Identifier
- St000496: Set partitions ⟶ ℤ
Values
=>
Cc0009;cc-rep
{{1}}=>0
{{1,2}}=>0
{{1},{2}}=>0
{{1,2,3}}=>0
{{1,2},{3}}=>0
{{1,3},{2}}=>1
{{1},{2,3}}=>0
{{1},{2},{3}}=>0
{{1,2,3,4}}=>0
{{1,2,3},{4}}=>0
{{1,2,4},{3}}=>1
{{1,2},{3,4}}=>0
{{1,2},{3},{4}}=>0
{{1,3,4},{2}}=>2
{{1,3},{2,4}}=>0
{{1,3},{2},{4}}=>1
{{1,4},{2,3}}=>1
{{1},{2,3,4}}=>0
{{1},{2,3},{4}}=>0
{{1,4},{2},{3}}=>2
{{1},{2,4},{3}}=>1
{{1},{2},{3,4}}=>0
{{1},{2},{3},{4}}=>0
{{1,2,3,4,5}}=>0
{{1,2,3,4},{5}}=>0
{{1,2,3,5},{4}}=>1
{{1,2,3},{4,5}}=>0
{{1,2,3},{4},{5}}=>0
{{1,2,4,5},{3}}=>2
{{1,2,4},{3,5}}=>0
{{1,2,4},{3},{5}}=>1
{{1,2,5},{3,4}}=>1
{{1,2},{3,4,5}}=>0
{{1,2},{3,4},{5}}=>0
{{1,2,5},{3},{4}}=>2
{{1,2},{3,5},{4}}=>1
{{1,2},{3},{4,5}}=>0
{{1,2},{3},{4},{5}}=>0
{{1,3,4,5},{2}}=>3
{{1,3,4},{2,5}}=>0
{{1,3,4},{2},{5}}=>2
{{1,3,5},{2,4}}=>1
{{1,3},{2,4,5}}=>0
{{1,3},{2,4},{5}}=>0
{{1,3,5},{2},{4}}=>3
{{1,3},{2,5},{4}}=>1
{{1,3},{2},{4,5}}=>1
{{1,3},{2},{4},{5}}=>1
{{1,4,5},{2,3}}=>2
{{1,4},{2,3,5}}=>0
{{1,4},{2,3},{5}}=>1
{{1,5},{2,3,4}}=>1
{{1},{2,3,4,5}}=>0
{{1},{2,3,4},{5}}=>0
{{1,5},{2,3},{4}}=>2
{{1},{2,3,5},{4}}=>1
{{1},{2,3},{4,5}}=>0
{{1},{2,3},{4},{5}}=>0
{{1,4,5},{2},{3}}=>4
{{1,4},{2,5},{3}}=>2
{{1,4},{2},{3,5}}=>1
{{1,4},{2},{3},{5}}=>2
{{1,5},{2,4},{3}}=>3
{{1},{2,4,5},{3}}=>2
{{1},{2,4},{3,5}}=>0
{{1},{2,4},{3},{5}}=>1
{{1,5},{2},{3,4}}=>2
{{1},{2,5},{3,4}}=>1
{{1},{2},{3,4,5}}=>0
{{1},{2},{3,4},{5}}=>0
{{1,5},{2},{3},{4}}=>3
{{1},{2,5},{3},{4}}=>2
{{1},{2},{3,5},{4}}=>1
{{1},{2},{3},{4,5}}=>0
{{1},{2},{3},{4},{5}}=>0
{{1,2,3,4,5,6}}=>0
{{1,2,3,4,5},{6}}=>0
{{1,2,3,4,6},{5}}=>1
{{1,2,3,4},{5,6}}=>0
{{1,2,3,4},{5},{6}}=>0
{{1,2,3,5,6},{4}}=>2
{{1,2,3,5},{4,6}}=>0
{{1,2,3,5},{4},{6}}=>1
{{1,2,3,6},{4,5}}=>1
{{1,2,3},{4,5,6}}=>0
{{1,2,3},{4,5},{6}}=>0
{{1,2,3,6},{4},{5}}=>2
{{1,2,3},{4,6},{5}}=>1
{{1,2,3},{4},{5,6}}=>0
