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Identifier
Values
=>
Cc0009;cc-rep
{{1}}=>0 {{1,2}}=>0 {{1},{2}}=>0 {{1,2,3}}=>0 {{1,2},{3}}=>0 {{1,3},{2}}=>0 {{1},{2,3}}=>0 {{1},{2},{3}}=>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}}=>0 {{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}}=>0 {{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}}=>1 {{1,3,4},{2},{5}}=>0 {{1,3,5},{2,4}}=>2 {{1,3},{2,4,5}}=>1 {{1,3},{2,4},{5}}=>1 {{1,3,5},{2},{4}}=>0 {{1,3},{2,5},{4}}=>1 {{1,3},{2},{4,5}}=>0 {{1,3},{2},{4},{5}}=>0 {{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}}=>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}}=>0 {{1,5},{2,4},{3}}=>0 {{1},{2,4,5},{3}}=>0 {{1},{2,4},{3,5}}=>1 {{1},{2,4},{3},{5}}=>0 {{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}}=>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}}=>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}}=>1 {{1,2,4,5},{3},{6}}=>0 {{1,2,4,6},{3,5}}=>2 {{1,2,4},{3,5,6}}=>1 {{1,2,4},{3,5},{6}}=>1 {{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}}=>0 {{1,2,5},{3,4,6}}=>1 {{1,2,5},{3,4},{6}}=>0 {{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}}=>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}}=>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 {{1,2,6},{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}}=>1 {{1,3,4,5},{2},{6}}=>0 {{1,3,4,6},{2,5}}=>2 {{1,3,4},{2,5,6}}=>1 {{1,3,4},{2,5},{6}}=>1 {{1,3,4,6},{2},{5}}=>0 {{1,3,4},{2,6},{5}}=>1 {{1,3,4},{2},{5,6}}=>0 {{1,3,4},{2},{5},{6}}=>0 {{1,3,5,6},{2,4}}=>2 {{1,3,5},{2,4,6}}=>3 {{1,3,5},{2,4},{6}}=>2 {{1,3,6},{2,4,5}}=>2 {{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}}=>0 {{1,3,5},{2,6},{4}}=>1 {{1,3,5},{2},{4,6}}=>1 {{1,3,5},{2},{4},{6}}=>0 {{1,3,6},{2,5},{4}}=>2 {{1,3},{2,5,6},{4}}=>1 {{1,3},{2,5},{4,6}}=>2 {{1,3},{2,5},{4},{6}}=>1 {{1,3,6},{2},{4,5}}=>0 {{1,3},{2,6},{4,5}}=>1 {{1,3},{2},{4,5,6}}=>0 {{1,3},{2},{4,5},{6}}=>0 {{1,3,6},{2},{4},{5}}=>0 {{1,3},{2,6},{4},{5}}=>1 {{1,3},{2},{4,6},{5}}=>0 {{1,3},{2},{4},{5,6}}=>0 {{1,3},{2},{4},{5},{6}}=>0 {{1,4,5,6},{2,3}}=>0 {{1,4,5},{2,3,6}}=>1 {{1,4,5},{2,3},{6}}=>0 {{1,4,6},{2,3,5}}=>2 {{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}}=>1 {{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}}=>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}}=>0 {{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}}=>0 {{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}}=>1 {{1,4,5},{2},{3,6}}=>1 {{1,4,5},{2},{3},{6}}=>0 {{1,4,6},{2,5},{3}}=>2 {{1,4},{2,5,6},{3}}=>1 {{1,4},{2,5},{3,6}}=>3 {{1,4},{2,5},{3},{6}}=>1 {{1,4,6},{2},{3,5}}=>2 {{1,4},{2,6},{3,5}}=>2 {{1,4},{2},{3,5,6}}=>1 {{1,4},{2},{3,5},{6}}=>1 {{1,4,6},{2},{3},{5}}=>0 {{1,4},{2,6},{3},{5}}=>1 {{1,4},{2},{3,6},{5}}=>1 {{1,4},{2},{3},{5,6}}=>0 {{1,4},{2},{3},{5},{6}}=>0 {{1,5,6},{2,4},{3}}=>0 {{1,5},{2,4,6},{3}}=>1 {{1,5},{2,4},{3,6}}=>2 {{1,5},{2,4},{3},{6}}=>0 {{1,6},{2,4,5},{3}}=>0 {{1},{2,4,5,6},{3}}=>0 {{1},{2,4,5},{3,6}}=>1 {{1},{2,4,5},{3},{6}}=>0 {{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}}=>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 {{1,5,6},{2},{3,4}}=>0 {{1,5},{2,6},{3,4}}=>1 {{1,5},{2},{3,4,6}}=>1 {{1,5},{2},{3,4},{6}}=>0 {{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}}=>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}}=>0 {{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}}=>0 {{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}}=>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},{4,5,6}}=>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}}=>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}}=>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}}=>1 {{1,2,3,5,6},{4},{7}}=>0 {{1,2,3,5,7},{4,6}}=>2 {{1,2,3,5},{4,6,7}}=>1 {{1,2,3,5},{4,6},{7}}=>1 {{1,2,3,5,7},{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}}=>1 {{1,2,3,6},{4,5},{7}}=>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 {{1,2,3,7},{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}}=>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}}=>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 {{1,2,3,7},{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}}=>1 {{1,2,4,5,6},{3},{7}}=>0 {{1,2,4,5,7},{3,6}}=>2 {{1,2,4,5},{3,6,7}}=>1 {{1,2,4,5},{3,6},{7}}=>1 {{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}}=>2 {{1,2,4,6},{3,5,7}}=>3 {{1,2,4,6},{3,5},{7}}=>2 {{1,2,4,7},{3,5,6}}=>2 {{1,2,4},{3,5,6,7}}=>1 {{1,2,4},{3,5,6},{7}}=>1 {{1,2,4,7},{3,5},{6}}=>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 {{1,2,4,6,7},{3},{5}}=>0 {{1,2,4,6},{3,7},{5}}=>1 {{1,2,4,6},{3},{5,7}}=>1 {{1,2,4,6},{3},{5},{7}}=>0 {{1,2,4,7},{3,6},{5}}=>2 {{1,2,4},{3,6,7},{5}}=>1 {{1,2,4},{3,6},{5,7}}=>2 {{1,2,4},{3,6},{5},{7}}=>1 {{1,2,4,7},{3},{5,6}}=>0 {{1,2,4},{3,7},{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},{3,7},{5},{6}}=>1 {{1,2,4},{3},{5,7},{6}}=>0 {{1,2,4},{3},{5},{6,7}}=>0 {{1,2,4},{3},{5},{6},{7}}=>0 {{1,2,5,6,7},{3,4}}=>0 {{1,2,5,6},{3,4,7}}=>1 {{1,2,5,6},{3,4},{7}}=>0 {{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}}=>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 {{1,2,6,7},{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}}=>0 {{1,2,6},{3,4,7},{5}}=>1 {{1,2,6},{3,4},{5,7}}=>1 {{1,2,6},{3,4},{5},{7}}=>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}}=>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 {{1,2,7},{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}}=>1 {{1,2,5,6},{3},{4,7}}=>1 {{1,2,5,6},{3},{4},{7}}=>0 {{1,2,5,7},{3,6},{4}}=>2 {{1,2,5},{3,6,7},{4}}=>1 {{1,2,5},{3,6},{4,7}}=>3 {{1,2,5},{3,6},{4},{7}}=>1 {{1,2,5,7},{3},{4,6}}=>2 {{1,2,5},{3,7},{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}}=>0 {{1,2,5},{3,7},{4},{6}}=>1 {{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}}=>0 {{1,2,6},{3,5,7},{4}}=>1 {{1,2,6},{3,5},{4,7}}=>2 {{1,2,6},{3,5},{4},{7}}=>0 {{1,2,7},{3,5,6},{4}}=>0 {{1,2},{3,5,6,7},{4}}=>0 {{1,2},{3,5,6},{4,7}}=>1 {{1,2},{3,5,6},{4},{7}}=>0 {{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 {{1,2,7},{3,5},{4},{6}}=>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 {{1,2,6,7},{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}}=>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}}=>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}}=>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}}=>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}}=>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}}=>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 {{1,2,7},{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}}=>1 {{1,3,4,5,6},{2},{7}}=>0 {{1,3,4,5,7},{2,6}}=>2 {{1,3,4,5},{2,6,7}}=>1 {{1,3,4,5},{2,6},{7}}=>1 {{1,3,4,5,7},{2},{6}}=>0 {{1,3,4,5},{2,7},{6}}=>1 {{1,3,4,5},{2},{6,7}}=>0 {{1,3,4,5},{2},{6},{7}}=>0 {{1,3,4,6,7},{2,5}}=>2 {{1,3,4,6},{2,5,7}}=>3 {{1,3,4,6},{2,5},{7}}=>2 {{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}}=>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 {{1,3,4,6,7},{2},{5}}=>0 {{1,3,4,6},{2,7},{5}}=>1 {{1,3,4,6},{2},{5,7}}=>1 {{1,3,4,6},{2},{5},{7}}=>0 {{1,3,4,7},{2,6},{5}}=>2 {{1,3,4},{2,6,7},{5}}=>1 {{1,3,4},{2,6},{5,7}}=>2 {{1,3,4},{2,6},{5},{7}}=>1 {{1,3,4,7},{2},{5,6}}=>0 {{1,3,4},{2,7},{5,6}}=>1 {{1,3,4},{2},{5,6,7}}=>0 {{1,3,4},{2},{5,6},{7}}=>0 {{1,3,4,7},{2},{5},{6}}=>0 {{1,3,4},{2,7},{5},{6}}=>1 {{1,3,4},{2},{5,7},{6}}=>0 {{1,3,4},{2},{5},{6,7}}=>0 {{1,3,4},{2},{5},{6},{7}}=>0 {{1,3,5,6,7},{2,4}}=>2 {{1,3,5,6},{2,4,7}}=>3 {{1,3,5,6},{2,4},{7}}=>2 {{1,3,5,7},{2,4,6}}=>4 {{1,3,5},{2,4,6,7}}=>3 {{1,3,5},{2,4,6},{7}}=>3 {{1,3,5,7},{2,4},{6}}=>2 {{1,3,5},{2,4,7},{6}}=>3 {{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}}=>3 {{1,3,6},{2,4,5},{7}}=>2 {{1,3,7},{2,4,5,6}}=>2 {{1,3},{2,4,5,6,7}}=>1 {{1,3},{2,4,5,6},{7}}=>1 {{1,3,7},{2,4,5},{6}}=>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}}=>2 {{1,3,6},{2,4,7},{5}}=>3 {{1,3,6},{2,4},{5,7}}=>3 {{1,3,6},{2,4},{5},{7}}=>2 {{1,3,7},{2,4,6},{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}}=>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}}=>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 {{1,3,5,6,7},{2},{4}}=>0 {{1,3,5,6},{2,7},{4}}=>1 {{1,3,5,6},{2},{4,7}}=>1 {{1,3,5,6},{2},{4},{7}}=>0 {{1,3,5,7},{2,6},{4}}=>2 {{1,3,5},{2,6,7},{4}}=>1 {{1,3,5},{2,6},{4,7}}=>3 {{1,3,5},{2,6},{4},{7}}=>1 {{1,3,5,7},{2},{4,6}}=>2 {{1,3,5},{2,7},{4,6}}=>2 {{1,3,5},{2},{4,6,7}}=>1 {{1,3,5},{2},{4,6},{7}}=>1 {{1,3,5,7},{2},{4},{6}}=>0 {{1,3,5},{2,7},{4},{6}}=>1 {{1,3,5},{2},{4,7},{6}}=>1 {{1,3,5},{2},{4},{6,7}}=>0 {{1,3,5},{2},{4},{6},{7}}=>0 {{1,3,6,7},{2,5},{4}}=>2 {{1,3,6},{2,5,7},{4}}=>3 {{1,3,6},{2,5},{4,7}}=>4 {{1,3,6},{2,5},{4},{7}}=>2 {{1,3,7},{2,5,6},{4}}=>2 {{1,3},{2,5,6,7},{4}}=>1 {{1,3},{2,5,6},{4,7}}=>2 {{1,3},{2,5,6},{4},{7}}=>1 {{1,3,7},{2,5},{4,6}}=>3 {{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}}=>2 {{1,3},{2,5,7},{4},{6}}=>1 {{1,3},{2,5},{4,7},{6}}=>2 {{1,3},{2,5},{4},{6,7}}=>1 {{1,3},{2,5},{4},{6},{7}}=>1 {{1,3,6,7},{2},{4,5}}=>0 {{1,3,6},{2,7},{4,5}}=>1 {{1,3,6},{2},{4,5,7}}=>1 {{1,3,6},{2},{4,5},{7}}=>0 {{1,3,7},{2,6},{4,5}}=>2 {{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}}=>0 {{1,3},{2,7},{4,5,6}}=>1 {{1,3},{2},{4,5,6,7}}=>0 {{1,3},{2},{4,5,6},{7}}=>0 {{1,3,7},{2},{4,5},{6}}=>0 {{1,3},{2,7},{4,5},{6}}=>1 {{1,3},{2},{4,5,7},{6}}=>0 {{1,3},{2},{4,5},{6,7}}=>0 {{1,3},{2},{4,5},{6},{7}}=>0 {{1,3,6,7},{2},{4},{5}}=>0 {{1,3,6},{2,7},{4},{5}}=>1 {{1,3,6},{2},{4,7},{5}}=>1 {{1,3,6},{2},{4},{5,7}}=>1 {{1,3,6},{2},{4},{5},{7}}=>0 {{1,3,7},{2,6},{4},{5}}=>2 {{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}}=>1 {{1,3,7},{2},{4,6},{5}}=>0 {{1,3},{2,7},{4,6},{5}}=>1 {{1,3},{2},{4,6,7},{5}}=>0 {{1,3},{2},{4,6},{5,7}}=>1 {{1,3},{2},{4,6},{5},{7}}=>0 {{1,3,7},{2},{4},{5,6}}=>0 {{1,3},{2,7},{4},{5,6}}=>1 {{1,3},{2},{4,7},{5,6}}=>0 {{1,3},{2},{4},{5,6,7}}=>0 {{1,3},{2},{4},{5,6},{7}}=>0 {{1,3,7},{2},{4},{5},{6}}=>0 {{1,3},{2,7},{4},{5},{6}}=>1 {{1,3},{2},{4,7},{5},{6}}=>0 {{1,3},{2},{4},{5,7},{6}}=>0 {{1,3},{2},{4},{5},{6,7}}=>0 {{1,3},{2},{4},{5},{6},{7}}=>0 {{1,4,5,6,7},{2,3}}=>0 {{1,4,5,6},{2,3,7}}=>1 {{1,4,5,6},{2,3},{7}}=>0 {{1,4,5,7},{2,3,6}}=>2 {{1,4,5},{2,3,6,7}}=>1 {{1,4,5},{2,3,6},{7}}=>1 {{1,4,5,7},{2,3},{6}}=>0 {{1,4,5},{2,3,7},{6}}=>1 {{1,4,5},{2,3},{6,7}}=>0 {{1,4,5},{2,3},{6},{7}}=>0 {{1,4,6,7},{2,3,5}}=>2 {{1,4,6},{2,3,5,7}}=>3 {{1,4,6},{2,3,5},{7}}=>2 {{1,4,7},{2,3,5,6}}=>2 {{1,4},{2,3,5,6,7}}=>1 {{1,4},{2,3,5,6},{7}}=>1 {{1,4,7},{2,3,5},{6}}=>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 {{1,4,6,7},{2,3},{5}}=>0 {{1,4,6},{2,3,7},{5}}=>1 {{1,4,6},{2,3},{5,7}}=>1 {{1,4,6},{2,3},{5},{7}}=>0 {{1,4,7},{2,3,6},{5}}=>2 {{1,4},{2,3,6,7},{5}}=>1 {{1,4},{2,3,6},{5,7}}=>2 {{1,4},{2,3,6},{5},{7}}=>1 {{1,4,7},{2,3},{5,6}}=>0 {{1,4},{2,3,7},{5,6}}=>1 {{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}}=>0 {{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}}=>2 {{1,5},{2,3,4,6,7}}=>1 {{1,5},{2,3,4,6},{7}}=>1 {{1,5,7},{2,3,4},{6}}=>0 {{1,5},{2,3,4,7},{6}}=>1 {{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}}=>1 {{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}}=>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}}=>0 {{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}}=>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}}=>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}}=>1 {{1,5,6},{2,3},{4,7}}=>1 {{1,5,6},{2,3},{4},{7}}=>0 {{1,5,7},{2,3,6},{4}}=>2 {{1,5},{2,3,6,7},{4}}=>1 {{1,5},{2,3,6},{4,7}}=>3 {{1,5},{2,3,6},{4},{7}}=>1 {{1,5,7},{2,3},{4,6}}=>2 {{1,5},{2,3,7},{4,6}}=>2 {{1,5},{2,3},{4,6,7}}=>1 {{1,5},{2,3},{4,6},{7}}=>1 {{1,5,7},{2,3},{4},{6}}=>0 {{1,5},{2,3,7},{4},{6}}=>1 {{1,5},{2,3},{4,7},{6}}=>1 {{1,5},{2,3},{4},{6,7}}=>0 {{1,5},{2,3},{4},{6},{7}}=>0 {{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}}=>0 {{1,7},{2,3,5,6},{4}}=>0 {{1},{2,3,5,6,7},{4}}=>0 {{1},{2,3,5,6},{4,7}}=>1 {{1},{2,3,5,6},{4},{7}}=>0 {{1,7},{2,3,5},{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}}=>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 {{1,6,7},{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}}=>0 {{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}}=>0 {{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}}=>0 {{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}}=>0 {{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}}=>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},{5,6,7}}=>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}}=>1 {{1,4,5,6},{2},{3,7}}=>1 {{1,4,5,6},{2},{3},{7}}=>0 {{1,4,5,7},{2,6},{3}}=>2 {{1,4,5},{2,6,7},{3}}=>1 {{1,4,5},{2,6},{3,7}}=>3 {{1,4,5},{2,6},{3},{7}}=>1 {{1,4,5,7},{2},{3,6}}=>2 {{1,4,5},{2,7},{3,6}}=>2 {{1,4,5},{2},{3,6,7}}=>1 {{1,4,5},{2},{3,6},{7}}=>1 {{1,4,5,7},{2},{3},{6}}=>0 {{1,4,5},{2,7},{3},{6}}=>1 {{1,4,5},{2},{3,7},{6}}=>1 {{1,4,5},{2},{3},{6,7}}=>0 {{1,4,5},{2},{3},{6},{7}}=>0 {{1,4,6,7},{2,5},{3}}=>2 {{1,4,6},{2,5,7},{3}}=>3 {{1,4,6},{2,5},{3,7}}=>4 {{1,4,6},{2,5},{3},{7}}=>2 {{1,4,7},{2,5,6},{3}}=>2 {{1,4},{2,5,6,7},{3}}=>1 {{1,4},{2,5,6},{3,7}}=>3 {{1,4},{2,5,6},{3},{7}}=>1 {{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}}=>2 {{1,4},{2,5,7},{3},{6}}=>1 {{1,4},{2,5},{3,7},{6}}=>3 {{1,4},{2,5},{3},{6,7}}=>1 {{1,4},{2,5},{3},{6},{7}}=>1 {{1,4,6,7},{2},{3,5}}=>2 {{1,4,6},{2,7},{3,5}}=>3 {{1,4,6},{2},{3,5,7}}=>3 {{1,4,6},{2},{3,5},{7}}=>2 {{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}}=>1 {{1,4},{2},{3,5,6},{7}}=>1 {{1,4,7},{2},{3,5},{6}}=>2 {{1,4},{2,7},{3,5},{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 {{1,4,6,7},{2},{3},{5}}=>0 {{1,4,6},{2,7},{3},{5}}=>1 {{1,4,6},{2},{3,7},{5}}=>1 {{1,4,6},{2},{3},{5,7}}=>1 {{1,4,6},{2},{3},{5},{7}}=>0 {{1,4,7},{2,6},{3},{5}}=>2 {{1,4},{2,6,7},{3},{5}}=>1 {{1,4},{2,6},{3,7},{5}}=>3 {{1,4},{2,6},{3},{5,7}}=>2 {{1,4},{2,6},{3},{5},{7}}=>1 {{1,4,7},{2},{3,6},{5}}=>2 {{1,4},{2,7},{3,6},{5}}=>2 {{1,4},{2},{3,6,7},{5}}=>1 {{1,4},{2},{3,6},{5,7}}=>2 {{1,4},{2},{3,6},{5},{7}}=>1 {{1,4,7},{2},{3},{5,6}}=>0 {{1,4},{2,7},{3},{5,6}}=>1 {{1,4},{2},{3,7},{5,6}}=>1 {{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},{2,7},{3},{5},{6}}=>1 {{1,4},{2},{3,7},{5},{6}}=>1 {{1,4},{2},{3},{5,7},{6}}=>0 {{1,4},{2},{3},{5},{6,7}}=>0 {{1,4},{2},{3},{5},{6},{7}}=>0 {{1,5,6,7},{2,4},{3}}=>0 {{1,5,6},{2,4,7},{3}}=>1 {{1,5,6},{2,4},{3,7}}=>2 {{1,5,6},{2,4},{3},{7}}=>0 {{1,5,7},{2,4,6},{3}}=>2 {{1,5},{2,4,6,7},{3}}=>1 {{1,5},{2,4,6},{3,7}}=>3 {{1,5},{2,4,6},{3},{7}}=>1 {{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}}=>0 {{1,5},{2,4,7},{3},{6}}=>1 {{1,5},{2,4},{3,7},{6}}=>2 {{1,5},{2,4},{3},{6,7}}=>0 {{1,5},{2,4},{3},{6},{7}}=>0 {{1,6,7},{2,4,5},{3}}=>0 {{1,6},{2,4,5,7},{3}}=>1 {{1,6},{2,4,5},{3,7}}=>2 {{1,6},{2,4,5},{3},{7}}=>0 {{1,7},{2,4,5,6},{3}}=>0 {{1},{2,4,5,6,7},{3}}=>0 {{1},{2,4,5,6},{3,7}}=>1 {{1},{2,4,5,6},{3},{7}}=>0 {{1,7},{2,4,5},{3,6}}=>1 {{1},{2,4,5,7},{3,6}}=>2 {{1},{2,4,5},{3,6,7}}=>1 {{1},{2,4,5},{3,6},{7}}=>1 {{1,7},{2,4,5},{3},{6}}=>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 {{1,6,7},{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}}=>3 {{1},{2,4,6},{3,5},{7}}=>2 {{1,7},{2,4},{3,5,6}}=>1 {{1},{2,4,7},{3,5,6}}=>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}}=>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}}=>0 {{1,6},{2,4,7},{3},{5}}=>1 {{1,6},{2,4},{3,7},{5}}=>2 {{1,6},{2,4},{3},{5,7}}=>1 {{1,6},{2,4},{3},{5},{7}}=>0 {{1,7},{2,4,6},{3},{5}}=>0 {{1},{2,4,6,7},{3},{5}}=>0 {{1},{2,4,6},{3,7},{5}}=>1 {{1},{2,4,6},{3},{5,7}}=>1 {{1},{2,4,6},{3},{5},{7}}=>0 {{1,7},{2,4},{3,6},{5}}=>1 {{1},{2,4,7},{3,6},{5}}=>2 {{1},{2,4},{3,6,7},{5}}=>1 {{1},{2,4},{3,6},{5,7}}=>2 {{1},{2,4},{3,6},{5},{7}}=>1 {{1,7},{2,4},{3},{5,6}}=>0 {{1},{2,4,7},{3},{5,6}}=>0 {{1},{2,4},{3,7},{5,6}}=>1 {{1},{2,4},{3},{5,6,7}}=>0 {{1},{2,4},{3},{5,6},{7}}=>0 {{1,7},{2,4},{3},{5},{6}}=>0 {{1},{2,4,7},{3},{5},{6}}=>0 {{1},{2,4},{3,7},{5},{6}}=>1 {{1},{2,4},{3},{5,7},{6}}=>0 {{1},{2,4},{3},{5},{6,7}}=>0 {{1},{2,4},{3},{5},{6},{7}}=>0 {{1,5,6,7},{2},{3,4}}=>0 {{1,5,6},{2,7},{3,4}}=>1 {{1,5,6},{2},{3,4,7}}=>1 {{1,5,6},{2},{3,4},{7}}=>0 {{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}}=>1 {{1,5},{2},{3,4,6},{7}}=>1 {{1,5,7},{2},{3,4},{6}}=>0 {{1,5},{2,7},{3,4},{6}}=>1 {{1,5},{2},{3,4,7},{6}}=>1 {{1,5},{2},{3,4},{6,7}}=>0 {{1,5},{2},{3,4},{6},{7}}=>0 {{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}}=>1 {{1},{2,5,6},{3,4},{7}}=>0 {{1,7},{2,5},{3,4,6}}=>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 {{1,7},{2,5},{3,4},{6}}=>0 {{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}}=>0 {{1,6},{2,7},{3,4,5}}=>1 {{1,6},{2},{3,4,5,7}}=>1 {{1,6},{2},{3,4,5},{7}}=>0 {{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}}=>0 {{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}}=>0 {{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}}=>0 {{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}}=>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},{5,6,7}}=>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}}=>1 {{1,5,6},{2},{3,7},{4}}=>1 {{1,5,6},{2},{3},{4,7}}=>1 {{1,5,6},{2},{3},{4},{7}}=>0 {{1,5,7},{2,6},{3},{4}}=>2 {{1,5},{2,6,7},{3},{4}}=>1 {{1,5},{2,6},{3,7},{4}}=>3 {{1,5},{2,6},{3},{4,7}}=>3 {{1,5},{2,6},{3},{4},{7}}=>1 {{1,5,7},{2},{3,6},{4}}=>2 {{1,5},{2,7},{3,6},{4}}=>2 {{1,5},{2},{3,6,7},{4}}=>1 {{1,5},{2},{3,6},{4,7}}=>3 {{1,5},{2},{3,6},{4},{7}}=>1 {{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}}=>1 {{1,5},{2},{3},{4,6},{7}}=>1 {{1,5,7},{2},{3},{4},{6}}=>0 {{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}}=>0 {{1,5},{2},{3},{4},{6},{7}}=>0 {{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}}=>0 {{1,7},{2,5,6},{3},{4}}=>0 {{1},{2,5,6,7},{3},{4}}=>0 {{1},{2,5,6},{3,7},{4}}=>1 {{1},{2,5,6},{3},{4,7}}=>1 {{1},{2,5,6},{3},{4},{7}}=>0 {{1,7},{2,5},{3,6},{4}}=>1 {{1},{2,5,7},{3,6},{4}}=>2 {{1},{2,5},{3,6,7},{4}}=>1 {{1},{2,5},{3,6},{4,7}}=>3 {{1},{2,5},{3,6},{4},{7}}=>1 {{1,7},{2,5},{3},{4,6}}=>1 {{1},{2,5,7},{3},{4,6}}=>2 {{1},{2,5},{3,7},{4,6}}=>2 {{1},{2,5},{3},{4,6,7}}=>1 {{1},{2,5},{3},{4,6},{7}}=>1 {{1,7},{2,5},{3},{4},{6}}=>0 {{1},{2,5,7},{3},{4},{6}}=>0 {{1},{2,5},{3,7},{4},{6}}=>1 {{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},{3,5},{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}}=>0 {{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}}=>0 {{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}}=>1 {{1},{2},{3,5,6},{4},{7}}=>0 {{1,7},{2},{3,5},{4,6}}=>1 {{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}}=>0 {{1},{2,7},{3,5},{4},{6}}=>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 {{1,6,7},{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}}=>0 {{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}}=>0 {{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}}=>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},{4,5,6,7}}=>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}}=>0 {{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}}=>0 {{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}}=>0 {{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}}=>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},{5,6,7}}=>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 {{1,3},{2,4},{5,6},{7,8}}=>1 {{1,4},{2,3},{5,6},{7,8}}=>0 {{1,5},{2,3},{4,6},{7,8}}=>1 {{1,6},{2,3},{4,5},{7,8}}=>0 {{1,7},{2,3},{4,5},{6,8}}=>1 {{1,8},{2,3},{4,5},{6,7}}=>0 {{1,8},{2,4},{3,5},{6,7}}=>1 {{1,7},{2,4},{3,5},{6,8}}=>2 {{1,6},{2,4},{3,5},{7,8}}=>1 {{1,5},{2,4},{3,6},{7,8}}=>2 {{1,4},{2,5},{3,6},{7,8}}=>3 {{1,3},{2,5},{4,6},{7,8}}=>2 {{1,2},{3,5},{4,6},{7,8}}=>1 {{1,2},{3,6},{4,5},{7,8}}=>0 {{1,3},{2,6},{4,5},{7,8}}=>1 {{1,4},{2,6},{3,5},{7,8}}=>2 {{1,5},{2,6},{3,4},{7,8}}=>1 {{1,6},{2,5},{3,4},{7,8}}=>0 {{1,7},{2,5},{3,4},{6,8}}=>1 {{1,8},{2,5},{3,4},{6,7}}=>0 {{1,8},{2,6},{3,4},{5,7}}=>1 {{1,7},{2,6},{3,4},{5,8}}=>2 {{1,6},{2,7},{3,4},{5,8}}=>3 {{1,5},{2,7},{3,4},{6,8}}=>2 {{1,4},{2,7},{3,5},{6,8}}=>3 {{1,3},{2,7},{4,5},{6,8}}=>2 {{1,2},{3,7},{4,5},{6,8}}=>1 {{1,2},{3,8},{4,5},{6,7}}=>0 {{1,3},{2,8},{4,5},{6,7}}=>1 {{1,4},{2,8},{3,5},{6,7}}=>2 {{1,5},{2,8},{3,4},{6,7}}=>1 {{1,6},{2,8},{3,4},{5,7}}=>2 {{1,7},{2,8},{3,4},{5,6}}=>1 {{1,8},{2,7},{3,4},{5,6}}=>0 {{1,8},{2,7},{3,5},{4,6}}=>1 {{1,7},{2,8},{3,5},{4,6}}=>2 {{1,6},{2,8},{3,5},{4,7}}=>3 {{1,5},{2,8},{3,6},{4,7}}=>4 {{1,4},{2,8},{3,6},{5,7}}=>3 {{1,3},{2,8},{4,6},{5,7}}=>2 {{1,2},{3,8},{4,6},{5,7}}=>1 {{1,2},{3,7},{4,6},{5,8}}=>2 {{1,3},{2,7},{4,6},{5,8}}=>3 {{1,4},{2,7},{3,6},{5,8}}=>4 {{1,5},{2,7},{3,6},{4,8}}=>5 {{1,6},{2,7},{3,5},{4,8}}=>4 {{1,7},{2,6},{3,5},{4,8}}=>3 {{1,8},{2,6},{3,5},{4,7}}=>2 {{1,8},{2,5},{3,6},{4,7}}=>3 {{1,7},{2,5},{3,6},{4,8}}=>4 {{1,6},{2,5},{3,7},{4,8}}=>5 {{1,5},{2,6},{3,7},{4,8}}=>6 {{1,4},{2,6},{3,7},{5,8}}=>5 {{1,3},{2,6},{4,7},{5,8}}=>4 {{1,2},{3,6},{4,7},{5,8}}=>3 {{1,2},{3,5},{4,7},{6,8}}=>2 {{1,3},{2,5},{4,7},{6,8}}=>3 {{1,4},{2,5},{3,7},{6,8}}=>4 {{1,5},{2,4},{3,7},{6,8}}=>3 {{1,6},{2,4},{3,7},{5,8}}=>4 {{1,7},{2,4},{3,6},{5,8}}=>3 {{1,8},{2,4},{3,6},{5,7}}=>2 {{1,8},{2,3},{4,6},{5,7}}=>1 {{1,7},{2,3},{4,6},{5,8}}=>2 {{1,6},{2,3},{4,7},{5,8}}=>3 {{1,5},{2,3},{4,7},{6,8}}=>2 {{1,4},{2,3},{5,7},{6,8}}=>1 {{1,3},{2,4},{5,7},{6,8}}=>2 {{1,2},{3,4},{5,7},{6,8}}=>1 {{1,2},{3,4},{5,8},{6,7}}=>0 {{1,3},{2,4},{5,8},{6,7}}=>1 {{1,4},{2,3},{5,8},{6,7}}=>0 {{1,5},{2,3},{4,8},{6,7}}=>1 {{1,6},{2,3},{4,8},{5,7}}=>2 {{1,7},{2,3},{4,8},{5,6}}=>1 {{1,8},{2,3},{4,7},{5,6}}=>0 {{1,8},{2,4},{3,7},{5,6}}=>1 {{1,7},{2,4},{3,8},{5,6}}=>2 {{1,6},{2,4},{3,8},{5,7}}=>3 {{1,5},{2,4},{3,8},{6,7}}=>2 {{1,4},{2,5},{3,8},{6,7}}=>3 {{1,3},{2,5},{4,8},{6,7}}=>2 {{1,2},{3,5},{4,8},{6,7}}=>1 {{1,2},{3,6},{4,8},{5,7}}=>2 {{1,3},{2,6},{4,8},{5,7}}=>3 {{1,4},{2,6},{3,8},{5,7}}=>4 {{1,5},{2,6},{3,8},{4,7}}=>5 {{1,6},{2,5},{3,8},{4,7}}=>4 {{1,7},{2,5},{3,8},{4,6}}=>3 {{1,8},{2,5},{3,7},{4,6}}=>2 {{1,8},{2,6},{3,7},{4,5}}=>1 {{1,7},{2,6},{3,8},{4,5}}=>2 {{1,6},{2,7},{3,8},{4,5}}=>3 {{1,5},{2,7},{3,8},{4,6}}=>4 {{1,4},{2,7},{3,8},{5,6}}=>3 {{1,3},{2,7},{4,8},{5,6}}=>2 {{1,2},{3,7},{4,8},{5,6}}=>1 {{1,2},{3,8},{4,7},{5,6}}=>0 {{1,3},{2,8},{4,7},{5,6}}=>1 {{1,4},{2,8},{3,7},{5,6}}=>2 {{1,5},{2,8},{3,7},{4,6}}=>3 {{1,6},{2,8},{3,7},{4,5}}=>2 {{1,7},{2,8},{3,6},{4,5}}=>1 {{1,8},{2,7},{3,6},{4,5}}=>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},{2,3,4,5,8},{6},{7}}=>0 {{1},{2,3,4,5,7,8},{6}}=>0 {{1},{2,3,4,5,6,7},{8}}=>0 {{1},{2,3,4,8},{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 {{1,2},{3,4,5,6,7,8}}=>0 {{1,4,5,6,7,8},{2},{3}}=>0 {{1,3,5,6,7,8},{2},{4}}=>0 {{1,3,4,5,6,7,8},{2}}=>0 {{1,4,5,6,7,8},{2,3}}=>0 {{1,2,4,5,6,7,8},{3}}=>0 {{1,2,5,6,7,8},{3,4}}=>0 {{1,2,3,5,6,7},{4},{8}}=>0 {{1,2,3,5,6,7,8},{4}}=>0 {{1,2,3,6,7,8},{4,5}}=>0 {{1,2,3,4,7},{5},{6},{8}}=>0 {{1,2,3,4,6,7},{5},{8}}=>0 {{1,2,3,4,6,7,8},{5}}=>0 {{1,2,3,4,5,6},{7,8}}=>0 {{1,2,3,7},{4,5,6},{8}}=>0 {{1,2,3,4,7},{5,6},{8}}=>0 {{1,2,3,4,7,8},{5,6}}=>0 {{1,2,3,4,5,7},{6},{8}}=>0 {{1,2,3,4,5,7,8},{6}}=>0 {{1,2,3,4,5,6,7},{8}}=>0 {{1,8},{2,3,4,5,6,7}}=>0 {{1,2,3,4,5,8},{6,7}}=>0 {{1,2,3,4,5,6,8},{7}}=>0 {{1,2,3,4,5,6,7,8}}=>0 {{1,2,4,5,7,8},{3,6}}=>2 {{1,3,4,5,7,8},{2,6}}=>2 {{1,2,4,5,6,8},{3,7}}=>2 {{1,2,3,4,5,7},{6,8}}=>1 {{1,3,5,6,7,8},{2,4}}=>2 {{1,3,4,5,6,8},{2,7}}=>2 {{1,2,3,5,7,8},{4,6}}=>2 {{1,2,4,6,7,8},{3,5}}=>2 {{1,3,4,5,6,7},{2,8}}=>1 {{1,7},{2,3,4,5,6,8}}=>1 {{1,2,3,4,6,8},{5,7}}=>2 {{1,2,3,5,6,7},{4,8}}=>1 {{1,2,3,5,6,8},{4,7}}=>2 {{1,3,4,6,7,8},{2,5}}=>2 {{1,2,3,4,6,7},{5,8}}=>1 {{1,4},{2,3,5,6,7,8}}=>1 {{1,2,4,5,6,7},{3,8}}=>1 {{1,3},{2,4,5,6,7,8}}=>1 {{1,5},{2,3,4,6,7,8}}=>1 {{1,6},{2,3,4,5,7,8}}=>1 {{1,2,3,4,5,6,7,8},{9}}=>0 {{1},{2,3,4,5,6,7,8,9}}=>0 {{1,2,3,4,5,6,8},{7},{9}}=>0 {{1},{2,3,4,5,6,7,9},{8}}=>0 {{1,2,3,4,5,8},{6,7},{9}}=>0 {{1,2,3,4,5,7,8},{6},{9}}=>0 {{1},{2,3,4,5,6,9},{7,8}}=>0 {{1},{2,3,4,5,6,8,9},{7}}=>0 {{1,2},{3,4},{5,6},{7,8},{9,10}}=>0 {{1,4},{2,3},{5,6},{7,8},{9,10}}=>0 {{1,6},{2,3},{4,5},{7,8},{9,10}}=>0 {{1,8},{2,3},{4,5},{6,7},{9,10}}=>0 {{1,10},{2,3},{4,5},{6,7},{8,9}}=>0 {{1,2},{3,6},{4,5},{7,8},{9,10}}=>0 {{1,6},{2,5},{3,4},{7,8},{9,10}}=>0 {{1,8},{2,5},{3,4},{6,7},{9,10}}=>0 {{1,10},{2,5},{3,4},{6,7},{8,9}}=>0 {{1,2},{3,8},{4,5},{6,7},{9,10}}=>0 {{1,8},{2,7},{3,4},{5,6},{9,10}}=>0 {{1,10},{2,7},{3,4},{5,6},{8,9}}=>0 {{1,2},{3,10},{4,5},{6,7},{8,9}}=>0 {{1,10},{2,9},{3,4},{5,6},{7,8}}=>0 {{1,2},{3,4},{5,8},{6,7},{9,10}}=>0 {{1,4},{2,3},{5,8},{6,7},{9,10}}=>0 {{1,8},{2,3},{4,7},{5,6},{9,10}}=>0 {{1,10},{2,3},{4,7},{5,6},{8,9}}=>0 {{1,2},{3,8},{4,7},{5,6},{9,10}}=>0 {{1,8},{2,7},{3,6},{4,5},{9,10}}=>0 {{1,10},{2,7},{3,6},{4,5},{8,9}}=>0 {{1,2},{3,10},{4,7},{5,6},{8,9}}=>0 {{1,10},{2,9},{3,6},{4,5},{7,8}}=>0 {{1,2},{3,4},{5,10},{6,7},{8,9}}=>0 {{1,4},{2,3},{5,10},{6,7},{8,9}}=>0 {{1,10},{2,3},{4,9},{5,6},{7,8}}=>0 {{1,2},{3,10},{4,9},{5,6},{7,8}}=>0 {{1,10},{2,9},{3,8},{4,5},{6,7}}=>0 {{1,2},{3,4},{5,6},{7,10},{8,9}}=>0 {{1,4},{2,3},{5,6},{7,10},{8,9}}=>0 {{1,6},{2,3},{4,5},{7,10},{8,9}}=>0 {{1,10},{2,3},{4,5},{6,9},{7,8}}=>0 {{1,2},{3,6},{4,5},{7,10},{8,9}}=>0 {{1,6},{2,5},{3,4},{7,10},{8,9}}=>0 {{1,10},{2,5},{3,4},{6,9},{7,8}}=>0 {{1,2},{3,10},{4,5},{6,9},{7,8}}=>0 {{1,10},{2,9},{3,4},{5,8},{6,7}}=>0 {{1,2},{3,4},{5,10},{6,9},{7,8}}=>0 {{1,4},{2,3},{5,10},{6,9},{7,8}}=>0 {{1,10},{2,3},{4,9},{5,8},{6,7}}=>0 {{1,2},{3,10},{4,9},{5,8},{6,7}}=>0 {{1,10},{2,9},{3,8},{4,7},{5,6}}=>0 {{1,2,3,4,5,6,7,8,9},{10}}=>0 {{1},{2,3,4,5,6,7,8,9,10}}=>0 {{1,2,3,4,5,6,7,9},{8},{10}}=>0 {{1},{2,3,4,5,6,7,8,10},{9}}=>0 {{1,2,3,4,5,6,7,8,9,10},{11}}=>0 {{1},{2,3,4,5,6,7,8,9,10,11}}=>0 {{1,10},{2,9},{3,8},{4,7},{5,6},{11,12}}=>0 {{1,2},{3,12},{4,11},{5,10},{6,9},{7,8}}=>0 {{1,2},{3,12},{4,11},{5,10},{6,7},{8,9}}=>0 {{1,10},{2,9},{3,8},{4,5},{6,7},{11,12}}=>0 {{1,2},{3,12},{4,11},{5,6},{7,10},{8,9}}=>0 {{1,2},{3,12},{4,11},{5,8},{6,7},{9,10}}=>0 {{1,10},{2,9},{3,4},{5,8},{6,7},{11,12}}=>0 {{1,10},{2,9},{3,6},{4,5},{7,8},{11,12}}=>0 {{1,2},{3,12},{4,5},{6,11},{7,10},{8,9}}=>0 {{1,2},{3,12},{4,11},{5,6},{7,8},{9,10}}=>0 {{1,2},{3,12},{4,9},{5,8},{6,7},{10,11}}=>0 {{1,4},{2,3},{5,12},{6,11},{7,10},{8,9}}=>0 {{1,10},{2,3},{4,9},{5,8},{6,7},{11,12}}=>0 {{1,10},{2,9},{3,4},{5,6},{7,8},{11,12}}=>0 {{1,8},{2,7},{3,6},{4,5},{9,12},{10,11}}=>0 {{1,10},{2,7},{3,6},{4,5},{8,9},{11,12}}=>0 {{1,2},{3,4},{5,12},{6,11},{7,10},{8,9}}=>0 {{1,2},{3,12},{4,5},{6,11},{7,8},{9,10}}=>0 {{1,2},{3,12},{4,7},{5,6},{8,11},{9,10}}=>0 {{1,2},{3,12},{4,9},{5,6},{7,8},{10,11}}=>0 {{1,2},{3,10},{4,9},{5,8},{6,7},{11,12}}=>0 {{1,4},{2,3},{5,12},{6,11},{7,8},{9,10}}=>0 {{1,10},{2,3},{4,9},{5,6},{7,8},{11,12}}=>0 {{1,6},{2,5},{3,4},{7,12},{8,11},{9,10}}=>0 {{1,10},{2,5},{3,4},{6,9},{7,8},{11,12}}=>0 {{1,8},{2,7},{3,4},{5,6},{9,12},{10,11}}=>0 {{1,10},{2,7},{3,4},{5,6},{8,9},{11,12}}=>0 {{1,8},{2,7},{3,6},{4,5},{9,10},{11,12}}=>0 {{1,2},{3,4},{5,12},{6,11},{7,8},{9,10}}=>0 {{1,2},{3,12},{4,5},{6,7},{8,11},{9,10}}=>0 {{1,2},{3,12},{4,5},{6,9},{7,8},{10,11}}=>0 {{1,2},{3,12},{4,7},{5,6},{8,9},{10,11}}=>0 {{1,2},{3,10},{4,9},{5,6},{7,8},{11,12}}=>0 {{1,4},{2,3},{5,12},{6,7},{8,11},{9,10}}=>0 {{1,4},{2,3},{5,12},{6,9},{7,8},{10,11}}=>0 {{1,6},{2,3},{4,5},{7,12},{8,11},{9,10}}=>0 {{1,10},{2,3},{4,5},{6,9},{7,8},{11,12}}=>0 {{1,8},{2,3},{4,7},{5,6},{9,12},{10,11}}=>0 {{1,10},{2,3},{4,7},{5,6},{8,9},{11,12}}=>0 {{1,6},{2,5},{3,4},{7,12},{8,9},{10,11}}=>0 {{1,8},{2,5},{3,4},{6,7},{9,12},{10,11}}=>0 {{1,10},{2,5},{3,4},{6,7},{8,9},{11,12}}=>0 {{1,8},{2,7},{3,4},{5,6},{9,10},{11,12}}=>0 {{1,2},{3,4},{5,6},{7,12},{8,9},{10,11}}=>0 {{1,2},{3,4},{5,6},{7,8},{9,12},{10,11}}=>0 {{1,4},{2,3},{5,6},{7,12},{8,9},{10,11}}=>0 {{1,4},{2,3},{5,6},{7,8},{9,12},{10,11}}=>0 {{1,6},{2,3},{4,5},{7,12},{8,9},{10,11}}=>0 {{1,2},{3,6},{4,5},{7,12},{8,9},{10,11}}=>0 {{1,6},{2,3},{4,5},{7,8},{9,12},{10,11}}=>0 {{1,2},{3,6},{4,5},{7,8},{9,12},{10,11}}=>0 {{1,2},{3,4},{5,12},{6,9},{7,8},{10,11}}=>0 {{1,2},{3,12},{4,5},{6,7},{8,9},{10,11}}=>0 {{1,2},{3,8},{4,5},{6,7},{9,12},{10,11}}=>0 {{1,6},{2,5},{3,4},{7,8},{9,12},{10,11}}=>0 {{1,2},{3,4},{5,12},{6,7},{8,9},{10,11}}=>0 {{1,2},{3,4},{5,8},{6,7},{9,12},{10,11}}=>0 {{1,12},{2,5},{3,4},{6,9},{7,8},{10,11}}=>0 {{1,12},{2,3},{4,5},{6,9},{7,8},{10,11}}=>0 {{1,2},{3,4},{5,12},{6,7},{8,11},{9,10}}=>0 {{1,12},{2,5},{3,4},{6,7},{8,9},{10,11}}=>0 {{1,12},{2,3},{4,5},{6,7},{8,9},{10,11}}=>0 {{1,8},{2,3},{4,5},{6,7},{9,12},{10,11}}=>0 {{1,4},{2,3},{5,12},{6,7},{8,9},{10,11}}=>0 {{1,4},{2,3},{5,8},{6,7},{9,12},{10,11}}=>0 {{1,2},{3,4},{5,6},{7,12},{8,11},{9,10}}=>0 {{1,12},{2,9},{3,4},{5,8},{6,7},{10,11}}=>0 {{1,12},{2,3},{4,9},{5,8},{6,7},{10,11}}=>0 {{1,12},{2,9},{3,4},{5,6},{7,8},{10,11}}=>0 {{1,12},{2,3},{4,9},{5,6},{7,8},{10,11}}=>0 {{1,12},{2,7},{3,4},{5,6},{8,9},{10,11}}=>0 {{1,12},{2,3},{4,7},{5,6},{8,9},{10,11}}=>0 {{1,2},{3,8},{4,7},{5,6},{9,12},{10,11}}=>0 {{1,4},{2,3},{5,6},{7,12},{8,11},{9,10}}=>0 {{1,6},{2,5},{3,4},{7,8},{9,10},{11,12}}=>0 {{1,8},{2,3},{4,7},{5,6},{9,10},{11,12}}=>0 {{1,2},{3,8},{4,7},{5,6},{9,10},{11,12}}=>0 {{1,4},{2,3},{5,10},{6,9},{7,8},{11,12}}=>0 {{1,2},{3,4},{5,10},{6,9},{7,8},{11,12}}=>0 {{1,12},{2,11},{3,4},{5,6},{7,8},{9,10}}=>0 {{1,12},{2,7},{3,4},{5,6},{8,11},{9,10}}=>0 {{1,12},{2,5},{3,4},{6,7},{8,11},{9,10}}=>0 {{1,12},{2,3},{4,5},{6,7},{8,11},{9,10}}=>0 {{1,2},{3,10},{4,5},{6,9},{7,8},{11,12}}=>0 {{1,12},{2,11},{3,6},{4,5},{7,8},{9,10}}=>0 {{1,12},{2,5},{3,4},{6,11},{7,8},{9,10}}=>0 {{1,12},{2,9},{3,6},{4,5},{7,8},{10,11}}=>0 {{1,12},{2,3},{4,7},{5,6},{8,11},{9,10}}=>0 {{1,12},{2,7},{3,6},{4,5},{8,9},{10,11}}=>0 {{1,2},{3,6},{4,5},{7,12},{8,11},{9,10}}=>0 {{1,6},{2,5},{3,4},{7,10},{8,9},{11,12}}=>0 {{1,2},{3,6},{4,5},{7,10},{8,9},{11,12}}=>0 {{1,4},{2,3},{5,6},{7,8},{9,10},{11,12}}=>0 {{1,4},{2,3},{5,6},{7,10},{8,9},{11,12}}=>0 {{1,12},{2,3},{4,5},{6,11},{7,8},{9,10}}=>0 {{1,4},{2,3},{5,8},{6,7},{9,10},{11,12}}=>0 {{1,6},{2,3},{4,5},{7,8},{9,10},{11,12}}=>0 {{1,12},{2,3},{4,5},{6,11},{7,10},{8,9}}=>0 {{1,10},{2,3},{4,5},{6,7},{8,9},{11,12}}=>0 {{1,12},{2,3},{4,11},{5,6},{7,8},{9,10}}=>0 {{1,4},{2,3},{5,10},{6,7},{8,9},{11,12}}=>0 {{1,8},{2,3},{4,5},{6,7},{9,10},{11,12}}=>0 {{1,12},{2,3},{4,11},{5,6},{7,10},{8,9}}=>0 {{1,6},{2,3},{4,5},{7,10},{8,9},{11,12}}=>0 {{1,12},{2,3},{4,11},{5,8},{6,7},{9,10}}=>0 {{1,12},{2,3},{4,11},{5,10},{6,7},{8,9}}=>0 {{1,12},{2,11},{3,4},{5,6},{7,10},{8,9}}=>0 {{1,2},{3,8},{4,5},{6,7},{9,10},{11,12}}=>0 {{1,2},{3,4},{5,10},{6,7},{8,9},{11,12}}=>0 {{1,2},{3,6},{4,5},{7,8},{9,10},{11,12}}=>0 {{1,2},{3,4},{5,8},{6,7},{9,10},{11,12}}=>0 {{1,2},{3,4},{5,6},{7,10},{8,9},{11,12}}=>0 {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>0 {{1,12},{2,9},{3,8},{4,7},{5,6},{10,11}}=>0 {{1,12},{2,9},{3,8},{4,5},{6,7},{10,11}}=>0 {{1,12},{2,7},{3,6},{4,5},{8,11},{9,10}}=>0 {{1,12},{2,11},{3,8},{4,7},{5,6},{9,10}}=>0 {{1,12},{2,11},{3,8},{4,5},{6,7},{9,10}}=>0 {{1,8},{2,5},{3,4},{6,7},{9,10},{11,12}}=>0 {{1,2},{3,10},{4,7},{5,6},{8,9},{11,12}}=>0 {{1,12},{2,11},{3,10},{4,7},{5,6},{8,9}}=>0 {{1,12},{2,11},{3,10},{4,9},{5,6},{7,8}}=>0 {{1,12},{2,11},{3,4},{5,8},{6,7},{9,10}}=>0 {{1,12},{2,11},{3,6},{4,5},{7,10},{8,9}}=>0 {{1,12},{2,11},{3,4},{5,10},{6,7},{8,9}}=>0 {{1,12},{2,11},{3,10},{4,5},{6,7},{8,9}}=>0 {{1,12},{2,11},{3,4},{5,10},{6,9},{7,8}}=>0 {{1,12},{2,11},{3,10},{4,9},{5,8},{6,7}}=>0 {{1,12},{2,11},{3,10},{4,5},{6,9},{7,8}}=>0 {{1,12},{2,3},{4,11},{5,10},{6,9},{7,8}}=>0 {{1,12},{2,5},{3,4},{6,11},{7,10},{8,9}}=>0 {{1,2},{3,10},{4,5},{6,7},{8,9},{11,12}}=>0
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Description
The number of crossings of a set partition.
This is given by the number of $i < i' < j < j'$ such that $i,j$ are two consecutive entries on one block, and $i',j'$ are consecutive entries in another block.
References
[1] Chern, B., Diaconis, P., Kane, D. M., Rhoades, R. C. Central Limit Theorems for some Set Partition Statistics arXiv:1502.00938
[2] Kasraoui, A., Zeng, J. Distribution of crossings, nestings and alignments of two edges in matchings and partitions MathSciNet:2212506
[3] Rubey, M., Stump, C. Crossings and nestings in set partitions of classical types MathSciNet:2729369
Code
def statistic(pi):
    pi_sorted = sorted([sorted(b) for b in pi])
    edges = [(a,b) for block in pi_sorted for (a,b) in zip(block, block[1:])]
    count = 0
    for (i1,j1),(i2,j2) in Subsets(edges, 2):
        if i1 < i2 < j1 < j2 or i2 < i1 < j2 < j1:
            count += 1
    return count
Created
Feb 04, 2015 at 11:31 by Christian Stump
Updated
Dec 25, 2017 at 17:20 by Martin Rubey