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Identifier
Values
=>
Cc0009;cc-rep
{{1,2}}=>0 {{1},{2}}=>1 {{1,2,3}}=>0 {{1,2},{3}}=>1 {{1,3},{2}}=>1 {{1},{2,3}}=>2 {{1},{2},{3}}=>3 {{1,2,3,4}}=>0 {{1,2,3},{4}}=>1 {{1,2,4},{3}}=>1 {{1,2},{3,4}}=>2 {{1,2},{3},{4}}=>3 {{1,3,4},{2}}=>1 {{1,3},{2,4}}=>2 {{1,3},{2},{4}}=>3 {{1,4},{2,3}}=>2 {{1},{2,3,4}}=>3 {{1},{2,3},{4}}=>4 {{1,4},{2},{3}}=>3 {{1},{2,4},{3}}=>4 {{1},{2},{3,4}}=>5 {{1},{2},{3},{4}}=>6 {{1,2,3,4,5}}=>0 {{1,2,3,4},{5}}=>1 {{1,2,3,5},{4}}=>1 {{1,2,3},{4,5}}=>2 {{1,2,3},{4},{5}}=>3 {{1,2,4,5},{3}}=>1 {{1,2,4},{3,5}}=>2 {{1,2,4},{3},{5}}=>3 {{1,2,5},{3,4}}=>2 {{1,2},{3,4,5}}=>3 {{1,2},{3,4},{5}}=>4 {{1,2,5},{3},{4}}=>3 {{1,2},{3,5},{4}}=>4 {{1,2},{3},{4,5}}=>5 {{1,2},{3},{4},{5}}=>6 {{1,3,4,5},{2}}=>1 {{1,3,4},{2,5}}=>2 {{1,3,4},{2},{5}}=>3 {{1,3,5},{2,4}}=>2 {{1,3},{2,4,5}}=>3 {{1,3},{2,4},{5}}=>4 {{1,3,5},{2},{4}}=>3 {{1,3},{2,5},{4}}=>4 {{1,3},{2},{4,5}}=>5 {{1,3},{2},{4},{5}}=>6 {{1,4,5},{2,3}}=>2 {{1,4},{2,3,5}}=>3 {{1,4},{2,3},{5}}=>4 {{1,5},{2,3,4}}=>3 {{1},{2,3,4,5}}=>4 {{1},{2,3,4},{5}}=>5 {{1,5},{2,3},{4}}=>4 {{1},{2,3,5},{4}}=>5 {{1},{2,3},{4,5}}=>6 {{1},{2,3},{4},{5}}=>7 {{1,4,5},{2},{3}}=>3 {{1,4},{2,5},{3}}=>4 {{1,4},{2},{3,5}}=>5 {{1,4},{2},{3},{5}}=>6 {{1,5},{2,4},{3}}=>4 {{1},{2,4,5},{3}}=>5 {{1},{2,4},{3,5}}=>6 {{1},{2,4},{3},{5}}=>7 {{1,5},{2},{3,4}}=>5 {{1},{2,5},{3,4}}=>6 {{1},{2},{3,4,5}}=>7 {{1},{2},{3,4},{5}}=>8 {{1,5},{2},{3},{4}}=>6 {{1},{2,5},{3},{4}}=>7 {{1},{2},{3,5},{4}}=>8 {{1},{2},{3},{4,5}}=>9 {{1},{2},{3},{4},{5}}=>10 {{1,2,3,4,5,6}}=>0 {{1,2,3,4,5},{6}}=>1 {{1,2,3,4,6},{5}}=>1 {{1,2,3,4},{5,6}}=>2 {{1,2,3,4},{5},{6}}=>3 {{1,2,3,5,6},{4}}=>1 {{1,2,3,5},{4,6}}=>2 {{1,2,3,5},{4},{6}}=>3 {{1,2,3,6},{4,5}}=>2 {{1,2,3},{4,5,6}}=>3 {{1,2,3},{4,5},{6}}=>4 {{1,2,3,6},{4},{5}}=>3 {{1,2,3},{4,6},{5}}=>4 {{1,2,3},{4},{5,6}}=>5 {{1,2,3},{4},{5},{6}}=>6 {{1,2,4,5,6},{3}}=>1 {{1,2,4,5},{3,6}}=>2 {{1,2,4,5},{3},{6}}=>3 {{1,2,4,6},{3,5}}=>2 {{1,2,4},{3,5,6}}=>3 {{1,2,4},{3,5},{6}}=>4 {{1,2,4,6},{3},{5}}=>3 {{1,2,4},{3,6},{5}}=>4 {{1,2,4},{3},{5,6}}=>5 {{1,2,4},{3},{5},{6}}=>6 {{1,2,5,6},{3,4}}=>2 {{1,2,5},{3,4,6}}=>3 {{1,2,5},{3,4},{6}}=>4 {{1,2,6},{3,4,5}}=>3 {{1,2},{3,4,5,6}}=>4 {{1,2},{3,4,5},{6}}=>5 {{1,2,6},{3,4},{5}}=>4 {{1,2},{3,4,6},{5}}=>5 {{1,2},{3,4},{5,6}}=>6 {{1,2},{3,4},{5},{6}}=>7 {{1,2,5,6},{3},{4}}=>3 {{1,2,5},{3,6},{4}}=>4 {{1,2,5},{3},{4,6}}=>5 {{1,2,5},{3},{4},{6}}=>6 {{1,2,6},{3,5},{4}}=>4 {{1,2},{3,5,6},{4}}=>5 {{1,2},{3,5},{4,6}}=>6 {{1,2},{3,5},{4},{6}}=>7 {{1,2,6},{3},{4,5}}=>5 {{1,2},{3,6},{4,5}}=>6 {{1,2},{3},{4,5,6}}=>7 {{1,2},{3},{4,5},{6}}=>8 {{1,2,6},{3},{4},{5}}=>6 {{1,2},{3,6},{4},{5}}=>7 {{1,2},{3},{4,6},{5}}=>8 {{1,2},{3},{4},{5,6}}=>9 {{1,2},{3},{4},{5},{6}}=>10 {{1,3,4,5,6},{2}}=>1 {{1,3,4,5},{2,6}}=>2 {{1,3,4,5},{2},{6}}=>3 {{1,3,4,6},{2,5}}=>2 {{1,3,4},{2,5,6}}=>3 {{1,3,4},{2,5},{6}}=>4 {{1,3,4,6},{2},{5}}=>3 {{1,3,4},{2,6},{5}}=>4 {{1,3,4},{2},{5,6}}=>5 {{1,3,4},{2},{5},{6}}=>6 {{1,3,5,6},{2,4}}=>2 {{1,3,5},{2,4,6}}=>3 {{1,3,5},{2,4},{6}}=>4 {{1,3,6},{2,4,5}}=>3 {{1,3},{2,4,5,6}}=>4 {{1,3},{2,4,5},{6}}=>5 {{1,3,6},{2,4},{5}}=>4 {{1,3},{2,4,6},{5}}=>5 {{1,3},{2,4},{5,6}}=>6 {{1,3},{2,4},{5},{6}}=>7 {{1,3,5,6},{2},{4}}=>3 {{1,3,5},{2,6},{4}}=>4 {{1,3,5},{2},{4,6}}=>5 {{1,3,5},{2},{4},{6}}=>6 {{1,3,6},{2,5},{4}}=>4 {{1,3},{2,5,6},{4}}=>5 {{1,3},{2,5},{4,6}}=>6 {{1,3},{2,5},{4},{6}}=>7 {{1,3,6},{2},{4,5}}=>5 {{1,3},{2,6},{4,5}}=>6 {{1,3},{2},{4,5,6}}=>7 {{1,3},{2},{4,5},{6}}=>8 {{1,3,6},{2},{4},{5}}=>6 {{1,3},{2,6},{4},{5}}=>7 {{1,3},{2},{4,6},{5}}=>8 {{1,3},{2},{4},{5,6}}=>9 {{1,3},{2},{4},{5},{6}}=>10 {{1,4,5,6},{2,3}}=>2 {{1,4,5},{2,3,6}}=>3 {{1,4,5},{2,3},{6}}=>4 {{1,4,6},{2,3,5}}=>3 {{1,4},{2,3,5,6}}=>4 {{1,4},{2,3,5},{6}}=>5 {{1,4,6},{2,3},{5}}=>4 {{1,4},{2,3,6},{5}}=>5 {{1,4},{2,3},{5,6}}=>6 {{1,4},{2,3},{5},{6}}=>7 {{1,5,6},{2,3,4}}=>3 {{1,5},{2,3,4,6}}=>4 {{1,5},{2,3,4},{6}}=>5 {{1,6},{2,3,4,5}}=>4 {{1},{2,3,4,5,6}}=>5 {{1},{2,3,4,5},{6}}=>6 {{1,6},{2,3,4},{5}}=>5 {{1},{2,3,4,6},{5}}=>6 {{1},{2,3,4},{5,6}}=>7 {{1},{2,3,4},{5},{6}}=>8 {{1,5,6},{2,3},{4}}=>4 {{1,5},{2,3,6},{4}}=>5 {{1,5},{2,3},{4,6}}=>6 {{1,5},{2,3},{4},{6}}=>7 {{1,6},{2,3,5},{4}}=>5 {{1},{2,3,5,6},{4}}=>6 {{1},{2,3,5},{4,6}}=>7 {{1},{2,3,5},{4},{6}}=>8 {{1,6},{2,3},{4,5}}=>6 {{1},{2,3,6},{4,5}}=>7 {{1},{2,3},{4,5,6}}=>8 {{1},{2,3},{4,5},{6}}=>9 {{1,6},{2,3},{4},{5}}=>7 {{1},{2,3,6},{4},{5}}=>8 {{1},{2,3},{4,6},{5}}=>9 {{1},{2,3},{4},{5,6}}=>10 {{1},{2,3},{4},{5},{6}}=>11 {{1,4,5,6},{2},{3}}=>3 {{1,4,5},{2,6},{3}}=>4 {{1,4,5},{2},{3,6}}=>5 {{1,4,5},{2},{3},{6}}=>6 {{1,4,6},{2,5},{3}}=>4 {{1,4},{2,5,6},{3}}=>5 {{1,4},{2,5},{3,6}}=>6 {{1,4},{2,5},{3},{6}}=>7 {{1,4,6},{2},{3,5}}=>5 {{1,4},{2,6},{3,5}}=>6 {{1,4},{2},{3,5,6}}=>7 {{1,4},{2},{3,5},{6}}=>8 {{1,4,6},{2},{3},{5}}=>6 {{1,4},{2,6},{3},{5}}=>7 {{1,4},{2},{3,6},{5}}=>8 {{1,4},{2},{3},{5,6}}=>9 {{1,4},{2},{3},{5},{6}}=>10 {{1,5,6},{2,4},{3}}=>4 {{1,5},{2,4,6},{3}}=>5 {{1,5},{2,4},{3,6}}=>6 {{1,5},{2,4},{3},{6}}=>7 {{1,6},{2,4,5},{3}}=>5 {{1},{2,4,5,6},{3}}=>6 {{1},{2,4,5},{3,6}}=>7 {{1},{2,4,5},{3},{6}}=>8 {{1,6},{2,4},{3,5}}=>6 {{1},{2,4,6},{3,5}}=>7 {{1},{2,4},{3,5,6}}=>8 {{1},{2,4},{3,5},{6}}=>9 {{1,6},{2,4},{3},{5}}=>7 {{1},{2,4,6},{3},{5}}=>8 {{1},{2,4},{3,6},{5}}=>9 {{1},{2,4},{3},{5,6}}=>10 {{1},{2,4},{3},{5},{6}}=>11 {{1,5,6},{2},{3,4}}=>5 {{1,5},{2,6},{3,4}}=>6 {{1,5},{2},{3,4,6}}=>7 {{1,5},{2},{3,4},{6}}=>8 {{1,6},{2,5},{3,4}}=>6 {{1},{2,5,6},{3,4}}=>7 {{1},{2,5},{3,4,6}}=>8 {{1},{2,5},{3,4},{6}}=>9 {{1,6},{2},{3,4,5}}=>7 {{1},{2,6},{3,4,5}}=>8 {{1},{2},{3,4,5,6}}=>9 {{1},{2},{3,4,5},{6}}=>10 {{1,6},{2},{3,4},{5}}=>8 {{1},{2,6},{3,4},{5}}=>9 {{1},{2},{3,4,6},{5}}=>10 {{1},{2},{3,4},{5,6}}=>11 {{1},{2},{3,4},{5},{6}}=>12 {{1,5,6},{2},{3},{4}}=>6 {{1,5},{2,6},{3},{4}}=>7 {{1,5},{2},{3,6},{4}}=>8 {{1,5},{2},{3},{4,6}}=>9 {{1,5},{2},{3},{4},{6}}=>10 {{1,6},{2,5},{3},{4}}=>7 {{1},{2,5,6},{3},{4}}=>8 {{1},{2,5},{3,6},{4}}=>9 {{1},{2,5},{3},{4,6}}=>10 {{1},{2,5},{3},{4},{6}}=>11 {{1,6},{2},{3,5},{4}}=>8 {{1},{2,6},{3,5},{4}}=>9 {{1},{2},{3,5,6},{4}}=>10 {{1},{2},{3,5},{4,6}}=>11 {{1},{2},{3,5},{4},{6}}=>12 {{1,6},{2},{3},{4,5}}=>9 {{1},{2,6},{3},{4,5}}=>10 {{1},{2},{3,6},{4,5}}=>11 {{1},{2},{3},{4,5,6}}=>12 {{1},{2},{3},{4,5},{6}}=>13 {{1,6},{2},{3},{4},{5}}=>10 {{1},{2,6},{3},{4},{5}}=>11 {{1},{2},{3,6},{4},{5}}=>12 {{1},{2},{3},{4,6},{5}}=>13 {{1},{2},{3},{4},{5,6}}=>14 {{1},{2},{3},{4},{5},{6}}=>15 {{1,2,3,4,5,6,7}}=>0 {{1,2,3,4,5,6},{7}}=>1 {{1,2,3,4,5,7},{6}}=>1 {{1,2,3,4,5},{6,7}}=>2 {{1,2,3,4,5},{6},{7}}=>3 {{1,2,3,4,6,7},{5}}=>1 {{1,2,3,4,6},{5,7}}=>2 {{1,2,3,4,6},{5},{7}}=>3 {{1,2,3,4,7},{5,6}}=>2 {{1,2,3,4},{5,6,7}}=>3 {{1,2,3,4},{5,6},{7}}=>4 {{1,2,3,4,7},{5},{6}}=>3 {{1,2,3,4},{5,7},{6}}=>4 {{1,2,3,4},{5},{6,7}}=>5 {{1,2,3,4},{5},{6},{7}}=>6 {{1,2,3,5,6,7},{4}}=>1 {{1,2,3,5,6},{4,7}}=>2 {{1,2,3,5,6},{4},{7}}=>3 {{1,2,3,5,7},{4,6}}=>2 {{1,2,3,5},{4,6,7}}=>3 {{1,2,3,5},{4,6},{7}}=>4 {{1,2,3,5,7},{4},{6}}=>3 {{1,2,3,5},{4,7},{6}}=>4 {{1,2,3,5},{4},{6,7}}=>5 {{1,2,3,5},{4},{6},{7}}=>6 {{1,2,3,6,7},{4,5}}=>2 {{1,2,3,6},{4,5,7}}=>3 {{1,2,3,6},{4,5},{7}}=>4 {{1,2,3,7},{4,5,6}}=>3 {{1,2,3},{4,5,6,7}}=>4 {{1,2,3},{4,5,6},{7}}=>5 {{1,2,3,7},{4,5},{6}}=>4 {{1,2,3},{4,5,7},{6}}=>5 {{1,2,3},{4,5},{6,7}}=>6 {{1,2,3},{4,5},{6},{7}}=>7 {{1,2,3,6,7},{4},{5}}=>3 {{1,2,3,6},{4,7},{5}}=>4 {{1,2,3,6},{4},{5,7}}=>5 {{1,2,3,6},{4},{5},{7}}=>6 {{1,2,3,7},{4,6},{5}}=>4 {{1,2,3},{4,6,7},{5}}=>5 {{1,2,3},{4,6},{5,7}}=>6 {{1,2,3},{4,6},{5},{7}}=>7 {{1,2,3,7},{4},{5,6}}=>5 {{1,2,3},{4,7},{5,6}}=>6 {{1,2,3},{4},{5,6,7}}=>7 {{1,2,3},{4},{5,6},{7}}=>8 {{1,2,3,7},{4},{5},{6}}=>6 {{1,2,3},{4,7},{5},{6}}=>7 {{1,2,3},{4},{5,7},{6}}=>8 {{1,2,3},{4},{5},{6,7}}=>9 {{1,2,3},{4},{5},{6},{7}}=>10 {{1,2,4,5,6,7},{3}}=>1 {{1,2,4,5,6},{3,7}}=>2 {{1,2,4,5,6},{3},{7}}=>3 {{1,2,4,5,7},{3,6}}=>2 {{1,2,4,5},{3,6,7}}=>3 {{1,2,4,5},{3,6},{7}}=>4 {{1,2,4,5,7},{3},{6}}=>3 {{1,2,4,5},{3,7},{6}}=>4 {{1,2,4,5},{3},{6,7}}=>5 {{1,2,4,5},{3},{6},{7}}=>6 {{1,2,4,6,7},{3,5}}=>2 {{1,2,4,6},{3,5,7}}=>3 {{1,2,4,6},{3,5},{7}}=>4 {{1,2,4,7},{3,5,6}}=>3 {{1,2,4},{3,5,6,7}}=>4 {{1,2,4},{3,5,6},{7}}=>5 {{1,2,4,7},{3,5},{6}}=>4 {{1,2,4},{3,5,7},{6}}=>5 {{1,2,4},{3,5},{6,7}}=>6 {{1,2,4},{3,5},{6},{7}}=>7 {{1,2,4,6,7},{3},{5}}=>3 {{1,2,4,6},{3,7},{5}}=>4 {{1,2,4,6},{3},{5,7}}=>5 {{1,2,4,6},{3},{5},{7}}=>6 {{1,2,4,7},{3,6},{5}}=>4 {{1,2,4},{3,6,7},{5}}=>5 {{1,2,4},{3,6},{5,7}}=>6 {{1,2,4},{3,6},{5},{7}}=>7 {{1,2,4,7},{3},{5,6}}=>5 {{1,2,4},{3,7},{5,6}}=>6 {{1,2,4},{3},{5,6,7}}=>7 {{1,2,4},{3},{5,6},{7}}=>8 {{1,2,4,7},{3},{5},{6}}=>6 {{1,2,4},{3,7},{5},{6}}=>7 {{1,2,4},{3},{5,7},{6}}=>8 {{1,2,4},{3},{5},{6,7}}=>9 {{1,2,4},{3},{5},{6},{7}}=>10 {{1,2,5,6,7},{3,4}}=>2 {{1,2,5,6},{3,4,7}}=>3 {{1,2,5,6},{3,4},{7}}=>4 {{1,2,5,7},{3,4,6}}=>3 {{1,2,5},{3,4,6,7}}=>4 {{1,2,5},{3,4,6},{7}}=>5 {{1,2,5,7},{3,4},{6}}=>4 {{1,2,5},{3,4,7},{6}}=>5 {{1,2,5},{3,4},{6,7}}=>6 {{1,2,5},{3,4},{6},{7}}=>7 {{1,2,6,7},{3,4,5}}=>3 {{1,2,6},{3,4,5,7}}=>4 {{1,2,6},{3,4,5},{7}}=>5 {{1,2,7},{3,4,5,6}}=>4 {{1,2},{3,4,5,6,7}}=>5 {{1,2},{3,4,5,6},{7}}=>6 {{1,2,7},{3,4,5},{6}}=>5 {{1,2},{3,4,5,7},{6}}=>6 {{1,2},{3,4,5},{6,7}}=>7 {{1,2},{3,4,5},{6},{7}}=>8 {{1,2,6,7},{3,4},{5}}=>4 {{1,2,6},{3,4,7},{5}}=>5 {{1,2,6},{3,4},{5,7}}=>6 {{1,2,6},{3,4},{5},{7}}=>7 {{1,2,7},{3,4,6},{5}}=>5 {{1,2},{3,4,6,7},{5}}=>6 {{1,2},{3,4,6},{5,7}}=>7 {{1,2},{3,4,6},{5},{7}}=>8 {{1,2,7},{3,4},{5,6}}=>6 {{1,2},{3,4,7},{5,6}}=>7 {{1,2},{3,4},{5,6,7}}=>8 {{1,2},{3,4},{5,6},{7}}=>9 {{1,2,7},{3,4},{5},{6}}=>7 {{1,2},{3,4,7},{5},{6}}=>8 {{1,2},{3,4},{5,7},{6}}=>9 {{1,2},{3,4},{5},{6,7}}=>10 {{1,2},{3,4},{5},{6},{7}}=>11 {{1,2,5,6,7},{3},{4}}=>3 {{1,2,5,6},{3,7},{4}}=>4 {{1,2,5,6},{3},{4,7}}=>5 {{1,2,5,6},{3},{4},{7}}=>6 {{1,2,5,7},{3,6},{4}}=>4 {{1,2,5},{3,6,7},{4}}=>5 {{1,2,5},{3,6},{4,7}}=>6 {{1,2,5},{3,6},{4},{7}}=>7 {{1,2,5,7},{3},{4,6}}=>5 {{1,2,5},{3,7},{4,6}}=>6 {{1,2,5},{3},{4,6,7}}=>7 {{1,2,5},{3},{4,6},{7}}=>8 {{1,2,5,7},{3},{4},{6}}=>6 {{1,2,5},{3,7},{4},{6}}=>7 {{1,2,5},{3},{4,7},{6}}=>8 {{1,2,5},{3},{4},{6,7}}=>9 {{1,2,5},{3},{4},{6},{7}}=>10 {{1,2,6,7},{3,5},{4}}=>4 {{1,2,6},{3,5,7},{4}}=>5 {{1,2,6},{3,5},{4,7}}=>6 {{1,2,6},{3,5},{4},{7}}=>7 {{1,2,7},{3,5,6},{4}}=>5 {{1,2},{3,5,6,7},{4}}=>6 {{1,2},{3,5,6},{4,7}}=>7 {{1,2},{3,5,6},{4},{7}}=>8 {{1,2,7},{3,5},{4,6}}=>6 {{1,2},{3,5,7},{4,6}}=>7 {{1,2},{3,5},{4,6,7}}=>8 {{1,2},{3,5},{4,6},{7}}=>9 {{1,2,7},{3,5},{4},{6}}=>7 {{1,2},{3,5,7},{4},{6}}=>8 {{1,2},{3,5},{4,7},{6}}=>9 {{1,2},{3,5},{4},{6,7}}=>10 {{1,2},{3,5},{4},{6},{7}}=>11 {{1,2,6,7},{3},{4,5}}=>5 {{1,2,6},{3,7},{4,5}}=>6 {{1,2,6},{3},{4,5,7}}=>7 {{1,2,6},{3},{4,5},{7}}=>8 {{1,2,7},{3,6},{4,5}}=>6 {{1,2},{3,6,7},{4,5}}=>7 {{1,2},{3,6},{4,5,7}}=>8 {{1,2},{3,6},{4,5},{7}}=>9 {{1,2,7},{3},{4,5,6}}=>7 {{1,2},{3,7},{4,5,6}}=>8 {{1,2},{3},{4,5,6,7}}=>9 {{1,2},{3},{4,5,6},{7}}=>10 {{1,2,7},{3},{4,5},{6}}=>8 {{1,2},{3,7},{4,5},{6}}=>9 {{1,2},{3},{4,5,7},{6}}=>10 {{1,2},{3},{4,5},{6,7}}=>11 {{1,2},{3},{4,5},{6},{7}}=>12 {{1,2,6,7},{3},{4},{5}}=>6 {{1,2,6},{3,7},{4},{5}}=>7 {{1,2,6},{3},{4,7},{5}}=>8 {{1,2,6},{3},{4},{5,7}}=>9 {{1,2,6},{3},{4},{5},{7}}=>10 {{1,2,7},{3,6},{4},{5}}=>7 {{1,2},{3,6,7},{4},{5}}=>8 {{1,2},{3,6},{4,7},{5}}=>9 {{1,2},{3,6},{4},{5,7}}=>10 {{1,2},{3,6},{4},{5},{7}}=>11 {{1,2,7},{3},{4,6},{5}}=>8 {{1,2},{3,7},{4,6},{5}}=>9 {{1,2},{3},{4,6,7},{5}}=>10 {{1,2},{3},{4,6},{5,7}}=>11 {{1,2},{3},{4,6},{5},{7}}=>12 {{1,2,7},{3},{4},{5,6}}=>9 {{1,2},{3,7},{4},{5,6}}=>10 {{1,2},{3},{4,7},{5,6}}=>11 {{1,2},{3},{4},{5,6,7}}=>12 {{1,2},{3},{4},{5,6},{7}}=>13 {{1,2,7},{3},{4},{5},{6}}=>10 {{1,2},{3,7},{4},{5},{6}}=>11 {{1,2},{3},{4,7},{5},{6}}=>12 {{1,2},{3},{4},{5,7},{6}}=>13 {{1,2},{3},{4},{5},{6,7}}=>14 {{1,2},{3},{4},{5},{6},{7}}=>15 {{1,3,4,5,6,7},{2}}=>1 {{1,3,4,5,6},{2,7}}=>2 {{1,3,4,5,6},{2},{7}}=>3 {{1,3,4,5,7},{2,6}}=>2 {{1,3,4,5},{2,6,7}}=>3 {{1,3,4,5},{2,6},{7}}=>4 {{1,3,4,5,7},{2},{6}}=>3 {{1,3,4,5},{2,7},{6}}=>4 {{1,3,4,5},{2},{6,7}}=>5 {{1,3,4,5},{2},{6},{7}}=>6 {{1,3,4,6,7},{2,5}}=>2 {{1,3,4,6},{2,5,7}}=>3 {{1,3,4,6},{2,5},{7}}=>4 {{1,3,4,7},{2,5,6}}=>3 {{1,3,4},{2,5,6,7}}=>4 {{1,3,4},{2,5,6},{7}}=>5 {{1,3,4,7},{2,5},{6}}=>4 {{1,3,4},{2,5,7},{6}}=>5 {{1,3,4},{2,5},{6,7}}=>6 {{1,3,4},{2,5},{6},{7}}=>7 {{1,3,4,6,7},{2},{5}}=>3 {{1,3,4,6},{2,7},{5}}=>4 {{1,3,4,6},{2},{5,7}}=>5 {{1,3,4,6},{2},{5},{7}}=>6 {{1,3,4,7},{2,6},{5}}=>4 {{1,3,4},{2,6,7},{5}}=>5 {{1,3,4},{2,6},{5,7}}=>6 {{1,3,4},{2,6},{5},{7}}=>7 {{1,3,4,7},{2},{5,6}}=>5 {{1,3,4},{2,7},{5,6}}=>6 {{1,3,4},{2},{5,6,7}}=>7 {{1,3,4},{2},{5,6},{7}}=>8 {{1,3,4,7},{2},{5},{6}}=>6 {{1,3,4},{2,7},{5},{6}}=>7 {{1,3,4},{2},{5,7},{6}}=>8 {{1,3,4},{2},{5},{6,7}}=>9 {{1,3,4},{2},{5},{6},{7}}=>10 {{1,3,5,6,7},{2,4}}=>2 {{1,3,5,6},{2,4,7}}=>3 {{1,3,5,6},{2,4},{7}}=>4 {{1,3,5,7},{2,4,6}}=>3 {{1,3,5},{2,4,6,7}}=>4 {{1,3,5},{2,4,6},{7}}=>5 {{1,3,5,7},{2,4},{6}}=>4 {{1,3,5},{2,4,7},{6}}=>5 {{1,3,5},{2,4},{6,7}}=>6 {{1,3,5},{2,4},{6},{7}}=>7 {{1,3,6,7},{2,4,5}}=>3 {{1,3,6},{2,4,5,7}}=>4 {{1,3,6},{2,4,5},{7}}=>5 {{1,3,7},{2,4,5,6}}=>4 {{1,3},{2,4,5,6,7}}=>5 {{1,3},{2,4,5,6},{7}}=>6 {{1,3,7},{2,4,5},{6}}=>5 {{1,3},{2,4,5,7},{6}}=>6 {{1,3},{2,4,5},{6,7}}=>7 {{1,3},{2,4,5},{6},{7}}=>8 {{1,3,6,7},{2,4},{5}}=>4 {{1,3,6},{2,4,7},{5}}=>5 {{1,3,6},{2,4},{5,7}}=>6 {{1,3,6},{2,4},{5},{7}}=>7 {{1,3,7},{2,4,6},{5}}=>5 {{1,3},{2,4,6,7},{5}}=>6 {{1,3},{2,4,6},{5,7}}=>7 {{1,3},{2,4,6},{5},{7}}=>8 {{1,3,7},{2,4},{5,6}}=>6 {{1,3},{2,4,7},{5,6}}=>7 {{1,3},{2,4},{5,6,7}}=>8 {{1,3},{2,4},{5,6},{7}}=>9 {{1,3,7},{2,4},{5},{6}}=>7 {{1,3},{2,4,7},{5},{6}}=>8 {{1,3},{2,4},{5,7},{6}}=>9 {{1,3},{2,4},{5},{6,7}}=>10 {{1,3},{2,4},{5},{6},{7}}=>11 {{1,3,5,6,7},{2},{4}}=>3 {{1,3,5,6},{2,7},{4}}=>4 {{1,3,5,6},{2},{4,7}}=>5 {{1,3,5,6},{2},{4},{7}}=>6 {{1,3,5,7},{2,6},{4}}=>4 {{1,3,5},{2,6,7},{4}}=>5 {{1,3,5},{2,6},{4,7}}=>6 {{1,3,5},{2,6},{4},{7}}=>7 {{1,3,5,7},{2},{4,6}}=>5 {{1,3,5},{2,7},{4,6}}=>6 {{1,3,5},{2},{4,6,7}}=>7 {{1,3,5},{2},{4,6},{7}}=>8 {{1,3,5,7},{2},{4},{6}}=>6 {{1,3,5},{2,7},{4},{6}}=>7 {{1,3,5},{2},{4,7},{6}}=>8 {{1,3,5},{2},{4},{6,7}}=>9 {{1,3,5},{2},{4},{6},{7}}=>10 {{1,3,6,7},{2,5},{4}}=>4 {{1,3,6},{2,5,7},{4}}=>5 {{1,3,6},{2,5},{4,7}}=>6 {{1,3,6},{2,5},{4},{7}}=>7 {{1,3,7},{2,5,6},{4}}=>5 {{1,3},{2,5,6,7},{4}}=>6 {{1,3},{2,5,6},{4,7}}=>7 {{1,3},{2,5,6},{4},{7}}=>8 {{1,3,7},{2,5},{4,6}}=>6 {{1,3},{2,5,7},{4,6}}=>7 {{1,3},{2,5},{4,6,7}}=>8 {{1,3},{2,5},{4,6},{7}}=>9 {{1,3,7},{2,5},{4},{6}}=>7 {{1,3},{2,5,7},{4},{6}}=>8 {{1,3},{2,5},{4,7},{6}}=>9 {{1,3},{2,5},{4},{6,7}}=>10 {{1,3},{2,5},{4},{6},{7}}=>11 {{1,3,6,7},{2},{4,5}}=>5 {{1,3,6},{2,7},{4,5}}=>6 {{1,3,6},{2},{4,5,7}}=>7 {{1,3,6},{2},{4,5},{7}}=>8 {{1,3,7},{2,6},{4,5}}=>6 {{1,3},{2,6,7},{4,5}}=>7 {{1,3},{2,6},{4,5,7}}=>8 {{1,3},{2,6},{4,5},{7}}=>9 {{1,3,7},{2},{4,5,6}}=>7 {{1,3},{2,7},{4,5,6}}=>8 {{1,3},{2},{4,5,6,7}}=>9 {{1,3},{2},{4,5,6},{7}}=>10 {{1,3,7},{2},{4,5},{6}}=>8 {{1,3},{2,7},{4,5},{6}}=>9 {{1,3},{2},{4,5,7},{6}}=>10 {{1,3},{2},{4,5},{6,7}}=>11 {{1,3},{2},{4,5},{6},{7}}=>12 {{1,3,6,7},{2},{4},{5}}=>6 {{1,3,6},{2,7},{4},{5}}=>7 {{1,3,6},{2},{4,7},{5}}=>8 {{1,3,6},{2},{4},{5,7}}=>9 {{1,3,6},{2},{4},{5},{7}}=>10 {{1,3,7},{2,6},{4},{5}}=>7 {{1,3},{2,6,7},{4},{5}}=>8 {{1,3},{2,6},{4,7},{5}}=>9 {{1,3},{2,6},{4},{5,7}}=>10 {{1,3},{2,6},{4},{5},{7}}=>11 {{1,3,7},{2},{4,6},{5}}=>8 {{1,3},{2,7},{4,6},{5}}=>9 {{1,3},{2},{4,6,7},{5}}=>10 {{1,3},{2},{4,6},{5,7}}=>11 {{1,3},{2},{4,6},{5},{7}}=>12 {{1,3,7},{2},{4},{5,6}}=>9 {{1,3},{2,7},{4},{5,6}}=>10 {{1,3},{2},{4,7},{5,6}}=>11 {{1,3},{2},{4},{5,6,7}}=>12 {{1,3},{2},{4},{5,6},{7}}=>13 {{1,3,7},{2},{4},{5},{6}}=>10 {{1,3},{2,7},{4},{5},{6}}=>11 {{1,3},{2},{4,7},{5},{6}}=>12 {{1,3},{2},{4},{5,7},{6}}=>13 {{1,3},{2},{4},{5},{6,7}}=>14 {{1,3},{2},{4},{5},{6},{7}}=>15 {{1,4,5,6,7},{2,3}}=>2 {{1,4,5,6},{2,3,7}}=>3 {{1,4,5,6},{2,3},{7}}=>4 {{1,4,5,7},{2,3,6}}=>3 {{1,4,5},{2,3,6,7}}=>4 {{1,4,5},{2,3,6},{7}}=>5 {{1,4,5,7},{2,3},{6}}=>4 {{1,4,5},{2,3,7},{6}}=>5 {{1,4,5},{2,3},{6,7}}=>6 {{1,4,5},{2,3},{6},{7}}=>7 {{1,4,6,7},{2,3,5}}=>3 {{1,4,6},{2,3,5,7}}=>4 {{1,4,6},{2,3,5},{7}}=>5 {{1,4,7},{2,3,5,6}}=>4 {{1,4},{2,3,5,6,7}}=>5 {{1,4},{2,3,5,6},{7}}=>6 {{1,4,7},{2,3,5},{6}}=>5 {{1,4},{2,3,5,7},{6}}=>6 {{1,4},{2,3,5},{6,7}}=>7 {{1,4},{2,3,5},{6},{7}}=>8 {{1,4,6,7},{2,3},{5}}=>4 {{1,4,6},{2,3,7},{5}}=>5 {{1,4,6},{2,3},{5,7}}=>6 {{1,4,6},{2,3},{5},{7}}=>7 {{1,4,7},{2,3,6},{5}}=>5 {{1,4},{2,3,6,7},{5}}=>6 {{1,4},{2,3,6},{5,7}}=>7 {{1,4},{2,3,6},{5},{7}}=>8 {{1,4,7},{2,3},{5,6}}=>6 {{1,4},{2,3,7},{5,6}}=>7 {{1,4},{2,3},{5,6,7}}=>8 {{1,4},{2,3},{5,6},{7}}=>9 {{1,4,7},{2,3},{5},{6}}=>7 {{1,4},{2,3,7},{5},{6}}=>8 {{1,4},{2,3},{5,7},{6}}=>9 {{1,4},{2,3},{5},{6,7}}=>10 {{1,4},{2,3},{5},{6},{7}}=>11 {{1,5,6,7},{2,3,4}}=>3 {{1,5,6},{2,3,4,7}}=>4 {{1,5,6},{2,3,4},{7}}=>5 {{1,5,7},{2,3,4,6}}=>4 {{1,5},{2,3,4,6,7}}=>5 {{1,5},{2,3,4,6},{7}}=>6 {{1,5,7},{2,3,4},{6}}=>5 {{1,5},{2,3,4,7},{6}}=>6 {{1,5},{2,3,4},{6,7}}=>7 {{1,5},{2,3,4},{6},{7}}=>8 {{1,6,7},{2,3,4,5}}=>4 {{1,6},{2,3,4,5,7}}=>5 {{1,6},{2,3,4,5},{7}}=>6 {{1,7},{2,3,4,5,6}}=>5 {{1},{2,3,4,5,6,7}}=>6 {{1},{2,3,4,5,6},{7}}=>7 {{1,7},{2,3,4,5},{6}}=>6 {{1},{2,3,4,5,7},{6}}=>7 {{1},{2,3,4,5},{6,7}}=>8 {{1},{2,3,4,5},{6},{7}}=>9 {{1,6,7},{2,3,4},{5}}=>5 {{1,6},{2,3,4,7},{5}}=>6 {{1,6},{2,3,4},{5,7}}=>7 {{1,6},{2,3,4},{5},{7}}=>8 {{1,7},{2,3,4,6},{5}}=>6 {{1},{2,3,4,6,7},{5}}=>7 {{1},{2,3,4,6},{5,7}}=>8 {{1},{2,3,4,6},{5},{7}}=>9 {{1,7},{2,3,4},{5,6}}=>7 {{1},{2,3,4,7},{5,6}}=>8 {{1},{2,3,4},{5,6,7}}=>9 {{1},{2,3,4},{5,6},{7}}=>10 {{1,7},{2,3,4},{5},{6}}=>8 {{1},{2,3,4,7},{5},{6}}=>9 {{1},{2,3,4},{5,7},{6}}=>10 {{1},{2,3,4},{5},{6,7}}=>11 {{1},{2,3,4},{5},{6},{7}}=>12 {{1,5,6,7},{2,3},{4}}=>4 {{1,5,6},{2,3,7},{4}}=>5 {{1,5,6},{2,3},{4,7}}=>6 {{1,5,6},{2,3},{4},{7}}=>7 {{1,5,7},{2,3,6},{4}}=>5 {{1,5},{2,3,6,7},{4}}=>6 {{1,5},{2,3,6},{4,7}}=>7 {{1,5},{2,3,6},{4},{7}}=>8 {{1,5,7},{2,3},{4,6}}=>6 {{1,5},{2,3,7},{4,6}}=>7 {{1,5},{2,3},{4,6,7}}=>8 {{1,5},{2,3},{4,6},{7}}=>9 {{1,5,7},{2,3},{4},{6}}=>7 {{1,5},{2,3,7},{4},{6}}=>8 {{1,5},{2,3},{4,7},{6}}=>9 {{1,5},{2,3},{4},{6,7}}=>10 {{1,5},{2,3},{4},{6},{7}}=>11 {{1,6,7},{2,3,5},{4}}=>5 {{1,6},{2,3,5,7},{4}}=>6 {{1,6},{2,3,5},{4,7}}=>7 {{1,6},{2,3,5},{4},{7}}=>8 {{1,7},{2,3,5,6},{4}}=>6 {{1},{2,3,5,6,7},{4}}=>7 {{1},{2,3,5,6},{4,7}}=>8 {{1},{2,3,5,6},{4},{7}}=>9 {{1,7},{2,3,5},{4,6}}=>7 {{1},{2,3,5,7},{4,6}}=>8 {{1},{2,3,5},{4,6,7}}=>9 {{1},{2,3,5},{4,6},{7}}=>10 {{1,7},{2,3,5},{4},{6}}=>8 {{1},{2,3,5,7},{4},{6}}=>9 {{1},{2,3,5},{4,7},{6}}=>10 {{1},{2,3,5},{4},{6,7}}=>11 {{1},{2,3,5},{4},{6},{7}}=>12 {{1,6,7},{2,3},{4,5}}=>6 {{1,6},{2,3,7},{4,5}}=>7 {{1,6},{2,3},{4,5,7}}=>8 {{1,6},{2,3},{4,5},{7}}=>9 {{1,7},{2,3,6},{4,5}}=>7 {{1},{2,3,6,7},{4,5}}=>8 {{1},{2,3,6},{4,5,7}}=>9 {{1},{2,3,6},{4,5},{7}}=>10 {{1,7},{2,3},{4,5,6}}=>8 {{1},{2,3,7},{4,5,6}}=>9 {{1},{2,3},{4,5,6,7}}=>10 {{1},{2,3},{4,5,6},{7}}=>11 {{1,7},{2,3},{4,5},{6}}=>9 {{1},{2,3,7},{4,5},{6}}=>10 {{1},{2,3},{4,5,7},{6}}=>11 {{1},{2,3},{4,5},{6,7}}=>12 {{1},{2,3},{4,5},{6},{7}}=>13 {{1,6,7},{2,3},{4},{5}}=>7 {{1,6},{2,3,7},{4},{5}}=>8 {{1,6},{2,3},{4,7},{5}}=>9 {{1,6},{2,3},{4},{5,7}}=>10 {{1,6},{2,3},{4},{5},{7}}=>11 {{1,7},{2,3,6},{4},{5}}=>8 {{1},{2,3,6,7},{4},{5}}=>9 {{1},{2,3,6},{4,7},{5}}=>10 {{1},{2,3,6},{4},{5,7}}=>11 {{1},{2,3,6},{4},{5},{7}}=>12 {{1,7},{2,3},{4,6},{5}}=>9 {{1},{2,3,7},{4,6},{5}}=>10 {{1},{2,3},{4,6,7},{5}}=>11 {{1},{2,3},{4,6},{5,7}}=>12 {{1},{2,3},{4,6},{5},{7}}=>13 {{1,7},{2,3},{4},{5,6}}=>10 {{1},{2,3,7},{4},{5,6}}=>11 {{1},{2,3},{4,7},{5,6}}=>12 {{1},{2,3},{4},{5,6,7}}=>13 {{1},{2,3},{4},{5,6},{7}}=>14 {{1,7},{2,3},{4},{5},{6}}=>11 {{1},{2,3,7},{4},{5},{6}}=>12 {{1},{2,3},{4,7},{5},{6}}=>13 {{1},{2,3},{4},{5,7},{6}}=>14 {{1},{2,3},{4},{5},{6,7}}=>15 {{1},{2,3},{4},{5},{6},{7}}=>16 {{1,4,5,6,7},{2},{3}}=>3 {{1,4,5,6},{2,7},{3}}=>4 {{1,4,5,6},{2},{3,7}}=>5 {{1,4,5,6},{2},{3},{7}}=>6 {{1,4,5,7},{2,6},{3}}=>4 {{1,4,5},{2,6,7},{3}}=>5 {{1,4,5},{2,6},{3,7}}=>6 {{1,4,5},{2,6},{3},{7}}=>7 {{1,4,5,7},{2},{3,6}}=>5 {{1,4,5},{2,7},{3,6}}=>6 {{1,4,5},{2},{3,6,7}}=>7 {{1,4,5},{2},{3,6},{7}}=>8 {{1,4,5,7},{2},{3},{6}}=>6 {{1,4,5},{2,7},{3},{6}}=>7 {{1,4,5},{2},{3,7},{6}}=>8 {{1,4,5},{2},{3},{6,7}}=>9 {{1,4,5},{2},{3},{6},{7}}=>10 {{1,4,6,7},{2,5},{3}}=>4 {{1,4,6},{2,5,7},{3}}=>5 {{1,4,6},{2,5},{3,7}}=>6 {{1,4,6},{2,5},{3},{7}}=>7 {{1,4,7},{2,5,6},{3}}=>5 {{1,4},{2,5,6,7},{3}}=>6 {{1,4},{2,5,6},{3,7}}=>7 {{1,4},{2,5,6},{3},{7}}=>8 {{1,4,7},{2,5},{3,6}}=>6 {{1,4},{2,5,7},{3,6}}=>7 {{1,4},{2,5},{3,6,7}}=>8 {{1,4},{2,5},{3,6},{7}}=>9 {{1,4,7},{2,5},{3},{6}}=>7 {{1,4},{2,5,7},{3},{6}}=>8 {{1,4},{2,5},{3,7},{6}}=>9 {{1,4},{2,5},{3},{6,7}}=>10 {{1,4},{2,5},{3},{6},{7}}=>11 {{1,4,6,7},{2},{3,5}}=>5 {{1,4,6},{2,7},{3,5}}=>6 {{1,4,6},{2},{3,5,7}}=>7 {{1,4,6},{2},{3,5},{7}}=>8 {{1,4,7},{2,6},{3,5}}=>6 {{1,4},{2,6,7},{3,5}}=>7 {{1,4},{2,6},{3,5,7}}=>8 {{1,4},{2,6},{3,5},{7}}=>9 {{1,4,7},{2},{3,5,6}}=>7 {{1,4},{2,7},{3,5,6}}=>8 {{1,4},{2},{3,5,6,7}}=>9 {{1,4},{2},{3,5,6},{7}}=>10 {{1,4,7},{2},{3,5},{6}}=>8 {{1,4},{2,7},{3,5},{6}}=>9 {{1,4},{2},{3,5,7},{6}}=>10 {{1,4},{2},{3,5},{6,7}}=>11 {{1,4},{2},{3,5},{6},{7}}=>12 {{1,4,6,7},{2},{3},{5}}=>6 {{1,4,6},{2,7},{3},{5}}=>7 {{1,4,6},{2},{3,7},{5}}=>8 {{1,4,6},{2},{3},{5,7}}=>9 {{1,4,6},{2},{3},{5},{7}}=>10 {{1,4,7},{2,6},{3},{5}}=>7 {{1,4},{2,6,7},{3},{5}}=>8 {{1,4},{2,6},{3,7},{5}}=>9 {{1,4},{2,6},{3},{5,7}}=>10 {{1,4},{2,6},{3},{5},{7}}=>11 {{1,4,7},{2},{3,6},{5}}=>8 {{1,4},{2,7},{3,6},{5}}=>9 {{1,4},{2},{3,6,7},{5}}=>10 {{1,4},{2},{3,6},{5,7}}=>11 {{1,4},{2},{3,6},{5},{7}}=>12 {{1,4,7},{2},{3},{5,6}}=>9 {{1,4},{2,7},{3},{5,6}}=>10 {{1,4},{2},{3,7},{5,6}}=>11 {{1,4},{2},{3},{5,6,7}}=>12 {{1,4},{2},{3},{5,6},{7}}=>13 {{1,4,7},{2},{3},{5},{6}}=>10 {{1,4},{2,7},{3},{5},{6}}=>11 {{1,4},{2},{3,7},{5},{6}}=>12 {{1,4},{2},{3},{5,7},{6}}=>13 {{1,4},{2},{3},{5},{6,7}}=>14 {{1,4},{2},{3},{5},{6},{7}}=>15 {{1,5,6,7},{2,4},{3}}=>4 {{1,5,6},{2,4,7},{3}}=>5 {{1,5,6},{2,4},{3,7}}=>6 {{1,5,6},{2,4},{3},{7}}=>7 {{1,5,7},{2,4,6},{3}}=>5 {{1,5},{2,4,6,7},{3}}=>6 {{1,5},{2,4,6},{3,7}}=>7 {{1,5},{2,4,6},{3},{7}}=>8 {{1,5,7},{2,4},{3,6}}=>6 {{1,5},{2,4,7},{3,6}}=>7 {{1,5},{2,4},{3,6,7}}=>8 {{1,5},{2,4},{3,6},{7}}=>9 {{1,5,7},{2,4},{3},{6}}=>7 {{1,5},{2,4,7},{3},{6}}=>8 {{1,5},{2,4},{3,7},{6}}=>9 {{1,5},{2,4},{3},{6,7}}=>10 {{1,5},{2,4},{3},{6},{7}}=>11 {{1,6,7},{2,4,5},{3}}=>5 {{1,6},{2,4,5,7},{3}}=>6 {{1,6},{2,4,5},{3,7}}=>7 {{1,6},{2,4,5},{3},{7}}=>8 {{1,7},{2,4,5,6},{3}}=>6 {{1},{2,4,5,6,7},{3}}=>7 {{1},{2,4,5,6},{3,7}}=>8 {{1},{2,4,5,6},{3},{7}}=>9 {{1,7},{2,4,5},{3,6}}=>7 {{1},{2,4,5,7},{3,6}}=>8 {{1},{2,4,5},{3,6,7}}=>9 {{1},{2,4,5},{3,6},{7}}=>10 {{1,7},{2,4,5},{3},{6}}=>8 {{1},{2,4,5,7},{3},{6}}=>9 {{1},{2,4,5},{3,7},{6}}=>10 {{1},{2,4,5},{3},{6,7}}=>11 {{1},{2,4,5},{3},{6},{7}}=>12 {{1,6,7},{2,4},{3,5}}=>6 {{1,6},{2,4,7},{3,5}}=>7 {{1,6},{2,4},{3,5,7}}=>8 {{1,6},{2,4},{3,5},{7}}=>9 {{1,7},{2,4,6},{3,5}}=>7 {{1},{2,4,6,7},{3,5}}=>8 {{1},{2,4,6},{3,5,7}}=>9 {{1},{2,4,6},{3,5},{7}}=>10 {{1,7},{2,4},{3,5,6}}=>8 {{1},{2,4,7},{3,5,6}}=>9 {{1},{2,4},{3,5,6,7}}=>10 {{1},{2,4},{3,5,6},{7}}=>11 {{1,7},{2,4},{3,5},{6}}=>9 {{1},{2,4,7},{3,5},{6}}=>10 {{1},{2,4},{3,5,7},{6}}=>11 {{1},{2,4},{3,5},{6,7}}=>12 {{1},{2,4},{3,5},{6},{7}}=>13 {{1,6,7},{2,4},{3},{5}}=>7 {{1,6},{2,4,7},{3},{5}}=>8 {{1,6},{2,4},{3,7},{5}}=>9 {{1,6},{2,4},{3},{5,7}}=>10 {{1,6},{2,4},{3},{5},{7}}=>11 {{1,7},{2,4,6},{3},{5}}=>8 {{1},{2,4,6,7},{3},{5}}=>9 {{1},{2,4,6},{3,7},{5}}=>10 {{1},{2,4,6},{3},{5,7}}=>11 {{1},{2,4,6},{3},{5},{7}}=>12 {{1,7},{2,4},{3,6},{5}}=>9 {{1},{2,4,7},{3,6},{5}}=>10 {{1},{2,4},{3,6,7},{5}}=>11 {{1},{2,4},{3,6},{5,7}}=>12 {{1},{2,4},{3,6},{5},{7}}=>13 {{1,7},{2,4},{3},{5,6}}=>10 {{1},{2,4,7},{3},{5,6}}=>11 {{1},{2,4},{3,7},{5,6}}=>12 {{1},{2,4},{3},{5,6,7}}=>13 {{1},{2,4},{3},{5,6},{7}}=>14 {{1,7},{2,4},{3},{5},{6}}=>11 {{1},{2,4,7},{3},{5},{6}}=>12 {{1},{2,4},{3,7},{5},{6}}=>13 {{1},{2,4},{3},{5,7},{6}}=>14 {{1},{2,4},{3},{5},{6,7}}=>15 {{1},{2,4},{3},{5},{6},{7}}=>16 {{1,5,6,7},{2},{3,4}}=>5 {{1,5,6},{2,7},{3,4}}=>6 {{1,5,6},{2},{3,4,7}}=>7 {{1,5,6},{2},{3,4},{7}}=>8 {{1,5,7},{2,6},{3,4}}=>6 {{1,5},{2,6,7},{3,4}}=>7 {{1,5},{2,6},{3,4,7}}=>8 {{1,5},{2,6},{3,4},{7}}=>9 {{1,5,7},{2},{3,4,6}}=>7 {{1,5},{2,7},{3,4,6}}=>8 {{1,5},{2},{3,4,6,7}}=>9 {{1,5},{2},{3,4,6},{7}}=>10 {{1,5,7},{2},{3,4},{6}}=>8 {{1,5},{2,7},{3,4},{6}}=>9 {{1,5},{2},{3,4,7},{6}}=>10 {{1,5},{2},{3,4},{6,7}}=>11 {{1,5},{2},{3,4},{6},{7}}=>12 {{1,6,7},{2,5},{3,4}}=>6 {{1,6},{2,5,7},{3,4}}=>7 {{1,6},{2,5},{3,4,7}}=>8 {{1,6},{2,5},{3,4},{7}}=>9 {{1,7},{2,5,6},{3,4}}=>7 {{1},{2,5,6,7},{3,4}}=>8 {{1},{2,5,6},{3,4,7}}=>9 {{1},{2,5,6},{3,4},{7}}=>10 {{1,7},{2,5},{3,4,6}}=>8 {{1},{2,5,7},{3,4,6}}=>9 {{1},{2,5},{3,4,6,7}}=>10 {{1},{2,5},{3,4,6},{7}}=>11 {{1,7},{2,5},{3,4},{6}}=>9 {{1},{2,5,7},{3,4},{6}}=>10 {{1},{2,5},{3,4,7},{6}}=>11 {{1},{2,5},{3,4},{6,7}}=>12 {{1},{2,5},{3,4},{6},{7}}=>13 {{1,6,7},{2},{3,4,5}}=>7 {{1,6},{2,7},{3,4,5}}=>8 {{1,6},{2},{3,4,5,7}}=>9 {{1,6},{2},{3,4,5},{7}}=>10 {{1,7},{2,6},{3,4,5}}=>8 {{1},{2,6,7},{3,4,5}}=>9 {{1},{2,6},{3,4,5,7}}=>10 {{1},{2,6},{3,4,5},{7}}=>11 {{1,7},{2},{3,4,5,6}}=>9 {{1},{2,7},{3,4,5,6}}=>10 {{1},{2},{3,4,5,6,7}}=>11 {{1},{2},{3,4,5,6},{7}}=>12 {{1,7},{2},{3,4,5},{6}}=>10 {{1},{2,7},{3,4,5},{6}}=>11 {{1},{2},{3,4,5,7},{6}}=>12 {{1},{2},{3,4,5},{6,7}}=>13 {{1},{2},{3,4,5},{6},{7}}=>14 {{1,6,7},{2},{3,4},{5}}=>8 {{1,6},{2,7},{3,4},{5}}=>9 {{1,6},{2},{3,4,7},{5}}=>10 {{1,6},{2},{3,4},{5,7}}=>11 {{1,6},{2},{3,4},{5},{7}}=>12 {{1,7},{2,6},{3,4},{5}}=>9 {{1},{2,6,7},{3,4},{5}}=>10 {{1},{2,6},{3,4,7},{5}}=>11 {{1},{2,6},{3,4},{5,7}}=>12 {{1},{2,6},{3,4},{5},{7}}=>13 {{1,7},{2},{3,4,6},{5}}=>10 {{1},{2,7},{3,4,6},{5}}=>11 {{1},{2},{3,4,6,7},{5}}=>12 {{1},{2},{3,4,6},{5,7}}=>13 {{1},{2},{3,4,6},{5},{7}}=>14 {{1,7},{2},{3,4},{5,6}}=>11 {{1},{2,7},{3,4},{5,6}}=>12 {{1},{2},{3,4,7},{5,6}}=>13 {{1},{2},{3,4},{5,6,7}}=>14 {{1},{2},{3,4},{5,6},{7}}=>15 {{1,7},{2},{3,4},{5},{6}}=>12 {{1},{2,7},{3,4},{5},{6}}=>13 {{1},{2},{3,4,7},{5},{6}}=>14 {{1},{2},{3,4},{5,7},{6}}=>15 {{1},{2},{3,4},{5},{6,7}}=>16 {{1},{2},{3,4},{5},{6},{7}}=>17 {{1,5,6,7},{2},{3},{4}}=>6 {{1,5,6},{2,7},{3},{4}}=>7 {{1,5,6},{2},{3,7},{4}}=>8 {{1,5,6},{2},{3},{4,7}}=>9 {{1,5,6},{2},{3},{4},{7}}=>10 {{1,5,7},{2,6},{3},{4}}=>7 {{1,5},{2,6,7},{3},{4}}=>8 {{1,5},{2,6},{3,7},{4}}=>9 {{1,5},{2,6},{3},{4,7}}=>10 {{1,5},{2,6},{3},{4},{7}}=>11 {{1,5,7},{2},{3,6},{4}}=>8 {{1,5},{2,7},{3,6},{4}}=>9 {{1,5},{2},{3,6,7},{4}}=>10 {{1,5},{2},{3,6},{4,7}}=>11 {{1,5},{2},{3,6},{4},{7}}=>12 {{1,5,7},{2},{3},{4,6}}=>9 {{1,5},{2,7},{3},{4,6}}=>10 {{1,5},{2},{3,7},{4,6}}=>11 {{1,5},{2},{3},{4,6,7}}=>12 {{1,5},{2},{3},{4,6},{7}}=>13 {{1,5,7},{2},{3},{4},{6}}=>10 {{1,5},{2,7},{3},{4},{6}}=>11 {{1,5},{2},{3,7},{4},{6}}=>12 {{1,5},{2},{3},{4,7},{6}}=>13 {{1,5},{2},{3},{4},{6,7}}=>14 {{1,5},{2},{3},{4},{6},{7}}=>15 {{1,6,7},{2,5},{3},{4}}=>7 {{1,6},{2,5,7},{3},{4}}=>8 {{1,6},{2,5},{3,7},{4}}=>9 {{1,6},{2,5},{3},{4,7}}=>10 {{1,6},{2,5},{3},{4},{7}}=>11 {{1,7},{2,5,6},{3},{4}}=>8 {{1},{2,5,6,7},{3},{4}}=>9 {{1},{2,5,6},{3,7},{4}}=>10 {{1},{2,5,6},{3},{4,7}}=>11 {{1},{2,5,6},{3},{4},{7}}=>12 {{1,7},{2,5},{3,6},{4}}=>9 {{1},{2,5,7},{3,6},{4}}=>10 {{1},{2,5},{3,6,7},{4}}=>11 {{1},{2,5},{3,6},{4,7}}=>12 {{1},{2,5},{3,6},{4},{7}}=>13 {{1,7},{2,5},{3},{4,6}}=>10 {{1},{2,5,7},{3},{4,6}}=>11 {{1},{2,5},{3,7},{4,6}}=>12 {{1},{2,5},{3},{4,6,7}}=>13 {{1},{2,5},{3},{4,6},{7}}=>14 {{1,7},{2,5},{3},{4},{6}}=>11 {{1},{2,5,7},{3},{4},{6}}=>12 {{1},{2,5},{3,7},{4},{6}}=>13 {{1},{2,5},{3},{4,7},{6}}=>14 {{1},{2,5},{3},{4},{6,7}}=>15 {{1},{2,5},{3},{4},{6},{7}}=>16 {{1,6,7},{2},{3,5},{4}}=>8 {{1,6},{2,7},{3,5},{4}}=>9 {{1,6},{2},{3,5,7},{4}}=>10 {{1,6},{2},{3,5},{4,7}}=>11 {{1,6},{2},{3,5},{4},{7}}=>12 {{1,7},{2,6},{3,5},{4}}=>9 {{1},{2,6,7},{3,5},{4}}=>10 {{1},{2,6},{3,5,7},{4}}=>11 {{1},{2,6},{3,5},{4,7}}=>12 {{1},{2,6},{3,5},{4},{7}}=>13 {{1,7},{2},{3,5,6},{4}}=>10 {{1},{2,7},{3,5,6},{4}}=>11 {{1},{2},{3,5,6,7},{4}}=>12 {{1},{2},{3,5,6},{4,7}}=>13 {{1},{2},{3,5,6},{4},{7}}=>14 {{1,7},{2},{3,5},{4,6}}=>11 {{1},{2,7},{3,5},{4,6}}=>12 {{1},{2},{3,5,7},{4,6}}=>13 {{1},{2},{3,5},{4,6,7}}=>14 {{1},{2},{3,5},{4,6},{7}}=>15 {{1,7},{2},{3,5},{4},{6}}=>12 {{1},{2,7},{3,5},{4},{6}}=>13 {{1},{2},{3,5,7},{4},{6}}=>14 {{1},{2},{3,5},{4,7},{6}}=>15 {{1},{2},{3,5},{4},{6,7}}=>16 {{1},{2},{3,5},{4},{6},{7}}=>17 {{1,6,7},{2},{3},{4,5}}=>9 {{1,6},{2,7},{3},{4,5}}=>10 {{1,6},{2},{3,7},{4,5}}=>11 {{1,6},{2},{3},{4,5,7}}=>12 {{1,6},{2},{3},{4,5},{7}}=>13 {{1,7},{2,6},{3},{4,5}}=>10 {{1},{2,6,7},{3},{4,5}}=>11 {{1},{2,6},{3,7},{4,5}}=>12 {{1},{2,6},{3},{4,5,7}}=>13 {{1},{2,6},{3},{4,5},{7}}=>14 {{1,7},{2},{3,6},{4,5}}=>11 {{1},{2,7},{3,6},{4,5}}=>12 {{1},{2},{3,6,7},{4,5}}=>13 {{1},{2},{3,6},{4,5,7}}=>14 {{1},{2},{3,6},{4,5},{7}}=>15 {{1,7},{2},{3},{4,5,6}}=>12 {{1},{2,7},{3},{4,5,6}}=>13 {{1},{2},{3,7},{4,5,6}}=>14 {{1},{2},{3},{4,5,6,7}}=>15 {{1},{2},{3},{4,5,6},{7}}=>16 {{1,7},{2},{3},{4,5},{6}}=>13 {{1},{2,7},{3},{4,5},{6}}=>14 {{1},{2},{3,7},{4,5},{6}}=>15 {{1},{2},{3},{4,5,7},{6}}=>16 {{1},{2},{3},{4,5},{6,7}}=>17 {{1},{2},{3},{4,5},{6},{7}}=>18 {{1,6,7},{2},{3},{4},{5}}=>10 {{1,6},{2,7},{3},{4},{5}}=>11 {{1,6},{2},{3,7},{4},{5}}=>12 {{1,6},{2},{3},{4,7},{5}}=>13 {{1,6},{2},{3},{4},{5,7}}=>14 {{1,6},{2},{3},{4},{5},{7}}=>15 {{1,7},{2,6},{3},{4},{5}}=>11 {{1},{2,6,7},{3},{4},{5}}=>12 {{1},{2,6},{3,7},{4},{5}}=>13 {{1},{2,6},{3},{4,7},{5}}=>14 {{1},{2,6},{3},{4},{5,7}}=>15 {{1},{2,6},{3},{4},{5},{7}}=>16 {{1,7},{2},{3,6},{4},{5}}=>12 {{1},{2,7},{3,6},{4},{5}}=>13 {{1},{2},{3,6,7},{4},{5}}=>14 {{1},{2},{3,6},{4,7},{5}}=>15 {{1},{2},{3,6},{4},{5,7}}=>16 {{1},{2},{3,6},{4},{5},{7}}=>17 {{1,7},{2},{3},{4,6},{5}}=>13 {{1},{2,7},{3},{4,6},{5}}=>14 {{1},{2},{3,7},{4,6},{5}}=>15 {{1},{2},{3},{4,6,7},{5}}=>16 {{1},{2},{3},{4,6},{5,7}}=>17 {{1},{2},{3},{4,6},{5},{7}}=>18 {{1,7},{2},{3},{4},{5,6}}=>14 {{1},{2,7},{3},{4},{5,6}}=>15 {{1},{2},{3,7},{4},{5,6}}=>16 {{1},{2},{3},{4,7},{5,6}}=>17 {{1},{2},{3},{4},{5,6,7}}=>18 {{1},{2},{3},{4},{5,6},{7}}=>19 {{1,7},{2},{3},{4},{5},{6}}=>15 {{1},{2,7},{3},{4},{5},{6}}=>16 {{1},{2},{3,7},{4},{5},{6}}=>17 {{1},{2},{3},{4,7},{5},{6}}=>18 {{1},{2},{3},{4},{5,7},{6}}=>19 {{1},{2},{3},{4},{5},{6,7}}=>20 {{1},{2},{3},{4},{5},{6},{7}}=>21 {{1},{2},{3,4,5,6,7,8}}=>13 {{1},{2,4,5,6,7,8},{3}}=>8 {{1},{2,3,5,6,7,8},{4}}=>8 {{1},{2,3,4,6,7,8},{5}}=>8 {{1},{2,3,4,5,7,8},{6}}=>8 {{1},{2,3,4,5,6,7},{8}}=>8 {{1},{2,3,4,5,6,8},{7}}=>8 {{1},{2,3,4,5,6,7,8}}=>7 {{1,2},{3,4,5,6,7,8}}=>6 {{1,4,5,6,7,8},{2},{3}}=>3 {{1,3,5,6,7,8},{2},{4}}=>3 {{1,3,4,5,6,7,8},{2}}=>1 {{1,4,5,6,7,8},{2,3}}=>2 {{1,2,4,5,6,7,8},{3}}=>1 {{1,2,5,6,7,8},{3,4}}=>2 {{1,2,3,5,6,7,8},{4}}=>1 {{1,2,3,6,7,8},{4,5}}=>2 {{1,2,3,4,6,7,8},{5}}=>1 {{1,2,3,4,5,6},{7,8}}=>2 {{1,2,3,4,7,8},{5,6}}=>2 {{1,2,3,4,5,7,8},{6}}=>1 {{1,2,3,4,5,6,7},{8}}=>1 {{1,8},{2,3,4,5,6,7}}=>6 {{1,2,3,4,5,8},{6,7}}=>2 {{1,2,3,4,5,6,8},{7}}=>1 {{1,2,3,4,5,6,7,8}}=>0 {{1,3,5,6,7,8},{2,4}}=>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 {{1,3},{2,4,5,6,7,8}}=>6 {{1,4},{2,3,5,6,7,8}}=>6 {{1,5},{2,3,4,6,7,8}}=>6 {{1,6},{2,3,4,5,7,8}}=>6 {{1,7},{2,3,4,5,6,8}}=>6
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Description
The los statistic of a set partition.
Let $S = B_1,\ldots,B_k$ be a set partition with ordered blocks $B_i$ and with $\operatorname{min} B_a < \operatorname{min} B_b$ for $a < b$.
According to [1, Definition 3], a los (left-opener-smaller) of $S$ is given by a pair $i > j$ such that $j = \operatorname{min} B_b$ and $i \in B_a$ for $a > b$.
This is also the dual major index of [2].
References
[1] Steingrimsson, E. Statistics on ordered partitions of sets arXiv:math/0605670
[2] Sagan, B. E. A maj statistic for set partitions MathSciNet:1087650
Code
def statistic(S):
    S = sorted( sorted(B) for B in S )
    n = sum( len(B) for B in S )
    los = 0
    for k in range(len(S)):
        j = S[k][0]
        for l in range(k+1,len(S)):
            for i in S[l]:
                if i > j:
                    los += 1
    return los
Created
May 18, 2016 at 12:26 by Christian Stump
Updated
Aug 06, 2016 at 15:47 by Martin Rubey