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Identifier
Values
=>
Cc0009;cc-rep
{{1,2}}=>0 {{1},{2}}=>0 {{1,2,3}}=>0 {{1,2},{3}}=>1 {{1,3},{2}}=>2 {{1},{2,3}}=>0 {{1},{2},{3}}=>0 {{1,2,3,4}}=>0 {{1,2,3},{4}}=>2 {{1,2,4},{3}}=>3 {{1,2},{3,4}}=>1 {{1,2},{3},{4}}=>2 {{1,3,4},{2}}=>3 {{1,3},{2,4}}=>2 {{1,3},{2},{4}}=>3 {{1,4},{2,3}}=>2 {{1},{2,3,4}}=>0 {{1},{2,3},{4}}=>1 {{1,4},{2},{3}}=>3 {{1},{2,4},{3}}=>3 {{1},{2},{3,4}}=>0 {{1},{2},{3},{4}}=>0 {{1,2,3,4,5}}=>0 {{1,2,3,4},{5}}=>3 {{1,2,3,5},{4}}=>4 {{1,2,3},{4,5}}=>2 {{1,2,3},{4},{5}}=>4 {{1,2,4,5},{3}}=>4 {{1,2,4},{3,5}}=>3 {{1,2,4},{3},{5}}=>5 {{1,2,5},{3,4}}=>3 {{1,2},{3,4,5}}=>1 {{1,2},{3,4},{5}}=>3 {{1,2,5},{3},{4}}=>5 {{1,2},{3,5},{4}}=>5 {{1,2},{3},{4,5}}=>2 {{1,2},{3},{4},{5}}=>3 {{1,3,4,5},{2}}=>4 {{1,3,4},{2,5}}=>3 {{1,3,4},{2},{5}}=>5 {{1,3,5},{2,4}}=>3 {{1,3},{2,4,5}}=>2 {{1,3},{2,4},{5}}=>4 {{1,3,5},{2},{4}}=>5 {{1,3},{2,5},{4}}=>6 {{1,3},{2},{4,5}}=>3 {{1,3},{2},{4},{5}}=>4 {{1,4,5},{2,3}}=>3 {{1,4},{2,3,5}}=>2 {{1,4},{2,3},{5}}=>4 {{1,5},{2,3,4}}=>2 {{1},{2,3,4,5}}=>0 {{1},{2,3,4},{5}}=>2 {{1,5},{2,3},{4}}=>4 {{1},{2,3,5},{4}}=>4 {{1},{2,3},{4,5}}=>1 {{1},{2,3},{4},{5}}=>2 {{1,4,5},{2},{3}}=>5 {{1,4},{2,5},{3}}=>6 {{1,4},{2},{3,5}}=>3 {{1,4},{2},{3},{5}}=>4 {{1,5},{2,4},{3}}=>6 {{1},{2,4,5},{3}}=>4 {{1},{2,4},{3,5}}=>3 {{1},{2,4},{3},{5}}=>4 {{1,5},{2},{3,4}}=>3 {{1},{2,5},{3,4}}=>3 {{1},{2},{3,4,5}}=>0 {{1},{2},{3,4},{5}}=>1 {{1,5},{2},{3},{4}}=>4 {{1},{2,5},{3},{4}}=>4 {{1},{2},{3,5},{4}}=>4 {{1},{2},{3},{4,5}}=>0 {{1},{2},{3},{4},{5}}=>0 {{1,2,3,4,5,6}}=>0 {{1,2,3,4,5},{6}}=>4 {{1,2,3,4,6},{5}}=>5 {{1,2,3,4},{5,6}}=>3 {{1,2,3,4},{5},{6}}=>6 {{1,2,3,5,6},{4}}=>5 {{1,2,3,5},{4,6}}=>4 {{1,2,3,5},{4},{6}}=>7 {{1,2,3,6},{4,5}}=>4 {{1,2,3},{4,5,6}}=>2 {{1,2,3},{4,5},{6}}=>5 {{1,2,3,6},{4},{5}}=>7 {{1,2,3},{4,6},{5}}=>7 {{1,2,3},{4},{5,6}}=>4 {{1,2,3},{4},{5},{6}}=>6 {{1,2,4,5,6},{3}}=>5 {{1,2,4,5},{3,6}}=>4 {{1,2,4,5},{3},{6}}=>7 {{1,2,4,6},{3,5}}=>4 {{1,2,4},{3,5,6}}=>3 {{1,2,4},{3,5},{6}}=>6 {{1,2,4,6},{3},{5}}=>7 {{1,2,4},{3,6},{5}}=>8 {{1,2,4},{3},{5,6}}=>5 {{1,2,4},{3},{5},{6}}=>7 {{1,2,5,6},{3,4}}=>4 {{1,2,5},{3,4,6}}=>3 {{1,2,5},{3,4},{6}}=>6 {{1,2,6},{3,4,5}}=>3 {{1,2},{3,4,5,6}}=>1 {{1,2},{3,4,5},{6}}=>4 {{1,2,6},{3,4},{5}}=>6 {{1,2},{3,4,6},{5}}=>6 {{1,2},{3,4},{5,6}}=>3 {{1,2},{3,4},{5},{6}}=>5 {{1,2,5,6},{3},{4}}=>7 {{1,2,5},{3,6},{4}}=>8 {{1,2,5},{3},{4,6}}=>5 {{1,2,5},{3},{4},{6}}=>7 {{1,2,6},{3,5},{4}}=>8 {{1,2},{3,5,6},{4}}=>6 {{1,2},{3,5},{4,6}}=>5 {{1,2},{3,5},{4},{6}}=>7 {{1,2,6},{3},{4,5}}=>5 {{1,2},{3,6},{4,5}}=>5 {{1,2},{3},{4,5,6}}=>2 {{1,2},{3},{4,5},{6}}=>4 {{1,2,6},{3},{4},{5}}=>7 {{1,2},{3,6},{4},{5}}=>7 {{1,2},{3},{4,6},{5}}=>7 {{1,2},{3},{4},{5,6}}=>3 {{1,2},{3},{4},{5},{6}}=>4 {{1,3,4,5,6},{2}}=>5 {{1,3,4,5},{2,6}}=>4 {{1,3,4,5},{2},{6}}=>7 {{1,3,4,6},{2,5}}=>4 {{1,3,4},{2,5,6}}=>3 {{1,3,4},{2,5},{6}}=>6 {{1,3,4,6},{2},{5}}=>7 {{1,3,4},{2,6},{5}}=>8 {{1,3,4},{2},{5,6}}=>5 {{1,3,4},{2},{5},{6}}=>7 {{1,3,5,6},{2,4}}=>4 {{1,3,5},{2,4,6}}=>3 {{1,3,5},{2,4},{6}}=>6 {{1,3,6},{2,4,5}}=>3 {{1,3},{2,4,5,6}}=>2 {{1,3},{2,4,5},{6}}=>5 {{1,3,6},{2,4},{5}}=>6 {{1,3},{2,4,6},{5}}=>7 {{1,3},{2,4},{5,6}}=>4 {{1,3},{2,4},{5},{6}}=>6 {{1,3,5,6},{2},{4}}=>7 {{1,3,5},{2,6},{4}}=>8 {{1,3,5},{2},{4,6}}=>5 {{1,3,5},{2},{4},{6}}=>7 {{1,3,6},{2,5},{4}}=>8 {{1,3},{2,5,6},{4}}=>7 {{1,3},{2,5},{4,6}}=>6 {{1,3},{2,5},{4},{6}}=>8 {{1,3,6},{2},{4,5}}=>5 {{1,3},{2,6},{4,5}}=>6 {{1,3},{2},{4,5,6}}=>3 {{1,3},{2},{4,5},{6}}=>5 {{1,3,6},{2},{4},{5}}=>7 {{1,3},{2,6},{4},{5}}=>8 {{1,3},{2},{4,6},{5}}=>8 {{1,3},{2},{4},{5,6}}=>4 {{1,3},{2},{4},{5},{6}}=>5 {{1,4,5,6},{2,3}}=>4 {{1,4,5},{2,3,6}}=>3 {{1,4,5},{2,3},{6}}=>6 {{1,4,6},{2,3,5}}=>3 {{1,4},{2,3,5,6}}=>2 {{1,4},{2,3,5},{6}}=>5 {{1,4,6},{2,3},{5}}=>6 {{1,4},{2,3,6},{5}}=>7 {{1,4},{2,3},{5,6}}=>4 {{1,4},{2,3},{5},{6}}=>6 {{1,5,6},{2,3,4}}=>3 {{1,5},{2,3,4,6}}=>2 {{1,5},{2,3,4},{6}}=>5 {{1,6},{2,3,4,5}}=>2 {{1},{2,3,4,5,6}}=>0 {{1},{2,3,4,5},{6}}=>3 {{1,6},{2,3,4},{5}}=>5 {{1},{2,3,4,6},{5}}=>5 {{1},{2,3,4},{5,6}}=>2 {{1},{2,3,4},{5},{6}}=>4 {{1,5,6},{2,3},{4}}=>6 {{1,5},{2,3,6},{4}}=>7 {{1,5},{2,3},{4,6}}=>4 {{1,5},{2,3},{4},{6}}=>6 {{1,6},{2,3,5},{4}}=>7 {{1},{2,3,5,6},{4}}=>5 {{1},{2,3,5},{4,6}}=>4 {{1},{2,3,5},{4},{6}}=>6 {{1,6},{2,3},{4,5}}=>4 {{1},{2,3,6},{4,5}}=>4 {{1},{2,3},{4,5,6}}=>1 {{1},{2,3},{4,5},{6}}=>3 {{1,6},{2,3},{4},{5}}=>6 {{1},{2,3,6},{4},{5}}=>6 {{1},{2,3},{4,6},{5}}=>6 {{1},{2,3},{4},{5,6}}=>2 {{1},{2,3},{4},{5},{6}}=>3 {{1,4,5,6},{2},{3}}=>7 {{1,4,5},{2,6},{3}}=>8 {{1,4,5},{2},{3,6}}=>5 {{1,4,5},{2},{3},{6}}=>7 {{1,4,6},{2,5},{3}}=>8 {{1,4},{2,5,6},{3}}=>7 {{1,4},{2,5},{3,6}}=>6 {{1,4},{2,5},{3},{6}}=>8 {{1,4,6},{2},{3,5}}=>5 {{1,4},{2,6},{3,5}}=>6 {{1,4},{2},{3,5,6}}=>3 {{1,4},{2},{3,5},{6}}=>5 {{1,4,6},{2},{3},{5}}=>7 {{1,4},{2,6},{3},{5}}=>8 {{1,4},{2},{3,6},{5}}=>8 {{1,4},{2},{3},{5,6}}=>4 {{1,4},{2},{3},{5},{6}}=>5 {{1,5,6},{2,4},{3}}=>8 {{1,5},{2,4,6},{3}}=>7 {{1,5},{2,4},{3,6}}=>6 {{1,5},{2,4},{3},{6}}=>8 {{1,6},{2,4,5},{3}}=>7 {{1},{2,4,5,6},{3}}=>5 {{1},{2,4,5},{3,6}}=>4 {{1},{2,4,5},{3},{6}}=>6 {{1,6},{2,4},{3,5}}=>6 {{1},{2,4,6},{3,5}}=>4 {{1},{2,4},{3,5,6}}=>3 {{1},{2,4},{3,5},{6}}=>5 {{1,6},{2,4},{3},{5}}=>8 {{1},{2,4,6},{3},{5}}=>6 {{1},{2,4},{3,6},{5}}=>8 {{1},{2,4},{3},{5,6}}=>4 {{1},{2,4},{3},{5},{6}}=>5 {{1,5,6},{2},{3,4}}=>5 {{1,5},{2,6},{3,4}}=>6 {{1,5},{2},{3,4,6}}=>3 {{1,5},{2},{3,4},{6}}=>5 {{1,6},{2,5},{3,4}}=>6 {{1},{2,5,6},{3,4}}=>4 {{1},{2,5},{3,4,6}}=>3 {{1},{2,5},{3,4},{6}}=>5 {{1,6},{2},{3,4,5}}=>3 {{1},{2,6},{3,4,5}}=>3 {{1},{2},{3,4,5,6}}=>0 {{1},{2},{3,4,5},{6}}=>2 {{1,6},{2},{3,4},{5}}=>5 {{1},{2,6},{3,4},{5}}=>5 {{1},{2},{3,4,6},{5}}=>5 {{1},{2},{3,4},{5,6}}=>1 {{1},{2},{3,4},{5},{6}}=>2 {{1,5,6},{2},{3},{4}}=>7 {{1,5},{2,6},{3},{4}}=>8 {{1,5},{2},{3,6},{4}}=>8 {{1,5},{2},{3},{4,6}}=>4 {{1,5},{2},{3},{4},{6}}=>5 {{1,6},{2,5},{3},{4}}=>8 {{1},{2,5,6},{3},{4}}=>6 {{1},{2,5},{3,6},{4}}=>8 {{1},{2,5},{3},{4,6}}=>4 {{1},{2,5},{3},{4},{6}}=>5 {{1,6},{2},{3,5},{4}}=>8 {{1},{2,6},{3,5},{4}}=>8 {{1},{2},{3,5,6},{4}}=>5 {{1},{2},{3,5},{4,6}}=>4 {{1},{2},{3,5},{4},{6}}=>5 {{1,6},{2},{3},{4,5}}=>4 {{1},{2,6},{3},{4,5}}=>4 {{1},{2},{3,6},{4,5}}=>4 {{1},{2},{3},{4,5,6}}=>0 {{1},{2},{3},{4,5},{6}}=>1 {{1,6},{2},{3},{4},{5}}=>5 {{1},{2,6},{3},{4},{5}}=>5 {{1},{2},{3,6},{4},{5}}=>5 {{1},{2},{3},{4,6},{5}}=>5 {{1},{2},{3},{4},{5,6}}=>0 {{1},{2},{3},{4},{5},{6}}=>0 {{1,2,3,4,5,6,7}}=>0 {{1,2,3,4,5,6},{7}}=>5 {{1,2,3,4,5,7},{6}}=>6 {{1,2,3,4,5},{6,7}}=>4 {{1,2,3,4,5},{6},{7}}=>8 {{1,2,3,4,6,7},{5}}=>6 {{1,2,3,4,6},{5,7}}=>5 {{1,2,3,4,6},{5},{7}}=>9 {{1,2,3,4,7},{5,6}}=>5 {{1,2,3,4},{5,6,7}}=>3 {{1,2,3,4},{5,6},{7}}=>7 {{1,2,3,4,7},{5},{6}}=>9 {{1,2,3,4},{5,7},{6}}=>9 {{1,2,3,4},{5},{6,7}}=>6 {{1,2,3,4},{5},{6},{7}}=>9 {{1,2,3,5,6,7},{4}}=>6 {{1,2,3,5,6},{4,7}}=>5 {{1,2,3,5,6},{4},{7}}=>9 {{1,2,3,5,7},{4,6}}=>5 {{1,2,3,5},{4,6,7}}=>4 {{1,2,3,5},{4,6},{7}}=>8 {{1,2,3,5,7},{4},{6}}=>9 {{1,2,3,5},{4,7},{6}}=>10 {{1,2,3,5},{4},{6,7}}=>7 {{1,2,3,5},{4},{6},{7}}=>10 {{1,2,3,6,7},{4,5}}=>5 {{1,2,3,6},{4,5,7}}=>4 {{1,2,3,6},{4,5},{7}}=>8 {{1,2,3,7},{4,5,6}}=>4 {{1,2,3},{4,5,6,7}}=>2 {{1,2,3},{4,5,6},{7}}=>6 {{1,2,3,7},{4,5},{6}}=>8 {{1,2,3},{4,5,7},{6}}=>8 {{1,2,3},{4,5},{6,7}}=>5 {{1,2,3},{4,5},{6},{7}}=>8 {{1,2,3,6,7},{4},{5}}=>9 {{1,2,3,6},{4,7},{5}}=>10 {{1,2,3,6},{4},{5,7}}=>7 {{1,2,3,6},{4},{5},{7}}=>10 {{1,2,3,7},{4,6},{5}}=>10 {{1,2,3},{4,6,7},{5}}=>8 {{1,2,3},{4,6},{5,7}}=>7 {{1,2,3},{4,6},{5},{7}}=>10 {{1,2,3,7},{4},{5,6}}=>7 {{1,2,3},{4,7},{5,6}}=>7 {{1,2,3},{4},{5,6,7}}=>4 {{1,2,3},{4},{5,6},{7}}=>7 {{1,2,3,7},{4},{5},{6}}=>10 {{1,2,3},{4,7},{5},{6}}=>10 {{1,2,3},{4},{5,7},{6}}=>10 {{1,2,3},{4},{5},{6,7}}=>6 {{1,2,3},{4},{5},{6},{7}}=>8 {{1,2,4,5,6,7},{3}}=>6 {{1,2,4,5,6},{3,7}}=>5 {{1,2,4,5,6},{3},{7}}=>9 {{1,2,4,5,7},{3,6}}=>5 {{1,2,4,5},{3,6,7}}=>4 {{1,2,4,5},{3,6},{7}}=>8 {{1,2,4,5,7},{3},{6}}=>9 {{1,2,4,5},{3,7},{6}}=>10 {{1,2,4,5},{3},{6,7}}=>7 {{1,2,4,5},{3},{6},{7}}=>10 {{1,2,4,6,7},{3,5}}=>5 {{1,2,4,6},{3,5,7}}=>4 {{1,2,4,6},{3,5},{7}}=>8 {{1,2,4,7},{3,5,6}}=>4 {{1,2,4},{3,5,6,7}}=>3 {{1,2,4},{3,5,6},{7}}=>7 {{1,2,4,7},{3,5},{6}}=>8 {{1,2,4},{3,5,7},{6}}=>9 {{1,2,4},{3,5},{6,7}}=>6 {{1,2,4},{3,5},{6},{7}}=>9 {{1,2,4,6,7},{3},{5}}=>9 {{1,2,4,6},{3,7},{5}}=>10 {{1,2,4,6},{3},{5,7}}=>7 {{1,2,4,6},{3},{5},{7}}=>10 {{1,2,4,7},{3,6},{5}}=>10 {{1,2,4},{3,6,7},{5}}=>9 {{1,2,4},{3,6},{5,7}}=>8 {{1,2,4},{3,6},{5},{7}}=>11 {{1,2,4,7},{3},{5,6}}=>7 {{1,2,4},{3,7},{5,6}}=>8 {{1,2,4},{3},{5,6,7}}=>5 {{1,2,4},{3},{5,6},{7}}=>8 {{1,2,4,7},{3},{5},{6}}=>10 {{1,2,4},{3,7},{5},{6}}=>11 {{1,2,4},{3},{5,7},{6}}=>11 {{1,2,4},{3},{5},{6,7}}=>7 {{1,2,4},{3},{5},{6},{7}}=>9 {{1,2,5,6,7},{3,4}}=>5 {{1,2,5,6},{3,4,7}}=>4 {{1,2,5,6},{3,4},{7}}=>8 {{1,2,5,7},{3,4,6}}=>4 {{1,2,5},{3,4,6,7}}=>3 {{1,2,5},{3,4,6},{7}}=>7 {{1,2,5,7},{3,4},{6}}=>8 {{1,2,5},{3,4,7},{6}}=>9 {{1,2,5},{3,4},{6,7}}=>6 {{1,2,5},{3,4},{6},{7}}=>9 {{1,2,6,7},{3,4,5}}=>4 {{1,2,6},{3,4,5,7}}=>3 {{1,2,6},{3,4,5},{7}}=>7 {{1,2,7},{3,4,5,6}}=>3 {{1,2},{3,4,5,6,7}}=>1 {{1,2},{3,4,5,6},{7}}=>5 {{1,2,7},{3,4,5},{6}}=>7 {{1,2},{3,4,5,7},{6}}=>7 {{1,2},{3,4,5},{6,7}}=>4 {{1,2},{3,4,5},{6},{7}}=>7 {{1,2,6,7},{3,4},{5}}=>8 {{1,2,6},{3,4,7},{5}}=>9 {{1,2,6},{3,4},{5,7}}=>6 {{1,2,6},{3,4},{5},{7}}=>9 {{1,2,7},{3,4,6},{5}}=>9 {{1,2},{3,4,6,7},{5}}=>7 {{1,2},{3,4,6},{5,7}}=>6 {{1,2},{3,4,6},{5},{7}}=>9 {{1,2,7},{3,4},{5,6}}=>6 {{1,2},{3,4,7},{5,6}}=>6 {{1,2},{3,4},{5,6,7}}=>3 {{1,2},{3,4},{5,6},{7}}=>6 {{1,2,7},{3,4},{5},{6}}=>9 {{1,2},{3,4,7},{5},{6}}=>9 {{1,2},{3,4},{5,7},{6}}=>9 {{1,2},{3,4},{5},{6,7}}=>5 {{1,2},{3,4},{5},{6},{7}}=>7 {{1,2,5,6,7},{3},{4}}=>9 {{1,2,5,6},{3,7},{4}}=>10 {{1,2,5,6},{3},{4,7}}=>7 {{1,2,5,6},{3},{4},{7}}=>10 {{1,2,5,7},{3,6},{4}}=>10 {{1,2,5},{3,6,7},{4}}=>9 {{1,2,5},{3,6},{4,7}}=>8 {{1,2,5},{3,6},{4},{7}}=>11 {{1,2,5,7},{3},{4,6}}=>7 {{1,2,5},{3,7},{4,6}}=>8 {{1,2,5},{3},{4,6,7}}=>5 {{1,2,5},{3},{4,6},{7}}=>8 {{1,2,5,7},{3},{4},{6}}=>10 {{1,2,5},{3,7},{4},{6}}=>11 {{1,2,5},{3},{4,7},{6}}=>11 {{1,2,5},{3},{4},{6,7}}=>7 {{1,2,5},{3},{4},{6},{7}}=>9 {{1,2,6,7},{3,5},{4}}=>10 {{1,2,6},{3,5,7},{4}}=>9 {{1,2,6},{3,5},{4,7}}=>8 {{1,2,6},{3,5},{4},{7}}=>11 {{1,2,7},{3,5,6},{4}}=>9 {{1,2},{3,5,6,7},{4}}=>7 {{1,2},{3,5,6},{4,7}}=>6 {{1,2},{3,5,6},{4},{7}}=>9 {{1,2,7},{3,5},{4,6}}=>8 {{1,2},{3,5,7},{4,6}}=>6 {{1,2},{3,5},{4,6,7}}=>5 {{1,2},{3,5},{4,6},{7}}=>8 {{1,2,7},{3,5},{4},{6}}=>11 {{1,2},{3,5,7},{4},{6}}=>9 {{1,2},{3,5},{4,7},{6}}=>11 {{1,2},{3,5},{4},{6,7}}=>7 {{1,2},{3,5},{4},{6},{7}}=>9 {{1,2,6,7},{3},{4,5}}=>7 {{1,2,6},{3,7},{4,5}}=>8 {{1,2,6},{3},{4,5,7}}=>5 {{1,2,6},{3},{4,5},{7}}=>8 {{1,2,7},{3,6},{4,5}}=>8 {{1,2},{3,6,7},{4,5}}=>6 {{1,2},{3,6},{4,5,7}}=>5 {{1,2},{3,6},{4,5},{7}}=>8 {{1,2,7},{3},{4,5,6}}=>5 {{1,2},{3,7},{4,5,6}}=>5 {{1,2},{3},{4,5,6,7}}=>2 {{1,2},{3},{4,5,6},{7}}=>5 {{1,2,7},{3},{4,5},{6}}=>8 {{1,2},{3,7},{4,5},{6}}=>8 {{1,2},{3},{4,5,7},{6}}=>8 {{1,2},{3},{4,5},{6,7}}=>4 {{1,2},{3},{4,5},{6},{7}}=>6 {{1,2,6,7},{3},{4},{5}}=>10 {{1,2,6},{3,7},{4},{5}}=>11 {{1,2,6},{3},{4,7},{5}}=>11 {{1,2,6},{3},{4},{5,7}}=>7 {{1,2,6},{3},{4},{5},{7}}=>9 {{1,2,7},{3,6},{4},{5}}=>11 {{1,2},{3,6,7},{4},{5}}=>9 {{1,2},{3,6},{4,7},{5}}=>11 {{1,2},{3,6},{4},{5,7}}=>7 {{1,2},{3,6},{4},{5},{7}}=>9 {{1,2,7},{3},{4,6},{5}}=>11 {{1,2},{3,7},{4,6},{5}}=>11 {{1,2},{3},{4,6,7},{5}}=>8 {{1,2},{3},{4,6},{5,7}}=>7 {{1,2},{3},{4,6},{5},{7}}=>9 {{1,2,7},{3},{4},{5,6}}=>7 {{1,2},{3,7},{4},{5,6}}=>7 {{1,2},{3},{4,7},{5,6}}=>7 {{1,2},{3},{4},{5,6,7}}=>3 {{1,2},{3},{4},{5,6},{7}}=>5 {{1,2,7},{3},{4},{5},{6}}=>9 {{1,2},{3,7},{4},{5},{6}}=>9 {{1,2},{3},{4,7},{5},{6}}=>9 {{1,2},{3},{4},{5,7},{6}}=>9 {{1,2},{3},{4},{5},{6,7}}=>4 {{1,2},{3},{4},{5},{6},{7}}=>5 {{1,3,4,5,6,7},{2}}=>6 {{1,3,4,5,6},{2,7}}=>5 {{1,3,4,5,6},{2},{7}}=>9 {{1,3,4,5,7},{2,6}}=>5 {{1,3,4,5},{2,6,7}}=>4 {{1,3,4,5},{2,6},{7}}=>8 {{1,3,4,5,7},{2},{6}}=>9 {{1,3,4,5},{2,7},{6}}=>10 {{1,3,4,5},{2},{6,7}}=>7 {{1,3,4,5},{2},{6},{7}}=>10 {{1,3,4,6,7},{2,5}}=>5 {{1,3,4,6},{2,5,7}}=>4 {{1,3,4,6},{2,5},{7}}=>8 {{1,3,4,7},{2,5,6}}=>4 {{1,3,4},{2,5,6,7}}=>3 {{1,3,4},{2,5,6},{7}}=>7 {{1,3,4,7},{2,5},{6}}=>8 {{1,3,4},{2,5,7},{6}}=>9 {{1,3,4},{2,5},{6,7}}=>6 {{1,3,4},{2,5},{6},{7}}=>9 {{1,3,4,6,7},{2},{5}}=>9 {{1,3,4,6},{2,7},{5}}=>10 {{1,3,4,6},{2},{5,7}}=>7 {{1,3,4,6},{2},{5},{7}}=>10 {{1,3,4,7},{2,6},{5}}=>10 {{1,3,4},{2,6,7},{5}}=>9 {{1,3,4},{2,6},{5,7}}=>8 {{1,3,4},{2,6},{5},{7}}=>11 {{1,3,4,7},{2},{5,6}}=>7 {{1,3,4},{2,7},{5,6}}=>8 {{1,3,4},{2},{5,6,7}}=>5 {{1,3,4},{2},{5,6},{7}}=>8 {{1,3,4,7},{2},{5},{6}}=>10 {{1,3,4},{2,7},{5},{6}}=>11 {{1,3,4},{2},{5,7},{6}}=>11 {{1,3,4},{2},{5},{6,7}}=>7 {{1,3,4},{2},{5},{6},{7}}=>9 {{1,3,5,6,7},{2,4}}=>5 {{1,3,5,6},{2,4,7}}=>4 {{1,3,5,6},{2,4},{7}}=>8 {{1,3,5,7},{2,4,6}}=>4 {{1,3,5},{2,4,6,7}}=>3 {{1,3,5},{2,4,6},{7}}=>7 {{1,3,5,7},{2,4},{6}}=>8 {{1,3,5},{2,4,7},{6}}=>9 {{1,3,5},{2,4},{6,7}}=>6 {{1,3,5},{2,4},{6},{7}}=>9 {{1,3,6,7},{2,4,5}}=>4 {{1,3,6},{2,4,5,7}}=>3 {{1,3,6},{2,4,5},{7}}=>7 {{1,3,7},{2,4,5,6}}=>3 {{1,3},{2,4,5,6,7}}=>2 {{1,3},{2,4,5,6},{7}}=>6 {{1,3,7},{2,4,5},{6}}=>7 {{1,3},{2,4,5,7},{6}}=>8 {{1,3},{2,4,5},{6,7}}=>5 {{1,3},{2,4,5},{6},{7}}=>8 {{1,3,6,7},{2,4},{5}}=>8 {{1,3,6},{2,4,7},{5}}=>9 {{1,3,6},{2,4},{5,7}}=>6 {{1,3,6},{2,4},{5},{7}}=>9 {{1,3,7},{2,4,6},{5}}=>9 {{1,3},{2,4,6,7},{5}}=>8 {{1,3},{2,4,6},{5,7}}=>7 {{1,3},{2,4,6},{5},{7}}=>10 {{1,3,7},{2,4},{5,6}}=>6 {{1,3},{2,4,7},{5,6}}=>7 {{1,3},{2,4},{5,6,7}}=>4 {{1,3},{2,4},{5,6},{7}}=>7 {{1,3,7},{2,4},{5},{6}}=>9 {{1,3},{2,4,7},{5},{6}}=>10 {{1,3},{2,4},{5,7},{6}}=>10 {{1,3},{2,4},{5},{6,7}}=>6 {{1,3},{2,4},{5},{6},{7}}=>8 {{1,3,5,6,7},{2},{4}}=>9 {{1,3,5,6},{2,7},{4}}=>10 {{1,3,5,6},{2},{4,7}}=>7 {{1,3,5,6},{2},{4},{7}}=>10 {{1,3,5,7},{2,6},{4}}=>10 {{1,3,5},{2,6,7},{4}}=>9 {{1,3,5},{2,6},{4,7}}=>8 {{1,3,5},{2,6},{4},{7}}=>11 {{1,3,5,7},{2},{4,6}}=>7 {{1,3,5},{2,7},{4,6}}=>8 {{1,3,5},{2},{4,6,7}}=>5 {{1,3,5},{2},{4,6},{7}}=>8 {{1,3,5,7},{2},{4},{6}}=>10 {{1,3,5},{2,7},{4},{6}}=>11 {{1,3,5},{2},{4,7},{6}}=>11 {{1,3,5},{2},{4},{6,7}}=>7 {{1,3,5},{2},{4},{6},{7}}=>9 {{1,3,6,7},{2,5},{4}}=>10 {{1,3,6},{2,5,7},{4}}=>9 {{1,3,6},{2,5},{4,7}}=>8 {{1,3,6},{2,5},{4},{7}}=>11 {{1,3,7},{2,5,6},{4}}=>9 {{1,3},{2,5,6,7},{4}}=>8 {{1,3},{2,5,6},{4,7}}=>7 {{1,3},{2,5,6},{4},{7}}=>10 {{1,3,7},{2,5},{4,6}}=>8 {{1,3},{2,5,7},{4,6}}=>7 {{1,3},{2,5},{4,6,7}}=>6 {{1,3},{2,5},{4,6},{7}}=>9 {{1,3,7},{2,5},{4},{6}}=>11 {{1,3},{2,5,7},{4},{6}}=>10 {{1,3},{2,5},{4,7},{6}}=>12 {{1,3},{2,5},{4},{6,7}}=>8 {{1,3},{2,5},{4},{6},{7}}=>10 {{1,3,6,7},{2},{4,5}}=>7 {{1,3,6},{2,7},{4,5}}=>8 {{1,3,6},{2},{4,5,7}}=>5 {{1,3,6},{2},{4,5},{7}}=>8 {{1,3,7},{2,6},{4,5}}=>8 {{1,3},{2,6,7},{4,5}}=>7 {{1,3},{2,6},{4,5,7}}=>6 {{1,3},{2,6},{4,5},{7}}=>9 {{1,3,7},{2},{4,5,6}}=>5 {{1,3},{2,7},{4,5,6}}=>6 {{1,3},{2},{4,5,6,7}}=>3 {{1,3},{2},{4,5,6},{7}}=>6 {{1,3,7},{2},{4,5},{6}}=>8 {{1,3},{2,7},{4,5},{6}}=>9 {{1,3},{2},{4,5,7},{6}}=>9 {{1,3},{2},{4,5},{6,7}}=>5 {{1,3},{2},{4,5},{6},{7}}=>7 {{1,3,6,7},{2},{4},{5}}=>10 {{1,3,6},{2,7},{4},{5}}=>11 {{1,3,6},{2},{4,7},{5}}=>11 {{1,3,6},{2},{4},{5,7}}=>7 {{1,3,6},{2},{4},{5},{7}}=>9 {{1,3,7},{2,6},{4},{5}}=>11 {{1,3},{2,6,7},{4},{5}}=>10 {{1,3},{2,6},{4,7},{5}}=>12 {{1,3},{2,6},{4},{5,7}}=>8 {{1,3},{2,6},{4},{5},{7}}=>10 {{1,3,7},{2},{4,6},{5}}=>11 {{1,3},{2,7},{4,6},{5}}=>12 {{1,3},{2},{4,6,7},{5}}=>9 {{1,3},{2},{4,6},{5,7}}=>8 {{1,3},{2},{4,6},{5},{7}}=>10 {{1,3,7},{2},{4},{5,6}}=>7 {{1,3},{2,7},{4},{5,6}}=>8 {{1,3},{2},{4,7},{5,6}}=>8 {{1,3},{2},{4},{5,6,7}}=>4 {{1,3},{2},{4},{5,6},{7}}=>6 {{1,3,7},{2},{4},{5},{6}}=>9 {{1,3},{2,7},{4},{5},{6}}=>10 {{1,3},{2},{4,7},{5},{6}}=>10 {{1,3},{2},{4},{5,7},{6}}=>10 {{1,3},{2},{4},{5},{6,7}}=>5 {{1,3},{2},{4},{5},{6},{7}}=>6 {{1,4,5,6,7},{2,3}}=>5 {{1,4,5,6},{2,3,7}}=>4 {{1,4,5,6},{2,3},{7}}=>8 {{1,4,5,7},{2,3,6}}=>4 {{1,4,5},{2,3,6,7}}=>3 {{1,4,5},{2,3,6},{7}}=>7 {{1,4,5,7},{2,3},{6}}=>8 {{1,4,5},{2,3,7},{6}}=>9 {{1,4,5},{2,3},{6,7}}=>6 {{1,4,5},{2,3},{6},{7}}=>9 {{1,4,6,7},{2,3,5}}=>4 {{1,4,6},{2,3,5,7}}=>3 {{1,4,6},{2,3,5},{7}}=>7 {{1,4,7},{2,3,5,6}}=>3 {{1,4},{2,3,5,6,7}}=>2 {{1,4},{2,3,5,6},{7}}=>6 {{1,4,7},{2,3,5},{6}}=>7 {{1,4},{2,3,5,7},{6}}=>8 {{1,4},{2,3,5},{6,7}}=>5 {{1,4},{2,3,5},{6},{7}}=>8 {{1,4,6,7},{2,3},{5}}=>8 {{1,4,6},{2,3,7},{5}}=>9 {{1,4,6},{2,3},{5,7}}=>6 {{1,4,6},{2,3},{5},{7}}=>9 {{1,4,7},{2,3,6},{5}}=>9 {{1,4},{2,3,6,7},{5}}=>8 {{1,4},{2,3,6},{5,7}}=>7 {{1,4},{2,3,6},{5},{7}}=>10 {{1,4,7},{2,3},{5,6}}=>6 {{1,4},{2,3,7},{5,6}}=>7 {{1,4},{2,3},{5,6,7}}=>4 {{1,4},{2,3},{5,6},{7}}=>7 {{1,4,7},{2,3},{5},{6}}=>9 {{1,4},{2,3,7},{5},{6}}=>10 {{1,4},{2,3},{5,7},{6}}=>10 {{1,4},{2,3},{5},{6,7}}=>6 {{1,4},{2,3},{5},{6},{7}}=>8 {{1,5,6,7},{2,3,4}}=>4 {{1,5,6},{2,3,4,7}}=>3 {{1,5,6},{2,3,4},{7}}=>7 {{1,5,7},{2,3,4,6}}=>3 {{1,5},{2,3,4,6,7}}=>2 {{1,5},{2,3,4,6},{7}}=>6 {{1,5,7},{2,3,4},{6}}=>7 {{1,5},{2,3,4,7},{6}}=>8 {{1,5},{2,3,4},{6,7}}=>5 {{1,5},{2,3,4},{6},{7}}=>8 {{1,6,7},{2,3,4,5}}=>3 {{1,6},{2,3,4,5,7}}=>2 {{1,6},{2,3,4,5},{7}}=>6 {{1,7},{2,3,4,5,6}}=>2 {{1},{2,3,4,5,6,7}}=>0 {{1},{2,3,4,5,6},{7}}=>4 {{1,7},{2,3,4,5},{6}}=>6 {{1},{2,3,4,5,7},{6}}=>6 {{1},{2,3,4,5},{6,7}}=>3 {{1},{2,3,4,5},{6},{7}}=>6 {{1,6,7},{2,3,4},{5}}=>7 {{1,6},{2,3,4,7},{5}}=>8 {{1,6},{2,3,4},{5,7}}=>5 {{1,6},{2,3,4},{5},{7}}=>8 {{1,7},{2,3,4,6},{5}}=>8 {{1},{2,3,4,6,7},{5}}=>6 {{1},{2,3,4,6},{5,7}}=>5 {{1},{2,3,4,6},{5},{7}}=>8 {{1,7},{2,3,4},{5,6}}=>5 {{1},{2,3,4,7},{5,6}}=>5 {{1},{2,3,4},{5,6,7}}=>2 {{1},{2,3,4},{5,6},{7}}=>5 {{1,7},{2,3,4},{5},{6}}=>8 {{1},{2,3,4,7},{5},{6}}=>8 {{1},{2,3,4},{5,7},{6}}=>8 {{1},{2,3,4},{5},{6,7}}=>4 {{1},{2,3,4},{5},{6},{7}}=>6 {{1,5,6,7},{2,3},{4}}=>8 {{1,5,6},{2,3,7},{4}}=>9 {{1,5,6},{2,3},{4,7}}=>6 {{1,5,6},{2,3},{4},{7}}=>9 {{1,5,7},{2,3,6},{4}}=>9 {{1,5},{2,3,6,7},{4}}=>8 {{1,5},{2,3,6},{4,7}}=>7 {{1,5},{2,3,6},{4},{7}}=>10 {{1,5,7},{2,3},{4,6}}=>6 {{1,5},{2,3,7},{4,6}}=>7 {{1,5},{2,3},{4,6,7}}=>4 {{1,5},{2,3},{4,6},{7}}=>7 {{1,5,7},{2,3},{4},{6}}=>9 {{1,5},{2,3,7},{4},{6}}=>10 {{1,5},{2,3},{4,7},{6}}=>10 {{1,5},{2,3},{4},{6,7}}=>6 {{1,5},{2,3},{4},{6},{7}}=>8 {{1,6,7},{2,3,5},{4}}=>9 {{1,6},{2,3,5,7},{4}}=>8 {{1,6},{2,3,5},{4,7}}=>7 {{1,6},{2,3,5},{4},{7}}=>10 {{1,7},{2,3,5,6},{4}}=>8 {{1},{2,3,5,6,7},{4}}=>6 {{1},{2,3,5,6},{4,7}}=>5 {{1},{2,3,5,6},{4},{7}}=>8 {{1,7},{2,3,5},{4,6}}=>7 {{1},{2,3,5,7},{4,6}}=>5 {{1},{2,3,5},{4,6,7}}=>4 {{1},{2,3,5},{4,6},{7}}=>7 {{1,7},{2,3,5},{4},{6}}=>10 {{1},{2,3,5,7},{4},{6}}=>8 {{1},{2,3,5},{4,7},{6}}=>10 {{1},{2,3,5},{4},{6,7}}=>6 {{1},{2,3,5},{4},{6},{7}}=>8 {{1,6,7},{2,3},{4,5}}=>6 {{1,6},{2,3,7},{4,5}}=>7 {{1,6},{2,3},{4,5,7}}=>4 {{1,6},{2,3},{4,5},{7}}=>7 {{1,7},{2,3,6},{4,5}}=>7 {{1},{2,3,6,7},{4,5}}=>5 {{1},{2,3,6},{4,5,7}}=>4 {{1},{2,3,6},{4,5},{7}}=>7 {{1,7},{2,3},{4,5,6}}=>4 {{1},{2,3,7},{4,5,6}}=>4 {{1},{2,3},{4,5,6,7}}=>1 {{1},{2,3},{4,5,6},{7}}=>4 {{1,7},{2,3},{4,5},{6}}=>7 {{1},{2,3,7},{4,5},{6}}=>7 {{1},{2,3},{4,5,7},{6}}=>7 {{1},{2,3},{4,5},{6,7}}=>3 {{1},{2,3},{4,5},{6},{7}}=>5 {{1,6,7},{2,3},{4},{5}}=>9 {{1,6},{2,3,7},{4},{5}}=>10 {{1,6},{2,3},{4,7},{5}}=>10 {{1,6},{2,3},{4},{5,7}}=>6 {{1,6},{2,3},{4},{5},{7}}=>8 {{1,7},{2,3,6},{4},{5}}=>10 {{1},{2,3,6,7},{4},{5}}=>8 {{1},{2,3,6},{4,7},{5}}=>10 {{1},{2,3,6},{4},{5,7}}=>6 {{1},{2,3,6},{4},{5},{7}}=>8 {{1,7},{2,3},{4,6},{5}}=>10 {{1},{2,3,7},{4,6},{5}}=>10 {{1},{2,3},{4,6,7},{5}}=>7 {{1},{2,3},{4,6},{5,7}}=>6 {{1},{2,3},{4,6},{5},{7}}=>8 {{1,7},{2,3},{4},{5,6}}=>6 {{1},{2,3,7},{4},{5,6}}=>6 {{1},{2,3},{4,7},{5,6}}=>6 {{1},{2,3},{4},{5,6,7}}=>2 {{1},{2,3},{4},{5,6},{7}}=>4 {{1,7},{2,3},{4},{5},{6}}=>8 {{1},{2,3,7},{4},{5},{6}}=>8 {{1},{2,3},{4,7},{5},{6}}=>8 {{1},{2,3},{4},{5,7},{6}}=>8 {{1},{2,3},{4},{5},{6,7}}=>3 {{1},{2,3},{4},{5},{6},{7}}=>4 {{1,4,5,6,7},{2},{3}}=>9 {{1,4,5,6},{2,7},{3}}=>10 {{1,4,5,6},{2},{3,7}}=>7 {{1,4,5,6},{2},{3},{7}}=>10 {{1,4,5,7},{2,6},{3}}=>10 {{1,4,5},{2,6,7},{3}}=>9 {{1,4,5},{2,6},{3,7}}=>8 {{1,4,5},{2,6},{3},{7}}=>11 {{1,4,5,7},{2},{3,6}}=>7 {{1,4,5},{2,7},{3,6}}=>8 {{1,4,5},{2},{3,6,7}}=>5 {{1,4,5},{2},{3,6},{7}}=>8 {{1,4,5,7},{2},{3},{6}}=>10 {{1,4,5},{2,7},{3},{6}}=>11 {{1,4,5},{2},{3,7},{6}}=>11 {{1,4,5},{2},{3},{6,7}}=>7 {{1,4,5},{2},{3},{6},{7}}=>9 {{1,4,6,7},{2,5},{3}}=>10 {{1,4,6},{2,5,7},{3}}=>9 {{1,4,6},{2,5},{3,7}}=>8 {{1,4,6},{2,5},{3},{7}}=>11 {{1,4,7},{2,5,6},{3}}=>9 {{1,4},{2,5,6,7},{3}}=>8 {{1,4},{2,5,6},{3,7}}=>7 {{1,4},{2,5,6},{3},{7}}=>10 {{1,4,7},{2,5},{3,6}}=>8 {{1,4},{2,5,7},{3,6}}=>7 {{1,4},{2,5},{3,6,7}}=>6 {{1,4},{2,5},{3,6},{7}}=>9 {{1,4,7},{2,5},{3},{6}}=>11 {{1,4},{2,5,7},{3},{6}}=>10 {{1,4},{2,5},{3,7},{6}}=>12 {{1,4},{2,5},{3},{6,7}}=>8 {{1,4},{2,5},{3},{6},{7}}=>10 {{1,4,6,7},{2},{3,5}}=>7 {{1,4,6},{2,7},{3,5}}=>8 {{1,4,6},{2},{3,5,7}}=>5 {{1,4,6},{2},{3,5},{7}}=>8 {{1,4,7},{2,6},{3,5}}=>8 {{1,4},{2,6,7},{3,5}}=>7 {{1,4},{2,6},{3,5,7}}=>6 {{1,4},{2,6},{3,5},{7}}=>9 {{1,4,7},{2},{3,5,6}}=>5 {{1,4},{2,7},{3,5,6}}=>6 {{1,4},{2},{3,5,6,7}}=>3 {{1,4},{2},{3,5,6},{7}}=>6 {{1,4,7},{2},{3,5},{6}}=>8 {{1,4},{2,7},{3,5},{6}}=>9 {{1,4},{2},{3,5,7},{6}}=>9 {{1,4},{2},{3,5},{6,7}}=>5 {{1,4},{2},{3,5},{6},{7}}=>7 {{1,4,6,7},{2},{3},{5}}=>10 {{1,4,6},{2,7},{3},{5}}=>11 {{1,4,6},{2},{3,7},{5}}=>11 {{1,4,6},{2},{3},{5,7}}=>7 {{1,4,6},{2},{3},{5},{7}}=>9 {{1,4,7},{2,6},{3},{5}}=>11 {{1,4},{2,6,7},{3},{5}}=>10 {{1,4},{2,6},{3,7},{5}}=>12 {{1,4},{2,6},{3},{5,7}}=>8 {{1,4},{2,6},{3},{5},{7}}=>10 {{1,4,7},{2},{3,6},{5}}=>11 {{1,4},{2,7},{3,6},{5}}=>12 {{1,4},{2},{3,6,7},{5}}=>9 {{1,4},{2},{3,6},{5,7}}=>8 {{1,4},{2},{3,6},{5},{7}}=>10 {{1,4,7},{2},{3},{5,6}}=>7 {{1,4},{2,7},{3},{5,6}}=>8 {{1,4},{2},{3,7},{5,6}}=>8 {{1,4},{2},{3},{5,6,7}}=>4 {{1,4},{2},{3},{5,6},{7}}=>6 {{1,4,7},{2},{3},{5},{6}}=>9 {{1,4},{2,7},{3},{5},{6}}=>10 {{1,4},{2},{3,7},{5},{6}}=>10 {{1,4},{2},{3},{5,7},{6}}=>10 {{1,4},{2},{3},{5},{6,7}}=>5 {{1,4},{2},{3},{5},{6},{7}}=>6 {{1,5,6,7},{2,4},{3}}=>10 {{1,5,6},{2,4,7},{3}}=>9 {{1,5,6},{2,4},{3,7}}=>8 {{1,5,6},{2,4},{3},{7}}=>11 {{1,5,7},{2,4,6},{3}}=>9 {{1,5},{2,4,6,7},{3}}=>8 {{1,5},{2,4,6},{3,7}}=>7 {{1,5},{2,4,6},{3},{7}}=>10 {{1,5,7},{2,4},{3,6}}=>8 {{1,5},{2,4,7},{3,6}}=>7 {{1,5},{2,4},{3,6,7}}=>6 {{1,5},{2,4},{3,6},{7}}=>9 {{1,5,7},{2,4},{3},{6}}=>11 {{1,5},{2,4,7},{3},{6}}=>10 {{1,5},{2,4},{3,7},{6}}=>12 {{1,5},{2,4},{3},{6,7}}=>8 {{1,5},{2,4},{3},{6},{7}}=>10 {{1,6,7},{2,4,5},{3}}=>9 {{1,6},{2,4,5,7},{3}}=>8 {{1,6},{2,4,5},{3,7}}=>7 {{1,6},{2,4,5},{3},{7}}=>10 {{1,7},{2,4,5,6},{3}}=>8 {{1},{2,4,5,6,7},{3}}=>6 {{1},{2,4,5,6},{3,7}}=>5 {{1},{2,4,5,6},{3},{7}}=>8 {{1,7},{2,4,5},{3,6}}=>7 {{1},{2,4,5,7},{3,6}}=>5 {{1},{2,4,5},{3,6,7}}=>4 {{1},{2,4,5},{3,6},{7}}=>7 {{1,7},{2,4,5},{3},{6}}=>10 {{1},{2,4,5,7},{3},{6}}=>8 {{1},{2,4,5},{3,7},{6}}=>10 {{1},{2,4,5},{3},{6,7}}=>6 {{1},{2,4,5},{3},{6},{7}}=>8 {{1,6,7},{2,4},{3,5}}=>8 {{1,6},{2,4,7},{3,5}}=>7 {{1,6},{2,4},{3,5,7}}=>6 {{1,6},{2,4},{3,5},{7}}=>9 {{1,7},{2,4,6},{3,5}}=>7 {{1},{2,4,6,7},{3,5}}=>5 {{1},{2,4,6},{3,5,7}}=>4 {{1},{2,4,6},{3,5},{7}}=>7 {{1,7},{2,4},{3,5,6}}=>6 {{1},{2,4,7},{3,5,6}}=>4 {{1},{2,4},{3,5,6,7}}=>3 {{1},{2,4},{3,5,6},{7}}=>6 {{1,7},{2,4},{3,5},{6}}=>9 {{1},{2,4,7},{3,5},{6}}=>7 {{1},{2,4},{3,5,7},{6}}=>9 {{1},{2,4},{3,5},{6,7}}=>5 {{1},{2,4},{3,5},{6},{7}}=>7 {{1,6,7},{2,4},{3},{5}}=>11 {{1,6},{2,4,7},{3},{5}}=>10 {{1,6},{2,4},{3,7},{5}}=>12 {{1,6},{2,4},{3},{5,7}}=>8 {{1,6},{2,4},{3},{5},{7}}=>10 {{1,7},{2,4,6},{3},{5}}=>10 {{1},{2,4,6,7},{3},{5}}=>8 {{1},{2,4,6},{3,7},{5}}=>10 {{1},{2,4,6},{3},{5,7}}=>6 {{1},{2,4,6},{3},{5},{7}}=>8 {{1,7},{2,4},{3,6},{5}}=>12 {{1},{2,4,7},{3,6},{5}}=>10 {{1},{2,4},{3,6,7},{5}}=>9 {{1},{2,4},{3,6},{5,7}}=>8 {{1},{2,4},{3,6},{5},{7}}=>10 {{1,7},{2,4},{3},{5,6}}=>8 {{1},{2,4,7},{3},{5,6}}=>6 {{1},{2,4},{3,7},{5,6}}=>8 {{1},{2,4},{3},{5,6,7}}=>4 {{1},{2,4},{3},{5,6},{7}}=>6 {{1,7},{2,4},{3},{5},{6}}=>10 {{1},{2,4,7},{3},{5},{6}}=>8 {{1},{2,4},{3,7},{5},{6}}=>10 {{1},{2,4},{3},{5,7},{6}}=>10 {{1},{2,4},{3},{5},{6,7}}=>5 {{1},{2,4},{3},{5},{6},{7}}=>6 {{1,5,6,7},{2},{3,4}}=>7 {{1,5,6},{2,7},{3,4}}=>8 {{1,5,6},{2},{3,4,7}}=>5 {{1,5,6},{2},{3,4},{7}}=>8 {{1,5,7},{2,6},{3,4}}=>8 {{1,5},{2,6,7},{3,4}}=>7 {{1,5},{2,6},{3,4,7}}=>6 {{1,5},{2,6},{3,4},{7}}=>9 {{1,5,7},{2},{3,4,6}}=>5 {{1,5},{2,7},{3,4,6}}=>6 {{1,5},{2},{3,4,6,7}}=>3 {{1,5},{2},{3,4,6},{7}}=>6 {{1,5,7},{2},{3,4},{6}}=>8 {{1,5},{2,7},{3,4},{6}}=>9 {{1,5},{2},{3,4,7},{6}}=>9 {{1,5},{2},{3,4},{6,7}}=>5 {{1,5},{2},{3,4},{6},{7}}=>7 {{1,6,7},{2,5},{3,4}}=>8 {{1,6},{2,5,7},{3,4}}=>7 {{1,6},{2,5},{3,4,7}}=>6 {{1,6},{2,5},{3,4},{7}}=>9 {{1,7},{2,5,6},{3,4}}=>7 {{1},{2,5,6,7},{3,4}}=>5 {{1},{2,5,6},{3,4,7}}=>4 {{1},{2,5,6},{3,4},{7}}=>7 {{1,7},{2,5},{3,4,6}}=>6 {{1},{2,5,7},{3,4,6}}=>4 {{1},{2,5},{3,4,6,7}}=>3 {{1},{2,5},{3,4,6},{7}}=>6 {{1,7},{2,5},{3,4},{6}}=>9 {{1},{2,5,7},{3,4},{6}}=>7 {{1},{2,5},{3,4,7},{6}}=>9 {{1},{2,5},{3,4},{6,7}}=>5 {{1},{2,5},{3,4},{6},{7}}=>7 {{1,6,7},{2},{3,4,5}}=>5 {{1,6},{2,7},{3,4,5}}=>6 {{1,6},{2},{3,4,5,7}}=>3 {{1,6},{2},{3,4,5},{7}}=>6 {{1,7},{2,6},{3,4,5}}=>6 {{1},{2,6,7},{3,4,5}}=>4 {{1},{2,6},{3,4,5,7}}=>3 {{1},{2,6},{3,4,5},{7}}=>6 {{1,7},{2},{3,4,5,6}}=>3 {{1},{2,7},{3,4,5,6}}=>3 {{1},{2},{3,4,5,6,7}}=>0 {{1},{2},{3,4,5,6},{7}}=>3 {{1,7},{2},{3,4,5},{6}}=>6 {{1},{2,7},{3,4,5},{6}}=>6 {{1},{2},{3,4,5,7},{6}}=>6 {{1},{2},{3,4,5},{6,7}}=>2 {{1},{2},{3,4,5},{6},{7}}=>4 {{1,6,7},{2},{3,4},{5}}=>8 {{1,6},{2,7},{3,4},{5}}=>9 {{1,6},{2},{3,4,7},{5}}=>9 {{1,6},{2},{3,4},{5,7}}=>5 {{1,6},{2},{3,4},{5},{7}}=>7 {{1,7},{2,6},{3,4},{5}}=>9 {{1},{2,6,7},{3,4},{5}}=>7 {{1},{2,6},{3,4,7},{5}}=>9 {{1},{2,6},{3,4},{5,7}}=>5 {{1},{2,6},{3,4},{5},{7}}=>7 {{1,7},{2},{3,4,6},{5}}=>9 {{1},{2,7},{3,4,6},{5}}=>9 {{1},{2},{3,4,6,7},{5}}=>6 {{1},{2},{3,4,6},{5,7}}=>5 {{1},{2},{3,4,6},{5},{7}}=>7 {{1,7},{2},{3,4},{5,6}}=>5 {{1},{2,7},{3,4},{5,6}}=>5 {{1},{2},{3,4,7},{5,6}}=>5 {{1},{2},{3,4},{5,6,7}}=>1 {{1},{2},{3,4},{5,6},{7}}=>3 {{1,7},{2},{3,4},{5},{6}}=>7 {{1},{2,7},{3,4},{5},{6}}=>7 {{1},{2},{3,4,7},{5},{6}}=>7 {{1},{2},{3,4},{5,7},{6}}=>7 {{1},{2},{3,4},{5},{6,7}}=>2 {{1},{2},{3,4},{5},{6},{7}}=>3 {{1,5,6,7},{2},{3},{4}}=>10 {{1,5,6},{2,7},{3},{4}}=>11 {{1,5,6},{2},{3,7},{4}}=>11 {{1,5,6},{2},{3},{4,7}}=>7 {{1,5,6},{2},{3},{4},{7}}=>9 {{1,5,7},{2,6},{3},{4}}=>11 {{1,5},{2,6,7},{3},{4}}=>10 {{1,5},{2,6},{3,7},{4}}=>12 {{1,5},{2,6},{3},{4,7}}=>8 {{1,5},{2,6},{3},{4},{7}}=>10 {{1,5,7},{2},{3,6},{4}}=>11 {{1,5},{2,7},{3,6},{4}}=>12 {{1,5},{2},{3,6,7},{4}}=>9 {{1,5},{2},{3,6},{4,7}}=>8 {{1,5},{2},{3,6},{4},{7}}=>10 {{1,5,7},{2},{3},{4,6}}=>7 {{1,5},{2,7},{3},{4,6}}=>8 {{1,5},{2},{3,7},{4,6}}=>8 {{1,5},{2},{3},{4,6,7}}=>4 {{1,5},{2},{3},{4,6},{7}}=>6 {{1,5,7},{2},{3},{4},{6}}=>9 {{1,5},{2,7},{3},{4},{6}}=>10 {{1,5},{2},{3,7},{4},{6}}=>10 {{1,5},{2},{3},{4,7},{6}}=>10 {{1,5},{2},{3},{4},{6,7}}=>5 {{1,5},{2},{3},{4},{6},{7}}=>6 {{1,6,7},{2,5},{3},{4}}=>11 {{1,6},{2,5,7},{3},{4}}=>10 {{1,6},{2,5},{3,7},{4}}=>12 {{1,6},{2,5},{3},{4,7}}=>8 {{1,6},{2,5},{3},{4},{7}}=>10 {{1,7},{2,5,6},{3},{4}}=>10 {{1},{2,5,6,7},{3},{4}}=>8 {{1},{2,5,6},{3,7},{4}}=>10 {{1},{2,5,6},{3},{4,7}}=>6 {{1},{2,5,6},{3},{4},{7}}=>8 {{1,7},{2,5},{3,6},{4}}=>12 {{1},{2,5,7},{3,6},{4}}=>10 {{1},{2,5},{3,6,7},{4}}=>9 {{1},{2,5},{3,6},{4,7}}=>8 {{1},{2,5},{3,6},{4},{7}}=>10 {{1,7},{2,5},{3},{4,6}}=>8 {{1},{2,5,7},{3},{4,6}}=>6 {{1},{2,5},{3,7},{4,6}}=>8 {{1},{2,5},{3},{4,6,7}}=>4 {{1},{2,5},{3},{4,6},{7}}=>6 {{1,7},{2,5},{3},{4},{6}}=>10 {{1},{2,5,7},{3},{4},{6}}=>8 {{1},{2,5},{3,7},{4},{6}}=>10 {{1},{2,5},{3},{4,7},{6}}=>10 {{1},{2,5},{3},{4},{6,7}}=>5 {{1},{2,5},{3},{4},{6},{7}}=>6 {{1,6,7},{2},{3,5},{4}}=>11 {{1,6},{2,7},{3,5},{4}}=>12 {{1,6},{2},{3,5,7},{4}}=>9 {{1,6},{2},{3,5},{4,7}}=>8 {{1,6},{2},{3,5},{4},{7}}=>10 {{1,7},{2,6},{3,5},{4}}=>12 {{1},{2,6,7},{3,5},{4}}=>10 {{1},{2,6},{3,5,7},{4}}=>9 {{1},{2,6},{3,5},{4,7}}=>8 {{1},{2,6},{3,5},{4},{7}}=>10 {{1,7},{2},{3,5,6},{4}}=>9 {{1},{2,7},{3,5,6},{4}}=>9 {{1},{2},{3,5,6,7},{4}}=>6 {{1},{2},{3,5,6},{4,7}}=>5 {{1},{2},{3,5,6},{4},{7}}=>7 {{1,7},{2},{3,5},{4,6}}=>8 {{1},{2,7},{3,5},{4,6}}=>8 {{1},{2},{3,5,7},{4,6}}=>5 {{1},{2},{3,5},{4,6,7}}=>4 {{1},{2},{3,5},{4,6},{7}}=>6 {{1,7},{2},{3,5},{4},{6}}=>10 {{1},{2,7},{3,5},{4},{6}}=>10 {{1},{2},{3,5,7},{4},{6}}=>7 {{1},{2},{3,5},{4,7},{6}}=>10 {{1},{2},{3,5},{4},{6,7}}=>5 {{1},{2},{3,5},{4},{6},{7}}=>6 {{1,6,7},{2},{3},{4,5}}=>7 {{1,6},{2,7},{3},{4,5}}=>8 {{1,6},{2},{3,7},{4,5}}=>8 {{1,6},{2},{3},{4,5,7}}=>4 {{1,6},{2},{3},{4,5},{7}}=>6 {{1,7},{2,6},{3},{4,5}}=>8 {{1},{2,6,7},{3},{4,5}}=>6 {{1},{2,6},{3,7},{4,5}}=>8 {{1},{2,6},{3},{4,5,7}}=>4 {{1},{2,6},{3},{4,5},{7}}=>6 {{1,7},{2},{3,6},{4,5}}=>8 {{1},{2,7},{3,6},{4,5}}=>8 {{1},{2},{3,6,7},{4,5}}=>5 {{1},{2},{3,6},{4,5,7}}=>4 {{1},{2},{3,6},{4,5},{7}}=>6 {{1,7},{2},{3},{4,5,6}}=>4 {{1},{2,7},{3},{4,5,6}}=>4 {{1},{2},{3,7},{4,5,6}}=>4 {{1},{2},{3},{4,5,6,7}}=>0 {{1},{2},{3},{4,5,6},{7}}=>2 {{1,7},{2},{3},{4,5},{6}}=>6 {{1},{2,7},{3},{4,5},{6}}=>6 {{1},{2},{3,7},{4,5},{6}}=>6 {{1},{2},{3},{4,5,7},{6}}=>6 {{1},{2},{3},{4,5},{6,7}}=>1 {{1},{2},{3},{4,5},{6},{7}}=>2 {{1,6,7},{2},{3},{4},{5}}=>9 {{1,6},{2,7},{3},{4},{5}}=>10 {{1,6},{2},{3,7},{4},{5}}=>10 {{1,6},{2},{3},{4,7},{5}}=>10 {{1,6},{2},{3},{4},{5,7}}=>5 {{1,6},{2},{3},{4},{5},{7}}=>6 {{1,7},{2,6},{3},{4},{5}}=>10 {{1},{2,6,7},{3},{4},{5}}=>8 {{1},{2,6},{3,7},{4},{5}}=>10 {{1},{2,6},{3},{4,7},{5}}=>10 {{1},{2,6},{3},{4},{5,7}}=>5 {{1},{2,6},{3},{4},{5},{7}}=>6 {{1,7},{2},{3,6},{4},{5}}=>10 {{1},{2,7},{3,6},{4},{5}}=>10 {{1},{2},{3,6,7},{4},{5}}=>7 {{1},{2},{3,6},{4,7},{5}}=>10 {{1},{2},{3,6},{4},{5,7}}=>5 {{1},{2},{3,6},{4},{5},{7}}=>6 {{1,7},{2},{3},{4,6},{5}}=>10 {{1},{2,7},{3},{4,6},{5}}=>10 {{1},{2},{3,7},{4,6},{5}}=>10 {{1},{2},{3},{4,6,7},{5}}=>6 {{1},{2},{3},{4,6},{5,7}}=>5 {{1},{2},{3},{4,6},{5},{7}}=>6 {{1,7},{2},{3},{4},{5,6}}=>5 {{1},{2,7},{3},{4},{5,6}}=>5 {{1},{2},{3,7},{4},{5,6}}=>5 {{1},{2},{3},{4,7},{5,6}}=>5 {{1},{2},{3},{4},{5,6,7}}=>0 {{1},{2},{3},{4},{5,6},{7}}=>1 {{1,7},{2},{3},{4},{5},{6}}=>6 {{1},{2,7},{3},{4},{5},{6}}=>6 {{1},{2},{3,7},{4},{5},{6}}=>6 {{1},{2},{3},{4,7},{5},{6}}=>6 {{1},{2},{3},{4},{5,7},{6}}=>6 {{1},{2},{3},{4},{5},{6,7}}=>0 {{1},{2},{3},{4},{5},{6},{7}}=>0 {{1},{2},{3,4,5,6,7,8}}=>0 {{1},{2,4,5,6,7,8},{3}}=>7 {{1},{2,3,5,6,7,8},{4}}=>7 {{1},{2,3,4,6,7,8},{5}}=>7 {{1},{2,3,4,5,7,8},{6}}=>7 {{1},{2,3,4,5,6,7},{8}}=>5 {{1},{2,3,4,5,6,8},{7}}=>7 {{1},{2,3,4,5,6,7,8}}=>0 {{1,2},{3,4,5,6,7,8}}=>1 {{1,4,5,6,7,8},{2},{3}}=>11 {{1,3,5,6,7,8},{2},{4}}=>11 {{1,3,4,5,6,7,8},{2}}=>7 {{1,4,5,6,7,8},{2,3}}=>6 {{1,2,4,5,6,7,8},{3}}=>7 {{1,2,5,6,7,8},{3,4}}=>6 {{1,2,3,5,6,7,8},{4}}=>7 {{1,2,3,6,7,8},{4,5}}=>6 {{1,2,3,4,6,7,8},{5}}=>7 {{1,2,3,4,5,6},{7,8}}=>5 {{1,2,3,4,7,8},{5,6}}=>6 {{1,2,3,4,5,7,8},{6}}=>7 {{1,2,3,4,5,6,7},{8}}=>6 {{1,8},{2,3,4,5,6,7}}=>2 {{1,2,3,4,5,8},{6,7}}=>6 {{1,2,3,4,5,6,8},{7}}=>7 {{1,2,3,4,5,6,7,8}}=>0 {{1,3,5,6,7,8},{2,4}}=>6 {{1,3,4,6,7,8},{2,5}}=>6 {{1,2,4,6,7,8},{3,5}}=>6 {{1,3,4,5,7,8},{2,6}}=>6 {{1,2,4,5,7,8},{3,6}}=>6 {{1,2,3,5,7,8},{4,6}}=>6 {{1,3,4,5,6,8},{2,7}}=>6 {{1,2,4,5,6,8},{3,7}}=>6 {{1,2,3,5,6,8},{4,7}}=>6 {{1,2,3,4,6,8},{5,7}}=>6 {{1,3,4,5,6,7},{2,8}}=>6 {{1,2,4,5,6,7},{3,8}}=>6 {{1,2,3,5,6,7},{4,8}}=>6 {{1,2,3,4,6,7},{5,8}}=>6 {{1,2,3,4,5,7},{6,8}}=>6 {{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
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Description
A variant of the major index of a set partition.
For a set partition $P = B_1|\dots|B_k$ in canonical form (this is, each block is ordered increasingly and all blocks are ordered by their smallest element), one defined $\pi = \pi(P)$ to be the permutation obtained by writing the letters in all blocks as one-line notation and $\omega = \omega(P) = (\omega_1,\ldots,\omega_k)$ be to be the integer composition of the ordered block sizes.
This statistic is then given in [1, (2.7)] by
$$\operatorname{maj}(\pi) + \sum_{max\ B_i < min\ B_{i+1}} (\omega_1 + \cdots + \omega_i - i).$$
References
[1] Huang, J., Rhoades, B. Ordered set partitions and the 0-Hecke algebra arXiv:1611.01251
Code
def statistic(SP):
    SP = sorted( sorted(B) for B in SP )
    pi = sum(SP,[])
    alpha = [ len(B)-Integer(1) for B in SP ]
    beta = [ sum(alpha[:i+1]) for i in range(len(alpha)) ]
    return sum( i+1 for i in range(len(pi)-1) if pi[i] > pi[i+1] ) + sum( beta[i] for i in range(len(SP)-1) if SP[i][-1] < SP[i+1][0] )
Created
Apr 04, 2017 at 17:44 by Christian Stump
Updated
Apr 04, 2017 at 17:44 by Christian Stump