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Identifier
Values
=>
Cc0009;cc-rep
{{1}}=>0 {{1,2}}=>1 {{1},{2}}=>0 {{1,2,3}}=>3 {{1,2},{3}}=>2 {{1,3},{2}}=>1 {{1},{2,3}}=>2 {{1},{2},{3}}=>0 {{1,2,3,4}}=>6 {{1,2,3},{4}}=>5 {{1,2,4},{3}}=>4 {{1,2},{3,4}}=>5 {{1,2},{3},{4}}=>3 {{1,3,4},{2}}=>4 {{1,3},{2,4}}=>3 {{1,3},{2},{4}}=>2 {{1,4},{2,3}}=>4 {{1},{2,3,4}}=>5 {{1},{2,3},{4}}=>3 {{1,4},{2},{3}}=>1 {{1},{2,4},{3}}=>2 {{1},{2},{3,4}}=>3 {{1},{2},{3},{4}}=>0 {{1,2,3,4,5}}=>10 {{1,2,3,4},{5}}=>9 {{1,2,3,5},{4}}=>8 {{1,2,3},{4,5}}=>9 {{1,2,3},{4},{5}}=>7 {{1,2,4,5},{3}}=>8 {{1,2,4},{3,5}}=>7 {{1,2,4},{3},{5}}=>6 {{1,2,5},{3,4}}=>8 {{1,2},{3,4,5}}=>9 {{1,2},{3,4},{5}}=>7 {{1,2,5},{3},{4}}=>5 {{1,2},{3,5},{4}}=>6 {{1,2},{3},{4,5}}=>7 {{1,2},{3},{4},{5}}=>4 {{1,3,4,5},{2}}=>8 {{1,3,4},{2,5}}=>7 {{1,3,4},{2},{5}}=>6 {{1,3,5},{2,4}}=>6 {{1,3},{2,4,5}}=>7 {{1,3},{2,4},{5}}=>5 {{1,3,5},{2},{4}}=>5 {{1,3},{2,5},{4}}=>4 {{1,3},{2},{4,5}}=>6 {{1,3},{2},{4},{5}}=>3 {{1,4,5},{2,3}}=>8 {{1,4},{2,3,5}}=>7 {{1,4},{2,3},{5}}=>6 {{1,5},{2,3,4}}=>8 {{1},{2,3,4,5}}=>9 {{1},{2,3,4},{5}}=>7 {{1,5},{2,3},{4}}=>5 {{1},{2,3,5},{4}}=>6 {{1},{2,3},{4,5}}=>7 {{1},{2,3},{4},{5}}=>4 {{1,4,5},{2},{3}}=>5 {{1,4},{2,5},{3}}=>3 {{1,4},{2},{3,5}}=>4 {{1,4},{2},{3},{5}}=>2 {{1,5},{2,4},{3}}=>4 {{1},{2,4,5},{3}}=>6 {{1},{2,4},{3,5}}=>5 {{1},{2,4},{3},{5}}=>3 {{1,5},{2},{3,4}}=>5 {{1},{2,5},{3,4}}=>6 {{1},{2},{3,4,5}}=>7 {{1},{2},{3,4},{5}}=>4 {{1,5},{2},{3},{4}}=>1 {{1},{2,5},{3},{4}}=>2 {{1},{2},{3,5},{4}}=>3 {{1},{2},{3},{4,5}}=>4 {{1},{2},{3},{4},{5}}=>0 {{1,2,3,4,5,6}}=>15 {{1,2,3,4,5},{6}}=>14 {{1,2,3,4,6},{5}}=>13 {{1,2,3,4},{5,6}}=>14 {{1,2,3,4},{5},{6}}=>12 {{1,2,3,5,6},{4}}=>13 {{1,2,3,5},{4,6}}=>12 {{1,2,3,5},{4},{6}}=>11 {{1,2,3,6},{4,5}}=>13 {{1,2,3},{4,5,6}}=>14 {{1,2,3},{4,5},{6}}=>12 {{1,2,3,6},{4},{5}}=>10 {{1,2,3},{4,6},{5}}=>11 {{1,2,3},{4},{5,6}}=>12 {{1,2,3},{4},{5},{6}}=>9 {{1,2,4,5,6},{3}}=>13 {{1,2,4,5},{3,6}}=>12 {{1,2,4,5},{3},{6}}=>11 {{1,2,4,6},{3,5}}=>11 {{1,2,4},{3,5,6}}=>12 {{1,2,4},{3,5},{6}}=>10 {{1,2,4,6},{3},{5}}=>10 {{1,2,4},{3,6},{5}}=>9 {{1,2,4},{3},{5,6}}=>11 {{1,2,4},{3},{5},{6}}=>8 {{1,2,5,6},{3,4}}=>13 {{1,2,5},{3,4,6}}=>12 {{1,2,5},{3,4},{6}}=>11 {{1,2,6},{3,4,5}}=>13 {{1,2},{3,4,5,6}}=>14 {{1,2},{3,4,5},{6}}=>12 {{1,2,6},{3,4},{5}}=>10 {{1,2},{3,4,6},{5}}=>11 {{1,2},{3,4},{5,6}}=>12 {{1,2},{3,4},{5},{6}}=>9 {{1,2,5,6},{3},{4}}=>10 {{1,2,5},{3,6},{4}}=>8 {{1,2,5},{3},{4,6}}=>9 {{1,2,5},{3},{4},{6}}=>7 {{1,2,6},{3,5},{4}}=>9 {{1,2},{3,5,6},{4}}=>11 {{1,2},{3,5},{4,6}}=>10 {{1,2},{3,5},{4},{6}}=>8 {{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}}=>9 {{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}}=>5 {{1,3,4,5,6},{2}}=>13 {{1,3,4,5},{2,6}}=>12 {{1,3,4,5},{2},{6}}=>11 {{1,3,4,6},{2,5}}=>11 {{1,3,4},{2,5,6}}=>12 {{1,3,4},{2,5},{6}}=>10 {{1,3,4,6},{2},{5}}=>10 {{1,3,4},{2,6},{5}}=>9 {{1,3,4},{2},{5,6}}=>11 {{1,3,4},{2},{5},{6}}=>8 {{1,3,5,6},{2,4}}=>11 {{1,3,5},{2,4,6}}=>10 {{1,3,5},{2,4},{6}}=>9 {{1,3,6},{2,4,5}}=>11 {{1,3},{2,4,5,6}}=>12 {{1,3},{2,4,5},{6}}=>10 {{1,3,6},{2,4},{5}}=>8 {{1,3},{2,4,6},{5}}=>9 {{1,3},{2,4},{5,6}}=>10 {{1,3},{2,4},{5},{6}}=>7 {{1,3,5,6},{2},{4}}=>10 {{1,3,5},{2,6},{4}}=>8 {{1,3,5},{2},{4,6}}=>9 {{1,3,5},{2},{4},{6}}=>7 {{1,3,6},{2,5},{4}}=>7 {{1,3},{2,5,6},{4}}=>9 {{1,3},{2,5},{4,6}}=>8 {{1,3},{2,5},{4},{6}}=>6 {{1,3,6},{2},{4,5}}=>10 {{1,3},{2,6},{4,5}}=>9 {{1,3},{2},{4,5,6}}=>11 {{1,3},{2},{4,5},{6}}=>8 {{1,3,6},{2},{4},{5}}=>6 {{1,3},{2,6},{4},{5}}=>5 {{1,3},{2},{4,6},{5}}=>7 {{1,3},{2},{4},{5,6}}=>8 {{1,3},{2},{4},{5},{6}}=>4 {{1,4,5,6},{2,3}}=>13 {{1,4,5},{2,3,6}}=>12 {{1,4,5},{2,3},{6}}=>11 {{1,4,6},{2,3,5}}=>11 {{1,4},{2,3,5,6}}=>12 {{1,4},{2,3,5},{6}}=>10 {{1,4,6},{2,3},{5}}=>10 {{1,4},{2,3,6},{5}}=>9 {{1,4},{2,3},{5,6}}=>11 {{1,4},{2,3},{5},{6}}=>8 {{1,5,6},{2,3,4}}=>13 {{1,5},{2,3,4,6}}=>12 {{1,5},{2,3,4},{6}}=>11 {{1,6},{2,3,4,5}}=>13 {{1},{2,3,4,5,6}}=>14 {{1},{2,3,4,5},{6}}=>12 {{1,6},{2,3,4},{5}}=>10 {{1},{2,3,4,6},{5}}=>11 {{1},{2,3,4},{5,6}}=>12 {{1},{2,3,4},{5},{6}}=>9 {{1,5,6},{2,3},{4}}=>10 {{1,5},{2,3,6},{4}}=>8 {{1,5},{2,3},{4,6}}=>9 {{1,5},{2,3},{4},{6}}=>7 {{1,6},{2,3,5},{4}}=>9 {{1},{2,3,5,6},{4}}=>11 {{1},{2,3,5},{4,6}}=>10 {{1},{2,3,5},{4},{6}}=>8 {{1,6},{2,3},{4,5}}=>10 {{1},{2,3,6},{4,5}}=>11 {{1},{2,3},{4,5,6}}=>12 {{1},{2,3},{4,5},{6}}=>9 {{1,6},{2,3},{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}}=>5 {{1,4,5,6},{2},{3}}=>10 {{1,4,5},{2,6},{3}}=>8 {{1,4,5},{2},{3,6}}=>9 {{1,4,5},{2},{3},{6}}=>7 {{1,4,6},{2,5},{3}}=>7 {{1,4},{2,5,6},{3}}=>8 {{1,4},{2,5},{3,6}}=>6 {{1,4},{2,5},{3},{6}}=>5 {{1,4,6},{2},{3,5}}=>8 {{1,4},{2,6},{3,5}}=>7 {{1,4},{2},{3,5,6}}=>9 {{1,4},{2},{3,5},{6}}=>6 {{1,4,6},{2},{3},{5}}=>6 {{1,4},{2,6},{3},{5}}=>4 {{1,4},{2},{3,6},{5}}=>5 {{1,4},{2},{3},{5,6}}=>7 {{1,4},{2},{3},{5},{6}}=>3 {{1,5,6},{2,4},{3}}=>9 {{1,5},{2,4,6},{3}}=>8 {{1,5},{2,4},{3,6}}=>7 {{1,5},{2,4},{3},{6}}=>6 {{1,6},{2,4,5},{3}}=>9 {{1},{2,4,5,6},{3}}=>11 {{1},{2,4,5},{3,6}}=>10 {{1},{2,4,5},{3},{6}}=>8 {{1,6},{2,4},{3,5}}=>8 {{1},{2,4,6},{3,5}}=>9 {{1},{2,4},{3,5,6}}=>10 {{1},{2,4},{3,5},{6}}=>7 {{1,6},{2,4},{3},{5}}=>5 {{1},{2,4,6},{3},{5}}=>7 {{1},{2,4},{3,6},{5}}=>6 {{1},{2,4},{3},{5,6}}=>8 {{1},{2,4},{3},{5},{6}}=>4 {{1,5,6},{2},{3,4}}=>10 {{1,5},{2,6},{3,4}}=>8 {{1,5},{2},{3,4,6}}=>9 {{1,5},{2},{3,4},{6}}=>7 {{1,6},{2,5},{3,4}}=>9 {{1},{2,5,6},{3,4}}=>11 {{1},{2,5},{3,4,6}}=>10 {{1},{2,5},{3,4},{6}}=>8 {{1,6},{2},{3,4,5}}=>10 {{1},{2,6},{3,4,5}}=>11 {{1},{2},{3,4,5,6}}=>12 {{1},{2},{3,4,5},{6}}=>9 {{1,6},{2},{3,4},{5}}=>6 {{1},{2,6},{3,4},{5}}=>7 {{1},{2},{3,4,6},{5}}=>8 {{1},{2},{3,4},{5,6}}=>9 {{1},{2},{3,4},{5},{6}}=>5 {{1,5,6},{2},{3},{4}}=>6 {{1,5},{2,6},{3},{4}}=>3 {{1,5},{2},{3,6},{4}}=>4 {{1,5},{2},{3},{4,6}}=>5 {{1,5},{2},{3},{4},{6}}=>2 {{1,6},{2,5},{3},{4}}=>4 {{1},{2,5,6},{3},{4}}=>7 {{1},{2,5},{3,6},{4}}=>5 {{1},{2,5},{3},{4,6}}=>6 {{1},{2,5},{3},{4},{6}}=>3 {{1,6},{2},{3,5},{4}}=>5 {{1},{2,6},{3,5},{4}}=>6 {{1},{2},{3,5,6},{4}}=>8 {{1},{2},{3,5},{4,6}}=>7 {{1},{2},{3,5},{4},{6}}=>4 {{1,6},{2},{3},{4,5}}=>6 {{1},{2,6},{3},{4,5}}=>7 {{1},{2},{3,6},{4,5}}=>8 {{1},{2},{3},{4,5,6}}=>9 {{1},{2},{3},{4,5},{6}}=>5 {{1,6},{2},{3},{4},{5}}=>1 {{1},{2,6},{3},{4},{5}}=>2 {{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}}=>0 {{1,2,3,4,5,6,7}}=>21 {{1,2,3,4,5,6},{7}}=>20 {{1,2,3,4,5,7},{6}}=>19 {{1,2,3,4,5},{6,7}}=>20 {{1,2,3,4,5},{6},{7}}=>18 {{1,2,3,4,6,7},{5}}=>19 {{1,2,3,4,6},{5,7}}=>18 {{1,2,3,4,6},{5},{7}}=>17 {{1,2,3,4,7},{5,6}}=>19 {{1,2,3,4},{5,6,7}}=>20 {{1,2,3,4},{5,6},{7}}=>18 {{1,2,3,4,7},{5},{6}}=>16 {{1,2,3,4},{5,7},{6}}=>17 {{1,2,3,4},{5},{6,7}}=>18 {{1,2,3,4},{5},{6},{7}}=>15 {{1,2,3,5,6,7},{4}}=>19 {{1,2,3,5,6},{4,7}}=>18 {{1,2,3,5,6},{4},{7}}=>17 {{1,2,3,5,7},{4,6}}=>17 {{1,2,3,5},{4,6,7}}=>18 {{1,2,3,5},{4,6},{7}}=>16 {{1,2,3,5,7},{4},{6}}=>16 {{1,2,3,5},{4,7},{6}}=>15 {{1,2,3,5},{4},{6,7}}=>17 {{1,2,3,5},{4},{6},{7}}=>14 {{1,2,3,6,7},{4,5}}=>19 {{1,2,3,6},{4,5,7}}=>18 {{1,2,3,6},{4,5},{7}}=>17 {{1,2,3,7},{4,5,6}}=>19 {{1,2,3},{4,5,6,7}}=>20 {{1,2,3},{4,5,6},{7}}=>18 {{1,2,3,7},{4,5},{6}}=>16 {{1,2,3},{4,5,7},{6}}=>17 {{1,2,3},{4,5},{6,7}}=>18 {{1,2,3},{4,5},{6},{7}}=>15 {{1,2,3,6,7},{4},{5}}=>16 {{1,2,3,6},{4,7},{5}}=>14 {{1,2,3,6},{4},{5,7}}=>15 {{1,2,3,6},{4},{5},{7}}=>13 {{1,2,3,7},{4,6},{5}}=>15 {{1,2,3},{4,6,7},{5}}=>17 {{1,2,3},{4,6},{5,7}}=>16 {{1,2,3},{4,6},{5},{7}}=>14 {{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}}=>15 {{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}}=>11 {{1,2,4,5,6,7},{3}}=>19 {{1,2,4,5,6},{3,7}}=>18 {{1,2,4,5,6},{3},{7}}=>17 {{1,2,4,5,7},{3,6}}=>17 {{1,2,4,5},{3,6,7}}=>18 {{1,2,4,5},{3,6},{7}}=>16 {{1,2,4,5,7},{3},{6}}=>16 {{1,2,4,5},{3,7},{6}}=>15 {{1,2,4,5},{3},{6,7}}=>17 {{1,2,4,5},{3},{6},{7}}=>14 {{1,2,4,6,7},{3,5}}=>17 {{1,2,4,6},{3,5,7}}=>16 {{1,2,4,6},{3,5},{7}}=>15 {{1,2,4,7},{3,5,6}}=>17 {{1,2,4},{3,5,6,7}}=>18 {{1,2,4},{3,5,6},{7}}=>16 {{1,2,4,7},{3,5},{6}}=>14 {{1,2,4},{3,5,7},{6}}=>15 {{1,2,4},{3,5},{6,7}}=>16 {{1,2,4},{3,5},{6},{7}}=>13 {{1,2,4,6,7},{3},{5}}=>16 {{1,2,4,6},{3,7},{5}}=>14 {{1,2,4,6},{3},{5,7}}=>15 {{1,2,4,6},{3},{5},{7}}=>13 {{1,2,4,7},{3,6},{5}}=>13 {{1,2,4},{3,6,7},{5}}=>15 {{1,2,4},{3,6},{5,7}}=>14 {{1,2,4},{3,6},{5},{7}}=>12 {{1,2,4,7},{3},{5,6}}=>16 {{1,2,4},{3,7},{5,6}}=>15 {{1,2,4},{3},{5,6,7}}=>17 {{1,2,4},{3},{5,6},{7}}=>14 {{1,2,4,7},{3},{5},{6}}=>12 {{1,2,4},{3,7},{5},{6}}=>11 {{1,2,4},{3},{5,7},{6}}=>13 {{1,2,4},{3},{5},{6,7}}=>14 {{1,2,4},{3},{5},{6},{7}}=>10 {{1,2,5,6,7},{3,4}}=>19 {{1,2,5,6},{3,4,7}}=>18 {{1,2,5,6},{3,4},{7}}=>17 {{1,2,5,7},{3,4,6}}=>17 {{1,2,5},{3,4,6,7}}=>18 {{1,2,5},{3,4,6},{7}}=>16 {{1,2,5,7},{3,4},{6}}=>16 {{1,2,5},{3,4,7},{6}}=>15 {{1,2,5},{3,4},{6,7}}=>17 {{1,2,5},{3,4},{6},{7}}=>14 {{1,2,6,7},{3,4,5}}=>19 {{1,2,6},{3,4,5,7}}=>18 {{1,2,6},{3,4,5},{7}}=>17 {{1,2,7},{3,4,5,6}}=>19 {{1,2},{3,4,5,6,7}}=>20 {{1,2},{3,4,5,6},{7}}=>18 {{1,2,7},{3,4,5},{6}}=>16 {{1,2},{3,4,5,7},{6}}=>17 {{1,2},{3,4,5},{6,7}}=>18 {{1,2},{3,4,5},{6},{7}}=>15 {{1,2,6,7},{3,4},{5}}=>16 {{1,2,6},{3,4,7},{5}}=>14 {{1,2,6},{3,4},{5,7}}=>15 {{1,2,6},{3,4},{5},{7}}=>13 {{1,2,7},{3,4,6},{5}}=>15 {{1,2},{3,4,6,7},{5}}=>17 {{1,2},{3,4,6},{5,7}}=>16 {{1,2},{3,4,6},{5},{7}}=>14 {{1,2,7},{3,4},{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}}=>15 {{1,2,7},{3,4},{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}}=>11 {{1,2,5,6,7},{3},{4}}=>16 {{1,2,5,6},{3,7},{4}}=>14 {{1,2,5,6},{3},{4,7}}=>15 {{1,2,5,6},{3},{4},{7}}=>13 {{1,2,5,7},{3,6},{4}}=>13 {{1,2,5},{3,6,7},{4}}=>14 {{1,2,5},{3,6},{4,7}}=>12 {{1,2,5},{3,6},{4},{7}}=>11 {{1,2,5,7},{3},{4,6}}=>14 {{1,2,5},{3,7},{4,6}}=>13 {{1,2,5},{3},{4,6,7}}=>15 {{1,2,5},{3},{4,6},{7}}=>12 {{1,2,5,7},{3},{4},{6}}=>12 {{1,2,5},{3,7},{4},{6}}=>10 {{1,2,5},{3},{4,7},{6}}=>11 {{1,2,5},{3},{4},{6,7}}=>13 {{1,2,5},{3},{4},{6},{7}}=>9 {{1,2,6,7},{3,5},{4}}=>15 {{1,2,6},{3,5,7},{4}}=>14 {{1,2,6},{3,5},{4,7}}=>13 {{1,2,6},{3,5},{4},{7}}=>12 {{1,2,7},{3,5,6},{4}}=>15 {{1,2},{3,5,6,7},{4}}=>17 {{1,2},{3,5,6},{4,7}}=>16 {{1,2},{3,5,6},{4},{7}}=>14 {{1,2,7},{3,5},{4,6}}=>14 {{1,2},{3,5,7},{4,6}}=>15 {{1,2},{3,5},{4,6,7}}=>16 {{1,2},{3,5},{4,6},{7}}=>13 {{1,2,7},{3,5},{4},{6}}=>11 {{1,2},{3,5,7},{4},{6}}=>13 {{1,2},{3,5},{4,7},{6}}=>12 {{1,2},{3,5},{4},{6,7}}=>14 {{1,2},{3,5},{4},{6},{7}}=>10 {{1,2,6,7},{3},{4,5}}=>16 {{1,2,6},{3,7},{4,5}}=>14 {{1,2,6},{3},{4,5,7}}=>15 {{1,2,6},{3},{4,5},{7}}=>13 {{1,2,7},{3,6},{4,5}}=>15 {{1,2},{3,6,7},{4,5}}=>17 {{1,2},{3,6},{4,5,7}}=>16 {{1,2},{3,6},{4,5},{7}}=>14 {{1,2,7},{3},{4,5,6}}=>16 {{1,2},{3,7},{4,5,6}}=>17 {{1,2},{3},{4,5,6,7}}=>18 {{1,2},{3},{4,5,6},{7}}=>15 {{1,2,7},{3},{4,5},{6}}=>12 {{1,2},{3,7},{4,5},{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}}=>11 {{1,2,6,7},{3},{4},{5}}=>12 {{1,2,6},{3,7},{4},{5}}=>9 {{1,2,6},{3},{4,7},{5}}=>10 {{1,2,6},{3},{4},{5,7}}=>11 {{1,2,6},{3},{4},{5},{7}}=>8 {{1,2,7},{3,6},{4},{5}}=>10 {{1,2},{3,6,7},{4},{5}}=>13 {{1,2},{3,6},{4,7},{5}}=>11 {{1,2},{3,6},{4},{5,7}}=>12 {{1,2},{3,6},{4},{5},{7}}=>9 {{1,2,7},{3},{4,6},{5}}=>11 {{1,2},{3,7},{4,6},{5}}=>12 {{1,2},{3},{4,6,7},{5}}=>14 {{1,2},{3},{4,6},{5,7}}=>13 {{1,2},{3},{4,6},{5},{7}}=>10 {{1,2,7},{3},{4},{5,6}}=>12 {{1,2},{3,7},{4},{5,6}}=>13 {{1,2},{3},{4,7},{5,6}}=>14 {{1,2},{3},{4},{5,6,7}}=>15 {{1,2},{3},{4},{5,6},{7}}=>11 {{1,2,7},{3},{4},{5},{6}}=>7 {{1,2},{3,7},{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}}=>6 {{1,3,4,5,6,7},{2}}=>19 {{1,3,4,5,6},{2,7}}=>18 {{1,3,4,5,6},{2},{7}}=>17 {{1,3,4,5,7},{2,6}}=>17 {{1,3,4,5},{2,6,7}}=>18 {{1,3,4,5},{2,6},{7}}=>16 {{1,3,4,5,7},{2},{6}}=>16 {{1,3,4,5},{2,7},{6}}=>15 {{1,3,4,5},{2},{6,7}}=>17 {{1,3,4,5},{2},{6},{7}}=>14 {{1,3,4,6,7},{2,5}}=>17 {{1,3,4,6},{2,5,7}}=>16 {{1,3,4,6},{2,5},{7}}=>15 {{1,3,4,7},{2,5,6}}=>17 {{1,3,4},{2,5,6,7}}=>18 {{1,3,4},{2,5,6},{7}}=>16 {{1,3,4,7},{2,5},{6}}=>14 {{1,3,4},{2,5,7},{6}}=>15 {{1,3,4},{2,5},{6,7}}=>16 {{1,3,4},{2,5},{6},{7}}=>13 {{1,3,4,6,7},{2},{5}}=>16 {{1,3,4,6},{2,7},{5}}=>14 {{1,3,4,6},{2},{5,7}}=>15 {{1,3,4,6},{2},{5},{7}}=>13 {{1,3,4,7},{2,6},{5}}=>13 {{1,3,4},{2,6,7},{5}}=>15 {{1,3,4},{2,6},{5,7}}=>14 {{1,3,4},{2,6},{5},{7}}=>12 {{1,3,4,7},{2},{5,6}}=>16 {{1,3,4},{2,7},{5,6}}=>15 {{1,3,4},{2},{5,6,7}}=>17 {{1,3,4},{2},{5,6},{7}}=>14 {{1,3,4,7},{2},{5},{6}}=>12 {{1,3,4},{2,7},{5},{6}}=>11 {{1,3,4},{2},{5,7},{6}}=>13 {{1,3,4},{2},{5},{6,7}}=>14 {{1,3,4},{2},{5},{6},{7}}=>10 {{1,3,5,6,7},{2,4}}=>17 {{1,3,5,6},{2,4,7}}=>16 {{1,3,5,6},{2,4},{7}}=>15 {{1,3,5,7},{2,4,6}}=>15 {{1,3,5},{2,4,6,7}}=>16 {{1,3,5},{2,4,6},{7}}=>14 {{1,3,5,7},{2,4},{6}}=>14 {{1,3,5},{2,4,7},{6}}=>13 {{1,3,5},{2,4},{6,7}}=>15 {{1,3,5},{2,4},{6},{7}}=>12 {{1,3,6,7},{2,4,5}}=>17 {{1,3,6},{2,4,5,7}}=>16 {{1,3,6},{2,4,5},{7}}=>15 {{1,3,7},{2,4,5,6}}=>17 {{1,3},{2,4,5,6,7}}=>18 {{1,3},{2,4,5,6},{7}}=>16 {{1,3,7},{2,4,5},{6}}=>14 {{1,3},{2,4,5,7},{6}}=>15 {{1,3},{2,4,5},{6,7}}=>16 {{1,3},{2,4,5},{6},{7}}=>13 {{1,3,6,7},{2,4},{5}}=>14 {{1,3,6},{2,4,7},{5}}=>12 {{1,3,6},{2,4},{5,7}}=>13 {{1,3,6},{2,4},{5},{7}}=>11 {{1,3,7},{2,4,6},{5}}=>13 {{1,3},{2,4,6,7},{5}}=>15 {{1,3},{2,4,6},{5,7}}=>14 {{1,3},{2,4,6},{5},{7}}=>12 {{1,3,7},{2,4},{5,6}}=>14 {{1,3},{2,4,7},{5,6}}=>15 {{1,3},{2,4},{5,6,7}}=>16 {{1,3},{2,4},{5,6},{7}}=>13 {{1,3,7},{2,4},{5},{6}}=>10 {{1,3},{2,4,7},{5},{6}}=>11 {{1,3},{2,4},{5,7},{6}}=>12 {{1,3},{2,4},{5},{6,7}}=>13 {{1,3},{2,4},{5},{6},{7}}=>9 {{1,3,5,6,7},{2},{4}}=>16 {{1,3,5,6},{2,7},{4}}=>14 {{1,3,5,6},{2},{4,7}}=>15 {{1,3,5,6},{2},{4},{7}}=>13 {{1,3,5,7},{2,6},{4}}=>13 {{1,3,5},{2,6,7},{4}}=>14 {{1,3,5},{2,6},{4,7}}=>12 {{1,3,5},{2,6},{4},{7}}=>11 {{1,3,5,7},{2},{4,6}}=>14 {{1,3,5},{2,7},{4,6}}=>13 {{1,3,5},{2},{4,6,7}}=>15 {{1,3,5},{2},{4,6},{7}}=>12 {{1,3,5,7},{2},{4},{6}}=>12 {{1,3,5},{2,7},{4},{6}}=>10 {{1,3,5},{2},{4,7},{6}}=>11 {{1,3,5},{2},{4},{6,7}}=>13 {{1,3,5},{2},{4},{6},{7}}=>9 {{1,3,6,7},{2,5},{4}}=>13 {{1,3,6},{2,5,7},{4}}=>12 {{1,3,6},{2,5},{4,7}}=>11 {{1,3,6},{2,5},{4},{7}}=>10 {{1,3,7},{2,5,6},{4}}=>13 {{1,3},{2,5,6,7},{4}}=>15 {{1,3},{2,5,6},{4,7}}=>14 {{1,3},{2,5,6},{4},{7}}=>12 {{1,3,7},{2,5},{4,6}}=>12 {{1,3},{2,5,7},{4,6}}=>13 {{1,3},{2,5},{4,6,7}}=>14 {{1,3},{2,5},{4,6},{7}}=>11 {{1,3,7},{2,5},{4},{6}}=>9 {{1,3},{2,5,7},{4},{6}}=>11 {{1,3},{2,5},{4,7},{6}}=>10 {{1,3},{2,5},{4},{6,7}}=>12 {{1,3},{2,5},{4},{6},{7}}=>8 {{1,3,6,7},{2},{4,5}}=>16 {{1,3,6},{2,7},{4,5}}=>14 {{1,3,6},{2},{4,5,7}}=>15 {{1,3,6},{2},{4,5},{7}}=>13 {{1,3,7},{2,6},{4,5}}=>13 {{1,3},{2,6,7},{4,5}}=>15 {{1,3},{2,6},{4,5,7}}=>14 {{1,3},{2,6},{4,5},{7}}=>12 {{1,3,7},{2},{4,5,6}}=>16 {{1,3},{2,7},{4,5,6}}=>15 {{1,3},{2},{4,5,6,7}}=>17 {{1,3},{2},{4,5,6},{7}}=>14 {{1,3,7},{2},{4,5},{6}}=>12 {{1,3},{2,7},{4,5},{6}}=>11 {{1,3},{2},{4,5,7},{6}}=>13 {{1,3},{2},{4,5},{6,7}}=>14 {{1,3},{2},{4,5},{6},{7}}=>10 {{1,3,6,7},{2},{4},{5}}=>12 {{1,3,6},{2,7},{4},{5}}=>9 {{1,3,6},{2},{4,7},{5}}=>10 {{1,3,6},{2},{4},{5,7}}=>11 {{1,3,6},{2},{4},{5},{7}}=>8 {{1,3,7},{2,6},{4},{5}}=>8 {{1,3},{2,6,7},{4},{5}}=>11 {{1,3},{2,6},{4,7},{5}}=>9 {{1,3},{2,6},{4},{5,7}}=>10 {{1,3},{2,6},{4},{5},{7}}=>7 {{1,3,7},{2},{4,6},{5}}=>11 {{1,3},{2,7},{4,6},{5}}=>10 {{1,3},{2},{4,6,7},{5}}=>13 {{1,3},{2},{4,6},{5,7}}=>12 {{1,3},{2},{4,6},{5},{7}}=>9 {{1,3,7},{2},{4},{5,6}}=>12 {{1,3},{2,7},{4},{5,6}}=>11 {{1,3},{2},{4,7},{5,6}}=>13 {{1,3},{2},{4},{5,6,7}}=>14 {{1,3},{2},{4},{5,6},{7}}=>10 {{1,3,7},{2},{4},{5},{6}}=>7 {{1,3},{2,7},{4},{5},{6}}=>6 {{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}}=>5 {{1,4,5,6,7},{2,3}}=>19 {{1,4,5,6},{2,3,7}}=>18 {{1,4,5,6},{2,3},{7}}=>17 {{1,4,5,7},{2,3,6}}=>17 {{1,4,5},{2,3,6,7}}=>18 {{1,4,5},{2,3,6},{7}}=>16 {{1,4,5,7},{2,3},{6}}=>16 {{1,4,5},{2,3,7},{6}}=>15 {{1,4,5},{2,3},{6,7}}=>17 {{1,4,5},{2,3},{6},{7}}=>14 {{1,4,6,7},{2,3,5}}=>17 {{1,4,6},{2,3,5,7}}=>16 {{1,4,6},{2,3,5},{7}}=>15 {{1,4,7},{2,3,5,6}}=>17 {{1,4},{2,3,5,6,7}}=>18 {{1,4},{2,3,5,6},{7}}=>16 {{1,4,7},{2,3,5},{6}}=>14 {{1,4},{2,3,5,7},{6}}=>15 {{1,4},{2,3,5},{6,7}}=>16 {{1,4},{2,3,5},{6},{7}}=>13 {{1,4,6,7},{2,3},{5}}=>16 {{1,4,6},{2,3,7},{5}}=>14 {{1,4,6},{2,3},{5,7}}=>15 {{1,4,6},{2,3},{5},{7}}=>13 {{1,4,7},{2,3,6},{5}}=>13 {{1,4},{2,3,6,7},{5}}=>15 {{1,4},{2,3,6},{5,7}}=>14 {{1,4},{2,3,6},{5},{7}}=>12 {{1,4,7},{2,3},{5,6}}=>16 {{1,4},{2,3,7},{5,6}}=>15 {{1,4},{2,3},{5,6,7}}=>17 {{1,4},{2,3},{5,6},{7}}=>14 {{1,4,7},{2,3},{5},{6}}=>12 {{1,4},{2,3,7},{5},{6}}=>11 {{1,4},{2,3},{5,7},{6}}=>13 {{1,4},{2,3},{5},{6,7}}=>14 {{1,4},{2,3},{5},{6},{7}}=>10 {{1,5,6,7},{2,3,4}}=>19 {{1,5,6},{2,3,4,7}}=>18 {{1,5,6},{2,3,4},{7}}=>17 {{1,5,7},{2,3,4,6}}=>17 {{1,5},{2,3,4,6,7}}=>18 {{1,5},{2,3,4,6},{7}}=>16 {{1,5,7},{2,3,4},{6}}=>16 {{1,5},{2,3,4,7},{6}}=>15 {{1,5},{2,3,4},{6,7}}=>17 {{1,5},{2,3,4},{6},{7}}=>14 {{1,6,7},{2,3,4,5}}=>19 {{1,6},{2,3,4,5,7}}=>18 {{1,6},{2,3,4,5},{7}}=>17 {{1,7},{2,3,4,5,6}}=>19 {{1},{2,3,4,5,6,7}}=>20 {{1},{2,3,4,5,6},{7}}=>18 {{1,7},{2,3,4,5},{6}}=>16 {{1},{2,3,4,5,7},{6}}=>17 {{1},{2,3,4,5},{6,7}}=>18 {{1},{2,3,4,5},{6},{7}}=>15 {{1,6,7},{2,3,4},{5}}=>16 {{1,6},{2,3,4,7},{5}}=>14 {{1,6},{2,3,4},{5,7}}=>15 {{1,6},{2,3,4},{5},{7}}=>13 {{1,7},{2,3,4,6},{5}}=>15 {{1},{2,3,4,6,7},{5}}=>17 {{1},{2,3,4,6},{5,7}}=>16 {{1},{2,3,4,6},{5},{7}}=>14 {{1,7},{2,3,4},{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}}=>15 {{1,7},{2,3,4},{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}}=>11 {{1,5,6,7},{2,3},{4}}=>16 {{1,5,6},{2,3,7},{4}}=>14 {{1,5,6},{2,3},{4,7}}=>15 {{1,5,6},{2,3},{4},{7}}=>13 {{1,5,7},{2,3,6},{4}}=>13 {{1,5},{2,3,6,7},{4}}=>14 {{1,5},{2,3,6},{4,7}}=>12 {{1,5},{2,3,6},{4},{7}}=>11 {{1,5,7},{2,3},{4,6}}=>14 {{1,5},{2,3,7},{4,6}}=>13 {{1,5},{2,3},{4,6,7}}=>15 {{1,5},{2,3},{4,6},{7}}=>12 {{1,5,7},{2,3},{4},{6}}=>12 {{1,5},{2,3,7},{4},{6}}=>10 {{1,5},{2,3},{4,7},{6}}=>11 {{1,5},{2,3},{4},{6,7}}=>13 {{1,5},{2,3},{4},{6},{7}}=>9 {{1,6,7},{2,3,5},{4}}=>15 {{1,6},{2,3,5,7},{4}}=>14 {{1,6},{2,3,5},{4,7}}=>13 {{1,6},{2,3,5},{4},{7}}=>12 {{1,7},{2,3,5,6},{4}}=>15 {{1},{2,3,5,6,7},{4}}=>17 {{1},{2,3,5,6},{4,7}}=>16 {{1},{2,3,5,6},{4},{7}}=>14 {{1,7},{2,3,5},{4,6}}=>14 {{1},{2,3,5,7},{4,6}}=>15 {{1},{2,3,5},{4,6,7}}=>16 {{1},{2,3,5},{4,6},{7}}=>13 {{1,7},{2,3,5},{4},{6}}=>11 {{1},{2,3,5,7},{4},{6}}=>13 {{1},{2,3,5},{4,7},{6}}=>12 {{1},{2,3,5},{4},{6,7}}=>14 {{1},{2,3,5},{4},{6},{7}}=>10 {{1,6,7},{2,3},{4,5}}=>16 {{1,6},{2,3,7},{4,5}}=>14 {{1,6},{2,3},{4,5,7}}=>15 {{1,6},{2,3},{4,5},{7}}=>13 {{1,7},{2,3,6},{4,5}}=>15 {{1},{2,3,6,7},{4,5}}=>17 {{1},{2,3,6},{4,5,7}}=>16 {{1},{2,3,6},{4,5},{7}}=>14 {{1,7},{2,3},{4,5,6}}=>16 {{1},{2,3,7},{4,5,6}}=>17 {{1},{2,3},{4,5,6,7}}=>18 {{1},{2,3},{4,5,6},{7}}=>15 {{1,7},{2,3},{4,5},{6}}=>12 {{1},{2,3,7},{4,5},{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}}=>11 {{1,6,7},{2,3},{4},{5}}=>12 {{1,6},{2,3,7},{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}}=>8 {{1,7},{2,3,6},{4},{5}}=>10 {{1},{2,3,6,7},{4},{5}}=>13 {{1},{2,3,6},{4,7},{5}}=>11 {{1},{2,3,6},{4},{5,7}}=>12 {{1},{2,3,6},{4},{5},{7}}=>9 {{1,7},{2,3},{4,6},{5}}=>11 {{1},{2,3,7},{4,6},{5}}=>12 {{1},{2,3},{4,6,7},{5}}=>14 {{1},{2,3},{4,6},{5,7}}=>13 {{1},{2,3},{4,6},{5},{7}}=>10 {{1,7},{2,3},{4},{5,6}}=>12 {{1},{2,3,7},{4},{5,6}}=>13 {{1},{2,3},{4,7},{5,6}}=>14 {{1},{2,3},{4},{5,6,7}}=>15 {{1},{2,3},{4},{5,6},{7}}=>11 {{1,7},{2,3},{4},{5},{6}}=>7 {{1},{2,3,7},{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}}=>6 {{1,4,5,6,7},{2},{3}}=>16 {{1,4,5,6},{2,7},{3}}=>14 {{1,4,5,6},{2},{3,7}}=>15 {{1,4,5,6},{2},{3},{7}}=>13 {{1,4,5,7},{2,6},{3}}=>13 {{1,4,5},{2,6,7},{3}}=>14 {{1,4,5},{2,6},{3,7}}=>12 {{1,4,5},{2,6},{3},{7}}=>11 {{1,4,5,7},{2},{3,6}}=>14 {{1,4,5},{2,7},{3,6}}=>13 {{1,4,5},{2},{3,6,7}}=>15 {{1,4,5},{2},{3,6},{7}}=>12 {{1,4,5,7},{2},{3},{6}}=>12 {{1,4,5},{2,7},{3},{6}}=>10 {{1,4,5},{2},{3,7},{6}}=>11 {{1,4,5},{2},{3},{6,7}}=>13 {{1,4,5},{2},{3},{6},{7}}=>9 {{1,4,6,7},{2,5},{3}}=>13 {{1,4,6},{2,5,7},{3}}=>12 {{1,4,6},{2,5},{3,7}}=>11 {{1,4,6},{2,5},{3},{7}}=>10 {{1,4,7},{2,5,6},{3}}=>13 {{1,4},{2,5,6,7},{3}}=>14 {{1,4},{2,5,6},{3,7}}=>12 {{1,4},{2,5,6},{3},{7}}=>11 {{1,4,7},{2,5},{3,6}}=>10 {{1,4},{2,5,7},{3,6}}=>11 {{1,4},{2,5},{3,6,7}}=>12 {{1,4},{2,5},{3,6},{7}}=>9 {{1,4,7},{2,5},{3},{6}}=>9 {{1,4},{2,5,7},{3},{6}}=>10 {{1,4},{2,5},{3,7},{6}}=>8 {{1,4},{2,5},{3},{6,7}}=>11 {{1,4},{2,5},{3},{6},{7}}=>7 {{1,4,6,7},{2},{3,5}}=>14 {{1,4,6},{2,7},{3,5}}=>12 {{1,4,6},{2},{3,5,7}}=>13 {{1,4,6},{2},{3,5},{7}}=>11 {{1,4,7},{2,6},{3,5}}=>11 {{1,4},{2,6,7},{3,5}}=>13 {{1,4},{2,6},{3,5,7}}=>12 {{1,4},{2,6},{3,5},{7}}=>10 {{1,4,7},{2},{3,5,6}}=>14 {{1,4},{2,7},{3,5,6}}=>13 {{1,4},{2},{3,5,6,7}}=>15 {{1,4},{2},{3,5,6},{7}}=>12 {{1,4,7},{2},{3,5},{6}}=>10 {{1,4},{2,7},{3,5},{6}}=>9 {{1,4},{2},{3,5,7},{6}}=>11 {{1,4},{2},{3,5},{6,7}}=>12 {{1,4},{2},{3,5},{6},{7}}=>8 {{1,4,6,7},{2},{3},{5}}=>12 {{1,4,6},{2,7},{3},{5}}=>9 {{1,4,6},{2},{3,7},{5}}=>10 {{1,4,6},{2},{3},{5,7}}=>11 {{1,4,6},{2},{3},{5},{7}}=>8 {{1,4,7},{2,6},{3},{5}}=>8 {{1,4},{2,6,7},{3},{5}}=>10 {{1,4},{2,6},{3,7},{5}}=>7 {{1,4},{2,6},{3},{5,7}}=>9 {{1,4},{2,6},{3},{5},{7}}=>6 {{1,4,7},{2},{3,6},{5}}=>9 {{1,4},{2,7},{3,6},{5}}=>8 {{1,4},{2},{3,6,7},{5}}=>11 {{1,4},{2},{3,6},{5,7}}=>10 {{1,4},{2},{3,6},{5},{7}}=>7 {{1,4,7},{2},{3},{5,6}}=>12 {{1,4},{2,7},{3},{5,6}}=>10 {{1,4},{2},{3,7},{5,6}}=>11 {{1,4},{2},{3},{5,6,7}}=>13 {{1,4},{2},{3},{5,6},{7}}=>9 {{1,4,7},{2},{3},{5},{6}}=>7 {{1,4},{2,7},{3},{5},{6}}=>5 {{1,4},{2},{3,7},{5},{6}}=>6 {{1,4},{2},{3},{5,7},{6}}=>8 {{1,4},{2},{3},{5},{6,7}}=>9 {{1,4},{2},{3},{5},{6},{7}}=>4 {{1,5,6,7},{2,4},{3}}=>15 {{1,5,6},{2,4,7},{3}}=>14 {{1,5,6},{2,4},{3,7}}=>13 {{1,5,6},{2,4},{3},{7}}=>12 {{1,5,7},{2,4,6},{3}}=>13 {{1,5},{2,4,6,7},{3}}=>14 {{1,5},{2,4,6},{3,7}}=>12 {{1,5},{2,4,6},{3},{7}}=>11 {{1,5,7},{2,4},{3,6}}=>12 {{1,5},{2,4,7},{3,6}}=>11 {{1,5},{2,4},{3,6,7}}=>13 {{1,5},{2,4},{3,6},{7}}=>10 {{1,5,7},{2,4},{3},{6}}=>11 {{1,5},{2,4,7},{3},{6}}=>10 {{1,5},{2,4},{3,7},{6}}=>9 {{1,5},{2,4},{3},{6,7}}=>12 {{1,5},{2,4},{3},{6},{7}}=>8 {{1,6,7},{2,4,5},{3}}=>15 {{1,6},{2,4,5,7},{3}}=>14 {{1,6},{2,4,5},{3,7}}=>13 {{1,6},{2,4,5},{3},{7}}=>12 {{1,7},{2,4,5,6},{3}}=>15 {{1},{2,4,5,6,7},{3}}=>17 {{1},{2,4,5,6},{3,7}}=>16 {{1},{2,4,5,6},{3},{7}}=>14 {{1,7},{2,4,5},{3,6}}=>14 {{1},{2,4,5,7},{3,6}}=>15 {{1},{2,4,5},{3,6,7}}=>16 {{1},{2,4,5},{3,6},{7}}=>13 {{1,7},{2,4,5},{3},{6}}=>11 {{1},{2,4,5,7},{3},{6}}=>13 {{1},{2,4,5},{3,7},{6}}=>12 {{1},{2,4,5},{3},{6,7}}=>14 {{1},{2,4,5},{3},{6},{7}}=>10 {{1,6,7},{2,4},{3,5}}=>14 {{1,6},{2,4,7},{3,5}}=>12 {{1,6},{2,4},{3,5,7}}=>13 {{1,6},{2,4},{3,5},{7}}=>11 {{1,7},{2,4,6},{3,5}}=>13 {{1},{2,4,6,7},{3,5}}=>15 {{1},{2,4,6},{3,5,7}}=>14 {{1},{2,4,6},{3,5},{7}}=>12 {{1,7},{2,4},{3,5,6}}=>14 {{1},{2,4,7},{3,5,6}}=>15 {{1},{2,4},{3,5,6,7}}=>16 {{1},{2,4},{3,5,6},{7}}=>13 {{1,7},{2,4},{3,5},{6}}=>10 {{1},{2,4,7},{3,5},{6}}=>11 {{1},{2,4},{3,5,7},{6}}=>12 {{1},{2,4},{3,5},{6,7}}=>13 {{1},{2,4},{3,5},{6},{7}}=>9 {{1,6,7},{2,4},{3},{5}}=>11 {{1,6},{2,4,7},{3},{5}}=>9 {{1,6},{2,4},{3,7},{5}}=>8 {{1,6},{2,4},{3},{5,7}}=>10 {{1,6},{2,4},{3},{5},{7}}=>7 {{1,7},{2,4,6},{3},{5}}=>10 {{1},{2,4,6,7},{3},{5}}=>13 {{1},{2,4,6},{3,7},{5}}=>11 {{1},{2,4,6},{3},{5,7}}=>12 {{1},{2,4,6},{3},{5},{7}}=>9 {{1,7},{2,4},{3,6},{5}}=>9 {{1},{2,4,7},{3,6},{5}}=>10 {{1},{2,4},{3,6,7},{5}}=>12 {{1},{2,4},{3,6},{5,7}}=>11 {{1},{2,4},{3,6},{5},{7}}=>8 {{1,7},{2,4},{3},{5,6}}=>11 {{1},{2,4,7},{3},{5,6}}=>13 {{1},{2,4},{3,7},{5,6}}=>12 {{1},{2,4},{3},{5,6,7}}=>14 {{1},{2,4},{3},{5,6},{7}}=>10 {{1,7},{2,4},{3},{5},{6}}=>6 {{1},{2,4,7},{3},{5},{6}}=>8 {{1},{2,4},{3,7},{5},{6}}=>7 {{1},{2,4},{3},{5,7},{6}}=>9 {{1},{2,4},{3},{5},{6,7}}=>10 {{1},{2,4},{3},{5},{6},{7}}=>5 {{1,5,6,7},{2},{3,4}}=>16 {{1,5,6},{2,7},{3,4}}=>14 {{1,5,6},{2},{3,4,7}}=>15 {{1,5,6},{2},{3,4},{7}}=>13 {{1,5,7},{2,6},{3,4}}=>13 {{1,5},{2,6,7},{3,4}}=>14 {{1,5},{2,6},{3,4,7}}=>12 {{1,5},{2,6},{3,4},{7}}=>11 {{1,5,7},{2},{3,4,6}}=>14 {{1,5},{2,7},{3,4,6}}=>13 {{1,5},{2},{3,4,6,7}}=>15 {{1,5},{2},{3,4,6},{7}}=>12 {{1,5,7},{2},{3,4},{6}}=>12 {{1,5},{2,7},{3,4},{6}}=>10 {{1,5},{2},{3,4,7},{6}}=>11 {{1,5},{2},{3,4},{6,7}}=>13 {{1,5},{2},{3,4},{6},{7}}=>9 {{1,6,7},{2,5},{3,4}}=>15 {{1,6},{2,5,7},{3,4}}=>14 {{1,6},{2,5},{3,4,7}}=>13 {{1,6},{2,5},{3,4},{7}}=>12 {{1,7},{2,5,6},{3,4}}=>15 {{1},{2,5,6,7},{3,4}}=>17 {{1},{2,5,6},{3,4,7}}=>16 {{1},{2,5,6},{3,4},{7}}=>14 {{1,7},{2,5},{3,4,6}}=>14 {{1},{2,5,7},{3,4,6}}=>15 {{1},{2,5},{3,4,6,7}}=>16 {{1},{2,5},{3,4,6},{7}}=>13 {{1,7},{2,5},{3,4},{6}}=>11 {{1},{2,5,7},{3,4},{6}}=>13 {{1},{2,5},{3,4,7},{6}}=>12 {{1},{2,5},{3,4},{6,7}}=>14 {{1},{2,5},{3,4},{6},{7}}=>10 {{1,6,7},{2},{3,4,5}}=>16 {{1,6},{2,7},{3,4,5}}=>14 {{1,6},{2},{3,4,5,7}}=>15 {{1,6},{2},{3,4,5},{7}}=>13 {{1,7},{2,6},{3,4,5}}=>15 {{1},{2,6,7},{3,4,5}}=>17 {{1},{2,6},{3,4,5,7}}=>16 {{1},{2,6},{3,4,5},{7}}=>14 {{1,7},{2},{3,4,5,6}}=>16 {{1},{2,7},{3,4,5,6}}=>17 {{1},{2},{3,4,5,6,7}}=>18 {{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},{3,4,5,7},{6}}=>14 {{1},{2},{3,4,5},{6,7}}=>15 {{1},{2},{3,4,5},{6},{7}}=>11 {{1,6,7},{2},{3,4},{5}}=>12 {{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}}=>8 {{1,7},{2,6},{3,4},{5}}=>10 {{1},{2,6,7},{3,4},{5}}=>13 {{1},{2,6},{3,4,7},{5}}=>11 {{1},{2,6},{3,4},{5,7}}=>12 {{1},{2,6},{3,4},{5},{7}}=>9 {{1,7},{2},{3,4,6},{5}}=>11 {{1},{2,7},{3,4,6},{5}}=>12 {{1},{2},{3,4,6,7},{5}}=>14 {{1},{2},{3,4,6},{5,7}}=>13 {{1},{2},{3,4,6},{5},{7}}=>10 {{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},{5,6,7}}=>15 {{1},{2},{3,4},{5,6},{7}}=>11 {{1,7},{2},{3,4},{5},{6}}=>7 {{1},{2,7},{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}}=>6 {{1,5,6,7},{2},{3},{4}}=>12 {{1,5,6},{2,7},{3},{4}}=>9 {{1,5,6},{2},{3,7},{4}}=>10 {{1,5,6},{2},{3},{4,7}}=>11 {{1,5,6},{2},{3},{4},{7}}=>8 {{1,5,7},{2,6},{3},{4}}=>8 {{1,5},{2,6,7},{3},{4}}=>9 {{1,5},{2,6},{3,7},{4}}=>6 {{1,5},{2,6},{3},{4,7}}=>7 {{1,5},{2,6},{3},{4},{7}}=>5 {{1,5,7},{2},{3,6},{4}}=>9 {{1,5},{2,7},{3,6},{4}}=>7 {{1,5},{2},{3,6,7},{4}}=>10 {{1,5},{2},{3,6},{4,7}}=>8 {{1,5},{2},{3,6},{4},{7}}=>6 {{1,5,7},{2},{3},{4,6}}=>10 {{1,5},{2,7},{3},{4,6}}=>8 {{1,5},{2},{3,7},{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}}=>7 {{1,5},{2,7},{3},{4},{6}}=>4 {{1,5},{2},{3,7},{4},{6}}=>5 {{1,5},{2},{3},{4,7},{6}}=>6 {{1,5},{2},{3},{4},{6,7}}=>8 {{1,5},{2},{3},{4},{6},{7}}=>3 {{1,6,7},{2,5},{3},{4}}=>10 {{1,6},{2,5,7},{3},{4}}=>9 {{1,6},{2,5},{3,7},{4}}=>7 {{1,6},{2,5},{3},{4,7}}=>8 {{1,6},{2,5},{3},{4},{7}}=>6 {{1,7},{2,5,6},{3},{4}}=>10 {{1},{2,5,6,7},{3},{4}}=>13 {{1},{2,5,6},{3,7},{4}}=>11 {{1},{2,5,6},{3},{4,7}}=>12 {{1},{2,5,6},{3},{4},{7}}=>9 {{1,7},{2,5},{3,6},{4}}=>8 {{1},{2,5,7},{3,6},{4}}=>10 {{1},{2,5},{3,6,7},{4}}=>11 {{1},{2,5},{3,6},{4,7}}=>9 {{1},{2,5},{3,6},{4},{7}}=>7 {{1,7},{2,5},{3},{4,6}}=>9 {{1},{2,5,7},{3},{4,6}}=>11 {{1},{2,5},{3,7},{4,6}}=>10 {{1},{2,5},{3},{4,6,7}}=>12 {{1},{2,5},{3},{4,6},{7}}=>8 {{1,7},{2,5},{3},{4},{6}}=>5 {{1},{2,5,7},{3},{4},{6}}=>8 {{1},{2,5},{3,7},{4},{6}}=>6 {{1},{2,5},{3},{4,7},{6}}=>7 {{1},{2,5},{3},{4},{6,7}}=>9 {{1},{2,5},{3},{4},{6},{7}}=>4 {{1,6,7},{2},{3,5},{4}}=>11 {{1,6},{2,7},{3,5},{4}}=>8 {{1,6},{2},{3,5,7},{4}}=>10 {{1,6},{2},{3,5},{4,7}}=>9 {{1,6},{2},{3,5},{4},{7}}=>7 {{1,7},{2,6},{3,5},{4}}=>9 {{1},{2,6,7},{3,5},{4}}=>12 {{1},{2,6},{3,5,7},{4}}=>11 {{1},{2,6},{3,5},{4,7}}=>10 {{1},{2,6},{3,5},{4},{7}}=>8 {{1,7},{2},{3,5,6},{4}}=>11 {{1},{2,7},{3,5,6},{4}}=>12 {{1},{2},{3,5,6,7},{4}}=>14 {{1},{2},{3,5,6},{4,7}}=>13 {{1},{2},{3,5,6},{4},{7}}=>10 {{1,7},{2},{3,5},{4,6}}=>10 {{1},{2,7},{3,5},{4,6}}=>11 {{1},{2},{3,5,7},{4,6}}=>12 {{1},{2},{3,5},{4,6,7}}=>13 {{1},{2},{3,5},{4,6},{7}}=>9 {{1,7},{2},{3,5},{4},{6}}=>6 {{1},{2,7},{3,5},{4},{6}}=>7 {{1},{2},{3,5,7},{4},{6}}=>9 {{1},{2},{3,5},{4,7},{6}}=>8 {{1},{2},{3,5},{4},{6,7}}=>10 {{1},{2},{3,5},{4},{6},{7}}=>5 {{1,6,7},{2},{3},{4,5}}=>12 {{1,6},{2,7},{3},{4,5}}=>9 {{1,6},{2},{3,7},{4,5}}=>10 {{1,6},{2},{3},{4,5,7}}=>11 {{1,6},{2},{3},{4,5},{7}}=>8 {{1,7},{2,6},{3},{4,5}}=>10 {{1},{2,6,7},{3},{4,5}}=>13 {{1},{2,6},{3,7},{4,5}}=>11 {{1},{2,6},{3},{4,5,7}}=>12 {{1},{2,6},{3},{4,5},{7}}=>9 {{1,7},{2},{3,6},{4,5}}=>11 {{1},{2,7},{3,6},{4,5}}=>12 {{1},{2},{3,6,7},{4,5}}=>14 {{1},{2},{3,6},{4,5,7}}=>13 {{1},{2},{3,6},{4,5},{7}}=>10 {{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}}=>11 {{1,7},{2},{3},{4,5},{6}}=>7 {{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}}=>6 {{1,6,7},{2},{3},{4},{5}}=>7 {{1,6},{2,7},{3},{4},{5}}=>3 {{1,6},{2},{3,7},{4},{5}}=>4 {{1,6},{2},{3},{4,7},{5}}=>5 {{1,6},{2},{3},{4},{5,7}}=>6 {{1,6},{2},{3},{4},{5},{7}}=>2 {{1,7},{2,6},{3},{4},{5}}=>4 {{1},{2,6,7},{3},{4},{5}}=>8 {{1},{2,6},{3,7},{4},{5}}=>5 {{1},{2,6},{3},{4,7},{5}}=>6 {{1},{2,6},{3},{4},{5,7}}=>7 {{1},{2,6},{3},{4},{5},{7}}=>3 {{1,7},{2},{3,6},{4},{5}}=>5 {{1},{2,7},{3,6},{4},{5}}=>6 {{1},{2},{3,6,7},{4},{5}}=>9 {{1},{2},{3,6},{4,7},{5}}=>7 {{1},{2},{3,6},{4},{5,7}}=>8 {{1},{2},{3,6},{4},{5},{7}}=>4 {{1,7},{2},{3},{4,6},{5}}=>6 {{1},{2,7},{3},{4,6},{5}}=>7 {{1},{2},{3,7},{4,6},{5}}=>8 {{1},{2},{3},{4,6,7},{5}}=>10 {{1},{2},{3},{4,6},{5,7}}=>9 {{1},{2},{3},{4,6},{5},{7}}=>5 {{1,7},{2},{3},{4},{5,6}}=>7 {{1},{2,7},{3},{4},{5,6}}=>8 {{1},{2},{3,7},{4},{5,6}}=>9 {{1},{2},{3},{4,7},{5,6}}=>10 {{1},{2},{3},{4},{5,6,7}}=>11 {{1},{2},{3},{4},{5,6},{7}}=>6 {{1,7},{2},{3},{4},{5},{6}}=>1 {{1},{2,7},{3},{4},{5},{6}}=>2 {{1},{2},{3,7},{4},{5},{6}}=>3 {{1},{2},{3},{4,7},{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}}=>0 {{1,2},{3,4},{5,6},{7,8}}=>22 {{1,3},{2,4},{5,6},{7,8}}=>20 {{1,4},{2,3},{5,6},{7,8}}=>21 {{1,5},{2,3},{4,6},{7,8}}=>19 {{1,6},{2,3},{4,5},{7,8}}=>20 {{1,7},{2,3},{4,5},{6,8}}=>18 {{1,8},{2,3},{4,5},{6,7}}=>19 {{1,8},{2,4},{3,5},{6,7}}=>17 {{1,7},{2,4},{3,5},{6,8}}=>16 {{1,6},{2,4},{3,5},{7,8}}=>18 {{1,5},{2,4},{3,6},{7,8}}=>17 {{1,4},{2,5},{3,6},{7,8}}=>16 {{1,3},{2,5},{4,6},{7,8}}=>18 {{1,2},{3,5},{4,6},{7,8}}=>20 {{1,2},{3,6},{4,5},{7,8}}=>21 {{1,3},{2,6},{4,5},{7,8}}=>19 {{1,4},{2,6},{3,5},{7,8}}=>17 {{1,5},{2,6},{3,4},{7,8}}=>18 {{1,6},{2,5},{3,4},{7,8}}=>19 {{1,7},{2,5},{3,4},{6,8}}=>17 {{1,8},{2,5},{3,4},{6,7}}=>18 {{1,8},{2,6},{3,4},{5,7}}=>16 {{1,7},{2,6},{3,4},{5,8}}=>15 {{1,6},{2,7},{3,4},{5,8}}=>14 {{1,5},{2,7},{3,4},{6,8}}=>16 {{1,4},{2,7},{3,5},{6,8}}=>15 {{1,3},{2,7},{4,5},{6,8}}=>17 {{1,2},{3,7},{4,5},{6,8}}=>19 {{1,2},{3,8},{4,5},{6,7}}=>20 {{1,3},{2,8},{4,5},{6,7}}=>18 {{1,4},{2,8},{3,5},{6,7}}=>16 {{1,5},{2,8},{3,4},{6,7}}=>17 {{1,6},{2,8},{3,4},{5,7}}=>15 {{1,7},{2,8},{3,4},{5,6}}=>16 {{1,8},{2,7},{3,4},{5,6}}=>17 {{1,8},{2,7},{3,5},{4,6}}=>15 {{1,7},{2,8},{3,5},{4,6}}=>14 {{1,6},{2,8},{3,5},{4,7}}=>13 {{1,5},{2,8},{3,6},{4,7}}=>12 {{1,4},{2,8},{3,6},{5,7}}=>14 {{1,3},{2,8},{4,6},{5,7}}=>16 {{1,2},{3,8},{4,6},{5,7}}=>18 {{1,2},{3,7},{4,6},{5,8}}=>17 {{1,3},{2,7},{4,6},{5,8}}=>15 {{1,4},{2,7},{3,6},{5,8}}=>13 {{1,5},{2,7},{3,6},{4,8}}=>11 {{1,6},{2,7},{3,5},{4,8}}=>12 {{1,7},{2,6},{3,5},{4,8}}=>13 {{1,8},{2,6},{3,5},{4,7}}=>14 {{1,8},{2,5},{3,6},{4,7}}=>13 {{1,7},{2,5},{3,6},{4,8}}=>12 {{1,6},{2,5},{3,7},{4,8}}=>11 {{1,5},{2,6},{3,7},{4,8}}=>10 {{1,4},{2,6},{3,7},{5,8}}=>12 {{1,3},{2,6},{4,7},{5,8}}=>14 {{1,2},{3,6},{4,7},{5,8}}=>16 {{1,2},{3,5},{4,7},{6,8}}=>18 {{1,3},{2,5},{4,7},{6,8}}=>16 {{1,4},{2,5},{3,7},{6,8}}=>14 {{1,5},{2,4},{3,7},{6,8}}=>15 {{1,6},{2,4},{3,7},{5,8}}=>13 {{1,7},{2,4},{3,6},{5,8}}=>14 {{1,8},{2,4},{3,6},{5,7}}=>15 {{1,8},{2,3},{4,6},{5,7}}=>17 {{1,7},{2,3},{4,6},{5,8}}=>16 {{1,6},{2,3},{4,7},{5,8}}=>15 {{1,5},{2,3},{4,7},{6,8}}=>17 {{1,4},{2,3},{5,7},{6,8}}=>19 {{1,3},{2,4},{5,7},{6,8}}=>18 {{1,2},{3,4},{5,7},{6,8}}=>20 {{1,2},{3,4},{5,8},{6,7}}=>21 {{1,3},{2,4},{5,8},{6,7}}=>19 {{1,4},{2,3},{5,8},{6,7}}=>20 {{1,5},{2,3},{4,8},{6,7}}=>18 {{1,6},{2,3},{4,8},{5,7}}=>16 {{1,7},{2,3},{4,8},{5,6}}=>17 {{1,8},{2,3},{4,7},{5,6}}=>18 {{1,8},{2,4},{3,7},{5,6}}=>16 {{1,7},{2,4},{3,8},{5,6}}=>15 {{1,6},{2,4},{3,8},{5,7}}=>14 {{1,5},{2,4},{3,8},{6,7}}=>16 {{1,4},{2,5},{3,8},{6,7}}=>15 {{1,3},{2,5},{4,8},{6,7}}=>17 {{1,2},{3,5},{4,8},{6,7}}=>19 {{1,2},{3,6},{4,8},{5,7}}=>17 {{1,3},{2,6},{4,8},{5,7}}=>15 {{1,4},{2,6},{3,8},{5,7}}=>13 {{1,5},{2,6},{3,8},{4,7}}=>11 {{1,6},{2,5},{3,8},{4,7}}=>12 {{1,7},{2,5},{3,8},{4,6}}=>13 {{1,8},{2,5},{3,7},{4,6}}=>14 {{1,8},{2,6},{3,7},{4,5}}=>15 {{1,7},{2,6},{3,8},{4,5}}=>14 {{1,6},{2,7},{3,8},{4,5}}=>13 {{1,5},{2,7},{3,8},{4,6}}=>12 {{1,4},{2,7},{3,8},{5,6}}=>14 {{1,3},{2,7},{4,8},{5,6}}=>16 {{1,2},{3,7},{4,8},{5,6}}=>18 {{1,2},{3,8},{4,7},{5,6}}=>19 {{1,3},{2,8},{4,7},{5,6}}=>17 {{1,4},{2,8},{3,7},{5,6}}=>15 {{1,5},{2,8},{3,7},{4,6}}=>13 {{1,6},{2,8},{3,7},{4,5}}=>14 {{1,7},{2,8},{3,6},{4,5}}=>15 {{1,8},{2,7},{3,6},{4,5}}=>16 {{1},{2},{3,4,5,6,7,8}}=>25 {{1},{2,4,5,6,7,8},{3}}=>24 {{1},{2,3,5,6,7,8},{4}}=>24 {{1},{2,3,4,6,7,8},{5}}=>24 {{1},{2,3,4,5,8},{6},{7}}=>20 {{1},{2,3,4,5,7,8},{6}}=>24 {{1},{2,3,4,5,6,7},{8}}=>25 {{1},{2,3,4,8},{5,6,7}}=>24 {{1},{2,3,4,5,8},{6,7}}=>24 {{1},{2,3,4,5,6,8},{7}}=>24 {{1},{2,3,4,5,6,7,8}}=>27 {{1,2},{3,4,5,6,7,8}}=>27 {{1,4,5,6,7,8},{2},{3}}=>23 {{1,3,5,6,7,8},{2},{4}}=>23 {{1,3,4,5,6,7,8},{2}}=>26 {{1,4,5,6,7,8},{2,3}}=>26 {{1,2,4,5,6,7,8},{3}}=>26 {{1,2,5,6,7,8},{3,4}}=>26 {{1,2,3,5,6,7},{4},{8}}=>24 {{1,2,3,5,6,7,8},{4}}=>26 {{1,2,3,6,7,8},{4,5}}=>26 {{1,2,3,4,7},{5},{6},{8}}=>20 {{1,2,3,4,6,7},{5},{8}}=>24 {{1,2,3,4,6,7,8},{5}}=>26 {{1,2,3,4,5,6},{7,8}}=>27 {{1,2,3,7},{4,5,6},{8}}=>24 {{1,2,3,4,7},{5,6},{8}}=>24 {{1,2,3,4,7,8},{5,6}}=>26 {{1,2,3,4,5,7},{6},{8}}=>24 {{1,2,3,4,5,7,8},{6}}=>26 {{1,2,3,4,5,6,7},{8}}=>27 {{1,8},{2,3,4,5,6,7}}=>26 {{1,2,3,4,5,8},{6,7}}=>26 {{1,2,3,4,5,6,8},{7}}=>26 {{1,2,3,4,5,6,7,8}}=>28 {{1,2,4,6,7,8},{3,5}}=>24 {{1,2,3,5,7,8},{4,6}}=>24 {{1,2,3,4,6,8},{5,7}}=>24 {{1,2,3,4,5,7},{6,8}}=>25 {{1,2,3,4,5,6,7,8},{9}}=>35 {{1},{2,3,4,5,6,7,8,9}}=>35 {{1,2,3,4,5,6,8},{7},{9}}=>32 {{1},{2,3,4,5,6,7,9},{8}}=>32 {{1,2,3,4,5,8},{6,7},{9}}=>32 {{1,2,3,4,5,7,8},{6},{9}}=>32 {{1},{2,3,4,5,6,9},{7,8}}=>32 {{1},{2,3,4,5,6,8,9},{7}}=>32 {{1,2},{3,4},{5,6},{7,8},{9,10}}=>35 {{1,4},{2,3},{5,6},{7,8},{9,10}}=>34 {{1,6},{2,3},{4,5},{7,8},{9,10}}=>33 {{1,8},{2,3},{4,5},{6,7},{9,10}}=>32 {{1,10},{2,3},{4,5},{6,7},{8,9}}=>31 {{1,2},{3,6},{4,5},{7,8},{9,10}}=>34 {{1,6},{2,5},{3,4},{7,8},{9,10}}=>32 {{1,8},{2,5},{3,4},{6,7},{9,10}}=>31 {{1,10},{2,5},{3,4},{6,7},{8,9}}=>30 {{1,2},{3,8},{4,5},{6,7},{9,10}}=>33 {{1,8},{2,7},{3,4},{5,6},{9,10}}=>30 {{1,10},{2,7},{3,4},{5,6},{8,9}}=>29 {{1,2},{3,10},{4,5},{6,7},{8,9}}=>32 {{1,10},{2,9},{3,4},{5,6},{7,8}}=>28 {{1,2},{3,4},{5,8},{6,7},{9,10}}=>34 {{1,4},{2,3},{5,8},{6,7},{9,10}}=>33 {{1,8},{2,3},{4,7},{5,6},{9,10}}=>31 {{1,10},{2,3},{4,7},{5,6},{8,9}}=>30 {{1,2},{3,8},{4,7},{5,6},{9,10}}=>32 {{1,8},{2,7},{3,6},{4,5},{9,10}}=>29 {{1,10},{2,7},{3,6},{4,5},{8,9}}=>28 {{1,2},{3,10},{4,7},{5,6},{8,9}}=>31 {{1,10},{2,9},{3,6},{4,5},{7,8}}=>27 {{1,2},{3,4},{5,10},{6,7},{8,9}}=>33 {{1,4},{2,3},{5,10},{6,7},{8,9}}=>32 {{1,10},{2,3},{4,9},{5,6},{7,8}}=>29 {{1,2},{3,10},{4,9},{5,6},{7,8}}=>30 {{1,10},{2,9},{3,8},{4,5},{6,7}}=>26 {{1,2},{3,4},{5,6},{7,10},{8,9}}=>34 {{1,4},{2,3},{5,6},{7,10},{8,9}}=>33 {{1,6},{2,3},{4,5},{7,10},{8,9}}=>32 {{1,10},{2,3},{4,5},{6,9},{7,8}}=>30 {{1,2},{3,6},{4,5},{7,10},{8,9}}=>33 {{1,6},{2,5},{3,4},{7,10},{8,9}}=>31 {{1,10},{2,5},{3,4},{6,9},{7,8}}=>29 {{1,2},{3,10},{4,5},{6,9},{7,8}}=>31 {{1,10},{2,9},{3,4},{5,8},{6,7}}=>27 {{1,2},{3,4},{5,10},{6,9},{7,8}}=>32 {{1,4},{2,3},{5,10},{6,9},{7,8}}=>31 {{1,10},{2,3},{4,9},{5,8},{6,7}}=>28 {{1,2},{3,10},{4,9},{5,8},{6,7}}=>29 {{1,10},{2,9},{3,8},{4,7},{5,6}}=>25 {{1,2,3,4,5,6,7,8,9},{10}}=>44 {{1},{2,3,4,5,6,7,8,9,10}}=>44 {{1,2,3,4,5,6,7,9},{8},{10}}=>41 {{1},{2,3,4,5,6,7,8,10},{9}}=>41 {{1,2,3,4,5,6,7,8,9,10},{11}}=>54 {{1},{2,3,4,5,6,7,8,9,10,11}}=>54 {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>51 {{1,2},{3,4},{5,6},{7,8},{9,12},{10,11}}=>50 {{1,2},{3,4},{5,6},{7,10},{8,9},{11,12}}=>50 {{1,2},{3,4},{5,6},{7,12},{8,9},{10,11}}=>49 {{1,2},{3,4},{5,6},{7,12},{8,11},{9,10}}=>48 {{1,2},{3,4},{5,8},{6,7},{9,10},{11,12}}=>50 {{1,2},{3,4},{5,8},{6,7},{9,12},{10,11}}=>49 {{1,2},{3,4},{5,10},{6,7},{8,9},{11,12}}=>49 {{1,2},{3,4},{5,12},{6,7},{8,9},{10,11}}=>48 {{1,2},{3,4},{5,12},{6,7},{8,11},{9,10}}=>47 {{1,2},{3,4},{5,10},{6,9},{7,8},{11,12}}=>48 {{1,2},{3,4},{5,12},{6,9},{7,8},{10,11}}=>47 {{1,2},{3,4},{5,12},{6,11},{7,8},{9,10}}=>46 {{1,2},{3,4},{5,12},{6,11},{7,10},{8,9}}=>45 {{1,2},{3,6},{4,5},{7,8},{9,10},{11,12}}=>50 {{1,2},{3,6},{4,5},{7,8},{9,12},{10,11}}=>49 {{1,2},{3,6},{4,5},{7,10},{8,9},{11,12}}=>49 {{1,2},{3,6},{4,5},{7,12},{8,9},{10,11}}=>48 {{1,2},{3,6},{4,5},{7,12},{8,11},{9,10}}=>47 {{1,2},{3,8},{4,5},{6,7},{9,10},{11,12}}=>49 {{1,2},{3,8},{4,5},{6,7},{9,12},{10,11}}=>48 {{1,2},{3,10},{4,5},{6,7},{8,9},{11,12}}=>48 {{1,2},{3,12},{4,5},{6,7},{8,9},{10,11}}=>47 {{1,2},{3,12},{4,5},{6,7},{8,11},{9,10}}=>46 {{1,2},{3,10},{4,5},{6,9},{7,8},{11,12}}=>47 {{1,2},{3,12},{4,5},{6,9},{7,8},{10,11}}=>46 {{1,2},{3,12},{4,5},{6,11},{7,8},{9,10}}=>45 {{1,2},{3,12},{4,5},{6,11},{7,10},{8,9}}=>44 {{1,2},{3,8},{4,7},{5,6},{9,10},{11,12}}=>48 {{1,2},{3,8},{4,7},{5,6},{9,12},{10,11}}=>47 {{1,2},{3,10},{4,7},{5,6},{8,9},{11,12}}=>47 {{1,2},{3,12},{4,7},{5,6},{8,9},{10,11}}=>46 {{1,2},{3,12},{4,7},{5,6},{8,11},{9,10}}=>45 {{1,2},{3,10},{4,9},{5,6},{7,8},{11,12}}=>46 {{1,2},{3,12},{4,9},{5,6},{7,8},{10,11}}=>45 {{1,2},{3,12},{4,11},{5,6},{7,8},{9,10}}=>44 {{1,2},{3,12},{4,11},{5,6},{7,10},{8,9}}=>43 {{1,2},{3,10},{4,9},{5,8},{6,7},{11,12}}=>45 {{1,2},{3,12},{4,9},{5,8},{6,7},{10,11}}=>44 {{1,2},{3,12},{4,11},{5,8},{6,7},{9,10}}=>43 {{1,2},{3,12},{4,11},{5,10},{6,7},{8,9}}=>42 {{1,2},{3,12},{4,11},{5,10},{6,9},{7,8}}=>41 {{1,4},{2,3},{5,6},{7,8},{9,10},{11,12}}=>50 {{1,4},{2,3},{5,6},{7,8},{9,12},{10,11}}=>49 {{1,4},{2,3},{5,6},{7,10},{8,9},{11,12}}=>49 {{1,4},{2,3},{5,6},{7,12},{8,9},{10,11}}=>48 {{1,4},{2,3},{5,6},{7,12},{8,11},{9,10}}=>47 {{1,4},{2,3},{5,8},{6,7},{9,10},{11,12}}=>49 {{1,4},{2,3},{5,8},{6,7},{9,12},{10,11}}=>48 {{1,4},{2,3},{5,10},{6,7},{8,9},{11,12}}=>48 {{1,4},{2,3},{5,12},{6,7},{8,9},{10,11}}=>47 {{1,4},{2,3},{5,12},{6,7},{8,11},{9,10}}=>46 {{1,4},{2,3},{5,10},{6,9},{7,8},{11,12}}=>47 {{1,4},{2,3},{5,12},{6,9},{7,8},{10,11}}=>46 {{1,4},{2,3},{5,12},{6,11},{7,8},{9,10}}=>45 {{1,4},{2,3},{5,12},{6,11},{7,10},{8,9}}=>44 {{1,6},{2,3},{4,5},{7,8},{9,10},{11,12}}=>49 {{1,6},{2,3},{4,5},{7,8},{9,12},{10,11}}=>48 {{1,6},{2,3},{4,5},{7,10},{8,9},{11,12}}=>48 {{1,6},{2,3},{4,5},{7,12},{8,9},{10,11}}=>47 {{1,6},{2,3},{4,5},{7,12},{8,11},{9,10}}=>46 {{1,8},{2,3},{4,5},{6,7},{9,10},{11,12}}=>48 {{1,8},{2,3},{4,5},{6,7},{9,12},{10,11}}=>47 {{1,10},{2,3},{4,5},{6,7},{8,9},{11,12}}=>47 {{1,12},{2,3},{4,5},{6,7},{8,9},{10,11}}=>46 {{1,12},{2,3},{4,5},{6,7},{8,11},{9,10}}=>45 {{1,10},{2,3},{4,5},{6,9},{7,8},{11,12}}=>46 {{1,12},{2,3},{4,5},{6,9},{7,8},{10,11}}=>45 {{1,12},{2,3},{4,5},{6,11},{7,8},{9,10}}=>44 {{1,12},{2,3},{4,5},{6,11},{7,10},{8,9}}=>43 {{1,8},{2,3},{4,7},{5,6},{9,10},{11,12}}=>47 {{1,8},{2,3},{4,7},{5,6},{9,12},{10,11}}=>46 {{1,10},{2,3},{4,7},{5,6},{8,9},{11,12}}=>46 {{1,12},{2,3},{4,7},{5,6},{8,9},{10,11}}=>45 {{1,12},{2,3},{4,7},{5,6},{8,11},{9,10}}=>44 {{1,10},{2,3},{4,9},{5,6},{7,8},{11,12}}=>45 {{1,12},{2,3},{4,9},{5,6},{7,8},{10,11}}=>44 {{1,12},{2,3},{4,11},{5,6},{7,8},{9,10}}=>43 {{1,12},{2,3},{4,11},{5,6},{7,10},{8,9}}=>42 {{1,10},{2,3},{4,9},{5,8},{6,7},{11,12}}=>44 {{1,12},{2,3},{4,9},{5,8},{6,7},{10,11}}=>43 {{1,12},{2,3},{4,11},{5,8},{6,7},{9,10}}=>42 {{1,12},{2,3},{4,11},{5,10},{6,7},{8,9}}=>41 {{1,12},{2,3},{4,11},{5,10},{6,9},{7,8}}=>40 {{1,6},{2,5},{3,4},{7,8},{9,10},{11,12}}=>48 {{1,6},{2,5},{3,4},{7,8},{9,12},{10,11}}=>47 {{1,6},{2,5},{3,4},{7,10},{8,9},{11,12}}=>47 {{1,6},{2,5},{3,4},{7,12},{8,9},{10,11}}=>46 {{1,6},{2,5},{3,4},{7,12},{8,11},{9,10}}=>45 {{1,8},{2,5},{3,4},{6,7},{9,10},{11,12}}=>47 {{1,8},{2,5},{3,4},{6,7},{9,12},{10,11}}=>46 {{1,10},{2,5},{3,4},{6,7},{8,9},{11,12}}=>46 {{1,12},{2,5},{3,4},{6,7},{8,9},{10,11}}=>45 {{1,12},{2,5},{3,4},{6,7},{8,11},{9,10}}=>44 {{1,10},{2,5},{3,4},{6,9},{7,8},{11,12}}=>45 {{1,12},{2,5},{3,4},{6,9},{7,8},{10,11}}=>44 {{1,12},{2,5},{3,4},{6,11},{7,8},{9,10}}=>43 {{1,12},{2,5},{3,4},{6,11},{7,10},{8,9}}=>42 {{1,8},{2,7},{3,4},{5,6},{9,10},{11,12}}=>46 {{1,8},{2,7},{3,4},{5,6},{9,12},{10,11}}=>45 {{1,10},{2,7},{3,4},{5,6},{8,9},{11,12}}=>45 {{1,12},{2,7},{3,4},{5,6},{8,9},{10,11}}=>44 {{1,12},{2,7},{3,4},{5,6},{8,11},{9,10}}=>43 {{1,10},{2,9},{3,4},{5,6},{7,8},{11,12}}=>44 {{1,12},{2,9},{3,4},{5,6},{7,8},{10,11}}=>43 {{1,12},{2,11},{3,4},{5,6},{7,8},{9,10}}=>42 {{1,12},{2,11},{3,4},{5,6},{7,10},{8,9}}=>41 {{1,10},{2,9},{3,4},{5,8},{6,7},{11,12}}=>43 {{1,12},{2,9},{3,4},{5,8},{6,7},{10,11}}=>42 {{1,12},{2,11},{3,4},{5,8},{6,7},{9,10}}=>41 {{1,12},{2,11},{3,4},{5,10},{6,7},{8,9}}=>40 {{1,12},{2,11},{3,4},{5,10},{6,9},{7,8}}=>39 {{1,8},{2,7},{3,6},{4,5},{9,10},{11,12}}=>45 {{1,8},{2,7},{3,6},{4,5},{9,12},{10,11}}=>44 {{1,10},{2,7},{3,6},{4,5},{8,9},{11,12}}=>44 {{1,12},{2,7},{3,6},{4,5},{8,9},{10,11}}=>43 {{1,12},{2,7},{3,6},{4,5},{8,11},{9,10}}=>42 {{1,10},{2,9},{3,6},{4,5},{7,8},{11,12}}=>43 {{1,12},{2,9},{3,6},{4,5},{7,8},{10,11}}=>42 {{1,12},{2,11},{3,6},{4,5},{7,8},{9,10}}=>41 {{1,12},{2,11},{3,6},{4,5},{7,10},{8,9}}=>40 {{1,10},{2,9},{3,8},{4,5},{6,7},{11,12}}=>42 {{1,12},{2,9},{3,8},{4,5},{6,7},{10,11}}=>41 {{1,12},{2,11},{3,8},{4,5},{6,7},{9,10}}=>40 {{1,12},{2,11},{3,10},{4,5},{6,7},{8,9}}=>39 {{1,12},{2,11},{3,10},{4,5},{6,9},{7,8}}=>38 {{1,10},{2,9},{3,8},{4,7},{5,6},{11,12}}=>41 {{1,12},{2,9},{3,8},{4,7},{5,6},{10,11}}=>40 {{1,12},{2,11},{3,8},{4,7},{5,6},{9,10}}=>39 {{1,12},{2,11},{3,10},{4,7},{5,6},{8,9}}=>38 {{1,12},{2,11},{3,10},{4,9},{5,6},{7,8}}=>37 {{1,12},{2,11},{3,10},{4,9},{5,8},{6,7}}=>36
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Description
The depth index of a set partition.
For a set partition $\Pi$ of $\{1,\dots,n\}$ with arcs $\mathcal A$, this is $$\sum_{i=1}^{|\mathcal A|} (n-i) - \sum_{j=1}^n depth(j) + \sum_{\alpha\in\mathcal A} depth(\alpha),$$
where the depth of an element $i$ is the number of arcs $(k,\ell)$ with $k < i < \ell$, and the depth of an arc $(i,j)$ is the number of arcs $(k,\ell)$ with $k < i$ and $j < \ell$.
References
[1] Bilen Can, M., Cherniavsky, Y. Stirling Posets arXiv:1801.08231
Code
def depth_vertex(P, i):
    """
    sage: P = SetPartition([{1, 2, 7, 8}, {3, 4, 6}, {5}, {9, 10}])
    sage: [depth_vertex(P, i) for i in range(1, P.size()+1)]
    [0, 0, 1, 1, 2, 1, 0, 0, 0, 0]
    """
    return sum(1 for a in P.arcs() if a[0] < i < a[1])


def depth_arc(P, a):
    """
    sage: P = SetPartition([{1, 2, 7, 8}, {3, 4, 6}, {5}, {9, 10}])
    sage: [(a, depth_arc(P, a)) for a in P.arcs()]
    [((1, 2), 0), ((2, 7), 0), ((7, 8), 0), ((3, 4), 1), ((4, 6), 1), ((9, 10), 0)]
    """
    return sum(1 for b in P.arcs() if b[0] < a[0] and a[1] < b[1])

def statistic(P):
    """
    sage: P = SetPartition([[1,8], [2,5,6,9], [3,7], [4]])
    sage: statistic(P)
    21
    """
    n = P.size()
    A = P.arcs()
    return (sum(n-i for i in range(1, len(A)+1)) -
            sum(depth_vertex(P, i) for i in range(1, n+1)) +
            sum(depth_arc(P, a) for a in A))
Created
Jan 26, 2018 at 08:45 by Martin Rubey
Updated
Feb 01, 2018 at 23:32 by Martin Rubey