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Identifier
Values
=>
Cc0009;cc-rep
{{1,2}}=>1 {{1},{2}}=>1 {{1,2,3}}=>1 {{1,2},{3}}=>1 {{1,3},{2}}=>2 {{1},{2,3}}=>1 {{1},{2},{3}}=>1 {{1,2,3,4}}=>1 {{1,2,3},{4}}=>1 {{1,2,4},{3}}=>2 {{1,2},{3,4}}=>1 {{1,2},{3},{4}}=>1 {{1,3,4},{2}}=>2 {{1,3},{2,4}}=>2 {{1,3},{2},{4}}=>2 {{1,4},{2,3}}=>2 {{1},{2,3,4}}=>1 {{1},{2,3},{4}}=>1 {{1,4},{2},{3}}=>3 {{1},{2,4},{3}}=>1 {{1},{2},{3,4}}=>1 {{1},{2},{3},{4}}=>1 {{1,2,3,4,5}}=>1 {{1,2,3,4},{5}}=>1 {{1,2,3,5},{4}}=>2 {{1,2,3},{4,5}}=>1 {{1,2,3},{4},{5}}=>1 {{1,2,4,5},{3}}=>2 {{1,2,4},{3,5}}=>2 {{1,2,4},{3},{5}}=>2 {{1,2,5},{3,4}}=>2 {{1,2},{3,4,5}}=>1 {{1,2},{3,4},{5}}=>1 {{1,2,5},{3},{4}}=>3 {{1,2},{3,5},{4}}=>1 {{1,2},{3},{4,5}}=>1 {{1,2},{3},{4},{5}}=>1 {{1,3,4,5},{2}}=>2 {{1,3,4},{2,5}}=>2 {{1,3,4},{2},{5}}=>2 {{1,3,5},{2,4}}=>2 {{1,3},{2,4,5}}=>2 {{1,3},{2,4},{5}}=>2 {{1,3,5},{2},{4}}=>3 {{1,3},{2,5},{4}}=>3 {{1,3},{2},{4,5}}=>2 {{1,3},{2},{4},{5}}=>2 {{1,4,5},{2,3}}=>2 {{1,4},{2,3,5}}=>2 {{1,4},{2,3},{5}}=>2 {{1,5},{2,3,4}}=>2 {{1},{2,3,4,5}}=>1 {{1},{2,3,4},{5}}=>1 {{1,5},{2,3},{4}}=>3 {{1},{2,3,5},{4}}=>1 {{1},{2,3},{4,5}}=>1 {{1},{2,3},{4},{5}}=>1 {{1,4,5},{2},{3}}=>3 {{1,4},{2,5},{3}}=>3 {{1,4},{2},{3,5}}=>3 {{1,4},{2},{3},{5}}=>3 {{1,5},{2,4},{3}}=>3 {{1},{2,4,5},{3}}=>1 {{1},{2,4},{3,5}}=>1 {{1},{2,4},{3},{5}}=>1 {{1,5},{2},{3,4}}=>3 {{1},{2,5},{3,4}}=>1 {{1},{2},{3,4,5}}=>1 {{1},{2},{3,4},{5}}=>1 {{1,5},{2},{3},{4}}=>4 {{1},{2,5},{3},{4}}=>1 {{1},{2},{3,5},{4}}=>1 {{1},{2},{3},{4,5}}=>1 {{1},{2},{3},{4},{5}}=>1 {{1,2,3,4,5,6}}=>1 {{1,2,3,4,5},{6}}=>1 {{1,2,3,4,6},{5}}=>2 {{1,2,3,4},{5,6}}=>1 {{1,2,3,4},{5},{6}}=>1 {{1,2,3,5,6},{4}}=>2 {{1,2,3,5},{4,6}}=>2 {{1,2,3,5},{4},{6}}=>2 {{1,2,3,6},{4,5}}=>2 {{1,2,3},{4,5,6}}=>1 {{1,2,3},{4,5},{6}}=>1 {{1,2,3,6},{4},{5}}=>3 {{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}}=>2 {{1,2,4,5},{3,6}}=>2 {{1,2,4,5},{3},{6}}=>2 {{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}}=>3 {{1,2,4},{3,6},{5}}=>3 {{1,2,4},{3},{5,6}}=>2 {{1,2,4},{3},{5},{6}}=>2 {{1,2,5,6},{3,4}}=>2 {{1,2,5},{3,4,6}}=>2 {{1,2,5},{3,4},{6}}=>2 {{1,2,6},{3,4,5}}=>2 {{1,2},{3,4,5,6}}=>1 {{1,2},{3,4,5},{6}}=>1 {{1,2,6},{3,4},{5}}=>3 {{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}}=>3 {{1,2,5},{3,6},{4}}=>3 {{1,2,5},{3},{4,6}}=>3 {{1,2,5},{3},{4},{6}}=>3 {{1,2,6},{3,5},{4}}=>3 {{1,2},{3,5,6},{4}}=>1 {{1,2},{3,5},{4,6}}=>1 {{1,2},{3,5},{4},{6}}=>1 {{1,2,6},{3},{4,5}}=>3 {{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}}=>4 {{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}}=>2 {{1,3,4,5},{2,6}}=>2 {{1,3,4,5},{2},{6}}=>2 {{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}}=>3 {{1,3,4},{2,6},{5}}=>3 {{1,3,4},{2},{5,6}}=>2 {{1,3,4},{2},{5},{6}}=>2 {{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}}=>3 {{1,3},{2,4,6},{5}}=>3 {{1,3},{2,4},{5,6}}=>2 {{1,3},{2,4},{5},{6}}=>2 {{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}}=>3 {{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}}=>3 {{1,3,6},{2},{4,5}}=>3 {{1,3},{2,6},{4,5}}=>3 {{1,3},{2},{4,5,6}}=>2 {{1,3},{2},{4,5},{6}}=>2 {{1,3,6},{2},{4},{5}}=>4 {{1,3},{2,6},{4},{5}}=>4 {{1,3},{2},{4,6},{5}}=>2 {{1,3},{2},{4},{5,6}}=>2 {{1,3},{2},{4},{5},{6}}=>2 {{1,4,5,6},{2,3}}=>2 {{1,4,5},{2,3,6}}=>2 {{1,4,5},{2,3},{6}}=>2 {{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}}=>3 {{1,4},{2,3,6},{5}}=>3 {{1,4},{2,3},{5,6}}=>2 {{1,4},{2,3},{5},{6}}=>2 {{1,5,6},{2,3,4}}=>2 {{1,5},{2,3,4,6}}=>2 {{1,5},{2,3,4},{6}}=>2 {{1,6},{2,3,4,5}}=>2 {{1},{2,3,4,5,6}}=>1 {{1},{2,3,4,5},{6}}=>1 {{1,6},{2,3,4},{5}}=>3 {{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}}=>3 {{1,5},{2,3,6},{4}}=>3 {{1,5},{2,3},{4,6}}=>3 {{1,5},{2,3},{4},{6}}=>3 {{1,6},{2,3,5},{4}}=>3 {{1},{2,3,5,6},{4}}=>1 {{1},{2,3,5},{4,6}}=>1 {{1},{2,3,5},{4},{6}}=>1 {{1,6},{2,3},{4,5}}=>3 {{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}}=>4 {{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}}=>3 {{1,4,5},{2,6},{3}}=>3 {{1,4,5},{2},{3,6}}=>3 {{1,4,5},{2},{3},{6}}=>3 {{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}}=>3 {{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}}=>3 {{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}}=>3 {{1,4},{2},{3},{5},{6}}=>3 {{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}}=>3 {{1,6},{2,4,5},{3}}=>3 {{1},{2,4,5,6},{3}}=>1 {{1},{2,4,5},{3,6}}=>1 {{1},{2,4,5},{3},{6}}=>1 {{1,6},{2,4},{3,5}}=>3 {{1},{2,4,6},{3,5}}=>1 {{1},{2,4},{3,5,6}}=>1 {{1},{2,4},{3,5},{6}}=>1 {{1,6},{2,4},{3},{5}}=>4 {{1},{2,4,6},{3},{5}}=>1 {{1},{2,4},{3,6},{5}}=>1 {{1},{2,4},{3},{5,6}}=>1 {{1},{2,4},{3},{5},{6}}=>1 {{1,5,6},{2},{3,4}}=>3 {{1,5},{2,6},{3,4}}=>3 {{1,5},{2},{3,4,6}}=>3 {{1,5},{2},{3,4},{6}}=>3 {{1,6},{2,5},{3,4}}=>3 {{1},{2,5,6},{3,4}}=>1 {{1},{2,5},{3,4,6}}=>1 {{1},{2,5},{3,4},{6}}=>1 {{1,6},{2},{3,4,5}}=>3 {{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}}=>4 {{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}}=>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}}=>4 {{1,6},{2,5},{3},{4}}=>4 {{1},{2,5,6},{3},{4}}=>1 {{1},{2,5},{3,6},{4}}=>1 {{1},{2,5},{3},{4,6}}=>1 {{1},{2,5},{3},{4},{6}}=>1 {{1,6},{2},{3,5},{4}}=>4 {{1},{2,6},{3,5},{4}}=>1 {{1},{2},{3,5,6},{4}}=>1 {{1},{2},{3,5},{4,6}}=>1 {{1},{2},{3,5},{4},{6}}=>1 {{1,6},{2},{3},{4,5}}=>4 {{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}}=>5 {{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 {{1,2,3,4,5,6,7}}=>1 {{1,2,3,4,5,6},{7}}=>1 {{1,2,3,4,5,7},{6}}=>2 {{1,2,3,4,5},{6,7}}=>1 {{1,2,3,4,5},{6},{7}}=>1 {{1,2,3,4,6,7},{5}}=>2 {{1,2,3,4,6},{5,7}}=>2 {{1,2,3,4,6},{5},{7}}=>2 {{1,2,3,4,7},{5,6}}=>2 {{1,2,3,4},{5,6,7}}=>1 {{1,2,3,4},{5,6},{7}}=>1 {{1,2,3,4,7},{5},{6}}=>3 {{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}}=>2 {{1,2,3,5,6},{4,7}}=>2 {{1,2,3,5,6},{4},{7}}=>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 {{1,2,3,5,7},{4},{6}}=>3 {{1,2,3,5},{4,7},{6}}=>3 {{1,2,3,5},{4},{6,7}}=>2 {{1,2,3,5},{4},{6},{7}}=>2 {{1,2,3,6,7},{4,5}}=>2 {{1,2,3,6},{4,5,7}}=>2 {{1,2,3,6},{4,5},{7}}=>2 {{1,2,3,7},{4,5,6}}=>2 {{1,2,3},{4,5,6,7}}=>1 {{1,2,3},{4,5,6},{7}}=>1 {{1,2,3,7},{4,5},{6}}=>3 {{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}}=>3 {{1,2,3,6},{4,7},{5}}=>3 {{1,2,3,6},{4},{5,7}}=>3 {{1,2,3,6},{4},{5},{7}}=>3 {{1,2,3,7},{4,6},{5}}=>3 {{1,2,3},{4,6,7},{5}}=>1 {{1,2,3},{4,6},{5,7}}=>1 {{1,2,3},{4,6},{5},{7}}=>1 {{1,2,3,7},{4},{5,6}}=>3 {{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}}=>4 {{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}}=>2 {{1,2,4,5,6},{3,7}}=>2 {{1,2,4,5,6},{3},{7}}=>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 {{1,2,4,5,7},{3},{6}}=>3 {{1,2,4,5},{3,7},{6}}=>3 {{1,2,4,5},{3},{6,7}}=>2 {{1,2,4,5},{3},{6},{7}}=>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 {{1,2,4,7},{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}}=>3 {{1,2,4},{3,5,7},{6}}=>3 {{1,2,4},{3,5},{6,7}}=>2 {{1,2,4},{3,5},{6},{7}}=>2 {{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}}=>3 {{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}}=>3 {{1,2,4,7},{3},{5,6}}=>3 {{1,2,4},{3,7},{5,6}}=>3 {{1,2,4},{3},{5,6,7}}=>2 {{1,2,4},{3},{5,6},{7}}=>2 {{1,2,4,7},{3},{5},{6}}=>4 {{1,2,4},{3,7},{5},{6}}=>4 {{1,2,4},{3},{5,7},{6}}=>2 {{1,2,4},{3},{5},{6,7}}=>2 {{1,2,4},{3},{5},{6},{7}}=>2 {{1,2,5,6,7},{3,4}}=>2 {{1,2,5,6},{3,4,7}}=>2 {{1,2,5,6},{3,4},{7}}=>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 {{1,2,5,7},{3,4},{6}}=>3 {{1,2,5},{3,4,7},{6}}=>3 {{1,2,5},{3,4},{6,7}}=>2 {{1,2,5},{3,4},{6},{7}}=>2 {{1,2,6,7},{3,4,5}}=>2 {{1,2,6},{3,4,5,7}}=>2 {{1,2,6},{3,4,5},{7}}=>2 {{1,2,7},{3,4,5,6}}=>2 {{1,2},{3,4,5,6,7}}=>1 {{1,2},{3,4,5,6},{7}}=>1 {{1,2,7},{3,4,5},{6}}=>3 {{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}}=>3 {{1,2,6},{3,4,7},{5}}=>3 {{1,2,6},{3,4},{5,7}}=>3 {{1,2,6},{3,4},{5},{7}}=>3 {{1,2,7},{3,4,6},{5}}=>3 {{1,2},{3,4,6,7},{5}}=>1 {{1,2},{3,4,6},{5,7}}=>1 {{1,2},{3,4,6},{5},{7}}=>1 {{1,2,7},{3,4},{5,6}}=>3 {{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}}=>4 {{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}}=>3 {{1,2,5,6},{3,7},{4}}=>3 {{1,2,5,6},{3},{4,7}}=>3 {{1,2,5,6},{3},{4},{7}}=>3 {{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}}=>3 {{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}}=>3 {{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}}=>3 {{1,2,5},{3},{4},{6},{7}}=>3 {{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}}=>3 {{1,2,7},{3,5,6},{4}}=>3 {{1,2},{3,5,6,7},{4}}=>1 {{1,2},{3,5,6},{4,7}}=>1 {{1,2},{3,5,6},{4},{7}}=>1 {{1,2,7},{3,5},{4,6}}=>3 {{1,2},{3,5,7},{4,6}}=>1 {{1,2},{3,5},{4,6,7}}=>1 {{1,2},{3,5},{4,6},{7}}=>1 {{1,2,7},{3,5},{4},{6}}=>4 {{1,2},{3,5,7},{4},{6}}=>1 {{1,2},{3,5},{4,7},{6}}=>1 {{1,2},{3,5},{4},{6,7}}=>1 {{1,2},{3,5},{4},{6},{7}}=>1 {{1,2,6,7},{3},{4,5}}=>3 {{1,2,6},{3,7},{4,5}}=>3 {{1,2,6},{3},{4,5,7}}=>3 {{1,2,6},{3},{4,5},{7}}=>3 {{1,2,7},{3,6},{4,5}}=>3 {{1,2},{3,6,7},{4,5}}=>1 {{1,2},{3,6},{4,5,7}}=>1 {{1,2},{3,6},{4,5},{7}}=>1 {{1,2,7},{3},{4,5,6}}=>3 {{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}}=>4 {{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}}=>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}}=>4 {{1,2,7},{3,6},{4},{5}}=>4 {{1,2},{3,6,7},{4},{5}}=>1 {{1,2},{3,6},{4,7},{5}}=>1 {{1,2},{3,6},{4},{5,7}}=>1 {{1,2},{3,6},{4},{5},{7}}=>1 {{1,2,7},{3},{4,6},{5}}=>4 {{1,2},{3,7},{4,6},{5}}=>1 {{1,2},{3},{4,6,7},{5}}=>1 {{1,2},{3},{4,6},{5,7}}=>1 {{1,2},{3},{4,6},{5},{7}}=>1 {{1,2,7},{3},{4},{5,6}}=>4 {{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}}=>5 {{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}}=>2 {{1,3,4,5,6},{2,7}}=>2 {{1,3,4,5,6},{2},{7}}=>2 {{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}}=>3 {{1,3,4,5},{2,7},{6}}=>3 {{1,3,4,5},{2},{6,7}}=>2 {{1,3,4,5},{2},{6},{7}}=>2 {{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}}=>3 {{1,3,4},{2,5,7},{6}}=>3 {{1,3,4},{2,5},{6,7}}=>2 {{1,3,4},{2,5},{6},{7}}=>2 {{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}}=>3 {{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}}=>3 {{1,3,4,7},{2},{5,6}}=>3 {{1,3,4},{2,7},{5,6}}=>3 {{1,3,4},{2},{5,6,7}}=>2 {{1,3,4},{2},{5,6},{7}}=>2 {{1,3,4,7},{2},{5},{6}}=>4 {{1,3,4},{2,7},{5},{6}}=>4 {{1,3,4},{2},{5,7},{6}}=>2 {{1,3,4},{2},{5},{6,7}}=>2 {{1,3,4},{2},{5},{6},{7}}=>2 {{1,3,5,6,7},{2,4}}=>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}}=>3 {{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}}=>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}}=>3 {{1,3},{2,4,5,7},{6}}=>3 {{1,3},{2,4,5},{6,7}}=>2 {{1,3},{2,4,5},{6},{7}}=>2 {{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}}=>3 {{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}}=>3 {{1,3,7},{2,4},{5,6}}=>3 {{1,3},{2,4,7},{5,6}}=>3 {{1,3},{2,4},{5,6,7}}=>2 {{1,3},{2,4},{5,6},{7}}=>2 {{1,3,7},{2,4},{5},{6}}=>4 {{1,3},{2,4,7},{5},{6}}=>4 {{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}}=>3 {{1,3,5,6},{2,7},{4}}=>3 {{1,3,5,6},{2},{4,7}}=>3 {{1,3,5,6},{2},{4},{7}}=>3 {{1,3,5,7},{2,6},{4}}=>3 {{1,3,5},{2,6,7},{4}}=>3 {{1,3,5},{2,6},{4,7}}=>3 {{1,3,5},{2,6},{4},{7}}=>3 {{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}}=>3 {{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}}=>3 {{1,3,5},{2},{4},{6},{7}}=>3 {{1,3,6,7},{2,5},{4}}=>3 {{1,3,6},{2,5,7},{4}}=>3 {{1,3,6},{2,5},{4,7}}=>3 {{1,3,6},{2,5},{4},{7}}=>3 {{1,3,7},{2,5,6},{4}}=>3 {{1,3},{2,5,6,7},{4}}=>3 {{1,3},{2,5,6},{4,7}}=>3 {{1,3},{2,5,6},{4},{7}}=>3 {{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}}=>3 {{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}}=>3 {{1,3},{2,5},{4},{6},{7}}=>3 {{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}}=>3 {{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}}=>3 {{1,3,7},{2},{4,5,6}}=>3 {{1,3},{2,7},{4,5,6}}=>3 {{1,3},{2},{4,5,6,7}}=>2 {{1,3},{2},{4,5,6},{7}}=>2 {{1,3,7},{2},{4,5},{6}}=>4 {{1,3},{2,7},{4,5},{6}}=>4 {{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}}=>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}}=>4 {{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}}=>4 {{1,3,7},{2},{4,6},{5}}=>4 {{1,3},{2,7},{4,6},{5}}=>4 {{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}}=>4 {{1,3},{2,7},{4},{5,6}}=>4 {{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}}=>5 {{1,3},{2,7},{4},{5},{6}}=>5 {{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 {{1,4,5,6,7},{2,3}}=>2 {{1,4,5,6},{2,3,7}}=>2 {{1,4,5,6},{2,3},{7}}=>2 {{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}}=>3 {{1,4,5},{2,3,7},{6}}=>3 {{1,4,5},{2,3},{6,7}}=>2 {{1,4,5},{2,3},{6},{7}}=>2 {{1,4,6,7},{2,3,5}}=>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}}=>3 {{1,4},{2,3,5,7},{6}}=>3 {{1,4},{2,3,5},{6,7}}=>2 {{1,4},{2,3,5},{6},{7}}=>2 {{1,4,6,7},{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}}=>3 {{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}}=>3 {{1,4,7},{2,3},{5,6}}=>3 {{1,4},{2,3,7},{5,6}}=>3 {{1,4},{2,3},{5,6,7}}=>2 {{1,4},{2,3},{5,6},{7}}=>2 {{1,4,7},{2,3},{5},{6}}=>4 {{1,4},{2,3,7},{5},{6}}=>4 {{1,4},{2,3},{5,7},{6}}=>2 {{1,4},{2,3},{5},{6,7}}=>2 {{1,4},{2,3},{5},{6},{7}}=>2 {{1,5,6,7},{2,3,4}}=>2 {{1,5,6},{2,3,4,7}}=>2 {{1,5,6},{2,3,4},{7}}=>2 {{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}}=>3 {{1,5},{2,3,4,7},{6}}=>3 {{1,5},{2,3,4},{6,7}}=>2 {{1,5},{2,3,4},{6},{7}}=>2 {{1,6,7},{2,3,4,5}}=>2 {{1,6},{2,3,4,5,7}}=>2 {{1,6},{2,3,4,5},{7}}=>2 {{1,7},{2,3,4,5,6}}=>2 {{1},{2,3,4,5,6,7}}=>1 {{1},{2,3,4,5,6},{7}}=>1 {{1,7},{2,3,4,5},{6}}=>3 {{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}}=>3 {{1,6},{2,3,4,7},{5}}=>3 {{1,6},{2,3,4},{5,7}}=>3 {{1,6},{2,3,4},{5},{7}}=>3 {{1,7},{2,3,4,6},{5}}=>3 {{1},{2,3,4,6,7},{5}}=>1 {{1},{2,3,4,6},{5,7}}=>1 {{1},{2,3,4,6},{5},{7}}=>1 {{1,7},{2,3,4},{5,6}}=>3 {{1},{2,3,4,7},{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}}=>4 {{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}}=>3 {{1,5,6},{2,3,7},{4}}=>3 {{1,5,6},{2,3},{4,7}}=>3 {{1,5,6},{2,3},{4},{7}}=>3 {{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}}=>3 {{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}}=>3 {{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}}=>3 {{1,5},{2,3},{4},{6},{7}}=>3 {{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}}=>3 {{1,7},{2,3,5,6},{4}}=>3 {{1},{2,3,5,6,7},{4}}=>1 {{1},{2,3,5,6},{4,7}}=>1 {{1},{2,3,5,6},{4},{7}}=>1 {{1,7},{2,3,5},{4,6}}=>3 {{1},{2,3,5,7},{4,6}}=>1 {{1},{2,3,5},{4,6,7}}=>1 {{1},{2,3,5},{4,6},{7}}=>1 {{1,7},{2,3,5},{4},{6}}=>4 {{1},{2,3,5,7},{4},{6}}=>1 {{1},{2,3,5},{4,7},{6}}=>1 {{1},{2,3,5},{4},{6,7}}=>1 {{1},{2,3,5},{4},{6},{7}}=>1 {{1,6,7},{2,3},{4,5}}=>3 {{1,6},{2,3,7},{4,5}}=>3 {{1,6},{2,3},{4,5,7}}=>3 {{1,6},{2,3},{4,5},{7}}=>3 {{1,7},{2,3,6},{4,5}}=>3 {{1},{2,3,6,7},{4,5}}=>1 {{1},{2,3,6},{4,5,7}}=>1 {{1},{2,3,6},{4,5},{7}}=>1 {{1,7},{2,3},{4,5,6}}=>3 {{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}}=>4 {{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}}=>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}}=>4 {{1,7},{2,3,6},{4},{5}}=>4 {{1},{2,3,6,7},{4},{5}}=>1 {{1},{2,3,6},{4,7},{5}}=>1 {{1},{2,3,6},{4},{5,7}}=>1 {{1},{2,3,6},{4},{5},{7}}=>1 {{1,7},{2,3},{4,6},{5}}=>4 {{1},{2,3,7},{4,6},{5}}=>1 {{1},{2,3},{4,6,7},{5}}=>1 {{1},{2,3},{4,6},{5,7}}=>1 {{1},{2,3},{4,6},{5},{7}}=>1 {{1,7},{2,3},{4},{5,6}}=>4 {{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}}=>5 {{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}}=>3 {{1,4,5,6},{2,7},{3}}=>3 {{1,4,5,6},{2},{3,7}}=>3 {{1,4,5,6},{2},{3},{7}}=>3 {{1,4,5,7},{2,6},{3}}=>3 {{1,4,5},{2,6,7},{3}}=>3 {{1,4,5},{2,6},{3,7}}=>3 {{1,4,5},{2,6},{3},{7}}=>3 {{1,4,5,7},{2},{3,6}}=>3 {{1,4,5},{2,7},{3,6}}=>3 {{1,4,5},{2},{3,6,7}}=>3 {{1,4,5},{2},{3,6},{7}}=>3 {{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}}=>3 {{1,4,5},{2},{3},{6},{7}}=>3 {{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}}=>3 {{1,4,7},{2,5,6},{3}}=>3 {{1,4},{2,5,6,7},{3}}=>3 {{1,4},{2,5,6},{3,7}}=>3 {{1,4},{2,5,6},{3},{7}}=>3 {{1,4,7},{2,5},{3,6}}=>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}}=>4 {{1,4},{2,5,7},{3},{6}}=>4 {{1,4},{2,5},{3,7},{6}}=>4 {{1,4},{2,5},{3},{6,7}}=>3 {{1,4},{2,5},{3},{6},{7}}=>3 {{1,4,6,7},{2},{3,5}}=>3 {{1,4,6},{2,7},{3,5}}=>3 {{1,4,6},{2},{3,5,7}}=>3 {{1,4,6},{2},{3,5},{7}}=>3 {{1,4,7},{2,6},{3,5}}=>3 {{1,4},{2,6,7},{3,5}}=>3 {{1,4},{2,6},{3,5,7}}=>3 {{1,4},{2,6},{3,5},{7}}=>3 {{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}}=>3 {{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}}=>3 {{1,4},{2},{3,5},{6},{7}}=>3 {{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}}=>4 {{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}}=>4 {{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}}=>4 {{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}}=>3 {{1,4},{2},{3},{5,6},{7}}=>3 {{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}}=>3 {{1,4},{2},{3},{5},{6,7}}=>3 {{1,4},{2},{3},{5},{6},{7}}=>3 {{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}}=>3 {{1,5,7},{2,4,6},{3}}=>3 {{1,5},{2,4,6,7},{3}}=>3 {{1,5},{2,4,6},{3,7}}=>3 {{1,5},{2,4,6},{3},{7}}=>3 {{1,5,7},{2,4},{3,6}}=>3 {{1,5},{2,4,7},{3,6}}=>3 {{1,5},{2,4},{3,6,7}}=>3 {{1,5},{2,4},{3,6},{7}}=>3 {{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}}=>3 {{1,5},{2,4},{3},{6},{7}}=>3 {{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}}=>3 {{1,7},{2,4,5,6},{3}}=>3 {{1},{2,4,5,6,7},{3}}=>1 {{1},{2,4,5,6},{3,7}}=>1 {{1},{2,4,5,6},{3},{7}}=>1 {{1,7},{2,4,5},{3,6}}=>3 {{1},{2,4,5,7},{3,6}}=>1 {{1},{2,4,5},{3,6,7}}=>1 {{1},{2,4,5},{3,6},{7}}=>1 {{1,7},{2,4,5},{3},{6}}=>4 {{1},{2,4,5,7},{3},{6}}=>1 {{1},{2,4,5},{3,7},{6}}=>1 {{1},{2,4,5},{3},{6,7}}=>1 {{1},{2,4,5},{3},{6},{7}}=>1 {{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}}=>3 {{1,7},{2,4,6},{3,5}}=>3 {{1},{2,4,6,7},{3,5}}=>1 {{1},{2,4,6},{3,5,7}}=>1 {{1},{2,4,6},{3,5},{7}}=>1 {{1,7},{2,4},{3,5,6}}=>3 {{1},{2,4,7},{3,5,6}}=>1 {{1},{2,4},{3,5,6,7}}=>1 {{1},{2,4},{3,5,6},{7}}=>1 {{1,7},{2,4},{3,5},{6}}=>4 {{1},{2,4,7},{3,5},{6}}=>1 {{1},{2,4},{3,5,7},{6}}=>1 {{1},{2,4},{3,5},{6,7}}=>1 {{1},{2,4},{3,5},{6},{7}}=>1 {{1,6,7},{2,4},{3},{5}}=>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}}=>4 {{1,7},{2,4,6},{3},{5}}=>4 {{1},{2,4,6,7},{3},{5}}=>1 {{1},{2,4,6},{3,7},{5}}=>1 {{1},{2,4,6},{3},{5,7}}=>1 {{1},{2,4,6},{3},{5},{7}}=>1 {{1,7},{2,4},{3,6},{5}}=>4 {{1},{2,4,7},{3,6},{5}}=>1 {{1},{2,4},{3,6,7},{5}}=>1 {{1},{2,4},{3,6},{5,7}}=>1 {{1},{2,4},{3,6},{5},{7}}=>1 {{1,7},{2,4},{3},{5,6}}=>4 {{1},{2,4,7},{3},{5,6}}=>1 {{1},{2,4},{3,7},{5,6}}=>1 {{1},{2,4},{3},{5,6,7}}=>1 {{1},{2,4},{3},{5,6},{7}}=>1 {{1,7},{2,4},{3},{5},{6}}=>5 {{1},{2,4,7},{3},{5},{6}}=>1 {{1},{2,4},{3,7},{5},{6}}=>1 {{1},{2,4},{3},{5,7},{6}}=>1 {{1},{2,4},{3},{5},{6,7}}=>1 {{1},{2,4},{3},{5},{6},{7}}=>1 {{1,5,6,7},{2},{3,4}}=>3 {{1,5,6},{2,7},{3,4}}=>3 {{1,5,6},{2},{3,4,7}}=>3 {{1,5,6},{2},{3,4},{7}}=>3 {{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}}=>3 {{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}}=>3 {{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}}=>3 {{1,5},{2},{3,4},{6},{7}}=>3 {{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}}=>3 {{1,7},{2,5,6},{3,4}}=>3 {{1},{2,5,6,7},{3,4}}=>1 {{1},{2,5,6},{3,4,7}}=>1 {{1},{2,5,6},{3,4},{7}}=>1 {{1,7},{2,5},{3,4,6}}=>3 {{1},{2,5,7},{3,4,6}}=>1 {{1},{2,5},{3,4,6,7}}=>1 {{1},{2,5},{3,4,6},{7}}=>1 {{1,7},{2,5},{3,4},{6}}=>4 {{1},{2,5,7},{3,4},{6}}=>1 {{1},{2,5},{3,4,7},{6}}=>1 {{1},{2,5},{3,4},{6,7}}=>1 {{1},{2,5},{3,4},{6},{7}}=>1 {{1,6,7},{2},{3,4,5}}=>3 {{1,6},{2,7},{3,4,5}}=>3 {{1,6},{2},{3,4,5,7}}=>3 {{1,6},{2},{3,4,5},{7}}=>3 {{1,7},{2,6},{3,4,5}}=>3 {{1},{2,6,7},{3,4,5}}=>1 {{1},{2,6},{3,4,5,7}}=>1 {{1},{2,6},{3,4,5},{7}}=>1 {{1,7},{2},{3,4,5,6}}=>3 {{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}}=>4 {{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}}=>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}}=>4 {{1,7},{2,6},{3,4},{5}}=>4 {{1},{2,6,7},{3,4},{5}}=>1 {{1},{2,6},{3,4,7},{5}}=>1 {{1},{2,6},{3,4},{5,7}}=>1 {{1},{2,6},{3,4},{5},{7}}=>1 {{1,7},{2},{3,4,6},{5}}=>4 {{1},{2,7},{3,4,6},{5}}=>1 {{1},{2},{3,4,6,7},{5}}=>1 {{1},{2},{3,4,6},{5,7}}=>1 {{1},{2},{3,4,6},{5},{7}}=>1 {{1,7},{2},{3,4},{5,6}}=>4 {{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}}=>5 {{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}}=>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}}=>4 {{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}}=>4 {{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}}=>4 {{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}}=>4 {{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}}=>4 {{1,5},{2},{3},{4},{6},{7}}=>4 {{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}}=>4 {{1,7},{2,5,6},{3},{4}}=>4 {{1},{2,5,6,7},{3},{4}}=>1 {{1},{2,5,6},{3,7},{4}}=>1 {{1},{2,5,6},{3},{4,7}}=>1 {{1},{2,5,6},{3},{4},{7}}=>1 {{1,7},{2,5},{3,6},{4}}=>4 {{1},{2,5,7},{3,6},{4}}=>1 {{1},{2,5},{3,6,7},{4}}=>1 {{1},{2,5},{3,6},{4,7}}=>1 {{1},{2,5},{3,6},{4},{7}}=>1 {{1,7},{2,5},{3},{4,6}}=>4 {{1},{2,5,7},{3},{4,6}}=>1 {{1},{2,5},{3,7},{4,6}}=>1 {{1},{2,5},{3},{4,6,7}}=>1 {{1},{2,5},{3},{4,6},{7}}=>1 {{1,7},{2,5},{3},{4},{6}}=>5 {{1},{2,5,7},{3},{4},{6}}=>1 {{1},{2,5},{3,7},{4},{6}}=>1 {{1},{2,5},{3},{4,7},{6}}=>1 {{1},{2,5},{3},{4},{6,7}}=>1 {{1},{2,5},{3},{4},{6},{7}}=>1 {{1,6,7},{2},{3,5},{4}}=>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}}=>4 {{1,7},{2,6},{3,5},{4}}=>4 {{1},{2,6,7},{3,5},{4}}=>1 {{1},{2,6},{3,5,7},{4}}=>1 {{1},{2,6},{3,5},{4,7}}=>1 {{1},{2,6},{3,5},{4},{7}}=>1 {{1,7},{2},{3,5,6},{4}}=>4 {{1},{2,7},{3,5,6},{4}}=>1 {{1},{2},{3,5,6,7},{4}}=>1 {{1},{2},{3,5,6},{4,7}}=>1 {{1},{2},{3,5,6},{4},{7}}=>1 {{1,7},{2},{3,5},{4,6}}=>4 {{1},{2,7},{3,5},{4,6}}=>1 {{1},{2},{3,5,7},{4,6}}=>1 {{1},{2},{3,5},{4,6,7}}=>1 {{1},{2},{3,5},{4,6},{7}}=>1 {{1,7},{2},{3,5},{4},{6}}=>5 {{1},{2,7},{3,5},{4},{6}}=>1 {{1},{2},{3,5,7},{4},{6}}=>1 {{1},{2},{3,5},{4,7},{6}}=>1 {{1},{2},{3,5},{4},{6,7}}=>1 {{1},{2},{3,5},{4},{6},{7}}=>1 {{1,6,7},{2},{3},{4,5}}=>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}}=>4 {{1,7},{2,6},{3},{4,5}}=>4 {{1},{2,6,7},{3},{4,5}}=>1 {{1},{2,6},{3,7},{4,5}}=>1 {{1},{2,6},{3},{4,5,7}}=>1 {{1},{2,6},{3},{4,5},{7}}=>1 {{1,7},{2},{3,6},{4,5}}=>4 {{1},{2,7},{3,6},{4,5}}=>1 {{1},{2},{3,6,7},{4,5}}=>1 {{1},{2},{3,6},{4,5,7}}=>1 {{1},{2},{3,6},{4,5},{7}}=>1 {{1,7},{2},{3},{4,5,6}}=>4 {{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}}=>5 {{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}}=>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}}=>5 {{1,7},{2,6},{3},{4},{5}}=>5 {{1},{2,6,7},{3},{4},{5}}=>1 {{1},{2,6},{3,7},{4},{5}}=>1 {{1},{2,6},{3},{4,7},{5}}=>1 {{1},{2,6},{3},{4},{5,7}}=>1 {{1},{2,6},{3},{4},{5},{7}}=>1 {{1,7},{2},{3,6},{4},{5}}=>5 {{1},{2,7},{3,6},{4},{5}}=>1 {{1},{2},{3,6,7},{4},{5}}=>1 {{1},{2},{3,6},{4,7},{5}}=>1 {{1},{2},{3,6},{4},{5,7}}=>1 {{1},{2},{3,6},{4},{5},{7}}=>1 {{1,7},{2},{3},{4,6},{5}}=>5 {{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}}=>1 {{1},{2},{3},{4,6},{5},{7}}=>1 {{1,7},{2},{3},{4},{5,6}}=>5 {{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}}=>6 {{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},{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}}=>3 {{1,3,5,6,7,8},{2},{4}}=>3 {{1,3,4,5,6,7,8},{2}}=>2 {{1,4,5,6,7,8},{2,3}}=>2 {{1,2,4,5,6,7,8},{3}}=>2 {{1,2,5,6,7,8},{3,4}}=>2 {{1,2,3,5,6,7,8},{4}}=>2 {{1,2,3,6,7,8},{4,5}}=>2 {{1,2,3,4,6,7,8},{5}}=>2 {{1,2,3,4,5,6},{7,8}}=>1 {{1,2,3,4,7,8},{5,6}}=>2 {{1,2,3,4,5,7,8},{6}}=>2 {{1,2,3,4,5,6,7},{8}}=>1 {{1,8},{2,3,4,5,6,7}}=>2 {{1,2,3,4,5,8},{6,7}}=>2 {{1,2,3,4,5,6,8},{7}}=>2 {{1,2,3,4,5,6,7,8}}=>1 {{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}}=>2 {{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}}=>2 {{1,7},{2,3,4,5,6,8}}=>2 {{1,2,3,4,6,8},{5,7}}=>2 {{1,2,3,5,6,7},{4,8}}=>2 {{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}}=>2 {{1,4},{2,3,5,6,7,8}}=>2 {{1,2,4,5,6,7},{3,8}}=>2 {{1,3},{2,4,5,6,7,8}}=>2 {{1,5},{2,3,4,6,7,8}}=>2 {{1,6},{2,3,4,5,7,8}}=>2
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Description
The number of blocks in the first part of the atomic decomposition of a set partition.
Let $\pi=(b_1,\dots,b_k)$ be a set partition with $k$ blocks, such that $\min b_i < \min b_{i+1}$. Then this statistic is the smallest number $\ell$ such that the union of the first $\ell$ blocks $b_1\cup\dots\cup b_\ell$ is an interval $\{1,\dots,m\}$.
The analogue for the decomposition of permutations is St000501The size of the first part in the decomposition of a permutation..
References
[1] Bergeron, N., Zabrocki, M. The Hopf algebras of symmetric functions and quasisymmetric functions in non-commutative variables are free and cofree arXiv:math/0509265
Code
def statistic(pi):
    """
    sage: pi = SetPartition([[1,7],[2,3,5],[4],[6,8]])
    sage: statistic(pi)
    4
    sage: pi = SetPartition([[1,2],[3,4,6],[5,7],[8]])
    sage: statistic(pi)
    1
    """
    blocks = sorted(sorted(b) for b in pi)
    u = []
    for i, b in enumerate(blocks, 1):
        u.extend(b)
        if max(u) == len(u):
            return i
Created
Feb 09, 2017 at 22:24 by Martin Rubey
Updated
Feb 09, 2017 at 22:24 by Martin Rubey