{{1,2,3},{4},{5},{6}}=>0
{{1,2,4,5,6},{3}}=>3
{{1,2,4,5},{3,6}}=>0
{{1,2,4,5},{3},{6}}=>2
{{1,2,4,6},{3,5}}=>1
{{1,2,4},{3,5,6}}=>0
{{1,2,4},{3,5},{6}}=>0
{{1,2,4,6},{3},{5}}=>3
{{1,2,4},{3,6},{5}}=>1
{{1,2,4},{3},{5,6}}=>1
{{1,2,4},{3},{5},{6}}=>1
{{1,2,5,6},{3,4}}=>2
{{1,2,5},{3,4,6}}=>0
{{1,2,5},{3,4},{6}}=>1
{{1,2,6},{3,4,5}}=>1
{{1,2},{3,4,5,6}}=>0
{{1,2},{3,4,5},{6}}=>0
{{1,2,6},{3,4},{5}}=>2
{{1,2},{3,4,6},{5}}=>1
{{1,2},{3,4},{5,6}}=>0
{{1,2},{3,4},{5},{6}}=>0
{{1,2,5,6},{3},{4}}=>4
{{1,2,5},{3,6},{4}}=>2
{{1,2,5},{3},{4,6}}=>1
{{1,2,5},{3},{4},{6}}=>2
{{1,2,6},{3,5},{4}}=>3
{{1,2},{3,5,6},{4}}=>2
{{1,2},{3,5},{4,6}}=>0
{{1,2},{3,5},{4},{6}}=>1
{{1,2,6},{3},{4,5}}=>2
{{1,2},{3,6},{4,5}}=>1
{{1,2},{3},{4,5,6}}=>0
{{1,2},{3},{4,5},{6}}=>0
{{1,2,6},{3},{4},{5}}=>3
{{1,2},{3,6},{4},{5}}=>2
{{1,2},{3},{4,6},{5}}=>1
{{1,2},{3},{4},{5,6}}=>0
{{1,2},{3},{4},{5},{6}}=>0
{{1,3,4,5,6},{2}}=>4
{{1,3,4,5},{2,6}}=>0
{{1,3,4,5},{2},{6}}=>3
{{1,3,4,6},{2,5}}=>1
{{1,3,4},{2,5,6}}=>0
{{1,3,4},{2,5},{6}}=>0
{{1,3,4,6},{2},{5}}=>4
{{1,3,4},{2,6},{5}}=>1
{{1,3,4},{2},{5,6}}=>2
{{1,3,4},{2},{5},{6}}=>2
{{1,3,5,6},{2,4}}=>2
{{1,3,5},{2,4,6}}=>0
{{1,3,5},{2,4},{6}}=>1
{{1,3,6},{2,4,5}}=>1
{{1,3},{2,4,5,6}}=>0
{{1,3},{2,4,5},{6}}=>0
{{1,3,6},{2,4},{5}}=>2
{{1,3},{2,4,6},{5}}=>1
{{1,3},{2,4},{5,6}}=>0
{{1,3},{2,4},{5},{6}}=>0
{{1,3,5,6},{2},{4}}=>5
{{1,3,5},{2,6},{4}}=>2
{{1,3,5},{2},{4,6}}=>2
{{1,3,5},{2},{4},{6}}=>3
{{1,3,6},{2,5},{4}}=>3
{{1,3},{2,5,6},{4}}=>2
{{1,3},{2,5},{4,6}}=>0
{{1,3},{2,5},{4},{6}}=>1
{{1,3,6},{2},{4,5}}=>3
{{1,3},{2,6},{4,5}}=>1
{{1,3},{2},{4,5,6}}=>1
{{1,3},{2},{4,5},{6}}=>1
{{1,3,6},{2},{4},{5}}=>4
{{1,3},{2,6},{4},{5}}=>2
{{1,3},{2},{4,6},{5}}=>2
{{1,3},{2},{4},{5,6}}=>1
{{1,3},{2},{4},{5},{6}}=>1
{{1,4,5,6},{2,3}}=>3
{{1,4,5},{2,3,6}}=>0
{{1,4,5},{2,3},{6}}=>2
{{1,4,6},{2,3,5}}=>1
{{1,4},{2,3,5,6}}=>0
