},{2,4},{3,5},{6,7}}=>2 {{1},{2,4},{3,5},{6},{7}}=>2 {{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}}=>1 {{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}}=>1 {{1,7},{2,4},{3,6},{5}}=>2 {{1},{2,4,7},{3,6},{5}}=>2 {{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}}=>1 {{1},{2,4,7},{3},{5,6}}=>1 {{1},{2,4},{3,7},{5,6}}=>2 {{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}}=>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 {{1,5,6,7},{2},{3,4}}=>1 {{1,5,6},{2,7},{3,4}}=>2 {{1,5,6},{2},{3,4,7}}=>2 {{1,5,6},{2},{3,4},{7}}=>1 {{1,5,7},{2,6},{3,4}}=>2 {{1,5},{2,6,7},{3,4}}=>2 {{1,5},{2,6},{3,4,7}}=>3 {{1,5},{2,6},{3,4},{7}}=>2 {{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}}=>1 {{1,6},{2,5,7},{3,4}}=>2 {{1,6},{2,5},{3,4,7}}=>2 {{1,6},{2,5},{3,4},{7}}=>1 {{1,7},{2,5,6},{3,4}}=>1 {{1},{2,5,6,7},{3,4}}=>1 {{1},{2,5,6},{3,4,7}}=>2 {{1},{2,5,6},{3,4},{7}}=>1 {{1,7},{2,5},{3,4,6}}=>2 {{1},{2,5,7},{3,4,6}}=>2 {{1},{2,5},{3,4,6,7}}=>2 {{1},{2,5},{3,4,6},{7}}=>2 {{1,7},{2,5},{3,4},{6}}=>1 {{1},{2,5,7},{3,4},{6}}=>1 {{1},{2,5},{3,4,7},{6}}=>2 {{1},{2,5},{3,4},{6,7}}=>1 {{1},{2,5},{3,4},{6},{7}}=>1 {{1,6,7},{2},{3,4,5}}=>1 {{1,6},{2,7},{3,4,5}}=>2 {{1,6},{2},{3,4,5,7}}=>2 {{1,6},{2},{3,4,5},{7}}=>1 {{1,7},{2,6},{3,4,5}}=>1 {{1},{2,6,7},{3,4,5}}=>1 {{1},{2,6},{3,4,5,7}}=>2 {{1},{2,6},{3,4,5},{7}}=>1 {{1,7},{2},{3,4,5,6}}=>1 {{1},{2,7},{3,4,5,6}}=>1 {{1},{2},{3,4,5,6,7}}=>1 {{1},{2},{3,4,5,6},{7}}=>1 {{1,7},{2},{3,4,5},{6}}=>1 {{1},{2,7},{3,4,5},{6}}=>1 {{1},{2},{3,4,5,7},{6}}=>1 {{1},{2},{3,4,5},{6,7}}=>1 {{1},{2},{3,4,5},{6},{7}}=>1 {{1,6,7},{2},{3,4},{5}}=>1 {{1,6},{2,7},{3,4},{5}}=>2 {{1,6},{2},{3,4,7},{5}}=>2 {{1,6},{2},{3,4},{5,7}}=>2 {{1,6},{2},{3,4},{5},{7}}=>1 {{1,7},{2,6},{3,4},{5}}=>1 {{1},{2,6,7},{3,4},{5}}=>1 {{1},{2,6},{3,4,7},{5}}=>2 {{1},{2,6},{3,4},{5,7}}=>2 {{1},{2,6},{3,4},{5},{7}}=>1 {{1,7},{2},{3,4,6},{5}}=>1 {{1},{2,7},{3,4,6},{5}}=>1 {{1},{2},{3,4,6,7},{5}}=>1 {{1},{2},{3,4,6},{5,7}}=>2 {{1},{2},{3,4,6},{5},{7}}=>1 {{1,7},{2},{3,4},{5,6}}=>1 {{1},{2,7},{3,4},{5,6}}=>1 {{1},{2},{3,4,7},{5,6}}=>1 {{1},{2},{3,4},{5,6,7}}=>1 {{1},{2},{3,4},{5,6},{7}}=>1 {{1,7},{2},{3,4},{5},{6}}=>1 {{1},{2,7},{3,4},{5},{6}}=>1 {{1},{2},{3,4,7},{5},{6}}=>1 {{1},{2},{3,4},{5,7},{6}}=>1 {{1},{2},{3,4},{5},{6,7}}=>1 {{1},{2},{3,4},{5},{6},{7}}=>1 {{1,5,6,7},{2},{3},{4}}=>1 {{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}}=>1 {{1,5,7},{2,6},{3},{4}}=>2 {{1,5},{2,6,7},{3},{4}}=>2 {{1,5},{2,6},{3,7},{4}}=>3 {{1,5},{2,6},{3},{4,7}}=>3 {{1,5},{2,6},{3},{4},{7}}=>2 {{1,5,7},{2},{3,6},{4}}=>2 {{1,5},{2,7},{3,6},{4}}=>2 {{1,5},{2},{3,6,7},{4}}=>2 {{1,5},{2},{3,6},{4,7}}=>3 {{1,5},{2},{3,6},{4},{7}}=>2 {{1,5,7},{2},{3},{4,6}}=>2 {{1,5},{2,7},{3},{4,6}}=>2 {{1,5},{2},{3,7},{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},{3,7},{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},{2,5},{3},{4}}=>1 {{1,6},{2,5,7},{3},{4}}=>2 {{1,6},{2,5},{3,7},{4}}=>2 {{1,6},{2,5},{3},{4,7}}=>2 {{1,6},{2,5},{3},{4},{7}}=>1 {{1,7},{2,5,6},{3},{4}}=>1 {{1},{2,5,6,7},{3},{4}}=>1 {{1},{2,5,6},{3,7},{4}}=>2 {{1},{2,5,6},{3},{4,7}}=>2 {{1},{2,5,6},{3},{4},{7}}=>1 {{1,7},{2,5},{3,6},{4}}=>2 {{1},{2,5,7},{3,6},{4}}=>2 {{1},{2,5},{3,6,7},{4}}=>2 {{1},{2,5},{3,6},{4,7}}=>3 {{1},{2,5},{3,6},{4},{7}}=>2 {{1,7},{2,5},{3},{4,6}}=>2 {{1},{2,5,7},{3},{4,6}}=>2 {{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}}=>1 {{1},{2,5,7},{3},{4},{6}}=>1 {{1},{2,5},{3,7},{4},{6}}=>2 {{1},{2,5},{3},{4,7},{6}}=>2 {{1},{2,5},{3},{4},{6,7}}=>1 {{1},{2,5},{3},{4},{6},{7}}=>1 {{1,6,7},{2},{3,5},{4}}=>1 {{1,6},{2,7},{3,5},{4}}=>2 {{1,6},{2},{3,5,7},{4}}=>2 {{1,6},{2},{3,5},{4,7}}=>2 {{1,6},{2},{3,5},{4},{7}}=>1 {{1,7},{2,6},{3,5},{4}}=>1 {{1},{2,6,7},{3,5},{4}}=>1 {{1},{2,6},{3,5,7},{4}}=>2 {{1},{2,6},{3,5},{4,7}}=>2 {{1},{2,6},{3,5},{4},{7}}=>1 {{1,7},{2},{3,5,6},{4}}=>1 {{1},{2,7},{3,5,6},{4}}=>1 {{1},{2},{3,5,6,7},{4}}=>1 {{1},{2},{3,5,6},{4,7}}=>2 {{1},{2},{3,5,6},{4},{7}}=>1 {{1,7},{2},{3,5},{4,6}}=>2 {{1},{2,7},{3,5},{4,6}}=>2 {{1},{2},{3,5,7},{4,6}}=>2 {{1},{2},{3,5},{4,6,7}}=>2 {{1},{2},{3,5},{4,6},{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},{4,7},{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}}=>1 {{1,6},{2,7},{3},{4,5}}=>2 {{1,6},{2},{3,7},{4,5}}=>2 {{1,6},{2},{3},{4,5,7}}=>2 {{1,6},{2},{3},{4,5},{7}}=>1 {{1,7},{2,6},{3},{4,5}}=>1 {{1},{2,6,7},{3},{4,5}}=>1 {{1},{2,6},{3,7},{4,5}}=>2 {{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}}=>1 {{1},{2},{3,6,7},{4,5}}=>1 {{1},{2},{3,6},{4,5,7}}=>2 {{1},{2},{3,6},{4,5},{7}}=>1 {{1,7},{2},{3},{4,5,6}}=>1 {{1},{2,7},{3},{4,5,6}}=>1 {{1},{2},{3,7},{4,5,6}}=>1 {{1},{2},{3},{4,5,6,7}}=>1 {{1},{2},{3},{4,5,6},{7}}=>1 {{1,7},{2},{3},{4,5},{6}}=>1 {{1},{2,7},{3},{4,5},{6}}=>1 {{1},{2},{3,7},{4,5},{6}}=>1 {{1},{2},{3},{4,5,7},{6}}=>1 {{1},{2},{3},{4,5},{6,7}}=>1 {{1},{2},{3},{4,5},{6},{7}}=>1 {{1,6,7},{2},{3},{4},{5}}=>1 {{1,6},{2,7},{3},{4},{5}}=>2 {{1,6},{2},{3,7},{4},{5}}=>2 {{1,6},{2},{3},{4,7},{5}}=>2 {{1,6},{2},{3},{4},{5,7}}=>2 {{1,6},{2},{3},{4},{5},{7}}=>1 {{1,7},{2,6},{3},{4},{5}}=>1 {{1},{2,6,7},{3},{4},{5}}=>1 {{1},{2,6},{3,7},{4},{5}}=>2 {{1},{2,6},{3},{4,7},{5}}=>2 {{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}}=>1 {{1},{2},{3,6,7},{4},{5}}=>1 {{1},{2},{3,6},{4,7},{5}}=>2 {{1},{2},{3,6},{4},{5,7}}=>2 {{1},{2},{3,6},{4},{5},{7}}=>1 {{1,7},{2},{3},{4,6},{5}}=>1 {{1},{2,7},{3},{4,6},{5}}=>1 {{1},{2},{3,7},{4,6},{5}}=>1 {{1},{2},{3},{4,6,7},{5}}=>1 {{1},{2},{3},{4,6},{5,7}}=>2 {{1},{2},{3},{4,6},{5},{7}}=>1 {{1,7},{2},{3},{4},{5,6}}=>1 {{1},{2,7},{3},{4},{5,6}}=>1 {{1},{2},{3,7},{4},{5,6}}=>1 {{1},{2},{3},{4,7},{5,6}}=>1 {{1},{2},{3},{4},{5,6,7}}=>1 {{1},{2},{3},{4},{5,6},{7}}=>1 {{1,7},{2},{3},{4},{5},{6}}=>1 {{1},{2,7},{3},{4},{5},{6}}=>1 {{1},{2},{3,7},{4},{5},{6}}=>1 {{1},{2},{3},{4,7},{5},{6}}=>1 {{1},{2},{3},{4},{5,7},{6}}=>1 {{1},{2},{3},{4},{5},{6,7}}=>1 {{1},{2},{3},{4},{5},{6},{7}}=>0 {{1},{2},{3,4,5,6,7,8}}=>1 {{1},{2,4,5,6,7,8},{3}}=>1 {{1},{2,3,5,6,7,8},{4}}=>1 {{1},{2,3,4,6,7,8},{5}}=>1 {{1},{2,3,4,5,7,8},{6}}=>1 {{1},{2,3,4,5,6,7},{8}}=>1 {{1},{2,3,4,5,6,8},{7}}=>1 {{1},{2,3,4,5,6,7,8}}=>1 {{1,2},{3,4,5,6,7,8}}=>1 {{1,4,5,6,7,8},{2},{3}}=>1 {{1,3,5,6,7,8},{2},{4}}=>1 {{1,3,4,5,6,7,8},{2}}=>1 {{1,4,5,6,7,8},{2,3}}=>1 {{1,2,4,5,6,7,8},{3}}=>1 {{1,2,5,6,7,8},{3,4}}=>1 {{1,2,3,5,6,7,8},{4}}=>1 {{1,2,3,6,7,8},{4,5}}=>1 {{1,2,3,4,6,7,8},{5}}=>1 {{1,2,3,4,5,6},{7,8}}=>1 {{1,2,3,4,7,8},{5,6}}=>1 {{1,2,3,4,5,7,8},{6}}=>1 {{1,2,3,4,5,6,7},{8}}=>1 {{1,8},{2,3,4,5,6,7}}=>1 {{1,2,3,4,5,8},{6,7}}=>1 {{1,2,3,4,5,6,8},{7}}=>1 {{1,2,3,4,5,6,7,8}}=>1 {{1,3,5,6,7,8},{2,4}}=>2 {{1,3,4,6,7,8},{2,5}}=>2 {{1,2,4,6,7,8},{3,5}}=>2 {{1,3,4,5,7,8},{2,6}}=>2 {{1,2,4,5,7,8},{3,6}}=>2 {{1,2,3,5,7,8},{4,6}}=>2 {{1,3,4,5,6,8},{2,7}}=>2 {{1,2,4,5,6,8},{3,7}}=>2 {{1,2,3,5,6,8},{4,7}}=>2 {{1,2,3,4,6,8},{5,7}}=>2 {{1,3,4,5,6,7},{2,8}}=>2 {{1,2,4,5,6,7},{3,8}}=>2 {{1,2,3,5,6,7},{4,8}}=>2 {{1,2,3,4,6,7},{5,8}}=>2 {{1,2,3,4,5,7},{6,8}}=>2 {{1,3},{2,4,5,6,7,8}}=>2 {{1,4},{2,3,5,6,7,8}}=>2 {{1,5},{2,3,4,6,7,8}}=>2 {{1,6},{2,3,4,5,7,8}}=>2 {{1,7},{2,3,4,5,6,8}}=>2
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Description
The crossing number of a set partition.
This is the maximal number of chords in the standard representation of a set partition, that mutually cross.
References
[1] Chen, W. Y. C., Deng, E. Y. P., Du, R. R. X., Stanley, R. P., Yan, C. H. Crossings and nestings of matchings and partitions MathSciNet:2272140 arXiv:math/0501230
Code
def statistic(pi):
    return max(len(p) for p in to_vacillating(pi))

