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Identifier
Values
=>
Cc0009;cc-rep
{{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}}=>1 {{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}}=>1 {{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}}=>1 {{1,3,4},{2},{5}}=>3 {{1,3,5},{2,4}}=>1 {{1,3},{2,4,5}}=>1 {{1,3},{2,4},{5}}=>2 {{1,3,5},{2},{4}}=>3 {{1,3},{2,5},{4}}=>2 {{1,3},{2},{4,5}}=>3 {{1,3},{2},{4},{5}}=>4 {{1,4,5},{2,3}}=>2 {{1,4},{2,3,5}}=>1 {{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}}=>2 {{1,4},{2},{3,5}}=>2 {{1,4},{2},{3},{5}}=>4 {{1,5},{2,4},{3}}=>3 {{1},{2,4,5},{3}}=>3 {{1},{2,4},{3,5}}=>2 {{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}}=>1 {{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}}=>1 {{1,2,4,5},{3},{6}}=>3 {{1,2,4,6},{3,5}}=>1 {{1,2,4},{3,5,6}}=>1 {{1,2,4},{3,5},{6}}=>2 {{1,2,4,6},{3},{5}}=>3 {{1,2,4},{3,6},{5}}=>2 {{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}}=>1 {{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}}=>2 {{1,2,5},{3},{4,6}}=>2 {{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}}=>2 {{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}}=>1 {{1,3,4,5},{2},{6}}=>3 {{1,3,4,6},{2,5}}=>1 {{1,3,4},{2,5,6}}=>1 {{1,3,4},{2,5},{6}}=>2 {{1,3,4,6},{2},{5}}=>3 {{1,3,4},{2,6},{5}}=>2 {{1,3,4},{2},{5,6}}=>3 {{1,3,4},{2},{5},{6}}=>4 {{1,3,5,6},{2,4}}=>1 {{1,3,5},{2,4,6}}=>1 {{1,3,5},{2,4},{6}}=>2 {{1,3,6},{2,4,5}}=>1 {{1,3},{2,4,5,6}}=>1 {{1,3},{2,4,5},{6}}=>2 {{1,3,6},{2,4},{5}}=>2 {{1,3},{2,4,6},{5}}=>2 {{1,3},{2,4},{5,6}}=>2 {{1,3},{2,4},{5},{6}}=>3 {{1,3,5,6},{2},{4}}=>3 {{1,3,5},{2,6},{4}}=>2 {{1,3,5},{2},{4,6}}=>2 {{1,3,5},{2},{4},{6}}=>4 {{1,3,6},{2,5},{4}}=>2 {{1,3},{2,5,6},{4}}=>2 {{1,3},{2,5},{4,6}}=>1 {{1,3},{2,5},{4},{6}}=>3 {{1,3,6},{2},{4,5}}=>3 {{1,3},{2,6},{4,5}}=>2 {{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}}=>3 {{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}}=>1 {{1,4,5},{2,3},{6}}=>3 {{1,4,6},{2,3,5}}=>1 {{1,4},{2,3,5,6}}=>1 {{1,4},{2,3,5},{6}}=>2 {{1,4,6},{2,3},{5}}=>3 {{1,4},{2,3,6},{5}}=>2 {{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}}=>1 {{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}}=>2 {{1,5},{2,3},{4,6}}=>2 {{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}}=>2 {{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}}=>2 {{1,4,5},{2},{3,6}}=>2 {{1,4,5},{2},{3},{6}}=>4 {{1,4,6},{2,5},{3}}=>2 {{1,4},{2,5,6},{3}}=>2 {{1,4},{2,5},{3,6}}=>1 {{1,4},{2,5},{3},{6}}=>3 {{1,4,6},{2},{3,5}}=>2 {{1,4},{2,6},{3,5}}=>1 {{1,4},{2},{3,5,6}}=>2 {{1,4},{2},{3,5},{6}}=>3 {{1,4,6},{2},{3},{5}}=>4 {{1,4},{2,6},{3},{5}}=>3 {{1,4},{2},{3,6},{5}}=>3 {{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}}=>2 {{1,5},{2,4},{3,6}}=>1 {{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}}=>2 {{1},{2,4,5},{3},{6}}=>4 {{1,6},{2,4},{3,5}}=>2 {{1},{2,4,6},{3,5}}=>2 {{1},{2,4},{3,5,6}}=>2 {{1},{2,4},{3,5},{6}}=>3 {{1,6},{2,4},{3},{5}}=>4 {{1},{2,4,6},{3},{5}}=>4 {{1},{2,4},{3,6},{5}}=>3 {{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}}=>2 {{1,5},{2},{3,4,6}}=>2 {{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}}=>2 {{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}}=>3 {{1,5},{2},{3,6},{4}}=>3 {{1,5},{2},{3},{4,6}}=>3 {{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}}=>3 {{1},{2,5},{3},{4,6}}=>3 {{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}}=>3 {{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}}=>1 {{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}}=>1 {{1,2,3,5,6},{4},{7}}=>3 {{1,2,3,5,7},{4,6}}=>1 {{1,2,3,5},{4,6,7}}=>1 {{1,2,3,5},{4,6},{7}}=>2 {{1,2,3,5,7},{4},{6}}=>3 {{1,2,3,5},{4,7},{6}}=>2 {{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}}=>1 {{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}}=>2 {{1,2,3,6},{4},{5,7}}=>2 {{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}}=>2 {{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}}=>1 {{1,2,4,5,6},{3},{7}}=>3 {{1,2,4,5,7},{3,6}}=>1 {{1,2,4,5},{3,6,7}}=>1 {{1,2,4,5},{3,6},{7}}=>2 {{1,2,4,5,7},{3},{6}}=>3 {{1,2,4,5},{3,7},{6}}=>2 {{1,2,4,5},{3},{6,7}}=>3 {{1,2,4,5},{3},{6},{7}}=>4 {{1,2,4,6,7},{3,5}}=>1 {{1,2,4,6},{3,5,7}}=>1 {{1,2,4,6},{3,5},{7}}=>2 {{1,2,4,7},{3,5,6}}=>1 {{1,2,4},{3,5,6,7}}=>1 {{1,2,4},{3,5,6},{7}}=>2 {{1,2,4,7},{3,5},{6}}=>2 {{1,2,4},{3,5,7},{6}}=>2 {{1,2,4},{3,5},{6,7}}=>2 {{1,2,4},{3,5},{6},{7}}=>3 {{1,2,4,6,7},{3},{5}}=>3 {{1,2,4,6},{3,7},{5}}=>2 {{1,2,4,6},{3},{5,7}}=>2 {{1,2,4,6},{3},{5},{7}}=>4 {{1,2,4,7},{3,6},{5}}=>2 {{1,2,4},{3,6,7},{5}}=>2 {{1,2,4},{3,6},{5,7}}=>1 {{1,2,4},{3,6},{5},{7}}=>3 {{1,2,4,7},{3},{5,6}}=>3 {{1,2,4},{3,7},{5,6}}=>2 {{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}}=>3 {{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}}=>1 {{1,2,5,6},{3,4},{7}}=>3 {{1,2,5,7},{3,4,6}}=>1 {{1,2,5},{3,4,6,7}}=>1 {{1,2,5},{3,4,6},{7}}=>2 {{1,2,5,7},{3,4},{6}}=>3 {{1,2,5},{3,4,7},{6}}=>2 {{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}}=>1 {{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}}=>2 {{1,2,6},{3,4},{5,7}}=>2 {{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}}=>2 {{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}}=>2 {{1,2,5,6},{3},{4,7}}=>2 {{1,2,5,6},{3},{4},{7}}=>4 {{1,2,5,7},{3,6},{4}}=>2 {{1,2,5},{3,6,7},{4}}=>2 {{1,2,5},{3,6},{4,7}}=>1 {{1,2,5},{3,6},{4},{7}}=>3 {{1,2,5,7},{3},{4,6}}=>2 {{1,2,5},{3,7},{4,6}}=>1 {{1,2,5},{3},{4,6,7}}=>2 {{1,2,5},{3},{4,6},{7}}=>3 {{1,2,5,7},{3},{4},{6}}=>4 {{1,2,5},{3,7},{4},{6}}=>3 {{1,2,5},{3},{4,7},{6}}=>3 {{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}}=>2 {{1,2,6},{3,5},{4,7}}=>1 {{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}}=>2 {{1,2},{3,5,6},{4},{7}}=>4 {{1,2,7},{3,5},{4,6}}=>2 {{1,2},{3,5,7},{4,6}}=>2 {{1,2},{3,5},{4,6,7}}=>2 {{1,2},{3,5},{4,6},{7}}=>3 {{1,2,7},{3,5},{4},{6}}=>4 {{1,2},{3,5,7},{4},{6}}=>4 {{1,2},{3,5},{4,7},{6}}=>3 {{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}}=>2 {{1,2,6},{3},{4,5,7}}=>2 {{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}}=>2 {{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}}=>3 {{1,2,6},{3},{4,7},{5}}=>3 {{1,2,6},{3},{4},{5,7}}=>3 {{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}}=>3 {{1,2},{3,6},{4},{5,7}}=>3 {{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}}=>3 {{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}}=>1 {{1,3,4,5,6},{2},{7}}=>3 {{1,3,4,5,7},{2,6}}=>1 {{1,3,4,5},{2,6,7}}=>1 {{1,3,4,5},{2,6},{7}}=>2 {{1,3,4,5,7},{2},{6}}=>3 {{1,3,4,5},{2,7},{6}}=>2 {{1,3,4,5},{2},{6,7}}=>3 {{1,3,4,5},{2},{6},{7}}=>4 {{1,3,4,6,7},{2,5}}=>1 {{1,3,4,6},{2,5,7}}=>1 {{1,3,4,6},{2,5},{7}}=>2 {{1,3,4,7},{2,5,6}}=>1 {{1,3,4},{2,5,6,7}}=>1 {{1,3,4},{2,5,6},{7}}=>2 {{1,3,4,7},{2,5},{6}}=>2 {{1,3,4},{2,5,7},{6}}=>2 {{1,3,4},{2,5},{6,7}}=>2 {{1,3,4},{2,5},{6},{7}}=>3 {{1,3,4,6,7},{2},{5}}=>3 {{1,3,4,6},{2,7},{5}}=>2 {{1,3,4,6},{2},{5,7}}=>2 {{1,3,4,6},{2},{5},{7}}=>4 {{1,3,4,7},{2,6},{5}}=>2 {{1,3,4},{2,6,7},{5}}=>2 {{1,3,4},{2,6},{5,7}}=>1 {{1,3,4},{2,6},{5},{7}}=>3 {{1,3,4,7},{2},{5,6}}=>3 {{1,3,4},{2,7},{5,6}}=>2 {{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}}=>3 {{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}}=>1 {{1,3,5,6},{2,4,7}}=>1 {{1,3,5,6},{2,4},{7}}=>2 {{1,3,5,7},{2,4,6}}=>1 {{1,3,5},{2,4,6,7}}=>1 {{1,3,5},{2,4,6},{7}}=>2 {{1,3,5,7},{2,4},{6}}=>2 {{1,3,5},{2,4,7},{6}}=>2 {{1,3,5},{2,4},{6,7}}=>2 {{1,3,5},{2,4},{6},{7}}=>3 {{1,3,6,7},{2,4,5}}=>1 {{1,3,6},{2,4,5,7}}=>1 {{1,3,6},{2,4,5},{7}}=>2 {{1,3,7},{2,4,5,6}}=>1 {{1,3},{2,4,5,6,7}}=>1 {{1,3},{2,4,5,6},{7}}=>2 {{1,3,7},{2,4,5},{6}}=>2 {{1,3},{2,4,5,7},{6}}=>2 {{1,3},{2,4,5},{6,7}}=>2 {{1,3},{2,4,5},{6},{7}}=>3 {{1,3,6,7},{2,4},{5}}=>2 {{1,3,6},{2,4,7},{5}}=>2 {{1,3,6},{2,4},{5,7}}=>1 {{1,3,6},{2,4},{5},{7}}=>3 {{1,3,7},{2,4,6},{5}}=>2 {{1,3},{2,4,6,7},{5}}=>2 {{1,3},{2,4,6},{5,7}}=>1 {{1,3},{2,4,6},{5},{7}}=>3 {{1,3,7},{2,4},{5,6}}=>2 {{1,3},{2,4,7},{5,6}}=>2 {{1,3},{2,4},{5,6,7}}=>2 {{1,3},{2,4},{5,6},{7}}=>3 {{1,3,7},{2,4},{5},{6}}=>3 {{1,3},{2,4,7},{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 {{1,3,5,6,7},{2},{4}}=>3 {{1,3,5,6},{2,7},{4}}=>2 {{1,3,5,6},{2},{4,7}}=>2 {{1,3,5,6},{2},{4},{7}}=>4 {{1,3,5,7},{2,6},{4}}=>2 {{1,3,5},{2,6,7},{4}}=>2 {{1,3,5},{2,6},{4,7}}=>1 {{1,3,5},{2,6},{4},{7}}=>3 {{1,3,5,7},{2},{4,6}}=>2 {{1,3,5},{2,7},{4,6}}=>1 {{1,3,5},{2},{4,6,7}}=>2 {{1,3,5},{2},{4,6},{7}}=>3 {{1,3,5,7},{2},{4},{6}}=>4 {{1,3,5},{2,7},{4},{6}}=>3 {{1,3,5},{2},{4,7},{6}}=>3 {{1,3,5},{2},{4},{6,7}}=>4 {{1,3,5},{2},{4},{6},{7}}=>5 {{1,3,6,7},{2,5},{4}}=>2 {{1,3,6},{2,5,7},{4}}=>2 {{1,3,6},{2,5},{4,7}}=>1 {{1,3,6},{2,5},{4},{7}}=>3 {{1,3,7},{2,5,6},{4}}=>2 {{1,3},{2,5,6,7},{4}}=>2 {{1,3},{2,5,6},{4,7}}=>1 {{1,3},{2,5,6},{4},{7}}=>3 {{1,3,7},{2,5},{4,6}}=>1 {{1,3},{2,5,7},{4,6}}=>1 {{1,3},{2,5},{4,6,7}}=>1 {{1,3},{2,5},{4,6},{7}}=>2 {{1,3,7},{2,5},{4},{6}}=>3 {{1,3},{2,5,7},{4},{6}}=>3 {{1,3},{2,5},{4,7},{6}}=>2 {{1,3},{2,5},{4},{6,7}}=>3 {{1,3},{2,5},{4},{6},{7}}=>4 {{1,3,6,7},{2},{4,5}}=>3 {{1,3,6},{2,7},{4,5}}=>2 {{1,3,6},{2},{4,5,7}}=>2 {{1,3,6},{2},{4,5},{7}}=>4 {{1,3,7},{2,6},{4,5}}=>2 {{1,3},{2,6,7},{4,5}}=>2 {{1,3},{2,6},{4,5,7}}=>1 {{1,3},{2,6},{4,5},{7}}=>3 {{1,3,7},{2},{4,5,6}}=>3 {{1,3},{2,7},{4,5,6}}=>2 {{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}}=>3 {{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}}=>3 {{1,3,6},{2},{4,7},{5}}=>3 {{1,3,6},{2},{4},{5,7}}=>3 {{1,3,6},{2},{4},{5},{7}}=>5 {{1,3,7},{2,6},{4},{5}}=>3 {{1,3},{2,6,7},{4},{5}}=>3 {{1,3},{2,6},{4,7},{5}}=>2 {{1,3},{2,6},{4},{5,7}}=>2 {{1,3},{2,6},{4},{5},{7}}=>4 {{1,3,7},{2},{4,6},{5}}=>4 {{1,3},{2,7},{4,6},{5}}=>3 {{1,3},{2},{4,6,7},{5}}=>4 {{1,3},{2},{4,6},{5,7}}=>3 {{1,3},{2},{4,6},{5},{7}}=>5 {{1,3,7},{2},{4},{5,6}}=>4 {{1,3},{2,7},{4},{5,6}}=>3 {{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}}=>4 {{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}}=>1 {{1,4,5,6},{2,3},{7}}=>3 {{1,4,5,7},{2,3,6}}=>1 {{1,4,5},{2,3,6,7}}=>1 {{1,4,5},{2,3,6},{7}}=>2 {{1,4,5,7},{2,3},{6}}=>3 {{1,4,5},{2,3,7},{6}}=>2 {{1,4,5},{2,3},{6,7}}=>3 {{1,4,5},{2,3},{6},{7}}=>4 {{1,4,6,7},{2,3,5}}=>1 {{1,4,6},{2,3,5,7}}=>1 {{1,4,6},{2,3,5},{7}}=>2 {{1,4,7},{2,3,5,6}}=>1 {{1,4},{2,3,5,6,7}}=>1 {{1,4},{2,3,5,6},{7}}=>2 {{1,4,7},{2,3,5},{6}}=>2 {{1,4},{2,3,5,7},{6}}=>2 {{1,4},{2,3,5},{6,7}}=>2 {{1,4},{2,3,5},{6},{7}}=>3 {{1,4,6,7},{2,3},{5}}=>3 {{1,4,6},{2,3,7},{5}}=>2 {{1,4,6},{2,3},{5,7}}=>2 {{1,4,6},{2,3},{5},{7}}=>4 {{1,4,7},{2,3,6},{5}}=>2 {{1,4},{2,3,6,7},{5}}=>2 {{1,4},{2,3,6},{5,7}}=>1 {{1,4},{2,3,6},{5},{7}}=>3 {{1,4,7},{2,3},{5,6}}=>3 {{1,4},{2,3,7},{5,6}}=>2 {{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}}=>3 {{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}}=>1 {{1,5,6},{2,3,4},{7}}=>3 {{1,5,7},{2,3,4,6}}=>1 {{1,5},{2,3,4,6,7}}=>1 {{1,5},{2,3,4,6},{7}}=>2 {{1,5,7},{2,3,4},{6}}=>3 {{1,5},{2,3,4,7},{6}}=>2 {{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}}=>1 {{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}}=>2 {{1,6},{2,3,4},{5,7}}=>2 {{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}}=>2 {{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}}=>2 {{1,5,6},{2,3},{4,7}}=>2 {{1,5,6},{2,3},{4},{7}}=>4 {{1,5,7},{2,3,6},{4}}=>2 {{1,5},{2,3,6,7},{4}}=>2 {{1,5},{2,3,6},{4,7}}=>1 {{1,5},{2,3,6},{4},{7}}=>3 {{1,5,7},{2,3},{4,6}}=>2 {{1,5},{2,3,7},{4,6}}=>1 {{1,5},{2,3},{4,6,7}}=>2 {{1,5},{2,3},{4,6},{7}}=>3 {{1,5,7},{2,3},{4},{6}}=>4 {{1,5},{2,3,7},{4},{6}}=>3 {{1,5},{2,3},{4,7},{6}}=>3 {{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}}=>2 {{1,6},{2,3,5},{4,7}}=>1 {{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}}=>2 {{1},{2,3,5,6},{4},{7}}=>4 {{1,7},{2,3,5},{4,6}}=>2 {{1},{2,3,5,7},{4,6}}=>2 {{1},{2,3,5},{4,6,7}}=>2 {{1},{2,3,5},{4,6},{7}}=>3 {{1,7},{2,3,5},{4},{6}}=>4 {{1},{2,3,5,7},{4},{6}}=>4 {{1},{2,3,5},{4,7},{6}}=>3 {{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}}=>2 {{1,6},{2,3},{4,5,7}}=>2 {{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}}=>2 {{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}}=>3 {{1,6},{2,3},{4,7},{5}}=>3 {{1,6},{2,3},{4},{5,7}}=>3 {{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}}=>3 {{1},{2,3,6},{4},{5,7}}=>3 {{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}}=>3 {{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}}=>2 {{1,4,5,6},{2},{3,7}}=>2 {{1,4,5,6},{2},{3},{7}}=>4 {{1,4,5,7},{2,6},{3}}=>2 {{1,4,5},{2,6,7},{3}}=>2 {{1,4,5},{2,6},{3,7}}=>1 {{1,4,5},{2,6},{3},{7}}=>3 {{1,4,5,7},{2},{3,6}}=>2 {{1,4,5},{2,7},{3,6}}=>1 {{1,4,5},{2},{3,6,7}}=>2 {{1,4,5},{2},{3,6},{7}}=>3 {{1,4,5,7},{2},{3},{6}}=>4 {{1,4,5},{2,7},{3},{6}}=>3 {{1,4,5},{2},{3,7},{6}}=>3 {{1,4,5},{2},{3},{6,7}}=>4 {{1,4,5},{2},{3},{6},{7}}=>5 {{1,4,6,7},{2,5},{3}}=>2 {{1,4,6},{2,5,7},{3}}=>2 {{1,4,6},{2,5},{3,7}}=>1 {{1,4,6},{2,5},{3},{7}}=>3 {{1,4,7},{2,5,6},{3}}=>2 {{1,4},{2,5,6,7},{3}}=>2 {{1,4},{2,5,6},{3,7}}=>1 {{1,4},{2,5,6},{3},{7}}=>3 {{1,4,7},{2,5},{3,6}}=>1 {{1,4},{2,5,7},{3,6}}=>1 {{1,4},{2,5},{3,6,7}}=>1 {{1,4},{2,5},{3,6},{7}}=>2 {{1,4,7},{2,5},{3},{6}}=>3 {{1,4},{2,5,7},{3},{6}}=>3 {{1,4},{2,5},{3,7},{6}}=>2 {{1,4},{2,5},{3},{6,7}}=>3 {{1,4},{2,5},{3},{6},{7}}=>4 {{1,4,6,7},{2},{3,5}}=>2 {{1,4,6},{2,7},{3,5}}=>1 {{1,4,6},{2},{3,5,7}}=>2 {{1,4,6},{2},{3,5},{7}}=>3 {{1,4,7},{2,6},{3,5}}=>1 {{1,4},{2,6,7},{3,5}}=>1 {{1,4},{2,6},{3,5,7}}=>1 {{1,4},{2,6},{3,5},{7}}=>2 {{1,4,7},{2},{3,5,6}}=>2 {{1,4},{2,7},{3,5,6}}=>1 {{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},{2,7},{3,5},{6}}=>2 {{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}}=>4 {{1,4,6},{2,7},{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}}=>5 {{1,4,7},{2,6},{3},{5}}=>3 {{1,4},{2,6,7},{3},{5}}=>3 {{1,4},{2,6},{3,7},{5}}=>2 {{1,4},{2,6},{3},{5,7}}=>2 {{1,4},{2,6},{3},{5},{7}}=>4 {{1,4,7},{2},{3,6},{5}}=>3 {{1,4},{2,7},{3,6},{5}}=>2 {{1,4},{2},{3,6,7},{5}}=>3 {{1,4},{2},{3,6},{5,7}}=>2 {{1,4},{2},{3,6},{5},{7}}=>4 {{1,4,7},{2},{3},{5,6}}=>4 {{1,4},{2,7},{3},{5,6}}=>3 {{1,4},{2},{3,7},{5,6}}=>3 {{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}}=>4 {{1,4},{2},{3,7},{5},{6}}=>4 {{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}}=>2 {{1,5,6},{2,4},{3,7}}=>1 {{1,5,6},{2,4},{3},{7}}=>4 {{1,5,7},{2,4,6},{3}}=>2 {{1,5},{2,4,6,7},{3}}=>2 {{1,5},{2,4,6},{3,7}}=>1 {{1,5},{2,4,6},{3},{7}}=>3 {{1,5,7},{2,4},{3,6}}=>1 {{1,5},{2,4,7},{3,6}}=>1 {{1,5},{2,4},{3,6,7}}=>1 {{1,5},{2,4},{3,6},{7}}=>2 {{1,5,7},{2,4},{3},{6}}=>4 {{1,5},{2,4,7},{3},{6}}=>3 {{1,5},{2,4},{3,7},{6}}=>2 {{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}}=>2 {{1,6},{2,4,5},{3,7}}=>1 {{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}}=>2 {{1},{2,4,5,6},{3},{7}}=>4 {{1,7},{2,4,5},{3,6}}=>2 {{1},{2,4,5,7},{3,6}}=>2 {{1},{2,4,5},{3,6,7}}=>2 {{1},{2,4,5},{3,6},{7}}=>3 {{1,7},{2,4,5},{3},{6}}=>4 {{1},{2,4,5,7},{3},{6}}=>4 {{1},{2,4,5},{3,7},{6}}=>3 {{1},{2,4,5},{3},{6,7}}=>4 {{1},{2,4,5},{3},{6},{7}}=>5 {{1,6,7},{2,4},{3,5}}=>2 {{1,6},{2,4,7},{3,5}}=>1 {{1,6},{2,4},{3,5,7}}=>1 {{1,6},{2,4},{3,5},{7}}=>3 {{1,7},{2,4,6},{3,5}}=>2 {{1},{2,4,6,7},{3,5}}=>2 {{1},{2,4,6},{3,5,7}}=>2 {{1},{2,4,6},{3,5},{7}}=>3 {{1,7},{2,4},{3,5,6}}=>2 {{1},{2,4,7},{3,5,6}}=>2 {{1},{2,4},{3,5,6,7}}=>2 {{1},{2,4},{3,5,6},{7}}=>3 {{1,7},{2,4},{3,5},{6}}=>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 {{1,6,7},{2,4},{3},{5}}=>4 {{1,6},{2,4,7},{3},{5}}=>3 {{1,6},{2,4},{3,7},{5}}=>2 {{1,6},{2,4},{3},{5,7}}=>3 {{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}}=>3 {{1},{2,4,6},{3},{5,7}}=>3 {{1},{2,4,6},{3},{5},{7}}=>5 {{1,7},{2,4},{3,6},{5}}=>3 {{1},{2,4,7},{3,6},{5}}=>3 {{1},{2,4},{3,6,7},{5}}=>3 {{1},{2,4},{3,6},{5,7}}=>2 {{1},{2,4},{3,6},{5},{7}}=>4 {{1,7},{2,4},{3},{5,6}}=>4 {{1},{2,4,7},{3},{5,6}}=>4 {{1},{2,4},{3,7},{5,6}}=>3 {{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}}=>4 {{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}}=>2 {{1,5,6},{2},{3,4,7}}=>2 {{1,5,6},{2},{3,4},{7}}=>4 {{1,5,7},{2,6},{3,4}}=>2 {{1,5},{2,6,7},{3,4}}=>2 {{1,5},{2,6},{3,4,7}}=>1 {{1,5},{2,6},{3,4},{7}}=>3 {{1,5,7},{2},{3,4,6}}=>2 {{1,5},{2,7},{3,4,6}}=>1 {{1,5},{2},{3,4,6,7}}=>2 {{1,5},{2},{3,4,6},{7}}=>3 {{1,5,7},{2},{3,4},{6}}=>4 {{1,5},{2,7},{3,4},{6}}=>3 {{1,5},{2},{3,4,7},{6}}=>3 {{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}}=>2 {{1,6},{2,5},{3,4,7}}=>1 {{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}}=>2 {{1},{2,5,6},{3,4},{7}}=>4 {{1,7},{2,5},{3,4,6}}=>2 {{1},{2,5,7},{3,4,6}}=>2 {{1},{2,5},{3,4,6,7}}=>2 {{1},{2,5},{3,4,6},{7}}=>3 {{1,7},{2,5},{3,4},{6}}=>4 {{1},{2,5,7},{3,4},{6}}=>4 {{1},{2,5},{3,4,7},{6}}=>3 {{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}}=>2 {{1,6},{2},{3,4,5,7}}=>2 {{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}}=>2 {{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}}=>3 {{1,6},{2},{3,4,7},{5}}=>3 {{1,6},{2},{3,4},{5,7}}=>3 {{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}}=>3 {{1},{2,6},{3,4},{5,7}}=>3 {{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}}=>3 {{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}}=>3 {{1,5,6},{2},{3,7},{4}}=>3 {{1,5,6},{2},{3},{4,7}}=>3 {{1,5,6},{2},{3},{4},{7}}=>5 {{1,5,7},{2,6},{3},{4}}=>3 {{1,5},{2,6,7},{3},{4}}=>3 {{1,5},{2,6},{3,7},{4}}=>2 {{1,5},{2,6},{3},{4,7}}=>2 {{1,5},{2,6},{3},{4},{7}}=>4 {{1,5,7},{2},{3,6},{4}}=>3 {{1,5},{2,7},{3,6},{4}}=>2 {{1,5},{2},{3,6,7},{4}}=>3 {{1,5},{2},{3,6},{4,7}}=>2 {{1,5},{2},{3,6},{4},{7}}=>4 {{1,5,7},{2},{3},{4,6}}=>3 {{1,5},{2,7},{3},{4,6}}=>2 {{1,5},{2},{3,7},{4,6}}=>2 {{1,5},{2},{3},{4,6,7}}=>3 {{1,5},{2},{3},{4,6},{7}}=>4 {{1,5,7},{2},{3},{4},{6}}=>5 {{1,5},{2,7},{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}}=>5 {{1,5},{2},{3},{4},{6},{7}}=>6 {{1,6,7},{2,5},{3},{4}}=>4 {{1,6},{2,5,7},{3},{4}}=>3 {{1,6},{2,5},{3,7},{4}}=>2 {{1,6},{2,5},{3},{4,7}}=>2 {{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}}=>3 {{1},{2,5,6},{3},{4,7}}=>3 {{1},{2,5,6},{3},{4},{7}}=>5 {{1,7},{2,5},{3,6},{4}}=>3 {{1},{2,5,7},{3,6},{4}}=>3 {{1},{2,5},{3,6,7},{4}}=>3 {{1},{2,5},{3,6},{4,7}}=>2 {{1},{2,5},{3,6},{4},{7}}=>4 {{1,7},{2,5},{3},{4,6}}=>3 {{1},{2,5,7},{3},{4,6}}=>3 {{1},{2,5},{3,7},{4,6}}=>2 {{1},{2,5},{3},{4,6,7}}=>3 {{1},{2,5},{3},{4,6},{7}}=>4 {{1,7},{2,5},{3},{4},{6}}=>5 {{1},{2,5,7},{3},{4},{6}}=>5 {{1},{2,5},{3,7},{4},{6}}=>4 {{1},{2,5},{3},{4,7},{6}}=>4 {{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}}=>3 {{1,6},{2},{3,5,7},{4}}=>3 {{1,6},{2},{3,5},{4,7}}=>2 {{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}}=>3 {{1},{2,6},{3,5},{4,7}}=>2 {{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}}=>3 {{1},{2},{3,5,6},{4},{7}}=>5 {{1,7},{2},{3,5},{4,6}}=>3 {{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 {{1,7},{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}}=>4 {{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}}=>3 {{1,6},{2},{3,7},{4,5}}=>3 {{1,6},{2},{3},{4,5,7}}=>3 {{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}}=>3 {{1},{2,6},{3},{4,5,7}}=>3 {{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}}=>3 {{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}}=>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}}=>6 {{1,7},{2,6},{3},{4},{5}}=>5 {{1},{2,6,7},{3},{4},{5}}=>5 {{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}}=>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}}=>4 {{1},{2},{3,6},{4},{5,7}}=>4 {{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}}=>4 {{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 {{1},{2},{3,4,5,6,7,8}}=>3 {{1},{2,4,5,6,7,8},{3}}=>3 {{1},{2,3,5,6,7,8},{4}}=>3 {{1},{2,3,4,6,7,8},{5}}=>3 {{1},{2,3,4,5,7,8},{6}}=>3 {{1},{2,3,4,5,6,7},{8}}=>3 {{1},{2,3,4,5,6,8},{7}}=>3 {{1},{2,3,4,5,6,7,8}}=>2 {{1,2},{3,4,5,6,7,8}}=>2 {{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}}=>2 {{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}}=>2 {{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 {{1,3,5,6,7,8},{2,4}}=>1 {{1,3,4,6,7,8},{2,5}}=>1 {{1,2,4,6,7,8},{3,5}}=>1 {{1,3,4,5,7,8},{2,6}}=>1 {{1,2,4,5,7,8},{3,6}}=>1 {{1,2,3,5,7,8},{4,6}}=>1 {{1,3,4,5,6,8},{2,7}}=>1 {{1,2,4,5,6,8},{3,7}}=>1 {{1,2,3,5,6,8},{4,7}}=>1 {{1,2,3,4,6,8},{5,7}}=>1 {{1,3,4,5,6,7},{2,8}}=>1 {{1,2,4,5,6,7},{3,8}}=>1 {{1,2,3,5,6,7},{4,8}}=>1 {{1,2,3,4,6,7},{5,8}}=>1 {{1,2,3,4,5,7},{6,8}}=>1 {{1,3},{2,4,5,6,7,8}}=>1 {{1,4},{2,3,5,6,7,8}}=>1 {{1,5},{2,3,4,6,7,8}}=>1 {{1,6},{2,3,4,5,7,8}}=>1 {{1,7},{2,3,4,5,6,8}}=>1
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Description
The number of topologically connected components of a set partition.
For example, the set partition $\{\{1,5\},\{2,3\},\{4,6\}\}$ has the two connected components $\{1,4,5,6\}$ and $\{2,3\}$.
The number of set partitions with only one block is oeis:A099947.
Code
def statistic(M):
    """The number of topologically connected components of the arc
    diagram of a set partition."""

    C = dict()
    for b in M:
        for i in b:
            C[i] = frozenset(b)

    for (i1,j1), (i2,j2) in Subsets(M.arcs(), 2):
        if i1 < i2 < j1 < j2 or i2 < i1 < j2 < j1:
            if C[i1] != C[i2]:
                C[i1] = C[i1].union(C[i2])
                for a in C[i1]:
                    C[a] = C[i1]

    return len(set(c for c in C.values()))
Created
Aug 03, 2017 at 09:48 by Martin Rubey
Updated
Aug 03, 2017 at 15:05 by Martin Rubey