{{1,4},{2,3,5},{6}}=>0
{{1,4,6},{2,3},{5}}=>3
{{1,4},{2,3,6},{5}}=>1
{{1,4},{2,3},{5,6}}=>1
{{1,4},{2,3},{5},{6}}=>1
{{1,5,6},{2,3,4}}=>2
{{1,5},{2,3,4,6}}=>0
{{1,5},{2,3,4},{6}}=>1
{{1,6},{2,3,4,5}}=>1
{{1},{2,3,4,5,6}}=>0
{{1},{2,3,4,5},{6}}=>0
{{1,6},{2,3,4},{5}}=>2
{{1},{2,3,4,6},{5}}=>1
{{1},{2,3,4},{5,6}}=>0
{{1},{2,3,4},{5},{6}}=>0
{{1,5,6},{2,3},{4}}=>4
{{1,5},{2,3,6},{4}}=>2
{{1,5},{2,3},{4,6}}=>1
{{1,5},{2,3},{4},{6}}=>2
{{1,6},{2,3,5},{4}}=>3
{{1},{2,3,5,6},{4}}=>2
{{1},{2,3,5},{4,6}}=>0
{{1},{2,3,5},{4},{6}}=>1
{{1,6},{2,3},{4,5}}=>2
{{1},{2,3,6},{4,5}}=>1
{{1},{2,3},{4,5,6}}=>0
{{1},{2,3},{4,5},{6}}=>0
{{1,6},{2,3},{4},{5}}=>3
{{1},{2,3,6},{4},{5}}=>2
{{1},{2,3},{4,6},{5}}=>1
{{1},{2,3},{4},{5,6}}=>0
{{1},{2,3},{4},{5},{6}}=>0
{{1,4,5,6},{2},{3}}=>6
{{1,4,5},{2,6},{3}}=>3
{{1,4,5},{2},{3,6}}=>2
{{1,4,5},{2},{3},{6}}=>4
{{1,4,6},{2,5},{3}}=>4
{{1,4},{2,5,6},{3}}=>3
{{1,4},{2,5},{3,6}}=>0
{{1,4},{2,5},{3},{6}}=>2
{{1,4,6},{2},{3,5}}=>3
{{1,4},{2,6},{3,5}}=>1
{{1,4},{2},{3,5,6}}=>1
{{1,4},{2},{3,5},{6}}=>1
{{1,4,6},{2},{3},{5}}=>5
{{1,4},{2,6},{3},{5}}=>3
{{1,4},{2},{3,6},{5}}=>2
{{1,4},{2},{3},{5,6}}=>2
{{1,4},{2},{3},{5},{6}}=>2
{{1,5,6},{2,4},{3}}=>5
{{1,5},{2,4,6},{3}}=>3
{{1,5},{2,4},{3,6}}=>1
{{1,5},{2,4},{3},{6}}=>3
{{1,6},{2,4,5},{3}}=>4
{{1},{2,4,5,6},{3}}=>3
{{1},{2,4,5},{3,6}}=>0
{{1},{2,4,5},{3},{6}}=>2
{{1,6},{2,4},{3,5}}=>2
{{1},{2,4,6},{3,5}}=>1
{{1},{2,4},{3,5,6}}=>0
{{1},{2,4},{3,5},{6}}=>0
{{1,6},{2,4},{3},{5}}=>4
{{1},{2,4,6},{3},{5}}=>3
{{1},{2,4},{3,6},{5}}=>1
{{1},{2,4},{3},{5,6}}=>1
{{1},{2,4},{3},{5},{6}}=>1
{{1,5,6},{2},{3,4}}=>4
{{1,5},{2,6},{3,4}}=>2
{{1,5},{2},{3,4,6}}=>1
{{1,5},{2},{3,4},{6}}=>2
{{1,6},{2,5},{3,4}}=>3
{{1},{2,5,6},{3,4}}=>2
{{1},{2,5},{3,4,6}}=>0
{{1},{2,5},{3,4},{6}}=>1
{{1,6},{2},{3,4,5}}=>2
{{1},{2,6},{3,4,5}}=>1
{{1},{2},{3,4,5,6}}=>0
{{1},{2},{3,4,5},{6}}=>0
