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Identifier
Values
=>
Cc0009;cc-rep
{{1}}=>0 {{1,2}}=>1 {{1},{2}}=>2 {{1,2,3}}=>1 {{1,2},{3}}=>2 {{1,3},{2}}=>2 {{1},{2,3}}=>2 {{1},{2},{3}}=>2 {{1,2,3,4}}=>1 {{1,2,3},{4}}=>2 {{1,2,4},{3}}=>2 {{1,2},{3,4}}=>2 {{1,2},{3},{4}}=>2 {{1,3,4},{2}}=>2 {{1,3},{2,4}}=>2 {{1,3},{2},{4}}=>2 {{1,4},{2,3}}=>2 {{1},{2,3,4}}=>2 {{1},{2,3},{4}}=>2 {{1,4},{2},{3}}=>3 {{1},{2,4},{3}}=>2 {{1},{2},{3,4}}=>2 {{1},{2},{3},{4}}=>2 {{1,2,3,4,5}}=>1 {{1,2,3,4},{5}}=>2 {{1,2,3,5},{4}}=>2 {{1,2,3},{4,5}}=>2 {{1,2,3},{4},{5}}=>2 {{1,2,4,5},{3}}=>2 {{1,2,4},{3,5}}=>2 {{1,2,4},{3},{5}}=>2 {{1,2,5},{3,4}}=>2 {{1,2},{3,4,5}}=>2 {{1,2},{3,4},{5}}=>2 {{1,2,5},{3},{4}}=>3 {{1,2},{3,5},{4}}=>2 {{1,2},{3},{4,5}}=>2 {{1,2},{3},{4},{5}}=>2 {{1,3,4,5},{2}}=>2 {{1,3,4},{2,5}}=>2 {{1,3,4},{2},{5}}=>2 {{1,3,5},{2,4}}=>2 {{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}}=>2 {{1,3},{2},{4},{5}}=>2 {{1,4,5},{2,3}}=>2 {{1,4},{2,3,5}}=>2 {{1,4},{2,3},{5}}=>2 {{1,5},{2,3,4}}=>2 {{1},{2,3,4,5}}=>2 {{1},{2,3,4},{5}}=>2 {{1,5},{2,3},{4}}=>3 {{1},{2,3,5},{4}}=>2 {{1},{2,3},{4,5}}=>2 {{1},{2,3},{4},{5}}=>2 {{1,4,5},{2},{3}}=>3 {{1,4},{2,5},{3}}=>3 {{1,4},{2},{3,5}}=>3 {{1,4},{2},{3},{5}}=>3 {{1,5},{2,4},{3}}=>2 {{1},{2,4,5},{3}}=>2 {{1},{2,4},{3,5}}=>2 {{1},{2,4},{3},{5}}=>2 {{1,5},{2},{3,4}}=>3 {{1},{2,5},{3,4}}=>2 {{1},{2},{3,4,5}}=>2 {{1},{2},{3,4},{5}}=>2 {{1,5},{2},{3},{4}}=>3 {{1},{2,5},{3},{4}}=>3 {{1},{2},{3,5},{4}}=>2 {{1},{2},{3},{4,5}}=>2 {{1},{2},{3},{4},{5}}=>2 {{1,2,3,4,5,6}}=>1 {{1,2,3,4,5},{6}}=>2 {{1,2,3,4,6},{5}}=>2 {{1,2,3,4},{5,6}}=>2 {{1,2,3,4},{5},{6}}=>2 {{1,2,3,5,6},{4}}=>2 {{1,2,3,5},{4,6}}=>2 {{1,2,3,5},{4},{6}}=>2 {{1,2,3,6},{4,5}}=>2 {{1,2,3},{4,5,6}}=>2 {{1,2,3},{4,5},{6}}=>2 {{1,2,3,6},{4},{5}}=>3 {{1,2,3},{4,6},{5}}=>2 {{1,2,3},{4},{5,6}}=>2 {{1,2,3},{4},{5},{6}}=>2 {{1,2,4,5,6},{3}}=>2 {{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}}=>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}}=>2 {{1,2,4},{3},{5},{6}}=>2 {{1,2,5,6},{3,4}}=>2 {{1,2,5},{3,4,6}}=>2 {{1,2,5},{3,4},{6}}=>2 {{1,2,6},{3,4,5}}=>2 {{1,2},{3,4,5,6}}=>2 {{1,2},{3,4,5},{6}}=>2 {{1,2,6},{3,4},{5}}=>3 {{1,2},{3,4,6},{5}}=>2 {{1,2},{3,4},{5,6}}=>2 {{1,2},{3,4},{5},{6}}=>2 {{1,2,5,6},{3},{4}}=>3 {{1,2,5},{3,6},{4}}=>3 {{1,2,5},{3},{4,6}}=>3 {{1,2,5},{3},{4},{6}}=>3 {{1,2,6},{3,5},{4}}=>2 {{1,2},{3,5,6},{4}}=>2 {{1,2},{3,5},{4,6}}=>2 {{1,2},{3,5},{4},{6}}=>2 {{1,2,6},{3},{4,5}}=>3 {{1,2},{3,6},{4,5}}=>2 {{1,2},{3},{4,5,6}}=>2 {{1,2},{3},{4,5},{6}}=>2 {{1,2,6},{3},{4},{5}}=>3 {{1,2},{3,6},{4},{5}}=>3 {{1,2},{3},{4,6},{5}}=>2 {{1,2},{3},{4},{5,6}}=>2 {{1,2},{3},{4},{5},{6}}=>2 {{1,3,4,5,6},{2}}=>2 {{1,3,4,5},{2,6}}=>2 {{1,3,4,5},{2},{6}}=>2 {{1,3,4,6},{2,5}}=>2 {{1,3,4},{2,5,6}}=>2 {{1,3,4},{2,5},{6}}=>2 {{1,3,4,6},{2},{5}}=>2 {{1,3,4},{2,6},{5}}=>3 {{1,3,4},{2},{5,6}}=>2 {{1,3,4},{2},{5},{6}}=>2 {{1,3,5,6},{2,4}}=>2 {{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}}=>2 {{1,3},{2,4,5},{6}}=>2 {{1,3,6},{2,4},{5}}=>3 {{1,3},{2,4,6},{5}}=>2 {{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}}=>2 {{1,3,5},{2},{4,6}}=>2 {{1,3,5},{2},{4},{6}}=>2 {{1,3,6},{2,5},{4}}=>3 {{1,3},{2,5,6},{4}}=>3 {{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}}=>2 {{1,3},{2},{4,5},{6}}=>2 {{1,3,6},{2},{4},{5}}=>3 {{1,3},{2,6},{4},{5}}=>3 {{1,3},{2},{4,6},{5}}=>2 {{1,3},{2},{4},{5,6}}=>2 {{1,3},{2},{4},{5},{6}}=>2 {{1,4,5,6},{2,3}}=>2 {{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}}=>2 {{1,4},{2,3,5},{6}}=>2 {{1,4,6},{2,3},{5}}=>2 {{1,4},{2,3,6},{5}}=>3 {{1,4},{2,3},{5,6}}=>2 {{1,4},{2,3},{5},{6}}=>2 {{1,5,6},{2,3,4}}=>2 {{1,5},{2,3,4,6}}=>2 {{1,5},{2,3,4},{6}}=>2 {{1,6},{2,3,4,5}}=>2 {{1},{2,3,4,5,6}}=>2 {{1},{2,3,4,5},{6}}=>2 {{1,6},{2,3,4},{5}}=>3 {{1},{2,3,4,6},{5}}=>2 {{1},{2,3,4},{5,6}}=>2 {{1},{2,3,4},{5},{6}}=>2 {{1,5,6},{2,3},{4}}=>3 {{1,5},{2,3,6},{4}}=>3 {{1,5},{2,3},{4,6}}=>3 {{1,5},{2,3},{4},{6}}=>3 {{1,6},{2,3,5},{4}}=>2 {{1},{2,3,5,6},{4}}=>2 {{1},{2,3,5},{4,6}}=>2 {{1},{2,3,5},{4},{6}}=>2 {{1,6},{2,3},{4,5}}=>3 {{1},{2,3,6},{4,5}}=>2 {{1},{2,3},{4,5,6}}=>2 {{1},{2,3},{4,5},{6}}=>2 {{1,6},{2,3},{4},{5}}=>3 {{1},{2,3,6},{4},{5}}=>3 {{1},{2,3},{4,6},{5}}=>2 {{1},{2,3},{4},{5,6}}=>2 {{1},{2,3},{4},{5},{6}}=>2 {{1,4,5,6},{2},{3}}=>3 {{1,4,5},{2,6},{3}}=>3 {{1,4,5},{2},{3,6}}=>3 {{1,4,5},{2},{3},{6}}=>3 {{1,4,6},{2,5},{3}}=>3 {{1,4},{2,5,6},{3}}=>3 {{1,4},{2,5},{3,6}}=>3 {{1,4},{2,5},{3},{6}}=>3 {{1,4,6},{2},{3,5}}=>3 {{1,4},{2,6},{3,5}}=>3 {{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}}=>3 {{1,4},{2},{3,6},{5}}=>3 {{1,4},{2},{3},{5,6}}=>3 {{1,4},{2},{3},{5},{6}}=>3 {{1,5,6},{2,4},{3}}=>2 {{1,5},{2,4,6},{3}}=>2 {{1,5},{2,4},{3,6}}=>3 {{1,5},{2,4},{3},{6}}=>2 {{1,6},{2,4,5},{3}}=>2 {{1},{2,4,5,6},{3}}=>2 {{1},{2,4,5},{3,6}}=>2 {{1},{2,4,5},{3},{6}}=>2 {{1,6},{2,4},{3,5}}=>2 {{1},{2,4,6},{3,5}}=>2 {{1},{2,4},{3,5,6}}=>2 {{1},{2,4},{3,5},{6}}=>2 {{1,6},{2,4},{3},{5}}=>3 {{1},{2,4,6},{3},{5}}=>2 {{1},{2,4},{3,6},{5}}=>3 {{1},{2,4},{3},{5,6}}=>2 {{1},{2,4},{3},{5},{6}}=>2 {{1,5,6},{2},{3,4}}=>3 {{1,5},{2,6},{3,4}}=>3 {{1,5},{2},{3,4,6}}=>3 {{1,5},{2},{3,4},{6}}=>3 {{1,6},{2,5},{3,4}}=>2 {{1},{2,5,6},{3,4}}=>2 {{1},{2,5},{3,4,6}}=>2 {{1},{2,5},{3,4},{6}}=>2 {{1,6},{2},{3,4,5}}=>3 {{1},{2,6},{3,4,5}}=>2 {{1},{2},{3,4,5,6}}=>2 {{1},{2},{3,4,5},{6}}=>2 {{1,6},{2},{3,4},{5}}=>3 {{1},{2,6},{3,4},{5}}=>3 {{1},{2},{3,4,6},{5}}=>2 {{1},{2},{3,4},{5,6}}=>2 {{1},{2},{3,4},{5},{6}}=>2 {{1,5,6},{2},{3},{4}}=>3 {{1,5},{2,6},{3},{4}}=>4 {{1,5},{2},{3,6},{4}}=>3 {{1,5},{2},{3},{4,6}}=>3 {{1,5},{2},{3},{4},{6}}=>3 {{1,6},{2,5},{3},{4}}=>3 {{1},{2,5,6},{3},{4}}=>3 {{1},{2,5},{3,6},{4}}=>3 {{1},{2,5},{3},{4,6}}=>3 {{1},{2,5},{3},{4},{6}}=>3 {{1,6},{2},{3,5},{4}}=>3 {{1},{2,6},{3,5},{4}}=>2 {{1},{2},{3,5,6},{4}}=>2 {{1},{2},{3,5},{4,6}}=>2 {{1},{2},{3,5},{4},{6}}=>2 {{1,6},{2},{3},{4,5}}=>3 {{1},{2,6},{3},{4,5}}=>3 {{1},{2},{3,6},{4,5}}=>2 {{1},{2},{3},{4,5,6}}=>2 {{1},{2},{3},{4,5},{6}}=>2 {{1,6},{2},{3},{4},{5}}=>3 {{1},{2,6},{3},{4},{5}}=>3 {{1},{2},{3,6},{4},{5}}=>3 {{1},{2},{3},{4,6},{5}}=>2 {{1},{2},{3},{4},{5,6}}=>2 {{1},{2},{3},{4},{5},{6}}=>2 {{1,2,3,4,5,6,7}}=>1 {{1,2,3,4,5,6},{7}}=>2 {{1,2,3,4,5,7},{6}}=>2 {{1,2,3,4,5},{6,7}}=>2 {{1,2,3,4,5},{6},{7}}=>2 {{1,2,3,4,6,7},{5}}=>2 {{1,2,3,4,6},{5,7}}=>2 {{1,2,3,4,6},{5},{7}}=>2 {{1,2,3,4,7},{5,6}}=>2 {{1,2,3,4},{5,6,7}}=>2 {{1,2,3,4},{5,6},{7}}=>2 {{1,2,3,4,7},{5},{6}}=>3 {{1,2,3,4},{5,7},{6}}=>2 {{1,2,3,4},{5},{6,7}}=>2 {{1,2,3,4},{5},{6},{7}}=>2 {{1,2,3,5,6,7},{4}}=>2 {{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}}=>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}}=>2 {{1,2,3,5},{4},{6},{7}}=>2 {{1,2,3,6,7},{4,5}}=>2 {{1,2,3,6},{4,5,7}}=>2 {{1,2,3,6},{4,5},{7}}=>2 {{1,2,3,7},{4,5,6}}=>2 {{1,2,3},{4,5,6,7}}=>2 {{1,2,3},{4,5,6},{7}}=>2 {{1,2,3,7},{4,5},{6}}=>3 {{1,2,3},{4,5,7},{6}}=>2 {{1,2,3},{4,5},{6,7}}=>2 {{1,2,3},{4,5},{6},{7}}=>2 {{1,2,3,6,7},{4},{5}}=>3 {{1,2,3,6},{4,7},{5}}=>3 {{1,2,3,6},{4},{5,7}}=>3 {{1,2,3,6},{4},{5},{7}}=>3 {{1,2,3,7},{4,6},{5}}=>2 {{1,2,3},{4,6,7},{5}}=>2 {{1,2,3},{4,6},{5,7}}=>2 {{1,2,3},{4,6},{5},{7}}=>2 {{1,2,3,7},{4},{5,6}}=>3 {{1,2,3},{4,7},{5,6}}=>2 {{1,2,3},{4},{5,6,7}}=>2 {{1,2,3},{4},{5,6},{7}}=>2 {{1,2,3,7},{4},{5},{6}}=>3 {{1,2,3},{4,7},{5},{6}}=>3 {{1,2,3},{4},{5,7},{6}}=>2 {{1,2,3},{4},{5},{6,7}}=>2 {{1,2,3},{4},{5},{6},{7}}=>2 {{1,2,4,5,6,7},{3}}=>2 {{1,2,4,5,6},{3,7}}=>2 {{1,2,4,5,6},{3},{7}}=>2 {{1,2,4,5,7},{3,6}}=>2 {{1,2,4,5},{3,6,7}}=>2 {{1,2,4,5},{3,6},{7}}=>2 {{1,2,4,5,7},{3},{6}}=>2 {{1,2,4,5},{3,7},{6}}=>3 {{1,2,4,5},{3},{6,7}}=>2 {{1,2,4,5},{3},{6},{7}}=>2 {{1,2,4,6,7},{3,5}}=>2 {{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}}=>2 {{1,2,4},{3,5,6},{7}}=>2 {{1,2,4,7},{3,5},{6}}=>3 {{1,2,4},{3,5,7},{6}}=>2 {{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}}=>2 {{1,2,4,6},{3},{5,7}}=>2 {{1,2,4,6},{3},{5},{7}}=>2 {{1,2,4,7},{3,6},{5}}=>3 {{1,2,4},{3,6,7},{5}}=>3 {{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}}=>2 {{1,2,4},{3},{5,6},{7}}=>2 {{1,2,4,7},{3},{5},{6}}=>3 {{1,2,4},{3,7},{5},{6}}=>3 {{1,2,4},{3},{5,7},{6}}=>2 {{1,2,4},{3},{5},{6,7}}=>2 {{1,2,4},{3},{5},{6},{7}}=>2 {{1,2,5,6,7},{3,4}}=>2 {{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}}=>2 {{1,2,5},{3,4,6},{7}}=>2 {{1,2,5,7},{3,4},{6}}=>2 {{1,2,5},{3,4,7},{6}}=>3 {{1,2,5},{3,4},{6,7}}=>2 {{1,2,5},{3,4},{6},{7}}=>2 {{1,2,6,7},{3,4,5}}=>2 {{1,2,6},{3,4,5,7}}=>2 {{1,2,6},{3,4,5},{7}}=>2 {{1,2,7},{3,4,5,6}}=>2 {{1,2},{3,4,5,6,7}}=>2 {{1,2},{3,4,5,6},{7}}=>2 {{1,2,7},{3,4,5},{6}}=>3 {{1,2},{3,4,5,7},{6}}=>2 {{1,2},{3,4,5},{6,7}}=>2 {{1,2},{3,4,5},{6},{7}}=>2 {{1,2,6,7},{3,4},{5}}=>3 {{1,2,6},{3,4,7},{5}}=>3 {{1,2,6},{3,4},{5,7}}=>3 {{1,2,6},{3,4},{5},{7}}=>3 {{1,2,7},{3,4,6},{5}}=>2 {{1,2},{3,4,6,7},{5}}=>2 {{1,2},{3,4,6},{5,7}}=>2 {{1,2},{3,4,6},{5},{7}}=>2 {{1,2,7},{3,4},{5,6}}=>3 {{1,2},{3,4,7},{5,6}}=>2 {{1,2},{3,4},{5,6,7}}=>2 {{1,2},{3,4},{5,6},{7}}=>2 {{1,2,7},{3,4},{5},{6}}=>3 {{1,2},{3,4,7},{5},{6}}=>3 {{1,2},{3,4},{5,7},{6}}=>2 {{1,2},{3,4},{5},{6,7}}=>2 {{1,2},{3,4},{5},{6},{7}}=>2 {{1,2,5,6,7},{3},{4}}=>3 {{1,2,5,6},{3,7},{4}}=>3 {{1,2,5,6},{3},{4,7}}=>3 {{1,2,5,6},{3},{4},{7}}=>3 {{1,2,5,7},{3,6},{4}}=>3 {{1,2,5},{3,6,7},{4}}=>3 {{1,2,5},{3,6},{4,7}}=>3 {{1,2,5},{3,6},{4},{7}}=>3 {{1,2,5,7},{3},{4,6}}=>3 {{1,2,5},{3,7},{4,6}}=>3 {{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}}=>3 {{1,2,5},{3},{4,7},{6}}=>3 {{1,2,5},{3},{4},{6,7}}=>3 {{1,2,5},{3},{4},{6},{7}}=>3 {{1,2,6,7},{3,5},{4}}=>2 {{1,2,6},{3,5,7},{4}}=>2 {{1,2,6},{3,5},{4,7}}=>3 {{1,2,6},{3,5},{4},{7}}=>2 {{1,2,7},{3,5,6},{4}}=>2 {{1,2},{3,5,6,7},{4}}=>2 {{1,2},{3,5,6},{4,7}}=>2 {{1,2},{3,5,6},{4},{7}}=>2 {{1,2,7},{3,5},{4,6}}=>2 {{1,2},{3,5,7},{4,6}}=>2 {{1,2},{3,5},{4,6,7}}=>2 {{1,2},{3,5},{4,6},{7}}=>2 {{1,2,7},{3,5},{4},{6}}=>3 {{1,2},{3,5,7},{4},{6}}=>2 {{1,2},{3,5},{4,7},{6}}=>3 {{1,2},{3,5},{4},{6,7}}=>2 {{1,2},{3,5},{4},{6},{7}}=>2 {{1,2,6,7},{3},{4,5}}=>3 {{1,2,6},{3,7},{4,5}}=>3 {{1,2,6},{3},{4,5,7}}=>3 {{1,2,6},{3},{4,5},{7}}=>3 {{1,2,7},{3,6},{4,5}}=>2 {{1,2},{3,6,7},{4,5}}=>2 {{1,2},{3,6},{4,5,7}}=>2 {{1,2},{3,6},{4,5},{7}}=>2 {{1,2,7},{3},{4,5,6}}=>3 {{1,2},{3,7},{4,5,6}}=>2 {{1,2},{3},{4,5,6,7}}=>2 {{1,2},{3},{4,5,6},{7}}=>2 {{1,2,7},{3},{4,5},{6}}=>3 {{1,2},{3,7},{4,5},{6}}=>3 {{1,2},{3},{4,5,7},{6}}=>2 {{1,2},{3},{4,5},{6,7}}=>2 {{1,2},{3},{4,5},{6},{7}}=>2 {{1,2,6,7},{3},{4},{5}}=>3 {{1,2,6},{3,7},{4},{5}}=>4 {{1,2,6},{3},{4,7},{5}}=>3 {{1,2,6},{3},{4},{5,7}}=>3 {{1,2,6},{3},{4},{5},{7}}=>3 {{1,2,7},{3,6},{4},{5}}=>3 {{1,2},{3,6,7},{4},{5}}=>3 {{1,2},{3,6},{4,7},{5}}=>3 {{1,2},{3,6},{4},{5,7}}=>3 {{1,2},{3,6},{4},{5},{7}}=>3 {{1,2,7},{3},{4,6},{5}}=>3 {{1,2},{3,7},{4,6},{5}}=>2 {{1,2},{3},{4,6,7},{5}}=>2 {{1,2},{3},{4,6},{5,7}}=>2 {{1,2},{3},{4,6},{5},{7}}=>2 {{1,2,7},{3},{4},{5,6}}=>3 {{1,2},{3,7},{4},{5,6}}=>3 {{1,2},{3},{4,7},{5,6}}=>2 {{1,2},{3},{4},{5,6,7}}=>2 {{1,2},{3},{4},{5,6},{7}}=>2 {{1,2,7},{3},{4},{5},{6}}=>3 {{1,2},{3,7},{4},{5},{6}}=>3 {{1,2},{3},{4,7},{5},{6}}=>3 {{1,2},{3},{4},{5,7},{6}}=>2 {{1,2},{3},{4},{5},{6,7}}=>2 {{1,2},{3},{4},{5},{6},{7}}=>2 {{1,3,4,5,6,7},{2}}=>2 {{1,3,4,5,6},{2,7}}=>2 {{1,3,4,5,6},{2},{7}}=>2 {{1,3,4,5,7},{2,6}}=>2 {{1,3,4,5},{2,6,7}}=>2 {{1,3,4,5},{2,6},{7}}=>2 {{1,3,4,5,7},{2},{6}}=>2 {{1,3,4,5},{2,7},{6}}=>3 {{1,3,4,5},{2},{6,7}}=>2 {{1,3,4,5},{2},{6},{7}}=>2 {{1,3,4,6,7},{2,5}}=>2 {{1,3,4,6},{2,5,7}}=>2 {{1,3,4,6},{2,5},{7}}=>2 {{1,3,4,7},{2,5,6}}=>2 {{1,3,4},{2,5,6,7}}=>2 {{1,3,4},{2,5,6},{7}}=>2 {{1,3,4,7},{2,5},{6}}=>3 {{1,3,4},{2,5,7},{6}}=>2 {{1,3,4},{2,5},{6,7}}=>2 {{1,3,4},{2,5},{6},{7}}=>2 {{1,3,4,6,7},{2},{5}}=>2 {{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}}=>3 {{1,3,4},{2,6,7},{5}}=>3 {{1,3,4},{2,6},{5,7}}=>3 {{1,3,4},{2,6},{5},{7}}=>3 {{1,3,4,7},{2},{5,6}}=>2 {{1,3,4},{2,7},{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},{2,7},{5},{6}}=>3 {{1,3,4},{2},{5,7},{6}}=>2 {{1,3,4},{2},{5},{6,7}}=>2 {{1,3,4},{2},{5},{6},{7}}=>2 {{1,3,5,6,7},{2,4}}=>2 {{1,3,5,6},{2,4,7}}=>2 {{1,3,5,6},{2,4},{7}}=>2 {{1,3,5,7},{2,4,6}}=>2 {{1,3,5},{2,4,6,7}}=>2 {{1,3,5},{2,4,6},{7}}=>2 {{1,3,5,7},{2,4},{6}}=>2 {{1,3,5},{2,4,7},{6}}=>3 {{1,3,5},{2,4},{6,7}}=>2 {{1,3,5},{2,4},{6},{7}}=>2 {{1,3,6,7},{2,4,5}}=>2 {{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}}=>2 {{1,3},{2,4,5,6},{7}}=>2 {{1,3,7},{2,4,5},{6}}=>3 {{1,3},{2,4,5,7},{6}}=>2 {{1,3},{2,4,5},{6,7}}=>2 {{1,3},{2,4,5},{6},{7}}=>2 {{1,3,6,7},{2,4},{5}}=>3 {{1,3,6},{2,4,7},{5}}=>3 {{1,3,6},{2,4},{5,7}}=>3 {{1,3,6},{2,4},{5},{7}}=>3 {{1,3,7},{2,4,6},{5}}=>2 {{1,3},{2,4,6,7},{5}}=>2 {{1,3},{2,4,6},{5,7}}=>2 {{1,3},{2,4,6},{5},{7}}=>2 {{1,3,7},{2,4},{5,6}}=>3 {{1,3},{2,4,7},{5,6}}=>2 {{1,3},{2,4},{5,6,7}}=>2 {{1,3},{2,4},{5,6},{7}}=>2 {{1,3,7},{2,4},{5},{6}}=>3 {{1,3},{2,4,7},{5},{6}}=>3 {{1,3},{2,4},{5,7},{6}}=>2 {{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}}=>2 {{1,3,5,6},{2},{4,7}}=>2 {{1,3,5,6},{2},{4},{7}}=>2 {{1,3,5,7},{2,6},{4}}=>2 {{1,3,5},{2,6,7},{4}}=>2 {{1,3,5},{2,6},{4,7}}=>3 {{1,3,5},{2,6},{4},{7}}=>2 {{1,3,5,7},{2},{4,6}}=>2 {{1,3,5},{2,7},{4,6}}=>2 {{1,3,5},{2},{4,6,7}}=>2 {{1,3,5},{2},{4,6},{7}}=>2 {{1,3,5,7},{2},{4},{6}}=>2 {{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}}=>2 {{1,3,6,7},{2,5},{4}}=>3 {{1,3,6},{2,5,7},{4}}=>3 {{1,3,6},{2,5},{4,7}}=>3 {{1,3,6},{2,5},{4},{7}}=>3 {{1,3,7},{2,5,6},{4}}=>3 {{1,3},{2,5,6,7},{4}}=>3 {{1,3},{2,5,6},{4,7}}=>3 {{1,3},{2,5,6},{4},{7}}=>3 {{1,3,7},{2,5},{4,6}}=>3 {{1,3},{2,5,7},{4,6}}=>3 {{1,3},{2,5},{4,6,7}}=>3 {{1,3},{2,5},{4,6},{7}}=>3 {{1,3,7},{2,5},{4},{6}}=>3 {{1,3},{2,5,7},{4},{6}}=>3 {{1,3},{2,5},{4,7},{6}}=>3 {{1,3},{2,5},{4},{6,7}}=>3 {{1,3},{2,5},{4},{6},{7}}=>3 {{1,3,6,7},{2},{4,5}}=>2 {{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}}=>3 {{1,3},{2,6,7},{4,5}}=>3 {{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}}=>2 {{1,3},{2},{4,5,6},{7}}=>2 {{1,3,7},{2},{4,5},{6}}=>3 {{1,3},{2,7},{4,5},{6}}=>3 {{1,3},{2},{4,5,7},{6}}=>2 {{1,3},{2},{4,5},{6,7}}=>2 {{1,3},{2},{4,5},{6},{7}}=>2 {{1,3,6,7},{2},{4},{5}}=>3 {{1,3,6},{2,7},{4},{5}}=>3 {{1,3,6},{2},{4,7},{5}}=>3 {{1,3,6},{2},{4},{5,7}}=>3 {{1,3,6},{2},{4},{5},{7}}=>3 {{1,3,7},{2,6},{4},{5}}=>4 {{1,3},{2,6,7},{4},{5}}=>3 {{1,3},{2,6},{4,7},{5}}=>3 {{1,3},{2,6},{4},{5,7}}=>3 {{1,3},{2,6},{4},{5},{7}}=>3 {{1,3,7},{2},{4,6},{5}}=>2 {{1,3},{2,7},{4,6},{5}}=>3 {{1,3},{2},{4,6,7},{5}}=>2 {{1,3},{2},{4,6},{5,7}}=>2 {{1,3},{2},{4,6},{5},{7}}=>2 {{1,3,7},{2},{4},{5,6}}=>3 {{1,3},{2,7},{4},{5,6}}=>3 {{1,3},{2},{4,7},{5,6}}=>2 {{1,3},{2},{4},{5,6,7}}=>2 {{1,3},{2},{4},{5,6},{7}}=>2 {{1,3,7},{2},{4},{5},{6}}=>3 {{1,3},{2,7},{4},{5},{6}}=>3 {{1,3},{2},{4,7},{5},{6}}=>3 {{1,3},{2},{4},{5,7},{6}}=>2 {{1,3},{2},{4},{5},{6,7}}=>2 {{1,3},{2},{4},{5},{6},{7}}=>2 {{1,4,5,6,7},{2,3}}=>2 {{1,4,5,6},{2,3,7}}=>2 {{1,4,5,6},{2,3},{7}}=>2 {{1,4,5,7},{2,3,6}}=>2 {{1,4,5},{2,3,6,7}}=>2 {{1,4,5},{2,3,6},{7}}=>2 {{1,4,5,7},{2,3},{6}}=>2 {{1,4,5},{2,3,7},{6}}=>3 {{1,4,5},{2,3},{6,7}}=>2 {{1,4,5},{2,3},{6},{7}}=>2 {{1,4,6,7},{2,3,5}}=>2 {{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}}=>2 {{1,4},{2,3,5,6},{7}}=>2 {{1,4,7},{2,3,5},{6}}=>3 {{1,4},{2,3,5,7},{6}}=>2 {{1,4},{2,3,5},{6,7}}=>2 {{1,4},{2,3,5},{6},{7}}=>2 {{1,4,6,7},{2,3},{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},{2,3,6},{5}}=>3 {{1,4},{2,3,6,7},{5}}=>3 {{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}}=>2 {{1,4},{2,3},{5,6},{7}}=>2 {{1,4,7},{2,3},{5},{6}}=>3 {{1,4},{2,3,7},{5},{6}}=>3 {{1,4},{2,3},{5,7},{6}}=>2 {{1,4},{2,3},{5},{6,7}}=>2 {{1,4},{2,3},{5},{6},{7}}=>2 {{1,5,6,7},{2,3,4}}=>2 {{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}}=>2 {{1,5},{2,3,4,6},{7}}=>2 {{1,5,7},{2,3,4},{6}}=>2 {{1,5},{2,3,4,7},{6}}=>3 {{1,5},{2,3,4},{6,7}}=>2 {{1,5},{2,3,4},{6},{7}}=>2 {{1,6,7},{2,3,4,5}}=>2 {{1,6},{2,3,4,5,7}}=>2 {{1,6},{2,3,4,5},{7}}=>2 {{1,7},{2,3,4,5,6}}=>2 {{1},{2,3,4,5,6,7}}=>2 {{1},{2,3,4,5,6},{7}}=>2 {{1,7},{2,3,4,5},{6}}=>3 {{1},{2,3,4,5,7},{6}}=>2 {{1},{2,3,4,5},{6,7}}=>2 {{1},{2,3,4,5},{6},{7}}=>2 {{1,6,7},{2,3,4},{5}}=>3 {{1,6},{2,3,4,7},{5}}=>3 {{1,6},{2,3,4},{5,7}}=>3 {{1,6},{2,3,4},{5},{7}}=>3 {{1,7},{2,3,4,6},{5}}=>2 {{1},{2,3,4,6,7},{5}}=>2 {{1},{2,3,4,6},{5,7}}=>2 {{1},{2,3,4,6},{5},{7}}=>2 {{1,7},{2,3,4},{5,6}}=>3 {{1},{2,3,4,7},{5,6}}=>2 {{1},{2,3,4},{5,6,7}}=>2 {{1},{2,3,4},{5,6},{7}}=>2 {{1,7},{2,3,4},{5},{6}}=>3 {{1},{2,3,4,7},{5},{6}}=>3 {{1},{2,3,4},{5,7},{6}}=>2 {{1},{2,3,4},{5},{6,7}}=>2 {{1},{2,3,4},{5},{6},{7}}=>2 {{1,5,6,7},{2,3},{4}}=>3 {{1,5,6},{2,3,7},{4}}=>3 {{1,5,6},{2,3},{4,7}}=>3 {{1,5,6},{2,3},{4},{7}}=>3 {{1,5,7},{2,3,6},{4}}=>3 {{1,5},{2,3,6,7},{4}}=>3 {{1,5},{2,3,6},{4,7}}=>3 {{1,5},{2,3,6},{4},{7}}=>3 {{1,5,7},{2,3},{4,6}}=>3 {{1,5},{2,3,7},{4,6}}=>3 {{1,5},{2,3},{4,6,7}}=>3 {{1,5},{2,3},{4,6},{7}}=>3 {{1,5,7},{2,3},{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}}=>3 {{1,5},{2,3},{4},{6},{7}}=>3 {{1,6,7},{2,3,5},{4}}=>2 {{1,6},{2,3,5,7},{4}}=>2 {{1,6},{2,3,5},{4,7}}=>3 {{1,6},{2,3,5},{4},{7}}=>2 {{1,7},{2,3,5,6},{4}}=>2 {{1},{2,3,5,6,7},{4}}=>2 {{1},{2,3,5,6},{4,7}}=>2 {{1},{2,3,5,6},{4},{7}}=>2 {{1,7},{2,3,5},{4,6}}=>2 {{1},{2,3,5,7},{4,6}}=>2 {{1},{2,3,5},{4,6,7}}=>2 {{1},{2,3,5},{4,6},{7}}=>2 {{1,7},{2,3,5},{4},{6}}=>3 {{1},{2,3,5,7},{4},{6}}=>2 {{1},{2,3,5},{4,7},{6}}=>3 {{1},{2,3,5},{4},{6,7}}=>2 {{1},{2,3,5},{4},{6},{7}}=>2 {{1,6,7},{2,3},{4,5}}=>3 {{1,6},{2,3,7},{4,5}}=>3 {{1,6},{2,3},{4,5,7}}=>3 {{1,6},{2,3},{4,5},{7}}=>3 {{1,7},{2,3,6},{4,5}}=>2 {{1},{2,3,6,7},{4,5}}=>2 {{1},{2,3,6},{4,5,7}}=>2 {{1},{2,3,6},{4,5},{7}}=>2 {{1,7},{2,3},{4,5,6}}=>3 {{1},{2,3,7},{4,5,6}}=>2 {{1},{2,3},{4,5,6,7}}=>2 {{1},{2,3},{4,5,6},{7}}=>2 {{1,7},{2,3},{4,5},{6}}=>3 {{1},{2,3,7},{4,5},{6}}=>3 {{1},{2,3},{4,5,7},{6}}=>2 {{1},{2,3},{4,5},{6,7}}=>2 {{1},{2,3},{4,5},{6},{7}}=>2 {{1,6,7},{2,3},{4},{5}}=>3 {{1,6},{2,3,7},{4},{5}}=>4 {{1,6},{2,3},{4,7},{5}}=>3 {{1,6},{2,3},{4},{5,7}}=>3 {{1,6},{2,3},{4},{5},{7}}=>3 {{1,7},{2,3,6},{4},{5}}=>3 {{1},{2,3,6,7},{4},{5}}=>3 {{1},{2,3,6},{4,7},{5}}=>3 {{1},{2,3,6},{4},{5,7}}=>3 {{1},{2,3,6},{4},{5},{7}}=>3 {{1,7},{2,3},{4,6},{5}}=>3 {{1},{2,3,7},{4,6},{5}}=>2 {{1},{2,3},{4,6,7},{5}}=>2 {{1},{2,3},{4,6},{5,7}}=>2 {{1},{2,3},{4,6},{5},{7}}=>2 {{1,7},{2,3},{4},{5,6}}=>3 {{1},{2,3,7},{4},{5,6}}=>3 {{1},{2,3},{4,7},{5,6}}=>2 {{1},{2,3},{4},{5,6,7}}=>2 {{1},{2,3},{4},{5,6},{7}}=>2 {{1,7},{2,3},{4},{5},{6}}=>3 {{1},{2,3,7},{4},{5},{6}}=>3 {{1},{2,3},{4,7},{5},{6}}=>3 {{1},{2,3},{4},{5,7},{6}}=>2 {{1},{2,3},{4},{5},{6,7}}=>2 {{1},{2,3},{4},{5},{6},{7}}=>2 {{1,4,5,6,7},{2},{3}}=>3 {{1,4,5,6},{2,7},{3}}=>3 {{1,4,5,6},{2},{3,7}}=>3 {{1,4,5,6},{2},{3},{7}}=>3 {{1,4,5,7},{2,6},{3}}=>3 {{1,4,5},{2,6,7},{3}}=>3 {{1,4,5},{2,6},{3,7}}=>3 {{1,4,5},{2,6},{3},{7}}=>3 {{1,4,5,7},{2},{3,6}}=>3 {{1,4,5},{2,7},{3,6}}=>3 {{1,4,5},{2},{3,6,7}}=>3 {{1,4,5},{2},{3,6},{7}}=>3 {{1,4,5,7},{2},{3},{6}}=>3 {{1,4,5},{2,7},{3},{6}}=>3 {{1,4,5},{2},{3,7},{6}}=>3 {{1,4,5},{2},{3},{6,7}}=>3 {{1,4,5},{2},{3},{6},{7}}=>3 {{1,4,6,7},{2,5},{3}}=>3 {{1,4,6},{2,5,7},{3}}=>3 {{1,4,6},{2,5},{3,7}}=>3 {{1,4,6},{2,5},{3},{7}}=>3 {{1,4,7},{2,5,6},{3}}=>3 {{1,4},{2,5,6,7},{3}}=>3 {{1,4},{2,5,6},{3,7}}=>3 {{1,4},{2,5,6},{3},{7}}=>3 {{1,4,7},{2,5},{3,6}}=>3 {{1,4},{2,5,7},{3,6}}=>3 {{1,4},{2,5},{3,6,7}}=>3 {{1,4},{2,5},{3,6},{7}}=>3 {{1,4,7},{2,5},{3},{6}}=>3 {{1,4},{2,5,7},{3},{6}}=>3 {{1,4},{2,5},{3,7},{6}}=>3 {{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}}=>3 {{1,4,6},{2},{3,5,7}}=>3 {{1,4,6},{2},{3,5},{7}}=>3 {{1,4,7},{2,6},{3,5}}=>3 {{1,4},{2,6,7},{3,5}}=>3 {{1,4},{2,6},{3,5,7}}=>3 {{1,4},{2,6},{3,5},{7}}=>3 {{1,4,7},{2},{3,5,6}}=>3 {{1,4},{2,7},{3,5,6}}=>3 {{1,4},{2},{3,5,6,7}}=>3 {{1,4},{2},{3,5,6},{7}}=>3 {{1,4,7},{2},{3,5},{6}}=>3 {{1,4},{2,7},{3,5},{6}}=>3 {{1,4},{2},{3,5,7},{6}}=>3 {{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}}=>3 {{1,4,6},{2},{3,7},{5}}=>3 {{1,4,6},{2},{3},{5,7}}=>3 {{1,4,6},{2},{3},{5},{7}}=>3 {{1,4,7},{2,6},{3},{5}}=>3 {{1,4},{2,6,7},{3},{5}}=>3 {{1,4},{2,6},{3,7},{5}}=>4 {{1,4},{2,6},{3},{5,7}}=>3 {{1,4},{2,6},{3},{5},{7}}=>3 {{1,4,7},{2},{3,6},{5}}=>3 {{1,4},{2,7},{3,6},{5}}=>3 {{1,4},{2},{3,6,7},{5}}=>3 {{1,4},{2},{3,6},{5,7}}=>3 {{1,4},{2},{3,6},{5},{7}}=>3 {{1,4,7},{2},{3},{5,6}}=>3 {{1,4},{2,7},{3},{5,6}}=>3 {{1,4},{2},{3,7},{5,6}}=>3 {{1,4},{2},{3},{5,6,7}}=>3 {{1,4},{2},{3},{5,6},{7}}=>3 {{1,4,7},{2},{3},{5},{6}}=>3 {{1,4},{2,7},{3},{5},{6}}=>3 {{1,4},{2},{3,7},{5},{6}}=>3 {{1,4},{2},{3},{5,7},{6}}=>3 {{1,4},{2},{3},{5},{6,7}}=>3 {{1,4},{2},{3},{5},{6},{7}}=>3 {{1,5,6,7},{2,4},{3}}=>2 {{1,5,6},{2,4,7},{3}}=>2 {{1,5,6},{2,4},{3,7}}=>3 {{1,5,6},{2,4},{3},{7}}=>2 {{1,5,7},{2,4,6},{3}}=>2 {{1,5},{2,4,6,7},{3}}=>2 {{1,5},{2,4,6},{3,7}}=>2 {{1,5},{2,4,6},{3},{7}}=>2 {{1,5,7},{2,4},{3,6}}=>3 {{1,5},{2,4,7},{3,6}}=>3 {{1,5},{2,4},{3,6,7}}=>3 {{1,5},{2,4},{3,6},{7}}=>3 {{1,5,7},{2,4},{3},{6}}=>2 {{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}}=>2 {{1,6,7},{2,4,5},{3}}=>2 {{1,6},{2,4,5,7},{3}}=>2 {{1,6},{2,4,5},{3,7}}=>3 {{1,6},{2,4,5},{3},{7}}=>2 {{1,7},{2,4,5,6},{3}}=>2 {{1},{2,4,5,6,7},{3}}=>2 {{1},{2,4,5,6},{3,7}}=>2 {{1},{2,4,5,6},{3},{7}}=>2 {{1,7},{2,4,5},{3,6}}=>2 {{1},{2,4,5,7},{3,6}}=>2 {{1},{2,4,5},{3,6,7}}=>2 {{1},{2,4,5},{3,6},{7}}=>2 {{1,7},{2,4,5},{3},{6}}=>3 {{1},{2,4,5,7},{3},{6}}=>2 {{1},{2,4,5},{3,7},{6}}=>3 {{1},{2,4,5},{3},{6,7}}=>2 {{1},{2,4,5},{3},{6},{7}}=>2 {{1,6,7},{2,4},{3,5}}=>2 {{1,6},{2,4,7},{3,5}}=>3 {{1,6},{2,4},{3,5,7}}=>2 {{1,6},{2,4},{3,5},{7}}=>2 {{1,7},{2,4,6},{3,5}}=>2 {{1},{2,4,6,7},{3,5}}=>2 {{1},{2,4,6},{3,5,7}}=>2 {{1},{2,4,6},{3,5},{7}}=>2 {{1,7},{2,4},{3,5,6}}=>2 {{1},{2,4,7},{3,5,6}}=>2 {{1},{2,4},{3,5,6,7}}=>2 {{1},{2,4},{3,5,6},{7}}=>2 {{1,7},{2,4},{3,5},{6}}=>3 {{1},{2,4,7},{3,5},{6}}=>3 {{1},{2,4},{3,5,7},{6}}=>2 {{1},{2,4},{3,5},{6,7}}=>2 {{1},{2,4},{3,5},{6},{7}}=>2 {{1,6,7},{2,4},{3},{5}}=>3 {{1,6},{2,4,7},{3},{5}}=>3 {{1,6},{2,4},{3,7},{5}}=>4 {{1,6},{2,4},{3},{5,7}}=>3 {{1,6},{2,4},{3},{5},{7}}=>3 {{1,7},{2,4,6},{3},{5}}=>3 {{1},{2,4,6,7},{3},{5}}=>2 {{1},{2,4,6},{3,7},{5}}=>2 {{1},{2,4,6},{3},{5,7}}=>2 {{1},{2,4,6},{3},{5},{7}}=>2 {{1,7},{2,4},{3,6},{5}}=>3 {{1},{2,4,7},{3,6},{5}}=>3 {{1},{2,4},{3,6,7},{5}}=>3 {{1},{2,4},{3,6},{5,7}}=>3 {{1},{2,4},{3,6},{5},{7}}=>3 {{1,7},{2,4},{3},{5,6}}=>3 {{1},{2,4,7},{3},{5,6}}=>2 {{1},{2,4},{3,7},{5,6}}=>3 {{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}}=>3 {{1},{2,4},{3,7},{5},{6}}=>3 {{1},{2,4},{3},{5,7},{6}}=>2 {{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}}=>3 {{1,5,6},{2},{3,4,7}}=>3 {{1,5,6},{2},{3,4},{7}}=>3 {{1,5,7},{2,6},{3,4}}=>3 {{1,5},{2,6,7},{3,4}}=>3 {{1,5},{2,6},{3,4,7}}=>3 {{1,5},{2,6},{3,4},{7}}=>3 {{1,5,7},{2},{3,4,6}}=>3 {{1,5},{2,7},{3,4,6}}=>3 {{1,5},{2},{3,4,6,7}}=>3 {{1,5},{2},{3,4,6},{7}}=>3 {{1,5,7},{2},{3,4},{6}}=>3 {{1,5},{2,7},{3,4},{6}}=>3 {{1,5},{2},{3,4,7},{6}}=>3 {{1,5},{2},{3,4},{6,7}}=>3 {{1,5},{2},{3,4},{6},{7}}=>3 {{1,6,7},{2,5},{3,4}}=>2 {{1,6},{2,5,7},{3,4}}=>2 {{1,6},{2,5},{3,4,7}}=>3 {{1,6},{2,5},{3,4},{7}}=>2 {{1,7},{2,5,6},{3,4}}=>2 {{1},{2,5,6,7},{3,4}}=>2 {{1},{2,5,6},{3,4,7}}=>2 {{1},{2,5,6},{3,4},{7}}=>2 {{1,7},{2,5},{3,4,6}}=>2 {{1},{2,5,7},{3,4,6}}=>2 {{1},{2,5},{3,4,6,7}}=>2 {{1},{2,5},{3,4,6},{7}}=>2 {{1,7},{2,5},{3,4},{6}}=>3 {{1},{2,5,7},{3,4},{6}}=>2 {{1},{2,5},{3,4,7},{6}}=>3 {{1},{2,5},{3,4},{6,7}}=>2 {{1},{2,5},{3,4},{6},{7}}=>2 {{1,6,7},{2},{3,4,5}}=>3 {{1,6},{2,7},{3,4,5}}=>3 {{1,6},{2},{3,4,5,7}}=>3 {{1,6},{2},{3,4,5},{7}}=>3 {{1,7},{2,6},{3,4,5}}=>2 {{1},{2,6,7},{3,4,5}}=>2 {{1},{2,6},{3,4,5,7}}=>2 {{1},{2,6},{3,4,5},{7}}=>2 {{1,7},{2},{3,4,5,6}}=>3 {{1},{2,7},{3,4,5,6}}=>2 {{1},{2},{3,4,5,6,7}}=>2 {{1},{2},{3,4,5,6},{7}}=>2 {{1,7},{2},{3,4,5},{6}}=>3 {{1},{2,7},{3,4,5},{6}}=>3 {{1},{2},{3,4,5,7},{6}}=>2 {{1},{2},{3,4,5},{6,7}}=>2 {{1},{2},{3,4,5},{6},{7}}=>2 {{1,6,7},{2},{3,4},{5}}=>3 {{1,6},{2,7},{3,4},{5}}=>4 {{1,6},{2},{3,4,7},{5}}=>3 {{1,6},{2},{3,4},{5,7}}=>3 {{1,6},{2},{3,4},{5},{7}}=>3 {{1,7},{2,6},{3,4},{5}}=>3 {{1},{2,6,7},{3,4},{5}}=>3 {{1},{2,6},{3,4,7},{5}}=>3 {{1},{2,6},{3,4},{5,7}}=>3 {{1},{2,6},{3,4},{5},{7}}=>3 {{1,7},{2},{3,4,6},{5}}=>3 {{1},{2,7},{3,4,6},{5}}=>2 {{1},{2},{3,4,6,7},{5}}=>2 {{1},{2},{3,4,6},{5,7}}=>2 {{1},{2},{3,4,6},{5},{7}}=>2 {{1,7},{2},{3,4},{5,6}}=>3 {{1},{2,7},{3,4},{5,6}}=>3 {{1},{2},{3,4,7},{5,6}}=>2 {{1},{2},{3,4},{5,6,7}}=>2 {{1},{2},{3,4},{5,6},{7}}=>2 {{1,7},{2},{3,4},{5},{6}}=>3 {{1},{2,7},{3,4},{5},{6}}=>3 {{1},{2},{3,4,7},{5},{6}}=>3 {{1},{2},{3,4},{5,7},{6}}=>2 {{1},{2},{3,4},{5},{6,7}}=>2 {{1},{2},{3,4},{5},{6},{7}}=>2 {{1,5,6,7},{2},{3},{4}}=>3 {{1,5,6},{2,7},{3},{4}}=>4 {{1,5,6},{2},{3,7},{4}}=>3 {{1,5,6},{2},{3},{4,7}}=>3 {{1,5,6},{2},{3},{4},{7}}=>3 {{1,5,7},{2,6},{3},{4}}=>4 {{1,5},{2,6,7},{3},{4}}=>4 {{1,5},{2,6},{3,7},{4}}=>4 {{1,5},{2,6},{3},{4,7}}=>4 {{1,5},{2,6},{3},{4},{7}}=>4 {{1,5,7},{2},{3,6},{4}}=>3 {{1,5},{2,7},{3,6},{4}}=>3 {{1,5},{2},{3,6,7},{4}}=>3 {{1,5},{2},{3,6},{4,7}}=>3 {{1,5},{2},{3,6},{4},{7}}=>3 {{1,5,7},{2},{3},{4,6}}=>3 {{1,5},{2,7},{3},{4,6}}=>4 {{1,5},{2},{3,7},{4,6}}=>3 {{1,5},{2},{3},{4,6,7}}=>3 {{1,5},{2},{3},{4,6},{7}}=>3 {{1,5,7},{2},{3},{4},{6}}=>3 {{1,5},{2,7},{3},{4},{6}}=>4 {{1,5},{2},{3,7},{4},{6}}=>3 {{1,5},{2},{3},{4,7},{6}}=>3 {{1,5},{2},{3},{4},{6,7}}=>3 {{1,5},{2},{3},{4},{6},{7}}=>3 {{1,6,7},{2,5},{3},{4}}=>3 {{1,6},{2,5,7},{3},{4}}=>3 {{1,6},{2,5},{3,7},{4}}=>3 {{1,6},{2,5},{3},{4,7}}=>3 {{1,6},{2,5},{3},{4},{7}}=>3 {{1,7},{2,5,6},{3},{4}}=>3 {{1},{2,5,6,7},{3},{4}}=>3 {{1},{2,5,6},{3,7},{4}}=>3 {{1},{2,5,6},{3},{4,7}}=>3 {{1},{2,5,6},{3},{4},{7}}=>3 {{1,7},{2,5},{3,6},{4}}=>3 {{1},{2,5,7},{3,6},{4}}=>3 {{1},{2,5},{3,6,7},{4}}=>3 {{1},{2,5},{3,6},{4,7}}=>3 {{1},{2,5},{3,6},{4},{7}}=>3 {{1,7},{2,5},{3},{4,6}}=>3 {{1},{2,5,7},{3},{4,6}}=>3 {{1},{2,5},{3,7},{4,6}}=>3 {{1},{2,5},{3},{4,6,7}}=>3 {{1},{2,5},{3},{4,6},{7}}=>3 {{1,7},{2,5},{3},{4},{6}}=>3 {{1},{2,5,7},{3},{4},{6}}=>3 {{1},{2,5},{3,7},{4},{6}}=>3 {{1},{2,5},{3},{4,7},{6}}=>3 {{1},{2,5},{3},{4},{6,7}}=>3 {{1},{2,5},{3},{4},{6},{7}}=>3 {{1,6,7},{2},{3,5},{4}}=>3 {{1,6},{2,7},{3,5},{4}}=>3 {{1,6},{2},{3,5,7},{4}}=>3 {{1,6},{2},{3,5},{4,7}}=>3 {{1,6},{2},{3,5},{4},{7}}=>3 {{1,7},{2,6},{3,5},{4}}=>2 {{1},{2,6,7},{3,5},{4}}=>2 {{1},{2,6},{3,5,7},{4}}=>2 {{1},{2,6},{3,5},{4,7}}=>3 {{1},{2,6},{3,5},{4},{7}}=>2 {{1,7},{2},{3,5,6},{4}}=>3 {{1},{2,7},{3,5,6},{4}}=>2 {{1},{2},{3,5,6,7},{4}}=>2 {{1},{2},{3,5,6},{4,7}}=>2 {{1},{2},{3,5,6},{4},{7}}=>2 {{1,7},{2},{3,5},{4,6}}=>3 {{1},{2,7},{3,5},{4,6}}=>2 {{1},{2},{3,5,7},{4,6}}=>2 {{1},{2},{3,5},{4,6,7}}=>2 {{1},{2},{3,5},{4,6},{7}}=>2 {{1,7},{2},{3,5},{4},{6}}=>3 {{1},{2,7},{3,5},{4},{6}}=>3 {{1},{2},{3,5,7},{4},{6}}=>2 {{1},{2},{3,5},{4,7},{6}}=>3 {{1},{2},{3,5},{4},{6,7}}=>2 {{1},{2},{3,5},{4},{6},{7}}=>2 {{1,6,7},{2},{3},{4,5}}=>3 {{1,6},{2,7},{3},{4,5}}=>4 {{1,6},{2},{3,7},{4,5}}=>3 {{1,6},{2},{3},{4,5,7}}=>3 {{1,6},{2},{3},{4,5},{7}}=>3 {{1,7},{2,6},{3},{4,5}}=>3 {{1},{2,6,7},{3},{4,5}}=>3 {{1},{2,6},{3,7},{4,5}}=>3 {{1},{2,6},{3},{4,5,7}}=>3 {{1},{2,6},{3},{4,5},{7}}=>3 {{1,7},{2},{3,6},{4,5}}=>3 {{1},{2,7},{3,6},{4,5}}=>2 {{1},{2},{3,6,7},{4,5}}=>2 {{1},{2},{3,6},{4,5,7}}=>2 {{1},{2},{3,6},{4,5},{7}}=>2 {{1,7},{2},{3},{4,5,6}}=>3 {{1},{2,7},{3},{4,5,6}}=>3 {{1},{2},{3,7},{4,5,6}}=>2 {{1},{2},{3},{4,5,6,7}}=>2 {{1},{2},{3},{4,5,6},{7}}=>2 {{1,7},{2},{3},{4,5},{6}}=>3 {{1},{2,7},{3},{4,5},{6}}=>3 {{1},{2},{3,7},{4,5},{6}}=>3 {{1},{2},{3},{4,5,7},{6}}=>2 {{1},{2},{3},{4,5},{6,7}}=>2 {{1},{2},{3},{4,5},{6},{7}}=>2 {{1,6,7},{2},{3},{4},{5}}=>3 {{1,6},{2,7},{3},{4},{5}}=>4 {{1,6},{2},{3,7},{4},{5}}=>4 {{1,6},{2},{3},{4,7},{5}}=>3 {{1,6},{2},{3},{4},{5,7}}=>3 {{1,6},{2},{3},{4},{5},{7}}=>3 {{1,7},{2,6},{3},{4},{5}}=>3 {{1},{2,6,7},{3},{4},{5}}=>3 {{1},{2,6},{3,7},{4},{5}}=>4 {{1},{2,6},{3},{4,7},{5}}=>3 {{1},{2,6},{3},{4},{5,7}}=>3 {{1},{2,6},{3},{4},{5},{7}}=>3 {{1,7},{2},{3,6},{4},{5}}=>3 {{1},{2,7},{3,6},{4},{5}}=>3 {{1},{2},{3,6,7},{4},{5}}=>3 {{1},{2},{3,6},{4,7},{5}}=>3 {{1},{2},{3,6},{4},{5,7}}=>3 {{1},{2},{3,6},{4},{5},{7}}=>3 {{1,7},{2},{3},{4,6},{5}}=>3 {{1},{2,7},{3},{4,6},{5}}=>3 {{1},{2},{3,7},{4,6},{5}}=>2 {{1},{2},{3},{4,6,7},{5}}=>2 {{1},{2},{3},{4,6},{5,7}}=>2 {{1},{2},{3},{4,6},{5},{7}}=>2 {{1,7},{2},{3},{4},{5,6}}=>3 {{1},{2,7},{3},{4},{5,6}}=>3 {{1},{2},{3,7},{4},{5,6}}=>3 {{1},{2},{3},{4,7},{5,6}}=>2 {{1},{2},{3},{4},{5,6,7}}=>2 {{1},{2},{3},{4},{5,6},{7}}=>2 {{1,7},{2},{3},{4},{5},{6}}=>3 {{1},{2,7},{3},{4},{5},{6}}=>3 {{1},{2},{3,7},{4},{5},{6}}=>3 {{1},{2},{3},{4,7},{5},{6}}=>3 {{1},{2},{3},{4},{5,7},{6}}=>2 {{1},{2},{3},{4},{5},{6,7}}=>2 {{1},{2},{3},{4},{5},{6},{7}}=>2 {{1,2},{3,4},{5,6},{7,8}}=>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}}=>3 {{1,6},{2,3},{4,5},{7,8}}=>3 {{1,7},{2,3},{4,5},{6,8}}=>3 {{1,8},{2,3},{4,5},{6,7}}=>3 {{1,8},{2,4},{3,5},{6,7}}=>3 {{1,7},{2,4},{3,5},{6,8}}=>3 {{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}}=>2 {{1,2},{3,6},{4,5},{7,8}}=>2 {{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}}=>3 {{1,8},{2,5},{3,4},{6,7}}=>3 {{1,8},{2,6},{3,4},{5,7}}=>3 {{1,7},{2,6},{3,4},{5,8}}=>3 {{1,6},{2,7},{3,4},{5,8}}=>4 {{1,5},{2,7},{3,4},{6,8}}=>3 {{1,4},{2,7},{3,5},{6,8}}=>3 {{1,3},{2,7},{4,5},{6,8}}=>3 {{1,2},{3,7},{4,5},{6,8}}=>3 {{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}}=>4 {{1,7},{2,8},{3,4},{5,6}}=>4 {{1,8},{2,7},{3,4},{5,6}}=>3 {{1,8},{2,7},{3,5},{4,6}}=>2 {{1,7},{2,8},{3,5},{4,6}}=>3 {{1,6},{2,8},{3,5},{4,7}}=>3 {{1,5},{2,8},{3,6},{4,7}}=>3 {{1,4},{2,8},{3,6},{5,7}}=>3 {{1,3},{2,8},{4,6},{5,7}}=>3 {{1,2},{3,8},{4,6},{5,7}}=>2 {{1,2},{3,7},{4,6},{5,8}}=>3 {{1,3},{2,7},{4,6},{5,8}}=>3 {{1,4},{2,7},{3,6},{5,8}}=>3 {{1,5},{2,7},{3,6},{4,8}}=>3 {{1,6},{2,7},{3,5},{4,8}}=>4 {{1,7},{2,6},{3,5},{4,8}}=>3 {{1,8},{2,6},{3,5},{4,7}}=>3 {{1,8},{2,5},{3,6},{4,7}}=>3 {{1,7},{2,5},{3,6},{4,8}}=>3 {{1,6},{2,5},{3,7},{4,8}}=>4 {{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}}=>3 {{1,2},{3,6},{4,7},{5,8}}=>3 {{1,2},{3,5},{4,7},{6,8}}=>3 {{1,3},{2,5},{4,7},{6,8}}=>3 {{1,4},{2,5},{3,7},{6,8}}=>3 {{1,5},{2,4},{3,7},{6,8}}=>3 {{1,6},{2,4},{3,7},{5,8}}=>4 {{1,7},{2,4},{3,6},{5,8}}=>3 {{1,8},{2,4},{3,6},{5,7}}=>3 {{1,8},{2,3},{4,6},{5,7}}=>3 {{1,7},{2,3},{4,6},{5,8}}=>3 {{1,6},{2,3},{4,7},{5,8}}=>3 {{1,5},{2,3},{4,7},{6,8}}=>3 {{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}}=>2 {{1,3},{2,4},{5,8},{6,7}}=>2 {{1,4},{2,3},{5,8},{6,7}}=>2 {{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}}=>3 {{1,8},{2,3},{4,7},{5,6}}=>3 {{1,8},{2,4},{3,7},{5,6}}=>3 {{1,7},{2,4},{3,8},{5,6}}=>4 {{1,6},{2,4},{3,8},{5,7}}=>4 {{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}}=>3 {{1,3},{2,6},{4,8},{5,7}}=>3 {{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}}=>3 {{1,8},{2,5},{3,7},{4,6}}=>3 {{1,8},{2,6},{3,7},{4,5}}=>3 {{1,7},{2,6},{3,8},{4,5}}=>3 {{1,6},{2,7},{3,8},{4,5}}=>4 {{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}}=>3 {{1,2},{3,7},{4,8},{5,6}}=>3 {{1,2},{3,8},{4,7},{5,6}}=>2 {{1,3},{2,8},{4,7},{5,6}}=>3 {{1,4},{2,8},{3,7},{5,6}}=>3 {{1,5},{2,8},{3,7},{4,6}}=>3 {{1,6},{2,8},{3,7},{4,5}}=>3 {{1,7},{2,8},{3,6},{4,5}}=>3 {{1,8},{2,7},{3,6},{4,5}}=>2 {{1},{2},{3},{4},{5},{6},{7},{8}}=>2 {{1},{2},{3},{4},{5},{6},{7,8}}=>2 {{1},{2},{3},{4},{5},{6,8},{7}}=>2 {{1},{2},{3},{4},{5},{6,7,8}}=>2 {{1},{2},{3},{4},{5,8},{6},{7}}=>3 {{1},{2},{3},{4},{5,8},{6,7}}=>2 {{1},{2},{3},{4},{5,6,8},{7}}=>2 {{1},{2},{3},{4},{5,6,7,8}}=>2 {{1},{2},{3},{4,8},{5},{6},{7}}=>3 {{1},{2},{3},{4,8},{5,6},{7}}=>3 {{1},{2},{3},{4,8},{5,7},{6}}=>2 {{1},{2},{3},{4,8},{5,6,7}}=>2 {{1},{2},{3},{4,5,6,7,8}}=>2 {{1},{2},{3,8},{4},{5},{6},{7}}=>3 {{1},{2},{3,8},{4,5},{6},{7}}=>3 {{1},{2},{3,8},{4,6},{5},{7}}=>3 {{1},{2},{3,8},{4,5,6},{7}}=>3 {{1},{2},{3,4,8},{5,6,7}}=>2 {{1},{2},{3,4,5,6,7,8}}=>2 {{1},{2,3},{4,7,8},{5,6}}=>2 {{1},{2,3},{4,5,6,8},{7}}=>2 {{1},{2,8},{3},{4},{5},{6},{7}}=>3 {{1},{2,4,6,8},{3},{5},{7}}=>2 {{1},{2,4,8},{3},{5,7},{6}}=>2 {{1},{2,4,5,8},{3},{6,7}}=>2 {{1},{2,4,5,6,7,8},{3}}=>2 {{1},{2,8},{3,4},{5},{6},{7}}=>3 {{1},{2,8},{3,4},{5,6,7}}=>3 {{1},{2,5,8},{3,4},{6,7}}=>2 {{1},{2,3,5},{4},{6,7,8}}=>2 {{1},{2,8},{3,5},{4},{6},{7}}=>3 {{1},{2,6,8},{3,5},{4},{7}}=>2 {{1},{2,8},{3,5,7},{4},{6}}=>3 {{1},{2,3,5,6,7,8},{4}}=>2 {{1},{2,8},{3,4,5},{6},{7}}=>3 {{1},{2,8},{3,4,5},{6,7}}=>3 {{1},{2,8},{3,7},{4,6},{5}}=>2 {{1},{2,3,4,7,8},{5},{6}}=>3 {{1},{2,3,4,6,7,8},{5}}=>2 {{1},{2,3,8},{4,5,7},{6}}=>2 {{1},{2,3,4,5,8},{6},{7}}=>3 {{1},{2,3,4,5,7,8},{6}}=>2 {{1},{2,3,4,5,6,7},{8}}=>2 {{1},{2,3,4,8},{5,6,7}}=>2 {{1},{2,3,4,5,8},{6,7}}=>2 {{1},{2,3,4,5,6,8},{7}}=>2 {{1},{2,3,4,5,6,7,8}}=>2 {{1,2},{3},{4,6,7,8},{5}}=>2 {{1,2},{3,4},{5,7,8},{6}}=>2 {{1,2},{3,4},{5,6,8},{7}}=>2 {{1,2},{3,6,7,8},{4},{5}}=>3 {{1,2},{3,5,6},{4},{7,8}}=>2 {{1,2},{3,7,8},{4},{5,6}}=>3 {{1,2},{3,5,8},{4},{6,7}}=>2 {{1,2},{3,5,6,8},{4},{7}}=>2 {{1,2},{3,6,8},{4,5},{7}}=>2 {{1,2},{3,4,6},{5},{7,8}}=>2 {{1,2},{3,7,8},{4,6},{5}}=>2 {{1,2},{3,8},{4,6,7},{5}}=>2 {{1,2},{3,4,8},{5},{6,7}}=>3 {{1,2},{3,4,6,8},{5},{7}}=>2 {{1,2},{3,8},{4,5,7},{6}}=>2 {{1,2},{3,4,8},{5,7},{6}}=>2 {{1,2},{3,4,5,6,7,8}}=>2 {{1,3},{2},{4,6,8},{5},{7}}=>2 {{1,3},{2},{4,7,8},{5,6}}=>2 {{1,3},{2},{4,8},{5,7},{6}}=>2 {{1,3},{2},{4,5,6,8},{7}}=>2 {{1,8},{2},{3},{4},{5},{6},{7}}=>3 {{1,5,6,7,8},{2},{3},{4}}=>3 {{1,6,7,8},{2},{3},{4,5}}=>3 {{1,4,5,6},{2},{3},{7,8}}=>3 {{1,4,7,8},{2},{3},{5,6}}=>3 {{1,4,5,8},{2},{3},{6,7}}=>3 {{1,4,5,6,7,8},{2},{3}}=>3 {{1,3,4},{2},{5,6},{7,8}}=>2 {{1,3,4},{2},{5,7,8},{6}}=>2 {{1,3,4},{2},{5,8},{6,7}}=>2 {{1,5,6},{2},{3,4},{7,8}}=>3 {{1,7,8},{2},{3,4},{5,6}}=>3 {{1,5,8},{2},{3,4},{6,7}}=>3 {{1,3,5},{2},{4},{6,8},{7}}=>2 {{1,3,5},{2},{4},{6,7,8}}=>2 {{1,6,7,8},{2},{3,5},{4}}=>3 {{1,7,8},{2},{3,5,6},{4}}=>3 {{1,3,5,7},{2},{4},{6},{8}}=>2 {{1,3,5,6,7,8},{2},{4}}=>2 {{1,3,6},{2},{4,5},{7,8}}=>2 {{1,7,8},{2},{3,6},{4,5}}=>3 {{1,3,8},{2},{4,5},{6,7}}=>3 {{1,3,7},{2},{4,6},{5},{8}}=>2 {{1,3,8},{2},{4,6,7},{5}}=>2 {{1,8},{2},{3,4,5,6},{7}}=>3 {{1,3,8},{2},{4,7},{5,6}}=>2 {{1,3,4,5,6,7,8},{2}}=>2 {{1,4},{2,3},{5,7,8},{6}}=>2 {{1,4},{2,3},{5,6,8},{7}}=>2 {{1,8},{2,3},{4},{5},{6},{7}}=>3 {{1,8},{2,3},{4},{5,6,7}}=>3 {{1,6,8},{2,3},{4,5},{7}}=>3 {{1,4,6},{2,3},{5},{7,8}}=>2 {{1,8},{2,3},{4,6,7},{5}}=>3 {{1,4,8},{2,3},{5},{6,7}}=>3 {{1,4,6,8},{2,3},{5},{7}}=>2 {{1,8},{2,3},{4,5,7},{6}}=>3 {{1,4,8},{2,3},{5,7},{6}}=>2 {{1,4,5,6,7,8},{2,3}}=>2 {{1,2,4},{3},{5,6},{7,8}}=>2 {{1,2,4},{3},{5,8},{6,7}}=>2 {{1,2,4},{3},{5,6,8},{7}}=>2 {{1,5},{2,4},{3},{6,8},{7}}=>2 {{1,8},{2,4},{3},{5},{6},{7}}=>3 {{1,5,6},{2,4},{3},{7,8}}=>2 {{1,7,8},{2,4},{3},{5,6}}=>3 {{1,5,7},{2,4},{3},{6},{8}}=>2 {{1,5,8},{2,4},{3},{6,7}}=>2 {{1,6,7,8},{2,5},{3},{4}}=>3 {{1,7,8},{2,5,6},{3},{4}}=>3 {{1,8},{2,5,6,7},{3},{4}}=>3 {{1,6},{2,4,5},{3},{7,8}}=>2 {{1,8},{2,4,5},{3},{6,7}}=>3 {{1,2,6},{3},{4,5},{7,8}}=>3 {{1,7,8},{2,6},{3},{4,5}}=>3 {{1,8},{2,6,7},{3},{4,5}}=>3 {{1,2,8},{3},{4,5},{6,7}}=>3 {{1,2,6,8},{3},{4,5},{7}}=>3 {{1,2,4,6},{3},{5},{7,8}}=>2 {{1,7},{2,4,6},{3},{5},{8}}=>3 {{1,2,4,8},{3},{5},{6,7}}=>3 {{1,2,4,6,8},{3},{5},{7}}=>2 {{1,8},{2,4,7},{3},{5,6}}=>3 {{1,2,8},{3},{4,7},{5,6}}=>3 {{1,2,8},{3},{4,5,7},{6}}=>3 {{1,2,4,8},{3},{5,7},{6}}=>2 {{1,2,4,5,6,7,8},{3}}=>2 {{1,8},{2,3,4},{5},{6},{7}}=>3 {{1,6,8},{2,3,4},{5},{7}}=>3 {{1,6,8},{2,5},{3,4},{7}}=>2 {{1,8},{2,5,7},{3,4},{6}}=>3 {{1,2,5,6,7,8},{3,4}}=>2 {{1,6},{2,3,5},{4},{7,8}}=>2 {{1,8},{2,3,5},{4},{6,7}}=>3 {{1,6,8},{2,3,5},{4},{7}}=>2 {{1,2,6},{3,5},{4},{7,8}}=>2 {{1,7},{2,6},{3,5},{4},{8}}=>2 {{1,7,8},{2,6},{3,5},{4}}=>2 {{1,8},{2,6,7},{3,5},{4}}=>2 {{1,2,8},{3,5},{4},{6,7}}=>3 {{1,2,6,8},{3,5},{4},{7}}=>2 {{1,8},{2,7},{3,5,6},{4}}=>2 {{1,2,8},{3,5,6},{4},{7}}=>3 {{1,8},{2,3,7},{4},{5,6}}=>3 {{1,2,8},{3,7},{4},{5,6}}=>3 {{1,8},{2,3,5,7},{4},{6}}=>3 {{1,2,8},{3,5,7},{4},{6}}=>3 {{1,2,3,5,6,7},{4},{8}}=>2 {{1,2,3,5,6,7,8},{4}}=>2 {{1,8},{2,3,6},{4,5},{7}}=>3 {{1,8},{2,3,7},{4,5},{6}}=>3 {{1,2,3,6,7,8},{4,5}}=>2 {{1,8},{2,7},{3,4,6},{5}}=>2 {{1,8},{2,3,7},{4,6},{5}}=>2 {{1,2,8},{3,7},{4,6},{5}}=>2 {{1,2,3,4,7},{5},{6},{8}}=>3 {{1,2,3,4,6,7},{5},{8}}=>2 {{1,2,3,4,6,7,8},{5}}=>2 {{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}}=>2 {{1,2,3,4,5,7},{6},{8}}=>2 {{1,2,3,4,5,7,8},{6}}=>2 {{1,2,3,4,5,6,7},{8}}=>2 {{1,8},{2,3,4,5,6,7}}=>2 {{1,2,3,4,5,8},{6,7}}=>2 {{1,2,3,4,5,6,8},{7}}=>2 {{1,2,3,4,5,6,7,8}}=>1 {{1,3,5,6,7,8},{2,4}}=>2 {{1,3,4,6,7,8},{2,5}}=>2 {{1,2,4,6,7,8},{3,5}}=>2 {{1,3,4,5,7,8},{2,6}}=>2 {{1,2,4,5,7,8},{3,6}}=>2 {{1,2,3,5,7,8},{4,6}}=>2 {{1,3,4,5,6,8},{2,7}}=>2 {{1,2,4,5,6,8},{3,7}}=>2 {{1,2,3,5,6,8},{4,7}}=>2 {{1,2,3,4,6,8},{5,7}}=>2 {{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 {{1,5,7,8},{2,6},{3},{4}}=>4 {{1,3,7,8},{2,5},{4},{6}}=>3 {{1,5,6,8},{2,7},{3},{4}}=>4 {{1,2,4,8},{3,7},{5},{6}}=>4 {{1,3,6,8},{2,4},{5},{7}}=>3 {{1,2,5,8},{3,6},{4},{7}}=>3 {{1,3,4,8},{2,6},{5},{7}}=>3 {{1,2,4,8},{3,6},{5},{7}}=>3 {{1,4,6,7},{2,8},{3},{5}}=>3 {{1,3,6,7},{2,8},{4},{5}}=>3 {{1,4,5,7},{2,8},{3},{6}}=>3 {{1,3,5,7},{2,8},{4},{6}}=>3 {{1,2,5,7},{3,8},{4},{6}}=>3 {{1,3,4,7},{2,8},{5},{6}}=>3 {{1,2,4,7},{3,8},{5},{6}}=>3 {{1,2,5,6},{3,8},{4},{7}}=>3 {{1,3,5,7},{2,6},{4},{8}}=>2 {{1,3,5,7},{2,4},{6},{8}}=>2 {{1,4,7},{2,6,8},{3},{5}}=>3 {{1,2,7},{3,6,8},{4},{5}}=>3 {{1,2,7},{3,5,8},{4},{6}}=>3 {{1,3,7},{2,4,8},{5},{6}}=>4 {{1,4,6},{2,7,8},{3},{5}}=>3 {{1,3,6},{2,7,8},{4},{5}}=>3 {{1,2,4},{3,7,8},{5},{6}}=>3 {{1,2,6},{3,5,8},{4},{7}}=>3 {{1,3,6},{2,4,8},{5},{7}}=>3 {{1,3,5},{2,6,8},{4},{7}}=>2 {{1,3,4},{2,6,8},{5},{7}}=>3 {{1,2,4},{3,6,8},{5},{7}}=>3 {{1,4,8},{2,6},{3,7},{5}}=>4 {{1,3,8},{2,6},{4,7},{5}}=>3 {{1,2,8},{3,6},{4,7},{5}}=>3 {{1,4,8},{2,5},{3,7},{6}}=>4 {{1,3,8},{2,5},{4,7},{6}}=>3 {{1,2,8},{3,5},{4,7},{6}}=>3 {{1,4,8},{2,5},{3,6},{7}}=>3 {{1,4,7},{2,6},{3,8},{5}}=>3 {{1,3,7},{2,6},{4,8},{5}}=>4 {{1,2,7},{3,6},{4,8},{5}}=>3 {{1,4,7},{2,5},{3,8},{6}}=>3 {{1,3,7},{2,5},{4,8},{6}}=>4 {{1,2,7},{3,5},{4,8},{6}}=>4 {{1,4,6},{2,7},{3,8},{5}}=>3 {{1,3,6},{2,7},{4,8},{5}}=>3 {{1,2,6},{3,7},{4,8},{5}}=>4 {{1,3,5},{2,7},{4,8},{6}}=>4 {{1,2,5},{3,7},{4,8},{6}}=>4 {{1,3,4},{2,7},{5,8},{6}}=>3 {{1,2,4},{3,7},{5,8},{6}}=>3 {{1,3,6},{2,5},{4,8},{7}}=>3 {{1,2,6},{3,5},{4,8},{7}}=>3 {{1,3,5},{2,6},{4,8},{7}}=>3 {{1,2,5},{3,6},{4,8},{7}}=>3 {{1,3,4},{2,6},{5,8},{7}}=>3 {{1,2,4},{3,6},{5,8},{7}}=>3 {{1,3,5},{2,4},{6,8},{7}}=>2 {{1,4,7},{2,5},{3,6},{8}}=>3 {{1,3,7},{2,5},{4,6},{8}}=>3 {{1,3,5,8},{2},{4,6},{7}}=>3 {{1,3,5,7},{2},{4},{6,8}}=>2 {{1,5,7},{2,4},{3},{6,8}}=>2 {{1,5},{2,4,8},{3},{6,7}}=>3 {{1,5,8},{2,4},{3,6},{7}}=>3 {{1,6,8},{2,4},{3,5},{7}}=>2 {{1},{2,3,5,8},{4,6},{7}}=>3 {{1,5,8},{2,6},{3,4},{7}}=>3 {{1,4,8},{2,6},{3,5},{7}}=>3 {{1,4},{2,5,8},{3},{6,7}}=>3 {{1,4,7},{2,5},{3},{6,8}}=>3 {{1,4},{2},{3,6,7},{5,8}}=>3 {{1,4},{2},{3,6},{5,7,8}}=>3 {{1,4},{2},{3,7},{5,6,8}}=>3 {{1,4},{2},{3,5,8},{6,7}}=>3 {{1,5},{2},{3,4,8},{6,7}}=>3 {{1,2,5},{3},{4,7,8},{6}}=>3 {{1,2,5,7},{3},{4,8},{6}}=>3 {{1},{2,3,5,7},{4},{6,8}}=>2 {{1,5,7},{2},{3,4},{6,8}}=>3 {{1,4,7},{2},{3,5},{6,8}}=>3 {{1,4},{2},{3,8},{5,6,7}}=>3 {{1,4,6},{2},{3,8},{5,7}}=>3 {{1,4,6},{2},{3,7},{5,8}}=>3 {{1},{2,6},{3,4,7},{5,8}}=>3 {{1,6},{2,3,7},{4},{5,8}}=>4 {{1,2},{3,6,7},{4,8},{5}}=>3 {{1,2},{3,6},{4,7,8},{5}}=>3 {{1,6},{2,3},{4},{5,7,8}}=>3 {{1},{2,6},{3,4},{5,7,8}}=>3 {{1},{2,7},{3,4},{5,6,8}}=>3 {{1,7},{2,3},{4},{5,6,8}}=>3 {{1,2},{3,7},{4,6,8},{5}}=>2 {{1,2},{3,5,8},{4,7},{6}}=>3 {{1,7},{2,3,8},{4,5},{6}}=>4 {{1},{2,5},{3,4,8},{6,7}}=>3 {{1},{2,4},{3,5,8},{6,7}}=>2 {{1},{2,4},{3,7},{5,6,8}}=>3 {{1},{2,4},{3,6},{5,7,8}}=>3 {{1},{2,4},{3,6,7},{5,8}}=>3 {{1,3},{2,6,7},{4},{5,8}}=>3 {{1,3},{2,6},{4},{5,7,8}}=>3 {{1,3},{2,7},{4},{5,6,8}}=>3 {{1,3},{2,7,8},{4,5},{6}}=>3 {{1,3,8},{2,4,7},{5},{6}}=>3 {{1,4,8},{2,3,7},{5},{6}}=>4 {{1,4,7},{2,3,8},{5},{6}}=>3 {{1,3,7},{2,8},{4,5},{6}}=>3 {{1,3},{2,8},{4},{5,6,7}}=>3 {{1,3,6},{2,8},{4},{5,7}}=>3 {{1,3,6},{2,7},{4},{5,8}}=>3 {{1},{2,4,6},{3,7},{5,8}}=>3 {{1},{2,4,6},{3,8},{5,7}}=>2 {{1},{2,4},{3,8},{5,6,7}}=>3 {{1},{2,4,7},{3,5},{6,8}}=>3 {{1},{2,5,7},{3,4},{6,8}}=>2 {{1},{2,8},{3,4,6},{5,7}}=>2 {{1,8},{2,3,6},{4},{5,7}}=>3 {{1,2,6},{3,8},{4,7},{5}}=>3 {{1,7},{2,3,6},{4},{5,8}}=>3 {{1},{2,7},{3,4,6},{5,8}}=>3 {{1,2},{3,6,8},{4,7},{5}}=>3 {{1,2},{3,5,7},{4,8},{6}}=>2 {{1,2},{3,7},{4,5,8},{6}}=>3 {{1,4,8},{2,7},{3},{5,6}}=>3 {{1,3,7},{2,8},{4},{5,6}}=>3 {{1,3,7},{2,8},{4,6},{5}}=>2 {{1,3,7},{2},{4,5,8},{6}}=>3 {{1,7},{2,3},{4,5,8},{6}}=>3 {{1,7},{2,3,8},{4,6},{5}}=>3 {{1,7},{2,3,8},{4},{5,6}}=>4 {{1,7,8},{2,5},{3,6},{4}}=>3 {{1,7},{2,4,6,8},{3},{5}}=>3 {{1,7},{2,4,5},{3,8},{6}}=>4 {{1,4,6},{2,5},{3},{7,8}}=>3 {{1,5,7,8},{2},{3,6},{4}}=>3 {{1,5,8},{2,7},{3,6},{4}}=>3 {{1,8},{2,5,7},{3,6},{4}}=>3 {{1,5,8},{2,6,7},{3},{4}}=>4 {{1,4,5,7},{2},{3,8},{6}}=>3 {{1,3,5},{2,6},{4},{7,8}}=>2 {{1,3,6},{2,8},{4,7},{5}}=>3 {{1,4,6,8},{2},{3,7},{5}}=>3 {{1,8},{2,4,6},{3,7},{5}}=>2 {{1,4,8},{2,5},{3},{6,7}}=>3 {{1,3,5},{2,8},{4},{6,7}}=>3 {{1,5},{2,3,8},{4},{6,7}}=>3 {{1,8},{2,6},{3,4,7},{5}}=>3 {{1,6,8},{2},{3,4,7},{5}}=>3 {{1,6,8},{2,4},{3,7},{5}}=>4 {{1,6},{2,3,8},{4,7},{5}}=>3 {{1,6},{2,3,7,8},{4},{5}}=>4 {{1,5},{2,3,7},{4,8},{6}}=>4 {{1,5},{2,3,6},{4},{7,8}}=>3 {{1,5,7},{2,4},{3,8},{6}}=>3 {{1,6,7},{2,4,8},{3},{5}}=>3 {{1,6,8},{2,5,7},{3},{4}}=>3 {{1,6,8},{2,7},{3,5},{4}}=>3 {{1,6,8},{2,7},{3},{4,5}}=>4 {{1,6,7},{2,8},{3,4},{5}}=>4 {{1,5,7},{2},{3,4,8},{6}}=>3 {{1,7},{2,5},{3,4,8},{6}}=>4 {{1,7},{2,6,8},{3,4},{5}}=>3 {{1,4,8},{2,3,6},{5},{7}}=>3 {{1,5},{2,4,8},{3,7},{6}}=>4 {{1,5},{2,4,7},{3,8},{6}}=>3 {{1,5},{2,4,8},{3,6},{7}}=>3 {{1,6},{2,4,8},{3,5},{7}}=>3 {{1,6},{2,5},{3,4,8},{7}}=>3 {{1,6},{2,3,5},{4,8},{7}}=>3 {{1,5},{2,3,6},{4,8},{7}}=>3 {{1,5},{2,6},{3,4,8},{7}}=>3 {{1,4,8},{2,7},{3,6},{5}}=>3 {{1,4,7},{2,8},{3,6},{5}}=>3 {{1,4,6},{2,8},{3,7},{5}}=>3 {{1,4,7},{2,8},{3,5},{6}}=>3 {{1,5},{2,8},{3,4,7},{6}}=>3 {{1,5},{2,3,8},{4,7},{6}}=>3 {{1,2,5},{3,8},{4,7},{6}}=>3 {{1,5},{2,7},{3,4,8},{6}}=>4 {{1,4,8},{2,7},{3,5},{6}}=>4 {{1,7},{2,6},{3,4,8},{5}}=>3 {{1,7},{2,3,6},{4,8},{5}}=>3 {{1,8},{2,3,6},{4,7},{5}}=>3 {{1,8},{2,3,5},{4,7},{6}}=>3 {{1,8},{2,5},{3,4,7},{6}}=>3 {{1,8},{2,4,7},{3,5},{6}}=>3 {{1,8},{2,4,7},{3,6},{5}}=>3 {{1,7},{2,4,8},{3,6},{5}}=>3 {{1,3,5},{2,8},{4,7},{6}}=>3 {{1,3,8},{2,7},{4,6},{5}}=>3 {{1,6},{2,4,8},{3,7},{5}}=>4 {{1,6},{2,4,7},{3,8},{5}}=>3 {{1,7},{2,4,6},{3,8},{5}}=>3 {{1,7},{2,4,8},{3,5},{6}}=>4 {{1,7},{2,3,5},{4,8},{6}}=>4 {{1,2,7},{3,8},{4,6},{5}}=>3 {{1,7},{2,8},{3,4,6},{5}}=>3 {{1,6},{2,8},{3,4,7},{5}}=>3 {{1,6},{2,3,7},{4,8},{5}}=>4 {{1,6},{2,7},{3,4,8},{5}}=>4 {{1,3,5},{2},{4,6,8},{7}}=>2 {{1,3},{2,4,6,8},{5},{7}}=>2 {{1},{2,4,6,8},{3},{5,7}}=>2 {{1,3},{2},{4,6,8},{5,7}}=>2 {{1,3,6},{2},{4,8},{5,7}}=>3 {{1,3,6},{2},{4,7},{5,8}}=>3 {{1,3,5},{2},{4,7},{6,8}}=>3 {{1,3,5,7},{2},{4,6},{8}}=>2 {{1,3,7},{2},{4,6,8},{5}}=>2 {{1,3,7},{2},{4,6},{5,8}}=>3 {{1,3,5,7},{2},{4,8},{6}}=>2 {{1,3},{2,4,8},{5,7},{6}}=>2 {{1},{2,4,8},{3,5,7},{6}}=>2 {{1,4},{2,8},{3,5,7},{6}}=>3 {{1,4},{2,5,7},{3,8},{6}}=>3 {{1,3},{2,5,7},{4,8},{6}}=>3 {{1,3},{2,7},{4,6,8},{5}}=>3 {{1,3,7},{2,4,6},{5},{8}}=>2 {{1,7},{2,4,6},{3},{5,8}}=>3 {{1,5,7},{2,4,8},{3},{6}}=>2 {{1},{2,8},{3,5,7},{4,6}}=>2 {{1,7},{2,4,6},{3,5},{8}}=>2 {{1,4,7},{2,6},{3,5},{8}}=>3 {{1},{2,5,8},{3,7},{4,6}}=>3 {{1},{2,5,8},{3,6},{4,7}}=>3 {{1},{2,4,8},{3,6},{5,7}}=>3 {{1},{2,4,6,8},{3,5},{7}}=>2 {{1,4},{2,6,8},{3,5},{7}}=>3 {{1,4},{2,5},{3,6,8},{7}}=>3 {{1,3},{2,5},{4,6,8},{7}}=>3 {{1,5},{2,4,6,8},{3},{7}}=>2 {{1,5},{2,4},{3,6,8},{7}}=>3 {{1},{2,6,8},{3,5,7},{4}}=>2 {{1,6},{2,8},{3,5,7},{4}}=>3 {{1,6},{2,4,8},{3},{5,7}}=>3 {{1,6},{2,4,7},{3},{5,8}}=>3 {{1,5},{2,4,7},{3},{6,8}}=>3 {{1,5,7},{2,4,6},{3},{8}}=>2 {{1,5,7},{2,4},{3,6},{8}}=>3 {{1},{2,6,8},{3,5},{4,7}}=>3 {{1},{2,4,6,8},{3,7},{5}}=>2 {{1,6},{2,7},{3,5,8},{4}}=>3 {{1,3,5},{2,7},{4},{6,8}}=>3 {{1,7},{2,6,8},{3,5},{4}}=>2 {{1,7},{2,6},{3,5,8},{4}}=>3 {{1,2},{3,4,6},{5,8},{7}}=>3 {{1,2},{3,6},{4,5,8},{7}}=>3 {{1,2},{3,5,6},{4,8},{7}}=>3 {{1,2,5,6},{3},{4,8},{7}}=>3 {{1,2,6},{3},{4,5,8},{7}}=>3 {{1,6},{2,3},{4,5,8},{7}}=>3 {{1,5,6},{2,3},{4,8},{7}}=>3 {{1,5,6},{2,3,8},{4},{7}}=>3 {{1,5,6},{2,8},{3,4},{7}}=>3 {{1,5},{2,8},{3,4,6},{7}}=>3 {{1,5},{2,3,8},{4,6},{7}}=>3 {{1,6},{2,3,5,8},{4},{7}}=>3 {{1,2,5},{3,8},{4,6},{7}}=>3 {{1,2,4},{3,6},{5},{7,8}}=>3 {{1,2,4,6},{3},{5,8},{7}}=>3 {{1,2,4},{3,8},{5,7},{6}}=>3 {{1,2,4},{3,8},{5},{6,7}}=>3 {{1,4},{2,3,8},{5},{6,7}}=>3 {{1,3,4},{2,8},{5},{6,7}}=>3 {{1,3,4},{2,8},{5,7},{6}}=>3 {{1,4},{2,3,8},{5,7},{6}}=>3 {{1,4,6},{2,3},{5,8},{7}}=>3 {{1,4},{2,3,6},{5},{7,8}}=>3 {{1,4},{2,3,6,8},{5},{7}}=>3 {{1,4},{2,3,6},{5,8},{7}}=>3 {{1,8},{2,4,5},{3,7},{6}}=>3 {{1,3,8},{2,6},{4,5},{7}}=>3 {{1,3,4},{2,6},{5},{7,8}}=>3 {{1,6},{2,5,8},{3,4},{7}}=>3 {{1,6},{2,4,5},{3,8},{7}}=>3 {{1,4,5},{2,8},{3,6},{7}}=>3 {{1,3,8},{2,5,6},{4},{7}}=>3 {{1,3,8},{2,5},{4},{6,7}}=>3 {{1,5},{2,4},{3,7,8},{6}}=>3 {{1,5,6},{2,4},{3,8},{7}}=>3 {{1,4},{2,8},{3,5,6},{7}}=>3 {{1,4},{2,7,8},{3,5},{6}}=>3 {{1,4,7},{2,8},{3},{5,6}}=>3 {{1,5,7},{2,8},{3,4},{6}}=>3 {{1,5,7},{2,3,8},{4},{6}}=>3 {{1,2,5},{3,7},{4},{6,8}}=>3 {{1,5},{2,3,7},{4},{6,8}}=>3 {{1,4,5},{2,7},{3},{6,8}}=>3 {{1,4},{2,7},{3},{5,6,8}}=>3 {{1,4},{2,6,7},{3},{5,8}}=>3 {{1,4},{2,6},{3},{5,7,8}}=>3 {{1,6},{2,5,7,8},{3},{4}}=>3 {{1,6,7},{2,5,8},{3},{4}}=>3 {{1,7},{2,5,6,8},{3},{4}}=>3 {{1,7},{2,6,8},{3},{4,5}}=>3 {{1,7},{2,3,6,8},{4},{5}}=>3 {{1,2,8},{3,6},{4},{5,7}}=>3 {{1,8},{2,6},{3},{4,5,7}}=>3 {{1,8},{2,5,6},{3},{4,7}}=>3 {{1,8},{2,5},{3},{4,6,7}}=>3 {{1,7,8},{2,5},{3},{4,6}}=>3 {{1,8},{2,4},{3,6,7},{5}}=>3 {{1,7,8},{2,4},{3,6},{5}}=>3 {{1,4},{2,3,7},{5,8},{6}}=>3 {{1,3},{2,7},{4,5,8},{6}}=>3 {{1,3},{2,6,7},{4,8},{5}}=>3 {{1,3},{2,6},{4,7,8},{5}}=>3 {{1,6},{2,4,7,8},{3},{5}}=>3 {{1,7},{2,4,8},{3},{5,6}}=>3 {{1,7},{2,4,5,8},{3},{6}}=>3 {{1,7},{2,5,8},{3,4},{6}}=>3 {{1,7},{2,3,5,8},{4},{6}}=>3 {{1,2,7},{3},{4,6},{5,8}}=>3 {{1,7},{2},{3,4,6},{5,8}}=>3 {{1,7},{2},{3,6},{4,5,8}}=>3 {{1,7},{2},{3,5,6},{4,8}}=>3 {{1,6,7},{2},{3,5},{4,8}}=>3 {{1,6},{2},{3,5},{4,7,8}}=>3 {{1,5},{2},{3,7,8},{4,6}}=>3 {{1,5},{2},{3,8},{4,6,7}}=>3 {{1,5,6},{2},{3,8},{4,7}}=>3 {{1,6},{2},{3,8},{4,5,7}}=>3 {{1,6},{2},{3,4,8},{5,7}}=>3 {{1,2,6},{3},{4,8},{5,7}}=>3 {{1,2,6,8},{3},{4,7},{5}}=>3 {{1,6,8},{2,3},{4,7},{5}}=>3 {{1,6,8},{2},{3,7},{4,5}}=>3 {{1,5,6,8},{2},{3,7},{4}}=>3 {{1,5,8},{2},{3,6,7},{4}}=>3 {{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},{2,4},{3},{5,7,8}}=>3 {{1,7},{2,4,5},{3},{6,8}}=>3 {{1,8},{2,4,5},{3,6},{7}}=>3 {{1,8},{2,4},{3,5,6},{7}}=>3 {{1,5,8},{2,3},{4,6},{7}}=>3 {{1,8},{2,5},{3,4,6},{7}}=>3 {{1,4,8},{2},{3,5,6},{7}}=>3 {{1,4},{2},{3,6,8},{5,7}}=>3 {{1,5,7},{2,3},{4},{6,8}}=>3 {{1,4,6},{2},{3},{5,7,8}}=>3 {{1},{2,5,6},{3,7},{4,8}}=>3 {{1},{2,5,6},{3},{4,7,8}}=>3 {{1},{2,5},{3,7},{4,6,8}}=>3 {{1},{2},{3,6,7},{4,5,8}}=>2 {{1},{2,3,6,7},{4},{5,8}}=>3 {{1},{2,3,6},{4,8},{5,7}}=>3 {{1},{2},{3,4,6,8},{5,7}}=>2 {{1},{2},{3,6},{4,5,7,8}}=>2 {{1},{2,5},{3},{4,6,7,8}}=>3 {{1},{2,5},{3,6},{4,7,8}}=>3 {{1},{2,5},{3,6,7},{4,8}}=>3 {{1},{2},{3,5,6,7},{4,8}}=>2 {{1},{2},{3,5,6},{4,7,8}}=>2 {{1},{2},{3,5},{4,6,7,8}}=>2 {{1},{2,4,8},{3,5},{6,7}}=>3 {{1},{2,4},{3,6,8},{5,7}}=>3 {{1},{2,4,7},{3,6},{5,8}}=>3 {{1,3},{2,8},{4,5,7},{6}}=>3 {{1,3},{2,4,7,8},{5},{6}}=>3 {{1,7},{2,3,4,8},{5},{6}}=>4 {{1},{2,4,7},{3},{5,6,8}}=>2 {{1,7},{2},{3,4,5},{6,8}}=>3 {{1},{2,3,7},{4,8},{5,6}}=>3 {{1},{2},{3,7},{4,5,6,8}}=>2 {{1},{2},{3,5,7},{4,6,8}}=>2 {{1},{2,6},{3,5},{4,7,8}}=>3 {{1},{2,6},{3,5,7},{4,8}}=>2 {{1,5},{2},{3,6,7},{4,8}}=>3 {{1,5},{2},{3,6},{4,7,8}}=>3 {{1,5},{2},{3},{4,6,7,8}}=>3 {{1},{2,6},{3},{4,5,7,8}}=>3 {{1,6},{2},{3,4},{5,7,8}}=>3 {{1,2,6},{3},{4,7,8},{5}}=>3 {{1,6},{2},{3,4,7},{5,8}}=>3 {{1},{2,6},{3,7},{4,5,8}}=>3 {{1,5},{2},{3,7},{4,6,8}}=>3 {{1,5},{2,6},{3},{4,7,8}}=>4 {{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},{7,9},{8}}=>2 {{1},{2},{3},{4},{5},{6,9},{7},{8}}=>3 {{1},{2},{3},{4},{5,9},{6},{7},{8}}=>3 {{1},{2},{3},{4,9},{5},{6},{7},{8}}=>3 {{1},{2},{3,9},{4},{5},{6},{7},{8}}=>3 {{1},{2,9},{3},{4},{5},{6},{7},{8}}=>3 {{1,9},{2},{3},{4},{5},{6},{7},{8}}=>3 {{1},{2},{3},{4},{5},{6},{7,8,9}}=>2 {{1},{2},{3},{4},{5},{6,9},{7,8}}=>2 {{1},{2},{3},{4},{5,9},{6,7},{8}}=>3 {{1},{2},{3},{4,9},{5,6},{7},{8}}=>3 {{1},{2},{3,9},{4,5},{6},{7},{8}}=>3 {{1},{2,9},{3,4},{5},{6},{7},{8}}=>3 {{1,9},{2,3},{4},{5},{6},{7},{8}}=>3 {{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}}=>2 {{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}}=>2 {{1},{2,3,4,5,6,8,9},{7}}=>2 {{1,2},{3,4},{5,6},{7,8},{9,10}}=>2 {{1,4},{2,3},{5,6},{7,8},{9,10}}=>2 {{1,6},{2,3},{4,5},{7,8},{9,10}}=>3 {{1,8},{2,3},{4,5},{6,7},{9,10}}=>3 {{1,10},{2,3},{4,5},{6,7},{8,9}}=>3 {{1,2},{3,6},{4,5},{7,8},{9,10}}=>2 {{1,6},{2,5},{3,4},{7,8},{9,10}}=>2 {{1,8},{2,5},{3,4},{6,7},{9,10}}=>3 {{1,10},{2,5},{3,4},{6,7},{8,9}}=>3 {{1,2},{3,8},{4,5},{6,7},{9,10}}=>3 {{1,8},{2,7},{3,4},{5,6},{9,10}}=>3 {{1,10},{2,7},{3,4},{5,6},{8,9}}=>3 {{1,2},{3,10},{4,5},{6,7},{8,9}}=>3 {{1,10},{2,9},{3,4},{5,6},{7,8}}=>3 {{1,2},{3,4},{5,8},{6,7},{9,10}}=>2 {{1,4},{2,3},{5,8},{6,7},{9,10}}=>2 {{1,8},{2,3},{4,7},{5,6},{9,10}}=>3 {{1,10},{2,3},{4,7},{5,6},{8,9}}=>3 {{1,2},{3,8},{4,7},{5,6},{9,10}}=>2 {{1,8},{2,7},{3,6},{4,5},{9,10}}=>2 {{1,10},{2,7},{3,6},{4,5},{8,9}}=>3 {{1,2},{3,10},{4,7},{5,6},{8,9}}=>3 {{1,10},{2,9},{3,6},{4,5},{7,8}}=>3 {{1,2},{3,4},{5,10},{6,7},{8,9}}=>3 {{1,4},{2,3},{5,10},{6,7},{8,9}}=>3 {{1,10},{2,3},{4,9},{5,6},{7,8}}=>3 {{1,2},{3,10},{4,9},{5,6},{7,8}}=>3 {{1,10},{2,9},{3,8},{4,5},{6,7}}=>3 {{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}}=>3 {{1,10},{2,3},{4,5},{6,9},{7,8}}=>3 {{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}}=>3 {{1,2},{3,10},{4,5},{6,9},{7,8}}=>3 {{1,10},{2,9},{3,4},{5,8},{6,7}}=>3 {{1,2},{3,4},{5,10},{6,9},{7,8}}=>2 {{1,4},{2,3},{5,10},{6,9},{7,8}}=>2 {{1,10},{2,3},{4,9},{5,8},{6,7}}=>3 {{1,2},{3,10},{4,9},{5,8},{6,7}}=>2 {{1,10},{2,9},{3,8},{4,7},{5,6}}=>2 {{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},{8,10},{9}}=>2 {{1},{2},{3},{4},{5},{6},{7,10},{8},{9}}=>3 {{1},{2},{3},{4},{5},{6,10},{7},{8},{9}}=>3 {{1},{2},{3},{4},{5,10},{6},{7},{8},{9}}=>3 {{1},{2},{3},{4,10},{5},{6},{7},{8},{9}}=>3 {{1},{2},{3,10},{4},{5},{6},{7},{8},{9}}=>3 {{1},{2,10},{3},{4},{5},{6},{7},{8},{9}}=>3 {{1,10},{2},{3},{4},{5},{6},{7},{8},{9}}=>3 {{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}}=>2 {{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}}=>2 {{1,2},{3,4},{5,6},{7,8},{9,12},{10,11}}=>2 {{1,2},{3,4},{5,6},{7,10},{8,9},{11,12}}=>2 {{1,2},{3,4},{5,6},{7,12},{8,9},{10,11}}=>3 {{1,2},{3,4},{5,6},{7,12},{8,11},{9,10}}=>2 {{1,2},{3,4},{5,8},{6,7},{9,10},{11,12}}=>2 {{1,2},{3,4},{5,8},{6,7},{9,12},{10,11}}=>2 {{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}}=>3 {{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}}=>2 {{1,2},{3,4},{5,12},{6,9},{7,8},{10,11}}=>3 {{1,2},{3,4},{5,12},{6,11},{7,8},{9,10}}=>3 {{1,2},{3,4},{5,12},{6,11},{7,10},{8,9}}=>2 {{1,2},{3,6},{4,5},{7,8},{9,10},{11,12}}=>2 {{1,2},{3,6},{4,5},{7,8},{9,12},{10,11}}=>2 {{1,2},{3,6},{4,5},{7,10},{8,9},{11,12}}=>2 {{1,2},{3,6},{4,5},{7,12},{8,9},{10,11}}=>3 {{1,2},{3,6},{4,5},{7,12},{8,11},{9,10}}=>2 {{1,2},{3,8},{4,5},{6,7},{9,10},{11,12}}=>3 {{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}}=>3 {{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}}=>3 {{1,2},{3,12},{4,5},{6,11},{7,8},{9,10}}=>3 {{1,2},{3,12},{4,5},{6,11},{7,10},{8,9}}=>3 {{1,2},{3,8},{4,7},{5,6},{9,10},{11,12}}=>2 {{1,2},{3,8},{4,7},{5,6},{9,12},{10,11}}=>2 {{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}}=>3 {{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}}=>3 {{1,2},{3,12},{4,11},{5,6},{7,8},{9,10}}=>3 {{1,2},{3,12},{4,11},{5,6},{7,10},{8,9}}=>3 {{1,2},{3,10},{4,9},{5,8},{6,7},{11,12}}=>2 {{1,2},{3,12},{4,9},{5,8},{6,7},{10,11}}=>3 {{1,2},{3,12},{4,11},{5,8},{6,7},{9,10}}=>3 {{1,2},{3,12},{4,11},{5,10},{6,7},{8,9}}=>3 {{1,2},{3,12},{4,11},{5,10},{6,9},{7,8}}=>2 {{1,4},{2,3},{5,6},{7,8},{9,10},{11,12}}=>2 {{1,4},{2,3},{5,6},{7,8},{9,12},{10,11}}=>2 {{1,4},{2,3},{5,6},{7,10},{8,9},{11,12}}=>2 {{1,4},{2,3},{5,6},{7,12},{8,9},{10,11}}=>3 {{1,4},{2,3},{5,6},{7,12},{8,11},{9,10}}=>2 {{1,4},{2,3},{5,8},{6,7},{9,10},{11,12}}=>2 {{1,4},{2,3},{5,8},{6,7},{9,12},{10,11}}=>2 {{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}}=>3 {{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}}=>2 {{1,4},{2,3},{5,12},{6,9},{7,8},{10,11}}=>3 {{1,4},{2,3},{5,12},{6,11},{7,8},{9,10}}=>3 {{1,4},{2,3},{5,12},{6,11},{7,10},{8,9}}=>2 {{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}}=>3 {{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}}=>3 {{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}}=>3 {{1,10},{2,3},{4,5},{6,7},{8,9},{11,12}}=>3 {{1,12},{2,3},{4,5},{6,7},{8,9},{10,11}}=>3 {{1,12},{2,3},{4,5},{6,7},{8,11},{9,10}}=>3 {{1,10},{2,3},{4,5},{6,9},{7,8},{11,12}}=>3 {{1,12},{2,3},{4,5},{6,9},{7,8},{10,11}}=>3 {{1,12},{2,3},{4,5},{6,11},{7,8},{9,10}}=>3 {{1,12},{2,3},{4,5},{6,11},{7,10},{8,9}}=>3 {{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}}=>3 {{1,10},{2,3},{4,7},{5,6},{8,9},{11,12}}=>3 {{1,12},{2,3},{4,7},{5,6},{8,9},{10,11}}=>3 {{1,12},{2,3},{4,7},{5,6},{8,11},{9,10}}=>3 {{1,10},{2,3},{4,9},{5,6},{7,8},{11,12}}=>3 {{1,12},{2,3},{4,9},{5,6},{7,8},{10,11}}=>3 {{1,12},{2,3},{4,11},{5,6},{7,8},{9,10}}=>3 {{1,12},{2,3},{4,11},{5,6},{7,10},{8,9}}=>3 {{1,10},{2,3},{4,9},{5,8},{6,7},{11,12}}=>3 {{1,12},{2,3},{4,9},{5,8},{6,7},{10,11}}=>3 {{1,12},{2,3},{4,11},{5,8},{6,7},{9,10}}=>3 {{1,12},{2,3},{4,11},{5,10},{6,7},{8,9}}=>3 {{1,12},{2,3},{4,11},{5,10},{6,9},{7,8}}=>3 {{1,6},{2,5},{3,4},{7,8},{9,10},{11,12}}=>2 {{1,6},{2,5},{3,4},{7,8},{9,12},{10,11}}=>2 {{1,6},{2,5},{3,4},{7,10},{8,9},{11,12}}=>2 {{1,6},{2,5},{3,4},{7,12},{8,9},{10,11}}=>3 {{1,6},{2,5},{3,4},{7,12},{8,11},{9,10}}=>2 {{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}}=>3 {{1,10},{2,5},{3,4},{6,7},{8,9},{11,12}}=>3 {{1,12},{2,5},{3,4},{6,7},{8,9},{10,11}}=>3 {{1,12},{2,5},{3,4},{6,7},{8,11},{9,10}}=>3 {{1,10},{2,5},{3,4},{6,9},{7,8},{11,12}}=>3 {{1,12},{2,5},{3,4},{6,9},{7,8},{10,11}}=>3 {{1,12},{2,5},{3,4},{6,11},{7,8},{9,10}}=>3 {{1,12},{2,5},{3,4},{6,11},{7,10},{8,9}}=>3 {{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}}=>3 {{1,10},{2,7},{3,4},{5,6},{8,9},{11,12}}=>3 {{1,12},{2,7},{3,4},{5,6},{8,9},{10,11}}=>3 {{1,12},{2,7},{3,4},{5,6},{8,11},{9,10}}=>3 {{1,10},{2,9},{3,4},{5,6},{7,8},{11,12}}=>3 {{1,12},{2,9},{3,4},{5,6},{7,8},{10,11}}=>3 {{1,12},{2,11},{3,4},{5,6},{7,8},{9,10}}=>3 {{1,12},{2,11},{3,4},{5,6},{7,10},{8,9}}=>3 {{1,10},{2,9},{3,4},{5,8},{6,7},{11,12}}=>3 {{1,12},{2,9},{3,4},{5,8},{6,7},{10,11}}=>3 {{1,12},{2,11},{3,4},{5,8},{6,7},{9,10}}=>3 {{1,12},{2,11},{3,4},{5,10},{6,7},{8,9}}=>3 {{1,12},{2,11},{3,4},{5,10},{6,9},{7,8}}=>3 {{1,8},{2,7},{3,6},{4,5},{9,10},{11,12}}=>2 {{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}}=>3 {{1,12},{2,7},{3,6},{4,5},{8,9},{10,11}}=>3 {{1,12},{2,7},{3,6},{4,5},{8,11},{9,10}}=>3 {{1,10},{2,9},{3,6},{4,5},{7,8},{11,12}}=>3 {{1,12},{2,9},{3,6},{4,5},{7,8},{10,11}}=>3 {{1,12},{2,11},{3,6},{4,5},{7,8},{9,10}}=>3 {{1,12},{2,11},{3,6},{4,5},{7,10},{8,9}}=>3 {{1,10},{2,9},{3,8},{4,5},{6,7},{11,12}}=>3 {{1,12},{2,9},{3,8},{4,5},{6,7},{10,11}}=>3 {{1,12},{2,11},{3,8},{4,5},{6,7},{9,10}}=>3 {{1,12},{2,11},{3,10},{4,5},{6,7},{8,9}}=>3 {{1,12},{2,11},{3,10},{4,5},{6,9},{7,8}}=>3 {{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}}=>3 {{1,12},{2,11},{3,8},{4,7},{5,6},{9,10}}=>3 {{1,12},{2,11},{3,10},{4,7},{5,6},{8,9}}=>3 {{1,12},{2,11},{3,10},{4,9},{5,6},{7,8}}=>3 {{1,12},{2,11},{3,10},{4,9},{5,8},{6,7}}=>2
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Description
The length of the longest partition in the vacillating tableau corresponding to a set partition.
To a set partition $\pi$ of $\{1,\dots,r\}$ with at most $n$ blocks we associate a vacillating tableau, following [1], as follows: create a triangular growth diagram by labelling the columns of a triangular grid with row lengths $r-1, \dots, 0$ from left to right $1$ to $r$, and the rows from the shortest to the longest $1$ to $r$. For each arc $(i,j)$ in the standard representation of $\pi$, place a cross into the cell in column $i$ and row $j$.
Next we label the corners of the first column beginning with the corners of the shortest row. The first corner is labelled with the partition $(n)$. If there is a cross in the row separating this corner from the next, label the next corner with the same partition, otherwise with the partition smaller by one. Do the same with the corners of the first row.
Finally, apply Fomin's local rules, to obtain the partitions along the diagonal. These will alternate in size between $n$ and $n-1$.
This statistic is the length of the longest partition on the diagonal of the diagram.
References
[1] Benkart, G., Halverson, T., Harman, N. Dimensions of irreducible modules for partition algebras and tensor power multiplicities for symmetric and alternating groups arXiv:1605.06543
Code
def from_partition(p, n):
    """
    sage: G = from_partition([[1,3,4],[2]], 4); G
      0  0  1
      1  0
      0
    sage: G.in_labels()
    [[3], [2], [2], [2], [2], [3], [3]]
    sage: G.out_labels()
    [[3], [3, 1], [3], [3, 1], [3], [4], [3]]

    sage: G = from_partition([[3,4],[1,2]], 4); G
    0  0  1
    0  0
    1
    sage: G.in_labels()
    [[3], [3], [2], [2], [2], [3], [3]]
    sage: G.out_labels()
    [[3], [4], [3], [3, 1], [3], [4], [3]]

    sage: G = from_partition([[3,4],[2],[1]], 4); G
    0  0  1
    0  0
    0
    sage: G.in_labels()
    [[3], [2], [1], [1], [2], [3], [3]]
    sage: G.out_labels()
    [[3], [3, 1], [2, 1], [3, 1], [3], [4], [3]]

    """
    p = SetPartition(p)
    r = p.size()
    filling = {(i-1, r-j): 1 for (i,j) in p.arcs()}
    shape = Partition([r-i-1 for i in range(r-1)])
    labels = [[n-1]]
    la = n-1
    O = [i for i,_ in p.arcs()]
    C = [j for _,j in p.arcs()]
    for j in range(2,r+1):
        if j not in C:
            la -= 1
        labels += [[la]]
    for i in range(1,r):
        if i not in O:
            la += 1
        labels += [[la]]
    return GrowthDiagram.rules.RSK()(filling, shape, labels)


def statistic(p):
    return max(len(mu) for mu in from_partition(p, p.size()).out_labels())
Created
May 10, 2017 at 22:55 by Martin Rubey
Updated
Nov 11, 2021 at 12:50 by Martin Rubey