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Identifier
Values
=>
Cc0009;cc-rep
{{1}}=>1 {{1,2}}=>1 {{1},{2}}=>2 {{1,2,3}}=>1 {{1,2},{3}}=>2 {{1,3},{2}}=>1 {{1},{2,3}}=>2 {{1},{2},{3}}=>3 {{1,2,3,4}}=>1 {{1,2,3},{4}}=>2 {{1,2,4},{3}}=>1 {{1,2},{3,4}}=>2 {{1,2},{3},{4}}=>3 {{1,3,4},{2}}=>1 {{1,3},{2,4}}=>2 {{1,3},{2},{4}}=>2 {{1,4},{2,3}}=>1 {{1},{2,3,4}}=>2 {{1},{2,3},{4}}=>3 {{1,4},{2},{3}}=>1 {{1},{2,4},{3}}=>3 {{1},{2},{3,4}}=>2 {{1},{2},{3},{4}}=>4 {{1,2,3,4,5}}=>1 {{1,2,3,4},{5}}=>2 {{1,2,3,5},{4}}=>1 {{1,2,3},{4,5}}=>2 {{1,2,3},{4},{5}}=>3 {{1,2,4,5},{3}}=>1 {{1,2,4},{3,5}}=>2 {{1,2,4},{3},{5}}=>2 {{1,2,5},{3,4}}=>1 {{1,2},{3,4,5}}=>2 {{1,2},{3,4},{5}}=>3 {{1,2,5},{3},{4}}=>1 {{1,2},{3,5},{4}}=>3 {{1,2},{3},{4,5}}=>2 {{1,2},{3},{4},{5}}=>4 {{1,3,4,5},{2}}=>1 {{1,3,4},{2,5}}=>2 {{1,3,4},{2},{5}}=>2 {{1,3,5},{2,4}}=>1 {{1,3},{2,4,5}}=>2 {{1,3},{2,4},{5}}=>3 {{1,3,5},{2},{4}}=>1 {{1,3},{2,5},{4}}=>3 {{1,3},{2},{4,5}}=>2 {{1,3},{2},{4},{5}}=>3 {{1,4,5},{2,3}}=>1 {{1,4},{2,3,5}}=>2 {{1,4},{2,3},{5}}=>2 {{1,5},{2,3,4}}=>1 {{1},{2,3,4,5}}=>2 {{1},{2,3,4},{5}}=>3 {{1,5},{2,3},{4}}=>1 {{1},{2,3,5},{4}}=>3 {{1},{2,3},{4,5}}=>2 {{1},{2,3},{4},{5}}=>4 {{1,4,5},{2},{3}}=>1 {{1,4},{2,5},{3}}=>2 {{1,4},{2},{3,5}}=>2 {{1,4},{2},{3},{5}}=>2 {{1,5},{2,4},{3}}=>1 {{1},{2,4,5},{3}}=>2 {{1},{2,4},{3,5}}=>3 {{1},{2,4},{3},{5}}=>4 {{1,5},{2},{3,4}}=>1 {{1},{2,5},{3,4}}=>3 {{1},{2},{3,4,5}}=>2 {{1},{2},{3,4},{5}}=>3 {{1,5},{2},{3},{4}}=>1 {{1},{2,5},{3},{4}}=>4 {{1},{2},{3,5},{4}}=>2 {{1},{2},{3},{4,5}}=>3 {{1},{2},{3},{4},{5}}=>5 {{1,2,3,4,5,6}}=>1 {{1,2,3,4,5},{6}}=>2 {{1,2,3,4,6},{5}}=>1 {{1,2,3,4},{5,6}}=>2 {{1,2,3,4},{5},{6}}=>3 {{1,2,3,5,6},{4}}=>1 {{1,2,3,5},{4,6}}=>2 {{1,2,3,5},{4},{6}}=>2 {{1,2,3,6},{4,5}}=>1 {{1,2,3},{4,5,6}}=>2 {{1,2,3},{4,5},{6}}=>3 {{1,2,3,6},{4},{5}}=>1 {{1,2,3},{4,6},{5}}=>3 {{1,2,3},{4},{5,6}}=>2 {{1,2,3},{4},{5},{6}}=>4 {{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}}=>1 {{1,2,4},{3,5,6}}=>2 {{1,2,4},{3,5},{6}}=>3 {{1,2,4,6},{3},{5}}=>1 {{1,2,4},{3,6},{5}}=>3 {{1,2,4},{3},{5,6}}=>2 {{1,2,4},{3},{5},{6}}=>3 {{1,2,5,6},{3,4}}=>1 {{1,2,5},{3,4,6}}=>2 {{1,2,5},{3,4},{6}}=>2 {{1,2,6},{3,4,5}}=>1 {{1,2},{3,4,5,6}}=>2 {{1,2},{3,4,5},{6}}=>3 {{1,2,6},{3,4},{5}}=>1 {{1,2},{3,4,6},{5}}=>3 {{1,2},{3,4},{5,6}}=>2 {{1,2},{3,4},{5},{6}}=>4 {{1,2,5,6},{3},{4}}=>1 {{1,2,5},{3,6},{4}}=>2 {{1,2,5},{3},{4,6}}=>2 {{1,2,5},{3},{4},{6}}=>2 {{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}}=>4 {{1,2,6},{3},{4,5}}=>1 {{1,2},{3,6},{4,5}}=>3 {{1,2},{3},{4,5,6}}=>2 {{1,2},{3},{4,5},{6}}=>3 {{1,2,6},{3},{4},{5}}=>1 {{1,2},{3,6},{4},{5}}=>4 {{1,2},{3},{4,6},{5}}=>2 {{1,2},{3},{4},{5,6}}=>3 {{1,2},{3},{4},{5},{6}}=>5 {{1,3,4,5,6},{2}}=>1 {{1,3,4,5},{2,6}}=>2 {{1,3,4,5},{2},{6}}=>2 {{1,3,4,6},{2,5}}=>1 {{1,3,4},{2,5,6}}=>2 {{1,3,4},{2,5},{6}}=>3 {{1,3,4,6},{2},{5}}=>1 {{1,3,4},{2,6},{5}}=>3 {{1,3,4},{2},{5,6}}=>2 {{1,3,4},{2},{5},{6}}=>3 {{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}}=>1 {{1,3},{2,4,5,6}}=>2 {{1,3},{2,4,5},{6}}=>3 {{1,3,6},{2,4},{5}}=>1 {{1,3},{2,4,6},{5}}=>3 {{1,3},{2,4},{5,6}}=>2 {{1,3},{2,4},{5},{6}}=>4 {{1,3,5,6},{2},{4}}=>1 {{1,3,5},{2,6},{4}}=>2 {{1,3,5},{2},{4,6}}=>2 {{1,3,5},{2},{4},{6}}=>2 {{1,3,6},{2,5},{4}}=>1 {{1,3},{2,5,6},{4}}=>2 {{1,3},{2,5},{4,6}}=>3 {{1,3},{2,5},{4},{6}}=>4 {{1,3,6},{2},{4,5}}=>1 {{1,3},{2,6},{4,5}}=>3 {{1,3},{2},{4,5,6}}=>2 {{1,3},{2},{4,5},{6}}=>3 {{1,3,6},{2},{4},{5}}=>1 {{1,3},{2,6},{4},{5}}=>4 {{1,3},{2},{4,6},{5}}=>2 {{1,3},{2},{4},{5,6}}=>3 {{1,3},{2},{4},{5},{6}}=>4 {{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}}=>1 {{1,4},{2,3,5,6}}=>2 {{1,4},{2,3,5},{6}}=>3 {{1,4,6},{2,3},{5}}=>1 {{1,4},{2,3,6},{5}}=>3 {{1,4},{2,3},{5,6}}=>2 {{1,4},{2,3},{5},{6}}=>3 {{1,5,6},{2,3,4}}=>1 {{1,5},{2,3,4,6}}=>2 {{1,5},{2,3,4},{6}}=>2 {{1,6},{2,3,4,5}}=>1 {{1},{2,3,4,5,6}}=>2 {{1},{2,3,4,5},{6}}=>3 {{1,6},{2,3,4},{5}}=>1 {{1},{2,3,4,6},{5}}=>3 {{1},{2,3,4},{5,6}}=>2 {{1},{2,3,4},{5},{6}}=>4 {{1,5,6},{2,3},{4}}=>1 {{1,5},{2,3,6},{4}}=>2 {{1,5},{2,3},{4,6}}=>2 {{1,5},{2,3},{4},{6}}=>2 {{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}}=>4 {{1,6},{2,3},{4,5}}=>1 {{1},{2,3,6},{4,5}}=>3 {{1},{2,3},{4,5,6}}=>2 {{1},{2,3},{4,5},{6}}=>3 {{1,6},{2,3},{4},{5}}=>1 {{1},{2,3,6},{4},{5}}=>4 {{1},{2,3},{4,6},{5}}=>2 {{1},{2,3},{4},{5,6}}=>3 {{1},{2,3},{4},{5},{6}}=>5 {{1,4,5,6},{2},{3}}=>1 {{1,4,5},{2,6},{3}}=>2 {{1,4,5},{2},{3,6}}=>2 {{1,4,5},{2},{3},{6}}=>2 {{1,4,6},{2,5},{3}}=>1 {{1,4},{2,5,6},{3}}=>2 {{1,4},{2,5},{3,6}}=>3 {{1,4},{2,5},{3},{6}}=>3 {{1,4,6},{2},{3,5}}=>1 {{1,4},{2,6},{3,5}}=>3 {{1,4},{2},{3,5,6}}=>2 {{1,4},{2},{3,5},{6}}=>3 {{1,4,6},{2},{3},{5}}=>1 {{1,4},{2,6},{3},{5}}=>3 {{1,4},{2},{3,6},{5}}=>3 {{1,4},{2},{3},{5,6}}=>2 {{1,4},{2},{3},{5},{6}}=>3 {{1,5,6},{2,4},{3}}=>1 {{1,5},{2,4,6},{3}}=>2 {{1,5},{2,4},{3,6}}=>2 {{1,5},{2,4},{3},{6}}=>2 {{1,6},{2,4,5},{3}}=>1 {{1},{2,4,5,6},{3}}=>2 {{1},{2,4,5},{3,6}}=>3 {{1},{2,4,5},{3},{6}}=>3 {{1,6},{2,4},{3,5}}=>1 {{1},{2,4,6},{3,5}}=>3 {{1},{2,4},{3,5,6}}=>2 {{1},{2,4},{3,5},{6}}=>4 {{1,6},{2,4},{3},{5}}=>1 {{1},{2,4,6},{3},{5}}=>2 {{1},{2,4},{3,6},{5}}=>4 {{1},{2,4},{3},{5,6}}=>3 {{1},{2,4},{3},{5},{6}}=>5 {{1,5,6},{2},{3,4}}=>1 {{1,5},{2,6},{3,4}}=>2 {{1,5},{2},{3,4,6}}=>2 {{1,5},{2},{3,4},{6}}=>2 {{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}}=>4 {{1,6},{2},{3,4,5}}=>1 {{1},{2,6},{3,4,5}}=>3 {{1},{2},{3,4,5,6}}=>2 {{1},{2},{3,4,5},{6}}=>3 {{1,6},{2},{3,4},{5}}=>1 {{1},{2,6},{3,4},{5}}=>4 {{1},{2},{3,4,6},{5}}=>2 {{1},{2},{3,4},{5,6}}=>3 {{1},{2},{3,4},{5},{6}}=>4 {{1,5,6},{2},{3},{4}}=>1 {{1,5},{2,6},{3},{4}}=>2 {{1,5},{2},{3,6},{4}}=>2 {{1,5},{2},{3},{4,6}}=>2 {{1,5},{2},{3},{4},{6}}=>2 {{1,6},{2,5},{3},{4}}=>1 {{1},{2,5,6},{3},{4}}=>3 {{1},{2,5},{3,6},{4}}=>4 {{1},{2,5},{3},{4,6}}=>2 {{1},{2,5},{3},{4},{6}}=>5 {{1,6},{2},{3,5},{4}}=>1 {{1},{2,6},{3,5},{4}}=>4 {{1},{2},{3,5,6},{4}}=>3 {{1},{2},{3,5},{4,6}}=>2 {{1},{2},{3,5},{4},{6}}=>3 {{1,6},{2},{3},{4,5}}=>1 {{1},{2,6},{3},{4,5}}=>3 {{1},{2},{3,6},{4,5}}=>3 {{1},{2},{3},{4,5,6}}=>2 {{1},{2},{3},{4,5},{6}}=>4 {{1,6},{2},{3},{4},{5}}=>1 {{1},{2,6},{3},{4},{5}}=>5 {{1},{2},{3,6},{4},{5}}=>2 {{1},{2},{3},{4,6},{5}}=>4 {{1},{2},{3},{4},{5,6}}=>3 {{1},{2},{3},{4},{5},{6}}=>6 {{1,2,3,4,5,6,7}}=>1 {{1,2,3,4,5,6},{7}}=>2 {{1,2,3,4,5,7},{6}}=>1 {{1,2,3,4,5},{6,7}}=>2 {{1,2,3,4,5},{6},{7}}=>3 {{1,2,3,4,6,7},{5}}=>1 {{1,2,3,4,6},{5,7}}=>2 {{1,2,3,4,6},{5},{7}}=>2 {{1,2,3,4,7},{5,6}}=>1 {{1,2,3,4},{5,6,7}}=>2 {{1,2,3,4},{5,6},{7}}=>3 {{1,2,3,4,7},{5},{6}}=>1 {{1,2,3,4},{5,7},{6}}=>3 {{1,2,3,4},{5},{6,7}}=>2 {{1,2,3,4},{5},{6},{7}}=>4 {{1,2,3,5,6,7},{4}}=>1 {{1,2,3,5,6},{4,7}}=>2 {{1,2,3,5,6},{4},{7}}=>2 {{1,2,3,5,7},{4,6}}=>1 {{1,2,3,5},{4,6,7}}=>2 {{1,2,3,5},{4,6},{7}}=>3 {{1,2,3,5,7},{4},{6}}=>1 {{1,2,3,5},{4,7},{6}}=>3 {{1,2,3,5},{4},{6,7}}=>2 {{1,2,3,5},{4},{6},{7}}=>3 {{1,2,3,6,7},{4,5}}=>1 {{1,2,3,6},{4,5,7}}=>2 {{1,2,3,6},{4,5},{7}}=>2 {{1,2,3,7},{4,5,6}}=>1 {{1,2,3},{4,5,6,7}}=>2 {{1,2,3},{4,5,6},{7}}=>3 {{1,2,3,7},{4,5},{6}}=>1 {{1,2,3},{4,5,7},{6}}=>3 {{1,2,3},{4,5},{6,7}}=>2 {{1,2,3},{4,5},{6},{7}}=>4 {{1,2,3,6,7},{4},{5}}=>1 {{1,2,3,6},{4,7},{5}}=>2 {{1,2,3,6},{4},{5,7}}=>2 {{1,2,3,6},{4},{5},{7}}=>2 {{1,2,3,7},{4,6},{5}}=>1 {{1,2,3},{4,6,7},{5}}=>2 {{1,2,3},{4,6},{5,7}}=>3 {{1,2,3},{4,6},{5},{7}}=>4 {{1,2,3,7},{4},{5,6}}=>1 {{1,2,3},{4,7},{5,6}}=>3 {{1,2,3},{4},{5,6,7}}=>2 {{1,2,3},{4},{5,6},{7}}=>3 {{1,2,3,7},{4},{5},{6}}=>1 {{1,2,3},{4,7},{5},{6}}=>4 {{1,2,3},{4},{5,7},{6}}=>2 {{1,2,3},{4},{5},{6,7}}=>3 {{1,2,3},{4},{5},{6},{7}}=>5 {{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}}=>1 {{1,2,4,5},{3,6,7}}=>2 {{1,2,4,5},{3,6},{7}}=>3 {{1,2,4,5,7},{3},{6}}=>1 {{1,2,4,5},{3,7},{6}}=>3 {{1,2,4,5},{3},{6,7}}=>2 {{1,2,4,5},{3},{6},{7}}=>3 {{1,2,4,6,7},{3,5}}=>1 {{1,2,4,6},{3,5,7}}=>2 {{1,2,4,6},{3,5},{7}}=>2 {{1,2,4,7},{3,5,6}}=>1 {{1,2,4},{3,5,6,7}}=>2 {{1,2,4},{3,5,6},{7}}=>3 {{1,2,4,7},{3,5},{6}}=>1 {{1,2,4},{3,5,7},{6}}=>3 {{1,2,4},{3,5},{6,7}}=>2 {{1,2,4},{3,5},{6},{7}}=>4 {{1,2,4,6,7},{3},{5}}=>1 {{1,2,4,6},{3,7},{5}}=>2 {{1,2,4,6},{3},{5,7}}=>2 {{1,2,4,6},{3},{5},{7}}=>2 {{1,2,4,7},{3,6},{5}}=>1 {{1,2,4},{3,6,7},{5}}=>2 {{1,2,4},{3,6},{5,7}}=>3 {{1,2,4},{3,6},{5},{7}}=>4 {{1,2,4,7},{3},{5,6}}=>1 {{1,2,4},{3,7},{5,6}}=>3 {{1,2,4},{3},{5,6,7}}=>2 {{1,2,4},{3},{5,6},{7}}=>3 {{1,2,4,7},{3},{5},{6}}=>1 {{1,2,4},{3,7},{5},{6}}=>4 {{1,2,4},{3},{5,7},{6}}=>2 {{1,2,4},{3},{5},{6,7}}=>3 {{1,2,4},{3},{5},{6},{7}}=>4 {{1,2,5,6,7},{3,4}}=>1 {{1,2,5,6},{3,4,7}}=>2 {{1,2,5,6},{3,4},{7}}=>2 {{1,2,5,7},{3,4,6}}=>1 {{1,2,5},{3,4,6,7}}=>2 {{1,2,5},{3,4,6},{7}}=>3 {{1,2,5,7},{3,4},{6}}=>1 {{1,2,5},{3,4,7},{6}}=>3 {{1,2,5},{3,4},{6,7}}=>2 {{1,2,5},{3,4},{6},{7}}=>3 {{1,2,6,7},{3,4,5}}=>1 {{1,2,6},{3,4,5,7}}=>2 {{1,2,6},{3,4,5},{7}}=>2 {{1,2,7},{3,4,5,6}}=>1 {{1,2},{3,4,5,6,7}}=>2 {{1,2},{3,4,5,6},{7}}=>3 {{1,2,7},{3,4,5},{6}}=>1 {{1,2},{3,4,5,7},{6}}=>3 {{1,2},{3,4,5},{6,7}}=>2 {{1,2},{3,4,5},{6},{7}}=>4 {{1,2,6,7},{3,4},{5}}=>1 {{1,2,6},{3,4,7},{5}}=>2 {{1,2,6},{3,4},{5,7}}=>2 {{1,2,6},{3,4},{5},{7}}=>2 {{1,2,7},{3,4,6},{5}}=>1 {{1,2},{3,4,6,7},{5}}=>2 {{1,2},{3,4,6},{5,7}}=>3 {{1,2},{3,4,6},{5},{7}}=>4 {{1,2,7},{3,4},{5,6}}=>1 {{1,2},{3,4,7},{5,6}}=>3 {{1,2},{3,4},{5,6,7}}=>2 {{1,2},{3,4},{5,6},{7}}=>3 {{1,2,7},{3,4},{5},{6}}=>1 {{1,2},{3,4,7},{5},{6}}=>4 {{1,2},{3,4},{5,7},{6}}=>2 {{1,2},{3,4},{5},{6,7}}=>3 {{1,2},{3,4},{5},{6},{7}}=>5 {{1,2,5,6,7},{3},{4}}=>1 {{1,2,5,6},{3,7},{4}}=>2 {{1,2,5,6},{3},{4,7}}=>2 {{1,2,5,6},{3},{4},{7}}=>2 {{1,2,5,7},{3,6},{4}}=>1 {{1,2,5},{3,6,7},{4}}=>2 {{1,2,5},{3,6},{4,7}}=>3 {{1,2,5},{3,6},{4},{7}}=>3 {{1,2,5,7},{3},{4,6}}=>1 {{1,2,5},{3,7},{4,6}}=>3 {{1,2,5},{3},{4,6,7}}=>2 {{1,2,5},{3},{4,6},{7}}=>3 {{1,2,5,7},{3},{4},{6}}=>1 {{1,2,5},{3,7},{4},{6}}=>3 {{1,2,5},{3},{4,7},{6}}=>3 {{1,2,5},{3},{4},{6,7}}=>2 {{1,2,5},{3},{4},{6},{7}}=>3 {{1,2,6,7},{3,5},{4}}=>1 {{1,2,6},{3,5,7},{4}}=>2 {{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}}=>1 {{1,2},{3,5,7},{4,6}}=>3 {{1,2},{3,5},{4,6,7}}=>2 {{1,2},{3,5},{4,6},{7}}=>4 {{1,2,7},{3,5},{4},{6}}=>1 {{1,2},{3,5,7},{4},{6}}=>2 {{1,2},{3,5},{4,7},{6}}=>4 {{1,2},{3,5},{4},{6,7}}=>3 {{1,2},{3,5},{4},{6},{7}}=>5 {{1,2,6,7},{3},{4,5}}=>1 {{1,2,6},{3,7},{4,5}}=>2 {{1,2,6},{3},{4,5,7}}=>2 {{1,2,6},{3},{4,5},{7}}=>2 {{1,2,7},{3,6},{4,5}}=>1 {{1,2},{3,6,7},{4,5}}=>2 {{1,2},{3,6},{4,5,7}}=>3 {{1,2},{3,6},{4,5},{7}}=>4 {{1,2,7},{3},{4,5,6}}=>1 {{1,2},{3,7},{4,5,6}}=>3 {{1,2},{3},{4,5,6,7}}=>2 {{1,2},{3},{4,5,6},{7}}=>3 {{1,2,7},{3},{4,5},{6}}=>1 {{1,2},{3,7},{4,5},{6}}=>4 {{1,2},{3},{4,5,7},{6}}=>2 {{1,2},{3},{4,5},{6,7}}=>3 {{1,2},{3},{4,5},{6},{7}}=>4 {{1,2,6,7},{3},{4},{5}}=>1 {{1,2,6},{3,7},{4},{5}}=>2 {{1,2,6},{3},{4,7},{5}}=>2 {{1,2,6},{3},{4},{5,7}}=>2 {{1,2,6},{3},{4},{5},{7}}=>2 {{1,2,7},{3,6},{4},{5}}=>1 {{1,2},{3,6,7},{4},{5}}=>3 {{1,2},{3,6},{4,7},{5}}=>4 {{1,2},{3,6},{4},{5,7}}=>2 {{1,2},{3,6},{4},{5},{7}}=>5 {{1,2,7},{3},{4,6},{5}}=>1 {{1,2},{3,7},{4,6},{5}}=>4 {{1,2},{3},{4,6,7},{5}}=>3 {{1,2},{3},{4,6},{5,7}}=>2 {{1,2},{3},{4,6},{5},{7}}=>3 {{1,2,7},{3},{4},{5,6}}=>1 {{1,2},{3,7},{4},{5,6}}=>3 {{1,2},{3},{4,7},{5,6}}=>3 {{1,2},{3},{4},{5,6,7}}=>2 {{1,2},{3},{4},{5,6},{7}}=>4 {{1,2,7},{3},{4},{5},{6}}=>1 {{1,2},{3,7},{4},{5},{6}}=>5 {{1,2},{3},{4,7},{5},{6}}=>2 {{1,2},{3},{4},{5,7},{6}}=>4 {{1,2},{3},{4},{5},{6,7}}=>3 {{1,2},{3},{4},{5},{6},{7}}=>6 {{1,3,4,5,6,7},{2}}=>1 {{1,3,4,5,6},{2,7}}=>2 {{1,3,4,5,6},{2},{7}}=>2 {{1,3,4,5,7},{2,6}}=>1 {{1,3,4,5},{2,6,7}}=>2 {{1,3,4,5},{2,6},{7}}=>3 {{1,3,4,5,7},{2},{6}}=>1 {{1,3,4,5},{2,7},{6}}=>3 {{1,3,4,5},{2},{6,7}}=>2 {{1,3,4,5},{2},{6},{7}}=>3 {{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}}=>1 {{1,3,4},{2,5,6,7}}=>2 {{1,3,4},{2,5,6},{7}}=>3 {{1,3,4,7},{2,5},{6}}=>1 {{1,3,4},{2,5,7},{6}}=>3 {{1,3,4},{2,5},{6,7}}=>2 {{1,3,4},{2,5},{6},{7}}=>4 {{1,3,4,6,7},{2},{5}}=>1 {{1,3,4,6},{2,7},{5}}=>2 {{1,3,4,6},{2},{5,7}}=>2 {{1,3,4,6},{2},{5},{7}}=>2 {{1,3,4,7},{2,6},{5}}=>1 {{1,3,4},{2,6,7},{5}}=>2 {{1,3,4},{2,6},{5,7}}=>3 {{1,3,4},{2,6},{5},{7}}=>4 {{1,3,4,7},{2},{5,6}}=>1 {{1,3,4},{2,7},{5,6}}=>3 {{1,3,4},{2},{5,6,7}}=>2 {{1,3,4},{2},{5,6},{7}}=>3 {{1,3,4,7},{2},{5},{6}}=>1 {{1,3,4},{2,7},{5},{6}}=>4 {{1,3,4},{2},{5,7},{6}}=>2 {{1,3,4},{2},{5},{6,7}}=>3 {{1,3,4},{2},{5},{6},{7}}=>4 {{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}}=>1 {{1,3,5},{2,4,6,7}}=>2 {{1,3,5},{2,4,6},{7}}=>3 {{1,3,5,7},{2,4},{6}}=>1 {{1,3,5},{2,4,7},{6}}=>3 {{1,3,5},{2,4},{6,7}}=>2 {{1,3,5},{2,4},{6},{7}}=>3 {{1,3,6,7},{2,4,5}}=>1 {{1,3,6},{2,4,5,7}}=>2 {{1,3,6},{2,4,5},{7}}=>2 {{1,3,7},{2,4,5,6}}=>1 {{1,3},{2,4,5,6,7}}=>2 {{1,3},{2,4,5,6},{7}}=>3 {{1,3,7},{2,4,5},{6}}=>1 {{1,3},{2,4,5,7},{6}}=>3 {{1,3},{2,4,5},{6,7}}=>2 {{1,3},{2,4,5},{6},{7}}=>4 {{1,3,6,7},{2,4},{5}}=>1 {{1,3,6},{2,4,7},{5}}=>2 {{1,3,6},{2,4},{5,7}}=>2 {{1,3,6},{2,4},{5},{7}}=>2 {{1,3,7},{2,4,6},{5}}=>1 {{1,3},{2,4,6,7},{5}}=>2 {{1,3},{2,4,6},{5,7}}=>3 {{1,3},{2,4,6},{5},{7}}=>4 {{1,3,7},{2,4},{5,6}}=>1 {{1,3},{2,4,7},{5,6}}=>3 {{1,3},{2,4},{5,6,7}}=>2 {{1,3},{2,4},{5,6},{7}}=>3 {{1,3,7},{2,4},{5},{6}}=>1 {{1,3},{2,4,7},{5},{6}}=>4 {{1,3},{2,4},{5,7},{6}}=>2 {{1,3},{2,4},{5},{6,7}}=>3 {{1,3},{2,4},{5},{6},{7}}=>5 {{1,3,5,6,7},{2},{4}}=>1 {{1,3,5,6},{2,7},{4}}=>2 {{1,3,5,6},{2},{4,7}}=>2 {{1,3,5,6},{2},{4},{7}}=>2 {{1,3,5,7},{2,6},{4}}=>1 {{1,3,5},{2,6,7},{4}}=>2 {{1,3,5},{2,6},{4,7}}=>3 {{1,3,5},{2,6},{4},{7}}=>3 {{1,3,5,7},{2},{4,6}}=>1 {{1,3,5},{2,7},{4,6}}=>3 {{1,3,5},{2},{4,6,7}}=>2 {{1,3,5},{2},{4,6},{7}}=>3 {{1,3,5,7},{2},{4},{6}}=>1 {{1,3,5},{2,7},{4},{6}}=>3 {{1,3,5},{2},{4,7},{6}}=>3 {{1,3,5},{2},{4},{6,7}}=>2 {{1,3,5},{2},{4},{6},{7}}=>3 {{1,3,6,7},{2,5},{4}}=>1 {{1,3,6},{2,5,7},{4}}=>2 {{1,3,6},{2,5},{4,7}}=>2 {{1,3,6},{2,5},{4},{7}}=>2 {{1,3,7},{2,5,6},{4}}=>1 {{1,3},{2,5,6,7},{4}}=>2 {{1,3},{2,5,6},{4,7}}=>3 {{1,3},{2,5,6},{4},{7}}=>3 {{1,3,7},{2,5},{4,6}}=>1 {{1,3},{2,5,7},{4,6}}=>3 {{1,3},{2,5},{4,6,7}}=>2 {{1,3},{2,5},{4,6},{7}}=>4 {{1,3,7},{2,5},{4},{6}}=>1 {{1,3},{2,5,7},{4},{6}}=>2 {{1,3},{2,5},{4,7},{6}}=>4 {{1,3},{2,5},{4},{6,7}}=>3 {{1,3},{2,5},{4},{6},{7}}=>5 {{1,3,6,7},{2},{4,5}}=>1 {{1,3,6},{2,7},{4,5}}=>2 {{1,3,6},{2},{4,5,7}}=>2 {{1,3,6},{2},{4,5},{7}}=>2 {{1,3,7},{2,6},{4,5}}=>1 {{1,3},{2,6,7},{4,5}}=>2 {{1,3},{2,6},{4,5,7}}=>3 {{1,3},{2,6},{4,5},{7}}=>4 {{1,3,7},{2},{4,5,6}}=>1 {{1,3},{2,7},{4,5,6}}=>3 {{1,3},{2},{4,5,6,7}}=>2 {{1,3},{2},{4,5,6},{7}}=>3 {{1,3,7},{2},{4,5},{6}}=>1 {{1,3},{2,7},{4,5},{6}}=>4 {{1,3},{2},{4,5,7},{6}}=>2 {{1,3},{2},{4,5},{6,7}}=>3 {{1,3},{2},{4,5},{6},{7}}=>4 {{1,3,6,7},{2},{4},{5}}=>1 {{1,3,6},{2,7},{4},{5}}=>2 {{1,3,6},{2},{4,7},{5}}=>2 {{1,3,6},{2},{4},{5,7}}=>2 {{1,3,6},{2},{4},{5},{7}}=>2 {{1,3,7},{2,6},{4},{5}}=>1 {{1,3},{2,6,7},{4},{5}}=>3 {{1,3},{2,6},{4,7},{5}}=>4 {{1,3},{2,6},{4},{5,7}}=>2 {{1,3},{2,6},{4},{5},{7}}=>5 {{1,3,7},{2},{4,6},{5}}=>1 {{1,3},{2,7},{4,6},{5}}=>4 {{1,3},{2},{4,6,7},{5}}=>3 {{1,3},{2},{4,6},{5,7}}=>2 {{1,3},{2},{4,6},{5},{7}}=>3 {{1,3,7},{2},{4},{5,6}}=>1 {{1,3},{2,7},{4},{5,6}}=>3 {{1,3},{2},{4,7},{5,6}}=>3 {{1,3},{2},{4},{5,6,7}}=>2 {{1,3},{2},{4},{5,6},{7}}=>4 {{1,3,7},{2},{4},{5},{6}}=>1 {{1,3},{2,7},{4},{5},{6}}=>5 {{1,3},{2},{4,7},{5},{6}}=>2 {{1,3},{2},{4},{5,7},{6}}=>4 {{1,3},{2},{4},{5},{6,7}}=>3 {{1,3},{2},{4},{5},{6},{7}}=>5 {{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}}=>1 {{1,4,5},{2,3,6,7}}=>2 {{1,4,5},{2,3,6},{7}}=>3 {{1,4,5,7},{2,3},{6}}=>1 {{1,4,5},{2,3,7},{6}}=>3 {{1,4,5},{2,3},{6,7}}=>2 {{1,4,5},{2,3},{6},{7}}=>3 {{1,4,6,7},{2,3,5}}=>1 {{1,4,6},{2,3,5,7}}=>2 {{1,4,6},{2,3,5},{7}}=>2 {{1,4,7},{2,3,5,6}}=>1 {{1,4},{2,3,5,6,7}}=>2 {{1,4},{2,3,5,6},{7}}=>3 {{1,4,7},{2,3,5},{6}}=>1 {{1,4},{2,3,5,7},{6}}=>3 {{1,4},{2,3,5},{6,7}}=>2 {{1,4},{2,3,5},{6},{7}}=>4 {{1,4,6,7},{2,3},{5}}=>1 {{1,4,6},{2,3,7},{5}}=>2 {{1,4,6},{2,3},{5,7}}=>2 {{1,4,6},{2,3},{5},{7}}=>2 {{1,4,7},{2,3,6},{5}}=>1 {{1,4},{2,3,6,7},{5}}=>2 {{1,4},{2,3,6},{5,7}}=>3 {{1,4},{2,3,6},{5},{7}}=>4 {{1,4,7},{2,3},{5,6}}=>1 {{1,4},{2,3,7},{5,6}}=>3 {{1,4},{2,3},{5,6,7}}=>2 {{1,4},{2,3},{5,6},{7}}=>3 {{1,4,7},{2,3},{5},{6}}=>1 {{1,4},{2,3,7},{5},{6}}=>4 {{1,4},{2,3},{5,7},{6}}=>2 {{1,4},{2,3},{5},{6,7}}=>3 {{1,4},{2,3},{5},{6},{7}}=>4 {{1,5,6,7},{2,3,4}}=>1 {{1,5,6},{2,3,4,7}}=>2 {{1,5,6},{2,3,4},{7}}=>2 {{1,5,7},{2,3,4,6}}=>1 {{1,5},{2,3,4,6,7}}=>2 {{1,5},{2,3,4,6},{7}}=>3 {{1,5,7},{2,3,4},{6}}=>1 {{1,5},{2,3,4,7},{6}}=>3 {{1,5},{2,3,4},{6,7}}=>2 {{1,5},{2,3,4},{6},{7}}=>3 {{1,6,7},{2,3,4,5}}=>1 {{1,6},{2,3,4,5,7}}=>2 {{1,6},{2,3,4,5},{7}}=>2 {{1,7},{2,3,4,5,6}}=>1 {{1},{2,3,4,5,6,7}}=>2 {{1},{2,3,4,5,6},{7}}=>3 {{1,7},{2,3,4,5},{6}}=>1 {{1},{2,3,4,5,7},{6}}=>3 {{1},{2,3,4,5},{6,7}}=>2 {{1},{2,3,4,5},{6},{7}}=>4 {{1,6,7},{2,3,4},{5}}=>1 {{1,6},{2,3,4,7},{5}}=>2 {{1,6},{2,3,4},{5,7}}=>2 {{1,6},{2,3,4},{5},{7}}=>2 {{1,7},{2,3,4,6},{5}}=>1 {{1},{2,3,4,6,7},{5}}=>2 {{1},{2,3,4,6},{5,7}}=>3 {{1},{2,3,4,6},{5},{7}}=>4 {{1,7},{2,3,4},{5,6}}=>1 {{1},{2,3,4,7},{5,6}}=>3 {{1},{2,3,4},{5,6,7}}=>2 {{1},{2,3,4},{5,6},{7}}=>3 {{1,7},{2,3,4},{5},{6}}=>1 {{1},{2,3,4,7},{5},{6}}=>4 {{1},{2,3,4},{5,7},{6}}=>2 {{1},{2,3,4},{5},{6,7}}=>3 {{1},{2,3,4},{5},{6},{7}}=>5 {{1,5,6,7},{2,3},{4}}=>1 {{1,5,6},{2,3,7},{4}}=>2 {{1,5,6},{2,3},{4,7}}=>2 {{1,5,6},{2,3},{4},{7}}=>2 {{1,5,7},{2,3,6},{4}}=>1 {{1,5},{2,3,6,7},{4}}=>2 {{1,5},{2,3,6},{4,7}}=>3 {{1,5},{2,3,6},{4},{7}}=>3 {{1,5,7},{2,3},{4,6}}=>1 {{1,5},{2,3,7},{4,6}}=>3 {{1,5},{2,3},{4,6,7}}=>2 {{1,5},{2,3},{4,6},{7}}=>3 {{1,5,7},{2,3},{4},{6}}=>1 {{1,5},{2,3,7},{4},{6}}=>3 {{1,5},{2,3},{4,7},{6}}=>3 {{1,5},{2,3},{4},{6,7}}=>2 {{1,5},{2,3},{4},{6},{7}}=>3 {{1,6,7},{2,3,5},{4}}=>1 {{1,6},{2,3,5,7},{4}}=>2 {{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}}=>1 {{1},{2,3,5,7},{4,6}}=>3 {{1},{2,3,5},{4,6,7}}=>2 {{1},{2,3,5},{4,6},{7}}=>4 {{1,7},{2,3,5},{4},{6}}=>1 {{1},{2,3,5,7},{4},{6}}=>2 {{1},{2,3,5},{4,7},{6}}=>4 {{1},{2,3,5},{4},{6,7}}=>3 {{1},{2,3,5},{4},{6},{7}}=>5 {{1,6,7},{2,3},{4,5}}=>1 {{1,6},{2,3,7},{4,5}}=>2 {{1,6},{2,3},{4,5,7}}=>2 {{1,6},{2,3},{4,5},{7}}=>2 {{1,7},{2,3,6},{4,5}}=>1 {{1},{2,3,6,7},{4,5}}=>2 {{1},{2,3,6},{4,5,7}}=>3 {{1},{2,3,6},{4,5},{7}}=>4 {{1,7},{2,3},{4,5,6}}=>1 {{1},{2,3,7},{4,5,6}}=>3 {{1},{2,3},{4,5,6,7}}=>2 {{1},{2,3},{4,5,6},{7}}=>3 {{1,7},{2,3},{4,5},{6}}=>1 {{1},{2,3,7},{4,5},{6}}=>4 {{1},{2,3},{4,5,7},{6}}=>2 {{1},{2,3},{4,5},{6,7}}=>3 {{1},{2,3},{4,5},{6},{7}}=>4 {{1,6,7},{2,3},{4},{5}}=>1 {{1,6},{2,3,7},{4},{5}}=>2 {{1,6},{2,3},{4,7},{5}}=>2 {{1,6},{2,3},{4},{5,7}}=>2 {{1,6},{2,3},{4},{5},{7}}=>2 {{1,7},{2,3,6},{4},{5}}=>1 {{1},{2,3,6,7},{4},{5}}=>3 {{1},{2,3,6},{4,7},{5}}=>4 {{1},{2,3,6},{4},{5,7}}=>2 {{1},{2,3,6},{4},{5},{7}}=>5 {{1,7},{2,3},{4,6},{5}}=>1 {{1},{2,3,7},{4,6},{5}}=>4 {{1},{2,3},{4,6,7},{5}}=>3 {{1},{2,3},{4,6},{5,7}}=>2 {{1},{2,3},{4,6},{5},{7}}=>3 {{1,7},{2,3},{4},{5,6}}=>1 {{1},{2,3,7},{4},{5,6}}=>3 {{1},{2,3},{4,7},{5,6}}=>3 {{1},{2,3},{4},{5,6,7}}=>2 {{1},{2,3},{4},{5,6},{7}}=>4 {{1,7},{2,3},{4},{5},{6}}=>1 {{1},{2,3,7},{4},{5},{6}}=>5 {{1},{2,3},{4,7},{5},{6}}=>2 {{1},{2,3},{4},{5,7},{6}}=>4 {{1},{2,3},{4},{5},{6,7}}=>3 {{1},{2,3},{4},{5},{6},{7}}=>6 {{1,4,5,6,7},{2},{3}}=>1 {{1,4,5,6},{2,7},{3}}=>2 {{1,4,5,6},{2},{3,7}}=>2 {{1,4,5,6},{2},{3},{7}}=>2 {{1,4,5,7},{2,6},{3}}=>1 {{1,4,5},{2,6,7},{3}}=>2 {{1,4,5},{2,6},{3,7}}=>3 {{1,4,5},{2,6},{3},{7}}=>3 {{1,4,5,7},{2},{3,6}}=>1 {{1,4,5},{2,7},{3,6}}=>3 {{1,4,5},{2},{3,6,7}}=>2 {{1,4,5},{2},{3,6},{7}}=>3 {{1,4,5,7},{2},{3},{6}}=>1 {{1,4,5},{2,7},{3},{6}}=>3 {{1,4,5},{2},{3,7},{6}}=>3 {{1,4,5},{2},{3},{6,7}}=>2 {{1,4,5},{2},{3},{6},{7}}=>3 {{1,4,6,7},{2,5},{3}}=>1 {{1,4,6},{2,5,7},{3}}=>2 {{1,4,6},{2,5},{3,7}}=>2 {{1,4,6},{2,5},{3},{7}}=>2 {{1,4,7},{2,5,6},{3}}=>1 {{1,4},{2,5,6,7},{3}}=>2 {{1,4},{2,5,6},{3,7}}=>3 {{1,4},{2,5,6},{3},{7}}=>3 {{1,4,7},{2,5},{3,6}}=>1 {{1,4},{2,5,7},{3,6}}=>3 {{1,4},{2,5},{3,6,7}}=>2 {{1,4},{2,5},{3,6},{7}}=>4 {{1,4,7},{2,5},{3},{6}}=>1 {{1,4},{2,5,7},{3},{6}}=>2 {{1,4},{2,5},{3,7},{6}}=>4 {{1,4},{2,5},{3},{6,7}}=>3 {{1,4},{2,5},{3},{6},{7}}=>4 {{1,4,6,7},{2},{3,5}}=>1 {{1,4,6},{2,7},{3,5}}=>2 {{1,4,6},{2},{3,5,7}}=>2 {{1,4,6},{2},{3,5},{7}}=>2 {{1,4,7},{2,6},{3,5}}=>1 {{1,4},{2,6,7},{3,5}}=>2 {{1,4},{2,6},{3,5,7}}=>3 {{1,4},{2,6},{3,5},{7}}=>4 {{1,4,7},{2},{3,5,6}}=>1 {{1,4},{2,7},{3,5,6}}=>3 {{1,4},{2},{3,5,6,7}}=>2 {{1,4},{2},{3,5,6},{7}}=>3 {{1,4,7},{2},{3,5},{6}}=>1 {{1,4},{2,7},{3,5},{6}}=>4 {{1,4},{2},{3,5,7},{6}}=>2 {{1,4},{2},{3,5},{6,7}}=>3 {{1,4},{2},{3,5},{6},{7}}=>4 {{1,4,6,7},{2},{3},{5}}=>1 {{1,4,6},{2,7},{3},{5}}=>2 {{1,4,6},{2},{3,7},{5}}=>2 {{1,4,6},{2},{3},{5,7}}=>2 {{1,4,6},{2},{3},{5},{7}}=>2 {{1,4,7},{2,6},{3},{5}}=>1 {{1,4},{2,6,7},{3},{5}}=>3 {{1,4},{2,6},{3,7},{5}}=>4 {{1,4},{2,6},{3},{5,7}}=>2 {{1,4},{2,6},{3},{5},{7}}=>4 {{1,4,7},{2},{3,6},{5}}=>1 {{1,4},{2,7},{3,6},{5}}=>4 {{1,4},{2},{3,6,7},{5}}=>3 {{1,4},{2},{3,6},{5,7}}=>2 {{1,4},{2},{3,6},{5},{7}}=>4 {{1,4,7},{2},{3},{5,6}}=>1 {{1,4},{2,7},{3},{5,6}}=>3 {{1,4},{2},{3,7},{5,6}}=>3 {{1,4},{2},{3},{5,6,7}}=>2 {{1,4},{2},{3},{5,6},{7}}=>3 {{1,4,7},{2},{3},{5},{6}}=>1 {{1,4},{2,7},{3},{5},{6}}=>4 {{1,4},{2},{3,7},{5},{6}}=>4 {{1,4},{2},{3},{5,7},{6}}=>2 {{1,4},{2},{3},{5},{6,7}}=>3 {{1,4},{2},{3},{5},{6},{7}}=>4 {{1,5,6,7},{2,4},{3}}=>1 {{1,5,6},{2,4,7},{3}}=>2 {{1,5,6},{2,4},{3,7}}=>2 {{1,5,6},{2,4},{3},{7}}=>2 {{1,5,7},{2,4,6},{3}}=>1 {{1,5},{2,4,6,7},{3}}=>2 {{1,5},{2,4,6},{3,7}}=>3 {{1,5},{2,4,6},{3},{7}}=>3 {{1,5,7},{2,4},{3,6}}=>1 {{1,5},{2,4,7},{3,6}}=>3 {{1,5},{2,4},{3,6,7}}=>2 {{1,5},{2,4},{3,6},{7}}=>3 {{1,5,7},{2,4},{3},{6}}=>1 {{1,5},{2,4,7},{3},{6}}=>3 {{1,5},{2,4},{3,7},{6}}=>3 {{1,5},{2,4},{3},{6,7}}=>2 {{1,5},{2,4},{3},{6},{7}}=>3 {{1,6,7},{2,4,5},{3}}=>1 {{1,6},{2,4,5,7},{3}}=>2 {{1,6},{2,4,5},{3,7}}=>2 {{1,6},{2,4,5},{3},{7}}=>2 {{1,7},{2,4,5,6},{3}}=>1 {{1},{2,4,5,6,7},{3}}=>2 {{1},{2,4,5,6},{3,7}}=>3 {{1},{2,4,5,6},{3},{7}}=>3 {{1,7},{2,4,5},{3,6}}=>1 {{1},{2,4,5,7},{3,6}}=>3 {{1},{2,4,5},{3,6,7}}=>2 {{1},{2,4,5},{3,6},{7}}=>4 {{1,7},{2,4,5},{3},{6}}=>1 {{1},{2,4,5,7},{3},{6}}=>2 {{1},{2,4,5},{3,7},{6}}=>4 {{1},{2,4,5},{3},{6,7}}=>3 {{1},{2,4,5},{3},{6},{7}}=>4 {{1,6,7},{2,4},{3,5}}=>1 {{1,6},{2,4,7},{3,5}}=>2 {{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}}=>4 {{1,7},{2,4},{3,5,6}}=>1 {{1},{2,4,7},{3,5,6}}=>3 {{1},{2,4},{3,5,6,7}}=>2 {{1},{2,4},{3,5,6},{7}}=>3 {{1,7},{2,4},{3,5},{6}}=>1 {{1},{2,4,7},{3,5},{6}}=>4 {{1},{2,4},{3,5,7},{6}}=>2 {{1},{2,4},{3,5},{6,7}}=>3 {{1},{2,4},{3,5},{6},{7}}=>5 {{1,6,7},{2,4},{3},{5}}=>1 {{1,6},{2,4,7},{3},{5}}=>2 {{1,6},{2,4},{3,7},{5}}=>2 {{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}}=>3 {{1},{2,4,6},{3,7},{5}}=>4 {{1},{2,4,6},{3},{5,7}}=>2 {{1},{2,4,6},{3},{5},{7}}=>3 {{1,7},{2,4},{3,6},{5}}=>1 {{1},{2,4,7},{3,6},{5}}=>4 {{1},{2,4},{3,6,7},{5}}=>3 {{1},{2,4},{3,6},{5,7}}=>2 {{1},{2,4},{3,6},{5},{7}}=>5 {{1,7},{2,4},{3},{5,6}}=>1 {{1},{2,4,7},{3},{5,6}}=>3 {{1},{2,4},{3,7},{5,6}}=>3 {{1},{2,4},{3},{5,6,7}}=>2 {{1},{2,4},{3},{5,6},{7}}=>4 {{1,7},{2,4},{3},{5},{6}}=>1 {{1},{2,4,7},{3},{5},{6}}=>2 {{1},{2,4},{3,7},{5},{6}}=>5 {{1},{2,4},{3},{5,7},{6}}=>3 {{1},{2,4},{3},{5},{6,7}}=>4 {{1},{2,4},{3},{5},{6},{7}}=>6 {{1,5,6,7},{2},{3,4}}=>1 {{1,5,6},{2,7},{3,4}}=>2 {{1,5,6},{2},{3,4,7}}=>2 {{1,5,6},{2},{3,4},{7}}=>2 {{1,5,7},{2,6},{3,4}}=>1 {{1,5},{2,6,7},{3,4}}=>2 {{1,5},{2,6},{3,4,7}}=>3 {{1,5},{2,6},{3,4},{7}}=>3 {{1,5,7},{2},{3,4,6}}=>1 {{1,5},{2,7},{3,4,6}}=>3 {{1,5},{2},{3,4,6,7}}=>2 {{1,5},{2},{3,4,6},{7}}=>3 {{1,5,7},{2},{3,4},{6}}=>1 {{1,5},{2,7},{3,4},{6}}=>3 {{1,5},{2},{3,4,7},{6}}=>3 {{1,5},{2},{3,4},{6,7}}=>2 {{1,5},{2},{3,4},{6},{7}}=>3 {{1,6,7},{2,5},{3,4}}=>1 {{1,6},{2,5,7},{3,4}}=>2 {{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}}=>1 {{1},{2,5,7},{3,4,6}}=>3 {{1},{2,5},{3,4,6,7}}=>2 {{1},{2,5},{3,4,6},{7}}=>4 {{1,7},{2,5},{3,4},{6}}=>1 {{1},{2,5,7},{3,4},{6}}=>2 {{1},{2,5},{3,4,7},{6}}=>4 {{1},{2,5},{3,4},{6,7}}=>3 {{1},{2,5},{3,4},{6},{7}}=>5 {{1,6,7},{2},{3,4,5}}=>1 {{1,6},{2,7},{3,4,5}}=>2 {{1,6},{2},{3,4,5,7}}=>2 {{1,6},{2},{3,4,5},{7}}=>2 {{1,7},{2,6},{3,4,5}}=>1 {{1},{2,6,7},{3,4,5}}=>2 {{1},{2,6},{3,4,5,7}}=>3 {{1},{2,6},{3,4,5},{7}}=>4 {{1,7},{2},{3,4,5,6}}=>1 {{1},{2,7},{3,4,5,6}}=>3 {{1},{2},{3,4,5,6,7}}=>2 {{1},{2},{3,4,5,6},{7}}=>3 {{1,7},{2},{3,4,5},{6}}=>1 {{1},{2,7},{3,4,5},{6}}=>4 {{1},{2},{3,4,5,7},{6}}=>2 {{1},{2},{3,4,5},{6,7}}=>3 {{1},{2},{3,4,5},{6},{7}}=>4 {{1,6,7},{2},{3,4},{5}}=>1 {{1,6},{2,7},{3,4},{5}}=>2 {{1,6},{2},{3,4,7},{5}}=>2 {{1,6},{2},{3,4},{5,7}}=>2 {{1,6},{2},{3,4},{5},{7}}=>2 {{1,7},{2,6},{3,4},{5}}=>1 {{1},{2,6,7},{3,4},{5}}=>3 {{1},{2,6},{3,4,7},{5}}=>4 {{1},{2,6},{3,4},{5,7}}=>2 {{1},{2,6},{3,4},{5},{7}}=>5 {{1,7},{2},{3,4,6},{5}}=>1 {{1},{2,7},{3,4,6},{5}}=>4 {{1},{2},{3,4,6,7},{5}}=>3 {{1},{2},{3,4,6},{5,7}}=>2 {{1},{2},{3,4,6},{5},{7}}=>3 {{1,7},{2},{3,4},{5,6}}=>1 {{1},{2,7},{3,4},{5,6}}=>3 {{1},{2},{3,4,7},{5,6}}=>3 {{1},{2},{3,4},{5,6,7}}=>2 {{1},{2},{3,4},{5,6},{7}}=>4 {{1,7},{2},{3,4},{5},{6}}=>1 {{1},{2,7},{3,4},{5},{6}}=>5 {{1},{2},{3,4,7},{5},{6}}=>2 {{1},{2},{3,4},{5,7},{6}}=>4 {{1},{2},{3,4},{5},{6,7}}=>3 {{1},{2},{3,4},{5},{6},{7}}=>5 {{1,5,6,7},{2},{3},{4}}=>1 {{1,5,6},{2,7},{3},{4}}=>2 {{1,5,6},{2},{3,7},{4}}=>2 {{1,5,6},{2},{3},{4,7}}=>2 {{1,5,6},{2},{3},{4},{7}}=>2 {{1,5,7},{2,6},{3},{4}}=>1 {{1,5},{2,6,7},{3},{4}}=>2 {{1,5},{2,6},{3,7},{4}}=>3 {{1,5},{2,6},{3},{4,7}}=>3 {{1,5},{2,6},{3},{4},{7}}=>3 {{1,5,7},{2},{3,6},{4}}=>1 {{1,5},{2,7},{3,6},{4}}=>3 {{1,5},{2},{3,6,7},{4}}=>2 {{1,5},{2},{3,6},{4,7}}=>3 {{1,5},{2},{3,6},{4},{7}}=>3 {{1,5,7},{2},{3},{4,6}}=>1 {{1,5},{2,7},{3},{4,6}}=>3 {{1,5},{2},{3,7},{4,6}}=>3 {{1,5},{2},{3},{4,6,7}}=>2 {{1,5},{2},{3},{4,6},{7}}=>3 {{1,5,7},{2},{3},{4},{6}}=>1 {{1,5},{2,7},{3},{4},{6}}=>3 {{1,5},{2},{3,7},{4},{6}}=>3 {{1,5},{2},{3},{4,7},{6}}=>3 {{1,5},{2},{3},{4},{6,7}}=>2 {{1,5},{2},{3},{4},{6},{7}}=>3 {{1,6,7},{2,5},{3},{4}}=>1 {{1,6},{2,5,7},{3},{4}}=>2 {{1,6},{2,5},{3,7},{4}}=>2 {{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}}=>3 {{1},{2,5,6},{3},{4,7}}=>3 {{1},{2,5,6},{3},{4},{7}}=>4 {{1,7},{2,5},{3,6},{4}}=>1 {{1},{2,5,7},{3,6},{4}}=>2 {{1},{2,5},{3,6,7},{4}}=>3 {{1},{2,5},{3,6},{4,7}}=>4 {{1},{2,5},{3,6},{4},{7}}=>5 {{1,7},{2,5},{3},{4,6}}=>1 {{1},{2,5,7},{3},{4,6}}=>2 {{1},{2,5},{3,7},{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}}=>1 {{1},{2,5,7},{3},{4},{6}}=>4 {{1},{2,5},{3,7},{4},{6}}=>5 {{1},{2,5},{3},{4,7},{6}}=>2 {{1},{2,5},{3},{4},{6,7}}=>3 {{1},{2,5},{3},{4},{6},{7}}=>6 {{1,6,7},{2},{3,5},{4}}=>1 {{1,6},{2,7},{3,5},{4}}=>2 {{1,6},{2},{3,5,7},{4}}=>2 {{1,6},{2},{3,5},{4,7}}=>2 {{1,6},{2},{3,5},{4},{7}}=>2 {{1,7},{2,6},{3,5},{4}}=>1 {{1},{2,6,7},{3,5},{4}}=>3 {{1},{2,6},{3,5,7},{4}}=>2 {{1},{2,6},{3,5},{4,7}}=>4 {{1},{2,6},{3,5},{4},{7}}=>5 {{1,7},{2},{3,5,6},{4}}=>1 {{1},{2,7},{3,5,6},{4}}=>3 {{1},{2},{3,5,6,7},{4}}=>2 {{1},{2},{3,5,6},{4,7}}=>3 {{1},{2},{3,5,6},{4},{7}}=>4 {{1,7},{2},{3,5},{4,6}}=>1 {{1},{2,7},{3,5},{4,6}}=>4 {{1},{2},{3,5,7},{4,6}}=>2 {{1},{2},{3,5},{4,6,7}}=>3 {{1},{2},{3,5},{4,6},{7}}=>3 {{1,7},{2},{3,5},{4},{6}}=>1 {{1},{2,7},{3,5},{4},{6}}=>5 {{1},{2},{3,5,7},{4},{6}}=>4 {{1},{2},{3,5},{4,7},{6}}=>2 {{1},{2},{3,5},{4},{6,7}}=>3 {{1},{2},{3,5},{4},{6},{7}}=>4 {{1,6,7},{2},{3},{4,5}}=>1 {{1,6},{2,7},{3},{4,5}}=>2 {{1,6},{2},{3,7},{4,5}}=>2 {{1,6},{2},{3},{4,5,7}}=>2 {{1,6},{2},{3},{4,5},{7}}=>2 {{1,7},{2,6},{3},{4,5}}=>1 {{1},{2,6,7},{3},{4,5}}=>3 {{1},{2,6},{3,7},{4,5}}=>4 {{1},{2,6},{3},{4,5,7}}=>2 {{1},{2,6},{3},{4,5},{7}}=>4 {{1,7},{2},{3,6},{4,5}}=>1 {{1},{2,7},{3,6},{4,5}}=>4 {{1},{2},{3,6,7},{4,5}}=>3 {{1},{2},{3,6},{4,5,7}}=>2 {{1},{2},{3,6},{4,5},{7}}=>4 {{1,7},{2},{3},{4,5,6}}=>1 {{1},{2,7},{3},{4,5,6}}=>3 {{1},{2},{3,7},{4,5,6}}=>3 {{1},{2},{3},{4,5,6,7}}=>2 {{1},{2},{3},{4,5,6},{7}}=>3 {{1,7},{2},{3},{4,5},{6}}=>1 {{1},{2,7},{3},{4,5},{6}}=>4 {{1},{2},{3,7},{4,5},{6}}=>4 {{1},{2},{3},{4,5,7},{6}}=>2 {{1},{2},{3},{4,5},{6,7}}=>3 {{1},{2},{3},{4,5},{6},{7}}=>5 {{1,6,7},{2},{3},{4},{5}}=>1 {{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}}=>2 {{1,6},{2},{3},{4},{5},{7}}=>2 {{1,7},{2,6},{3},{4},{5}}=>1 {{1},{2,6,7},{3},{4},{5}}=>3 {{1},{2,6},{3,7},{4},{5}}=>5 {{1},{2,6},{3},{4,7},{5}}=>2 {{1},{2,6},{3},{4},{5,7}}=>4 {{1},{2,6},{3},{4},{5},{7}}=>6 {{1,7},{2},{3,6},{4},{5}}=>1 {{1},{2,7},{3,6},{4},{5}}=>5 {{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}}=>3 {{1,7},{2},{3},{4,6},{5}}=>1 {{1},{2,7},{3},{4,6},{5}}=>3 {{1},{2},{3,7},{4,6},{5}}=>3 {{1},{2},{3},{4,6,7},{5}}=>2 {{1},{2},{3},{4,6},{5,7}}=>3 {{1},{2},{3},{4,6},{5},{7}}=>5 {{1,7},{2},{3},{4},{5,6}}=>1 {{1},{2,7},{3},{4},{5,6}}=>4 {{1},{2},{3,7},{4},{5,6}}=>4 {{1},{2},{3},{4,7},{5,6}}=>2 {{1},{2},{3},{4},{5,6,7}}=>3 {{1},{2},{3},{4},{5,6},{7}}=>4 {{1,7},{2},{3},{4},{5},{6}}=>1 {{1},{2,7},{3},{4},{5},{6}}=>6 {{1},{2},{3,7},{4},{5},{6}}=>2 {{1},{2},{3},{4,7},{5},{6}}=>5 {{1},{2},{3},{4},{5,7},{6}}=>3 {{1},{2},{3},{4},{5},{6,7}}=>4 {{1},{2},{3},{4},{5},{6},{7}}=>7 {{1,2},{3,4},{5,6},{7,8}}=>3 {{1,3},{2,4},{5,6},{7,8}}=>3 {{1,4},{2,3},{5,6},{7,8}}=>3 {{1,5},{2,3},{4,6},{7,8}}=>3 {{1,6},{2,3},{4,5},{7,8}}=>2 {{1,7},{2,3},{4,5},{6,8}}=>2 {{1,8},{2,3},{4,5},{6,7}}=>1 {{1,8},{2,4},{3,5},{6,7}}=>1 {{1,7},{2,4},{3,5},{6,8}}=>2 {{1,6},{2,4},{3,5},{7,8}}=>2 {{1,5},{2,4},{3,6},{7,8}}=>3 {{1,4},{2,5},{3,6},{7,8}}=>3 {{1,3},{2,5},{4,6},{7,8}}=>3 {{1,2},{3,5},{4,6},{7,8}}=>3 {{1,2},{3,6},{4,5},{7,8}}=>3 {{1,3},{2,6},{4,5},{7,8}}=>3 {{1,4},{2,6},{3,5},{7,8}}=>3 {{1,5},{2,6},{3,4},{7,8}}=>3 {{1,6},{2,5},{3,4},{7,8}}=>2 {{1,7},{2,5},{3,4},{6,8}}=>2 {{1,8},{2,5},{3,4},{6,7}}=>1 {{1,8},{2,6},{3,4},{5,7}}=>1 {{1,7},{2,6},{3,4},{5,8}}=>2 {{1,6},{2,7},{3,4},{5,8}}=>3 {{1,5},{2,7},{3,4},{6,8}}=>2 {{1,4},{2,7},{3,5},{6,8}}=>2 {{1,3},{2,7},{4,5},{6,8}}=>2 {{1,2},{3,7},{4,5},{6,8}}=>2 {{1,2},{3,8},{4,5},{6,7}}=>3 {{1,3},{2,8},{4,5},{6,7}}=>3 {{1,4},{2,8},{3,5},{6,7}}=>3 {{1,5},{2,8},{3,4},{6,7}}=>3 {{1,6},{2,8},{3,4},{5,7}}=>3 {{1,7},{2,8},{3,4},{5,6}}=>2 {{1,8},{2,7},{3,4},{5,6}}=>1 {{1,8},{2,7},{3,5},{4,6}}=>1 {{1,7},{2,8},{3,5},{4,6}}=>2 {{1,6},{2,8},{3,5},{4,7}}=>3 {{1,5},{2,8},{3,6},{4,7}}=>4 {{1,4},{2,8},{3,6},{5,7}}=>4 {{1,3},{2,8},{4,6},{5,7}}=>4 {{1,2},{3,8},{4,6},{5,7}}=>4 {{1,2},{3,7},{4,6},{5,8}}=>4 {{1,3},{2,7},{4,6},{5,8}}=>4 {{1,4},{2,7},{3,6},{5,8}}=>4 {{1,5},{2,7},{3,6},{4,8}}=>4 {{1,6},{2,7},{3,5},{4,8}}=>3 {{1,7},{2,6},{3,5},{4,8}}=>2 {{1,8},{2,6},{3,5},{4,7}}=>1 {{1,8},{2,5},{3,6},{4,7}}=>1 {{1,7},{2,5},{3,6},{4,8}}=>2 {{1,6},{2,5},{3,7},{4,8}}=>3 {{1,5},{2,6},{3,7},{4,8}}=>4 {{1,4},{2,6},{3,7},{5,8}}=>4 {{1,3},{2,6},{4,7},{5,8}}=>4 {{1,2},{3,6},{4,7},{5,8}}=>4 {{1,2},{3,5},{4,7},{6,8}}=>2 {{1,3},{2,5},{4,7},{6,8}}=>2 {{1,4},{2,5},{3,7},{6,8}}=>2 {{1,5},{2,4},{3,7},{6,8}}=>2 {{1,6},{2,4},{3,7},{5,8}}=>3 {{1,7},{2,4},{3,6},{5,8}}=>2 {{1,8},{2,4},{3,6},{5,7}}=>1 {{1,8},{2,3},{4,6},{5,7}}=>1 {{1,7},{2,3},{4,6},{5,8}}=>2 {{1,6},{2,3},{4,7},{5,8}}=>3 {{1,5},{2,3},{4,7},{6,8}}=>2 {{1,4},{2,3},{5,7},{6,8}}=>2 {{1,3},{2,4},{5,7},{6,8}}=>2 {{1,2},{3,4},{5,7},{6,8}}=>2 {{1,2},{3,4},{5,8},{6,7}}=>3 {{1,3},{2,4},{5,8},{6,7}}=>3 {{1,4},{2,3},{5,8},{6,7}}=>3 {{1,5},{2,3},{4,8},{6,7}}=>3 {{1,6},{2,3},{4,8},{5,7}}=>3 {{1,7},{2,3},{4,8},{5,6}}=>2 {{1,8},{2,3},{4,7},{5,6}}=>1 {{1,8},{2,4},{3,7},{5,6}}=>1 {{1,7},{2,4},{3,8},{5,6}}=>2 {{1,6},{2,4},{3,8},{5,7}}=>3 {{1,5},{2,4},{3,8},{6,7}}=>3 {{1,4},{2,5},{3,8},{6,7}}=>3 {{1,3},{2,5},{4,8},{6,7}}=>3 {{1,2},{3,5},{4,8},{6,7}}=>3 {{1,2},{3,6},{4,8},{5,7}}=>4 {{1,3},{2,6},{4,8},{5,7}}=>4 {{1,4},{2,6},{3,8},{5,7}}=>4 {{1,5},{2,6},{3,8},{4,7}}=>4 {{1,6},{2,5},{3,8},{4,7}}=>3 {{1,7},{2,5},{3,8},{4,6}}=>2 {{1,8},{2,5},{3,7},{4,6}}=>1 {{1,8},{2,6},{3,7},{4,5}}=>1 {{1,7},{2,6},{3,8},{4,5}}=>2 {{1,6},{2,7},{3,8},{4,5}}=>3 {{1,5},{2,7},{3,8},{4,6}}=>4 {{1,4},{2,7},{3,8},{5,6}}=>4 {{1,3},{2,7},{4,8},{5,6}}=>4 {{1,2},{3,7},{4,8},{5,6}}=>4 {{1,2},{3,8},{4,7},{5,6}}=>4 {{1,3},{2,8},{4,7},{5,6}}=>4 {{1,4},{2,8},{3,7},{5,6}}=>4 {{1,5},{2,8},{3,7},{4,6}}=>4 {{1,6},{2,8},{3,7},{4,5}}=>3 {{1,7},{2,8},{3,6},{4,5}}=>2 {{1,8},{2,7},{3,6},{4,5}}=>1 {{1},{2},{3,4,5,6,7,8}}=>2 {{1},{2,4,5,6,7,8},{3}}=>2 {{1},{2,3,5,6,7,8},{4}}=>2 {{1},{2,3,4,6,7,8},{5}}=>2 {{1},{2,3,4,5,8},{6},{7}}=>4 {{1},{2,3,4,5,7,8},{6}}=>2 {{1},{2,3,4,5,6,7},{8}}=>3 {{1},{2,3,4,8},{5,6,7}}=>3 {{1},{2,3,4,5,8},{6,7}}=>3 {{1},{2,3,4,5,6,8},{7}}=>3 {{1},{2,3,4,5,6,7,8}}=>2 {{1,2},{3,4,5,6,7,8}}=>2 {{1,4,5,6,7,8},{2},{3}}=>1 {{1,3,5,6,7,8},{2},{4}}=>1 {{1,3,4,5,6,7,8},{2}}=>1 {{1,4,5,6,7,8},{2,3}}=>1 {{1,2,4,5,6,7,8},{3}}=>1 {{1,2,5,6,7,8},{3,4}}=>1 {{1,2,3,5,6,7},{4},{8}}=>2 {{1,2,3,5,6,7,8},{4}}=>1 {{1,2,3,6,7,8},{4,5}}=>1 {{1,2,3,4,7},{5},{6},{8}}=>2 {{1,2,3,4,6,7},{5},{8}}=>2 {{1,2,3,4,6,7,8},{5}}=>1 {{1,2,3,4,5,6},{7,8}}=>2 {{1,2,3,7},{4,5,6},{8}}=>2 {{1,2,3,4,7},{5,6},{8}}=>2 {{1,2,3,4,7,8},{5,6}}=>1 {{1,2,3,4,5,7},{6},{8}}=>2 {{1,2,3,4,5,7,8},{6}}=>1 {{1,2,3,4,5,6,7},{8}}=>2 {{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}}=>1 {{1,3,5,6,7,8},{2,4}}=>1 {{1,3,4,6,7,8},{2,5}}=>1 {{1,2,4,6,7,8},{3,5}}=>1 {{1,3,4,5,7,8},{2,6}}=>1 {{1,2,4,5,7,8},{3,6}}=>1 {{1,2,3,5,7,8},{4,6}}=>1 {{1,3,4,5,6,8},{2,7}}=>1 {{1,2,4,5,6,8},{3,7}}=>1 {{1,2,3,5,6,8},{4,7}}=>1 {{1,2,3,4,6,8},{5,7}}=>1 {{1,3,4,5,6,7},{2,8}}=>2 {{1,2,4,5,6,7},{3,8}}=>2 {{1,2,3,5,6,7},{4,8}}=>2 {{1,2,3,4,6,7},{5,8}}=>2 {{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}}=>2 {{1,5},{2,3,4,6,7,8}}=>2 {{1,6},{2,3,4,5,7,8}}=>2 {{1,7},{2,3,4,5,6,8}}=>2 {{1,2,3,4,5,6,7,8},{9}}=>2 {{1},{2,3,4,5,6,7,8,9}}=>2 {{1,2,3,4,5,6,8},{7},{9}}=>2 {{1},{2,3,4,5,6,7,9},{8}}=>3 {{1,2,3,4,5,8},{6,7},{9}}=>2 {{1,2,3,4,5,7,8},{6},{9}}=>2 {{1},{2,3,4,5,6,9},{7,8}}=>3 {{1},{2,3,4,5,6,8,9},{7}}=>2 {{1,2},{3,4},{5,6},{7,8},{9,10}}=>3 {{1,4},{2,3},{5,6},{7,8},{9,10}}=>3 {{1,6},{2,3},{4,5},{7,8},{9,10}}=>3 {{1,8},{2,3},{4,5},{6,7},{9,10}}=>2 {{1,10},{2,3},{4,5},{6,7},{8,9}}=>1 {{1,2},{3,6},{4,5},{7,8},{9,10}}=>3 {{1,6},{2,5},{3,4},{7,8},{9,10}}=>3 {{1,8},{2,5},{3,4},{6,7},{9,10}}=>2 {{1,10},{2,5},{3,4},{6,7},{8,9}}=>1 {{1,2},{3,8},{4,5},{6,7},{9,10}}=>3 {{1,8},{2,7},{3,4},{5,6},{9,10}}=>2 {{1,10},{2,7},{3,4},{5,6},{8,9}}=>1 {{1,2},{3,10},{4,5},{6,7},{8,9}}=>4 {{1,10},{2,9},{3,4},{5,6},{7,8}}=>1 {{1,2},{3,4},{5,8},{6,7},{9,10}}=>3 {{1,4},{2,3},{5,8},{6,7},{9,10}}=>3 {{1,8},{2,3},{4,7},{5,6},{9,10}}=>2 {{1,10},{2,3},{4,7},{5,6},{8,9}}=>1 {{1,2},{3,8},{4,7},{5,6},{9,10}}=>4 {{1,8},{2,7},{3,6},{4,5},{9,10}}=>2 {{1,10},{2,7},{3,6},{4,5},{8,9}}=>1 {{1,2},{3,10},{4,7},{5,6},{8,9}}=>4 {{1,10},{2,9},{3,6},{4,5},{7,8}}=>1 {{1,2},{3,4},{5,10},{6,7},{8,9}}=>4 {{1,4},{2,3},{5,10},{6,7},{8,9}}=>4 {{1,10},{2,3},{4,9},{5,6},{7,8}}=>1 {{1,2},{3,10},{4,9},{5,6},{7,8}}=>4 {{1,10},{2,9},{3,8},{4,5},{6,7}}=>1 {{1,2},{3,4},{5,6},{7,10},{8,9}}=>2 {{1,4},{2,3},{5,6},{7,10},{8,9}}=>2 {{1,6},{2,3},{4,5},{7,10},{8,9}}=>2 {{1,10},{2,3},{4,5},{6,9},{7,8}}=>1 {{1,2},{3,6},{4,5},{7,10},{8,9}}=>2 {{1,6},{2,5},{3,4},{7,10},{8,9}}=>2 {{1,10},{2,5},{3,4},{6,9},{7,8}}=>1 {{1,2},{3,10},{4,5},{6,9},{7,8}}=>4 {{1,10},{2,9},{3,4},{5,8},{6,7}}=>1 {{1,2},{3,4},{5,10},{6,9},{7,8}}=>4 {{1,4},{2,3},{5,10},{6,9},{7,8}}=>4 {{1,10},{2,3},{4,9},{5,8},{6,7}}=>1 {{1,2},{3,10},{4,9},{5,8},{6,7}}=>5 {{1,10},{2,9},{3,8},{4,7},{5,6}}=>1 {{1,2,3,4,5,6,7,8,9},{10}}=>2 {{1},{2,3,4,5,6,7,8,9,10}}=>2 {{1,2,3,4,5,6,7,9},{8},{10}}=>2 {{1},{2,3,4,5,6,7,8,10},{9}}=>3 {{1,2,3,4,5,6,7,8,9,10},{11}}=>2 {{1},{2,3,4,5,6,7,8,9,10,11}}=>2 {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>3 {{1,2},{3,4},{5,6},{7,8},{9,12},{10,11}}=>4 {{1,2},{3,4},{5,6},{7,10},{8,9},{11,12}}=>3 {{1,2},{3,4},{5,6},{7,12},{8,9},{10,11}}=>4 {{1,2},{3,4},{5,6},{7,12},{8,11},{9,10}}=>3 {{1,2},{3,4},{5,8},{6,7},{9,10},{11,12}}=>4 {{1,2},{3,4},{5,8},{6,7},{9,12},{10,11}}=>4 {{1,2},{3,4},{5,10},{6,7},{8,9},{11,12}}=>3 {{1,2},{3,4},{5,12},{6,7},{8,9},{10,11}}=>4 {{1,2},{3,4},{5,12},{6,7},{8,11},{9,10}}=>3 {{1,2},{3,4},{5,10},{6,9},{7,8},{11,12}}=>3 {{1,2},{3,4},{5,12},{6,9},{7,8},{10,11}}=>4 {{1,2},{3,4},{5,12},{6,11},{7,8},{9,10}}=>5 {{1,2},{3,4},{5,12},{6,11},{7,10},{8,9}}=>5 {{1,2},{3,6},{4,5},{7,8},{9,10},{11,12}}=>3 {{1,2},{3,6},{4,5},{7,8},{9,12},{10,11}}=>4 {{1,2},{3,6},{4,5},{7,10},{8,9},{11,12}}=>3 {{1,2},{3,6},{4,5},{7,12},{8,9},{10,11}}=>4 {{1,2},{3,6},{4,5},{7,12},{8,11},{9,10}}=>3 {{1,2},{3,8},{4,5},{6,7},{9,10},{11,12}}=>4 {{1,2},{3,8},{4,5},{6,7},{9,12},{10,11}}=>3 {{1,2},{3,10},{4,5},{6,7},{8,9},{11,12}}=>3 {{1,2},{3,12},{4,5},{6,7},{8,9},{10,11}}=>4 {{1,2},{3,12},{4,5},{6,7},{8,11},{9,10}}=>3 {{1,2},{3,10},{4,5},{6,9},{7,8},{11,12}}=>3 {{1,2},{3,12},{4,5},{6,9},{7,8},{10,11}}=>4 {{1,2},{3,12},{4,5},{6,11},{7,8},{9,10}}=>5 {{1,2},{3,12},{4,5},{6,11},{7,10},{8,9}}=>5 {{1,2},{3,8},{4,7},{5,6},{9,10},{11,12}}=>4 {{1,2},{3,8},{4,7},{5,6},{9,12},{10,11}}=>3 {{1,2},{3,10},{4,7},{5,6},{8,9},{11,12}}=>3 {{1,2},{3,12},{4,7},{5,6},{8,9},{10,11}}=>4 {{1,2},{3,12},{4,7},{5,6},{8,11},{9,10}}=>3 {{1,2},{3,10},{4,9},{5,6},{7,8},{11,12}}=>3 {{1,2},{3,12},{4,9},{5,6},{7,8},{10,11}}=>4 {{1,2},{3,12},{4,11},{5,6},{7,8},{9,10}}=>5 {{1,2},{3,12},{4,11},{5,6},{7,10},{8,9}}=>5 {{1,2},{3,10},{4,9},{5,8},{6,7},{11,12}}=>5 {{1,2},{3,12},{4,9},{5,8},{6,7},{10,11}}=>5 {{1,2},{3,12},{4,11},{5,8},{6,7},{9,10}}=>5 {{1,2},{3,12},{4,11},{5,10},{6,7},{8,9}}=>5 {{1,2},{3,12},{4,11},{5,10},{6,9},{7,8}}=>6 {{1,4},{2,3},{5,6},{7,8},{9,10},{11,12}}=>3 {{1,4},{2,3},{5,6},{7,8},{9,12},{10,11}}=>4 {{1,4},{2,3},{5,6},{7,10},{8,9},{11,12}}=>3 {{1,4},{2,3},{5,6},{7,12},{8,9},{10,11}}=>4 {{1,4},{2,3},{5,6},{7,12},{8,11},{9,10}}=>3 {{1,4},{2,3},{5,8},{6,7},{9,10},{11,12}}=>4 {{1,4},{2,3},{5,8},{6,7},{9,12},{10,11}}=>4 {{1,4},{2,3},{5,10},{6,7},{8,9},{11,12}}=>3 {{1,4},{2,3},{5,12},{6,7},{8,9},{10,11}}=>4 {{1,4},{2,3},{5,12},{6,7},{8,11},{9,10}}=>3 {{1,4},{2,3},{5,10},{6,9},{7,8},{11,12}}=>3 {{1,4},{2,3},{5,12},{6,9},{7,8},{10,11}}=>4 {{1,4},{2,3},{5,12},{6,11},{7,8},{9,10}}=>5 {{1,4},{2,3},{5,12},{6,11},{7,10},{8,9}}=>5 {{1,6},{2,3},{4,5},{7,8},{9,10},{11,12}}=>3 {{1,6},{2,3},{4,5},{7,8},{9,12},{10,11}}=>4 {{1,6},{2,3},{4,5},{7,10},{8,9},{11,12}}=>3 {{1,6},{2,3},{4,5},{7,12},{8,9},{10,11}}=>4 {{1,6},{2,3},{4,5},{7,12},{8,11},{9,10}}=>3 {{1,8},{2,3},{4,5},{6,7},{9,10},{11,12}}=>3 {{1,8},{2,3},{4,5},{6,7},{9,12},{10,11}}=>2 {{1,10},{2,3},{4,5},{6,7},{8,9},{11,12}}=>2 {{1,12},{2,3},{4,5},{6,7},{8,9},{10,11}}=>1 {{1,12},{2,3},{4,5},{6,7},{8,11},{9,10}}=>1 {{1,10},{2,3},{4,5},{6,9},{7,8},{11,12}}=>2 {{1,12},{2,3},{4,5},{6,9},{7,8},{10,11}}=>1 {{1,12},{2,3},{4,5},{6,11},{7,8},{9,10}}=>1 {{1,12},{2,3},{4,5},{6,11},{7,10},{8,9}}=>1 {{1,8},{2,3},{4,7},{5,6},{9,10},{11,12}}=>3 {{1,8},{2,3},{4,7},{5,6},{9,12},{10,11}}=>2 {{1,10},{2,3},{4,7},{5,6},{8,9},{11,12}}=>2 {{1,12},{2,3},{4,7},{5,6},{8,9},{10,11}}=>1 {{1,12},{2,3},{4,7},{5,6},{8,11},{9,10}}=>1 {{1,10},{2,3},{4,9},{5,6},{7,8},{11,12}}=>2 {{1,12},{2,3},{4,9},{5,6},{7,8},{10,11}}=>1 {{1,12},{2,3},{4,11},{5,6},{7,8},{9,10}}=>1 {{1,12},{2,3},{4,11},{5,6},{7,10},{8,9}}=>1 {{1,10},{2,3},{4,9},{5,8},{6,7},{11,12}}=>2 {{1,12},{2,3},{4,9},{5,8},{6,7},{10,11}}=>1 {{1,12},{2,3},{4,11},{5,8},{6,7},{9,10}}=>1 {{1,12},{2,3},{4,11},{5,10},{6,7},{8,9}}=>1 {{1,12},{2,3},{4,11},{5,10},{6,9},{7,8}}=>1 {{1,6},{2,5},{3,4},{7,8},{9,10},{11,12}}=>3 {{1,6},{2,5},{3,4},{7,8},{9,12},{10,11}}=>4 {{1,6},{2,5},{3,4},{7,10},{8,9},{11,12}}=>3 {{1,6},{2,5},{3,4},{7,12},{8,9},{10,11}}=>4 {{1,6},{2,5},{3,4},{7,12},{8,11},{9,10}}=>3 {{1,8},{2,5},{3,4},{6,7},{9,10},{11,12}}=>3 {{1,8},{2,5},{3,4},{6,7},{9,12},{10,11}}=>2 {{1,10},{2,5},{3,4},{6,7},{8,9},{11,12}}=>2 {{1,12},{2,5},{3,4},{6,7},{8,9},{10,11}}=>1 {{1,12},{2,5},{3,4},{6,7},{8,11},{9,10}}=>1 {{1,10},{2,5},{3,4},{6,9},{7,8},{11,12}}=>2 {{1,12},{2,5},{3,4},{6,9},{7,8},{10,11}}=>1 {{1,12},{2,5},{3,4},{6,11},{7,8},{9,10}}=>1 {{1,12},{2,5},{3,4},{6,11},{7,10},{8,9}}=>1 {{1,8},{2,7},{3,4},{5,6},{9,10},{11,12}}=>3 {{1,8},{2,7},{3,4},{5,6},{9,12},{10,11}}=>2 {{1,10},{2,7},{3,4},{5,6},{8,9},{11,12}}=>2 {{1,12},{2,7},{3,4},{5,6},{8,9},{10,11}}=>1 {{1,12},{2,7},{3,4},{5,6},{8,11},{9,10}}=>1 {{1,10},{2,9},{3,4},{5,6},{7,8},{11,12}}=>2 {{1,12},{2,9},{3,4},{5,6},{7,8},{10,11}}=>1 {{1,12},{2,11},{3,4},{5,6},{7,8},{9,10}}=>1 {{1,12},{2,11},{3,4},{5,6},{7,10},{8,9}}=>1 {{1,10},{2,9},{3,4},{5,8},{6,7},{11,12}}=>2 {{1,12},{2,9},{3,4},{5,8},{6,7},{10,11}}=>1 {{1,12},{2,11},{3,4},{5,8},{6,7},{9,10}}=>1 {{1,12},{2,11},{3,4},{5,10},{6,7},{8,9}}=>1 {{1,12},{2,11},{3,4},{5,10},{6,9},{7,8}}=>1 {{1,8},{2,7},{3,6},{4,5},{9,10},{11,12}}=>3 {{1,8},{2,7},{3,6},{4,5},{9,12},{10,11}}=>2 {{1,10},{2,7},{3,6},{4,5},{8,9},{11,12}}=>2 {{1,12},{2,7},{3,6},{4,5},{8,9},{10,11}}=>1 {{1,12},{2,7},{3,6},{4,5},{8,11},{9,10}}=>1 {{1,10},{2,9},{3,6},{4,5},{7,8},{11,12}}=>2 {{1,12},{2,9},{3,6},{4,5},{7,8},{10,11}}=>1 {{1,12},{2,11},{3,6},{4,5},{7,8},{9,10}}=>1 {{1,12},{2,11},{3,6},{4,5},{7,10},{8,9}}=>1 {{1,10},{2,9},{3,8},{4,5},{6,7},{11,12}}=>2 {{1,12},{2,9},{3,8},{4,5},{6,7},{10,11}}=>1 {{1,12},{2,11},{3,8},{4,5},{6,7},{9,10}}=>1 {{1,12},{2,11},{3,10},{4,5},{6,7},{8,9}}=>1 {{1,12},{2,11},{3,10},{4,5},{6,9},{7,8}}=>1 {{1,10},{2,9},{3,8},{4,7},{5,6},{11,12}}=>2 {{1,12},{2,9},{3,8},{4,7},{5,6},{10,11}}=>1 {{1,12},{2,11},{3,8},{4,7},{5,6},{9,10}}=>1 {{1,12},{2,11},{3,10},{4,7},{5,6},{8,9}}=>1 {{1,12},{2,11},{3,10},{4,9},{5,6},{7,8}}=>1 {{1,12},{2,11},{3,10},{4,9},{5,8},{6,7}}=>1
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Description
The depth of the label 1 in the decreasing labelled unordered tree associated with the set partition.
The bijection between set partitions of $\{1,\dots,n\}$ into $k$ blocks and trees with $n+1-k$ leaves is described in Theorem 1 of [1].
References
[1] Erdős, Péter L., Székely, L. A. Applications of antilexicographic order. I. An enumerative theory of trees MathSciNet:1023945
Code
def statistic(p):
    return depth_of_1(set_partition_to_tree(p))

def depth_of_1(T):
    if T.label() == 1:
        return 0
    if T.node_number() == 1:
        return infinity
    else:
        return 1 + min(depth_of_1(C) for C in T)

def set_partition_to_tree(p):
    # the children of the smallest label are the largest remaining
    # element and its partner
    trees = [LabelledRootedTree([LabelledRootedTree([], label=e) for e in b]) for b in p]
    max_label = p.size()+1-len(p) # last labelled node
    while len(trees) > 1:
        max_label += 1
        # find tree with smallest child and all children smaller than max_label
        A = sorted([T for T in trees if max(C.label() for C in T) < max_label],
                   key = lambda T: min(C.label() for C in T))[0]
        trees.remove(A)
        # give it's root node the new label
        A = LabelledRootedTree(A, label=max_label)
        # find tree with child having label max_label
        B = (T for T in trees
             if any(C.label() == max_label for C in T)).next()
        trees.remove(B)

        # replace the child of B carrying max_label with A
        C = LabelledRootedTree([A] + [T for T in B if T.label() != max_label])

        trees.append(C)

    return trees[0]
Created
Nov 18, 2017 at 18:23 by Martin Rubey
Updated
Apr 03, 2018 at 21:07 by Martin Rubey