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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}}=>1 {{1,3},{2,4}}=>2 {{1,3},{2},{4}}=>1 {{1,4},{2,3}}=>2 {{1},{2,3,4}}=>0 {{1},{2,3},{4}}=>0 {{1,4},{2},{3}}=>2 {{1},{2,4},{3}}=>1 {{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}}=>1 {{1,2,4},{3,5}}=>2 {{1,2,4},{3},{5}}=>1 {{1,2,5},{3,4}}=>2 {{1,2},{3,4,5}}=>0 {{1,2},{3,4},{5}}=>0 {{1,2,5},{3},{4}}=>2 {{1,2},{3,5},{4}}=>1 {{1,2},{3},{4,5}}=>0 {{1,2},{3},{4},{5}}=>0 {{1,3,4,5},{2}}=>1 {{1,3,4},{2,5}}=>3 {{1,3,4},{2},{5}}=>1 {{1,3,5},{2,4}}=>3 {{1,3},{2,4,5}}=>2 {{1,3},{2,4},{5}}=>2 {{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}}=>3 {{1,4},{2,3},{5}}=>2 {{1,5},{2,3,4}}=>3 {{1},{2,3,4,5}}=>0 {{1},{2,3,4},{5}}=>0 {{1,5},{2,3},{4}}=>3 {{1},{2,3,5},{4}}=>1 {{1},{2,3},{4,5}}=>0 {{1},{2,3},{4},{5}}=>0 {{1,4,5},{2},{3}}=>2 {{1,4},{2,5},{3}}=>4 {{1,4},{2},{3,5}}=>3 {{1,4},{2},{3},{5}}=>2 {{1,5},{2,4},{3}}=>4 {{1},{2,4,5},{3}}=>1 {{1},{2,4},{3,5}}=>2 {{1},{2,4},{3},{5}}=>1 {{1,5},{2},{3,4}}=>3 {{1},{2,5},{3,4}}=>2 {{1},{2},{3,4,5}}=>0 {{1},{2},{3,4},{5}}=>0 {{1,5},{2},{3},{4}}=>3 {{1},{2,5},{3},{4}}=>2 {{1},{2},{3,5},{4}}=>1 {{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}}=>1 {{1,2,3,5},{4,6}}=>2 {{1,2,3,5},{4},{6}}=>1 {{1,2,3,6},{4,5}}=>2 {{1,2,3},{4,5,6}}=>0 {{1,2,3},{4,5},{6}}=>0 {{1,2,3,6},{4},{5}}=>2 {{1,2,3},{4,6},{5}}=>1 {{1,2,3},{4},{5,6}}=>0 {{1,2,3},{4},{5},{6}}=>0 {{1,2,4,5,6},{3}}=>1 {{1,2,4,5},{3,6}}=>3 {{1,2,4,5},{3},{6}}=>1 {{1,2,4,6},{3,5}}=>3 {{1,2,4},{3,5,6}}=>2 {{1,2,4},{3,5},{6}}=>2 {{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}}=>3 {{1,2,5},{3,4},{6}}=>2 {{1,2,6},{3,4,5}}=>3 {{1,2},{3,4,5,6}}=>0 {{1,2},{3,4,5},{6}}=>0 {{1,2,6},{3,4},{5}}=>3 {{1,2},{3,4,6},{5}}=>1 {{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}}=>4 {{1,2,5},{3},{4,6}}=>3 {{1,2,5},{3},{4},{6}}=>2 {{1,2,6},{3,5},{4}}=>4 {{1,2},{3,5,6},{4}}=>1 {{1,2},{3,5},{4,6}}=>2 {{1,2},{3,5},{4},{6}}=>1 {{1,2,6},{3},{4,5}}=>3 {{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}}=>3 {{1,2},{3,6},{4},{5}}=>2 {{1,2},{3},{4,6},{5}}=>1 {{1,2},{3},{4},{5,6}}=>0 {{1,2},{3},{4},{5},{6}}=>0 {{1,3,4,5,6},{2}}=>1 {{1,3,4,5},{2,6}}=>4 {{1,3,4,5},{2},{6}}=>1 {{1,3,4,6},{2,5}}=>4 {{1,3,4},{2,5,6}}=>3 {{1,3,4},{2,5},{6}}=>3 {{1,3,4,6},{2},{5}}=>2 {{1,3,4},{2,6},{5}}=>4 {{1,3,4},{2},{5,6}}=>1 {{1,3,4},{2},{5},{6}}=>1 {{1,3,5,6},{2,4}}=>3 {{1,3,5},{2,4,6}}=>4 {{1,3,5},{2,4},{6}}=>3 {{1,3,6},{2,4,5}}=>4 {{1,3},{2,4,5,6}}=>2 {{1,3},{2,4,5},{6}}=>2 {{1,3,6},{2,4},{5}}=>4 {{1,3},{2,4,6},{5}}=>3 {{1,3},{2,4},{5,6}}=>2 {{1,3},{2,4},{5},{6}}=>2 {{1,3,5,6},{2},{4}}=>2 {{1,3,5},{2,6},{4}}=>5 {{1,3,5},{2},{4,6}}=>3 {{1,3,5},{2},{4},{6}}=>2 {{1,3,6},{2,5},{4}}=>5 {{1,3},{2,5,6},{4}}=>3 {{1,3},{2,5},{4,6}}=>4 {{1,3},{2,5},{4},{6}}=>3 {{1,3,6},{2},{4,5}}=>3 {{1,3},{2,6},{4,5}}=>4 {{1,3},{2},{4,5,6}}=>1 {{1,3},{2},{4,5},{6}}=>1 {{1,3,6},{2},{4},{5}}=>3 {{1,3},{2,6},{4},{5}}=>4 {{1,3},{2},{4,6},{5}}=>2 {{1,3},{2},{4},{5,6}}=>1 {{1,3},{2},{4},{5},{6}}=>1 {{1,4,5,6},{2,3}}=>2 {{1,4,5},{2,3,6}}=>4 {{1,4,5},{2,3},{6}}=>2 {{1,4,6},{2,3,5}}=>4 {{1,4},{2,3,5,6}}=>3 {{1,4},{2,3,5},{6}}=>3 {{1,4,6},{2,3},{5}}=>3 {{1,4},{2,3,6},{5}}=>4 {{1,4},{2,3},{5,6}}=>2 {{1,4},{2,3},{5},{6}}=>2 {{1,5,6},{2,3,4}}=>3 {{1,5},{2,3,4,6}}=>4 {{1,5},{2,3,4},{6}}=>3 {{1,6},{2,3,4,5}}=>4 {{1},{2,3,4,5,6}}=>0 {{1},{2,3,4,5},{6}}=>0 {{1,6},{2,3,4},{5}}=>4 {{1},{2,3,4,6},{5}}=>1 {{1},{2,3,4},{5,6}}=>0 {{1},{2,3,4},{5},{6}}=>0 {{1,5,6},{2,3},{4}}=>3 {{1,5},{2,3,6},{4}}=>5 {{1,5},{2,3},{4,6}}=>4 {{1,5},{2,3},{4},{6}}=>3 {{1,6},{2,3,5},{4}}=>5 {{1},{2,3,5,6},{4}}=>1 {{1},{2,3,5},{4,6}}=>2 {{1},{2,3,5},{4},{6}}=>1 {{1,6},{2,3},{4,5}}=>4 {{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}}=>4 {{1},{2,3,6},{4},{5}}=>2 {{1},{2,3},{4,6},{5}}=>1 {{1},{2,3},{4},{5,6}}=>0 {{1},{2,3},{4},{5},{6}}=>0 {{1,4,5,6},{2},{3}}=>2 {{1,4,5},{2,6},{3}}=>5 {{1,4,5},{2},{3,6}}=>4 {{1,4,5},{2},{3},{6}}=>2 {{1,4,6},{2,5},{3}}=>5 {{1,4},{2,5,6},{3}}=>4 {{1,4},{2,5},{3,6}}=>6 {{1,4},{2,5},{3},{6}}=>4 {{1,4,6},{2},{3,5}}=>4 {{1,4},{2,6},{3,5}}=>6 {{1,4},{2},{3,5,6}}=>3 {{1,4},{2},{3,5},{6}}=>3 {{1,4,6},{2},{3},{5}}=>3 {{1,4},{2,6},{3},{5}}=>5 {{1,4},{2},{3,6},{5}}=>4 {{1,4},{2},{3},{5,6}}=>2 {{1,4},{2},{3},{5},{6}}=>2 {{1,5,6},{2,4},{3}}=>4 {{1,5},{2,4,6},{3}}=>5 {{1,5},{2,4},{3,6}}=>6 {{1,5},{2,4},{3},{6}}=>4 {{1,6},{2,4,5},{3}}=>5 {{1},{2,4,5,6},{3}}=>1 {{1},{2,4,5},{3,6}}=>3 {{1},{2,4,5},{3},{6}}=>1 {{1,6},{2,4},{3,5}}=>6 {{1},{2,4,6},{3,5}}=>3 {{1},{2,4},{3,5,6}}=>2 {{1},{2,4},{3,5},{6}}=>2 {{1,6},{2,4},{3},{5}}=>5 {{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 {{1,5,6},{2},{3,4}}=>3 {{1,5},{2,6},{3,4}}=>6 {{1,5},{2},{3,4,6}}=>4 {{1,5},{2},{3,4},{6}}=>3 {{1,6},{2,5},{3,4}}=>6 {{1},{2,5,6},{3,4}}=>2 {{1},{2,5},{3,4,6}}=>3 {{1},{2,5},{3,4},{6}}=>2 {{1,6},{2},{3,4,5}}=>4 {{1},{2,6},{3,4,5}}=>3 {{1},{2},{3,4,5,6}}=>0 {{1},{2},{3,4,5},{6}}=>0 {{1,6},{2},{3,4},{5}}=>4 {{1},{2,6},{3,4},{5}}=>3 {{1},{2},{3,4,6},{5}}=>1 {{1},{2},{3,4},{5,6}}=>0 {{1},{2},{3,4},{5},{6}}=>0 {{1,5,6},{2},{3},{4}}=>3 {{1,5},{2,6},{3},{4}}=>6 {{1,5},{2},{3,6},{4}}=>5 {{1,5},{2},{3},{4,6}}=>4 {{1,5},{2},{3},{4},{6}}=>3 {{1,6},{2,5},{3},{4}}=>6 {{1},{2,5,6},{3},{4}}=>2 {{1},{2,5},{3,6},{4}}=>4 {{1},{2,5},{3},{4,6}}=>3 {{1},{2,5},{3},{4},{6}}=>2 {{1,6},{2},{3,5},{4}}=>5 {{1},{2,6},{3,5},{4}}=>4 {{1},{2},{3,5,6},{4}}=>1 {{1},{2},{3,5},{4,6}}=>2 {{1},{2},{3,5},{4},{6}}=>1 {{1,6},{2},{3},{4,5}}=>4 {{1},{2,6},{3},{4,5}}=>3 {{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}}=>4 {{1},{2,6},{3},{4},{5}}=>3 {{1},{2},{3,6},{4},{5}}=>2 {{1},{2},{3},{4,6},{5}}=>1 {{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}}=>1 {{1,2,3,4,6},{5,7}}=>2 {{1,2,3,4,6},{5},{7}}=>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 {{1,2,3,4,7},{5},{6}}=>2 {{1,2,3,4},{5,7},{6}}=>1 {{1,2,3,4},{5},{6,7}}=>0 {{1,2,3,4},{5},{6},{7}}=>0 {{1,2,3,5,6,7},{4}}=>1 {{1,2,3,5,6},{4,7}}=>3 {{1,2,3,5,6},{4},{7}}=>1 {{1,2,3,5,7},{4,6}}=>3 {{1,2,3,5},{4,6,7}}=>2 {{1,2,3,5},{4,6},{7}}=>2 {{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}}=>3 {{1,2,3,6},{4,5},{7}}=>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 {{1,2,3,7},{4,5},{6}}=>3 {{1,2,3},{4,5,7},{6}}=>1 {{1,2,3},{4,5},{6,7}}=>0 {{1,2,3},{4,5},{6},{7}}=>0 {{1,2,3,6,7},{4},{5}}=>2 {{1,2,3,6},{4,7},{5}}=>4 {{1,2,3,6},{4},{5,7}}=>3 {{1,2,3,6},{4},{5},{7}}=>2 {{1,2,3,7},{4,6},{5}}=>4 {{1,2,3},{4,6,7},{5}}=>1 {{1,2,3},{4,6},{5,7}}=>2 {{1,2,3},{4,6},{5},{7}}=>1 {{1,2,3,7},{4},{5,6}}=>3 {{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}}=>3 {{1,2,3},{4,7},{5},{6}}=>2 {{1,2,3},{4},{5,7},{6}}=>1 {{1,2,3},{4},{5},{6,7}}=>0 {{1,2,3},{4},{5},{6},{7}}=>0 {{1,2,4,5,6,7},{3}}=>1 {{1,2,4,5,6},{3,7}}=>4 {{1,2,4,5,6},{3},{7}}=>1 {{1,2,4,5,7},{3,6}}=>4 {{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}}=>4 {{1,2,4,5},{3},{6,7}}=>1 {{1,2,4,5},{3},{6},{7}}=>1 {{1,2,4,6,7},{3,5}}=>3 {{1,2,4,6},{3,5,7}}=>4 {{1,2,4,6},{3,5},{7}}=>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 {{1,2,4,7},{3,5},{6}}=>4 {{1,2,4},{3,5,7},{6}}=>3 {{1,2,4},{3,5},{6,7}}=>2 {{1,2,4},{3,5},{6},{7}}=>2 {{1,2,4,6,7},{3},{5}}=>2 {{1,2,4,6},{3,7},{5}}=>5 {{1,2,4,6},{3},{5,7}}=>3 {{1,2,4,6},{3},{5},{7}}=>2 {{1,2,4,7},{3,6},{5}}=>5 {{1,2,4},{3,6,7},{5}}=>3 {{1,2,4},{3,6},{5,7}}=>4 {{1,2,4},{3,6},{5},{7}}=>3 {{1,2,4,7},{3},{5,6}}=>3 {{1,2,4},{3,7},{5,6}}=>4 {{1,2,4},{3},{5,6,7}}=>1 {{1,2,4},{3},{5,6},{7}}=>1 {{1,2,4,7},{3},{5},{6}}=>3 {{1,2,4},{3,7},{5},{6}}=>4 {{1,2,4},{3},{5,7},{6}}=>2 {{1,2,4},{3},{5},{6,7}}=>1 {{1,2,4},{3},{5},{6},{7}}=>1 {{1,2,5,6,7},{3,4}}=>2 {{1,2,5,6},{3,4,7}}=>4 {{1,2,5,6},{3,4},{7}}=>2 {{1,2,5,7},{3,4,6}}=>4 {{1,2,5},{3,4,6,7}}=>3 {{1,2,5},{3,4,6},{7}}=>3 {{1,2,5,7},{3,4},{6}}=>3 {{1,2,5},{3,4,7},{6}}=>4 {{1,2,5},{3,4},{6,7}}=>2 {{1,2,5},{3,4},{6},{7}}=>2 {{1,2,6,7},{3,4,5}}=>3 {{1,2,6},{3,4,5,7}}=>4 {{1,2,6},{3,4,5},{7}}=>3 {{1,2,7},{3,4,5,6}}=>4 {{1,2},{3,4,5,6,7}}=>0 {{1,2},{3,4,5,6},{7}}=>0 {{1,2,7},{3,4,5},{6}}=>4 {{1,2},{3,4,5,7},{6}}=>1 {{1,2},{3,4,5},{6,7}}=>0 {{1,2},{3,4,5},{6},{7}}=>0 {{1,2,6,7},{3,4},{5}}=>3 {{1,2,6},{3,4,7},{5}}=>5 {{1,2,6},{3,4},{5,7}}=>4 {{1,2,6},{3,4},{5},{7}}=>3 {{1,2,7},{3,4,6},{5}}=>5 {{1,2},{3,4,6,7},{5}}=>1 {{1,2},{3,4,6},{5,7}}=>2 {{1,2},{3,4,6},{5},{7}}=>1 {{1,2,7},{3,4},{5,6}}=>4 {{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}}=>4 {{1,2},{3,4,7},{5},{6}}=>2 {{1,2},{3,4},{5,7},{6}}=>1 {{1,2},{3,4},{5},{6,7}}=>0 {{1,2},{3,4},{5},{6},{7}}=>0 {{1,2,5,6,7},{3},{4}}=>2 {{1,2,5,6},{3,7},{4}}=>5 {{1,2,5,6},{3},{4,7}}=>4 {{1,2,5,6},{3},{4},{7}}=>2 {{1,2,5,7},{3,6},{4}}=>5 {{1,2,5},{3,6,7},{4}}=>4 {{1,2,5},{3,6},{4,7}}=>6 {{1,2,5},{3,6},{4},{7}}=>4 {{1,2,5,7},{3},{4,6}}=>4 {{1,2,5},{3,7},{4,6}}=>6 {{1,2,5},{3},{4,6,7}}=>3 {{1,2,5},{3},{4,6},{7}}=>3 {{1,2,5,7},{3},{4},{6}}=>3 {{1,2,5},{3,7},{4},{6}}=>5 {{1,2,5},{3},{4,7},{6}}=>4 {{1,2,5},{3},{4},{6,7}}=>2 {{1,2,5},{3},{4},{6},{7}}=>2 {{1,2,6,7},{3,5},{4}}=>4 {{1,2,6},{3,5,7},{4}}=>5 {{1,2,6},{3,5},{4,7}}=>6 {{1,2,6},{3,5},{4},{7}}=>4 {{1,2,7},{3,5,6},{4}}=>5 {{1,2},{3,5,6,7},{4}}=>1 {{1,2},{3,5,6},{4,7}}=>3 {{1,2},{3,5,6},{4},{7}}=>1 {{1,2,7},{3,5},{4,6}}=>6 {{1,2},{3,5,7},{4,6}}=>3 {{1,2},{3,5},{4,6,7}}=>2 {{1,2},{3,5},{4,6},{7}}=>2 {{1,2,7},{3,5},{4},{6}}=>5 {{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 {{1,2,6,7},{3},{4,5}}=>3 {{1,2,6},{3,7},{4,5}}=>6 {{1,2,6},{3},{4,5,7}}=>4 {{1,2,6},{3},{4,5},{7}}=>3 {{1,2,7},{3,6},{4,5}}=>6 {{1,2},{3,6,7},{4,5}}=>2 {{1,2},{3,6},{4,5,7}}=>3 {{1,2},{3,6},{4,5},{7}}=>2 {{1,2,7},{3},{4,5,6}}=>4 {{1,2},{3,7},{4,5,6}}=>3 {{1,2},{3},{4,5,6,7}}=>0 {{1,2},{3},{4,5,6},{7}}=>0 {{1,2,7},{3},{4,5},{6}}=>4 {{1,2},{3,7},{4,5},{6}}=>3 {{1,2},{3},{4,5,7},{6}}=>1 {{1,2},{3},{4,5},{6,7}}=>0 {{1,2},{3},{4,5},{6},{7}}=>0 {{1,2,6,7},{3},{4},{5}}=>3 {{1,2,6},{3,7},{4},{5}}=>6 {{1,2,6},{3},{4,7},{5}}=>5 {{1,2,6},{3},{4},{5,7}}=>4 {{1,2,6},{3},{4},{5},{7}}=>3 {{1,2,7},{3,6},{4},{5}}=>6 {{1,2},{3,6,7},{4},{5}}=>2 {{1,2},{3,6},{4,7},{5}}=>4 {{1,2},{3,6},{4},{5,7}}=>3 {{1,2},{3,6},{4},{5},{7}}=>2 {{1,2,7},{3},{4,6},{5}}=>5 {{1,2},{3,7},{4,6},{5}}=>4 {{1,2},{3},{4,6,7},{5}}=>1 {{1,2},{3},{4,6},{5,7}}=>2 {{1,2},{3},{4,6},{5},{7}}=>1 {{1,2,7},{3},{4},{5,6}}=>4 {{1,2},{3,7},{4},{5,6}}=>3 {{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}}=>4 {{1,2},{3,7},{4},{5},{6}}=>3 {{1,2},{3},{4,7},{5},{6}}=>2 {{1,2},{3},{4},{5,7},{6}}=>1 {{1,2},{3},{4},{5},{6,7}}=>0 {{1,2},{3},{4},{5},{6},{7}}=>0 {{1,3,4,5,6,7},{2}}=>1 {{1,3,4,5,6},{2,7}}=>5 {{1,3,4,5,6},{2},{7}}=>1 {{1,3,4,5,7},{2,6}}=>5 {{1,3,4,5},{2,6,7}}=>4 {{1,3,4,5},{2,6},{7}}=>4 {{1,3,4,5,7},{2},{6}}=>2 {{1,3,4,5},{2,7},{6}}=>5 {{1,3,4,5},{2},{6,7}}=>1 {{1,3,4,5},{2},{6},{7}}=>1 {{1,3,4,6,7},{2,5}}=>4 {{1,3,4,6},{2,5,7}}=>5 {{1,3,4,6},{2,5},{7}}=>4 {{1,3,4,7},{2,5,6}}=>5 {{1,3,4},{2,5,6,7}}=>3 {{1,3,4},{2,5,6},{7}}=>3 {{1,3,4,7},{2,5},{6}}=>5 {{1,3,4},{2,5,7},{6}}=>4 {{1,3,4},{2,5},{6,7}}=>3 {{1,3,4},{2,5},{6},{7}}=>3 {{1,3,4,6,7},{2},{5}}=>2 {{1,3,4,6},{2,7},{5}}=>6 {{1,3,4,6},{2},{5,7}}=>3 {{1,3,4,6},{2},{5},{7}}=>2 {{1,3,4,7},{2,6},{5}}=>6 {{1,3,4},{2,6,7},{5}}=>4 {{1,3,4},{2,6},{5,7}}=>5 {{1,3,4},{2,6},{5},{7}}=>4 {{1,3,4,7},{2},{5,6}}=>3 {{1,3,4},{2,7},{5,6}}=>5 {{1,3,4},{2},{5,6,7}}=>1 {{1,3,4},{2},{5,6},{7}}=>1 {{1,3,4,7},{2},{5},{6}}=>3 {{1,3,4},{2,7},{5},{6}}=>5 {{1,3,4},{2},{5,7},{6}}=>2 {{1,3,4},{2},{5},{6,7}}=>1 {{1,3,4},{2},{5},{6},{7}}=>1 {{1,3,5,6,7},{2,4}}=>3 {{1,3,5,6},{2,4,7}}=>5 {{1,3,5,6},{2,4},{7}}=>3 {{1,3,5,7},{2,4,6}}=>5 {{1,3,5},{2,4,6,7}}=>4 {{1,3,5},{2,4,6},{7}}=>4 {{1,3,5,7},{2,4},{6}}=>4 {{1,3,5},{2,4,7},{6}}=>5 {{1,3,5},{2,4},{6,7}}=>3 {{1,3,5},{2,4},{6},{7}}=>3 {{1,3,6,7},{2,4,5}}=>4 {{1,3,6},{2,4,5,7}}=>5 {{1,3,6},{2,4,5},{7}}=>4 {{1,3,7},{2,4,5,6}}=>5 {{1,3},{2,4,5,6,7}}=>2 {{1,3},{2,4,5,6},{7}}=>2 {{1,3,7},{2,4,5},{6}}=>5 {{1,3},{2,4,5,7},{6}}=>3 {{1,3},{2,4,5},{6,7}}=>2 {{1,3},{2,4,5},{6},{7}}=>2 {{1,3,6,7},{2,4},{5}}=>4 {{1,3,6},{2,4,7},{5}}=>6 {{1,3,6},{2,4},{5,7}}=>5 {{1,3,6},{2,4},{5},{7}}=>4 {{1,3,7},{2,4,6},{5}}=>6 {{1,3},{2,4,6,7},{5}}=>3 {{1,3},{2,4,6},{5,7}}=>4 {{1,3},{2,4,6},{5},{7}}=>3 {{1,3,7},{2,4},{5,6}}=>5 {{1,3},{2,4,7},{5,6}}=>4 {{1,3},{2,4},{5,6,7}}=>2 {{1,3},{2,4},{5,6},{7}}=>2 {{1,3,7},{2,4},{5},{6}}=>5 {{1,3},{2,4,7},{5},{6}}=>4 {{1,3},{2,4},{5,7},{6}}=>3 {{1,3},{2,4},{5},{6,7}}=>2 {{1,3},{2,4},{5},{6},{7}}=>2 {{1,3,5,6,7},{2},{4}}=>2 {{1,3,5,6},{2,7},{4}}=>6 {{1,3,5,6},{2},{4,7}}=>4 {{1,3,5,6},{2},{4},{7}}=>2 {{1,3,5,7},{2,6},{4}}=>6 {{1,3,5},{2,6,7},{4}}=>5 {{1,3,5},{2,6},{4,7}}=>7 {{1,3,5},{2,6},{4},{7}}=>5 {{1,3,5,7},{2},{4,6}}=>4 {{1,3,5},{2,7},{4,6}}=>7 {{1,3,5},{2},{4,6,7}}=>3 {{1,3,5},{2},{4,6},{7}}=>3 {{1,3,5,7},{2},{4},{6}}=>3 {{1,3,5},{2,7},{4},{6}}=>6 {{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},{2,5},{4}}=>5 {{1,3,6},{2,5,7},{4}}=>6 {{1,3,6},{2,5},{4,7}}=>7 {{1,3,6},{2,5},{4},{7}}=>5 {{1,3,7},{2,5,6},{4}}=>6 {{1,3},{2,5,6,7},{4}}=>3 {{1,3},{2,5,6},{4,7}}=>5 {{1,3},{2,5,6},{4},{7}}=>3 {{1,3,7},{2,5},{4,6}}=>7 {{1,3},{2,5,7},{4,6}}=>5 {{1,3},{2,5},{4,6,7}}=>4 {{1,3},{2,5},{4,6},{7}}=>4 {{1,3,7},{2,5},{4},{6}}=>6 {{1,3},{2,5,7},{4},{6}}=>4 {{1,3},{2,5},{4,7},{6}}=>5 {{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}}=>7 {{1,3,6},{2},{4,5,7}}=>4 {{1,3,6},{2},{4,5},{7}}=>3 {{1,3,7},{2,6},{4,5}}=>7 {{1,3},{2,6,7},{4,5}}=>4 {{1,3},{2,6},{4,5,7}}=>5 {{1,3},{2,6},{4,5},{7}}=>4 {{1,3,7},{2},{4,5,6}}=>4 {{1,3},{2,7},{4,5,6}}=>5 {{1,3},{2},{4,5,6,7}}=>1 {{1,3},{2},{4,5,6},{7}}=>1 {{1,3,7},{2},{4,5},{6}}=>4 {{1,3},{2,7},{4,5},{6}}=>5 {{1,3},{2},{4,5,7},{6}}=>2 {{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}}=>7 {{1,3,6},{2},{4,7},{5}}=>5 {{1,3,6},{2},{4},{5,7}}=>4 {{1,3,6},{2},{4},{5},{7}}=>3 {{1,3,7},{2,6},{4},{5}}=>7 {{1,3},{2,6,7},{4},{5}}=>4 {{1,3},{2,6},{4,7},{5}}=>6 {{1,3},{2,6},{4},{5,7}}=>5 {{1,3},{2,6},{4},{5},{7}}=>4 {{1,3,7},{2},{4,6},{5}}=>5 {{1,3},{2,7},{4,6},{5}}=>6 {{1,3},{2},{4,6,7},{5}}=>2 {{1,3},{2},{4,6},{5,7}}=>3 {{1,3},{2},{4,6},{5},{7}}=>2 {{1,3,7},{2},{4},{5,6}}=>4 {{1,3},{2,7},{4},{5,6}}=>5 {{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}}=>4 {{1,3},{2,7},{4},{5},{6}}=>5 {{1,3},{2},{4,7},{5},{6}}=>3 {{1,3},{2},{4},{5,7},{6}}=>2 {{1,3},{2},{4},{5},{6,7}}=>1 {{1,3},{2},{4},{5},{6},{7}}=>1 {{1,4,5,6,7},{2,3}}=>2 {{1,4,5,6},{2,3,7}}=>5 {{1,4,5,6},{2,3},{7}}=>2 {{1,4,5,7},{2,3,6}}=>5 {{1,4,5},{2,3,6,7}}=>4 {{1,4,5},{2,3,6},{7}}=>4 {{1,4,5,7},{2,3},{6}}=>3 {{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},{2,3,5}}=>4 {{1,4,6},{2,3,5,7}}=>5 {{1,4,6},{2,3,5},{7}}=>4 {{1,4,7},{2,3,5,6}}=>5 {{1,4},{2,3,5,6,7}}=>3 {{1,4},{2,3,5,6},{7}}=>3 {{1,4,7},{2,3,5},{6}}=>5 {{1,4},{2,3,5,7},{6}}=>4 {{1,4},{2,3,5},{6,7}}=>3 {{1,4},{2,3,5},{6},{7}}=>3 {{1,4,6,7},{2,3},{5}}=>3 {{1,4,6},{2,3,7},{5}}=>6 {{1,4,6},{2,3},{5,7}}=>4 {{1,4,6},{2,3},{5},{7}}=>3 {{1,4,7},{2,3,6},{5}}=>6 {{1,4},{2,3,6,7},{5}}=>4 {{1,4},{2,3,6},{5,7}}=>5 {{1,4},{2,3,6},{5},{7}}=>4 {{1,4,7},{2,3},{5,6}}=>4 {{1,4},{2,3,7},{5,6}}=>5 {{1,4},{2,3},{5,6,7}}=>2 {{1,4},{2,3},{5,6},{7}}=>2 {{1,4,7},{2,3},{5},{6}}=>4 {{1,4},{2,3,7},{5},{6}}=>5 {{1,4},{2,3},{5,7},{6}}=>3 {{1,4},{2,3},{5},{6,7}}=>2 {{1,4},{2,3},{5},{6},{7}}=>2 {{1,5,6,7},{2,3,4}}=>3 {{1,5,6},{2,3,4,7}}=>5 {{1,5,6},{2,3,4},{7}}=>3 {{1,5,7},{2,3,4,6}}=>5 {{1,5},{2,3,4,6,7}}=>4 {{1,5},{2,3,4,6},{7}}=>4 {{1,5,7},{2,3,4},{6}}=>4 {{1,5},{2,3,4,7},{6}}=>5 {{1,5},{2,3,4},{6,7}}=>3 {{1,5},{2,3,4},{6},{7}}=>3 {{1,6,7},{2,3,4,5}}=>4 {{1,6},{2,3,4,5,7}}=>5 {{1,6},{2,3,4,5},{7}}=>4 {{1,7},{2,3,4,5,6}}=>5 {{1},{2,3,4,5,6,7}}=>0 {{1},{2,3,4,5,6},{7}}=>0 {{1,7},{2,3,4,5},{6}}=>5 {{1},{2,3,4,5,7},{6}}=>1 {{1},{2,3,4,5},{6,7}}=>0 {{1},{2,3,4,5},{6},{7}}=>0 {{1,6,7},{2,3,4},{5}}=>4 {{1,6},{2,3,4,7},{5}}=>6 {{1,6},{2,3,4},{5,7}}=>5 {{1,6},{2,3,4},{5},{7}}=>4 {{1,7},{2,3,4,6},{5}}=>6 {{1},{2,3,4,6,7},{5}}=>1 {{1},{2,3,4,6},{5,7}}=>2 {{1},{2,3,4,6},{5},{7}}=>1 {{1,7},{2,3,4},{5,6}}=>5 {{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}}=>5 {{1},{2,3,4,7},{5},{6}}=>2 {{1},{2,3,4},{5,7},{6}}=>1 {{1},{2,3,4},{5},{6,7}}=>0 {{1},{2,3,4},{5},{6},{7}}=>0 {{1,5,6,7},{2,3},{4}}=>3 {{1,5,6},{2,3,7},{4}}=>6 {{1,5,6},{2,3},{4,7}}=>5 {{1,5,6},{2,3},{4},{7}}=>3 {{1,5,7},{2,3,6},{4}}=>6 {{1,5},{2,3,6,7},{4}}=>5 {{1,5},{2,3,6},{4,7}}=>7 {{1,5},{2,3,6},{4},{7}}=>5 {{1,5,7},{2,3},{4,6}}=>5 {{1,5},{2,3,7},{4,6}}=>7 {{1,5},{2,3},{4,6,7}}=>4 {{1,5},{2,3},{4,6},{7}}=>4 {{1,5,7},{2,3},{4},{6}}=>4 {{1,5},{2,3,7},{4},{6}}=>6 {{1,5},{2,3},{4,7},{6}}=>5 {{1,5},{2,3},{4},{6,7}}=>3 {{1,5},{2,3},{4},{6},{7}}=>3 {{1,6,7},{2,3,5},{4}}=>5 {{1,6},{2,3,5,7},{4}}=>6 {{1,6},{2,3,5},{4,7}}=>7 {{1,6},{2,3,5},{4},{7}}=>5 {{1,7},{2,3,5,6},{4}}=>6 {{1},{2,3,5,6,7},{4}}=>1 {{1},{2,3,5,6},{4,7}}=>3 {{1},{2,3,5,6},{4},{7}}=>1 {{1,7},{2,3,5},{4,6}}=>7 {{1},{2,3,5,7},{4,6}}=>3 {{1},{2,3,5},{4,6,7}}=>2 {{1},{2,3,5},{4,6},{7}}=>2 {{1,7},{2,3,5},{4},{6}}=>6 {{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 {{1,6,7},{2,3},{4,5}}=>4 {{1,6},{2,3,7},{4,5}}=>7 {{1,6},{2,3},{4,5,7}}=>5 {{1,6},{2,3},{4,5},{7}}=>4 {{1,7},{2,3,6},{4,5}}=>7 {{1},{2,3,6,7},{4,5}}=>2 {{1},{2,3,6},{4,5,7}}=>3 {{1},{2,3,6},{4,5},{7}}=>2 {{1,7},{2,3},{4,5,6}}=>5 {{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}}=>5 {{1},{2,3,7},{4,5},{6}}=>3 {{1},{2,3},{4,5,7},{6}}=>1 {{1},{2,3},{4,5},{6,7}}=>0 {{1},{2,3},{4,5},{6},{7}}=>0 {{1,6,7},{2,3},{4},{5}}=>4 {{1,6},{2,3,7},{4},{5}}=>7 {{1,6},{2,3},{4,7},{5}}=>6 {{1,6},{2,3},{4},{5,7}}=>5 {{1,6},{2,3},{4},{5},{7}}=>4 {{1,7},{2,3,6},{4},{5}}=>7 {{1},{2,3,6,7},{4},{5}}=>2 {{1},{2,3,6},{4,7},{5}}=>4 {{1},{2,3,6},{4},{5,7}}=>3 {{1},{2,3,6},{4},{5},{7}}=>2 {{1,7},{2,3},{4,6},{5}}=>6 {{1},{2,3,7},{4,6},{5}}=>4 {{1},{2,3},{4,6,7},{5}}=>1 {{1},{2,3},{4,6},{5,7}}=>2 {{1},{2,3},{4,6},{5},{7}}=>1 {{1,7},{2,3},{4},{5,6}}=>5 {{1},{2,3,7},{4},{5,6}}=>3 {{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}}=>5 {{1},{2,3,7},{4},{5},{6}}=>3 {{1},{2,3},{4,7},{5},{6}}=>2 {{1},{2,3},{4},{5,7},{6}}=>1 {{1},{2,3},{4},{5},{6,7}}=>0 {{1},{2,3},{4},{5},{6},{7}}=>0 {{1,4,5,6,7},{2},{3}}=>2 {{1,4,5,6},{2,7},{3}}=>6 {{1,4,5,6},{2},{3,7}}=>5 {{1,4,5,6},{2},{3},{7}}=>2 {{1,4,5,7},{2,6},{3}}=>6 {{1,4,5},{2,6,7},{3}}=>5 {{1,4,5},{2,6},{3,7}}=>8 {{1,4,5},{2,6},{3},{7}}=>5 {{1,4,5,7},{2},{3,6}}=>5 {{1,4,5},{2,7},{3,6}}=>8 {{1,4,5},{2},{3,6,7}}=>4 {{1,4,5},{2},{3,6},{7}}=>4 {{1,4,5,7},{2},{3},{6}}=>3 {{1,4,5},{2,7},{3},{6}}=>6 {{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}}=>8 {{1,4,6},{2,5},{3},{7}}=>5 {{1,4,7},{2,5,6},{3}}=>6 {{1,4},{2,5,6,7},{3}}=>4 {{1,4},{2,5,6},{3,7}}=>7 {{1,4},{2,5,6},{3},{7}}=>4 {{1,4,7},{2,5},{3,6}}=>8 {{1,4},{2,5,7},{3,6}}=>7 {{1,4},{2,5},{3,6,7}}=>6 {{1,4},{2,5},{3,6},{7}}=>6 {{1,4,7},{2,5},{3},{6}}=>6 {{1,4},{2,5,7},{3},{6}}=>5 {{1,4},{2,5},{3,7},{6}}=>7 {{1,4},{2,5},{3},{6,7}}=>4 {{1,4},{2,5},{3},{6},{7}}=>4 {{1,4,6,7},{2},{3,5}}=>4 {{1,4,6},{2,7},{3,5}}=>8 {{1,4,6},{2},{3,5,7}}=>5 {{1,4,6},{2},{3,5},{7}}=>4 {{1,4,7},{2,6},{3,5}}=>8 {{1,4},{2,6,7},{3,5}}=>6 {{1,4},{2,6},{3,5,7}}=>7 {{1,4},{2,6},{3,5},{7}}=>6 {{1,4,7},{2},{3,5,6}}=>5 {{1,4},{2,7},{3,5,6}}=>7 {{1,4},{2},{3,5,6,7}}=>3 {{1,4},{2},{3,5,6},{7}}=>3 {{1,4,7},{2},{3,5},{6}}=>5 {{1,4},{2,7},{3,5},{6}}=>7 {{1,4},{2},{3,5,7},{6}}=>4 {{1,4},{2},{3,5},{6,7}}=>3 {{1,4},{2},{3,5},{6},{7}}=>3 {{1,4,6,7},{2},{3},{5}}=>3 {{1,4,6},{2,7},{3},{5}}=>7 {{1,4,6},{2},{3,7},{5}}=>6 {{1,4,6},{2},{3},{5,7}}=>4 {{1,4,6},{2},{3},{5},{7}}=>3 {{1,4,7},{2,6},{3},{5}}=>7 {{1,4},{2,6,7},{3},{5}}=>5 {{1,4},{2,6},{3,7},{5}}=>8 {{1,4},{2,6},{3},{5,7}}=>6 {{1,4},{2,6},{3},{5},{7}}=>5 {{1,4,7},{2},{3,6},{5}}=>6 {{1,4},{2,7},{3,6},{5}}=>8 {{1,4},{2},{3,6,7},{5}}=>4 {{1,4},{2},{3,6},{5,7}}=>5 {{1,4},{2},{3,6},{5},{7}}=>4 {{1,4,7},{2},{3},{5,6}}=>4 {{1,4},{2,7},{3},{5,6}}=>6 {{1,4},{2},{3,7},{5,6}}=>5 {{1,4},{2},{3},{5,6,7}}=>2 {{1,4},{2},{3},{5,6},{7}}=>2 {{1,4,7},{2},{3},{5},{6}}=>4 {{1,4},{2,7},{3},{5},{6}}=>6 {{1,4},{2},{3,7},{5},{6}}=>5 {{1,4},{2},{3},{5,7},{6}}=>3 {{1,4},{2},{3},{5},{6,7}}=>2 {{1,4},{2},{3},{5},{6},{7}}=>2 {{1,5,6,7},{2,4},{3}}=>4 {{1,5,6},{2,4,7},{3}}=>6 {{1,5,6},{2,4},{3,7}}=>7 {{1,5,6},{2,4},{3},{7}}=>4 {{1,5,7},{2,4,6},{3}}=>6 {{1,5},{2,4,6,7},{3}}=>5 {{1,5},{2,4,6},{3,7}}=>8 {{1,5},{2,4,6},{3},{7}}=>5 {{1,5,7},{2,4},{3,6}}=>7 {{1,5},{2,4,7},{3,6}}=>8 {{1,5},{2,4},{3,6,7}}=>6 {{1,5},{2,4},{3,6},{7}}=>6 {{1,5,7},{2,4},{3},{6}}=>5 {{1,5},{2,4,7},{3},{6}}=>6 {{1,5},{2,4},{3,7},{6}}=>7 {{1,5},{2,4},{3},{6,7}}=>4 {{1,5},{2,4},{3},{6},{7}}=>4 {{1,6,7},{2,4,5},{3}}=>5 {{1,6},{2,4,5,7},{3}}=>6 {{1,6},{2,4,5},{3,7}}=>8 {{1,6},{2,4,5},{3},{7}}=>5 {{1,7},{2,4,5,6},{3}}=>6 {{1},{2,4,5,6,7},{3}}=>1 {{1},{2,4,5,6},{3,7}}=>4 {{1},{2,4,5,6},{3},{7}}=>1 {{1,7},{2,4,5},{3,6}}=>8 {{1},{2,4,5,7},{3,6}}=>4 {{1},{2,4,5},{3,6,7}}=>3 {{1},{2,4,5},{3,6},{7}}=>3 {{1,7},{2,4,5},{3},{6}}=>6 {{1},{2,4,5,7},{3},{6}}=>2 {{1},{2,4,5},{3,7},{6}}=>4 {{1},{2,4,5},{3},{6,7}}=>1 {{1},{2,4,5},{3},{6},{7}}=>1 {{1,6,7},{2,4},{3,5}}=>6 {{1,6},{2,4,7},{3,5}}=>8 {{1,6},{2,4},{3,5,7}}=>7 {{1,6},{2,4},{3,5},{7}}=>6 {{1,7},{2,4,6},{3,5}}=>8 {{1},{2,4,6,7},{3,5}}=>3 {{1},{2,4,6},{3,5,7}}=>4 {{1},{2,4,6},{3,5},{7}}=>3 {{1,7},{2,4},{3,5,6}}=>7 {{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}}=>7 {{1},{2,4,7},{3,5},{6}}=>4 {{1},{2,4},{3,5,7},{6}}=>3 {{1},{2,4},{3,5},{6,7}}=>2 {{1},{2,4},{3,5},{6},{7}}=>2 {{1,6,7},{2,4},{3},{5}}=>5 {{1,6},{2,4,7},{3},{5}}=>7 {{1,6},{2,4},{3,7},{5}}=>8 {{1,6},{2,4},{3},{5,7}}=>6 {{1,6},{2,4},{3},{5},{7}}=>5 {{1,7},{2,4,6},{3},{5}}=>7 {{1},{2,4,6,7},{3},{5}}=>2 {{1},{2,4,6},{3,7},{5}}=>5 {{1},{2,4,6},{3},{5,7}}=>3 {{1},{2,4,6},{3},{5},{7}}=>2 {{1,7},{2,4},{3,6},{5}}=>8 {{1},{2,4,7},{3,6},{5}}=>5 {{1},{2,4},{3,6,7},{5}}=>3 {{1},{2,4},{3,6},{5,7}}=>4 {{1},{2,4},{3,6},{5},{7}}=>3 {{1,7},{2,4},{3},{5,6}}=>6 {{1},{2,4,7},{3},{5,6}}=>3 {{1},{2,4},{3,7},{5,6}}=>4 {{1},{2,4},{3},{5,6,7}}=>1 {{1},{2,4},{3},{5,6},{7}}=>1 {{1,7},{2,4},{3},{5},{6}}=>6 {{1},{2,4,7},{3},{5},{6}}=>3 {{1},{2,4},{3,7},{5},{6}}=>4 {{1},{2,4},{3},{5,7},{6}}=>2 {{1},{2,4},{3},{5},{6,7}}=>1 {{1},{2,4},{3},{5},{6},{7}}=>1 {{1,5,6,7},{2},{3,4}}=>3 {{1,5,6},{2,7},{3,4}}=>7 {{1,5,6},{2},{3,4,7}}=>5 {{1,5,6},{2},{3,4},{7}}=>3 {{1,5,7},{2,6},{3,4}}=>7 {{1,5},{2,6,7},{3,4}}=>6 {{1,5},{2,6},{3,4,7}}=>8 {{1,5},{2,6},{3,4},{7}}=>6 {{1,5,7},{2},{3,4,6}}=>5 {{1,5},{2,7},{3,4,6}}=>8 {{1,5},{2},{3,4,6,7}}=>4 {{1,5},{2},{3,4,6},{7}}=>4 {{1,5,7},{2},{3,4},{6}}=>4 {{1,5},{2,7},{3,4},{6}}=>7 {{1,5},{2},{3,4,7},{6}}=>5 {{1,5},{2},{3,4},{6,7}}=>3 {{1,5},{2},{3,4},{6},{7}}=>3 {{1,6,7},{2,5},{3,4}}=>6 {{1,6},{2,5,7},{3,4}}=>7 {{1,6},{2,5},{3,4,7}}=>8 {{1,6},{2,5},{3,4},{7}}=>6 {{1,7},{2,5,6},{3,4}}=>7 {{1},{2,5,6,7},{3,4}}=>2 {{1},{2,5,6},{3,4,7}}=>4 {{1},{2,5,6},{3,4},{7}}=>2 {{1,7},{2,5},{3,4,6}}=>8 {{1},{2,5,7},{3,4,6}}=>4 {{1},{2,5},{3,4,6,7}}=>3 {{1},{2,5},{3,4,6},{7}}=>3 {{1,7},{2,5},{3,4},{6}}=>7 {{1},{2,5,7},{3,4},{6}}=>3 {{1},{2,5},{3,4,7},{6}}=>4 {{1},{2,5},{3,4},{6,7}}=>2 {{1},{2,5},{3,4},{6},{7}}=>2 {{1,6,7},{2},{3,4,5}}=>4 {{1,6},{2,7},{3,4,5}}=>8 {{1,6},{2},{3,4,5,7}}=>5 {{1,6},{2},{3,4,5},{7}}=>4 {{1,7},{2,6},{3,4,5}}=>8 {{1},{2,6,7},{3,4,5}}=>3 {{1},{2,6},{3,4,5,7}}=>4 {{1},{2,6},{3,4,5},{7}}=>3 {{1,7},{2},{3,4,5,6}}=>5 {{1},{2,7},{3,4,5,6}}=>4 {{1},{2},{3,4,5,6,7}}=>0 {{1},{2},{3,4,5,6},{7}}=>0 {{1,7},{2},{3,4,5},{6}}=>5 {{1},{2,7},{3,4,5},{6}}=>4 {{1},{2},{3,4,5,7},{6}}=>1 {{1},{2},{3,4,5},{6,7}}=>0 {{1},{2},{3,4,5},{6},{7}}=>0 {{1,6,7},{2},{3,4},{5}}=>4 {{1,6},{2,7},{3,4},{5}}=>8 {{1,6},{2},{3,4,7},{5}}=>6 {{1,6},{2},{3,4},{5,7}}=>5 {{1,6},{2},{3,4},{5},{7}}=>4 {{1,7},{2,6},{3,4},{5}}=>8 {{1},{2,6,7},{3,4},{5}}=>3 {{1},{2,6},{3,4,7},{5}}=>5 {{1},{2,6},{3,4},{5,7}}=>4 {{1},{2,6},{3,4},{5},{7}}=>3 {{1,7},{2},{3,4,6},{5}}=>6 {{1},{2,7},{3,4,6},{5}}=>5 {{1},{2},{3,4,6,7},{5}}=>1 {{1},{2},{3,4,6},{5,7}}=>2 {{1},{2},{3,4,6},{5},{7}}=>1 {{1,7},{2},{3,4},{5,6}}=>5 {{1},{2,7},{3,4},{5,6}}=>4 {{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}}=>5 {{1},{2,7},{3,4},{5},{6}}=>4 {{1},{2},{3,4,7},{5},{6}}=>2 {{1},{2},{3,4},{5,7},{6}}=>1 {{1},{2},{3,4},{5},{6,7}}=>0 {{1},{2},{3,4},{5},{6},{7}}=>0 {{1,5,6,7},{2},{3},{4}}=>3 {{1,5,6},{2,7},{3},{4}}=>7 {{1,5,6},{2},{3,7},{4}}=>6 {{1,5,6},{2},{3},{4,7}}=>5 {{1,5,6},{2},{3},{4},{7}}=>3 {{1,5,7},{2,6},{3},{4}}=>7 {{1,5},{2,6,7},{3},{4}}=>6 {{1,5},{2,6},{3,7},{4}}=>9 {{1,5},{2,6},{3},{4,7}}=>8 {{1,5},{2,6},{3},{4},{7}}=>6 {{1,5,7},{2},{3,6},{4}}=>6 {{1,5},{2,7},{3,6},{4}}=>9 {{1,5},{2},{3,6,7},{4}}=>5 {{1,5},{2},{3,6},{4,7}}=>7 {{1,5},{2},{3,6},{4},{7}}=>5 {{1,5,7},{2},{3},{4,6}}=>5 {{1,5},{2,7},{3},{4,6}}=>8 {{1,5},{2},{3,7},{4,6}}=>7 {{1,5},{2},{3},{4,6,7}}=>4 {{1,5},{2},{3},{4,6},{7}}=>4 {{1,5,7},{2},{3},{4},{6}}=>4 {{1,5},{2,7},{3},{4},{6}}=>7 {{1,5},{2},{3,7},{4},{6}}=>6 {{1,5},{2},{3},{4,7},{6}}=>5 {{1,5},{2},{3},{4},{6,7}}=>3 {{1,5},{2},{3},{4},{6},{7}}=>3 {{1,6,7},{2,5},{3},{4}}=>6 {{1,6},{2,5,7},{3},{4}}=>7 {{1,6},{2,5},{3,7},{4}}=>9 {{1,6},{2,5},{3},{4,7}}=>8 {{1,6},{2,5},{3},{4},{7}}=>6 {{1,7},{2,5,6},{3},{4}}=>7 {{1},{2,5,6,7},{3},{4}}=>2 {{1},{2,5,6},{3,7},{4}}=>5 {{1},{2,5,6},{3},{4,7}}=>4 {{1},{2,5,6},{3},{4},{7}}=>2 {{1,7},{2,5},{3,6},{4}}=>9 {{1},{2,5,7},{3,6},{4}}=>5 {{1},{2,5},{3,6,7},{4}}=>4 {{1},{2,5},{3,6},{4,7}}=>6 {{1},{2,5},{3,6},{4},{7}}=>4 {{1,7},{2,5},{3},{4,6}}=>8 {{1},{2,5,7},{3},{4,6}}=>4 {{1},{2,5},{3,7},{4,6}}=>6 {{1},{2,5},{3},{4,6,7}}=>3 {{1},{2,5},{3},{4,6},{7}}=>3 {{1,7},{2,5},{3},{4},{6}}=>7 {{1},{2,5,7},{3},{4},{6}}=>3 {{1},{2,5},{3,7},{4},{6}}=>5 {{1},{2,5},{3},{4,7},{6}}=>4 {{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}}=>9 {{1,6},{2},{3,5,7},{4}}=>6 {{1,6},{2},{3,5},{4,7}}=>7 {{1,6},{2},{3,5},{4},{7}}=>5 {{1,7},{2,6},{3,5},{4}}=>9 {{1},{2,6,7},{3,5},{4}}=>4 {{1},{2,6},{3,5,7},{4}}=>5 {{1},{2,6},{3,5},{4,7}}=>6 {{1},{2,6},{3,5},{4},{7}}=>4 {{1,7},{2},{3,5,6},{4}}=>6 {{1},{2,7},{3,5,6},{4}}=>5 {{1},{2},{3,5,6,7},{4}}=>1 {{1},{2},{3,5,6},{4,7}}=>3 {{1},{2},{3,5,6},{4},{7}}=>1 {{1,7},{2},{3,5},{4,6}}=>7 {{1},{2,7},{3,5},{4,6}}=>6 {{1},{2},{3,5,7},{4,6}}=>3 {{1},{2},{3,5},{4,6,7}}=>2 {{1},{2},{3,5},{4,6},{7}}=>2 {{1,7},{2},{3,5},{4},{6}}=>6 {{1},{2,7},{3,5},{4},{6}}=>5 {{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 {{1,6,7},{2},{3},{4,5}}=>4 {{1,6},{2,7},{3},{4,5}}=>8 {{1,6},{2},{3,7},{4,5}}=>7 {{1,6},{2},{3},{4,5,7}}=>5 {{1,6},{2},{3},{4,5},{7}}=>4 {{1,7},{2,6},{3},{4,5}}=>8 {{1},{2,6,7},{3},{4,5}}=>3 {{1},{2,6},{3,7},{4,5}}=>6 {{1},{2,6},{3},{4,5,7}}=>4 {{1},{2,6},{3},{4,5},{7}}=>3 {{1,7},{2},{3,6},{4,5}}=>7 {{1},{2,7},{3,6},{4,5}}=>6 {{1},{2},{3,6,7},{4,5}}=>2 {{1},{2},{3,6},{4,5,7}}=>3 {{1},{2},{3,6},{4,5},{7}}=>2 {{1,7},{2},{3},{4,5,6}}=>5 {{1},{2,7},{3},{4,5,6}}=>4 {{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}}=>5 {{1},{2,7},{3},{4,5},{6}}=>4 {{1},{2},{3,7},{4,5},{6}}=>3 {{1},{2},{3},{4,5,7},{6}}=>1 {{1},{2},{3},{4,5},{6,7}}=>0 {{1},{2},{3},{4,5},{6},{7}}=>0 {{1,6,7},{2},{3},{4},{5}}=>4 {{1,6},{2,7},{3},{4},{5}}=>8 {{1,6},{2},{3,7},{4},{5}}=>7 {{1,6},{2},{3},{4,7},{5}}=>6 {{1,6},{2},{3},{4},{5,7}}=>5 {{1,6},{2},{3},{4},{5},{7}}=>4 {{1,7},{2,6},{3},{4},{5}}=>8 {{1},{2,6,7},{3},{4},{5}}=>3 {{1},{2,6},{3,7},{4},{5}}=>6 {{1},{2,6},{3},{4,7},{5}}=>5 {{1},{2,6},{3},{4},{5,7}}=>4 {{1},{2,6},{3},{4},{5},{7}}=>3 {{1,7},{2},{3,6},{4},{5}}=>7 {{1},{2,7},{3,6},{4},{5}}=>6 {{1},{2},{3,6,7},{4},{5}}=>2 {{1},{2},{3,6},{4,7},{5}}=>4 {{1},{2},{3,6},{4},{5,7}}=>3 {{1},{2},{3,6},{4},{5},{7}}=>2 {{1,7},{2},{3},{4,6},{5}}=>6 {{1},{2,7},{3},{4,6},{5}}=>5 {{1},{2},{3,7},{4,6},{5}}=>4 {{1},{2},{3},{4,6,7},{5}}=>1 {{1},{2},{3},{4,6},{5,7}}=>2 {{1},{2},{3},{4,6},{5},{7}}=>1 {{1,7},{2},{3},{4},{5,6}}=>5 {{1},{2,7},{3},{4},{5,6}}=>4 {{1},{2},{3,7},{4},{5,6}}=>3 {{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}}=>5 {{1},{2,7},{3},{4},{5},{6}}=>4 {{1},{2},{3,7},{4},{5},{6}}=>3 {{1},{2},{3},{4,7},{5},{6}}=>2 {{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},{3,4,5,6,7,8}}=>0 {{1},{2,4,5,6,7,8},{3}}=>1 {{1},{2,3,5,6,7,8},{4}}=>1 {{1},{2,3,4,6,7,8},{5}}=>1 {{1},{2,3,4,5,7,8},{6}}=>1 {{1},{2,3,4,5,6,7},{8}}=>0 {{1},{2,3,4,5,6,8},{7}}=>1 {{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}}=>2 {{1,3,5,6,7,8},{2},{4}}=>2 {{1,3,4,5,6,7,8},{2}}=>1 {{1,4,5,6,7,8},{2,3}}=>2 {{1,2,4,5,6,7,8},{3}}=>1 {{1,2,5,6,7,8},{3,4}}=>2 {{1,2,3,5,6,7,8},{4}}=>1 {{1,2,3,6,7,8},{4,5}}=>2 {{1,2,3,4,6,7,8},{5}}=>1 {{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}}=>1 {{1,2,3,4,5,6,7},{8}}=>0 {{1,8},{2,3,4,5,6,7}}=>6 {{1,2,3,4,5,8},{6,7}}=>2 {{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}}=>3 {{1,3,4,6,7,8},{2,5}}=>4 {{1,2,4,6,7,8},{3,5}}=>3 {{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}}=>6 {{1,2,4,5,6,8},{3,7}}=>5 {{1,2,3,5,6,8},{4,7}}=>4 {{1,2,3,4,6,8},{5,7}}=>3 {{1,3,4,5,6,7},{2,8}}=>6 {{1,2,4,5,6,7},{3,8}}=>5 {{1,2,3,5,6,7},{4,8}}=>4 {{1,2,3,4,6,7},{5,8}}=>3 {{1,2,3,4,5,7},{6,8}}=>2 {{1,3},{2,4,5,6,7,8}}=>2 {{1,4},{2,3,5,6,7,8}}=>3 {{1,5},{2,3,4,6,7,8}}=>4 {{1,6},{2,3,4,5,7,8}}=>5 {{1,7},{2,3,4,5,6,8}}=>6
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Description
The dimension exponent of a set partition.
This is
$$\sum_{B\in\pi} (\max(B) - \min(B) + 1) - n$$
where the summation runs over the blocks of the set partition $\pi$ of $\{1,\dots,n\}$.
It is thus equal to the difference St000728The dimension of a set partition. - St000211The rank of the set partition..
This is also the number of occurrences of the pattern {{1, 3}, {2}}, such that 1 and 3 are consecutive elements in a block.
This is also the number of occurrences of the pattern {{1, 3}, {2}}, such that 1 is the minimal and 3 is the maximal element of the block.
References
[1] Chern, B., Diaconis, P., Kane, D. M., Rhoades, R. C. Closed expressions for averages of set partition statistics MathSciNet:3338726 arXiv:1304.4309
[2] De Stavola, D. A Plancherel measure associated to set partitions and its limit arXiv:1612.03061
Code
def statistic(S):
    return sum( max(I)-min(I)-(len(I)-1) for I in S )

def statistic_alt(pi):
    return len(pattern_occurrences(pi, [[1,3],[2]], [1], [3], [], []))

def statistic_alt_2(pi):
    return len(pattern_occurrences(pi, [[1,3],[2]], [], [], [(1,3)], []))

def pattern_occurrences(pi, P, First, Last, Arcs, Consecutives):
    """We assume that pi is a SetPartition of {1,2,...,n} and P is a
    SetPartition of {1,2,...,k}.
    """
    occurrences = []
    pi = SetPartition(pi)
    P = SetPartition(P)

    openers = [min(B) for B in pi]
    closers = [max(B) for B in pi]
    pi_sorted = sorted([sorted(b) for b in pi])
    edges = [(a,b) for B in pi_sorted for (a,b) in zip(B, B[1:])]

    for s in Subsets(pi.base_set(), P.size()):
        s = sorted(s)
        pi_r = pi.restriction(s)
        if pi_r.standardization() != P:
            continue

        X = pi_r.base_set()

        if any(X[i-1] not in openers for i in First):
            continue

        if any(X[i-1] not in closers for i in Last):
            continue

        if any((X[i-1], X[j-1]) not in edges for (i,j) in Arcs):
            continue

        if any(abs(X[i-1]-X[j-1]) != 1 for (i,j) in Consecutives):
            continue

        occurrences += [s]
    return occurrences
Created
Aug 10, 2016 at 15:33 by Martin Rubey
Updated
Jul 12, 2017 at 09:59 by Christian Stump