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Identifier
Values
=>
Cc0009;cc-rep
{{1}}=>1 {{1,2}}=>1 {{1},{2}}=>2 {{1,2,3}}=>1 {{1,2},{3}}=>2 {{1,3},{2}}=>2 {{1},{2,3}}=>2 {{1},{2},{3}}=>3 {{1,2,3,4}}=>1 {{1,2,3},{4}}=>2 {{1,2,4},{3}}=>2 {{1,2},{3,4}}=>2 {{1,2},{3},{4}}=>3 {{1,3,4},{2}}=>2 {{1,3},{2,4}}=>2 {{1,3},{2},{4}}=>3 {{1,4},{2,3}}=>2 {{1},{2,3,4}}=>2 {{1},{2,3},{4}}=>3 {{1,4},{2},{3}}=>3 {{1},{2,4},{3}}=>3 {{1},{2},{3,4}}=>3 {{1},{2},{3},{4}}=>4 {{1,2,3,4,5}}=>1 {{1,2,3,4},{5}}=>2 {{1,2,3,5},{4}}=>2 {{1,2,3},{4,5}}=>2 {{1,2,3},{4},{5}}=>3 {{1,2,4,5},{3}}=>2 {{1,2,4},{3,5}}=>2 {{1,2,4},{3},{5}}=>3 {{1,2,5},{3,4}}=>2 {{1,2},{3,4,5}}=>2 {{1,2},{3,4},{5}}=>3 {{1,2,5},{3},{4}}=>3 {{1,2},{3,5},{4}}=>3 {{1,2},{3},{4,5}}=>3 {{1,2},{3},{4},{5}}=>4 {{1,3,4,5},{2}}=>2 {{1,3,4},{2,5}}=>2 {{1,3,4},{2},{5}}=>3 {{1,3,5},{2,4}}=>2 {{1,3},{2,4,5}}=>2 {{1,3},{2,4},{5}}=>3 {{1,3,5},{2},{4}}=>3 {{1,3},{2,5},{4}}=>3 {{1,3},{2},{4,5}}=>3 {{1,3},{2},{4},{5}}=>4 {{1,4,5},{2,3}}=>2 {{1,4},{2,3,5}}=>2 {{1,4},{2,3},{5}}=>3 {{1,5},{2,3,4}}=>2 {{1},{2,3,4,5}}=>2 {{1},{2,3,4},{5}}=>3 {{1,5},{2,3},{4}}=>3 {{1},{2,3,5},{4}}=>3 {{1},{2,3},{4,5}}=>3 {{1},{2,3},{4},{5}}=>4 {{1,4,5},{2},{3}}=>3 {{1,4},{2,5},{3}}=>3 {{1,4},{2},{3,5}}=>3 {{1,4},{2},{3},{5}}=>4 {{1,5},{2,4},{3}}=>3 {{1},{2,4,5},{3}}=>3 {{1},{2,4},{3,5}}=>3 {{1},{2,4},{3},{5}}=>4 {{1,5},{2},{3,4}}=>3 {{1},{2,5},{3,4}}=>3 {{1},{2},{3,4,5}}=>3 {{1},{2},{3,4},{5}}=>4 {{1,5},{2},{3},{4}}=>4 {{1},{2,5},{3},{4}}=>4 {{1},{2},{3,5},{4}}=>4 {{1},{2},{3},{4,5}}=>4 {{1},{2},{3},{4},{5}}=>5 {{1,2,3,4,5,6}}=>1 {{1,2,3,4,5},{6}}=>2 {{1,2,3,4,6},{5}}=>2 {{1,2,3,4},{5,6}}=>2 {{1,2,3,4},{5},{6}}=>3 {{1,2,3,5,6},{4}}=>2 {{1,2,3,5},{4,6}}=>2 {{1,2,3,5},{4},{6}}=>3 {{1,2,3,6},{4,5}}=>2 {{1,2,3},{4,5,6}}=>2 {{1,2,3},{4,5},{6}}=>3 {{1,2,3,6},{4},{5}}=>3 {{1,2,3},{4,6},{5}}=>3 {{1,2,3},{4},{5,6}}=>3 {{1,2,3},{4},{5},{6}}=>4 {{1,2,4,5,6},{3}}=>2 {{1,2,4,5},{3,6}}=>2 {{1,2,4,5},{3},{6}}=>3 {{1,2,4,6},{3,5}}=>2 {{1,2,4},{3,5,6}}=>2 {{1,2,4},{3,5},{6}}=>3 {{1,2,4,6},{3},{5}}=>3 {{1,2,4},{3,6},{5}}=>3 {{1,2,4},{3},{5,6}}=>3 {{1,2,4},{3},{5},{6}}=>4 {{1,2,5,6},{3,4}}=>2 {{1,2,5},{3,4,6}}=>2 {{1,2,5},{3,4},{6}}=>3 {{1,2,6},{3,4,5}}=>2 {{1,2},{3,4,5,6}}=>2 {{1,2},{3,4,5},{6}}=>3 {{1,2,6},{3,4},{5}}=>3 {{1,2},{3,4,6},{5}}=>3 {{1,2},{3,4},{5,6}}=>3 {{1,2},{3,4},{5},{6}}=>4 {{1,2,5,6},{3},{4}}=>3 {{1,2,5},{3,6},{4}}=>3 {{1,2,5},{3},{4,6}}=>3 {{1,2,5},{3},{4},{6}}=>4 {{1,2,6},{3,5},{4}}=>3 {{1,2},{3,5,6},{4}}=>3 {{1,2},{3,5},{4,6}}=>3 {{1,2},{3,5},{4},{6}}=>4 {{1,2,6},{3},{4,5}}=>3 {{1,2},{3,6},{4,5}}=>3 {{1,2},{3},{4,5,6}}=>3 {{1,2},{3},{4,5},{6}}=>4 {{1,2,6},{3},{4},{5}}=>4 {{1,2},{3,6},{4},{5}}=>4 {{1,2},{3},{4,6},{5}}=>4 {{1,2},{3},{4},{5,6}}=>4 {{1,2},{3},{4},{5},{6}}=>5 {{1,3,4,5,6},{2}}=>2 {{1,3,4,5},{2,6}}=>2 {{1,3,4,5},{2},{6}}=>3 {{1,3,4,6},{2,5}}=>2 {{1,3,4},{2,5,6}}=>2 {{1,3,4},{2,5},{6}}=>3 {{1,3,4,6},{2},{5}}=>3 {{1,3,4},{2,6},{5}}=>3 {{1,3,4},{2},{5,6}}=>3 {{1,3,4},{2},{5},{6}}=>4 {{1,3,5,6},{2,4}}=>2 {{1,3,5},{2,4,6}}=>2 {{1,3,5},{2,4},{6}}=>3 {{1,3,6},{2,4,5}}=>2 {{1,3},{2,4,5,6}}=>2 {{1,3},{2,4,5},{6}}=>3 {{1,3,6},{2,4},{5}}=>3 {{1,3},{2,4,6},{5}}=>3 {{1,3},{2,4},{5,6}}=>3 {{1,3},{2,4},{5},{6}}=>4 {{1,3,5,6},{2},{4}}=>3 {{1,3,5},{2,6},{4}}=>3 {{1,3,5},{2},{4,6}}=>3 {{1,3,5},{2},{4},{6}}=>4 {{1,3,6},{2,5},{4}}=>3 {{1,3},{2,5,6},{4}}=>3 {{1,3},{2,5},{4,6}}=>3 {{1,3},{2,5},{4},{6}}=>4 {{1,3,6},{2},{4,5}}=>3 {{1,3},{2,6},{4,5}}=>3 {{1,3},{2},{4,5,6}}=>3 {{1,3},{2},{4,5},{6}}=>4 {{1,3,6},{2},{4},{5}}=>4 {{1,3},{2,6},{4},{5}}=>4 {{1,3},{2},{4,6},{5}}=>4 {{1,3},{2},{4},{5,6}}=>4 {{1,3},{2},{4},{5},{6}}=>5 {{1,4,5,6},{2,3}}=>2 {{1,4,5},{2,3,6}}=>2 {{1,4,5},{2,3},{6}}=>3 {{1,4,6},{2,3,5}}=>2 {{1,4},{2,3,5,6}}=>2 {{1,4},{2,3,5},{6}}=>3 {{1,4,6},{2,3},{5}}=>3 {{1,4},{2,3,6},{5}}=>3 {{1,4},{2,3},{5,6}}=>3 {{1,4},{2,3},{5},{6}}=>4 {{1,5,6},{2,3,4}}=>2 {{1,5},{2,3,4,6}}=>2 {{1,5},{2,3,4},{6}}=>3 {{1,6},{2,3,4,5}}=>2 {{1},{2,3,4,5,6}}=>2 {{1},{2,3,4,5},{6}}=>3 {{1,6},{2,3,4},{5}}=>3 {{1},{2,3,4,6},{5}}=>3 {{1},{2,3,4},{5,6}}=>3 {{1},{2,3,4},{5},{6}}=>4 {{1,5,6},{2,3},{4}}=>3 {{1,5},{2,3,6},{4}}=>3 {{1,5},{2,3},{4,6}}=>3 {{1,5},{2,3},{4},{6}}=>4 {{1,6},{2,3,5},{4}}=>3 {{1},{2,3,5,6},{4}}=>3 {{1},{2,3,5},{4,6}}=>3 {{1},{2,3,5},{4},{6}}=>4 {{1,6},{2,3},{4,5}}=>3 {{1},{2,3,6},{4,5}}=>3 {{1},{2,3},{4,5,6}}=>3 {{1},{2,3},{4,5},{6}}=>4 {{1,6},{2,3},{4},{5}}=>4 {{1},{2,3,6},{4},{5}}=>4 {{1},{2,3},{4,6},{5}}=>4 {{1},{2,3},{4},{5,6}}=>4 {{1},{2,3},{4},{5},{6}}=>5 {{1,4,5,6},{2},{3}}=>3 {{1,4,5},{2,6},{3}}=>3 {{1,4,5},{2},{3,6}}=>3 {{1,4,5},{2},{3},{6}}=>4 {{1,4,6},{2,5},{3}}=>3 {{1,4},{2,5,6},{3}}=>3 {{1,4},{2,5},{3,6}}=>3 {{1,4},{2,5},{3},{6}}=>4 {{1,4,6},{2},{3,5}}=>3 {{1,4},{2,6},{3,5}}=>3 {{1,4},{2},{3,5,6}}=>3 {{1,4},{2},{3,5},{6}}=>4 {{1,4,6},{2},{3},{5}}=>4 {{1,4},{2,6},{3},{5}}=>4 {{1,4},{2},{3,6},{5}}=>4 {{1,4},{2},{3},{5,6}}=>4 {{1,4},{2},{3},{5},{6}}=>5 {{1,5,6},{2,4},{3}}=>3 {{1,5},{2,4,6},{3}}=>3 {{1,5},{2,4},{3,6}}=>3 {{1,5},{2,4},{3},{6}}=>4 {{1,6},{2,4,5},{3}}=>3 {{1},{2,4,5,6},{3}}=>3 {{1},{2,4,5},{3,6}}=>3 {{1},{2,4,5},{3},{6}}=>4 {{1,6},{2,4},{3,5}}=>3 {{1},{2,4,6},{3,5}}=>3 {{1},{2,4},{3,5,6}}=>3 {{1},{2,4},{3,5},{6}}=>4 {{1,6},{2,4},{3},{5}}=>4 {{1},{2,4,6},{3},{5}}=>4 {{1},{2,4},{3,6},{5}}=>4 {{1},{2,4},{3},{5,6}}=>4 {{1},{2,4},{3},{5},{6}}=>5 {{1,5,6},{2},{3,4}}=>3 {{1,5},{2,6},{3,4}}=>3 {{1,5},{2},{3,4,6}}=>3 {{1,5},{2},{3,4},{6}}=>4 {{1,6},{2,5},{3,4}}=>3 {{1},{2,5,6},{3,4}}=>3 {{1},{2,5},{3,4,6}}=>3 {{1},{2,5},{3,4},{6}}=>4 {{1,6},{2},{3,4,5}}=>3 {{1},{2,6},{3,4,5}}=>3 {{1},{2},{3,4,5,6}}=>3 {{1},{2},{3,4,5},{6}}=>4 {{1,6},{2},{3,4},{5}}=>4 {{1},{2,6},{3,4},{5}}=>4 {{1},{2},{3,4,6},{5}}=>4 {{1},{2},{3,4},{5,6}}=>4 {{1},{2},{3,4},{5},{6}}=>5 {{1,5,6},{2},{3},{4}}=>4 {{1,5},{2,6},{3},{4}}=>4 {{1,5},{2},{3,6},{4}}=>4 {{1,5},{2},{3},{4,6}}=>4 {{1,5},{2},{3},{4},{6}}=>5 {{1,6},{2,5},{3},{4}}=>4 {{1},{2,5,6},{3},{4}}=>4 {{1},{2,5},{3,6},{4}}=>4 {{1},{2,5},{3},{4,6}}=>4 {{1},{2,5},{3},{4},{6}}=>5 {{1,6},{2},{3,5},{4}}=>4 {{1},{2,6},{3,5},{4}}=>4 {{1},{2},{3,5,6},{4}}=>4 {{1},{2},{3,5},{4,6}}=>4 {{1},{2},{3,5},{4},{6}}=>5 {{1,6},{2},{3},{4,5}}=>4 {{1},{2,6},{3},{4,5}}=>4 {{1},{2},{3,6},{4,5}}=>4 {{1},{2},{3},{4,5,6}}=>4 {{1},{2},{3},{4,5},{6}}=>5 {{1,6},{2},{3},{4},{5}}=>5 {{1},{2,6},{3},{4},{5}}=>5 {{1},{2},{3,6},{4},{5}}=>5 {{1},{2},{3},{4,6},{5}}=>5 {{1},{2},{3},{4},{5,6}}=>5 {{1},{2},{3},{4},{5},{6}}=>6 {{1,2,3,4,5,6,7}}=>1 {{1,2,3,4,5,6},{7}}=>2 {{1,2,3,4,5,7},{6}}=>2 {{1,2,3,4,5},{6,7}}=>2 {{1,2,3,4,5},{6},{7}}=>3 {{1,2,3,4,6,7},{5}}=>2 {{1,2,3,4,6},{5,7}}=>2 {{1,2,3,4,6},{5},{7}}=>3 {{1,2,3,4,7},{5,6}}=>2 {{1,2,3,4},{5,6,7}}=>2 {{1,2,3,4},{5,6},{7}}=>3 {{1,2,3,4,7},{5},{6}}=>3 {{1,2,3,4},{5,7},{6}}=>3 {{1,2,3,4},{5},{6,7}}=>3 {{1,2,3,4},{5},{6},{7}}=>4 {{1,2,3,5,6,7},{4}}=>2 {{1,2,3,5,6},{4,7}}=>2 {{1,2,3,5,6},{4},{7}}=>3 {{1,2,3,5,7},{4,6}}=>2 {{1,2,3,5},{4,6,7}}=>2 {{1,2,3,5},{4,6},{7}}=>3 {{1,2,3,5,7},{4},{6}}=>3 {{1,2,3,5},{4,7},{6}}=>3 {{1,2,3,5},{4},{6,7}}=>3 {{1,2,3,5},{4},{6},{7}}=>4 {{1,2,3,6,7},{4,5}}=>2 {{1,2,3,6},{4,5,7}}=>2 {{1,2,3,6},{4,5},{7}}=>3 {{1,2,3,7},{4,5,6}}=>2 {{1,2,3},{4,5,6,7}}=>2 {{1,2,3},{4,5,6},{7}}=>3 {{1,2,3,7},{4,5},{6}}=>3 {{1,2,3},{4,5,7},{6}}=>3 {{1,2,3},{4,5},{6,7}}=>3 {{1,2,3},{4,5},{6},{7}}=>4 {{1,2,3,6,7},{4},{5}}=>3 {{1,2,3,6},{4,7},{5}}=>3 {{1,2,3,6},{4},{5,7}}=>3 {{1,2,3,6},{4},{5},{7}}=>4 {{1,2,3,7},{4,6},{5}}=>3 {{1,2,3},{4,6,7},{5}}=>3 {{1,2,3},{4,6},{5,7}}=>3 {{1,2,3},{4,6},{5},{7}}=>4 {{1,2,3,7},{4},{5,6}}=>3 {{1,2,3},{4,7},{5,6}}=>3 {{1,2,3},{4},{5,6,7}}=>3 {{1,2,3},{4},{5,6},{7}}=>4 {{1,2,3,7},{4},{5},{6}}=>4 {{1,2,3},{4,7},{5},{6}}=>4 {{1,2,3},{4},{5,7},{6}}=>4 {{1,2,3},{4},{5},{6,7}}=>4 {{1,2,3},{4},{5},{6},{7}}=>5 {{1,2,4,5,6,7},{3}}=>2 {{1,2,4,5,6},{3,7}}=>2 {{1,2,4,5,6},{3},{7}}=>3 {{1,2,4,5,7},{3,6}}=>2 {{1,2,4,5},{3,6,7}}=>2 {{1,2,4,5},{3,6},{7}}=>3 {{1,2,4,5,7},{3},{6}}=>3 {{1,2,4,5},{3,7},{6}}=>3 {{1,2,4,5},{3},{6,7}}=>3 {{1,2,4,5},{3},{6},{7}}=>4 {{1,2,4,6,7},{3,5}}=>2 {{1,2,4,6},{3,5,7}}=>2 {{1,2,4,6},{3,5},{7}}=>3 {{1,2,4,7},{3,5,6}}=>2 {{1,2,4},{3,5,6,7}}=>2 {{1,2,4},{3,5,6},{7}}=>3 {{1,2,4,7},{3,5},{6}}=>3 {{1,2,4},{3,5,7},{6}}=>3 {{1,2,4},{3,5},{6,7}}=>3 {{1,2,4},{3,5},{6},{7}}=>4 {{1,2,4,6,7},{3},{5}}=>3 {{1,2,4,6},{3,7},{5}}=>3 {{1,2,4,6},{3},{5,7}}=>3 {{1,2,4,6},{3},{5},{7}}=>4 {{1,2,4,7},{3,6},{5}}=>3 {{1,2,4},{3,6,7},{5}}=>3 {{1,2,4},{3,6},{5,7}}=>3 {{1,2,4},{3,6},{5},{7}}=>4 {{1,2,4,7},{3},{5,6}}=>3 {{1,2,4},{3,7},{5,6}}=>3 {{1,2,4},{3},{5,6,7}}=>3 {{1,2,4},{3},{5,6},{7}}=>4 {{1,2,4,7},{3},{5},{6}}=>4 {{1,2,4},{3,7},{5},{6}}=>4 {{1,2,4},{3},{5,7},{6}}=>4 {{1,2,4},{3},{5},{6,7}}=>4 {{1,2,4},{3},{5},{6},{7}}=>5 {{1,2,5,6,7},{3,4}}=>2 {{1,2,5,6},{3,4,7}}=>2 {{1,2,5,6},{3,4},{7}}=>3 {{1,2,5,7},{3,4,6}}=>2 {{1,2,5},{3,4,6,7}}=>2 {{1,2,5},{3,4,6},{7}}=>3 {{1,2,5,7},{3,4},{6}}=>3 {{1,2,5},{3,4,7},{6}}=>3 {{1,2,5},{3,4},{6,7}}=>3 {{1,2,5},{3,4},{6},{7}}=>4 {{1,2,6,7},{3,4,5}}=>2 {{1,2,6},{3,4,5,7}}=>2 {{1,2,6},{3,4,5},{7}}=>3 {{1,2,7},{3,4,5,6}}=>2 {{1,2},{3,4,5,6,7}}=>2 {{1,2},{3,4,5,6},{7}}=>3 {{1,2,7},{3,4,5},{6}}=>3 {{1,2},{3,4,5,7},{6}}=>3 {{1,2},{3,4,5},{6,7}}=>3 {{1,2},{3,4,5},{6},{7}}=>4 {{1,2,6,7},{3,4},{5}}=>3 {{1,2,6},{3,4,7},{5}}=>3 {{1,2,6},{3,4},{5,7}}=>3 {{1,2,6},{3,4},{5},{7}}=>4 {{1,2,7},{3,4,6},{5}}=>3 {{1,2},{3,4,6,7},{5}}=>3 {{1,2},{3,4,6},{5,7}}=>3 {{1,2},{3,4,6},{5},{7}}=>4 {{1,2,7},{3,4},{5,6}}=>3 {{1,2},{3,4,7},{5,6}}=>3 {{1,2},{3,4},{5,6,7}}=>3 {{1,2},{3,4},{5,6},{7}}=>4 {{1,2,7},{3,4},{5},{6}}=>4 {{1,2},{3,4,7},{5},{6}}=>4 {{1,2},{3,4},{5,7},{6}}=>4 {{1,2},{3,4},{5},{6,7}}=>4 {{1,2},{3,4},{5},{6},{7}}=>5 {{1,2,5,6,7},{3},{4}}=>3 {{1,2,5,6},{3,7},{4}}=>3 {{1,2,5,6},{3},{4,7}}=>3 {{1,2,5,6},{3},{4},{7}}=>4 {{1,2,5,7},{3,6},{4}}=>3 {{1,2,5},{3,6,7},{4}}=>3 {{1,2,5},{3,6},{4,7}}=>3 {{1,2,5},{3,6},{4},{7}}=>4 {{1,2,5,7},{3},{4,6}}=>3 {{1,2,5},{3,7},{4,6}}=>3 {{1,2,5},{3},{4,6,7}}=>3 {{1,2,5},{3},{4,6},{7}}=>4 {{1,2,5,7},{3},{4},{6}}=>4 {{1,2,5},{3,7},{4},{6}}=>4 {{1,2,5},{3},{4,7},{6}}=>4 {{1,2,5},{3},{4},{6,7}}=>4 {{1,2,5},{3},{4},{6},{7}}=>5 {{1,2,6,7},{3,5},{4}}=>3 {{1,2,6},{3,5,7},{4}}=>3 {{1,2,6},{3,5},{4,7}}=>3 {{1,2,6},{3,5},{4},{7}}=>4 {{1,2,7},{3,5,6},{4}}=>3 {{1,2},{3,5,6,7},{4}}=>3 {{1,2},{3,5,6},{4,7}}=>3 {{1,2},{3,5,6},{4},{7}}=>4 {{1,2,7},{3,5},{4,6}}=>3 {{1,2},{3,5,7},{4,6}}=>3 {{1,2},{3,5},{4,6,7}}=>3 {{1,2},{3,5},{4,6},{7}}=>4 {{1,2,7},{3,5},{4},{6}}=>4 {{1,2},{3,5,7},{4},{6}}=>4 {{1,2},{3,5},{4,7},{6}}=>4 {{1,2},{3,5},{4},{6,7}}=>4 {{1,2},{3,5},{4},{6},{7}}=>5 {{1,2,6,7},{3},{4,5}}=>3 {{1,2,6},{3,7},{4,5}}=>3 {{1,2,6},{3},{4,5,7}}=>3 {{1,2,6},{3},{4,5},{7}}=>4 {{1,2,7},{3,6},{4,5}}=>3 {{1,2},{3,6,7},{4,5}}=>3 {{1,2},{3,6},{4,5,7}}=>3 {{1,2},{3,6},{4,5},{7}}=>4 {{1,2,7},{3},{4,5,6}}=>3 {{1,2},{3,7},{4,5,6}}=>3 {{1,2},{3},{4,5,6,7}}=>3 {{1,2},{3},{4,5,6},{7}}=>4 {{1,2,7},{3},{4,5},{6}}=>4 {{1,2},{3,7},{4,5},{6}}=>4 {{1,2},{3},{4,5,7},{6}}=>4 {{1,2},{3},{4,5},{6,7}}=>4 {{1,2},{3},{4,5},{6},{7}}=>5 {{1,2,6,7},{3},{4},{5}}=>4 {{1,2,6},{3,7},{4},{5}}=>4 {{1,2,6},{3},{4,7},{5}}=>4 {{1,2,6},{3},{4},{5,7}}=>4 {{1,2,6},{3},{4},{5},{7}}=>5 {{1,2,7},{3,6},{4},{5}}=>4 {{1,2},{3,6,7},{4},{5}}=>4 {{1,2},{3,6},{4,7},{5}}=>4 {{1,2},{3,6},{4},{5,7}}=>4 {{1,2},{3,6},{4},{5},{7}}=>5 {{1,2,7},{3},{4,6},{5}}=>4 {{1,2},{3,7},{4,6},{5}}=>4 {{1,2},{3},{4,6,7},{5}}=>4 {{1,2},{3},{4,6},{5,7}}=>4 {{1,2},{3},{4,6},{5},{7}}=>5 {{1,2,7},{3},{4},{5,6}}=>4 {{1,2},{3,7},{4},{5,6}}=>4 {{1,2},{3},{4,7},{5,6}}=>4 {{1,2},{3},{4},{5,6,7}}=>4 {{1,2},{3},{4},{5,6},{7}}=>5 {{1,2,7},{3},{4},{5},{6}}=>5 {{1,2},{3,7},{4},{5},{6}}=>5 {{1,2},{3},{4,7},{5},{6}}=>5 {{1,2},{3},{4},{5,7},{6}}=>5 {{1,2},{3},{4},{5},{6,7}}=>5 {{1,2},{3},{4},{5},{6},{7}}=>6 {{1,3,4,5,6,7},{2}}=>2 {{1,3,4,5,6},{2,7}}=>2 {{1,3,4,5,6},{2},{7}}=>3 {{1,3,4,5,7},{2,6}}=>2 {{1,3,4,5},{2,6,7}}=>2 {{1,3,4,5},{2,6},{7}}=>3 {{1,3,4,5,7},{2},{6}}=>3 {{1,3,4,5},{2,7},{6}}=>3 {{1,3,4,5},{2},{6,7}}=>3 {{1,3,4,5},{2},{6},{7}}=>4 {{1,3,4,6,7},{2,5}}=>2 {{1,3,4,6},{2,5,7}}=>2 {{1,3,4,6},{2,5},{7}}=>3 {{1,3,4,7},{2,5,6}}=>2 {{1,3,4},{2,5,6,7}}=>2 {{1,3,4},{2,5,6},{7}}=>3 {{1,3,4,7},{2,5},{6}}=>3 {{1,3,4},{2,5,7},{6}}=>3 {{1,3,4},{2,5},{6,7}}=>3 {{1,3,4},{2,5},{6},{7}}=>4 {{1,3,4,6,7},{2},{5}}=>3 {{1,3,4,6},{2,7},{5}}=>3 {{1,3,4,6},{2},{5,7}}=>3 {{1,3,4,6},{2},{5},{7}}=>4 {{1,3,4,7},{2,6},{5}}=>3 {{1,3,4},{2,6,7},{5}}=>3 {{1,3,4},{2,6},{5,7}}=>3 {{1,3,4},{2,6},{5},{7}}=>4 {{1,3,4,7},{2},{5,6}}=>3 {{1,3,4},{2,7},{5,6}}=>3 {{1,3,4},{2},{5,6,7}}=>3 {{1,3,4},{2},{5,6},{7}}=>4 {{1,3,4,7},{2},{5},{6}}=>4 {{1,3,4},{2,7},{5},{6}}=>4 {{1,3,4},{2},{5,7},{6}}=>4 {{1,3,4},{2},{5},{6,7}}=>4 {{1,3,4},{2},{5},{6},{7}}=>5 {{1,3,5,6,7},{2,4}}=>2 {{1,3,5,6},{2,4,7}}=>2 {{1,3,5,6},{2,4},{7}}=>3 {{1,3,5,7},{2,4,6}}=>2 {{1,3,5},{2,4,6,7}}=>2 {{1,3,5},{2,4,6},{7}}=>3 {{1,3,5,7},{2,4},{6}}=>3 {{1,3,5},{2,4,7},{6}}=>3 {{1,3,5},{2,4},{6,7}}=>3 {{1,3,5},{2,4},{6},{7}}=>4 {{1,3,6,7},{2,4,5}}=>2 {{1,3,6},{2,4,5,7}}=>2 {{1,3,6},{2,4,5},{7}}=>3 {{1,3,7},{2,4,5,6}}=>2 {{1,3},{2,4,5,6,7}}=>2 {{1,3},{2,4,5,6},{7}}=>3 {{1,3,7},{2,4,5},{6}}=>3 {{1,3},{2,4,5,7},{6}}=>3 {{1,3},{2,4,5},{6,7}}=>3 {{1,3},{2,4,5},{6},{7}}=>4 {{1,3,6,7},{2,4},{5}}=>3 {{1,3,6},{2,4,7},{5}}=>3 {{1,3,6},{2,4},{5,7}}=>3 {{1,3,6},{2,4},{5},{7}}=>4 {{1,3,7},{2,4,6},{5}}=>3 {{1,3},{2,4,6,7},{5}}=>3 {{1,3},{2,4,6},{5,7}}=>3 {{1,3},{2,4,6},{5},{7}}=>4 {{1,3,7},{2,4},{5,6}}=>3 {{1,3},{2,4,7},{5,6}}=>3 {{1,3},{2,4},{5,6,7}}=>3 {{1,3},{2,4},{5,6},{7}}=>4 {{1,3,7},{2,4},{5},{6}}=>4 {{1,3},{2,4,7},{5},{6}}=>4 {{1,3},{2,4},{5,7},{6}}=>4 {{1,3},{2,4},{5},{6,7}}=>4 {{1,3},{2,4},{5},{6},{7}}=>5 {{1,3,5,6,7},{2},{4}}=>3 {{1,3,5,6},{2,7},{4}}=>3 {{1,3,5,6},{2},{4,7}}=>3 {{1,3,5,6},{2},{4},{7}}=>4 {{1,3,5,7},{2,6},{4}}=>3 {{1,3,5},{2,6,7},{4}}=>3 {{1,3,5},{2,6},{4,7}}=>3 {{1,3,5},{2,6},{4},{7}}=>4 {{1,3,5,7},{2},{4,6}}=>3 {{1,3,5},{2,7},{4,6}}=>3 {{1,3,5},{2},{4,6,7}}=>3 {{1,3,5},{2},{4,6},{7}}=>4 {{1,3,5,7},{2},{4},{6}}=>4 {{1,3,5},{2,7},{4},{6}}=>4 {{1,3,5},{2},{4,7},{6}}=>4 {{1,3,5},{2},{4},{6,7}}=>4 {{1,3,5},{2},{4},{6},{7}}=>5 {{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}}=>4 {{1,3,7},{2,5,6},{4}}=>3 {{1,3},{2,5,6,7},{4}}=>3 {{1,3},{2,5,6},{4,7}}=>3 {{1,3},{2,5,6},{4},{7}}=>4 {{1,3,7},{2,5},{4,6}}=>3 {{1,3},{2,5,7},{4,6}}=>3 {{1,3},{2,5},{4,6,7}}=>3 {{1,3},{2,5},{4,6},{7}}=>4 {{1,3,7},{2,5},{4},{6}}=>4 {{1,3},{2,5,7},{4},{6}}=>4 {{1,3},{2,5},{4,7},{6}}=>4 {{1,3},{2,5},{4},{6,7}}=>4 {{1,3},{2,5},{4},{6},{7}}=>5 {{1,3,6,7},{2},{4,5}}=>3 {{1,3,6},{2,7},{4,5}}=>3 {{1,3,6},{2},{4,5,7}}=>3 {{1,3,6},{2},{4,5},{7}}=>4 {{1,3,7},{2,6},{4,5}}=>3 {{1,3},{2,6,7},{4,5}}=>3 {{1,3},{2,6},{4,5,7}}=>3 {{1,3},{2,6},{4,5},{7}}=>4 {{1,3,7},{2},{4,5,6}}=>3 {{1,3},{2,7},{4,5,6}}=>3 {{1,3},{2},{4,5,6,7}}=>3 {{1,3},{2},{4,5,6},{7}}=>4 {{1,3,7},{2},{4,5},{6}}=>4 {{1,3},{2,7},{4,5},{6}}=>4 {{1,3},{2},{4,5,7},{6}}=>4 {{1,3},{2},{4,5},{6,7}}=>4 {{1,3},{2},{4,5},{6},{7}}=>5 {{1,3,6,7},{2},{4},{5}}=>4 {{1,3,6},{2,7},{4},{5}}=>4 {{1,3,6},{2},{4,7},{5}}=>4 {{1,3,6},{2},{4},{5,7}}=>4 {{1,3,6},{2},{4},{5},{7}}=>5 {{1,3,7},{2,6},{4},{5}}=>4 {{1,3},{2,6,7},{4},{5}}=>4 {{1,3},{2,6},{4,7},{5}}=>4 {{1,3},{2,6},{4},{5,7}}=>4 {{1,3},{2,6},{4},{5},{7}}=>5 {{1,3,7},{2},{4,6},{5}}=>4 {{1,3},{2,7},{4,6},{5}}=>4 {{1,3},{2},{4,6,7},{5}}=>4 {{1,3},{2},{4,6},{5,7}}=>4 {{1,3},{2},{4,6},{5},{7}}=>5 {{1,3,7},{2},{4},{5,6}}=>4 {{1,3},{2,7},{4},{5,6}}=>4 {{1,3},{2},{4,7},{5,6}}=>4 {{1,3},{2},{4},{5,6,7}}=>4 {{1,3},{2},{4},{5,6},{7}}=>5 {{1,3,7},{2},{4},{5},{6}}=>5 {{1,3},{2,7},{4},{5},{6}}=>5 {{1,3},{2},{4,7},{5},{6}}=>5 {{1,3},{2},{4},{5,7},{6}}=>5 {{1,3},{2},{4},{5},{6,7}}=>5 {{1,3},{2},{4},{5},{6},{7}}=>6 {{1,4,5,6,7},{2,3}}=>2 {{1,4,5,6},{2,3,7}}=>2 {{1,4,5,6},{2,3},{7}}=>3 {{1,4,5,7},{2,3,6}}=>2 {{1,4,5},{2,3,6,7}}=>2 {{1,4,5},{2,3,6},{7}}=>3 {{1,4,5,7},{2,3},{6}}=>3 {{1,4,5},{2,3,7},{6}}=>3 {{1,4,5},{2,3},{6,7}}=>3 {{1,4,5},{2,3},{6},{7}}=>4 {{1,4,6,7},{2,3,5}}=>2 {{1,4,6},{2,3,5,7}}=>2 {{1,4,6},{2,3,5},{7}}=>3 {{1,4,7},{2,3,5,6}}=>2 {{1,4},{2,3,5,6,7}}=>2 {{1,4},{2,3,5,6},{7}}=>3 {{1,4,7},{2,3,5},{6}}=>3 {{1,4},{2,3,5,7},{6}}=>3 {{1,4},{2,3,5},{6,7}}=>3 {{1,4},{2,3,5},{6},{7}}=>4 {{1,4,6,7},{2,3},{5}}=>3 {{1,4,6},{2,3,7},{5}}=>3 {{1,4,6},{2,3},{5,7}}=>3 {{1,4,6},{2,3},{5},{7}}=>4 {{1,4,7},{2,3,6},{5}}=>3 {{1,4},{2,3,6,7},{5}}=>3 {{1,4},{2,3,6},{5,7}}=>3 {{1,4},{2,3,6},{5},{7}}=>4 {{1,4,7},{2,3},{5,6}}=>3 {{1,4},{2,3,7},{5,6}}=>3 {{1,4},{2,3},{5,6,7}}=>3 {{1,4},{2,3},{5,6},{7}}=>4 {{1,4,7},{2,3},{5},{6}}=>4 {{1,4},{2,3,7},{5},{6}}=>4 {{1,4},{2,3},{5,7},{6}}=>4 {{1,4},{2,3},{5},{6,7}}=>4 {{1,4},{2,3},{5},{6},{7}}=>5 {{1,5,6,7},{2,3,4}}=>2 {{1,5,6},{2,3,4,7}}=>2 {{1,5,6},{2,3,4},{7}}=>3 {{1,5,7},{2,3,4,6}}=>2 {{1,5},{2,3,4,6,7}}=>2 {{1,5},{2,3,4,6},{7}}=>3 {{1,5,7},{2,3,4},{6}}=>3 {{1,5},{2,3,4,7},{6}}=>3 {{1,5},{2,3,4},{6,7}}=>3 {{1,5},{2,3,4},{6},{7}}=>4 {{1,6,7},{2,3,4,5}}=>2 {{1,6},{2,3,4,5,7}}=>2 {{1,6},{2,3,4,5},{7}}=>3 {{1,7},{2,3,4,5,6}}=>2 {{1},{2,3,4,5,6,7}}=>2 {{1},{2,3,4,5,6},{7}}=>3 {{1,7},{2,3,4,5},{6}}=>3 {{1},{2,3,4,5,7},{6}}=>3 {{1},{2,3,4,5},{6,7}}=>3 {{1},{2,3,4,5},{6},{7}}=>4 {{1,6,7},{2,3,4},{5}}=>3 {{1,6},{2,3,4,7},{5}}=>3 {{1,6},{2,3,4},{5,7}}=>3 {{1,6},{2,3,4},{5},{7}}=>4 {{1,7},{2,3,4,6},{5}}=>3 {{1},{2,3,4,6,7},{5}}=>3 {{1},{2,3,4,6},{5,7}}=>3 {{1},{2,3,4,6},{5},{7}}=>4 {{1,7},{2,3,4},{5,6}}=>3 {{1},{2,3,4,7},{5,6}}=>3 {{1},{2,3,4},{5,6,7}}=>3 {{1},{2,3,4},{5,6},{7}}=>4 {{1,7},{2,3,4},{5},{6}}=>4 {{1},{2,3,4,7},{5},{6}}=>4 {{1},{2,3,4},{5,7},{6}}=>4 {{1},{2,3,4},{5},{6,7}}=>4 {{1},{2,3,4},{5},{6},{7}}=>5 {{1,5,6,7},{2,3},{4}}=>3 {{1,5,6},{2,3,7},{4}}=>3 {{1,5,6},{2,3},{4,7}}=>3 {{1,5,6},{2,3},{4},{7}}=>4 {{1,5,7},{2,3,6},{4}}=>3 {{1,5},{2,3,6,7},{4}}=>3 {{1,5},{2,3,6},{4,7}}=>3 {{1,5},{2,3,6},{4},{7}}=>4 {{1,5,7},{2,3},{4,6}}=>3 {{1,5},{2,3,7},{4,6}}=>3 {{1,5},{2,3},{4,6,7}}=>3 {{1,5},{2,3},{4,6},{7}}=>4 {{1,5,7},{2,3},{4},{6}}=>4 {{1,5},{2,3,7},{4},{6}}=>4 {{1,5},{2,3},{4,7},{6}}=>4 {{1,5},{2,3},{4},{6,7}}=>4 {{1,5},{2,3},{4},{6},{7}}=>5 {{1,6,7},{2,3,5},{4}}=>3 {{1,6},{2,3,5,7},{4}}=>3 {{1,6},{2,3,5},{4,7}}=>3 {{1,6},{2,3,5},{4},{7}}=>4 {{1,7},{2,3,5,6},{4}}=>3 {{1},{2,3,5,6,7},{4}}=>3 {{1},{2,3,5,6},{4,7}}=>3 {{1},{2,3,5,6},{4},{7}}=>4 {{1,7},{2,3,5},{4,6}}=>3 {{1},{2,3,5,7},{4,6}}=>3 {{1},{2,3,5},{4,6,7}}=>3 {{1},{2,3,5},{4,6},{7}}=>4 {{1,7},{2,3,5},{4},{6}}=>4 {{1},{2,3,5,7},{4},{6}}=>4 {{1},{2,3,5},{4,7},{6}}=>4 {{1},{2,3,5},{4},{6,7}}=>4 {{1},{2,3,5},{4},{6},{7}}=>5 {{1,6,7},{2,3},{4,5}}=>3 {{1,6},{2,3,7},{4,5}}=>3 {{1,6},{2,3},{4,5,7}}=>3 {{1,6},{2,3},{4,5},{7}}=>4 {{1,7},{2,3,6},{4,5}}=>3 {{1},{2,3,6,7},{4,5}}=>3 {{1},{2,3,6},{4,5,7}}=>3 {{1},{2,3,6},{4,5},{7}}=>4 {{1,7},{2,3},{4,5,6}}=>3 {{1},{2,3,7},{4,5,6}}=>3 {{1},{2,3},{4,5,6,7}}=>3 {{1},{2,3},{4,5,6},{7}}=>4 {{1,7},{2,3},{4,5},{6}}=>4 {{1},{2,3,7},{4,5},{6}}=>4 {{1},{2,3},{4,5,7},{6}}=>4 {{1},{2,3},{4,5},{6,7}}=>4 {{1},{2,3},{4,5},{6},{7}}=>5 {{1,6,7},{2,3},{4},{5}}=>4 {{1,6},{2,3,7},{4},{5}}=>4 {{1,6},{2,3},{4,7},{5}}=>4 {{1,6},{2,3},{4},{5,7}}=>4 {{1,6},{2,3},{4},{5},{7}}=>5 {{1,7},{2,3,6},{4},{5}}=>4 {{1},{2,3,6,7},{4},{5}}=>4 {{1},{2,3,6},{4,7},{5}}=>4 {{1},{2,3,6},{4},{5,7}}=>4 {{1},{2,3,6},{4},{5},{7}}=>5 {{1,7},{2,3},{4,6},{5}}=>4 {{1},{2,3,7},{4,6},{5}}=>4 {{1},{2,3},{4,6,7},{5}}=>4 {{1},{2,3},{4,6},{5,7}}=>4 {{1},{2,3},{4,6},{5},{7}}=>5 {{1,7},{2,3},{4},{5,6}}=>4 {{1},{2,3,7},{4},{5,6}}=>4 {{1},{2,3},{4,7},{5,6}}=>4 {{1},{2,3},{4},{5,6,7}}=>4 {{1},{2,3},{4},{5,6},{7}}=>5 {{1,7},{2,3},{4},{5},{6}}=>5 {{1},{2,3,7},{4},{5},{6}}=>5 {{1},{2,3},{4,7},{5},{6}}=>5 {{1},{2,3},{4},{5,7},{6}}=>5 {{1},{2,3},{4},{5},{6,7}}=>5 {{1},{2,3},{4},{5},{6},{7}}=>6 {{1,4,5,6,7},{2},{3}}=>3 {{1,4,5,6},{2,7},{3}}=>3 {{1,4,5,6},{2},{3,7}}=>3 {{1,4,5,6},{2},{3},{7}}=>4 {{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}}=>4 {{1,4,5,7},{2},{3,6}}=>3 {{1,4,5},{2,7},{3,6}}=>3 {{1,4,5},{2},{3,6,7}}=>3 {{1,4,5},{2},{3,6},{7}}=>4 {{1,4,5,7},{2},{3},{6}}=>4 {{1,4,5},{2,7},{3},{6}}=>4 {{1,4,5},{2},{3,7},{6}}=>4 {{1,4,5},{2},{3},{6,7}}=>4 {{1,4,5},{2},{3},{6},{7}}=>5 {{1,4,6,7},{2,5},{3}}=>3 {{1,4,6},{2,5,7},{3}}=>3 {{1,4,6},{2,5},{3,7}}=>3 {{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}}=>4 {{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}}=>4 {{1,4,7},{2,5},{3},{6}}=>4 {{1,4},{2,5,7},{3},{6}}=>4 {{1,4},{2,5},{3,7},{6}}=>4 {{1,4},{2,5},{3},{6,7}}=>4 {{1,4},{2,5},{3},{6},{7}}=>5 {{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}}=>4 {{1,4,7},{2,6},{3,5}}=>3 {{1,4},{2,6,7},{3,5}}=>3 {{1,4},{2,6},{3,5,7}}=>3 {{1,4},{2,6},{3,5},{7}}=>4 {{1,4,7},{2},{3,5,6}}=>3 {{1,4},{2,7},{3,5,6}}=>3 {{1,4},{2},{3,5,6,7}}=>3 {{1,4},{2},{3,5,6},{7}}=>4 {{1,4,7},{2},{3,5},{6}}=>4 {{1,4},{2,7},{3,5},{6}}=>4 {{1,4},{2},{3,5,7},{6}}=>4 {{1,4},{2},{3,5},{6,7}}=>4 {{1,4},{2},{3,5},{6},{7}}=>5 {{1,4,6,7},{2},{3},{5}}=>4 {{1,4,6},{2,7},{3},{5}}=>4 {{1,4,6},{2},{3,7},{5}}=>4 {{1,4,6},{2},{3},{5,7}}=>4 {{1,4,6},{2},{3},{5},{7}}=>5 {{1,4,7},{2,6},{3},{5}}=>4 {{1,4},{2,6,7},{3},{5}}=>4 {{1,4},{2,6},{3,7},{5}}=>4 {{1,4},{2,6},{3},{5,7}}=>4 {{1,4},{2,6},{3},{5},{7}}=>5 {{1,4,7},{2},{3,6},{5}}=>4 {{1,4},{2,7},{3,6},{5}}=>4 {{1,4},{2},{3,6,7},{5}}=>4 {{1,4},{2},{3,6},{5,7}}=>4 {{1,4},{2},{3,6},{5},{7}}=>5 {{1,4,7},{2},{3},{5,6}}=>4 {{1,4},{2,7},{3},{5,6}}=>4 {{1,4},{2},{3,7},{5,6}}=>4 {{1,4},{2},{3},{5,6,7}}=>4 {{1,4},{2},{3},{5,6},{7}}=>5 {{1,4,7},{2},{3},{5},{6}}=>5 {{1,4},{2,7},{3},{5},{6}}=>5 {{1,4},{2},{3,7},{5},{6}}=>5 {{1,4},{2},{3},{5,7},{6}}=>5 {{1,4},{2},{3},{5},{6,7}}=>5 {{1,4},{2},{3},{5},{6},{7}}=>6 {{1,5,6,7},{2,4},{3}}=>3 {{1,5,6},{2,4,7},{3}}=>3 {{1,5,6},{2,4},{3,7}}=>3 {{1,5,6},{2,4},{3},{7}}=>4 {{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}}=>4 {{1,5,7},{2,4},{3,6}}=>3 {{1,5},{2,4,7},{3,6}}=>3 {{1,5},{2,4},{3,6,7}}=>3 {{1,5},{2,4},{3,6},{7}}=>4 {{1,5,7},{2,4},{3},{6}}=>4 {{1,5},{2,4,7},{3},{6}}=>4 {{1,5},{2,4},{3,7},{6}}=>4 {{1,5},{2,4},{3},{6,7}}=>4 {{1,5},{2,4},{3},{6},{7}}=>5 {{1,6,7},{2,4,5},{3}}=>3 {{1,6},{2,4,5,7},{3}}=>3 {{1,6},{2,4,5},{3,7}}=>3 {{1,6},{2,4,5},{3},{7}}=>4 {{1,7},{2,4,5,6},{3}}=>3 {{1},{2,4,5,6,7},{3}}=>3 {{1},{2,4,5,6},{3,7}}=>3 {{1},{2,4,5,6},{3},{7}}=>4 {{1,7},{2,4,5},{3,6}}=>3 {{1},{2,4,5,7},{3,6}}=>3 {{1},{2,4,5},{3,6,7}}=>3 {{1},{2,4,5},{3,6},{7}}=>4 {{1,7},{2,4,5},{3},{6}}=>4 {{1},{2,4,5,7},{3},{6}}=>4 {{1},{2,4,5},{3,7},{6}}=>4 {{1},{2,4,5},{3},{6,7}}=>4 {{1},{2,4,5},{3},{6},{7}}=>5 {{1,6,7},{2,4},{3,5}}=>3 {{1,6},{2,4,7},{3,5}}=>3 {{1,6},{2,4},{3,5,7}}=>3 {{1,6},{2,4},{3,5},{7}}=>4 {{1,7},{2,4,6},{3,5}}=>3 {{1},{2,4,6,7},{3,5}}=>3 {{1},{2,4,6},{3,5,7}}=>3 {{1},{2,4,6},{3,5},{7}}=>4 {{1,7},{2,4},{3,5,6}}=>3 {{1},{2,4,7},{3,5,6}}=>3 {{1},{2,4},{3,5,6,7}}=>3 {{1},{2,4},{3,5,6},{7}}=>4 {{1,7},{2,4},{3,5},{6}}=>4 {{1},{2,4,7},{3,5},{6}}=>4 {{1},{2,4},{3,5,7},{6}}=>4 {{1},{2,4},{3,5},{6,7}}=>4 {{1},{2,4},{3,5},{6},{7}}=>5 {{1,6,7},{2,4},{3},{5}}=>4 {{1,6},{2,4,7},{3},{5}}=>4 {{1,6},{2,4},{3,7},{5}}=>4 {{1,6},{2,4},{3},{5,7}}=>4 {{1,6},{2,4},{3},{5},{7}}=>5 {{1,7},{2,4,6},{3},{5}}=>4 {{1},{2,4,6,7},{3},{5}}=>4 {{1},{2,4,6},{3,7},{5}}=>4 {{1},{2,4,6},{3},{5,7}}=>4 {{1},{2,4,6},{3},{5},{7}}=>5 {{1,7},{2,4},{3,6},{5}}=>4 {{1},{2,4,7},{3,6},{5}}=>4 {{1},{2,4},{3,6,7},{5}}=>4 {{1},{2,4},{3,6},{5,7}}=>4 {{1},{2,4},{3,6},{5},{7}}=>5 {{1,7},{2,4},{3},{5,6}}=>4 {{1},{2,4,7},{3},{5,6}}=>4 {{1},{2,4},{3,7},{5,6}}=>4 {{1},{2,4},{3},{5,6,7}}=>4 {{1},{2,4},{3},{5,6},{7}}=>5 {{1,7},{2,4},{3},{5},{6}}=>5 {{1},{2,4,7},{3},{5},{6}}=>5 {{1},{2,4},{3,7},{5},{6}}=>5 {{1},{2,4},{3},{5,7},{6}}=>5 {{1},{2,4},{3},{5},{6,7}}=>5 {{1},{2,4},{3},{5},{6},{7}}=>6 {{1,5,6,7},{2},{3,4}}=>3 {{1,5,6},{2,7},{3,4}}=>3 {{1,5,6},{2},{3,4,7}}=>3 {{1,5,6},{2},{3,4},{7}}=>4 {{1,5,7},{2,6},{3,4}}=>3 {{1,5},{2,6,7},{3,4}}=>3 {{1,5},{2,6},{3,4,7}}=>3 {{1,5},{2,6},{3,4},{7}}=>4 {{1,5,7},{2},{3,4,6}}=>3 {{1,5},{2,7},{3,4,6}}=>3 {{1,5},{2},{3,4,6,7}}=>3 {{1,5},{2},{3,4,6},{7}}=>4 {{1,5,7},{2},{3,4},{6}}=>4 {{1,5},{2,7},{3,4},{6}}=>4 {{1,5},{2},{3,4,7},{6}}=>4 {{1,5},{2},{3,4},{6,7}}=>4 {{1,5},{2},{3,4},{6},{7}}=>5 {{1,6,7},{2,5},{3,4}}=>3 {{1,6},{2,5,7},{3,4}}=>3 {{1,6},{2,5},{3,4,7}}=>3 {{1,6},{2,5},{3,4},{7}}=>4 {{1,7},{2,5,6},{3,4}}=>3 {{1},{2,5,6,7},{3,4}}=>3 {{1},{2,5,6},{3,4,7}}=>3 {{1},{2,5,6},{3,4},{7}}=>4 {{1,7},{2,5},{3,4,6}}=>3 {{1},{2,5,7},{3,4,6}}=>3 {{1},{2,5},{3,4,6,7}}=>3 {{1},{2,5},{3,4,6},{7}}=>4 {{1,7},{2,5},{3,4},{6}}=>4 {{1},{2,5,7},{3,4},{6}}=>4 {{1},{2,5},{3,4,7},{6}}=>4 {{1},{2,5},{3,4},{6,7}}=>4 {{1},{2,5},{3,4},{6},{7}}=>5 {{1,6,7},{2},{3,4,5}}=>3 {{1,6},{2,7},{3,4,5}}=>3 {{1,6},{2},{3,4,5,7}}=>3 {{1,6},{2},{3,4,5},{7}}=>4 {{1,7},{2,6},{3,4,5}}=>3 {{1},{2,6,7},{3,4,5}}=>3 {{1},{2,6},{3,4,5,7}}=>3 {{1},{2,6},{3,4,5},{7}}=>4 {{1,7},{2},{3,4,5,6}}=>3 {{1},{2,7},{3,4,5,6}}=>3 {{1},{2},{3,4,5,6,7}}=>3 {{1},{2},{3,4,5,6},{7}}=>4 {{1,7},{2},{3,4,5},{6}}=>4 {{1},{2,7},{3,4,5},{6}}=>4 {{1},{2},{3,4,5,7},{6}}=>4 {{1},{2},{3,4,5},{6,7}}=>4 {{1},{2},{3,4,5},{6},{7}}=>5 {{1,6,7},{2},{3,4},{5}}=>4 {{1,6},{2,7},{3,4},{5}}=>4 {{1,6},{2},{3,4,7},{5}}=>4 {{1,6},{2},{3,4},{5,7}}=>4 {{1,6},{2},{3,4},{5},{7}}=>5 {{1,7},{2,6},{3,4},{5}}=>4 {{1},{2,6,7},{3,4},{5}}=>4 {{1},{2,6},{3,4,7},{5}}=>4 {{1},{2,6},{3,4},{5,7}}=>4 {{1},{2,6},{3,4},{5},{7}}=>5 {{1,7},{2},{3,4,6},{5}}=>4 {{1},{2,7},{3,4,6},{5}}=>4 {{1},{2},{3,4,6,7},{5}}=>4 {{1},{2},{3,4,6},{5,7}}=>4 {{1},{2},{3,4,6},{5},{7}}=>5 {{1,7},{2},{3,4},{5,6}}=>4 {{1},{2,7},{3,4},{5,6}}=>4 {{1},{2},{3,4,7},{5,6}}=>4 {{1},{2},{3,4},{5,6,7}}=>4 {{1},{2},{3,4},{5,6},{7}}=>5 {{1,7},{2},{3,4},{5},{6}}=>5 {{1},{2,7},{3,4},{5},{6}}=>5 {{1},{2},{3,4,7},{5},{6}}=>5 {{1},{2},{3,4},{5,7},{6}}=>5 {{1},{2},{3,4},{5},{6,7}}=>5 {{1},{2},{3,4},{5},{6},{7}}=>6 {{1,5,6,7},{2},{3},{4}}=>4 {{1,5,6},{2,7},{3},{4}}=>4 {{1,5,6},{2},{3,7},{4}}=>4 {{1,5,6},{2},{3},{4,7}}=>4 {{1,5,6},{2},{3},{4},{7}}=>5 {{1,5,7},{2,6},{3},{4}}=>4 {{1,5},{2,6,7},{3},{4}}=>4 {{1,5},{2,6},{3,7},{4}}=>4 {{1,5},{2,6},{3},{4,7}}=>4 {{1,5},{2,6},{3},{4},{7}}=>5 {{1,5,7},{2},{3,6},{4}}=>4 {{1,5},{2,7},{3,6},{4}}=>4 {{1,5},{2},{3,6,7},{4}}=>4 {{1,5},{2},{3,6},{4,7}}=>4 {{1,5},{2},{3,6},{4},{7}}=>5 {{1,5,7},{2},{3},{4,6}}=>4 {{1,5},{2,7},{3},{4,6}}=>4 {{1,5},{2},{3,7},{4,6}}=>4 {{1,5},{2},{3},{4,6,7}}=>4 {{1,5},{2},{3},{4,6},{7}}=>5 {{1,5,7},{2},{3},{4},{6}}=>5 {{1,5},{2,7},{3},{4},{6}}=>5 {{1,5},{2},{3,7},{4},{6}}=>5 {{1,5},{2},{3},{4,7},{6}}=>5 {{1,5},{2},{3},{4},{6,7}}=>5 {{1,5},{2},{3},{4},{6},{7}}=>6 {{1,6,7},{2,5},{3},{4}}=>4 {{1,6},{2,5,7},{3},{4}}=>4 {{1,6},{2,5},{3,7},{4}}=>4 {{1,6},{2,5},{3},{4,7}}=>4 {{1,6},{2,5},{3},{4},{7}}=>5 {{1,7},{2,5,6},{3},{4}}=>4 {{1},{2,5,6,7},{3},{4}}=>4 {{1},{2,5,6},{3,7},{4}}=>4 {{1},{2,5,6},{3},{4,7}}=>4 {{1},{2,5,6},{3},{4},{7}}=>5 {{1,7},{2,5},{3,6},{4}}=>4 {{1},{2,5,7},{3,6},{4}}=>4 {{1},{2,5},{3,6,7},{4}}=>4 {{1},{2,5},{3,6},{4,7}}=>4 {{1},{2,5},{3,6},{4},{7}}=>5 {{1,7},{2,5},{3},{4,6}}=>4 {{1},{2,5,7},{3},{4,6}}=>4 {{1},{2,5},{3,7},{4,6}}=>4 {{1},{2,5},{3},{4,6,7}}=>4 {{1},{2,5},{3},{4,6},{7}}=>5 {{1,7},{2,5},{3},{4},{6}}=>5 {{1},{2,5,7},{3},{4},{6}}=>5 {{1},{2,5},{3,7},{4},{6}}=>5 {{1},{2,5},{3},{4,7},{6}}=>5 {{1},{2,5},{3},{4},{6,7}}=>5 {{1},{2,5},{3},{4},{6},{7}}=>6 {{1,6,7},{2},{3,5},{4}}=>4 {{1,6},{2,7},{3,5},{4}}=>4 {{1,6},{2},{3,5,7},{4}}=>4 {{1,6},{2},{3,5},{4,7}}=>4 {{1,6},{2},{3,5},{4},{7}}=>5 {{1,7},{2,6},{3,5},{4}}=>4 {{1},{2,6,7},{3,5},{4}}=>4 {{1},{2,6},{3,5,7},{4}}=>4 {{1},{2,6},{3,5},{4,7}}=>4 {{1},{2,6},{3,5},{4},{7}}=>5 {{1,7},{2},{3,5,6},{4}}=>4 {{1},{2,7},{3,5,6},{4}}=>4 {{1},{2},{3,5,6,7},{4}}=>4 {{1},{2},{3,5,6},{4,7}}=>4 {{1},{2},{3,5,6},{4},{7}}=>5 {{1,7},{2},{3,5},{4,6}}=>4 {{1},{2,7},{3,5},{4,6}}=>4 {{1},{2},{3,5,7},{4,6}}=>4 {{1},{2},{3,5},{4,6,7}}=>4 {{1},{2},{3,5},{4,6},{7}}=>5 {{1,7},{2},{3,5},{4},{6}}=>5 {{1},{2,7},{3,5},{4},{6}}=>5 {{1},{2},{3,5,7},{4},{6}}=>5 {{1},{2},{3,5},{4,7},{6}}=>5 {{1},{2},{3,5},{4},{6,7}}=>5 {{1},{2},{3,5},{4},{6},{7}}=>6 {{1,6,7},{2},{3},{4,5}}=>4 {{1,6},{2,7},{3},{4,5}}=>4 {{1,6},{2},{3,7},{4,5}}=>4 {{1,6},{2},{3},{4,5,7}}=>4 {{1,6},{2},{3},{4,5},{7}}=>5 {{1,7},{2,6},{3},{4,5}}=>4 {{1},{2,6,7},{3},{4,5}}=>4 {{1},{2,6},{3,7},{4,5}}=>4 {{1},{2,6},{3},{4,5,7}}=>4 {{1},{2,6},{3},{4,5},{7}}=>5 {{1,7},{2},{3,6},{4,5}}=>4 {{1},{2,7},{3,6},{4,5}}=>4 {{1},{2},{3,6,7},{4,5}}=>4 {{1},{2},{3,6},{4,5,7}}=>4 {{1},{2},{3,6},{4,5},{7}}=>5 {{1,7},{2},{3},{4,5,6}}=>4 {{1},{2,7},{3},{4,5,6}}=>4 {{1},{2},{3,7},{4,5,6}}=>4 {{1},{2},{3},{4,5,6,7}}=>4 {{1},{2},{3},{4,5,6},{7}}=>5 {{1,7},{2},{3},{4,5},{6}}=>5 {{1},{2,7},{3},{4,5},{6}}=>5 {{1},{2},{3,7},{4,5},{6}}=>5 {{1},{2},{3},{4,5,7},{6}}=>5 {{1},{2},{3},{4,5},{6,7}}=>5 {{1},{2},{3},{4,5},{6},{7}}=>6 {{1,6,7},{2},{3},{4},{5}}=>5 {{1,6},{2,7},{3},{4},{5}}=>5 {{1,6},{2},{3,7},{4},{5}}=>5 {{1,6},{2},{3},{4,7},{5}}=>5 {{1,6},{2},{3},{4},{5,7}}=>5 {{1,6},{2},{3},{4},{5},{7}}=>6 {{1,7},{2,6},{3},{4},{5}}=>5 {{1},{2,6,7},{3},{4},{5}}=>5 {{1},{2,6},{3,7},{4},{5}}=>5 {{1},{2,6},{3},{4,7},{5}}=>5 {{1},{2,6},{3},{4},{5,7}}=>5 {{1},{2,6},{3},{4},{5},{7}}=>6 {{1,7},{2},{3,6},{4},{5}}=>5 {{1},{2,7},{3,6},{4},{5}}=>5 {{1},{2},{3,6,7},{4},{5}}=>5 {{1},{2},{3,6},{4,7},{5}}=>5 {{1},{2},{3,6},{4},{5,7}}=>5 {{1},{2},{3,6},{4},{5},{7}}=>6 {{1,7},{2},{3},{4,6},{5}}=>5 {{1},{2,7},{3},{4,6},{5}}=>5 {{1},{2},{3,7},{4,6},{5}}=>5 {{1},{2},{3},{4,6,7},{5}}=>5 {{1},{2},{3},{4,6},{5,7}}=>5 {{1},{2},{3},{4,6},{5},{7}}=>6 {{1,7},{2},{3},{4},{5,6}}=>5 {{1},{2,7},{3},{4},{5,6}}=>5 {{1},{2},{3,7},{4},{5,6}}=>5 {{1},{2},{3},{4,7},{5,6}}=>5 {{1},{2},{3},{4},{5,6,7}}=>5 {{1},{2},{3},{4},{5,6},{7}}=>6 {{1,7},{2},{3},{4},{5},{6}}=>6 {{1},{2,7},{3},{4},{5},{6}}=>6 {{1},{2},{3,7},{4},{5},{6}}=>6 {{1},{2},{3},{4,7},{5},{6}}=>6 {{1},{2},{3},{4},{5,7},{6}}=>6 {{1},{2},{3},{4},{5},{6,7}}=>6 {{1},{2},{3},{4},{5},{6},{7}}=>7
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Description
The number of blocks in the set partition.
The generating function of this statistic yields the famous Stirling numbers of the second kind $S_2(n,k)$ given by the number of set partitions of $\{ 1,\ldots,n\}$ into $k$ blocks, see [1].
References
[1] Triangle of Stirling numbers of the second kind, S2(n,k), n >= 1, 1 <= k <= n. OEIS:A008277
Code
def statistic(s):
    return s.cardinality()
Created
Jun 14, 2013 at 03:49 by Jessica Striker
Updated
May 29, 2015 at 16:42 by Martin Rubey