{{1,6},{2},{3,4},{5}}=>3
{{1},{2,6},{3,4},{5}}=>2
{{1},{2},{3,4,6},{5}}=>1
{{1},{2},{3,4},{5,6}}=>0
{{1},{2},{3,4},{5},{6}}=>0
{{1,5,6},{2},{3},{4}}=>6
{{1,5},{2,6},{3},{4}}=>4
{{1,5},{2},{3,6},{4}}=>3
{{1,5},{2},{3},{4,6}}=>2
{{1,5},{2},{3},{4},{6}}=>3
{{1,6},{2,5},{3},{4}}=>5
{{1},{2,5,6},{3},{4}}=>4
{{1},{2,5},{3,6},{4}}=>2
{{1},{2,5},{3},{4,6}}=>1
{{1},{2,5},{3},{4},{6}}=>2
{{1,6},{2},{3,5},{4}}=>4
{{1},{2,6},{3,5},{4}}=>3
{{1},{2},{3,5,6},{4}}=>2
{{1},{2},{3,5},{4,6}}=>0
{{1},{2},{3,5},{4},{6}}=>1
{{1,6},{2},{3},{4,5}}=>3
{{1},{2,6},{3},{4,5}}=>2
{{1},{2},{3,6},{4,5}}=>1
{{1},{2},{3},{4,5,6}}=>0
{{1},{2},{3},{4,5},{6}}=>0
{{1,6},{2},{3},{4},{5}}=>4
{{1},{2,6},{3},{4},{5}}=>3
{{1},{2},{3,6},{4},{5}}=>2
{{1},{2},{3},{4,6},{5}}=>1
{{1},{2},{3},{4},{5,6}}=>0
{{1},{2},{3},{4},{5},{6}}=>0
{{1,2,3,4,5,6,7}}=>0
{{1,2,3,4,5,6},{7}}=>0
{{1,2,3,4,5,7},{6}}=>1
{{1,2,3,4,5},{6,7}}=>0
{{1,2,3,4,5},{6},{7}}=>0
{{1,2,3,4,6,7},{5}}=>2
{{1,2,3,4,6},{5,7}}=>0
{{1,2,3,4,6},{5},{7}}=>1
{{1,2,3,4,7},{5,6}}=>1
{{1,2,3,4},{5,6,7}}=>0
{{1,2,3,4},{5,6},{7}}=>0
{{1,2,3,4,7},{5},{6}}=>2
{{1,2,3,4},{5,7},{6}}=>1
{{1,2,3,4},{5},{6,7}}=>0
{{1,2,3,4},{5},{6},{7}}=>0
{{1,2,3,5,6,7},{4}}=>3
{{1,2,3,5,6},{4,7}}=>0
{{1,2,3,5,6},{4},{7}}=>2
{{1,2,3,5,7},{4,6}}=>1
{{1,2,3,5},{4,6,7}}=>0
{{1,2,3,5},{4,6},{7}}=>0
{{1,2,3,5,7},{4},{6}}=>3
{{1,2,3,5},{4,7},{6}}=>1
{{1,2,3,5},{4},{6,7}}=>1
{{1,2,3,5},{4},{6},{7}}=>1
{{1,2,3,6,7},{4,5}}=>2
{{1,2,3,6},{4,5,7}}=>0
{{1,2,3,6},{4,5},{7}}=>1
{{1,2,3,7},{4,5,6}}=>1
{{1,2,3},{4,5,6,7}}=>0
{{1,2,3},{4,5,6},{7}}=>0
{{1,2,3,7},{4,5},{6}}=>2
{{1,2,3},{4,5,7},{6}}=>1
{{1,2,3},{4,5},{6,7}}=>0
{{1,2,3},{4,5},{6},{7}}=>0
{{1,2,3,6,7},{4},{5}}=>4
{{1,2,3,6},{4,7},{5}}=>2
{{1,2,3,6},{4},{5,7}}=>1
{{1,2,3,6},{4},{5},{7}}=>2
{{1,2,3,7},{4,6},{5}}=>3
{{1,2,3},{4,6,7},{5}}=>2
{{1,2,3},{4,6},{5,7}}=>0
