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Identifier
Values
=>
Cc0009;cc-rep
{{1}}=>0 {{1,2}}=>1 {{1},{2}}=>1 {{1,2,3}}=>2 {{1,2},{3}}=>2 {{1,3},{2}}=>0 {{1},{2,3}}=>2 {{1},{2},{3}}=>2 {{1,2,3,4}}=>3 {{1,2,3},{4}}=>3 {{1,2,4},{3}}=>1 {{1,2},{3,4}}=>3 {{1,2},{3},{4}}=>3 {{1,3,4},{2}}=>0 {{1,3},{2,4}}=>1 {{1,3},{2},{4}}=>1 {{1,4},{2,3}}=>1 {{1},{2,3,4}}=>3 {{1},{2,3},{4}}=>3 {{1,4},{2},{3}}=>1 {{1},{2,4},{3}}=>1 {{1},{2},{3,4}}=>3 {{1},{2},{3},{4}}=>3 {{1,2,3,4,5}}=>4 {{1,2,3,4},{5}}=>4 {{1,2,3,5},{4}}=>2 {{1,2,3},{4,5}}=>4 {{1,2,3},{4},{5}}=>4 {{1,2,4,5},{3}}=>1 {{1,2,4},{3,5}}=>2 {{1,2,4},{3},{5}}=>2 {{1,2,5},{3,4}}=>2 {{1,2},{3,4,5}}=>4 {{1,2},{3,4},{5}}=>4 {{1,2,5},{3},{4}}=>2 {{1,2},{3,5},{4}}=>2 {{1,2},{3},{4,5}}=>4 {{1,2},{3},{4},{5}}=>4 {{1,3,4,5},{2}}=>0 {{1,3,4},{2,5}}=>1 {{1,3,4},{2},{5}}=>1 {{1,3,5},{2,4}}=>1 {{1,3},{2,4,5}}=>2 {{1,3},{2,4},{5}}=>2 {{1,3,5},{2},{4}}=>1 {{1,3},{2,5},{4}}=>0 {{1,3},{2},{4,5}}=>2 {{1,3},{2},{4},{5}}=>2 {{1,4,5},{2,3}}=>1 {{1,4},{2,3,5}}=>2 {{1,4},{2,3},{5}}=>2 {{1,5},{2,3,4}}=>2 {{1},{2,3,4,5}}=>4 {{1},{2,3,4},{5}}=>4 {{1,5},{2,3},{4}}=>2 {{1},{2,3,5},{4}}=>2 {{1},{2,3},{4,5}}=>4 {{1},{2,3},{4},{5}}=>4 {{1,4,5},{2},{3}}=>1 {{1,4},{2,5},{3}}=>0 {{1,4},{2},{3,5}}=>2 {{1,4},{2},{3},{5}}=>2 {{1,5},{2,4},{3}}=>0 {{1},{2,4,5},{3}}=>1 {{1},{2,4},{3,5}}=>2 {{1},{2,4},{3},{5}}=>2 {{1,5},{2},{3,4}}=>2 {{1},{2,5},{3,4}}=>2 {{1},{2},{3,4,5}}=>4 {{1},{2},{3,4},{5}}=>4 {{1,5},{2},{3},{4}}=>2 {{1},{2,5},{3},{4}}=>2 {{1},{2},{3,5},{4}}=>2 {{1},{2},{3},{4,5}}=>4 {{1},{2},{3},{4},{5}}=>4 {{1,2,3,4,5,6}}=>5 {{1,2,3,4,5},{6}}=>5 {{1,2,3,4,6},{5}}=>3 {{1,2,3,4},{5,6}}=>5 {{1,2,3,4},{5},{6}}=>5 {{1,2,3,5,6},{4}}=>2 {{1,2,3,5},{4,6}}=>3 {{1,2,3,5},{4},{6}}=>3 {{1,2,3,6},{4,5}}=>3 {{1,2,3},{4,5,6}}=>5 {{1,2,3},{4,5},{6}}=>5 {{1,2,3,6},{4},{5}}=>3 {{1,2,3},{4,6},{5}}=>3 {{1,2,3},{4},{5,6}}=>5 {{1,2,3},{4},{5},{6}}=>5 {{1,2,4,5,6},{3}}=>1 {{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}}=>3 {{1,2,4},{3,5},{6}}=>3 {{1,2,4,6},{3},{5}}=>2 {{1,2,4},{3,6},{5}}=>1 {{1,2,4},{3},{5,6}}=>3 {{1,2,4},{3},{5},{6}}=>3 {{1,2,5,6},{3,4}}=>2 {{1,2,5},{3,4,6}}=>3 {{1,2,5},{3,4},{6}}=>3 {{1,2,6},{3,4,5}}=>3 {{1,2},{3,4,5,6}}=>5 {{1,2},{3,4,5},{6}}=>5 {{1,2,6},{3,4},{5}}=>3 {{1,2},{3,4,6},{5}}=>3 {{1,2},{3,4},{5,6}}=>5 {{1,2},{3,4},{5},{6}}=>5 {{1,2,5,6},{3},{4}}=>2 {{1,2,5},{3,6},{4}}=>1 {{1,2,5},{3},{4,6}}=>3 {{1,2,5},{3},{4},{6}}=>3 {{1,2,6},{3,5},{4}}=>1 {{1,2},{3,5,6},{4}}=>2 {{1,2},{3,5},{4,6}}=>3 {{1,2},{3,5},{4},{6}}=>3 {{1,2,6},{3},{4,5}}=>3 {{1,2},{3,6},{4,5}}=>3 {{1,2},{3},{4,5,6}}=>5 {{1,2},{3},{4,5},{6}}=>5 {{1,2,6},{3},{4},{5}}=>3 {{1,2},{3,6},{4},{5}}=>3 {{1,2},{3},{4,6},{5}}=>3 {{1,2},{3},{4},{5,6}}=>5 {{1,2},{3},{4},{5},{6}}=>5 {{1,3,4,5,6},{2}}=>0 {{1,3,4,5},{2,6}}=>1 {{1,3,4,5},{2},{6}}=>1 {{1,3,4,6},{2,5}}=>1 {{1,3,4},{2,5,6}}=>2 {{1,3,4},{2,5},{6}}=>2 {{1,3,4,6},{2},{5}}=>1 {{1,3,4},{2,6},{5}}=>0 {{1,3,4},{2},{5,6}}=>2 {{1,3,4},{2},{5},{6}}=>2 {{1,3,5,6},{2,4}}=>1 {{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}}=>3 {{1,3},{2,4,5},{6}}=>3 {{1,3,6},{2,4},{5}}=>2 {{1,3},{2,4,6},{5}}=>1 {{1,3},{2,4},{5,6}}=>3 {{1,3},{2,4},{5},{6}}=>3 {{1,3,5,6},{2},{4}}=>1 {{1,3,5},{2,6},{4}}=>0 {{1,3,5},{2},{4,6}}=>2 {{1,3,5},{2},{4},{6}}=>2 {{1,3,6},{2,5},{4}}=>0 {{1,3},{2,5,6},{4}}=>0 {{1,3},{2,5},{4,6}}=>1 {{1,3},{2,5},{4},{6}}=>1 {{1,3,6},{2},{4,5}}=>2 {{1,3},{2,6},{4,5}}=>1 {{1,3},{2},{4,5,6}}=>3 {{1,3},{2},{4,5},{6}}=>3 {{1,3,6},{2},{4},{5}}=>2 {{1,3},{2,6},{4},{5}}=>1 {{1,3},{2},{4,6},{5}}=>1 {{1,3},{2},{4},{5,6}}=>3 {{1,3},{2},{4},{5},{6}}=>3 {{1,4,5,6},{2,3}}=>1 {{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}}=>3 {{1,4},{2,3,5},{6}}=>3 {{1,4,6},{2,3},{5}}=>2 {{1,4},{2,3,6},{5}}=>1 {{1,4},{2,3},{5,6}}=>3 {{1,4},{2,3},{5},{6}}=>3 {{1,5,6},{2,3,4}}=>2 {{1,5},{2,3,4,6}}=>3 {{1,5},{2,3,4},{6}}=>3 {{1,6},{2,3,4,5}}=>3 {{1},{2,3,4,5,6}}=>5 {{1},{2,3,4,5},{6}}=>5 {{1,6},{2,3,4},{5}}=>3 {{1},{2,3,4,6},{5}}=>3 {{1},{2,3,4},{5,6}}=>5 {{1},{2,3,4},{5},{6}}=>5 {{1,5,6},{2,3},{4}}=>2 {{1,5},{2,3,6},{4}}=>1 {{1,5},{2,3},{4,6}}=>3 {{1,5},{2,3},{4},{6}}=>3 {{1,6},{2,3,5},{4}}=>1 {{1},{2,3,5,6},{4}}=>2 {{1},{2,3,5},{4,6}}=>3 {{1},{2,3,5},{4},{6}}=>3 {{1,6},{2,3},{4,5}}=>3 {{1},{2,3,6},{4,5}}=>3 {{1},{2,3},{4,5,6}}=>5 {{1},{2,3},{4,5},{6}}=>5 {{1,6},{2,3},{4},{5}}=>3 {{1},{2,3,6},{4},{5}}=>3 {{1},{2,3},{4,6},{5}}=>3 {{1},{2,3},{4},{5,6}}=>5 {{1},{2,3},{4},{5},{6}}=>5 {{1,4,5,6},{2},{3}}=>1 {{1,4,5},{2,6},{3}}=>0 {{1,4,5},{2},{3,6}}=>2 {{1,4,5},{2},{3},{6}}=>2 {{1,4,6},{2,5},{3}}=>0 {{1,4},{2,5,6},{3}}=>0 {{1,4},{2,5},{3,6}}=>1 {{1,4},{2,5},{3},{6}}=>1 {{1,4,6},{2},{3,5}}=>2 {{1,4},{2,6},{3,5}}=>1 {{1,4},{2},{3,5,6}}=>3 {{1,4},{2},{3,5},{6}}=>3 {{1,4,6},{2},{3},{5}}=>2 {{1,4},{2,6},{3},{5}}=>1 {{1,4},{2},{3,6},{5}}=>1 {{1,4},{2},{3},{5,6}}=>3 {{1,4},{2},{3},{5},{6}}=>3 {{1,5,6},{2,4},{3}}=>0 {{1,5},{2,4,6},{3}}=>0 {{1,5},{2,4},{3,6}}=>1 {{1,5},{2,4},{3},{6}}=>1 {{1,6},{2,4,5},{3}}=>0 {{1},{2,4,5,6},{3}}=>1 {{1},{2,4,5},{3,6}}=>2 {{1},{2,4,5},{3},{6}}=>2 {{1,6},{2,4},{3,5}}=>1 {{1},{2,4,6},{3,5}}=>2 {{1},{2,4},{3,5,6}}=>3 {{1},{2,4},{3,5},{6}}=>3 {{1,6},{2,4},{3},{5}}=>1 {{1},{2,4,6},{3},{5}}=>2 {{1},{2,4},{3,6},{5}}=>1 {{1},{2,4},{3},{5,6}}=>3 {{1},{2,4},{3},{5},{6}}=>3 {{1,5,6},{2},{3,4}}=>2 {{1,5},{2,6},{3,4}}=>1 {{1,5},{2},{3,4,6}}=>3 {{1,5},{2},{3,4},{6}}=>3 {{1,6},{2,5},{3,4}}=>1 {{1},{2,5,6},{3,4}}=>2 {{1},{2,5},{3,4,6}}=>3 {{1},{2,5},{3,4},{6}}=>3 {{1,6},{2},{3,4,5}}=>3 {{1},{2,6},{3,4,5}}=>3 {{1},{2},{3,4,5,6}}=>5 {{1},{2},{3,4,5},{6}}=>5 {{1,6},{2},{3,4},{5}}=>3 {{1},{2,6},{3,4},{5}}=>3 {{1},{2},{3,4,6},{5}}=>3 {{1},{2},{3,4},{5,6}}=>5 {{1},{2},{3,4},{5},{6}}=>5 {{1,5,6},{2},{3},{4}}=>2 {{1,5},{2,6},{3},{4}}=>1 {{1,5},{2},{3,6},{4}}=>1 {{1,5},{2},{3},{4,6}}=>3 {{1,5},{2},{3},{4},{6}}=>3 {{1,6},{2,5},{3},{4}}=>1 {{1},{2,5,6},{3},{4}}=>2 {{1},{2,5},{3,6},{4}}=>1 {{1},{2,5},{3},{4,6}}=>3 {{1},{2,5},{3},{4},{6}}=>3 {{1,6},{2},{3,5},{4}}=>1 {{1},{2,6},{3,5},{4}}=>1 {{1},{2},{3,5,6},{4}}=>2 {{1},{2},{3,5},{4,6}}=>3 {{1},{2},{3,5},{4},{6}}=>3 {{1,6},{2},{3},{4,5}}=>3 {{1},{2,6},{3},{4,5}}=>3 {{1},{2},{3,6},{4,5}}=>3 {{1},{2},{3},{4,5,6}}=>5 {{1},{2},{3},{4,5},{6}}=>5 {{1,6},{2},{3},{4},{5}}=>3 {{1},{2,6},{3},{4},{5}}=>3 {{1},{2},{3,6},{4},{5}}=>3 {{1},{2},{3},{4,6},{5}}=>3 {{1},{2},{3},{4},{5,6}}=>5 {{1},{2},{3},{4},{5},{6}}=>5 {{1,2,3,4,5,6,7}}=>6 {{1,2,3,4,5,6},{7}}=>6 {{1,2,3,4,5,7},{6}}=>4 {{1,2,3,4,5},{6,7}}=>6 {{1,2,3,4,5},{6},{7}}=>6 {{1,2,3,4,6,7},{5}}=>3 {{1,2,3,4,6},{5,7}}=>4 {{1,2,3,4,6},{5},{7}}=>4 {{1,2,3,4,7},{5,6}}=>4 {{1,2,3,4},{5,6,7}}=>6 {{1,2,3,4},{5,6},{7}}=>6 {{1,2,3,4,7},{5},{6}}=>4 {{1,2,3,4},{5,7},{6}}=>4 {{1,2,3,4},{5},{6,7}}=>6 {{1,2,3,4},{5},{6},{7}}=>6 {{1,2,3,5,6,7},{4}}=>2 {{1,2,3,5,6},{4,7}}=>3 {{1,2,3,5,6},{4},{7}}=>3 {{1,2,3,5,7},{4,6}}=>3 {{1,2,3,5},{4,6,7}}=>4 {{1,2,3,5},{4,6},{7}}=>4 {{1,2,3,5,7},{4},{6}}=>3 {{1,2,3,5},{4,7},{6}}=>2 {{1,2,3,5},{4},{6,7}}=>4 {{1,2,3,5},{4},{6},{7}}=>4 {{1,2,3,6,7},{4,5}}=>3 {{1,2,3,6},{4,5,7}}=>4 {{1,2,3,6},{4,5},{7}}=>4 {{1,2,3,7},{4,5,6}}=>4 {{1,2,3},{4,5,6,7}}=>6 {{1,2,3},{4,5,6},{7}}=>6 {{1,2,3,7},{4,5},{6}}=>4 {{1,2,3},{4,5,7},{6}}=>4 {{1,2,3},{4,5},{6,7}}=>6 {{1,2,3},{4,5},{6},{7}}=>6 {{1,2,3,6,7},{4},{5}}=>3 {{1,2,3,6},{4,7},{5}}=>2 {{1,2,3,6},{4},{5,7}}=>4 {{1,2,3,6},{4},{5},{7}}=>4 {{1,2,3,7},{4,6},{5}}=>2 {{1,2,3},{4,6,7},{5}}=>3 {{1,2,3},{4,6},{5,7}}=>4 {{1,2,3},{4,6},{5},{7}}=>4 {{1,2,3,7},{4},{5,6}}=>4 {{1,2,3},{4,7},{5,6}}=>4 {{1,2,3},{4},{5,6,7}}=>6 {{1,2,3},{4},{5,6},{7}}=>6 {{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}}=>6 {{1,2,3},{4},{5},{6},{7}}=>6 {{1,2,4,5,6,7},{3}}=>1 {{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}}=>3 {{1,2,4,5},{3,6},{7}}=>3 {{1,2,4,5,7},{3},{6}}=>2 {{1,2,4,5},{3,7},{6}}=>1 {{1,2,4,5},{3},{6,7}}=>3 {{1,2,4,5},{3},{6},{7}}=>3 {{1,2,4,6,7},{3,5}}=>2 {{1,2,4,6},{3,5,7}}=>3 {{1,2,4,6},{3,5},{7}}=>3 {{1,2,4,7},{3,5,6}}=>3 {{1,2,4},{3,5,6,7}}=>4 {{1,2,4},{3,5,6},{7}}=>4 {{1,2,4,7},{3,5},{6}}=>3 {{1,2,4},{3,5,7},{6}}=>2 {{1,2,4},{3,5},{6,7}}=>4 {{1,2,4},{3,5},{6},{7}}=>4 {{1,2,4,6,7},{3},{5}}=>2 {{1,2,4,6},{3,7},{5}}=>1 {{1,2,4,6},{3},{5,7}}=>3 {{1,2,4,6},{3},{5},{7}}=>3 {{1,2,4,7},{3,6},{5}}=>1 {{1,2,4},{3,6,7},{5}}=>1 {{1,2,4},{3,6},{5,7}}=>2 {{1,2,4},{3,6},{5},{7}}=>2 {{1,2,4,7},{3},{5,6}}=>3 {{1,2,4},{3,7},{5,6}}=>2 {{1,2,4},{3},{5,6,7}}=>4 {{1,2,4},{3},{5,6},{7}}=>4 {{1,2,4,7},{3},{5},{6}}=>3 {{1,2,4},{3,7},{5},{6}}=>2 {{1,2,4},{3},{5,7},{6}}=>2 {{1,2,4},{3},{5},{6,7}}=>4 {{1,2,4},{3},{5},{6},{7}}=>4 {{1,2,5,6,7},{3,4}}=>2 {{1,2,5,6},{3,4,7}}=>3 {{1,2,5,6},{3,4},{7}}=>3 {{1,2,5,7},{3,4,6}}=>3 {{1,2,5},{3,4,6,7}}=>4 {{1,2,5},{3,4,6},{7}}=>4 {{1,2,5,7},{3,4},{6}}=>3 {{1,2,5},{3,4,7},{6}}=>2 {{1,2,5},{3,4},{6,7}}=>4 {{1,2,5},{3,4},{6},{7}}=>4 {{1,2,6,7},{3,4,5}}=>3 {{1,2,6},{3,4,5,7}}=>4 {{1,2,6},{3,4,5},{7}}=>4 {{1,2,7},{3,4,5,6}}=>4 {{1,2},{3,4,5,6,7}}=>6 {{1,2},{3,4,5,6},{7}}=>6 {{1,2,7},{3,4,5},{6}}=>4 {{1,2},{3,4,5,7},{6}}=>4 {{1,2},{3,4,5},{6,7}}=>6 {{1,2},{3,4,5},{6},{7}}=>6 {{1,2,6,7},{3,4},{5}}=>3 {{1,2,6},{3,4,7},{5}}=>2 {{1,2,6},{3,4},{5,7}}=>4 {{1,2,6},{3,4},{5},{7}}=>4 {{1,2,7},{3,4,6},{5}}=>2 {{1,2},{3,4,6,7},{5}}=>3 {{1,2},{3,4,6},{5,7}}=>4 {{1,2},{3,4,6},{5},{7}}=>4 {{1,2,7},{3,4},{5,6}}=>4 {{1,2},{3,4,7},{5,6}}=>4 {{1,2},{3,4},{5,6,7}}=>6 {{1,2},{3,4},{5,6},{7}}=>6 {{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}}=>6 {{1,2},{3,4},{5},{6},{7}}=>6 {{1,2,5,6,7},{3},{4}}=>2 {{1,2,5,6},{3,7},{4}}=>1 {{1,2,5,6},{3},{4,7}}=>3 {{1,2,5,6},{3},{4},{7}}=>3 {{1,2,5,7},{3,6},{4}}=>1 {{1,2,5},{3,6,7},{4}}=>1 {{1,2,5},{3,6},{4,7}}=>2 {{1,2,5},{3,6},{4},{7}}=>2 {{1,2,5,7},{3},{4,6}}=>3 {{1,2,5},{3,7},{4,6}}=>2 {{1,2,5},{3},{4,6,7}}=>4 {{1,2,5},{3},{4,6},{7}}=>4 {{1,2,5,7},{3},{4},{6}}=>3 {{1,2,5},{3,7},{4},{6}}=>2 {{1,2,5},{3},{4,7},{6}}=>2 {{1,2,5},{3},{4},{6,7}}=>4 {{1,2,5},{3},{4},{6},{7}}=>4 {{1,2,6,7},{3,5},{4}}=>1 {{1,2,6},{3,5,7},{4}}=>1 {{1,2,6},{3,5},{4,7}}=>2 {{1,2,6},{3,5},{4},{7}}=>2 {{1,2,7},{3,5,6},{4}}=>1 {{1,2},{3,5,6,7},{4}}=>2 {{1,2},{3,5,6},{4,7}}=>3 {{1,2},{3,5,6},{4},{7}}=>3 {{1,2,7},{3,5},{4,6}}=>2 {{1,2},{3,5,7},{4,6}}=>3 {{1,2},{3,5},{4,6,7}}=>4 {{1,2},{3,5},{4,6},{7}}=>4 {{1,2,7},{3,5},{4},{6}}=>2 {{1,2},{3,5,7},{4},{6}}=>3 {{1,2},{3,5},{4,7},{6}}=>2 {{1,2},{3,5},{4},{6,7}}=>4 {{1,2},{3,5},{4},{6},{7}}=>4 {{1,2,6,7},{3},{4,5}}=>3 {{1,2,6},{3,7},{4,5}}=>2 {{1,2,6},{3},{4,5,7}}=>4 {{1,2,6},{3},{4,5},{7}}=>4 {{1,2,7},{3,6},{4,5}}=>2 {{1,2},{3,6,7},{4,5}}=>3 {{1,2},{3,6},{4,5,7}}=>4 {{1,2},{3,6},{4,5},{7}}=>4 {{1,2,7},{3},{4,5,6}}=>4 {{1,2},{3,7},{4,5,6}}=>4 {{1,2},{3},{4,5,6,7}}=>6 {{1,2},{3},{4,5,6},{7}}=>6 {{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}}=>6 {{1,2},{3},{4,5},{6},{7}}=>6 {{1,2,6,7},{3},{4},{5}}=>3 {{1,2,6},{3,7},{4},{5}}=>2 {{1,2,6},{3},{4,7},{5}}=>2 {{1,2,6},{3},{4},{5,7}}=>4 {{1,2,6},{3},{4},{5},{7}}=>4 {{1,2,7},{3,6},{4},{5}}=>2 {{1,2},{3,6,7},{4},{5}}=>3 {{1,2},{3,6},{4,7},{5}}=>2 {{1,2},{3,6},{4},{5,7}}=>4 {{1,2},{3,6},{4},{5},{7}}=>4 {{1,2,7},{3},{4,6},{5}}=>2 {{1,2},{3,7},{4,6},{5}}=>2 {{1,2},{3},{4,6,7},{5}}=>3 {{1,2},{3},{4,6},{5,7}}=>4 {{1,2},{3},{4,6},{5},{7}}=>4 {{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}}=>6 {{1,2},{3},{4},{5,6},{7}}=>6 {{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},{5,7},{6}}=>4 {{1,2},{3},{4},{5},{6,7}}=>6 {{1,2},{3},{4},{5},{6},{7}}=>6 {{1,3,4,5,6,7},{2}}=>0 {{1,3,4,5,6},{2,7}}=>1 {{1,3,4,5,6},{2},{7}}=>1 {{1,3,4,5,7},{2,6}}=>1 {{1,3,4,5},{2,6,7}}=>2 {{1,3,4,5},{2,6},{7}}=>2 {{1,3,4,5,7},{2},{6}}=>1 {{1,3,4,5},{2,7},{6}}=>0 {{1,3,4,5},{2},{6,7}}=>2 {{1,3,4,5},{2},{6},{7}}=>2 {{1,3,4,6,7},{2,5}}=>1 {{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}}=>3 {{1,3,4},{2,5,6},{7}}=>3 {{1,3,4,7},{2,5},{6}}=>2 {{1,3,4},{2,5,7},{6}}=>1 {{1,3,4},{2,5},{6,7}}=>3 {{1,3,4},{2,5},{6},{7}}=>3 {{1,3,4,6,7},{2},{5}}=>1 {{1,3,4,6},{2,7},{5}}=>0 {{1,3,4,6},{2},{5,7}}=>2 {{1,3,4,6},{2},{5},{7}}=>2 {{1,3,4,7},{2,6},{5}}=>0 {{1,3,4},{2,6,7},{5}}=>0 {{1,3,4},{2,6},{5,7}}=>1 {{1,3,4},{2,6},{5},{7}}=>1 {{1,3,4,7},{2},{5,6}}=>2 {{1,3,4},{2,7},{5,6}}=>1 {{1,3,4},{2},{5,6,7}}=>3 {{1,3,4},{2},{5,6},{7}}=>3 {{1,3,4,7},{2},{5},{6}}=>2 {{1,3,4},{2,7},{5},{6}}=>1 {{1,3,4},{2},{5,7},{6}}=>1 {{1,3,4},{2},{5},{6,7}}=>3 {{1,3,4},{2},{5},{6},{7}}=>3 {{1,3,5,6,7},{2,4}}=>1 {{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}}=>3 {{1,3,5},{2,4,6},{7}}=>3 {{1,3,5,7},{2,4},{6}}=>2 {{1,3,5},{2,4,7},{6}}=>1 {{1,3,5},{2,4},{6,7}}=>3 {{1,3,5},{2,4},{6},{7}}=>3 {{1,3,6,7},{2,4,5}}=>2 {{1,3,6},{2,4,5,7}}=>3 {{1,3,6},{2,4,5},{7}}=>3 {{1,3,7},{2,4,5,6}}=>3 {{1,3},{2,4,5,6,7}}=>4 {{1,3},{2,4,5,6},{7}}=>4 {{1,3,7},{2,4,5},{6}}=>3 {{1,3},{2,4,5,7},{6}}=>2 {{1,3},{2,4,5},{6,7}}=>4 {{1,3},{2,4,5},{6},{7}}=>4 {{1,3,6,7},{2,4},{5}}=>2 {{1,3,6},{2,4,7},{5}}=>1 {{1,3,6},{2,4},{5,7}}=>3 {{1,3,6},{2,4},{5},{7}}=>3 {{1,3,7},{2,4,6},{5}}=>1 {{1,3},{2,4,6,7},{5}}=>1 {{1,3},{2,4,6},{5,7}}=>2 {{1,3},{2,4,6},{5},{7}}=>2 {{1,3,7},{2,4},{5,6}}=>3 {{1,3},{2,4,7},{5,6}}=>2 {{1,3},{2,4},{5,6,7}}=>4 {{1,3},{2,4},{5,6},{7}}=>4 {{1,3,7},{2,4},{5},{6}}=>3 {{1,3},{2,4,7},{5},{6}}=>2 {{1,3},{2,4},{5,7},{6}}=>2 {{1,3},{2,4},{5},{6,7}}=>4 {{1,3},{2,4},{5},{6},{7}}=>4 {{1,3,5,6,7},{2},{4}}=>1 {{1,3,5,6},{2,7},{4}}=>0 {{1,3,5,6},{2},{4,7}}=>2 {{1,3,5,6},{2},{4},{7}}=>2 {{1,3,5,7},{2,6},{4}}=>0 {{1,3,5},{2,6,7},{4}}=>0 {{1,3,5},{2,6},{4,7}}=>1 {{1,3,5},{2,6},{4},{7}}=>1 {{1,3,5,7},{2},{4,6}}=>2 {{1,3,5},{2,7},{4,6}}=>1 {{1,3,5},{2},{4,6,7}}=>3 {{1,3,5},{2},{4,6},{7}}=>3 {{1,3,5,7},{2},{4},{6}}=>2 {{1,3,5},{2,7},{4},{6}}=>1 {{1,3,5},{2},{4,7},{6}}=>1 {{1,3,5},{2},{4},{6,7}}=>3 {{1,3,5},{2},{4},{6},{7}}=>3 {{1,3,6,7},{2,5},{4}}=>0 {{1,3,6},{2,5,7},{4}}=>0 {{1,3,6},{2,5},{4,7}}=>1 {{1,3,6},{2,5},{4},{7}}=>1 {{1,3,7},{2,5,6},{4}}=>0 {{1,3},{2,5,6,7},{4}}=>0 {{1,3},{2,5,6},{4,7}}=>1 {{1,3},{2,5,6},{4},{7}}=>1 {{1,3,7},{2,5},{4,6}}=>1 {{1,3},{2,5,7},{4,6}}=>1 {{1,3},{2,5},{4,6,7}}=>2 {{1,3},{2,5},{4,6},{7}}=>2 {{1,3,7},{2,5},{4},{6}}=>1 {{1,3},{2,5,7},{4},{6}}=>1 {{1,3},{2,5},{4,7},{6}}=>0 {{1,3},{2,5},{4},{6,7}}=>2 {{1,3},{2,5},{4},{6},{7}}=>2 {{1,3,6,7},{2},{4,5}}=>2 {{1,3,6},{2,7},{4,5}}=>1 {{1,3,6},{2},{4,5,7}}=>3 {{1,3,6},{2},{4,5},{7}}=>3 {{1,3,7},{2,6},{4,5}}=>1 {{1,3},{2,6,7},{4,5}}=>1 {{1,3},{2,6},{4,5,7}}=>2 {{1,3},{2,6},{4,5},{7}}=>2 {{1,3,7},{2},{4,5,6}}=>3 {{1,3},{2,7},{4,5,6}}=>2 {{1,3},{2},{4,5,6,7}}=>4 {{1,3},{2},{4,5,6},{7}}=>4 {{1,3,7},{2},{4,5},{6}}=>3 {{1,3},{2,7},{4,5},{6}}=>2 {{1,3},{2},{4,5,7},{6}}=>2 {{1,3},{2},{4,5},{6,7}}=>4 {{1,3},{2},{4,5},{6},{7}}=>4 {{1,3,6,7},{2},{4},{5}}=>2 {{1,3,6},{2,7},{4},{5}}=>1 {{1,3,6},{2},{4,7},{5}}=>1 {{1,3,6},{2},{4},{5,7}}=>3 {{1,3,6},{2},{4},{5},{7}}=>3 {{1,3,7},{2,6},{4},{5}}=>1 {{1,3},{2,6,7},{4},{5}}=>1 {{1,3},{2,6},{4,7},{5}}=>0 {{1,3},{2,6},{4},{5,7}}=>2 {{1,3},{2,6},{4},{5},{7}}=>2 {{1,3,7},{2},{4,6},{5}}=>1 {{1,3},{2,7},{4,6},{5}}=>0 {{1,3},{2},{4,6,7},{5}}=>1 {{1,3},{2},{4,6},{5,7}}=>2 {{1,3},{2},{4,6},{5},{7}}=>2 {{1,3,7},{2},{4},{5,6}}=>3 {{1,3},{2,7},{4},{5,6}}=>2 {{1,3},{2},{4,7},{5,6}}=>2 {{1,3},{2},{4},{5,6,7}}=>4 {{1,3},{2},{4},{5,6},{7}}=>4 {{1,3,7},{2},{4},{5},{6}}=>3 {{1,3},{2,7},{4},{5},{6}}=>2 {{1,3},{2},{4,7},{5},{6}}=>2 {{1,3},{2},{4},{5,7},{6}}=>2 {{1,3},{2},{4},{5},{6,7}}=>4 {{1,3},{2},{4},{5},{6},{7}}=>4 {{1,4,5,6,7},{2,3}}=>1 {{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}}=>3 {{1,4,5},{2,3,6},{7}}=>3 {{1,4,5,7},{2,3},{6}}=>2 {{1,4,5},{2,3,7},{6}}=>1 {{1,4,5},{2,3},{6,7}}=>3 {{1,4,5},{2,3},{6},{7}}=>3 {{1,4,6,7},{2,3,5}}=>2 {{1,4,6},{2,3,5,7}}=>3 {{1,4,6},{2,3,5},{7}}=>3 {{1,4,7},{2,3,5,6}}=>3 {{1,4},{2,3,5,6,7}}=>4 {{1,4},{2,3,5,6},{7}}=>4 {{1,4,7},{2,3,5},{6}}=>3 {{1,4},{2,3,5,7},{6}}=>2 {{1,4},{2,3,5},{6,7}}=>4 {{1,4},{2,3,5},{6},{7}}=>4 {{1,4,6,7},{2,3},{5}}=>2 {{1,4,6},{2,3,7},{5}}=>1 {{1,4,6},{2,3},{5,7}}=>3 {{1,4,6},{2,3},{5},{7}}=>3 {{1,4,7},{2,3,6},{5}}=>1 {{1,4},{2,3,6,7},{5}}=>1 {{1,4},{2,3,6},{5,7}}=>2 {{1,4},{2,3,6},{5},{7}}=>2 {{1,4,7},{2,3},{5,6}}=>3 {{1,4},{2,3,7},{5,6}}=>2 {{1,4},{2,3},{5,6,7}}=>4 {{1,4},{2,3},{5,6},{7}}=>4 {{1,4,7},{2,3},{5},{6}}=>3 {{1,4},{2,3,7},{5},{6}}=>2 {{1,4},{2,3},{5,7},{6}}=>2 {{1,4},{2,3},{5},{6,7}}=>4 {{1,4},{2,3},{5},{6},{7}}=>4 {{1,5,6,7},{2,3,4}}=>2 {{1,5,6},{2,3,4,7}}=>3 {{1,5,6},{2,3,4},{7}}=>3 {{1,5,7},{2,3,4,6}}=>3 {{1,5},{2,3,4,6,7}}=>4 {{1,5},{2,3,4,6},{7}}=>4 {{1,5,7},{2,3,4},{6}}=>3 {{1,5},{2,3,4,7},{6}}=>2 {{1,5},{2,3,4},{6,7}}=>4 {{1,5},{2,3,4},{6},{7}}=>4 {{1,6,7},{2,3,4,5}}=>3 {{1,6},{2,3,4,5,7}}=>4 {{1,6},{2,3,4,5},{7}}=>4 {{1,7},{2,3,4,5,6}}=>4 {{1},{2,3,4,5,6,7}}=>6 {{1},{2,3,4,5,6},{7}}=>6 {{1,7},{2,3,4,5},{6}}=>4 {{1},{2,3,4,5,7},{6}}=>4 {{1},{2,3,4,5},{6,7}}=>6 {{1},{2,3,4,5},{6},{7}}=>6 {{1,6,7},{2,3,4},{5}}=>3 {{1,6},{2,3,4,7},{5}}=>2 {{1,6},{2,3,4},{5,7}}=>4 {{1,6},{2,3,4},{5},{7}}=>4 {{1,7},{2,3,4,6},{5}}=>2 {{1},{2,3,4,6,7},{5}}=>3 {{1},{2,3,4,6},{5,7}}=>4 {{1},{2,3,4,6},{5},{7}}=>4 {{1,7},{2,3,4},{5,6}}=>4 {{1},{2,3,4,7},{5,6}}=>4 {{1},{2,3,4},{5,6,7}}=>6 {{1},{2,3,4},{5,6},{7}}=>6 {{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}}=>6 {{1},{2,3,4},{5},{6},{7}}=>6 {{1,5,6,7},{2,3},{4}}=>2 {{1,5,6},{2,3,7},{4}}=>1 {{1,5,6},{2,3},{4,7}}=>3 {{1,5,6},{2,3},{4},{7}}=>3 {{1,5,7},{2,3,6},{4}}=>1 {{1,5},{2,3,6,7},{4}}=>1 {{1,5},{2,3,6},{4,7}}=>2 {{1,5},{2,3,6},{4},{7}}=>2 {{1,5,7},{2,3},{4,6}}=>3 {{1,5},{2,3,7},{4,6}}=>2 {{1,5},{2,3},{4,6,7}}=>4 {{1,5},{2,3},{4,6},{7}}=>4 {{1,5,7},{2,3},{4},{6}}=>3 {{1,5},{2,3,7},{4},{6}}=>2 {{1,5},{2,3},{4,7},{6}}=>2 {{1,5},{2,3},{4},{6,7}}=>4 {{1,5},{2,3},{4},{6},{7}}=>4 {{1,6,7},{2,3,5},{4}}=>1 {{1,6},{2,3,5,7},{4}}=>1 {{1,6},{2,3,5},{4,7}}=>2 {{1,6},{2,3,5},{4},{7}}=>2 {{1,7},{2,3,5,6},{4}}=>1 {{1},{2,3,5,6,7},{4}}=>2 {{1},{2,3,5,6},{4,7}}=>3 {{1},{2,3,5,6},{4},{7}}=>3 {{1,7},{2,3,5},{4,6}}=>2 {{1},{2,3,5,7},{4,6}}=>3 {{1},{2,3,5},{4,6,7}}=>4 {{1},{2,3,5},{4,6},{7}}=>4 {{1,7},{2,3,5},{4},{6}}=>2 {{1},{2,3,5,7},{4},{6}}=>3 {{1},{2,3,5},{4,7},{6}}=>2 {{1},{2,3,5},{4},{6,7}}=>4 {{1},{2,3,5},{4},{6},{7}}=>4 {{1,6,7},{2,3},{4,5}}=>3 {{1,6},{2,3,7},{4,5}}=>2 {{1,6},{2,3},{4,5,7}}=>4 {{1,6},{2,3},{4,5},{7}}=>4 {{1,7},{2,3,6},{4,5}}=>2 {{1},{2,3,6,7},{4,5}}=>3 {{1},{2,3,6},{4,5,7}}=>4 {{1},{2,3,6},{4,5},{7}}=>4 {{1,7},{2,3},{4,5,6}}=>4 {{1},{2,3,7},{4,5,6}}=>4 {{1},{2,3},{4,5,6,7}}=>6 {{1},{2,3},{4,5,6},{7}}=>6 {{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}}=>6 {{1},{2,3},{4,5},{6},{7}}=>6 {{1,6,7},{2,3},{4},{5}}=>3 {{1,6},{2,3,7},{4},{5}}=>2 {{1,6},{2,3},{4,7},{5}}=>2 {{1,6},{2,3},{4},{5,7}}=>4 {{1,6},{2,3},{4},{5},{7}}=>4 {{1,7},{2,3,6},{4},{5}}=>2 {{1},{2,3,6,7},{4},{5}}=>3 {{1},{2,3,6},{4,7},{5}}=>2 {{1},{2,3,6},{4},{5,7}}=>4 {{1},{2,3,6},{4},{5},{7}}=>4 {{1,7},{2,3},{4,6},{5}}=>2 {{1},{2,3,7},{4,6},{5}}=>2 {{1},{2,3},{4,6,7},{5}}=>3 {{1},{2,3},{4,6},{5,7}}=>4 {{1},{2,3},{4,6},{5},{7}}=>4 {{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}}=>6 {{1},{2,3},{4},{5,6},{7}}=>6 {{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},{5,7},{6}}=>4 {{1},{2,3},{4},{5},{6,7}}=>6 {{1},{2,3},{4},{5},{6},{7}}=>6 {{1,4,5,6,7},{2},{3}}=>1 {{1,4,5,6},{2,7},{3}}=>0 {{1,4,5,6},{2},{3,7}}=>2 {{1,4,5,6},{2},{3},{7}}=>2 {{1,4,5,7},{2,6},{3}}=>0 {{1,4,5},{2,6,7},{3}}=>0 {{1,4,5},{2,6},{3,7}}=>1 {{1,4,5},{2,6},{3},{7}}=>1 {{1,4,5,7},{2},{3,6}}=>2 {{1,4,5},{2,7},{3,6}}=>1 {{1,4,5},{2},{3,6,7}}=>3 {{1,4,5},{2},{3,6},{7}}=>3 {{1,4,5,7},{2},{3},{6}}=>2 {{1,4,5},{2,7},{3},{6}}=>1 {{1,4,5},{2},{3,7},{6}}=>1 {{1,4,5},{2},{3},{6,7}}=>3 {{1,4,5},{2},{3},{6},{7}}=>3 {{1,4,6,7},{2,5},{3}}=>0 {{1,4,6},{2,5,7},{3}}=>0 {{1,4,6},{2,5},{3,7}}=>1 {{1,4,6},{2,5},{3},{7}}=>1 {{1,4,7},{2,5,6},{3}}=>0 {{1,4},{2,5,6,7},{3}}=>0 {{1,4},{2,5,6},{3,7}}=>1 {{1,4},{2,5,6},{3},{7}}=>1 {{1,4,7},{2,5},{3,6}}=>1 {{1,4},{2,5,7},{3,6}}=>1 {{1,4},{2,5},{3,6,7}}=>2 {{1,4},{2,5},{3,6},{7}}=>2 {{1,4,7},{2,5},{3},{6}}=>1 {{1,4},{2,5,7},{3},{6}}=>1 {{1,4},{2,5},{3,7},{6}}=>0 {{1,4},{2,5},{3},{6,7}}=>2 {{1,4},{2,5},{3},{6},{7}}=>2 {{1,4,6,7},{2},{3,5}}=>2 {{1,4,6},{2,7},{3,5}}=>1 {{1,4,6},{2},{3,5,7}}=>3 {{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}}=>2 {{1,4},{2,6},{3,5},{7}}=>2 {{1,4,7},{2},{3,5,6}}=>3 {{1,4},{2,7},{3,5,6}}=>2 {{1,4},{2},{3,5,6,7}}=>4 {{1,4},{2},{3,5,6},{7}}=>4 {{1,4,7},{2},{3,5},{6}}=>3 {{1,4},{2,7},{3,5},{6}}=>2 {{1,4},{2},{3,5,7},{6}}=>2 {{1,4},{2},{3,5},{6,7}}=>4 {{1,4},{2},{3,5},{6},{7}}=>4 {{1,4,6,7},{2},{3},{5}}=>2 {{1,4,6},{2,7},{3},{5}}=>1 {{1,4,6},{2},{3,7},{5}}=>1 {{1,4,6},{2},{3},{5,7}}=>3 {{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},{3,7},{5}}=>0 {{1,4},{2,6},{3},{5,7}}=>2 {{1,4},{2,6},{3},{5},{7}}=>2 {{1,4,7},{2},{3,6},{5}}=>1 {{1,4},{2,7},{3,6},{5}}=>0 {{1,4},{2},{3,6,7},{5}}=>1 {{1,4},{2},{3,6},{5,7}}=>2 {{1,4},{2},{3,6},{5},{7}}=>2 {{1,4,7},{2},{3},{5,6}}=>3 {{1,4},{2,7},{3},{5,6}}=>2 {{1,4},{2},{3,7},{5,6}}=>2 {{1,4},{2},{3},{5,6,7}}=>4 {{1,4},{2},{3},{5,6},{7}}=>4 {{1,4,7},{2},{3},{5},{6}}=>3 {{1,4},{2,7},{3},{5},{6}}=>2 {{1,4},{2},{3,7},{5},{6}}=>2 {{1,4},{2},{3},{5,7},{6}}=>2 {{1,4},{2},{3},{5},{6,7}}=>4 {{1,4},{2},{3},{5},{6},{7}}=>4 {{1,5,6,7},{2,4},{3}}=>0 {{1,5,6},{2,4,7},{3}}=>0 {{1,5,6},{2,4},{3,7}}=>1 {{1,5,6},{2,4},{3},{7}}=>1 {{1,5,7},{2,4,6},{3}}=>0 {{1,5},{2,4,6,7},{3}}=>0 {{1,5},{2,4,6},{3,7}}=>1 {{1,5},{2,4,6},{3},{7}}=>1 {{1,5,7},{2,4},{3,6}}=>1 {{1,5},{2,4,7},{3,6}}=>1 {{1,5},{2,4},{3,6,7}}=>2 {{1,5},{2,4},{3,6},{7}}=>2 {{1,5,7},{2,4},{3},{6}}=>1 {{1,5},{2,4,7},{3},{6}}=>1 {{1,5},{2,4},{3,7},{6}}=>0 {{1,5},{2,4},{3},{6,7}}=>2 {{1,5},{2,4},{3},{6},{7}}=>2 {{1,6,7},{2,4,5},{3}}=>0 {{1,6},{2,4,5,7},{3}}=>0 {{1,6},{2,4,5},{3,7}}=>1 {{1,6},{2,4,5},{3},{7}}=>1 {{1,7},{2,4,5,6},{3}}=>0 {{1},{2,4,5,6,7},{3}}=>1 {{1},{2,4,5,6},{3,7}}=>2 {{1},{2,4,5,6},{3},{7}}=>2 {{1,7},{2,4,5},{3,6}}=>1 {{1},{2,4,5,7},{3,6}}=>2 {{1},{2,4,5},{3,6,7}}=>3 {{1},{2,4,5},{3,6},{7}}=>3 {{1,7},{2,4,5},{3},{6}}=>1 {{1},{2,4,5,7},{3},{6}}=>2 {{1},{2,4,5},{3,7},{6}}=>1 {{1},{2,4,5},{3},{6,7}}=>3 {{1},{2,4,5},{3},{6},{7}}=>3 {{1,6,7},{2,4},{3,5}}=>1 {{1,6},{2,4,7},{3,5}}=>1 {{1,6},{2,4},{3,5,7}}=>2 {{1,6},{2,4},{3,5},{7}}=>2 {{1,7},{2,4,6},{3,5}}=>1 {{1},{2,4,6,7},{3,5}}=>2 {{1},{2,4,6},{3,5,7}}=>3 {{1},{2,4,6},{3,5},{7}}=>3 {{1,7},{2,4},{3,5,6}}=>2 {{1},{2,4,7},{3,5,6}}=>3 {{1},{2,4},{3,5,6,7}}=>4 {{1},{2,4},{3,5,6},{7}}=>4 {{1,7},{2,4},{3,5},{6}}=>2 {{1},{2,4,7},{3,5},{6}}=>3 {{1},{2,4},{3,5,7},{6}}=>2 {{1},{2,4},{3,5},{6,7}}=>4 {{1},{2,4},{3,5},{6},{7}}=>4 {{1,6,7},{2,4},{3},{5}}=>1 {{1,6},{2,4,7},{3},{5}}=>1 {{1,6},{2,4},{3,7},{5}}=>0 {{1,6},{2,4},{3},{5,7}}=>2 {{1,6},{2,4},{3},{5},{7}}=>2 {{1,7},{2,4,6},{3},{5}}=>1 {{1},{2,4,6,7},{3},{5}}=>2 {{1},{2,4,6},{3,7},{5}}=>1 {{1},{2,4,6},{3},{5,7}}=>3 {{1},{2,4,6},{3},{5},{7}}=>3 {{1,7},{2,4},{3,6},{5}}=>0 {{1},{2,4,7},{3,6},{5}}=>1 {{1},{2,4},{3,6,7},{5}}=>1 {{1},{2,4},{3,6},{5,7}}=>2 {{1},{2,4},{3,6},{5},{7}}=>2 {{1,7},{2,4},{3},{5,6}}=>2 {{1},{2,4,7},{3},{5,6}}=>3 {{1},{2,4},{3,7},{5,6}}=>2 {{1},{2,4},{3},{5,6,7}}=>4 {{1},{2,4},{3},{5,6},{7}}=>4 {{1,7},{2,4},{3},{5},{6}}=>2 {{1},{2,4,7},{3},{5},{6}}=>3 {{1},{2,4},{3,7},{5},{6}}=>2 {{1},{2,4},{3},{5,7},{6}}=>2 {{1},{2,4},{3},{5},{6,7}}=>4 {{1},{2,4},{3},{5},{6},{7}}=>4 {{1,5,6,7},{2},{3,4}}=>2 {{1,5,6},{2,7},{3,4}}=>1 {{1,5,6},{2},{3,4,7}}=>3 {{1,5,6},{2},{3,4},{7}}=>3 {{1,5,7},{2,6},{3,4}}=>1 {{1,5},{2,6,7},{3,4}}=>1 {{1,5},{2,6},{3,4,7}}=>2 {{1,5},{2,6},{3,4},{7}}=>2 {{1,5,7},{2},{3,4,6}}=>3 {{1,5},{2,7},{3,4,6}}=>2 {{1,5},{2},{3,4,6,7}}=>4 {{1,5},{2},{3,4,6},{7}}=>4 {{1,5,7},{2},{3,4},{6}}=>3 {{1,5},{2,7},{3,4},{6}}=>2 {{1,5},{2},{3,4,7},{6}}=>2 {{1,5},{2},{3,4},{6,7}}=>4 {{1,5},{2},{3,4},{6},{7}}=>4 {{1,6,7},{2,5},{3,4}}=>1 {{1,6},{2,5,7},{3,4}}=>1 {{1,6},{2,5},{3,4,7}}=>2 {{1,6},{2,5},{3,4},{7}}=>2 {{1,7},{2,5,6},{3,4}}=>1 {{1},{2,5,6,7},{3,4}}=>2 {{1},{2,5,6},{3,4,7}}=>3 {{1},{2,5,6},{3,4},{7}}=>3 {{1,7},{2,5},{3,4,6}}=>2 {{1},{2,5,7},{3,4,6}}=>3 {{1},{2,5},{3,4,6,7}}=>4 {{1},{2,5},{3,4,6},{7}}=>4 {{1,7},{2,5},{3,4},{6}}=>2 {{1},{2,5,7},{3,4},{6}}=>3 {{1},{2,5},{3,4,7},{6}}=>2 {{1},{2,5},{3,4},{6,7}}=>4 {{1},{2,5},{3,4},{6},{7}}=>4 {{1,6,7},{2},{3,4,5}}=>3 {{1,6},{2,7},{3,4,5}}=>2 {{1,6},{2},{3,4,5,7}}=>4 {{1,6},{2},{3,4,5},{7}}=>4 {{1,7},{2,6},{3,4,5}}=>2 {{1},{2,6,7},{3,4,5}}=>3 {{1},{2,6},{3,4,5,7}}=>4 {{1},{2,6},{3,4,5},{7}}=>4 {{1,7},{2},{3,4,5,6}}=>4 {{1},{2,7},{3,4,5,6}}=>4 {{1},{2},{3,4,5,6,7}}=>6 {{1},{2},{3,4,5,6},{7}}=>6 {{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}}=>6 {{1},{2},{3,4,5},{6},{7}}=>6 {{1,6,7},{2},{3,4},{5}}=>3 {{1,6},{2,7},{3,4},{5}}=>2 {{1,6},{2},{3,4,7},{5}}=>2 {{1,6},{2},{3,4},{5,7}}=>4 {{1,6},{2},{3,4},{5},{7}}=>4 {{1,7},{2,6},{3,4},{5}}=>2 {{1},{2,6,7},{3,4},{5}}=>3 {{1},{2,6},{3,4,7},{5}}=>2 {{1},{2,6},{3,4},{5,7}}=>4 {{1},{2,6},{3,4},{5},{7}}=>4 {{1,7},{2},{3,4,6},{5}}=>2 {{1},{2,7},{3,4,6},{5}}=>2 {{1},{2},{3,4,6,7},{5}}=>3 {{1},{2},{3,4,6},{5,7}}=>4 {{1},{2},{3,4,6},{5},{7}}=>4 {{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}}=>6 {{1},{2},{3,4},{5,6},{7}}=>6 {{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},{5,7},{6}}=>4 {{1},{2},{3,4},{5},{6,7}}=>6 {{1},{2},{3,4},{5},{6},{7}}=>6 {{1,5,6,7},{2},{3},{4}}=>2 {{1,5,6},{2,7},{3},{4}}=>1 {{1,5,6},{2},{3,7},{4}}=>1 {{1,5,6},{2},{3},{4,7}}=>3 {{1,5,6},{2},{3},{4},{7}}=>3 {{1,5,7},{2,6},{3},{4}}=>1 {{1,5},{2,6,7},{3},{4}}=>1 {{1,5},{2,6},{3,7},{4}}=>0 {{1,5},{2,6},{3},{4,7}}=>2 {{1,5},{2,6},{3},{4},{7}}=>2 {{1,5,7},{2},{3,6},{4}}=>1 {{1,5},{2,7},{3,6},{4}}=>0 {{1,5},{2},{3,6,7},{4}}=>1 {{1,5},{2},{3,6},{4,7}}=>2 {{1,5},{2},{3,6},{4},{7}}=>2 {{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}}=>4 {{1,5},{2},{3},{4,6},{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},{4,7},{6}}=>2 {{1,5},{2},{3},{4},{6,7}}=>4 {{1,5},{2},{3},{4},{6},{7}}=>4 {{1,6,7},{2,5},{3},{4}}=>1 {{1,6},{2,5,7},{3},{4}}=>1 {{1,6},{2,5},{3,7},{4}}=>0 {{1,6},{2,5},{3},{4,7}}=>2 {{1,6},{2,5},{3},{4},{7}}=>2 {{1,7},{2,5,6},{3},{4}}=>1 {{1},{2,5,6,7},{3},{4}}=>2 {{1},{2,5,6},{3,7},{4}}=>1 {{1},{2,5,6},{3},{4,7}}=>3 {{1},{2,5,6},{3},{4},{7}}=>3 {{1,7},{2,5},{3,6},{4}}=>0 {{1},{2,5,7},{3,6},{4}}=>1 {{1},{2,5},{3,6,7},{4}}=>1 {{1},{2,5},{3,6},{4,7}}=>2 {{1},{2,5},{3,6},{4},{7}}=>2 {{1,7},{2,5},{3},{4,6}}=>2 {{1},{2,5,7},{3},{4,6}}=>3 {{1},{2,5},{3,7},{4,6}}=>2 {{1},{2,5},{3},{4,6,7}}=>4 {{1},{2,5},{3},{4,6},{7}}=>4 {{1,7},{2,5},{3},{4},{6}}=>2 {{1},{2,5,7},{3},{4},{6}}=>3 {{1},{2,5},{3,7},{4},{6}}=>2 {{1},{2,5},{3},{4,7},{6}}=>2 {{1},{2,5},{3},{4},{6,7}}=>4 {{1},{2,5},{3},{4},{6},{7}}=>4 {{1,6,7},{2},{3,5},{4}}=>1 {{1,6},{2,7},{3,5},{4}}=>0 {{1,6},{2},{3,5,7},{4}}=>1 {{1,6},{2},{3,5},{4,7}}=>2 {{1,6},{2},{3,5},{4},{7}}=>2 {{1,7},{2,6},{3,5},{4}}=>0 {{1},{2,6,7},{3,5},{4}}=>1 {{1},{2,6},{3,5,7},{4}}=>1 {{1},{2,6},{3,5},{4,7}}=>2 {{1},{2,6},{3,5},{4},{7}}=>2 {{1,7},{2},{3,5,6},{4}}=>1 {{1},{2,7},{3,5,6},{4}}=>1 {{1},{2},{3,5,6,7},{4}}=>2 {{1},{2},{3,5,6},{4,7}}=>3 {{1},{2},{3,5,6},{4},{7}}=>3 {{1,7},{2},{3,5},{4,6}}=>2 {{1},{2,7},{3,5},{4,6}}=>2 {{1},{2},{3,5,7},{4,6}}=>3 {{1},{2},{3,5},{4,6,7}}=>4 {{1},{2},{3,5},{4,6},{7}}=>4 {{1,7},{2},{3,5},{4},{6}}=>2 {{1},{2,7},{3,5},{4},{6}}=>2 {{1},{2},{3,5,7},{4},{6}}=>3 {{1},{2},{3,5},{4,7},{6}}=>2 {{1},{2},{3,5},{4},{6,7}}=>4 {{1},{2},{3,5},{4},{6},{7}}=>4 {{1,6,7},{2},{3},{4,5}}=>3 {{1,6},{2,7},{3},{4,5}}=>2 {{1,6},{2},{3,7},{4,5}}=>2 {{1,6},{2},{3},{4,5,7}}=>4 {{1,6},{2},{3},{4,5},{7}}=>4 {{1,7},{2,6},{3},{4,5}}=>2 {{1},{2,6,7},{3},{4,5}}=>3 {{1},{2,6},{3,7},{4,5}}=>2 {{1},{2,6},{3},{4,5,7}}=>4 {{1},{2,6},{3},{4,5},{7}}=>4 {{1,7},{2},{3,6},{4,5}}=>2 {{1},{2,7},{3,6},{4,5}}=>2 {{1},{2},{3,6,7},{4,5}}=>3 {{1},{2},{3,6},{4,5,7}}=>4 {{1},{2},{3,6},{4,5},{7}}=>4 {{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}}=>6 {{1},{2},{3},{4,5,6},{7}}=>6 {{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},{4,5,7},{6}}=>4 {{1},{2},{3},{4,5},{6,7}}=>6 {{1},{2},{3},{4,5},{6},{7}}=>6 {{1,6,7},{2},{3},{4},{5}}=>3 {{1,6},{2,7},{3},{4},{5}}=>2 {{1,6},{2},{3,7},{4},{5}}=>2 {{1,6},{2},{3},{4,7},{5}}=>2 {{1,6},{2},{3},{4},{5,7}}=>4 {{1,6},{2},{3},{4},{5},{7}}=>4 {{1,7},{2,6},{3},{4},{5}}=>2 {{1},{2,6,7},{3},{4},{5}}=>3 {{1},{2,6},{3,7},{4},{5}}=>2 {{1},{2,6},{3},{4,7},{5}}=>2 {{1},{2,6},{3},{4},{5,7}}=>4 {{1},{2,6},{3},{4},{5},{7}}=>4 {{1,7},{2},{3,6},{4},{5}}=>2 {{1},{2,7},{3,6},{4},{5}}=>2 {{1},{2},{3,6,7},{4},{5}}=>3 {{1},{2},{3,6},{4,7},{5}}=>2 {{1},{2},{3,6},{4},{5,7}}=>4 {{1},{2},{3,6},{4},{5},{7}}=>4 {{1,7},{2},{3},{4,6},{5}}=>2 {{1},{2,7},{3},{4,6},{5}}=>2 {{1},{2},{3,7},{4,6},{5}}=>2 {{1},{2},{3},{4,6,7},{5}}=>3 {{1},{2},{3},{4,6},{5,7}}=>4 {{1},{2},{3},{4,6},{5},{7}}=>4 {{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},{4,7},{5,6}}=>4 {{1},{2},{3},{4},{5,6,7}}=>6 {{1},{2},{3},{4},{5,6},{7}}=>6 {{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},{4,7},{5},{6}}=>4 {{1},{2},{3},{4},{5,7},{6}}=>4 {{1},{2},{3},{4},{5},{6,7}}=>6 {{1},{2},{3},{4},{5},{6},{7}}=>6
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Description
The number of ascent tops in the flattened set partition such that all smaller elements appear before.
Let $P$ be a set partition. The flattened set partition is the permutation obtained by sorting the set of blocks of $P$ according to their minimal element and the elements in each block in increasing order.
Given a set partition $P$, this statistic is the binary logarithm of the number of set partitions that flatten to the same permutation as $P$.
References
[1] Nabawanda, O., Rakotondrajao, F. The sets of flattened partitions with forbidden patterns arXiv:2011.07304
Code
def flatten(P):
    return tuple(e for B in sorted(P, key=min) for e in sorted(list(B)))

def statistic(P):
    p = flatten(P)
    return sum(1 for i in range(len(p)-1) if p[i] < p[i+1] and set(range(1, p[i+1])).issubset(sorted(p[:i+1])))
Created
Nov 17, 2020 at 11:00 by Martin Rubey
Updated
Nov 17, 2020 at 11:00 by Martin Rubey