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Identifier
Values
=>
Cc0009;cc-rep
{{1,2}}=>0 {{1},{2}}=>0 {{1,2,3}}=>0 {{1,2},{3}}=>0 {{1,3},{2}}=>1 {{1},{2,3}}=>0 {{1},{2},{3}}=>0 {{1,2,3,4}}=>0 {{1,2,3},{4}}=>0 {{1,2,4},{3}}=>1 {{1,2},{3,4}}=>0 {{1,2},{3},{4}}=>0 {{1,3,4},{2}}=>2 {{1,3},{2,4}}=>1 {{1,3},{2},{4}}=>1 {{1,4},{2,3}}=>1 {{1},{2,3,4}}=>0 {{1},{2,3},{4}}=>0 {{1,4},{2},{3}}=>1 {{1},{2,4},{3}}=>2 {{1},{2},{3,4}}=>0 {{1},{2},{3},{4}}=>0 {{1,2,3,4,5}}=>0 {{1,2,3,4},{5}}=>0 {{1,2,3,5},{4}}=>1 {{1,2,3},{4,5}}=>0 {{1,2,3},{4},{5}}=>0 {{1,2,4,5},{3}}=>2 {{1,2,4},{3,5}}=>1 {{1,2,4},{3},{5}}=>1 {{1,2,5},{3,4}}=>1 {{1,2},{3,4,5}}=>0 {{1,2},{3,4},{5}}=>0 {{1,2,5},{3},{4}}=>1 {{1,2},{3,5},{4}}=>2 {{1,2},{3},{4,5}}=>0 {{1,2},{3},{4},{5}}=>0 {{1,3,4,5},{2}}=>3 {{1,3,4},{2,5}}=>2 {{1,3,4},{2},{5}}=>2 {{1,3,5},{2,4}}=>2 {{1,3},{2,4,5}}=>1 {{1,3},{2,4},{5}}=>1 {{1,3,5},{2},{4}}=>2 {{1,3},{2,5},{4}}=>3 {{1,3},{2},{4,5}}=>1 {{1,3},{2},{4},{5}}=>1 {{1,4,5},{2,3}}=>2 {{1,4},{2,3,5}}=>1 {{1,4},{2,3},{5}}=>1 {{1,5},{2,3,4}}=>1 {{1},{2,3,4,5}}=>0 {{1},{2,3,4},{5}}=>0 {{1,5},{2,3},{4}}=>1 {{1},{2,3,5},{4}}=>2 {{1},{2,3},{4,5}}=>0 {{1},{2,3},{4},{5}}=>0 {{1,4,5},{2},{3}}=>2 {{1,4},{2,5},{3}}=>3 {{1,4},{2},{3,5}}=>1 {{1,4},{2},{3},{5}}=>1 {{1,5},{2,4},{3}}=>3 {{1},{2,4,5},{3}}=>4 {{1},{2,4},{3,5}}=>2 {{1},{2,4},{3},{5}}=>2 {{1,5},{2},{3,4}}=>1 {{1},{2,5},{3,4}}=>2 {{1},{2},{3,4,5}}=>0 {{1},{2},{3,4},{5}}=>0 {{1,5},{2},{3},{4}}=>1 {{1},{2,5},{3},{4}}=>2 {{1},{2},{3,5},{4}}=>3 {{1},{2},{3},{4,5}}=>0 {{1},{2},{3},{4},{5}}=>0 {{1,2,3,4,5,6}}=>0 {{1,2,3,4,5},{6}}=>0 {{1,2,3,4,6},{5}}=>1 {{1,2,3,4},{5,6}}=>0 {{1,2,3,4},{5},{6}}=>0 {{1,2,3,5,6},{4}}=>2 {{1,2,3,5},{4,6}}=>1 {{1,2,3,5},{4},{6}}=>1 {{1,2,3,6},{4,5}}=>1 {{1,2,3},{4,5,6}}=>0 {{1,2,3},{4,5},{6}}=>0 {{1,2,3,6},{4},{5}}=>1 {{1,2,3},{4,6},{5}}=>2 {{1,2,3},{4},{5,6}}=>0 {{1,2,3},{4},{5},{6}}=>0 {{1,2,4,5,6},{3}}=>3 {{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}}=>1 {{1,2,4},{3,5},{6}}=>1 {{1,2,4,6},{3},{5}}=>2 {{1,2,4},{3,6},{5}}=>3 {{1,2,4},{3},{5,6}}=>1 {{1,2,4},{3},{5},{6}}=>1 {{1,2,5,6},{3,4}}=>2 {{1,2,5},{3,4,6}}=>1 {{1,2,5},{3,4},{6}}=>1 {{1,2,6},{3,4,5}}=>1 {{1,2},{3,4,5,6}}=>0 {{1,2},{3,4,5},{6}}=>0 {{1,2,6},{3,4},{5}}=>1 {{1,2},{3,4,6},{5}}=>2 {{1,2},{3,4},{5,6}}=>0 {{1,2},{3,4},{5},{6}}=>0 {{1,2,5,6},{3},{4}}=>2 {{1,2,5},{3,6},{4}}=>3 {{1,2,5},{3},{4,6}}=>1 {{1,2,5},{3},{4},{6}}=>1 {{1,2,6},{3,5},{4}}=>3 {{1,2},{3,5,6},{4}}=>4 {{1,2},{3,5},{4,6}}=>2 {{1,2},{3,5},{4},{6}}=>2 {{1,2,6},{3},{4,5}}=>1 {{1,2},{3,6},{4,5}}=>2 {{1,2},{3},{4,5,6}}=>0 {{1,2},{3},{4,5},{6}}=>0 {{1,2,6},{3},{4},{5}}=>1 {{1,2},{3,6},{4},{5}}=>2 {{1,2},{3},{4,6},{5}}=>3 {{1,2},{3},{4},{5,6}}=>0 {{1,2},{3},{4},{5},{6}}=>0 {{1,3,4,5,6},{2}}=>4 {{1,3,4,5},{2,6}}=>3 {{1,3,4,5},{2},{6}}=>3 {{1,3,4,6},{2,5}}=>3 {{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}}=>4 {{1,3,4},{2},{5,6}}=>2 {{1,3,4},{2},{5},{6}}=>2 {{1,3,5,6},{2,4}}=>3 {{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}}=>1 {{1,3},{2,4,5},{6}}=>1 {{1,3,6},{2,4},{5}}=>2 {{1,3},{2,4,6},{5}}=>3 {{1,3},{2,4},{5,6}}=>1 {{1,3},{2,4},{5},{6}}=>1 {{1,3,5,6},{2},{4}}=>3 {{1,3,5},{2,6},{4}}=>4 {{1,3,5},{2},{4,6}}=>2 {{1,3,5},{2},{4},{6}}=>2 {{1,3,6},{2,5},{4}}=>4 {{1,3},{2,5,6},{4}}=>5 {{1,3},{2,5},{4,6}}=>3 {{1,3},{2,5},{4},{6}}=>3 {{1,3,6},{2},{4,5}}=>2 {{1,3},{2,6},{4,5}}=>3 {{1,3},{2},{4,5,6}}=>1 {{1,3},{2},{4,5},{6}}=>1 {{1,3,6},{2},{4},{5}}=>2 {{1,3},{2,6},{4},{5}}=>3 {{1,3},{2},{4,6},{5}}=>4 {{1,3},{2},{4},{5,6}}=>1 {{1,3},{2},{4},{5},{6}}=>1 {{1,4,5,6},{2,3}}=>3 {{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}}=>1 {{1,4},{2,3,5},{6}}=>1 {{1,4,6},{2,3},{5}}=>2 {{1,4},{2,3,6},{5}}=>3 {{1,4},{2,3},{5,6}}=>1 {{1,4},{2,3},{5},{6}}=>1 {{1,5,6},{2,3,4}}=>2 {{1,5},{2,3,4,6}}=>1 {{1,5},{2,3,4},{6}}=>1 {{1,6},{2,3,4,5}}=>1 {{1},{2,3,4,5,6}}=>0 {{1},{2,3,4,5},{6}}=>0 {{1,6},{2,3,4},{5}}=>1 {{1},{2,3,4,6},{5}}=>2 {{1},{2,3,4},{5,6}}=>0 {{1},{2,3,4},{5},{6}}=>0 {{1,5,6},{2,3},{4}}=>2 {{1,5},{2,3,6},{4}}=>3 {{1,5},{2,3},{4,6}}=>1 {{1,5},{2,3},{4},{6}}=>1 {{1,6},{2,3,5},{4}}=>3 {{1},{2,3,5,6},{4}}=>4 {{1},{2,3,5},{4,6}}=>2 {{1},{2,3,5},{4},{6}}=>2 {{1,6},{2,3},{4,5}}=>1 {{1},{2,3,6},{4,5}}=>2 {{1},{2,3},{4,5,6}}=>0 {{1},{2,3},{4,5},{6}}=>0 {{1,6},{2,3},{4},{5}}=>1 {{1},{2,3,6},{4},{5}}=>2 {{1},{2,3},{4,6},{5}}=>3 {{1},{2,3},{4},{5,6}}=>0 {{1},{2,3},{4},{5},{6}}=>0 {{1,4,5,6},{2},{3}}=>3 {{1,4,5},{2,6},{3}}=>4 {{1,4,5},{2},{3,6}}=>2 {{1,4,5},{2},{3},{6}}=>2 {{1,4,6},{2,5},{3}}=>4 {{1,4},{2,5,6},{3}}=>5 {{1,4},{2,5},{3,6}}=>3 {{1,4},{2,5},{3},{6}}=>3 {{1,4,6},{2},{3,5}}=>2 {{1,4},{2,6},{3,5}}=>3 {{1,4},{2},{3,5,6}}=>1 {{1,4},{2},{3,5},{6}}=>1 {{1,4,6},{2},{3},{5}}=>2 {{1,4},{2,6},{3},{5}}=>3 {{1,4},{2},{3,6},{5}}=>4 {{1,4},{2},{3},{5,6}}=>1 {{1,4},{2},{3},{5},{6}}=>1 {{1,5,6},{2,4},{3}}=>4 {{1,5},{2,4,6},{3}}=>5 {{1,5},{2,4},{3,6}}=>3 {{1,5},{2,4},{3},{6}}=>3 {{1,6},{2,4,5},{3}}=>5 {{1},{2,4,5,6},{3}}=>6 {{1},{2,4,5},{3,6}}=>4 {{1},{2,4,5},{3},{6}}=>4 {{1,6},{2,4},{3,5}}=>3 {{1},{2,4,6},{3,5}}=>4 {{1},{2,4},{3,5,6}}=>2 {{1},{2,4},{3,5},{6}}=>2 {{1,6},{2,4},{3},{5}}=>3 {{1},{2,4,6},{3},{5}}=>4 {{1},{2,4},{3,6},{5}}=>5 {{1},{2,4},{3},{5,6}}=>2 {{1},{2,4},{3},{5},{6}}=>2 {{1,5,6},{2},{3,4}}=>2 {{1,5},{2,6},{3,4}}=>3 {{1,5},{2},{3,4,6}}=>1 {{1,5},{2},{3,4},{6}}=>1 {{1,6},{2,5},{3,4}}=>3 {{1},{2,5,6},{3,4}}=>4 {{1},{2,5},{3,4,6}}=>2 {{1},{2,5},{3,4},{6}}=>2 {{1,6},{2},{3,4,5}}=>1 {{1},{2,6},{3,4,5}}=>2 {{1},{2},{3,4,5,6}}=>0 {{1},{2},{3,4,5},{6}}=>0 {{1,6},{2},{3,4},{5}}=>1 {{1},{2,6},{3,4},{5}}=>2 {{1},{2},{3,4,6},{5}}=>3 {{1},{2},{3,4},{5,6}}=>0 {{1},{2},{3,4},{5},{6}}=>0 {{1,5,6},{2},{3},{4}}=>2 {{1,5},{2,6},{3},{4}}=>3 {{1,5},{2},{3,6},{4}}=>4 {{1,5},{2},{3},{4,6}}=>1 {{1,5},{2},{3},{4},{6}}=>1 {{1,6},{2,5},{3},{4}}=>3 {{1},{2,5,6},{3},{4}}=>4 {{1},{2,5},{3,6},{4}}=>5 {{1},{2,5},{3},{4,6}}=>2 {{1},{2,5},{3},{4},{6}}=>2 {{1,6},{2},{3,5},{4}}=>4 {{1},{2,6},{3,5},{4}}=>5 {{1},{2},{3,5,6},{4}}=>6 {{1},{2},{3,5},{4,6}}=>3 {{1},{2},{3,5},{4},{6}}=>3 {{1,6},{2},{3},{4,5}}=>1 {{1},{2,6},{3},{4,5}}=>2 {{1},{2},{3,6},{4,5}}=>3 {{1},{2},{3},{4,5,6}}=>0 {{1},{2},{3},{4,5},{6}}=>0 {{1,6},{2},{3},{4},{5}}=>1 {{1},{2,6},{3},{4},{5}}=>2 {{1},{2},{3,6},{4},{5}}=>3 {{1},{2},{3},{4,6},{5}}=>4 {{1},{2},{3},{4},{5,6}}=>0 {{1},{2},{3},{4},{5},{6}}=>0 {{1,2,3,4,5,6,7}}=>0 {{1,2,3,4,5,6},{7}}=>0 {{1,2,3,4,5,7},{6}}=>1 {{1,2,3,4,5},{6,7}}=>0 {{1,2,3,4,5},{6},{7}}=>0 {{1,2,3,4,6,7},{5}}=>2 {{1,2,3,4,6},{5,7}}=>1 {{1,2,3,4,6},{5},{7}}=>1 {{1,2,3,4,7},{5,6}}=>1 {{1,2,3,4},{5,6,7}}=>0 {{1,2,3,4},{5,6},{7}}=>0 {{1,2,3,4,7},{5},{6}}=>1 {{1,2,3,4},{5,7},{6}}=>2 {{1,2,3,4},{5},{6,7}}=>0 {{1,2,3,4},{5},{6},{7}}=>0 {{1,2,3,5,6,7},{4}}=>3 {{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}}=>1 {{1,2,3,5},{4,6},{7}}=>1 {{1,2,3,5,7},{4},{6}}=>2 {{1,2,3,5},{4,7},{6}}=>3 {{1,2,3,5},{4},{6,7}}=>1 {{1,2,3,5},{4},{6},{7}}=>1 {{1,2,3,6,7},{4,5}}=>2 {{1,2,3,6},{4,5,7}}=>1 {{1,2,3,6},{4,5},{7}}=>1 {{1,2,3,7},{4,5,6}}=>1 {{1,2,3},{4,5,6,7}}=>0 {{1,2,3},{4,5,6},{7}}=>0 {{1,2,3,7},{4,5},{6}}=>1 {{1,2,3},{4,5,7},{6}}=>2 {{1,2,3},{4,5},{6,7}}=>0 {{1,2,3},{4,5},{6},{7}}=>0 {{1,2,3,6,7},{4},{5}}=>2 {{1,2,3,6},{4,7},{5}}=>3 {{1,2,3,6},{4},{5,7}}=>1 {{1,2,3,6},{4},{5},{7}}=>1 {{1,2,3,7},{4,6},{5}}=>3 {{1,2,3},{4,6,7},{5}}=>4 {{1,2,3},{4,6},{5,7}}=>2 {{1,2,3},{4,6},{5},{7}}=>2 {{1,2,3,7},{4},{5,6}}=>1 {{1,2,3},{4,7},{5,6}}=>2 {{1,2,3},{4},{5,6,7}}=>0 {{1,2,3},{4},{5,6},{7}}=>0 {{1,2,3,7},{4},{5},{6}}=>1 {{1,2,3},{4,7},{5},{6}}=>2 {{1,2,3},{4},{5,7},{6}}=>3 {{1,2,3},{4},{5},{6,7}}=>0 {{1,2,3},{4},{5},{6},{7}}=>0 {{1,2,4,5,6,7},{3}}=>4 {{1,2,4,5,6},{3,7}}=>3 {{1,2,4,5,6},{3},{7}}=>3 {{1,2,4,5,7},{3,6}}=>3 {{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}}=>4 {{1,2,4,5},{3},{6,7}}=>2 {{1,2,4,5},{3},{6},{7}}=>2 {{1,2,4,6,7},{3,5}}=>3 {{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}}=>1 {{1,2,4},{3,5,6},{7}}=>1 {{1,2,4,7},{3,5},{6}}=>2 {{1,2,4},{3,5,7},{6}}=>3 {{1,2,4},{3,5},{6,7}}=>1 {{1,2,4},{3,5},{6},{7}}=>1 {{1,2,4,6,7},{3},{5}}=>3 {{1,2,4,6},{3,7},{5}}=>4 {{1,2,4,6},{3},{5,7}}=>2 {{1,2,4,6},{3},{5},{7}}=>2 {{1,2,4,7},{3,6},{5}}=>4 {{1,2,4},{3,6,7},{5}}=>5 {{1,2,4},{3,6},{5,7}}=>3 {{1,2,4},{3,6},{5},{7}}=>3 {{1,2,4,7},{3},{5,6}}=>2 {{1,2,4},{3,7},{5,6}}=>3 {{1,2,4},{3},{5,6,7}}=>1 {{1,2,4},{3},{5,6},{7}}=>1 {{1,2,4,7},{3},{5},{6}}=>2 {{1,2,4},{3,7},{5},{6}}=>3 {{1,2,4},{3},{5,7},{6}}=>4 {{1,2,4},{3},{5},{6,7}}=>1 {{1,2,4},{3},{5},{6},{7}}=>1 {{1,2,5,6,7},{3,4}}=>3 {{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}}=>1 {{1,2,5},{3,4,6},{7}}=>1 {{1,2,5,7},{3,4},{6}}=>2 {{1,2,5},{3,4,7},{6}}=>3 {{1,2,5},{3,4},{6,7}}=>1 {{1,2,5},{3,4},{6},{7}}=>1 {{1,2,6,7},{3,4,5}}=>2 {{1,2,6},{3,4,5,7}}=>1 {{1,2,6},{3,4,5},{7}}=>1 {{1,2,7},{3,4,5,6}}=>1 {{1,2},{3,4,5,6,7}}=>0 {{1,2},{3,4,5,6},{7}}=>0 {{1,2,7},{3,4,5},{6}}=>1 {{1,2},{3,4,5,7},{6}}=>2 {{1,2},{3,4,5},{6,7}}=>0 {{1,2},{3,4,5},{6},{7}}=>0 {{1,2,6,7},{3,4},{5}}=>2 {{1,2,6},{3,4,7},{5}}=>3 {{1,2,6},{3,4},{5,7}}=>1 {{1,2,6},{3,4},{5},{7}}=>1 {{1,2,7},{3,4,6},{5}}=>3 {{1,2},{3,4,6,7},{5}}=>4 {{1,2},{3,4,6},{5,7}}=>2 {{1,2},{3,4,6},{5},{7}}=>2 {{1,2,7},{3,4},{5,6}}=>1 {{1,2},{3,4,7},{5,6}}=>2 {{1,2},{3,4},{5,6,7}}=>0 {{1,2},{3,4},{5,6},{7}}=>0 {{1,2,7},{3,4},{5},{6}}=>1 {{1,2},{3,4,7},{5},{6}}=>2 {{1,2},{3,4},{5,7},{6}}=>3 {{1,2},{3,4},{5},{6,7}}=>0 {{1,2},{3,4},{5},{6},{7}}=>0 {{1,2,5,6,7},{3},{4}}=>3 {{1,2,5,6},{3,7},{4}}=>4 {{1,2,5,6},{3},{4,7}}=>2 {{1,2,5,6},{3},{4},{7}}=>2 {{1,2,5,7},{3,6},{4}}=>4 {{1,2,5},{3,6,7},{4}}=>5 {{1,2,5},{3,6},{4,7}}=>3 {{1,2,5},{3,6},{4},{7}}=>3 {{1,2,5,7},{3},{4,6}}=>2 {{1,2,5},{3,7},{4,6}}=>3 {{1,2,5},{3},{4,6,7}}=>1 {{1,2,5},{3},{4,6},{7}}=>1 {{1,2,5,7},{3},{4},{6}}=>2 {{1,2,5},{3,7},{4},{6}}=>3 {{1,2,5},{3},{4,7},{6}}=>4 {{1,2,5},{3},{4},{6,7}}=>1 {{1,2,5},{3},{4},{6},{7}}=>1 {{1,2,6,7},{3,5},{4}}=>4 {{1,2,6},{3,5,7},{4}}=>5 {{1,2,6},{3,5},{4,7}}=>3 {{1,2,6},{3,5},{4},{7}}=>3 {{1,2,7},{3,5,6},{4}}=>5 {{1,2},{3,5,6,7},{4}}=>6 {{1,2},{3,5,6},{4,7}}=>4 {{1,2},{3,5,6},{4},{7}}=>4 {{1,2,7},{3,5},{4,6}}=>3 {{1,2},{3,5,7},{4,6}}=>4 {{1,2},{3,5},{4,6,7}}=>2 {{1,2},{3,5},{4,6},{7}}=>2 {{1,2,7},{3,5},{4},{6}}=>3 {{1,2},{3,5,7},{4},{6}}=>4 {{1,2},{3,5},{4,7},{6}}=>5 {{1,2},{3,5},{4},{6,7}}=>2 {{1,2},{3,5},{4},{6},{7}}=>2 {{1,2,6,7},{3},{4,5}}=>2 {{1,2,6},{3,7},{4,5}}=>3 {{1,2,6},{3},{4,5,7}}=>1 {{1,2,6},{3},{4,5},{7}}=>1 {{1,2,7},{3,6},{4,5}}=>3 {{1,2},{3,6,7},{4,5}}=>4 {{1,2},{3,6},{4,5,7}}=>2 {{1,2},{3,6},{4,5},{7}}=>2 {{1,2,7},{3},{4,5,6}}=>1 {{1,2},{3,7},{4,5,6}}=>2 {{1,2},{3},{4,5,6,7}}=>0 {{1,2},{3},{4,5,6},{7}}=>0 {{1,2,7},{3},{4,5},{6}}=>1 {{1,2},{3,7},{4,5},{6}}=>2 {{1,2},{3},{4,5,7},{6}}=>3 {{1,2},{3},{4,5},{6,7}}=>0 {{1,2},{3},{4,5},{6},{7}}=>0 {{1,2,6,7},{3},{4},{5}}=>2 {{1,2,6},{3,7},{4},{5}}=>3 {{1,2,6},{3},{4,7},{5}}=>4 {{1,2,6},{3},{4},{5,7}}=>1 {{1,2,6},{3},{4},{5},{7}}=>1 {{1,2,7},{3,6},{4},{5}}=>3 {{1,2},{3,6,7},{4},{5}}=>4 {{1,2},{3,6},{4,7},{5}}=>5 {{1,2},{3,6},{4},{5,7}}=>2 {{1,2},{3,6},{4},{5},{7}}=>2 {{1,2,7},{3},{4,6},{5}}=>4 {{1,2},{3,7},{4,6},{5}}=>5 {{1,2},{3},{4,6,7},{5}}=>6 {{1,2},{3},{4,6},{5,7}}=>3 {{1,2},{3},{4,6},{5},{7}}=>3 {{1,2,7},{3},{4},{5,6}}=>1 {{1,2},{3,7},{4},{5,6}}=>2 {{1,2},{3},{4,7},{5,6}}=>3 {{1,2},{3},{4},{5,6,7}}=>0 {{1,2},{3},{4},{5,6},{7}}=>0 {{1,2,7},{3},{4},{5},{6}}=>1 {{1,2},{3,7},{4},{5},{6}}=>2 {{1,2},{3},{4,7},{5},{6}}=>3 {{1,2},{3},{4},{5,7},{6}}=>4 {{1,2},{3},{4},{5},{6,7}}=>0 {{1,2},{3},{4},{5},{6},{7}}=>0 {{1,3,4,5,6,7},{2}}=>5 {{1,3,4,5,6},{2,7}}=>4 {{1,3,4,5,6},{2},{7}}=>4 {{1,3,4,5,7},{2,6}}=>4 {{1,3,4,5},{2,6,7}}=>3 {{1,3,4,5},{2,6},{7}}=>3 {{1,3,4,5,7},{2},{6}}=>4 {{1,3,4,5},{2,7},{6}}=>5 {{1,3,4,5},{2},{6,7}}=>3 {{1,3,4,5},{2},{6},{7}}=>3 {{1,3,4,6,7},{2,5}}=>4 {{1,3,4,6},{2,5,7}}=>3 {{1,3,4,6},{2,5},{7}}=>3 {{1,3,4,7},{2,5,6}}=>3 {{1,3,4},{2,5,6,7}}=>2 {{1,3,4},{2,5,6},{7}}=>2 {{1,3,4,7},{2,5},{6}}=>3 {{1,3,4},{2,5,7},{6}}=>4 {{1,3,4},{2,5},{6,7}}=>2 {{1,3,4},{2,5},{6},{7}}=>2 {{1,3,4,6,7},{2},{5}}=>4 {{1,3,4,6},{2,7},{5}}=>5 {{1,3,4,6},{2},{5,7}}=>3 {{1,3,4,6},{2},{5},{7}}=>3 {{1,3,4,7},{2,6},{5}}=>5 {{1,3,4},{2,6,7},{5}}=>6 {{1,3,4},{2,6},{5,7}}=>4 {{1,3,4},{2,6},{5},{7}}=>4 {{1,3,4,7},{2},{5,6}}=>3 {{1,3,4},{2,7},{5,6}}=>4 {{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},{2,7},{5},{6}}=>4 {{1,3,4},{2},{5,7},{6}}=>5 {{1,3,4},{2},{5},{6,7}}=>2 {{1,3,4},{2},{5},{6},{7}}=>2 {{1,3,5,6,7},{2,4}}=>4 {{1,3,5,6},{2,4,7}}=>3 {{1,3,5,6},{2,4},{7}}=>3 {{1,3,5,7},{2,4,6}}=>3 {{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}}=>4 {{1,3,5},{2,4},{6,7}}=>2 {{1,3,5},{2,4},{6},{7}}=>2 {{1,3,6,7},{2,4,5}}=>3 {{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}}=>1 {{1,3},{2,4,5,6},{7}}=>1 {{1,3,7},{2,4,5},{6}}=>2 {{1,3},{2,4,5,7},{6}}=>3 {{1,3},{2,4,5},{6,7}}=>1 {{1,3},{2,4,5},{6},{7}}=>1 {{1,3,6,7},{2,4},{5}}=>3 {{1,3,6},{2,4,7},{5}}=>4 {{1,3,6},{2,4},{5,7}}=>2 {{1,3,6},{2,4},{5},{7}}=>2 {{1,3,7},{2,4,6},{5}}=>4 {{1,3},{2,4,6,7},{5}}=>5 {{1,3},{2,4,6},{5,7}}=>3 {{1,3},{2,4,6},{5},{7}}=>3 {{1,3,7},{2,4},{5,6}}=>2 {{1,3},{2,4,7},{5,6}}=>3 {{1,3},{2,4},{5,6,7}}=>1 {{1,3},{2,4},{5,6},{7}}=>1 {{1,3,7},{2,4},{5},{6}}=>2 {{1,3},{2,4,7},{5},{6}}=>3 {{1,3},{2,4},{5,7},{6}}=>4 {{1,3},{2,4},{5},{6,7}}=>1 {{1,3},{2,4},{5},{6},{7}}=>1 {{1,3,5,6,7},{2},{4}}=>4 {{1,3,5,6},{2,7},{4}}=>5 {{1,3,5,6},{2},{4,7}}=>3 {{1,3,5,6},{2},{4},{7}}=>3 {{1,3,5,7},{2,6},{4}}=>5 {{1,3,5},{2,6,7},{4}}=>6 {{1,3,5},{2,6},{4,7}}=>4 {{1,3,5},{2,6},{4},{7}}=>4 {{1,3,5,7},{2},{4,6}}=>3 {{1,3,5},{2,7},{4,6}}=>4 {{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},{2,7},{4},{6}}=>4 {{1,3,5},{2},{4,7},{6}}=>5 {{1,3,5},{2},{4},{6,7}}=>2 {{1,3,5},{2},{4},{6},{7}}=>2 {{1,3,6,7},{2,5},{4}}=>5 {{1,3,6},{2,5,7},{4}}=>6 {{1,3,6},{2,5},{4,7}}=>4 {{1,3,6},{2,5},{4},{7}}=>4 {{1,3,7},{2,5,6},{4}}=>6 {{1,3},{2,5,6,7},{4}}=>7 {{1,3},{2,5,6},{4,7}}=>5 {{1,3},{2,5,6},{4},{7}}=>5 {{1,3,7},{2,5},{4,6}}=>4 {{1,3},{2,5,7},{4,6}}=>5 {{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}}=>5 {{1,3},{2,5},{4,7},{6}}=>6 {{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}}=>4 {{1,3,6},{2},{4,5,7}}=>2 {{1,3,6},{2},{4,5},{7}}=>2 {{1,3,7},{2,6},{4,5}}=>4 {{1,3},{2,6,7},{4,5}}=>5 {{1,3},{2,6},{4,5,7}}=>3 {{1,3},{2,6},{4,5},{7}}=>3 {{1,3,7},{2},{4,5,6}}=>2 {{1,3},{2,7},{4,5,6}}=>3 {{1,3},{2},{4,5,6,7}}=>1 {{1,3},{2},{4,5,6},{7}}=>1 {{1,3,7},{2},{4,5},{6}}=>2 {{1,3},{2,7},{4,5},{6}}=>3 {{1,3},{2},{4,5,7},{6}}=>4 {{1,3},{2},{4,5},{6,7}}=>1 {{1,3},{2},{4,5},{6},{7}}=>1 {{1,3,6,7},{2},{4},{5}}=>3 {{1,3,6},{2,7},{4},{5}}=>4 {{1,3,6},{2},{4,7},{5}}=>5 {{1,3,6},{2},{4},{5,7}}=>2 {{1,3,6},{2},{4},{5},{7}}=>2 {{1,3,7},{2,6},{4},{5}}=>4 {{1,3},{2,6,7},{4},{5}}=>5 {{1,3},{2,6},{4,7},{5}}=>6 {{1,3},{2,6},{4},{5,7}}=>3 {{1,3},{2,6},{4},{5},{7}}=>3 {{1,3,7},{2},{4,6},{5}}=>5 {{1,3},{2,7},{4,6},{5}}=>6 {{1,3},{2},{4,6,7},{5}}=>7 {{1,3},{2},{4,6},{5,7}}=>4 {{1,3},{2},{4,6},{5},{7}}=>4 {{1,3,7},{2},{4},{5,6}}=>2 {{1,3},{2,7},{4},{5,6}}=>3 {{1,3},{2},{4,7},{5,6}}=>4 {{1,3},{2},{4},{5,6,7}}=>1 {{1,3},{2},{4},{5,6},{7}}=>1 {{1,3,7},{2},{4},{5},{6}}=>2 {{1,3},{2,7},{4},{5},{6}}=>3 {{1,3},{2},{4,7},{5},{6}}=>4 {{1,3},{2},{4},{5,7},{6}}=>5 {{1,3},{2},{4},{5},{6,7}}=>1 {{1,3},{2},{4},{5},{6},{7}}=>1 {{1,4,5,6,7},{2,3}}=>4 {{1,4,5,6},{2,3,7}}=>3 {{1,4,5,6},{2,3},{7}}=>3 {{1,4,5,7},{2,3,6}}=>3 {{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}}=>4 {{1,4,5},{2,3},{6,7}}=>2 {{1,4,5},{2,3},{6},{7}}=>2 {{1,4,6,7},{2,3,5}}=>3 {{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}}=>1 {{1,4},{2,3,5,6},{7}}=>1 {{1,4,7},{2,3,5},{6}}=>2 {{1,4},{2,3,5,7},{6}}=>3 {{1,4},{2,3,5},{6,7}}=>1 {{1,4},{2,3,5},{6},{7}}=>1 {{1,4,6,7},{2,3},{5}}=>3 {{1,4,6},{2,3,7},{5}}=>4 {{1,4,6},{2,3},{5,7}}=>2 {{1,4,6},{2,3},{5},{7}}=>2 {{1,4,7},{2,3,6},{5}}=>4 {{1,4},{2,3,6,7},{5}}=>5 {{1,4},{2,3,6},{5,7}}=>3 {{1,4},{2,3,6},{5},{7}}=>3 {{1,4,7},{2,3},{5,6}}=>2 {{1,4},{2,3,7},{5,6}}=>3 {{1,4},{2,3},{5,6,7}}=>1 {{1,4},{2,3},{5,6},{7}}=>1 {{1,4,7},{2,3},{5},{6}}=>2 {{1,4},{2,3,7},{5},{6}}=>3 {{1,4},{2,3},{5,7},{6}}=>4 {{1,4},{2,3},{5},{6,7}}=>1 {{1,4},{2,3},{5},{6},{7}}=>1 {{1,5,6,7},{2,3,4}}=>3 {{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}}=>1 {{1,5},{2,3,4,6},{7}}=>1 {{1,5,7},{2,3,4},{6}}=>2 {{1,5},{2,3,4,7},{6}}=>3 {{1,5},{2,3,4},{6,7}}=>1 {{1,5},{2,3,4},{6},{7}}=>1 {{1,6,7},{2,3,4,5}}=>2 {{1,6},{2,3,4,5,7}}=>1 {{1,6},{2,3,4,5},{7}}=>1 {{1,7},{2,3,4,5,6}}=>1 {{1},{2,3,4,5,6,7}}=>0 {{1},{2,3,4,5,6},{7}}=>0 {{1,7},{2,3,4,5},{6}}=>1 {{1},{2,3,4,5,7},{6}}=>2 {{1},{2,3,4,5},{6,7}}=>0 {{1},{2,3,4,5},{6},{7}}=>0 {{1,6,7},{2,3,4},{5}}=>2 {{1,6},{2,3,4,7},{5}}=>3 {{1,6},{2,3,4},{5,7}}=>1 {{1,6},{2,3,4},{5},{7}}=>1 {{1,7},{2,3,4,6},{5}}=>3 {{1},{2,3,4,6,7},{5}}=>4 {{1},{2,3,4,6},{5,7}}=>2 {{1},{2,3,4,6},{5},{7}}=>2 {{1,7},{2,3,4},{5,6}}=>1 {{1},{2,3,4,7},{5,6}}=>2 {{1},{2,3,4},{5,6,7}}=>0 {{1},{2,3,4},{5,6},{7}}=>0 {{1,7},{2,3,4},{5},{6}}=>1 {{1},{2,3,4,7},{5},{6}}=>2 {{1},{2,3,4},{5,7},{6}}=>3 {{1},{2,3,4},{5},{6,7}}=>0 {{1},{2,3,4},{5},{6},{7}}=>0 {{1,5,6,7},{2,3},{4}}=>3 {{1,5,6},{2,3,7},{4}}=>4 {{1,5,6},{2,3},{4,7}}=>2 {{1,5,6},{2,3},{4},{7}}=>2 {{1,5,7},{2,3,6},{4}}=>4 {{1,5},{2,3,6,7},{4}}=>5 {{1,5},{2,3,6},{4,7}}=>3 {{1,5},{2,3,6},{4},{7}}=>3 {{1,5,7},{2,3},{4,6}}=>2 {{1,5},{2,3,7},{4,6}}=>3 {{1,5},{2,3},{4,6,7}}=>1 {{1,5},{2,3},{4,6},{7}}=>1 {{1,5,7},{2,3},{4},{6}}=>2 {{1,5},{2,3,7},{4},{6}}=>3 {{1,5},{2,3},{4,7},{6}}=>4 {{1,5},{2,3},{4},{6,7}}=>1 {{1,5},{2,3},{4},{6},{7}}=>1 {{1,6,7},{2,3,5},{4}}=>4 {{1,6},{2,3,5,7},{4}}=>5 {{1,6},{2,3,5},{4,7}}=>3 {{1,6},{2,3,5},{4},{7}}=>3 {{1,7},{2,3,5,6},{4}}=>5 {{1},{2,3,5,6,7},{4}}=>6 {{1},{2,3,5,6},{4,7}}=>4 {{1},{2,3,5,6},{4},{7}}=>4 {{1,7},{2,3,5},{4,6}}=>3 {{1},{2,3,5,7},{4,6}}=>4 {{1},{2,3,5},{4,6,7}}=>2 {{1},{2,3,5},{4,6},{7}}=>2 {{1,7},{2,3,5},{4},{6}}=>3 {{1},{2,3,5,7},{4},{6}}=>4 {{1},{2,3,5},{4,7},{6}}=>5 {{1},{2,3,5},{4},{6,7}}=>2 {{1},{2,3,5},{4},{6},{7}}=>2 {{1,6,7},{2,3},{4,5}}=>2 {{1,6},{2,3,7},{4,5}}=>3 {{1,6},{2,3},{4,5,7}}=>1 {{1,6},{2,3},{4,5},{7}}=>1 {{1,7},{2,3,6},{4,5}}=>3 {{1},{2,3,6,7},{4,5}}=>4 {{1},{2,3,6},{4,5,7}}=>2 {{1},{2,3,6},{4,5},{7}}=>2 {{1,7},{2,3},{4,5,6}}=>1 {{1},{2,3,7},{4,5,6}}=>2 {{1},{2,3},{4,5,6,7}}=>0 {{1},{2,3},{4,5,6},{7}}=>0 {{1,7},{2,3},{4,5},{6}}=>1 {{1},{2,3,7},{4,5},{6}}=>2 {{1},{2,3},{4,5,7},{6}}=>3 {{1},{2,3},{4,5},{6,7}}=>0 {{1},{2,3},{4,5},{6},{7}}=>0 {{1,6,7},{2,3},{4},{5}}=>2 {{1,6},{2,3,7},{4},{5}}=>3 {{1,6},{2,3},{4,7},{5}}=>4 {{1,6},{2,3},{4},{5,7}}=>1 {{1,6},{2,3},{4},{5},{7}}=>1 {{1,7},{2,3,6},{4},{5}}=>3 {{1},{2,3,6,7},{4},{5}}=>4 {{1},{2,3,6},{4,7},{5}}=>5 {{1},{2,3,6},{4},{5,7}}=>2 {{1},{2,3,6},{4},{5},{7}}=>2 {{1,7},{2,3},{4,6},{5}}=>4 {{1},{2,3,7},{4,6},{5}}=>5 {{1},{2,3},{4,6,7},{5}}=>6 {{1},{2,3},{4,6},{5,7}}=>3 {{1},{2,3},{4,6},{5},{7}}=>3 {{1,7},{2,3},{4},{5,6}}=>1 {{1},{2,3,7},{4},{5,6}}=>2 {{1},{2,3},{4,7},{5,6}}=>3 {{1},{2,3},{4},{5,6,7}}=>0 {{1},{2,3},{4},{5,6},{7}}=>0 {{1,7},{2,3},{4},{5},{6}}=>1 {{1},{2,3,7},{4},{5},{6}}=>2 {{1},{2,3},{4,7},{5},{6}}=>3 {{1},{2,3},{4},{5,7},{6}}=>4 {{1},{2,3},{4},{5},{6,7}}=>0 {{1},{2,3},{4},{5},{6},{7}}=>0 {{1,4,5,6,7},{2},{3}}=>4 {{1,4,5,6},{2,7},{3}}=>5 {{1,4,5,6},{2},{3,7}}=>3 {{1,4,5,6},{2},{3},{7}}=>3 {{1,4,5,7},{2,6},{3}}=>5 {{1,4,5},{2,6,7},{3}}=>6 {{1,4,5},{2,6},{3,7}}=>4 {{1,4,5},{2,6},{3},{7}}=>4 {{1,4,5,7},{2},{3,6}}=>3 {{1,4,5},{2,7},{3,6}}=>4 {{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},{2,7},{3},{6}}=>4 {{1,4,5},{2},{3,7},{6}}=>5 {{1,4,5},{2},{3},{6,7}}=>2 {{1,4,5},{2},{3},{6},{7}}=>2 {{1,4,6,7},{2,5},{3}}=>5 {{1,4,6},{2,5,7},{3}}=>6 {{1,4,6},{2,5},{3,7}}=>4 {{1,4,6},{2,5},{3},{7}}=>4 {{1,4,7},{2,5,6},{3}}=>6 {{1,4},{2,5,6,7},{3}}=>7 {{1,4},{2,5,6},{3,7}}=>5 {{1,4},{2,5,6},{3},{7}}=>5 {{1,4,7},{2,5},{3,6}}=>4 {{1,4},{2,5,7},{3,6}}=>5 {{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}}=>5 {{1,4},{2,5},{3,7},{6}}=>6 {{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}}=>4 {{1,4,6},{2},{3,5,7}}=>2 {{1,4,6},{2},{3,5},{7}}=>2 {{1,4,7},{2,6},{3,5}}=>4 {{1,4},{2,6,7},{3,5}}=>5 {{1,4},{2,6},{3,5,7}}=>3 {{1,4},{2,6},{3,5},{7}}=>3 {{1,4,7},{2},{3,5,6}}=>2 {{1,4},{2,7},{3,5,6}}=>3 {{1,4},{2},{3,5,6,7}}=>1 {{1,4},{2},{3,5,6},{7}}=>1 {{1,4,7},{2},{3,5},{6}}=>2 {{1,4},{2,7},{3,5},{6}}=>3 {{1,4},{2},{3,5,7},{6}}=>4 {{1,4},{2},{3,5},{6,7}}=>1 {{1,4},{2},{3,5},{6},{7}}=>1 {{1,4,6,7},{2},{3},{5}}=>3 {{1,4,6},{2,7},{3},{5}}=>4 {{1,4,6},{2},{3,7},{5}}=>5 {{1,4,6},{2},{3},{5,7}}=>2 {{1,4,6},{2},{3},{5},{7}}=>2 {{1,4,7},{2,6},{3},{5}}=>4 {{1,4},{2,6,7},{3},{5}}=>5 {{1,4},{2,6},{3,7},{5}}=>6 {{1,4},{2,6},{3},{5,7}}=>3 {{1,4},{2,6},{3},{5},{7}}=>3 {{1,4,7},{2},{3,6},{5}}=>5 {{1,4},{2,7},{3,6},{5}}=>6 {{1,4},{2},{3,6,7},{5}}=>7 {{1,4},{2},{3,6},{5,7}}=>4 {{1,4},{2},{3,6},{5},{7}}=>4 {{1,4,7},{2},{3},{5,6}}=>2 {{1,4},{2,7},{3},{5,6}}=>3 {{1,4},{2},{3,7},{5,6}}=>4 {{1,4},{2},{3},{5,6,7}}=>1 {{1,4},{2},{3},{5,6},{7}}=>1 {{1,4,7},{2},{3},{5},{6}}=>2 {{1,4},{2,7},{3},{5},{6}}=>3 {{1,4},{2},{3,7},{5},{6}}=>4 {{1,4},{2},{3},{5,7},{6}}=>5 {{1,4},{2},{3},{5},{6,7}}=>1 {{1,4},{2},{3},{5},{6},{7}}=>1 {{1,5,6,7},{2,4},{3}}=>5 {{1,5,6},{2,4,7},{3}}=>6 {{1,5,6},{2,4},{3,7}}=>4 {{1,5,6},{2,4},{3},{7}}=>4 {{1,5,7},{2,4,6},{3}}=>6 {{1,5},{2,4,6,7},{3}}=>7 {{1,5},{2,4,6},{3,7}}=>5 {{1,5},{2,4,6},{3},{7}}=>5 {{1,5,7},{2,4},{3,6}}=>4 {{1,5},{2,4,7},{3,6}}=>5 {{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}}=>5 {{1,5},{2,4},{3,7},{6}}=>6 {{1,5},{2,4},{3},{6,7}}=>3 {{1,5},{2,4},{3},{6},{7}}=>3 {{1,6,7},{2,4,5},{3}}=>6 {{1,6},{2,4,5,7},{3}}=>7 {{1,6},{2,4,5},{3,7}}=>5 {{1,6},{2,4,5},{3},{7}}=>5 {{1,7},{2,4,5,6},{3}}=>7 {{1},{2,4,5,6,7},{3}}=>8 {{1},{2,4,5,6},{3,7}}=>6 {{1},{2,4,5,6},{3},{7}}=>6 {{1,7},{2,4,5},{3,6}}=>5 {{1},{2,4,5,7},{3,6}}=>6 {{1},{2,4,5},{3,6,7}}=>4 {{1},{2,4,5},{3,6},{7}}=>4 {{1,7},{2,4,5},{3},{6}}=>5 {{1},{2,4,5,7},{3},{6}}=>6 {{1},{2,4,5},{3,7},{6}}=>7 {{1},{2,4,5},{3},{6,7}}=>4 {{1},{2,4,5},{3},{6},{7}}=>4 {{1,6,7},{2,4},{3,5}}=>4 {{1,6},{2,4,7},{3,5}}=>5 {{1,6},{2,4},{3,5,7}}=>3 {{1,6},{2,4},{3,5},{7}}=>3 {{1,7},{2,4,6},{3,5}}=>5 {{1},{2,4,6,7},{3,5}}=>6 {{1},{2,4,6},{3,5,7}}=>4 {{1},{2,4,6},{3,5},{7}}=>4 {{1,7},{2,4},{3,5,6}}=>3 {{1},{2,4,7},{3,5,6}}=>4 {{1},{2,4},{3,5,6,7}}=>2 {{1},{2,4},{3,5,6},{7}}=>2 {{1,7},{2,4},{3,5},{6}}=>3 {{1},{2,4,7},{3,5},{6}}=>4 {{1},{2,4},{3,5,7},{6}}=>5 {{1},{2,4},{3,5},{6,7}}=>2 {{1},{2,4},{3,5},{6},{7}}=>2 {{1,6,7},{2,4},{3},{5}}=>4 {{1,6},{2,4,7},{3},{5}}=>5 {{1,6},{2,4},{3,7},{5}}=>6 {{1,6},{2,4},{3},{5,7}}=>3 {{1,6},{2,4},{3},{5},{7}}=>3 {{1,7},{2,4,6},{3},{5}}=>5 {{1},{2,4,6,7},{3},{5}}=>6 {{1},{2,4,6},{3,7},{5}}=>7 {{1},{2,4,6},{3},{5,7}}=>4 {{1},{2,4,6},{3},{5},{7}}=>4 {{1,7},{2,4},{3,6},{5}}=>6 {{1},{2,4,7},{3,6},{5}}=>7 {{1},{2,4},{3,6,7},{5}}=>8 {{1},{2,4},{3,6},{5,7}}=>5 {{1},{2,4},{3,6},{5},{7}}=>5 {{1,7},{2,4},{3},{5,6}}=>3 {{1},{2,4,7},{3},{5,6}}=>4 {{1},{2,4},{3,7},{5,6}}=>5 {{1},{2,4},{3},{5,6,7}}=>2 {{1},{2,4},{3},{5,6},{7}}=>2 {{1,7},{2,4},{3},{5},{6}}=>3 {{1},{2,4,7},{3},{5},{6}}=>4 {{1},{2,4},{3,7},{5},{6}}=>5 {{1},{2,4},{3},{5,7},{6}}=>6 {{1},{2,4},{3},{5},{6,7}}=>2 {{1},{2,4},{3},{5},{6},{7}}=>2 {{1,5,6,7},{2},{3,4}}=>3 {{1,5,6},{2,7},{3,4}}=>4 {{1,5,6},{2},{3,4,7}}=>2 {{1,5,6},{2},{3,4},{7}}=>2 {{1,5,7},{2,6},{3,4}}=>4 {{1,5},{2,6,7},{3,4}}=>5 {{1,5},{2,6},{3,4,7}}=>3 {{1,5},{2,6},{3,4},{7}}=>3 {{1,5,7},{2},{3,4,6}}=>2 {{1,5},{2,7},{3,4,6}}=>3 {{1,5},{2},{3,4,6,7}}=>1 {{1,5},{2},{3,4,6},{7}}=>1 {{1,5,7},{2},{3,4},{6}}=>2 {{1,5},{2,7},{3,4},{6}}=>3 {{1,5},{2},{3,4,7},{6}}=>4 {{1,5},{2},{3,4},{6,7}}=>1 {{1,5},{2},{3,4},{6},{7}}=>1 {{1,6,7},{2,5},{3,4}}=>4 {{1,6},{2,5,7},{3,4}}=>5 {{1,6},{2,5},{3,4,7}}=>3 {{1,6},{2,5},{3,4},{7}}=>3 {{1,7},{2,5,6},{3,4}}=>5 {{1},{2,5,6,7},{3,4}}=>6 {{1},{2,5,6},{3,4,7}}=>4 {{1},{2,5,6},{3,4},{7}}=>4 {{1,7},{2,5},{3,4,6}}=>3 {{1},{2,5,7},{3,4,6}}=>4 {{1},{2,5},{3,4,6,7}}=>2 {{1},{2,5},{3,4,6},{7}}=>2 {{1,7},{2,5},{3,4},{6}}=>3 {{1},{2,5,7},{3,4},{6}}=>4 {{1},{2,5},{3,4,7},{6}}=>5 {{1},{2,5},{3,4},{6,7}}=>2 {{1},{2,5},{3,4},{6},{7}}=>2 {{1,6,7},{2},{3,4,5}}=>2 {{1,6},{2,7},{3,4,5}}=>3 {{1,6},{2},{3,4,5,7}}=>1 {{1,6},{2},{3,4,5},{7}}=>1 {{1,7},{2,6},{3,4,5}}=>3 {{1},{2,6,7},{3,4,5}}=>4 {{1},{2,6},{3,4,5,7}}=>2 {{1},{2,6},{3,4,5},{7}}=>2 {{1,7},{2},{3,4,5,6}}=>1 {{1},{2,7},{3,4,5,6}}=>2 {{1},{2},{3,4,5,6,7}}=>0 {{1},{2},{3,4,5,6},{7}}=>0 {{1,7},{2},{3,4,5},{6}}=>1 {{1},{2,7},{3,4,5},{6}}=>2 {{1},{2},{3,4,5,7},{6}}=>3 {{1},{2},{3,4,5},{6,7}}=>0 {{1},{2},{3,4,5},{6},{7}}=>0 {{1,6,7},{2},{3,4},{5}}=>2 {{1,6},{2,7},{3,4},{5}}=>3 {{1,6},{2},{3,4,7},{5}}=>4 {{1,6},{2},{3,4},{5,7}}=>1 {{1,6},{2},{3,4},{5},{7}}=>1 {{1,7},{2,6},{3,4},{5}}=>3 {{1},{2,6,7},{3,4},{5}}=>4 {{1},{2,6},{3,4,7},{5}}=>5 {{1},{2,6},{3,4},{5,7}}=>2 {{1},{2,6},{3,4},{5},{7}}=>2 {{1,7},{2},{3,4,6},{5}}=>4 {{1},{2,7},{3,4,6},{5}}=>5 {{1},{2},{3,4,6,7},{5}}=>6 {{1},{2},{3,4,6},{5,7}}=>3 {{1},{2},{3,4,6},{5},{7}}=>3 {{1,7},{2},{3,4},{5,6}}=>1 {{1},{2,7},{3,4},{5,6}}=>2 {{1},{2},{3,4,7},{5,6}}=>3 {{1},{2},{3,4},{5,6,7}}=>0 {{1},{2},{3,4},{5,6},{7}}=>0 {{1,7},{2},{3,4},{5},{6}}=>1 {{1},{2,7},{3,4},{5},{6}}=>2 {{1},{2},{3,4,7},{5},{6}}=>3 {{1},{2},{3,4},{5,7},{6}}=>4 {{1},{2},{3,4},{5},{6,7}}=>0 {{1},{2},{3,4},{5},{6},{7}}=>0 {{1,5,6,7},{2},{3},{4}}=>3 {{1,5,6},{2,7},{3},{4}}=>4 {{1,5,6},{2},{3,7},{4}}=>5 {{1,5,6},{2},{3},{4,7}}=>2 {{1,5,6},{2},{3},{4},{7}}=>2 {{1,5,7},{2,6},{3},{4}}=>4 {{1,5},{2,6,7},{3},{4}}=>5 {{1,5},{2,6},{3,7},{4}}=>6 {{1,5},{2,6},{3},{4,7}}=>3 {{1,5},{2,6},{3},{4},{7}}=>3 {{1,5,7},{2},{3,6},{4}}=>5 {{1,5},{2,7},{3,6},{4}}=>6 {{1,5},{2},{3,6,7},{4}}=>7 {{1,5},{2},{3,6},{4,7}}=>4 {{1,5},{2},{3,6},{4},{7}}=>4 {{1,5,7},{2},{3},{4,6}}=>2 {{1,5},{2,7},{3},{4,6}}=>3 {{1,5},{2},{3,7},{4,6}}=>4 {{1,5},{2},{3},{4,6,7}}=>1 {{1,5},{2},{3},{4,6},{7}}=>1 {{1,5,7},{2},{3},{4},{6}}=>2 {{1,5},{2,7},{3},{4},{6}}=>3 {{1,5},{2},{3,7},{4},{6}}=>4 {{1,5},{2},{3},{4,7},{6}}=>5 {{1,5},{2},{3},{4},{6,7}}=>1 {{1,5},{2},{3},{4},{6},{7}}=>1 {{1,6,7},{2,5},{3},{4}}=>4 {{1,6},{2,5,7},{3},{4}}=>5 {{1,6},{2,5},{3,7},{4}}=>6 {{1,6},{2,5},{3},{4,7}}=>3 {{1,6},{2,5},{3},{4},{7}}=>3 {{1,7},{2,5,6},{3},{4}}=>5 {{1},{2,5,6,7},{3},{4}}=>6 {{1},{2,5,6},{3,7},{4}}=>7 {{1},{2,5,6},{3},{4,7}}=>4 {{1},{2,5,6},{3},{4},{7}}=>4 {{1,7},{2,5},{3,6},{4}}=>6 {{1},{2,5,7},{3,6},{4}}=>7 {{1},{2,5},{3,6,7},{4}}=>8 {{1},{2,5},{3,6},{4,7}}=>5 {{1},{2,5},{3,6},{4},{7}}=>5 {{1,7},{2,5},{3},{4,6}}=>3 {{1},{2,5,7},{3},{4,6}}=>4 {{1},{2,5},{3,7},{4,6}}=>5 {{1},{2,5},{3},{4,6,7}}=>2 {{1},{2,5},{3},{4,6},{7}}=>2 {{1,7},{2,5},{3},{4},{6}}=>3 {{1},{2,5,7},{3},{4},{6}}=>4 {{1},{2,5},{3,7},{4},{6}}=>5 {{1},{2,5},{3},{4,7},{6}}=>6 {{1},{2,5},{3},{4},{6,7}}=>2 {{1},{2,5},{3},{4},{6},{7}}=>2 {{1,6,7},{2},{3,5},{4}}=>5 {{1,6},{2,7},{3,5},{4}}=>6 {{1,6},{2},{3,5,7},{4}}=>7 {{1,6},{2},{3,5},{4,7}}=>4 {{1,6},{2},{3,5},{4},{7}}=>4 {{1,7},{2,6},{3,5},{4}}=>6 {{1},{2,6,7},{3,5},{4}}=>7 {{1},{2,6},{3,5,7},{4}}=>8 {{1},{2,6},{3,5},{4,7}}=>5 {{1},{2,6},{3,5},{4},{7}}=>5 {{1,7},{2},{3,5,6},{4}}=>7 {{1},{2,7},{3,5,6},{4}}=>8 {{1},{2},{3,5,6,7},{4}}=>9 {{1},{2},{3,5,6},{4,7}}=>6 {{1},{2},{3,5,6},{4},{7}}=>6 {{1,7},{2},{3,5},{4,6}}=>4 {{1},{2,7},{3,5},{4,6}}=>5 {{1},{2},{3,5,7},{4,6}}=>6 {{1},{2},{3,5},{4,6,7}}=>3 {{1},{2},{3,5},{4,6},{7}}=>3 {{1,7},{2},{3,5},{4},{6}}=>4 {{1},{2,7},{3,5},{4},{6}}=>5 {{1},{2},{3,5,7},{4},{6}}=>6 {{1},{2},{3,5},{4,7},{6}}=>7 {{1},{2},{3,5},{4},{6,7}}=>3 {{1},{2},{3,5},{4},{6},{7}}=>3 {{1,6,7},{2},{3},{4,5}}=>2 {{1,6},{2,7},{3},{4,5}}=>3 {{1,6},{2},{3,7},{4,5}}=>4 {{1,6},{2},{3},{4,5,7}}=>1 {{1,6},{2},{3},{4,5},{7}}=>1 {{1,7},{2,6},{3},{4,5}}=>3 {{1},{2,6,7},{3},{4,5}}=>4 {{1},{2,6},{3,7},{4,5}}=>5 {{1},{2,6},{3},{4,5,7}}=>2 {{1},{2,6},{3},{4,5},{7}}=>2 {{1,7},{2},{3,6},{4,5}}=>4 {{1},{2,7},{3,6},{4,5}}=>5 {{1},{2},{3,6,7},{4,5}}=>6 {{1},{2},{3,6},{4,5,7}}=>3 {{1},{2},{3,6},{4,5},{7}}=>3 {{1,7},{2},{3},{4,5,6}}=>1 {{1},{2,7},{3},{4,5,6}}=>2 {{1},{2},{3,7},{4,5,6}}=>3 {{1},{2},{3},{4,5,6,7}}=>0 {{1},{2},{3},{4,5,6},{7}}=>0 {{1,7},{2},{3},{4,5},{6}}=>1 {{1},{2,7},{3},{4,5},{6}}=>2 {{1},{2},{3,7},{4,5},{6}}=>3 {{1},{2},{3},{4,5,7},{6}}=>4 {{1},{2},{3},{4,5},{6,7}}=>0 {{1},{2},{3},{4,5},{6},{7}}=>0 {{1,6,7},{2},{3},{4},{5}}=>2 {{1,6},{2,7},{3},{4},{5}}=>3 {{1,6},{2},{3,7},{4},{5}}=>4 {{1,6},{2},{3},{4,7},{5}}=>5 {{1,6},{2},{3},{4},{5,7}}=>1 {{1,6},{2},{3},{4},{5},{7}}=>1 {{1,7},{2,6},{3},{4},{5}}=>3 {{1},{2,6,7},{3},{4},{5}}=>4 {{1},{2,6},{3,7},{4},{5}}=>5 {{1},{2,6},{3},{4,7},{5}}=>6 {{1},{2,6},{3},{4},{5,7}}=>2 {{1},{2,6},{3},{4},{5},{7}}=>2 {{1,7},{2},{3,6},{4},{5}}=>4 {{1},{2,7},{3,6},{4},{5}}=>5 {{1},{2},{3,6,7},{4},{5}}=>6 {{1},{2},{3,6},{4,7},{5}}=>7 {{1},{2},{3,6},{4},{5,7}}=>3 {{1},{2},{3,6},{4},{5},{7}}=>3 {{1,7},{2},{3},{4,6},{5}}=>5 {{1},{2,7},{3},{4,6},{5}}=>6 {{1},{2},{3,7},{4,6},{5}}=>7 {{1},{2},{3},{4,6,7},{5}}=>8 {{1},{2},{3},{4,6},{5,7}}=>4 {{1},{2},{3},{4,6},{5},{7}}=>4 {{1,7},{2},{3},{4},{5,6}}=>1 {{1},{2,7},{3},{4},{5,6}}=>2 {{1},{2},{3,7},{4},{5,6}}=>3 {{1},{2},{3},{4,7},{5,6}}=>4 {{1},{2},{3},{4},{5,6,7}}=>0 {{1},{2},{3},{4},{5,6},{7}}=>0 {{1,7},{2},{3},{4},{5},{6}}=>1 {{1},{2,7},{3},{4},{5},{6}}=>2 {{1},{2},{3,7},{4},{5},{6}}=>3 {{1},{2},{3},{4,7},{5},{6}}=>4 {{1},{2},{3},{4},{5,7},{6}}=>5 {{1},{2},{3},{4},{5},{6,7}}=>0 {{1},{2},{3},{4},{5},{6},{7}}=>0 {{1},{2},{3,4,5,6,7,8}}=>0 {{1},{2,4,5,6,7,8},{3}}=>10 {{1},{2,3,5,6,7,8},{4}}=>8 {{1},{2,3,4,6,7,8},{5}}=>6 {{1},{2,3,4,5,7,8},{6}}=>4 {{1},{2,3,4,5,6,7},{8}}=>0 {{1},{2,3,4,5,6,8},{7}}=>2 {{1},{2,3,4,5,6,7,8}}=>0 {{1,2},{3,4,5,6,7,8}}=>0 {{1,4,5,6,7,8},{2},{3}}=>5 {{1,3,5,6,7,8},{2},{4}}=>5 {{1,3,4,5,6,7,8},{2}}=>6 {{1,4,5,6,7,8},{2,3}}=>5 {{1,2,4,5,6,7,8},{3}}=>5 {{1,2,5,6,7,8},{3,4}}=>4 {{1,2,3,5,6,7,8},{4}}=>4 {{1,2,3,6,7,8},{4,5}}=>3 {{1,2,3,4,6,7,8},{5}}=>3 {{1,2,3,4,5,6},{7,8}}=>0 {{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}}=>0 {{1,8},{2,3,4,5,6,7}}=>1 {{1,2,3,4,5,8},{6,7}}=>1 {{1,2,3,4,5,6,8},{7}}=>1 {{1,2,3,4,5,6,7,8}}=>0 {{1,3,5,6,7,8},{2,4}}=>5 {{1,3,4,6,7,8},{2,5}}=>5 {{1,2,4,6,7,8},{3,5}}=>4 {{1,3,4,5,7,8},{2,6}}=>5 {{1,2,4,5,7,8},{3,6}}=>4 {{1,2,3,5,7,8},{4,6}}=>3 {{1,3,4,5,6,8},{2,7}}=>5 {{1,2,4,5,6,8},{3,7}}=>4 {{1,2,3,5,6,8},{4,7}}=>3 {{1,2,3,4,6,8},{5,7}}=>2 {{1,3,4,5,6,7},{2,8}}=>5 {{1,2,4,5,6,7},{3,8}}=>4 {{1,2,3,5,6,7},{4,8}}=>3 {{1,2,3,4,6,7},{5,8}}=>2 {{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 major index of a set partition.
Let $\pi=B_1/B_2/\dots/B_k$ with $\min B_1<\min B_2<\dots<\min B_k$ a set partition. Let $d_i$ be the number of elements in $B_i$ larger than $\min B_{i+1}$. Then the major index of $\pi$ is $1d_1+2d_2+\dots+(k-1)d_{k-1}$.
References
[1] Sagan, B. E. A maj statistic for set partitions MathSciNet:1087650
Code
def statistic(pi):
    """
    sage: statistic([[1,3,8],[2],[4,6,7],[5,9]])
    8
    """
    pi_sorted = sorted([sorted(b) for b in pi])
    l = len(pi_sorted)-1
    des = [0]*l
    for i in range(l):
        min_next = min(pi_sorted[i+1])
        des[i] = len([e for e in pi_sorted[i] if e > min_next])
        
    return sum(i*d for i, d in enumerate(des, 1))
Created
Aug 06, 2016 at 15:22 by Martin Rubey
Updated
Aug 06, 2016 at 15:22 by Martin Rubey