{{1,2,3},{4,6},{5},{7}}=>1
{{1,2,3,7},{4},{5,6}}=>2
{{1,2,3},{4,7},{5,6}}=>1
{{1,2,3},{4},{5,6,7}}=>0
{{1,2,3},{4},{5,6},{7}}=>0
{{1,2,3,7},{4},{5},{6}}=>3
{{1,2,3},{4,7},{5},{6}}=>2
{{1,2,3},{4},{5,7},{6}}=>1
{{1,2,3},{4},{5},{6,7}}=>0
{{1,2,3},{4},{5},{6},{7}}=>0
{{1,2,4,5,6,7},{3}}=>4
{{1,2,4,5,6},{3,7}}=>0
{{1,2,4,5,6},{3},{7}}=>3
{{1,2,4,5,7},{3,6}}=>1
{{1,2,4,5},{3,6,7}}=>0
{{1,2,4,5},{3,6},{7}}=>0
{{1,2,4,5,7},{3},{6}}=>4
{{1,2,4,5},{3,7},{6}}=>1
{{1,2,4,5},{3},{6,7}}=>2
{{1,2,4,5},{3},{6},{7}}=>2
{{1,2,4,6,7},{3,5}}=>2
{{1,2,4,6},{3,5,7}}=>0
{{1,2,4,6},{3,5},{7}}=>1
{{1,2,4,7},{3,5,6}}=>1
{{1,2,4},{3,5,6,7}}=>0
{{1,2,4},{3,5,6},{7}}=>0
{{1,2,4,7},{3,5},{6}}=>2
{{1,2,4},{3,5,7},{6}}=>1
{{1,2,4},{3,5},{6,7}}=>0
{{1,2,4},{3,5},{6},{7}}=>0
{{1,2,4,6,7},{3},{5}}=>5
{{1,2,4,6},{3,7},{5}}=>2
{{1,2,4,6},{3},{5,7}}=>2
{{1,2,4,6},{3},{5},{7}}=>3
{{1,2,4,7},{3,6},{5}}=>3
{{1,2,4},{3,6,7},{5}}=>2
{{1,2,4},{3,6},{5,7}}=>0
{{1,2,4},{3,6},{5},{7}}=>1
{{1,2,4,7},{3},{5,6}}=>3
{{1,2,4},{3,7},{5,6}}=>1
{{1,2,4},{3},{5,6,7}}=>1
{{1,2,4},{3},{5,6},{7}}=>1
{{1,2,4,7},{3},{5},{6}}=>4
{{1,2,4},{3,7},{5},{6}}=>2
{{1,2,4},{3},{5,7},{6}}=>2
{{1,2,4},{3},{5},{6,7}}=>1
{{1,2,4},{3},{5},{6},{7}}=>1
{{1,2,5,6,7},{3,4}}=>3
{{1,2,5,6},{3,4,7}}=>0
{{1,2,5,6},{3,4},{7}}=>2
{{1,2,5,7},{3,4,6}}=>1
{{1,2,5},{3,4,6,7}}=>0
{{1,2,5},{3,4,6},{7}}=>0
{{1,2,5,7},{3,4},{6}}=>3
{{1,2,5},{3,4,7},{6}}=>1
{{1,2,5},{3,4},{6,7}}=>1
{{1,2,5},{3,4},{6},{7}}=>1
{{1,2,6,7},{3,4,5}}=>2
{{1,2,6},{3,4,5,7}}=>0
{{1,2,6},{3,4,5},{7}}=>1
{{1,2,7},{3,4,5,6}}=>1
{{1,2},{3,4,5,6,7}}=>0
{{1,2},{3,4,5,6},{7}}=>0
{{1,2,7},{3,4,5},{6}}=>2
{{1,2},{3,4,5,7},{6}}=>1
{{1,2},{3,4,5},{6,7}}=>0
{{1,2},{3,4,5},{6},{7}}=>0
{{1,2,6,7},{3,4},{5}}=>4
{{1,2,6},{3,4,7},{5}}=>2
{{1,2,6},{3,4},{5,7}}=>1
{{1,2,6},{3,4},{5},{7}}=>2
{{1,2,7},{3,4,6},{5}}=>3
{{1,2},{3,4,6,7},{5}}=>2
{{1,2},{3,4,6},{5,7}}=>0
