Identifier
Values
=>
Cc0009;cc-rep
{{1,2}}=>1 {{1},{2}}=>0 {{1,2,3}}=>3 {{1,2},{3}}=>1 {{1,3},{2}}=>1 {{1},{2,3}}=>1 {{1},{2},{3}}=>0 {{1,2,3,4}}=>6 {{1,2,3},{4}}=>3 {{1,2,4},{3}}=>3 {{1,2},{3,4}}=>2 {{1,2},{3},{4}}=>1 {{1,3,4},{2}}=>3 {{1,3},{2,4}}=>2 {{1,3},{2},{4}}=>1 {{1,4},{2,3}}=>2 {{1},{2,3,4}}=>3 {{1},{2,3},{4}}=>1 {{1,4},{2},{3}}=>1 {{1},{2,4},{3}}=>1 {{1},{2},{3,4}}=>1 {{1},{2},{3},{4}}=>0 {{1,2,3,4,5}}=>10 {{1,2,3,4},{5}}=>6 {{1,2,3,5},{4}}=>6 {{1,2,3},{4,5}}=>4 {{1,2,3},{4},{5}}=>3 {{1,2,4,5},{3}}=>6 {{1,2,4},{3,5}}=>4 {{1,2,4},{3},{5}}=>3 {{1,2,5},{3,4}}=>4 {{1,2},{3,4,5}}=>4 {{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}}=>1 {{1,3,4,5},{2}}=>6 {{1,3,4},{2,5}}=>4 {{1,3,4},{2},{5}}=>3 {{1,3,5},{2,4}}=>4 {{1,3},{2,4,5}}=>4 {{1,3},{2,4},{5}}=>2 {{1,3,5},{2},{4}}=>3 {{1,3},{2,5},{4}}=>2 {{1,3},{2},{4,5}}=>2 {{1,3},{2},{4},{5}}=>1 {{1,4,5},{2,3}}=>4 {{1,4},{2,3,5}}=>4 {{1,4},{2,3},{5}}=>2 {{1,5},{2,3,4}}=>4 {{1},{2,3,4,5}}=>6 {{1},{2,3,4},{5}}=>3 {{1,5},{2,3},{4}}=>2 {{1},{2,3,5},{4}}=>3 {{1},{2,3},{4,5}}=>2 {{1},{2,3},{4},{5}}=>1 {{1,4,5},{2},{3}}=>3 {{1,4},{2,5},{3}}=>2 {{1,4},{2},{3,5}}=>2 {{1,4},{2},{3},{5}}=>1 {{1,5},{2,4},{3}}=>2 {{1},{2,4,5},{3}}=>3 {{1},{2,4},{3,5}}=>2 {{1},{2,4},{3},{5}}=>1 {{1,5},{2},{3,4}}=>2 {{1},{2,5},{3,4}}=>2 {{1},{2},{3,4,5}}=>3 {{1},{2},{3,4},{5}}=>1 {{1,5},{2},{3},{4}}=>1 {{1},{2,5},{3},{4}}=>1 {{1},{2},{3,5},{4}}=>1 {{1},{2},{3},{4,5}}=>1 {{1},{2},{3},{4},{5}}=>0 {{1,2,3,4,5,6}}=>15 {{1,2,3,4,5},{6}}=>10 {{1,2,3,4,6},{5}}=>10 {{1,2,3,4},{5,6}}=>7 {{1,2,3,4},{5},{6}}=>6 {{1,2,3,5,6},{4}}=>10 {{1,2,3,5},{4,6}}=>7 {{1,2,3,5},{4},{6}}=>6 {{1,2,3,6},{4,5}}=>7 {{1,2,3},{4,5,6}}=>6 {{1,2,3},{4,5},{6}}=>4 {{1,2,3,6},{4},{5}}=>6 {{1,2,3},{4,6},{5}}=>4 {{1,2,3},{4},{5,6}}=>4 {{1,2,3},{4},{5},{6}}=>3 {{1,2,4,5,6},{3}}=>10 {{1,2,4,5},{3,6}}=>7 {{1,2,4,5},{3},{6}}=>6 {{1,2,4,6},{3,5}}=>7 {{1,2,4},{3,5,6}}=>6 {{1,2,4},{3,5},{6}}=>4 {{1,2,4,6},{3},{5}}=>6 {{1,2,4},{3,6},{5}}=>4 {{1,2,4},{3},{5,6}}=>4 {{1,2,4},{3},{5},{6}}=>3 {{1,2,5,6},{3,4}}=>7 {{1,2,5},{3,4,6}}=>6 {{1,2,5},{3,4},{6}}=>4 {{1,2,6},{3,4,5}}=>6 {{1,2},{3,4,5,6}}=>7 {{1,2},{3,4,5},{6}}=>4 {{1,2,6},{3,4},{5}}=>4 {{1,2},{3,4,6},{5}}=>4 {{1,2},{3,4},{5,6}}=>3 {{1,2},{3,4},{5},{6}}=>2 {{1,2,5,6},{3},{4}}=>6 {{1,2,5},{3,6},{4}}=>4 {{1,2,5},{3},{4,6}}=>4 {{1,2,5},{3},{4},{6}}=>3 {{1,2,6},{3,5},{4}}=>4 {{1,2},{3,5,6},{4}}=>4 {{1,2},{3,5},{4,6}}=>3 {{1,2},{3,5},{4},{6}}=>2 {{1,2,6},{3},{4,5}}=>4 {{1,2},{3,6},{4,5}}=>3 {{1,2},{3},{4,5,6}}=>4 {{1,2},{3},{4,5},{6}}=>2 {{1,2,6},{3},{4},{5}}=>3 {{1,2},{3,6},{4},{5}}=>2 {{1,2},{3},{4,6},{5}}=>2 {{1,2},{3},{4},{5,6}}=>2 {{1,2},{3},{4},{5},{6}}=>1 {{1,3,4,5,6},{2}}=>10 {{1,3,4,5},{2,6}}=>7 {{1,3,4,5},{2},{6}}=>6 {{1,3,4,6},{2,5}}=>7 {{1,3,4},{2,5,6}}=>6 {{1,3,4},{2,5},{6}}=>4 {{1,3,4,6},{2},{5}}=>6 {{1,3,4},{2,6},{5}}=>4 {{1,3,4},{2},{5,6}}=>4 {{1,3,4},{2},{5},{6}}=>3 {{1,3,5,6},{2,4}}=>7 {{1,3,5},{2,4,6}}=>6 {{1,3,5},{2,4},{6}}=>4 {{1,3,6},{2,4,5}}=>6 {{1,3},{2,4,5,6}}=>7 {{1,3},{2,4,5},{6}}=>4 {{1,3,6},{2,4},{5}}=>4 {{1,3},{2,4,6},{5}}=>4 {{1,3},{2,4},{5,6}}=>3 {{1,3},{2,4},{5},{6}}=>2 {{1,3,5,6},{2},{4}}=>6 {{1,3,5},{2,6},{4}}=>4 {{1,3,5},{2},{4,6}}=>4 {{1,3,5},{2},{4},{6}}=>3 {{1,3,6},{2,5},{4}}=>4 {{1,3},{2,5,6},{4}}=>4 {{1,3},{2,5},{4,6}}=>3 {{1,3},{2,5},{4},{6}}=>2 {{1,3,6},{2},{4,5}}=>4 {{1,3},{2,6},{4,5}}=>3 {{1,3},{2},{4,5,6}}=>4 {{1,3},{2},{4,5},{6}}=>2 {{1,3,6},{2},{4},{5}}=>3 {{1,3},{2,6},{4},{5}}=>2 {{1,3},{2},{4,6},{5}}=>2 {{1,3},{2},{4},{5,6}}=>2 {{1,3},{2},{4},{5},{6}}=>1 {{1,4,5,6},{2,3}}=>7 {{1,4,5},{2,3,6}}=>6 {{1,4,5},{2,3},{6}}=>4 {{1,4,6},{2,3,5}}=>6 {{1,4},{2,3,5,6}}=>7 {{1,4},{2,3,5},{6}}=>4 {{1,4,6},{2,3},{5}}=>4 {{1,4},{2,3,6},{5}}=>4 {{1,4},{2,3},{5,6}}=>3 {{1,4},{2,3},{5},{6}}=>2 {{1,5,6},{2,3,4}}=>6 {{1,5},{2,3,4,6}}=>7 {{1,5},{2,3,4},{6}}=>4 {{1,6},{2,3,4,5}}=>7 {{1},{2,3,4,5,6}}=>10 {{1},{2,3,4,5},{6}}=>6 {{1,6},{2,3,4},{5}}=>4 {{1},{2,3,4,6},{5}}=>6 {{1},{2,3,4},{5,6}}=>4 {{1},{2,3,4},{5},{6}}=>3 {{1,5,6},{2,3},{4}}=>4 {{1,5},{2,3,6},{4}}=>4 {{1,5},{2,3},{4,6}}=>3 {{1,5},{2,3},{4},{6}}=>2 {{1,6},{2,3,5},{4}}=>4 {{1},{2,3,5,6},{4}}=>6 {{1},{2,3,5},{4,6}}=>4 {{1},{2,3,5},{4},{6}}=>3 {{1,6},{2,3},{4,5}}=>3 {{1},{2,3,6},{4,5}}=>4 {{1},{2,3},{4,5,6}}=>4 {{1},{2,3},{4,5},{6}}=>2 {{1,6},{2,3},{4},{5}}=>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}}=>1 {{1,4,5,6},{2},{3}}=>6 {{1,4,5},{2,6},{3}}=>4 {{1,4,5},{2},{3,6}}=>4 {{1,4,5},{2},{3},{6}}=>3 {{1,4,6},{2,5},{3}}=>4 {{1,4},{2,5,6},{3}}=>4 {{1,4},{2,5},{3,6}}=>3 {{1,4},{2,5},{3},{6}}=>2 {{1,4,6},{2},{3,5}}=>4 {{1,4},{2,6},{3,5}}=>3 {{1,4},{2},{3,5,6}}=>4 {{1,4},{2},{3,5},{6}}=>2 {{1,4,6},{2},{3},{5}}=>3 {{1,4},{2,6},{3},{5}}=>2 {{1,4},{2},{3,6},{5}}=>2 {{1,4},{2},{3},{5,6}}=>2 {{1,4},{2},{3},{5},{6}}=>1 {{1,5,6},{2,4},{3}}=>4 {{1,5},{2,4,6},{3}}=>4 {{1,5},{2,4},{3,6}}=>3 {{1,5},{2,4},{3},{6}}=>2 {{1,6},{2,4,5},{3}}=>4 {{1},{2,4,5,6},{3}}=>6 {{1},{2,4,5},{3,6}}=>4 {{1},{2,4,5},{3},{6}}=>3 {{1,6},{2,4},{3,5}}=>3 {{1},{2,4,6},{3,5}}=>4 {{1},{2,4},{3,5,6}}=>4 {{1},{2,4},{3,5},{6}}=>2 {{1,6},{2,4},{3},{5}}=>2 {{1},{2,4,6},{3},{5}}=>3 {{1},{2,4},{3,6},{5}}=>2 {{1},{2,4},{3},{5,6}}=>2 {{1},{2,4},{3},{5},{6}}=>1 {{1,5,6},{2},{3,4}}=>4 {{1,5},{2,6},{3,4}}=>3 {{1,5},{2},{3,4,6}}=>4 {{1,5},{2},{3,4},{6}}=>2 {{1,6},{2,5},{3,4}}=>3 {{1},{2,5,6},{3,4}}=>4 {{1},{2,5},{3,4,6}}=>4 {{1},{2,5},{3,4},{6}}=>2 {{1,6},{2},{3,4,5}}=>4 {{1},{2,6},{3,4,5}}=>4 {{1},{2},{3,4,5,6}}=>6 {{1},{2},{3,4,5},{6}}=>3 {{1,6},{2},{3,4},{5}}=>2 {{1},{2,6},{3,4},{5}}=>2 {{1},{2},{3,4,6},{5}}=>3 {{1},{2},{3,4},{5,6}}=>2 {{1},{2},{3,4},{5},{6}}=>1 {{1,5,6},{2},{3},{4}}=>3 {{1,5},{2,6},{3},{4}}=>2 {{1,5},{2},{3,6},{4}}=>2 {{1,5},{2},{3},{4,6}}=>2 {{1,5},{2},{3},{4},{6}}=>1 {{1,6},{2,5},{3},{4}}=>2 {{1},{2,5,6},{3},{4}}=>3 {{1},{2,5},{3,6},{4}}=>2 {{1},{2,5},{3},{4,6}}=>2 {{1},{2,5},{3},{4},{6}}=>1 {{1,6},{2},{3,5},{4}}=>2 {{1},{2,6},{3,5},{4}}=>2 {{1},{2},{3,5,6},{4}}=>3 {{1},{2},{3,5},{4,6}}=>2 {{1},{2},{3,5},{4},{6}}=>1 {{1,6},{2},{3},{4,5}}=>2 {{1},{2,6},{3},{4,5}}=>2 {{1},{2},{3,6},{4,5}}=>2 {{1},{2},{3},{4,5,6}}=>3 {{1},{2},{3},{4,5},{6}}=>1 {{1,6},{2},{3},{4},{5}}=>1 {{1},{2,6},{3},{4},{5}}=>1 {{1},{2},{3,6},{4},{5}}=>1 {{1},{2},{3},{4,6},{5}}=>1 {{1},{2},{3},{4},{5,6}}=>1 {{1},{2},{3},{4},{5},{6}}=>0 {{1,2,3,4,5,6,7}}=>21 {{1,2,3,4,5,6},{7}}=>15 {{1,2,3,4,5,7},{6}}=>15 {{1,2,3,4,5},{6,7}}=>11 {{1,2,3,4,5},{6},{7}}=>10 {{1,2,3,4,6,7},{5}}=>15 {{1,2,3,4,6},{5,7}}=>11 {{1,2,3,4,6},{5},{7}}=>10 {{1,2,3,4,7},{5,6}}=>11 {{1,2,3,4},{5,6,7}}=>9 {{1,2,3,4},{5,6},{7}}=>7 {{1,2,3,4,7},{5},{6}}=>10 {{1,2,3,4},{5,7},{6}}=>7 {{1,2,3,4},{5},{6,7}}=>7 {{1,2,3,4},{5},{6},{7}}=>6 {{1,2,3,5,6,7},{4}}=>15 {{1,2,3,5,6},{4,7}}=>11 {{1,2,3,5,6},{4},{7}}=>10 {{1,2,3,5,7},{4,6}}=>11 {{1,2,3,5},{4,6,7}}=>9 {{1,2,3,5},{4,6},{7}}=>7 {{1,2,3,5,7},{4},{6}}=>10 {{1,2,3,5},{4,7},{6}}=>7 {{1,2,3,5},{4},{6,7}}=>7 {{1,2,3,5},{4},{6},{7}}=>6 {{1,2,3,6,7},{4,5}}=>11 {{1,2,3,6},{4,5,7}}=>9 {{1,2,3,6},{4,5},{7}}=>7 {{1,2,3,7},{4,5,6}}=>9 {{1,2,3},{4,5,6,7}}=>9 {{1,2,3},{4,5,6},{7}}=>6 {{1,2,3,7},{4,5},{6}}=>7 {{1,2,3},{4,5,7},{6}}=>6 {{1,2,3},{4,5},{6,7}}=>5 {{1,2,3},{4,5},{6},{7}}=>4 {{1,2,3,6,7},{4},{5}}=>10 {{1,2,3,6},{4,7},{5}}=>7 {{1,2,3,6},{4},{5,7}}=>7 {{1,2,3,6},{4},{5},{7}}=>6 {{1,2,3,7},{4,6},{5}}=>7 {{1,2,3},{4,6,7},{5}}=>6 {{1,2,3},{4,6},{5,7}}=>5 {{1,2,3},{4,6},{5},{7}}=>4 {{1,2,3,7},{4},{5,6}}=>7 {{1,2,3},{4,7},{5,6}}=>5 {{1,2,3},{4},{5,6,7}}=>6 {{1,2,3},{4},{5,6},{7}}=>4 {{1,2,3,7},{4},{5},{6}}=>6 {{1,2,3},{4,7},{5},{6}}=>4 {{1,2,3},{4},{5,7},{6}}=>4 {{1,2,3},{4},{5},{6,7}}=>4 {{1,2,3},{4},{5},{6},{7}}=>3 {{1,2,4,5,6,7},{3}}=>15 {{1,2,4,5,6},{3,7}}=>11 {{1,2,4,5,6},{3},{7}}=>10 {{1,2,4,5,7},{3,6}}=>11 {{1,2,4,5},{3,6,7}}=>9 {{1,2,4,5},{3,6},{7}}=>7 {{1,2,4,5,7},{3},{6}}=>10 {{1,2,4,5},{3,7},{6}}=>7 {{1,2,4,5},{3},{6,7}}=>7 {{1,2,4,5},{3},{6},{7}}=>6 {{1,2,4,6,7},{3,5}}=>11 {{1,2,4,6},{3,5,7}}=>9 {{1,2,4,6},{3,5},{7}}=>7 {{1,2,4,7},{3,5,6}}=>9 {{1,2,4},{3,5,6,7}}=>9 {{1,2,4},{3,5,6},{7}}=>6 {{1,2,4,7},{3,5},{6}}=>7 {{1,2,4},{3,5,7},{6}}=>6 {{1,2,4},{3,5},{6,7}}=>5 {{1,2,4},{3,5},{6},{7}}=>4 {{1,2,4,6,7},{3},{5}}=>10 {{1,2,4,6},{3,7},{5}}=>7 {{1,2,4,6},{3},{5,7}}=>7 {{1,2,4,6},{3},{5},{7}}=>6 {{1,2,4,7},{3,6},{5}}=>7 {{1,2,4},{3,6,7},{5}}=>6 {{1,2,4},{3,6},{5,7}}=>5 {{1,2,4},{3,6},{5},{7}}=>4 {{1,2,4,7},{3},{5,6}}=>7 {{1,2,4},{3,7},{5,6}}=>5 {{1,2,4},{3},{5,6,7}}=>6 {{1,2,4},{3},{5,6},{7}}=>4 {{1,2,4,7},{3},{5},{6}}=>6 {{1,2,4},{3,7},{5},{6}}=>4 {{1,2,4},{3},{5,7},{6}}=>4 {{1,2,4},{3},{5},{6,7}}=>4 {{1,2,4},{3},{5},{6},{7}}=>3 {{1,2,5,6,7},{3,4}}=>11 {{1,2,5,6},{3,4,7}}=>9 {{1,2,5,6},{3,4},{7}}=>7 {{1,2,5,7},{3,4,6}}=>9 {{1,2,5},{3,4,6,7}}=>9 {{1,2,5},{3,4,6},{7}}=>6 {{1,2,5,7},{3,4},{6}}=>7 {{1,2,5},{3,4,7},{6}}=>6 {{1,2,5},{3,4},{6,7}}=>5 {{1,2,5},{3,4},{6},{7}}=>4 {{1,2,6,7},{3,4,5}}=>9 {{1,2,6},{3,4,5,7}}=>9 {{1,2,6},{3,4,5},{7}}=>6 {{1,2,7},{3,4,5,6}}=>9 {{1,2},{3,4,5,6,7}}=>11 {{1,2},{3,4,5,6},{7}}=>7 {{1,2,7},{3,4,5},{6}}=>6 {{1,2},{3,4,5,7},{6}}=>7 {{1,2},{3,4,5},{6,7}}=>5 {{1,2},{3,4,5},{6},{7}}=>4 {{1,2,6,7},{3,4},{5}}=>7 {{1,2,6},{3,4,7},{5}}=>6 {{1,2,6},{3,4},{5,7}}=>5 {{1,2,6},{3,4},{5},{7}}=>4 {{1,2,7},{3,4,6},{5}}=>6 {{1,2},{3,4,6,7},{5}}=>7 {{1,2},{3,4,6},{5,7}}=>5 {{1,2},{3,4,6},{5},{7}}=>4 {{1,2,7},{3,4},{5,6}}=>5 {{1,2},{3,4,7},{5,6}}=>5 {{1,2},{3,4},{5,6,7}}=>5 {{1,2},{3,4},{5,6},{7}}=>3 {{1,2,7},{3,4},{5},{6}}=>4 {{1,2},{3,4,7},{5},{6}}=>4 {{1,2},{3,4},{5,7},{6}}=>3 {{1,2},{3,4},{5},{6,7}}=>3 {{1,2},{3,4},{5},{6},{7}}=>2 {{1,2,5,6,7},{3},{4}}=>10 {{1,2,5,6},{3,7},{4}}=>7 {{1,2,5,6},{3},{4,7}}=>7 {{1,2,5,6},{3},{4},{7}}=>6 {{1,2,5,7},{3,6},{4}}=>7 {{1,2,5},{3,6,7},{4}}=>6 {{1,2,5},{3,6},{4,7}}=>5 {{1,2,5},{3,6},{4},{7}}=>4 {{1,2,5,7},{3},{4,6}}=>7 {{1,2,5},{3,7},{4,6}}=>5 {{1,2,5},{3},{4,6,7}}=>6 {{1,2,5},{3},{4,6},{7}}=>4 {{1,2,5,7},{3},{4},{6}}=>6 {{1,2,5},{3,7},{4},{6}}=>4 {{1,2,5},{3},{4,7},{6}}=>4 {{1,2,5},{3},{4},{6,7}}=>4 {{1,2,5},{3},{4},{6},{7}}=>3 {{1,2,6,7},{3,5},{4}}=>7 {{1,2,6},{3,5,7},{4}}=>6 {{1,2,6},{3,5},{4,7}}=>5 {{1,2,6},{3,5},{4},{7}}=>4 {{1,2,7},{3,5,6},{4}}=>6 {{1,2},{3,5,6,7},{4}}=>7 {{1,2},{3,5,6},{4,7}}=>5 {{1,2},{3,5,6},{4},{7}}=>4 {{1,2,7},{3,5},{4,6}}=>5 {{1,2},{3,5,7},{4,6}}=>5 {{1,2},{3,5},{4,6,7}}=>5 {{1,2},{3,5},{4,6},{7}}=>3 {{1,2,7},{3,5},{4},{6}}=>4 {{1,2},{3,5,7},{4},{6}}=>4 {{1,2},{3,5},{4,7},{6}}=>3 {{1,2},{3,5},{4},{6,7}}=>3 {{1,2},{3,5},{4},{6},{7}}=>2 {{1,2,6,7},{3},{4,5}}=>7 {{1,2,6},{3,7},{4,5}}=>5 {{1,2,6},{3},{4,5,7}}=>6 {{1,2,6},{3},{4,5},{7}}=>4 {{1,2,7},{3,6},{4,5}}=>5 {{1,2},{3,6,7},{4,5}}=>5 {{1,2},{3,6},{4,5,7}}=>5 {{1,2},{3,6},{4,5},{7}}=>3 {{1,2,7},{3},{4,5,6}}=>6 {{1,2},{3,7},{4,5,6}}=>5 {{1,2},{3},{4,5,6,7}}=>7 {{1,2},{3},{4,5,6},{7}}=>4 {{1,2,7},{3},{4,5},{6}}=>4 {{1,2},{3,7},{4,5},{6}}=>3 {{1,2},{3},{4,5,7},{6}}=>4 {{1,2},{3},{4,5},{6,7}}=>3 {{1,2},{3},{4,5},{6},{7}}=>2 {{1,2,6,7},{3},{4},{5}}=>6 {{1,2,6},{3,7},{4},{5}}=>4 {{1,2,6},{3},{4,7},{5}}=>4 {{1,2,6},{3},{4},{5,7}}=>4 {{1,2,6},{3},{4},{5},{7}}=>3 {{1,2,7},{3,6},{4},{5}}=>4 {{1,2},{3,6,7},{4},{5}}=>4 {{1,2},{3,6},{4,7},{5}}=>3 {{1,2},{3,6},{4},{5,7}}=>3 {{1,2},{3,6},{4},{5},{7}}=>2 {{1,2,7},{3},{4,6},{5}}=>4 {{1,2},{3,7},{4,6},{5}}=>3 {{1,2},{3},{4,6,7},{5}}=>4 {{1,2},{3},{4,6},{5,7}}=>3 {{1,2},{3},{4,6},{5},{7}}=>2 {{1,2,7},{3},{4},{5,6}}=>4 {{1,2},{3,7},{4},{5,6}}=>3 {{1,2},{3},{4,7},{5,6}}=>3 {{1,2},{3},{4},{5,6,7}}=>4 {{1,2},{3},{4},{5,6},{7}}=>2 {{1,2,7},{3},{4},{5},{6}}=>3 {{1,2},{3,7},{4},{5},{6}}=>2 {{1,2},{3},{4,7},{5},{6}}=>2 {{1,2},{3},{4},{5,7},{6}}=>2 {{1,2},{3},{4},{5},{6,7}}=>2 {{1,2},{3},{4},{5},{6},{7}}=>1 {{1,3,4,5,6,7},{2}}=>15 {{1,3,4,5,6},{2,7}}=>11 {{1,3,4,5,6},{2},{7}}=>10 {{1,3,4,5,7},{2,6}}=>11 {{1,3,4,5},{2,6,7}}=>9 {{1,3,4,5},{2,6},{7}}=>7 {{1,3,4,5,7},{2},{6}}=>10 {{1,3,4,5},{2,7},{6}}=>7 {{1,3,4,5},{2},{6,7}}=>7 {{1,3,4,5},{2},{6},{7}}=>6 {{1,3,4,6,7},{2,5}}=>11 {{1,3,4,6},{2,5,7}}=>9 {{1,3,4,6},{2,5},{7}}=>7 {{1,3,4,7},{2,5,6}}=>9 {{1,3,4},{2,5,6,7}}=>9 {{1,3,4},{2,5,6},{7}}=>6 {{1,3,4,7},{2,5},{6}}=>7 {{1,3,4},{2,5,7},{6}}=>6 {{1,3,4},{2,5},{6,7}}=>5 {{1,3,4},{2,5},{6},{7}}=>4 {{1,3,4,6,7},{2},{5}}=>10 {{1,3,4,6},{2,7},{5}}=>7 {{1,3,4,6},{2},{5,7}}=>7 {{1,3,4,6},{2},{5},{7}}=>6 {{1,3,4,7},{2,6},{5}}=>7 {{1,3,4},{2,6,7},{5}}=>6 {{1,3,4},{2,6},{5,7}}=>5 {{1,3,4},{2,6},{5},{7}}=>4 {{1,3,4,7},{2},{5,6}}=>7 {{1,3,4},{2,7},{5,6}}=>5 {{1,3,4},{2},{5,6,7}}=>6 {{1,3,4},{2},{5,6},{7}}=>4 {{1,3,4,7},{2},{5},{6}}=>6 {{1,3,4},{2,7},{5},{6}}=>4 {{1,3,4},{2},{5,7},{6}}=>4 {{1,3,4},{2},{5},{6,7}}=>4 {{1,3,4},{2},{5},{6},{7}}=>3 {{1,3,5,6,7},{2,4}}=>11 {{1,3,5,6},{2,4,7}}=>9 {{1,3,5,6},{2,4},{7}}=>7 {{1,3,5,7},{2,4,6}}=>9 {{1,3,5},{2,4,6,7}}=>9 {{1,3,5},{2,4,6},{7}}=>6 {{1,3,5,7},{2,4},{6}}=>7 {{1,3,5},{2,4,7},{6}}=>6 {{1,3,5},{2,4},{6,7}}=>5 {{1,3,5},{2,4},{6},{7}}=>4 {{1,3,6,7},{2,4,5}}=>9 {{1,3,6},{2,4,5,7}}=>9 {{1,3,6},{2,4,5},{7}}=>6 {{1,3,7},{2,4,5,6}}=>9 {{1,3},{2,4,5,6,7}}=>11 {{1,3},{2,4,5,6},{7}}=>7 {{1,3,7},{2,4,5},{6}}=>6 {{1,3},{2,4,5,7},{6}}=>7 {{1,3},{2,4,5},{6,7}}=>5 {{1,3},{2,4,5},{6},{7}}=>4 {{1,3,6,7},{2,4},{5}}=>7 {{1,3,6},{2,4,7},{5}}=>6 {{1,3,6},{2,4},{5,7}}=>5 {{1,3,6},{2,4},{5},{7}}=>4 {{1,3,7},{2,4,6},{5}}=>6 {{1,3},{2,4,6,7},{5}}=>7 {{1,3},{2,4,6},{5,7}}=>5 {{1,3},{2,4,6},{5},{7}}=>4 {{1,3,7},{2,4},{5,6}}=>5 {{1,3},{2,4,7},{5,6}}=>5 {{1,3},{2,4},{5,6,7}}=>5 {{1,3},{2,4},{5,6},{7}}=>3 {{1,3,7},{2,4},{5},{6}}=>4 {{1,3},{2,4,7},{5},{6}}=>4 {{1,3},{2,4},{5,7},{6}}=>3 {{1,3},{2,4},{5},{6,7}}=>3 {{1,3},{2,4},{5},{6},{7}}=>2 {{1,3,5,6,7},{2},{4}}=>10 {{1,3,5,6},{2,7},{4}}=>7 {{1,3,5,6},{2},{4,7}}=>7 {{1,3,5,6},{2},{4},{7}}=>6 {{1,3,5,7},{2,6},{4}}=>7 {{1,3,5},{2,6,7},{4}}=>6 {{1,3,5},{2,6},{4,7}}=>5 {{1,3,5},{2,6},{4},{7}}=>4 {{1,3,5,7},{2},{4,6}}=>7 {{1,3,5},{2,7},{4,6}}=>5 {{1,3,5},{2},{4,6,7}}=>6 {{1,3,5},{2},{4,6},{7}}=>4 {{1,3,5,7},{2},{4},{6}}=>6 {{1,3,5},{2,7},{4},{6}}=>4 {{1,3,5},{2},{4,7},{6}}=>4 {{1,3,5},{2},{4},{6,7}}=>4 {{1,3,5},{2},{4},{6},{7}}=>3 {{1,3,6,7},{2,5},{4}}=>7 {{1,3,6},{2,5,7},{4}}=>6 {{1,3,6},{2,5},{4,7}}=>5 {{1,3,6},{2,5},{4},{7}}=>4 {{1,3,7},{2,5,6},{4}}=>6 {{1,3},{2,5,6,7},{4}}=>7 {{1,3},{2,5,6},{4,7}}=>5 {{1,3},{2,5,6},{4},{7}}=>4 {{1,3,7},{2,5},{4,6}}=>5 {{1,3},{2,5,7},{4,6}}=>5 {{1,3},{2,5},{4,6,7}}=>5 {{1,3},{2,5},{4,6},{7}}=>3 {{1,3,7},{2,5},{4},{6}}=>4 {{1,3},{2,5,7},{4},{6}}=>4 {{1,3},{2,5},{4,7},{6}}=>3 {{1,3},{2,5},{4},{6,7}}=>3 {{1,3},{2,5},{4},{6},{7}}=>2 {{1,3,6,7},{2},{4,5}}=>7 {{1,3,6},{2,7},{4,5}}=>5 {{1,3,6},{2},{4,5,7}}=>6 {{1,3,6},{2},{4,5},{7}}=>4 {{1,3,7},{2,6},{4,5}}=>5 {{1,3},{2,6,7},{4,5}}=>5 {{1,3},{2,6},{4,5,7}}=>5 {{1,3},{2,6},{4,5},{7}}=>3 {{1,3,7},{2},{4,5,6}}=>6 {{1,3},{2,7},{4,5,6}}=>5 {{1,3},{2},{4,5,6,7}}=>7 {{1,3},{2},{4,5,6},{7}}=>4 {{1,3,7},{2},{4,5},{6}}=>4 {{1,3},{2,7},{4,5},{6}}=>3 {{1,3},{2},{4,5,7},{6}}=>4 {{1,3},{2},{4,5},{6,7}}=>3 {{1,3},{2},{4,5},{6},{7}}=>2 {{1,3,6,7},{2},{4},{5}}=>6 {{1,3,6},{2,7},{4},{5}}=>4 {{1,3,6},{2},{4,7},{5}}=>4 {{1,3,6},{2},{4},{5,7}}=>4 {{1,3,6},{2},{4},{5},{7}}=>3 {{1,3,7},{2,6},{4},{5}}=>4 {{1,3},{2,6,7},{4},{5}}=>4 {{1,3},{2,6},{4,7},{5}}=>3 {{1,3},{2,6},{4},{5,7}}=>3 {{1,3},{2,6},{4},{5},{7}}=>2 {{1,3,7},{2},{4,6},{5}}=>4 {{1,3},{2,7},{4,6},{5}}=>3 {{1,3},{2},{4,6,7},{5}}=>4 {{1,3},{2},{4,6},{5,7}}=>3 {{1,3},{2},{4,6},{5},{7}}=>2 {{1,3,7},{2},{4},{5,6}}=>4 {{1,3},{2,7},{4},{5,6}}=>3 {{1,3},{2},{4,7},{5,6}}=>3 {{1,3},{2},{4},{5,6,7}}=>4 {{1,3},{2},{4},{5,6},{7}}=>2 {{1,3,7},{2},{4},{5},{6}}=>3 {{1,3},{2,7},{4},{5},{6}}=>2 {{1,3},{2},{4,7},{5},{6}}=>2 {{1,3},{2},{4},{5,7},{6}}=>2 {{1,3},{2},{4},{5},{6,7}}=>2 {{1,3},{2},{4},{5},{6},{7}}=>1 {{1,4,5,6,7},{2,3}}=>11 {{1,4,5,6},{2,3,7}}=>9 {{1,4,5,6},{2,3},{7}}=>7 {{1,4,5,7},{2,3,6}}=>9 {{1,4,5},{2,3,6,7}}=>9 {{1,4,5},{2,3,6},{7}}=>6 {{1,4,5,7},{2,3},{6}}=>7 {{1,4,5},{2,3,7},{6}}=>6 {{1,4,5},{2,3},{6,7}}=>5 {{1,4,5},{2,3},{6},{7}}=>4 {{1,4,6,7},{2,3,5}}=>9 {{1,4,6},{2,3,5,7}}=>9 {{1,4,6},{2,3,5},{7}}=>6 {{1,4,7},{2,3,5,6}}=>9 {{1,4},{2,3,5,6,7}}=>11 {{1,4},{2,3,5,6},{7}}=>7 {{1,4,7},{2,3,5},{6}}=>6 {{1,4},{2,3,5,7},{6}}=>7 {{1,4},{2,3,5},{6,7}}=>5 {{1,4},{2,3,5},{6},{7}}=>4 {{1,4,6,7},{2,3},{5}}=>7 {{1,4,6},{2,3,7},{5}}=>6 {{1,4,6},{2,3},{5,7}}=>5 {{1,4,6},{2,3},{5},{7}}=>4 {{1,4,7},{2,3,6},{5}}=>6 {{1,4},{2,3,6,7},{5}}=>7 {{1,4},{2,3,6},{5,7}}=>5 {{1,4},{2,3,6},{5},{7}}=>4 {{1,4,7},{2,3},{5,6}}=>5 {{1,4},{2,3,7},{5,6}}=>5 {{1,4},{2,3},{5,6,7}}=>5 {{1,4},{2,3},{5,6},{7}}=>3 {{1,4,7},{2,3},{5},{6}}=>4 {{1,4},{2,3,7},{5},{6}}=>4 {{1,4},{2,3},{5,7},{6}}=>3 {{1,4},{2,3},{5},{6,7}}=>3 {{1,4},{2,3},{5},{6},{7}}=>2 {{1,5,6,7},{2,3,4}}=>9 {{1,5,6},{2,3,4,7}}=>9 {{1,5,6},{2,3,4},{7}}=>6 {{1,5,7},{2,3,4,6}}=>9 {{1,5},{2,3,4,6,7}}=>11 {{1,5},{2,3,4,6},{7}}=>7 {{1,5,7},{2,3,4},{6}}=>6 {{1,5},{2,3,4,7},{6}}=>7 {{1,5},{2,3,4},{6,7}}=>5 {{1,5},{2,3,4},{6},{7}}=>4 {{1,6,7},{2,3,4,5}}=>9 {{1,6},{2,3,4,5,7}}=>11 {{1,6},{2,3,4,5},{7}}=>7 {{1,7},{2,3,4,5,6}}=>11 {{1},{2,3,4,5,6,7}}=>15 {{1},{2,3,4,5,6},{7}}=>10 {{1,7},{2,3,4,5},{6}}=>7 {{1},{2,3,4,5,7},{6}}=>10 {{1},{2,3,4,5},{6,7}}=>7 {{1},{2,3,4,5},{6},{7}}=>6 {{1,6,7},{2,3,4},{5}}=>6 {{1,6},{2,3,4,7},{5}}=>7 {{1,6},{2,3,4},{5,7}}=>5 {{1,6},{2,3,4},{5},{7}}=>4 {{1,7},{2,3,4,6},{5}}=>7 {{1},{2,3,4,6,7},{5}}=>10 {{1},{2,3,4,6},{5,7}}=>7 {{1},{2,3,4,6},{5},{7}}=>6 {{1,7},{2,3,4},{5,6}}=>5 {{1},{2,3,4,7},{5,6}}=>7 {{1},{2,3,4},{5,6,7}}=>6 {{1},{2,3,4},{5,6},{7}}=>4 {{1,7},{2,3,4},{5},{6}}=>4 {{1},{2,3,4,7},{5},{6}}=>6 {{1},{2,3,4},{5,7},{6}}=>4 {{1},{2,3,4},{5},{6,7}}=>4 {{1},{2,3,4},{5},{6},{7}}=>3 {{1,5,6,7},{2,3},{4}}=>7 {{1,5,6},{2,3,7},{4}}=>6 {{1,5,6},{2,3},{4,7}}=>5 {{1,5,6},{2,3},{4},{7}}=>4 {{1,5,7},{2,3,6},{4}}=>6 {{1,5},{2,3,6,7},{4}}=>7 {{1,5},{2,3,6},{4,7}}=>5 {{1,5},{2,3,6},{4},{7}}=>4 {{1,5,7},{2,3},{4,6}}=>5 {{1,5},{2,3,7},{4,6}}=>5 {{1,5},{2,3},{4,6,7}}=>5 {{1,5},{2,3},{4,6},{7}}=>3 {{1,5,7},{2,3},{4},{6}}=>4 {{1,5},{2,3,7},{4},{6}}=>4 {{1,5},{2,3},{4,7},{6}}=>3 {{1,5},{2,3},{4},{6,7}}=>3 {{1,5},{2,3},{4},{6},{7}}=>2 {{1,6,7},{2,3,5},{4}}=>6 {{1,6},{2,3,5,7},{4}}=>7 {{1,6},{2,3,5},{4,7}}=>5 {{1,6},{2,3,5},{4},{7}}=>4 {{1,7},{2,3,5,6},{4}}=>7 {{1},{2,3,5,6,7},{4}}=>10 {{1},{2,3,5,6},{4,7}}=>7 {{1},{2,3,5,6},{4},{7}}=>6 {{1,7},{2,3,5},{4,6}}=>5 {{1},{2,3,5,7},{4,6}}=>7 {{1},{2,3,5},{4,6,7}}=>6 {{1},{2,3,5},{4,6},{7}}=>4 {{1,7},{2,3,5},{4},{6}}=>4 {{1},{2,3,5,7},{4},{6}}=>6 {{1},{2,3,5},{4,7},{6}}=>4 {{1},{2,3,5},{4},{6,7}}=>4 {{1},{2,3,5},{4},{6},{7}}=>3 {{1,6,7},{2,3},{4,5}}=>5 {{1,6},{2,3,7},{4,5}}=>5 {{1,6},{2,3},{4,5,7}}=>5 {{1,6},{2,3},{4,5},{7}}=>3 {{1,7},{2,3,6},{4,5}}=>5 {{1},{2,3,6,7},{4,5}}=>7 {{1},{2,3,6},{4,5,7}}=>6 {{1},{2,3,6},{4,5},{7}}=>4 {{1,7},{2,3},{4,5,6}}=>5 {{1},{2,3,7},{4,5,6}}=>6 {{1},{2,3},{4,5,6,7}}=>7 {{1},{2,3},{4,5,6},{7}}=>4 {{1,7},{2,3},{4,5},{6}}=>3 {{1},{2,3,7},{4,5},{6}}=>4 {{1},{2,3},{4,5,7},{6}}=>4 {{1},{2,3},{4,5},{6,7}}=>3 {{1},{2,3},{4,5},{6},{7}}=>2 {{1,6,7},{2,3},{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}}=>2 {{1,7},{2,3,6},{4},{5}}=>4 {{1},{2,3,6,7},{4},{5}}=>6 {{1},{2,3,6},{4,7},{5}}=>4 {{1},{2,3,6},{4},{5,7}}=>4 {{1},{2,3,6},{4},{5},{7}}=>3 {{1,7},{2,3},{4,6},{5}}=>3 {{1},{2,3,7},{4,6},{5}}=>4 {{1},{2,3},{4,6,7},{5}}=>4 {{1},{2,3},{4,6},{5,7}}=>3 {{1},{2,3},{4,6},{5},{7}}=>2 {{1,7},{2,3},{4},{5,6}}=>3 {{1},{2,3,7},{4},{5,6}}=>4 {{1},{2,3},{4,7},{5,6}}=>3 {{1},{2,3},{4},{5,6,7}}=>4 {{1},{2,3},{4},{5,6},{7}}=>2 {{1,7},{2,3},{4},{5},{6}}=>2 {{1},{2,3,7},{4},{5},{6}}=>3 {{1},{2,3},{4,7},{5},{6}}=>2 {{1},{2,3},{4},{5,7},{6}}=>2 {{1},{2,3},{4},{5},{6,7}}=>2 {{1},{2,3},{4},{5},{6},{7}}=>1 {{1,4,5,6,7},{2},{3}}=>10 {{1,4,5,6},{2,7},{3}}=>7 {{1,4,5,6},{2},{3,7}}=>7 {{1,4,5,6},{2},{3},{7}}=>6 {{1,4,5,7},{2,6},{3}}=>7 {{1,4,5},{2,6,7},{3}}=>6 {{1,4,5},{2,6},{3,7}}=>5 {{1,4,5},{2,6},{3},{7}}=>4 {{1,4,5,7},{2},{3,6}}=>7 {{1,4,5},{2,7},{3,6}}=>5 {{1,4,5},{2},{3,6,7}}=>6 {{1,4,5},{2},{3,6},{7}}=>4 {{1,4,5,7},{2},{3},{6}}=>6 {{1,4,5},{2,7},{3},{6}}=>4 {{1,4,5},{2},{3,7},{6}}=>4 {{1,4,5},{2},{3},{6,7}}=>4 {{1,4,5},{2},{3},{6},{7}}=>3 {{1,4,6,7},{2,5},{3}}=>7 {{1,4,6},{2,5,7},{3}}=>6 {{1,4,6},{2,5},{3,7}}=>5 {{1,4,6},{2,5},{3},{7}}=>4 {{1,4,7},{2,5,6},{3}}=>6 {{1,4},{2,5,6,7},{3}}=>7 {{1,4},{2,5,6},{3,7}}=>5 {{1,4},{2,5,6},{3},{7}}=>4 {{1,4,7},{2,5},{3,6}}=>5 {{1,4},{2,5,7},{3,6}}=>5 {{1,4},{2,5},{3,6,7}}=>5 {{1,4},{2,5},{3,6},{7}}=>3 {{1,4,7},{2,5},{3},{6}}=>4 {{1,4},{2,5,7},{3},{6}}=>4 {{1,4},{2,5},{3,7},{6}}=>3 {{1,4},{2,5},{3},{6,7}}=>3 {{1,4},{2,5},{3},{6},{7}}=>2 {{1,4,6,7},{2},{3,5}}=>7 {{1,4,6},{2,7},{3,5}}=>5 {{1,4,6},{2},{3,5,7}}=>6 {{1,4,6},{2},{3,5},{7}}=>4 {{1,4,7},{2,6},{3,5}}=>5 {{1,4},{2,6,7},{3,5}}=>5 {{1,4},{2,6},{3,5,7}}=>5 {{1,4},{2,6},{3,5},{7}}=>3 {{1,4,7},{2},{3,5,6}}=>6 {{1,4},{2,7},{3,5,6}}=>5 {{1,4},{2},{3,5,6,7}}=>7 {{1,4},{2},{3,5,6},{7}}=>4 {{1,4,7},{2},{3,5},{6}}=>4 {{1,4},{2,7},{3,5},{6}}=>3 {{1,4},{2},{3,5,7},{6}}=>4 {{1,4},{2},{3,5},{6,7}}=>3 {{1,4},{2},{3,5},{6},{7}}=>2 {{1,4,6,7},{2},{3},{5}}=>6 {{1,4,6},{2,7},{3},{5}}=>4 {{1,4,6},{2},{3,7},{5}}=>4 {{1,4,6},{2},{3},{5,7}}=>4 {{1,4,6},{2},{3},{5},{7}}=>3 {{1,4,7},{2,6},{3},{5}}=>4 {{1,4},{2,6,7},{3},{5}}=>4 {{1,4},{2,6},{3,7},{5}}=>3 {{1,4},{2,6},{3},{5,7}}=>3 {{1,4},{2,6},{3},{5},{7}}=>2 {{1,4,7},{2},{3,6},{5}}=>4 {{1,4},{2,7},{3,6},{5}}=>3 {{1,4},{2},{3,6,7},{5}}=>4 {{1,4},{2},{3,6},{5,7}}=>3 {{1,4},{2},{3,6},{5},{7}}=>2 {{1,4,7},{2},{3},{5,6}}=>4 {{1,4},{2,7},{3},{5,6}}=>3 {{1,4},{2},{3,7},{5,6}}=>3 {{1,4},{2},{3},{5,6,7}}=>4 {{1,4},{2},{3},{5,6},{7}}=>2 {{1,4,7},{2},{3},{5},{6}}=>3 {{1,4},{2,7},{3},{5},{6}}=>2 {{1,4},{2},{3,7},{5},{6}}=>2 {{1,4},{2},{3},{5,7},{6}}=>2 {{1,4},{2},{3},{5},{6,7}}=>2 {{1,4},{2},{3},{5},{6},{7}}=>1 {{1,5,6,7},{2,4},{3}}=>7 {{1,5,6},{2,4,7},{3}}=>6 {{1,5,6},{2,4},{3,7}}=>5 {{1,5,6},{2,4},{3},{7}}=>4 {{1,5,7},{2,4,6},{3}}=>6 {{1,5},{2,4,6,7},{3}}=>7 {{1,5},{2,4,6},{3,7}}=>5 {{1,5},{2,4,6},{3},{7}}=>4 {{1,5,7},{2,4},{3,6}}=>5 {{1,5},{2,4,7},{3,6}}=>5 {{1,5},{2,4},{3,6,7}}=>5 {{1,5},{2,4},{3,6},{7}}=>3 {{1,5,7},{2,4},{3},{6}}=>4 {{1,5},{2,4,7},{3},{6}}=>4 {{1,5},{2,4},{3,7},{6}}=>3 {{1,5},{2,4},{3},{6,7}}=>3 {{1,5},{2,4},{3},{6},{7}}=>2 {{1,6,7},{2,4,5},{3}}=>6 {{1,6},{2,4,5,7},{3}}=>7 {{1,6},{2,4,5},{3,7}}=>5 {{1,6},{2,4,5},{3},{7}}=>4 {{1,7},{2,4,5,6},{3}}=>7 {{1},{2,4,5,6,7},{3}}=>10 {{1},{2,4,5,6},{3,7}}=>7 {{1},{2,4,5,6},{3},{7}}=>6 {{1,7},{2,4,5},{3,6}}=>5 {{1},{2,4,5,7},{3,6}}=>7 {{1},{2,4,5},{3,6,7}}=>6 {{1},{2,4,5},{3,6},{7}}=>4 {{1,7},{2,4,5},{3},{6}}=>4 {{1},{2,4,5,7},{3},{6}}=>6 {{1},{2,4,5},{3,7},{6}}=>4 {{1},{2,4,5},{3},{6,7}}=>4 {{1},{2,4,5},{3},{6},{7}}=>3 {{1,6,7},{2,4},{3,5}}=>5 {{1,6},{2,4,7},{3,5}}=>5 {{1,6},{2,4},{3,5,7}}=>5 {{1,6},{2,4},{3,5},{7}}=>3 {{1,7},{2,4,6},{3,5}}=>5 {{1},{2,4,6,7},{3,5}}=>7 {{1},{2,4,6},{3,5,7}}=>6 {{1},{2,4,6},{3,5},{7}}=>4 {{1,7},{2,4},{3,5,6}}=>5 {{1},{2,4,7},{3,5,6}}=>6 {{1},{2,4},{3,5,6,7}}=>7 {{1},{2,4},{3,5,6},{7}}=>4 {{1,7},{2,4},{3,5},{6}}=>3 {{1},{2,4,7},{3,5},{6}}=>4 {{1},{2,4},{3,5,7},{6}}=>4 {{1},{2,4},{3,5},{6,7}}=>3 {{1},{2,4},{3,5},{6},{7}}=>2 {{1,6,7},{2,4},{3},{5}}=>4 {{1,6},{2,4,7},{3},{5}}=>4 {{1,6},{2,4},{3,7},{5}}=>3 {{1,6},{2,4},{3},{5,7}}=>3 {{1,6},{2,4},{3},{5},{7}}=>2 {{1,7},{2,4,6},{3},{5}}=>4 {{1},{2,4,6,7},{3},{5}}=>6 {{1},{2,4,6},{3,7},{5}}=>4 {{1},{2,4,6},{3},{5,7}}=>4 {{1},{2,4,6},{3},{5},{7}}=>3 {{1,7},{2,4},{3,6},{5}}=>3 {{1},{2,4,7},{3,6},{5}}=>4 {{1},{2,4},{3,6,7},{5}}=>4 {{1},{2,4},{3,6},{5,7}}=>3 {{1},{2,4},{3,6},{5},{7}}=>2 {{1,7},{2,4},{3},{5,6}}=>3 {{1},{2,4,7},{3},{5,6}}=>4 {{1},{2,4},{3,7},{5,6}}=>3 {{1},{2,4},{3},{5,6,7}}=>4 {{1},{2,4},{3},{5,6},{7}}=>2 {{1,7},{2,4},{3},{5},{6}}=>2 {{1},{2,4,7},{3},{5},{6}}=>3 {{1},{2,4},{3,7},{5},{6}}=>2 {{1},{2,4},{3},{5,7},{6}}=>2 {{1},{2,4},{3},{5},{6,7}}=>2 {{1},{2,4},{3},{5},{6},{7}}=>1 {{1,5,6,7},{2},{3,4}}=>7 {{1,5,6},{2,7},{3,4}}=>5 {{1,5,6},{2},{3,4,7}}=>6 {{1,5,6},{2},{3,4},{7}}=>4 {{1,5,7},{2,6},{3,4}}=>5 {{1,5},{2,6,7},{3,4}}=>5 {{1,5},{2,6},{3,4,7}}=>5 {{1,5},{2,6},{3,4},{7}}=>3 {{1,5,7},{2},{3,4,6}}=>6 {{1,5},{2,7},{3,4,6}}=>5 {{1,5},{2},{3,4,6,7}}=>7 {{1,5},{2},{3,4,6},{7}}=>4 {{1,5,7},{2},{3,4},{6}}=>4 {{1,5},{2,7},{3,4},{6}}=>3 {{1,5},{2},{3,4,7},{6}}=>4 {{1,5},{2},{3,4},{6,7}}=>3 {{1,5},{2},{3,4},{6},{7}}=>2 {{1,6,7},{2,5},{3,4}}=>5 {{1,6},{2,5,7},{3,4}}=>5 {{1,6},{2,5},{3,4,7}}=>5 {{1,6},{2,5},{3,4},{7}}=>3 {{1,7},{2,5,6},{3,4}}=>5 {{1},{2,5,6,7},{3,4}}=>7 {{1},{2,5,6},{3,4,7}}=>6 {{1},{2,5,6},{3,4},{7}}=>4 {{1,7},{2,5},{3,4,6}}=>5 {{1},{2,5,7},{3,4,6}}=>6 {{1},{2,5},{3,4,6,7}}=>7 {{1},{2,5},{3,4,6},{7}}=>4 {{1,7},{2,5},{3,4},{6}}=>3 {{1},{2,5,7},{3,4},{6}}=>4 {{1},{2,5},{3,4,7},{6}}=>4 {{1},{2,5},{3,4},{6,7}}=>3 {{1},{2,5},{3,4},{6},{7}}=>2 {{1,6,7},{2},{3,4,5}}=>6 {{1,6},{2,7},{3,4,5}}=>5 {{1,6},{2},{3,4,5,7}}=>7 {{1,6},{2},{3,4,5},{7}}=>4 {{1,7},{2,6},{3,4,5}}=>5 {{1},{2,6,7},{3,4,5}}=>6 {{1},{2,6},{3,4,5,7}}=>7 {{1},{2,6},{3,4,5},{7}}=>4 {{1,7},{2},{3,4,5,6}}=>7 {{1},{2,7},{3,4,5,6}}=>7 {{1},{2},{3,4,5,6,7}}=>10 {{1},{2},{3,4,5,6},{7}}=>6 {{1,7},{2},{3,4,5},{6}}=>4 {{1},{2,7},{3,4,5},{6}}=>4 {{1},{2},{3,4,5,7},{6}}=>6 {{1},{2},{3,4,5},{6,7}}=>4 {{1},{2},{3,4,5},{6},{7}}=>3 {{1,6,7},{2},{3,4},{5}}=>4 {{1,6},{2,7},{3,4},{5}}=>3 {{1,6},{2},{3,4,7},{5}}=>4 {{1,6},{2},{3,4},{5,7}}=>3 {{1,6},{2},{3,4},{5},{7}}=>2 {{1,7},{2,6},{3,4},{5}}=>3 {{1},{2,6,7},{3,4},{5}}=>4 {{1},{2,6},{3,4,7},{5}}=>4 {{1},{2,6},{3,4},{5,7}}=>3 {{1},{2,6},{3,4},{5},{7}}=>2 {{1,7},{2},{3,4,6},{5}}=>4 {{1},{2,7},{3,4,6},{5}}=>4 {{1},{2},{3,4,6,7},{5}}=>6 {{1},{2},{3,4,6},{5,7}}=>4 {{1},{2},{3,4,6},{5},{7}}=>3 {{1,7},{2},{3,4},{5,6}}=>3 {{1},{2,7},{3,4},{5,6}}=>3 {{1},{2},{3,4,7},{5,6}}=>4 {{1},{2},{3,4},{5,6,7}}=>4 {{1},{2},{3,4},{5,6},{7}}=>2 {{1,7},{2},{3,4},{5},{6}}=>2 {{1},{2,7},{3,4},{5},{6}}=>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}}=>1 {{1,5,6,7},{2},{3},{4}}=>6 {{1,5,6},{2,7},{3},{4}}=>4 {{1,5,6},{2},{3,7},{4}}=>4 {{1,5,6},{2},{3},{4,7}}=>4 {{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}}=>3 {{1,5},{2,6},{3},{4,7}}=>3 {{1,5},{2,6},{3},{4},{7}}=>2 {{1,5,7},{2},{3,6},{4}}=>4 {{1,5},{2,7},{3,6},{4}}=>3 {{1,5},{2},{3,6,7},{4}}=>4 {{1,5},{2},{3,6},{4,7}}=>3 {{1,5},{2},{3,6},{4},{7}}=>2 {{1,5,7},{2},{3},{4,6}}=>4 {{1,5},{2,7},{3},{4,6}}=>3 {{1,5},{2},{3,7},{4,6}}=>3 {{1,5},{2},{3},{4,6,7}}=>4 {{1,5},{2},{3},{4,6},{7}}=>2 {{1,5,7},{2},{3},{4},{6}}=>3 {{1,5},{2,7},{3},{4},{6}}=>2 {{1,5},{2},{3,7},{4},{6}}=>2 {{1,5},{2},{3},{4,7},{6}}=>2 {{1,5},{2},{3},{4},{6,7}}=>2 {{1,5},{2},{3},{4},{6},{7}}=>1 {{1,6,7},{2,5},{3},{4}}=>4 {{1,6},{2,5,7},{3},{4}}=>4 {{1,6},{2,5},{3,7},{4}}=>3 {{1,6},{2,5},{3},{4,7}}=>3 {{1,6},{2,5},{3},{4},{7}}=>2 {{1,7},{2,5,6},{3},{4}}=>4 {{1},{2,5,6,7},{3},{4}}=>6 {{1},{2,5,6},{3,7},{4}}=>4 {{1},{2,5,6},{3},{4,7}}=>4 {{1},{2,5,6},{3},{4},{7}}=>3 {{1,7},{2,5},{3,6},{4}}=>3 {{1},{2,5,7},{3,6},{4}}=>4 {{1},{2,5},{3,6,7},{4}}=>4 {{1},{2,5},{3,6},{4,7}}=>3 {{1},{2,5},{3,6},{4},{7}}=>2 {{1,7},{2,5},{3},{4,6}}=>3 {{1},{2,5,7},{3},{4,6}}=>4 {{1},{2,5},{3,7},{4,6}}=>3 {{1},{2,5},{3},{4,6,7}}=>4 {{1},{2,5},{3},{4,6},{7}}=>2 {{1,7},{2,5},{3},{4},{6}}=>2 {{1},{2,5,7},{3},{4},{6}}=>3 {{1},{2,5},{3,7},{4},{6}}=>2 {{1},{2,5},{3},{4,7},{6}}=>2 {{1},{2,5},{3},{4},{6,7}}=>2 {{1},{2,5},{3},{4},{6},{7}}=>1 {{1,6,7},{2},{3,5},{4}}=>4 {{1,6},{2,7},{3,5},{4}}=>3 {{1,6},{2},{3,5,7},{4}}=>4 {{1,6},{2},{3,5},{4,7}}=>3 {{1,6},{2},{3,5},{4},{7}}=>2 {{1,7},{2,6},{3,5},{4}}=>3 {{1},{2,6,7},{3,5},{4}}=>4 {{1},{2,6},{3,5,7},{4}}=>4 {{1},{2,6},{3,5},{4,7}}=>3 {{1},{2,6},{3,5},{4},{7}}=>2 {{1,7},{2},{3,5,6},{4}}=>4 {{1},{2,7},{3,5,6},{4}}=>4 {{1},{2},{3,5,6,7},{4}}=>6 {{1},{2},{3,5,6},{4,7}}=>4 {{1},{2},{3,5,6},{4},{7}}=>3 {{1,7},{2},{3,5},{4,6}}=>3 {{1},{2,7},{3,5},{4,6}}=>3 {{1},{2},{3,5,7},{4,6}}=>4 {{1},{2},{3,5},{4,6,7}}=>4 {{1},{2},{3,5},{4,6},{7}}=>2 {{1,7},{2},{3,5},{4},{6}}=>2 {{1},{2,7},{3,5},{4},{6}}=>2 {{1},{2},{3,5,7},{4},{6}}=>3 {{1},{2},{3,5},{4,7},{6}}=>2 {{1},{2},{3,5},{4},{6,7}}=>2 {{1},{2},{3,5},{4},{6},{7}}=>1 {{1,6,7},{2},{3},{4,5}}=>4 {{1,6},{2,7},{3},{4,5}}=>3 {{1,6},{2},{3,7},{4,5}}=>3 {{1,6},{2},{3},{4,5,7}}=>4 {{1,6},{2},{3},{4,5},{7}}=>2 {{1,7},{2,6},{3},{4,5}}=>3 {{1},{2,6,7},{3},{4,5}}=>4 {{1},{2,6},{3,7},{4,5}}=>3 {{1},{2,6},{3},{4,5,7}}=>4 {{1},{2,6},{3},{4,5},{7}}=>2 {{1,7},{2},{3,6},{4,5}}=>3 {{1},{2,7},{3,6},{4,5}}=>3 {{1},{2},{3,6,7},{4,5}}=>4 {{1},{2},{3,6},{4,5,7}}=>4 {{1},{2},{3,6},{4,5},{7}}=>2 {{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}}=>6 {{1},{2},{3},{4,5,6},{7}}=>3 {{1,7},{2},{3},{4,5},{6}}=>2 {{1},{2,7},{3},{4,5},{6}}=>2 {{1},{2},{3,7},{4,5},{6}}=>2 {{1},{2},{3},{4,5,7},{6}}=>3 {{1},{2},{3},{4,5},{6,7}}=>2 {{1},{2},{3},{4,5},{6},{7}}=>1 {{1,6,7},{2},{3},{4},{5}}=>3 {{1,6},{2,7},{3},{4},{5}}=>2 {{1,6},{2},{3,7},{4},{5}}=>2 {{1,6},{2},{3},{4,7},{5}}=>2 {{1,6},{2},{3},{4},{5,7}}=>2 {{1,6},{2},{3},{4},{5},{7}}=>1 {{1,7},{2,6},{3},{4},{5}}=>2 {{1},{2,6,7},{3},{4},{5}}=>3 {{1},{2,6},{3,7},{4},{5}}=>2 {{1},{2,6},{3},{4,7},{5}}=>2 {{1},{2,6},{3},{4},{5,7}}=>2 {{1},{2,6},{3},{4},{5},{7}}=>1 {{1,7},{2},{3,6},{4},{5}}=>2 {{1},{2,7},{3,6},{4},{5}}=>2 {{1},{2},{3,6,7},{4},{5}}=>3 {{1},{2},{3,6},{4,7},{5}}=>2 {{1},{2},{3,6},{4},{5,7}}=>2 {{1},{2},{3,6},{4},{5},{7}}=>1 {{1,7},{2},{3},{4,6},{5}}=>2 {{1},{2,7},{3},{4,6},{5}}=>2 {{1},{2},{3,7},{4,6},{5}}=>2 {{1},{2},{3},{4,6,7},{5}}=>3 {{1},{2},{3},{4,6},{5,7}}=>2 {{1},{2},{3},{4,6},{5},{7}}=>1 {{1,7},{2},{3},{4},{5,6}}=>2 {{1},{2,7},{3},{4},{5,6}}=>2 {{1},{2},{3,7},{4},{5,6}}=>2 {{1},{2},{3},{4,7},{5,6}}=>2 {{1},{2},{3},{4},{5,6,7}}=>3 {{1},{2},{3},{4},{5,6},{7}}=>1 {{1,7},{2},{3},{4},{5},{6}}=>1 {{1},{2,7},{3},{4},{5},{6}}=>1 {{1},{2},{3,7},{4},{5},{6}}=>1 {{1},{2},{3},{4,7},{5},{6}}=>1 {{1},{2},{3},{4},{5,7},{6}}=>1 {{1},{2},{3},{4},{5},{6,7}}=>1 {{1},{2},{3},{4},{5},{6},{7}}=>0 {{1},{2},{3,4,5,6,7,8}}=>15 {{1},{2,4,5,6,7,8},{3}}=>15 {{1},{2,3,5,6,7,8},{4}}=>15 {{1},{2,3,4,6,7,8},{5}}=>15 {{1},{2,3,4,5,7,8},{6}}=>15 {{1},{2,3,4,5,6,7},{8}}=>15 {{1},{2,3,4,5,6,8},{7}}=>15 {{1},{2,3,4,5,6,7,8}}=>21 {{1,2},{3,4,5,6,7,8}}=>16 {{1,4,5,6,7,8},{2},{3}}=>15 {{1,3,5,6,7,8},{2},{4}}=>15 {{1,3,4,5,6,7,8},{2}}=>21 {{1,4,5,6,7,8},{2,3}}=>16 {{1,2,4,5,6,7,8},{3}}=>21 {{1,2,5,6,7,8},{3,4}}=>16 {{1,2,3,5,6,7,8},{4}}=>21 {{1,2,3,6,7,8},{4,5}}=>16 {{1,2,3,4,6,7,8},{5}}=>21 {{1,2,3,4,5,6},{7,8}}=>16 {{1,2,3,4,7,8},{5,6}}=>16 {{1,2,3,4,5,7,8},{6}}=>21 {{1,2,3,4,5,6,7},{8}}=>21 {{1,8},{2,3,4,5,6,7}}=>16 {{1,2,3,4,5,8},{6,7}}=>16 {{1,2,3,4,5,6,8},{7}}=>21 {{1,2,3,4,5,6,7,8}}=>28 {{1,2,4,5,7,8},{3,6}}=>16 {{1,3,4,5,7,8},{2,6}}=>16 {{1,2,4,5,6,8},{3,7}}=>16 {{1,2,3,4,5,7},{6,8}}=>16 {{1,3,5,6,7,8},{2,4}}=>16 {{1,3,4,5,6,8},{2,7}}=>16 {{1,2,3,5,7,8},{4,6}}=>16 {{1,2,4,6,7,8},{3,5}}=>16 {{1,3,4,5,6,7},{2,8}}=>16 {{1,7},{2,3,4,5,6,8}}=>16 {{1,2,3,4,6,8},{5,7}}=>16 {{1,2,3,5,6,7},{4,8}}=>16 {{1,2,3,5,6,8},{4,7}}=>16 {{1,3,4,6,7,8},{2,5}}=>16 {{1,2,3,4,6,7},{5,8}}=>16 {{1,4},{2,3,5,6,7,8}}=>16 {{1,2,4,5,6,7},{3,8}}=>16 {{1,3},{2,4,5,6,7,8}}=>16 {{1,5},{2,3,4,6,7,8}}=>16 {{1,6},{2,3,4,5,7,8}}=>16
click to show generating function       
Description
The number of occurrences of the pattern {{1,2}} in a set partition.
Code
def Klazar_occurrences(pi, pattern):
    """
    Return the number of occurrences of pattern in pi.

    EXAMPLES:

    From Mansour 2013, page 86, Example 3.24

    The set partition π = 135/26/4 contains four occurrences of
    the pattern 12/3, namely, 13/6, 13/4, 15/6, and 35/6. On the other hand, the
    set partition π avoids the pattern 12/34.

    sage: Klazar_occurrences([[1,3,5],[2,6],[4]], [[1,2],[3]])
    4
    sage: Klazar_occurrences([[1,3,5],[2,6],[4]], [[1,2],[3,4]])
    0
    """
    pi = SetPartition(pi).standardization()
    pattern = SetPartition(pattern).standardization()
    count = 0
    for s in Subsets(range(1,1+pi.size()), pattern.size()):
        if pi.restriction(s).standardization() == pattern:
            count += 1
    return count


def statistic(pi):
    return Klazar_occurrences(pi, [[1,2]])
Created
Aug 05, 2016 at 09:31 by Martin Rubey
Updated
Aug 05, 2016 at 09:31 by Martin Rubey