def to_vacillating(pi):
    """Return the vacillating tableau associated to the set partition pi.

    INPUT:

    - pi, a set partition

    OUTPUT:

    - a vacillating tableau.

    EXAMPLES:

    sage: pi = SetPartition([[1,4,5,7], [2,6],[3]])
    sage: to_vacillating(pi)
    [[], [], [1], [1], [1, 1], [1, 1], [1, 1], [1], [2], [1], [1, 1], [1], [1], [], []]
    """
    T = [StandardTableau([])]
    perm = pi.to_permutation()
    mrep = perm.inverse()
    for j in range(pi.size(), 0, -1):
        prev = mrep(j)
        next = perm(j)
        if j == next: # singleton block
            T += [T[-1], T[-1]]
        elif next < j: # maximal element of a non-singleton block
# do nothing, then insert prev
            T += [T[-1], T[-1].schensted_insert(prev)]
        elif prev > j: # minimal element of a non-singleton block
# delete j then do nothing
            if max(T[-1].entries()) == j:
                new = T[-1].restrict(j-1)
                T += [new, new]
            else:
                print("ERROR")
        else: # transient
# delete j then insert prev
            new = T[-1].restrict(j-1)
            T += [new, new.schensted_insert(prev)]

    return [t.shape() for t in T[::-1]]
Created
Jun 06, 2015 at 00:13 by Martin Rubey
Updated
May 27, 2021 at 11:26 by Martin Rubey