{{1,2},{3,4,6},{5},{7}}=>1
{{1,2,7},{3,4},{5,6}}=>2
{{1,2},{3,4,7},{5,6}}=>1
{{1,2},{3,4},{5,6,7}}=>0
{{1,2},{3,4},{5,6},{7}}=>0
{{1,2,7},{3,4},{5},{6}}=>3
{{1,2},{3,4,7},{5},{6}}=>2
{{1,2},{3,4},{5,7},{6}}=>1
{{1,2},{3,4},{5},{6,7}}=>0
{{1,2},{3,4},{5},{6},{7}}=>0
{{1,2,5,6,7},{3},{4}}=>6
{{1,2,5,6},{3,7},{4}}=>3
{{1,2,5,6},{3},{4,7}}=>2
{{1,2,5,6},{3},{4},{7}}=>4
{{1,2,5,7},{3,6},{4}}=>4
{{1,2,5},{3,6,7},{4}}=>3
{{1,2,5},{3,6},{4,7}}=>0
{{1,2,5},{3,6},{4},{7}}=>2
{{1,2,5,7},{3},{4,6}}=>3
{{1,2,5},{3,7},{4,6}}=>1
{{1,2,5},{3},{4,6,7}}=>1
{{1,2,5},{3},{4,6},{7}}=>1
{{1,2,5,7},{3},{4},{6}}=>5
{{1,2,5},{3,7},{4},{6}}=>3
{{1,2,5},{3},{4,7},{6}}=>2
{{1,2,5},{3},{4},{6,7}}=>2
{{1,2,5},{3},{4},{6},{7}}=>2
{{1,2,6,7},{3,5},{4}}=>5
{{1,2,6},{3,5,7},{4}}=>3
{{1,2,6},{3,5},{4,7}}=>1
{{1,2,6},{3,5},{4},{7}}=>3
{{1,2,7},{3,5,6},{4}}=>4
{{1,2},{3,5,6,7},{4}}=>3
{{1,2},{3,5,6},{4,7}}=>0
{{1,2},{3,5,6},{4},{7}}=>2
{{1,2,7},{3,5},{4,6}}=>2
{{1,2},{3,5,7},{4,6}}=>1
{{1,2},{3,5},{4,6,7}}=>0
{{1,2},{3,5},{4,6},{7}}=>0
{{1,2,7},{3,5},{4},{6}}=>4
{{1,2},{3,5,7},{4},{6}}=>3
{{1,2},{3,5},{4,7},{6}}=>1
{{1,2},{3,5},{4},{6,7}}=>1
{{1,2},{3,5},{4},{6},{7}}=>1
{{1,2,6,7},{3},{4,5}}=>4
{{1,2,6},{3,7},{4,5}}=>2
{{1,2,6},{3},{4,5,7}}=>1
{{1,2,6},{3},{4,5},{7}}=>2
{{1,2,7},{3,6},{4,5}}=>3
{{1,2},{3,6,7},{4,5}}=>2
{{1,2},{3,6},{4,5,7}}=>0
{{1,2},{3,6},{4,5},{7}}=>1
{{1,2,7},{3},{4,5,6}}=>2
{{1,2},{3,7},{4,5,6}}=>1
{{1,2},{3},{4,5,6,7}}=>0
{{1,2},{3},{4,5,6},{7}}=>0
{{1,2,7},{3},{4,5},{6}}=>3
{{1,2},{3,7},{4,5},{6}}=>2
{{1,2},{3},{4,5,7},{6}}=>1
{{1,2},{3},{4,5},{6,7}}=>0
{{1,2},{3},{4,5},{6},{7}}=>0
{{1,2,6,7},{3},{4},{5}}=>6
{{1,2,6},{3,7},{4},{5}}=>4
{{1,2,6},{3},{4,7},{5}}=>3
{{1,2,6},{3},{4},{5,7}}=>2
{{1,2,6},{3},{4},{5},{7}}=>3
{{1,2,7},{3,6},{4},{5}}=>5
{{1,2},{3,6,7},{4},{5}}=>4
{{1,2},{3,6},{4,7},{5}}=>2
{{1,2},{3,6},{4},{5,7}}=>1
{{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}}=>2
{{1,2},{3},{4,6},{5,7}}=>0
{{1,2},{3},{4,6},{5},{7}}=>1
{{1,2,7},{3},{4},{5,6}}=>3
{{1,2},{3,7},{4},{5,6}}=>2
{{1,2},{3},{4,7},{5,6}}=>1
{{1,2},{3},{4},{5,6,7}}=>0
{{1,2},{3},{4},{5,6},{7}}=>0
{{1,2,7},{3},{4},{5},{6}}=>4
{{1,2},{3,7},{4},{5},{6}}=>3
{{1,2},{3},{4,7},{5},{6}}=>2
{{1,2},{3},{4},{5,7},{6}}=>1
{{1,2},{3},{4},{5},{6,7}}=>0
{{1,2},{3},{4},{5},{6},{7}}=>0
{{1,3,4,5,6,7},{2}}=>5
{{1,3,4,5,6},{2,7}}=>0
{{1,3,4,5,6},{2},{7}}=>4
{{1,3,4,5,7},{2,6}}=>1
{{1,3,4,5},{2,6,7}}=>0
{{1,3,4,5},{2,6},{7}}=>0
{{1,3,4,5,7},{2},{6}}=>5
{{1,3,4,5},{2,7},{6}}=>1
{{1,3,4,5},{2},{6,7}}=>3
{{1,3,4,5},{2},{6},{7}}=>3
{{1,3,4,6,7},{2,5}}=>2
{{1,3,4,6},{2,5,7}}=>0
{{1,3,4,6},{2,5},{7}}=>1
{{1,3,4,7},{2,5,6}}=>1
{{1,3,4},{2,5,6,7}}=>0
{{1,3,4},{2,5,6},{7}}=>0
{{1,3,4,7},{2,5},{6}}=>2
{{1,3,4},{2,5,7},{6}}=>1
{{1,3,4},{2,5},{6,7}}=>0
{{1,3,4},{2,5},{6},{7}}=>0
{{1,3,4,6,7},{2},{5}}=>6
{{1,3,4,6},{2,7},{5}}=>2
{{1,3,4,6},{2},{5,7}}=>3
{{1,3,4,6},{2},{5},{7}}=>4
{{1,3,4,7},{2,6},{5}}=>3
{{1,3,4},{2,6,7},{5}}=>2
{{1,3,4},{2,6},{5,7}}=>0
{{1,3,4},{2,6},{5},{7}}=>1
{{1,3,4,7},{2},{5,6}}=>4
{{1,3,4},{2,7},{5,6}}=>1
{{1,3,4},{2},{5,6,7}}=>2
{{1,3,4},{2},{5,6},{7}}=>2
{{1,3,4,7},{2},{5},{6}}=>5
{{1,3,4},{2,7},{5},{6}}=>2
{{1,3,4},{2},{5,7},{6}}=>3
{{1,3,4},{2},{5},{6,7}}=>2
{{1,3,4},{2},{5},{6},{7}}=>2
{{1,3,5,6,7},{2,4}}=>3
{{1,3,5,6},{2,4,7}}=>0
{{1,3,5,6},{2,4},{7}}=>2
{{1,3,5,7},{2,4,6}}=>1
{{1,3,5},{2,4,6,7}}=>0
{{1,3,5},{2,4,6},{7}}=>0
{{1,3,5,7},{2,4},{6}}=>3
{{1,3,5},{2,4,7},{6}}=>1
{{1,3,5},{2,4},{6,7}}=>1
{{1,3,5},{2,4},{6},{7}}=>1
{{1,3,6,7},{2,4,5}}=>2
{{1,3,6},{2,4,5,7}}=>0
{{1,3,6},{2,4,5},{7}}=>1
{{1,3,7},{2,4,5,6}}=>1
{{1,3},{2,4,5,6,7}}=>0
{{1,3},{2,4,5,6},{7}}=>0
{{1,3,7},{2,4,5},{6}}=>2
{{1,3},{2,4,5,7},{6}}=>1
{{1,3},{2,4,5},{6,7}}=>0
{{1,3},{2,4,5},{6},{7}}=>0
{{1,3,6,7},{2,4},{5}}=>4
{{1,3,6},{2,4,7},{5}}=>2
{{1,3,6},{2,4},{5,7}}=>1
{{1,3,6},{2,4},{5},{7}}=>2
{{1,3,7},{2,4,6},{5}}=>3
{{1,3},{2,4,6,7},{5}}=>2
{{1,3},{2,4,6},{5,7}}=>0
{{1,3},{2,4,6},{5},{7}}=>1
{{1,3,7},{2,4},{5,6}}=>2
{{1,3},{2,4,7},{5,6}}=>1
{{1,3},{2,4},{5,6,7}}=>0
{{1,3},{2,4},{5,6},{7}}=>0
{{1,3,7},{2,4},{5},{6}}=>3
{{1,3},{2,4,7},{5},{6}}=>2
{{1,3},{2,4},{5,7},{6}}=>1
{{1,3},{2,4},{5},{6,7}}=>0
{{1,3},{2,4},{5},{6},{7}}=>0
{{1,3,5,6,7},{2},{4}}=>7
{{1,3,5,6},{2,7},{4}}=>3
{{1,3,5,6},{2},{4,7}}=>3
{{1,3,5,6},{2},{4},{7}}=>5
{{1,3,5,7},{2,6},{4}}=>4
{{1,3,5},{2,6,7},{4}}=>3
{{1,3,5},{2,6},{4,7}}=>0
{{1,3,5},{2,6},{4},{7}}=>2
{{1,3,5,7},{2},{4,6}}=>4
{{1,3,5},{2,7},{4,6}}=>1
{{1,3,5},{2},{4,6,7}}=>2
{{1,3,5},{2},{4,6},{7}}=>2
{{1,3,5,7},{2},{4},{6}}=>6
{{1,3,5},{2,7},{4},{6}}=>3
{{1,3,5},{2},{4,7},{6}}=>3
{{1,3,5},{2},{4},{6,7}}=>3
{{1,3,5},{2},{4},{6},{7}}=>3
{{1,3,6,7},{2,5},{4}}=>5
{{1,3,6},{2,5,7},{4}}=>3
{{1,3,6},{2,5},{4,7}}=>1
{{1,3,6},{2,5},{4},{7}}=>3
{{1,3,7},{2,5,6},{4}}=>4
{{1,3},{2,5,6,7},{4}}=>3
{{1,3},{2,5,6},{4,7}}=>0
{{1,3},{2,5,6},{4},{7}}=>2
{{1,3,7},{2,5},{4,6}}=>2
{{1,3},{2,5,7},{4,6}}=>1
{{1,3},{2,5},{4,6,7}}=>0
{{1,3},{2,5},{4,6},{7}}=>0
{{1,3,7},{2,5},{4},{6}}=>4
{{1,3},{2,5,7},{4},{6}}=>3
{{1,3},{2,5},{4,7},{6}}=>1
{{1,3},{2,5},{4},{6,7}}=>1
{{1,3},{2,5},{4},{6},{7}}=>1
{{1,3,6,7},{2},{4,5}}=>5
{{1,3,6},{2,7},{4,5}}=>2
{{1,3,6},{2},{4,5,7}}=>2
{{1,3,6},{2},{4,5},{7}}=>3
{{1,3,7},{2,6},{4,5}}=>3
{{1,3},{2,6,7},{4,5}}=>2
{{1,3},{2,6},{4,5,7}}=>0
{{1,3},{2,6},{4,5},{7}}=>1
{{1,3,7},{2},{4,5,6}}=>3
{{1,3},{2,7},{4,5,6}}=>1
{{1,3},{2},{4,5,6,7}}=>1
{{1,3},{2},{4,5,6},{7}}=>1
{{1,3,7},{2},{4,5},{6}}=>4
{{1,3},{2,7},{4,5},{6}}=>2
{{1,3},{2},{4,5,7},{6}}=>2
{{1,3},{2},{4,5},{6,7}}=>1
{{1,3},{2},{4,5},{6},{7}}=>1
{{1,3,6,7},{2},{4},{5}}=>7
{{1,3,6},{2,7},{4},{5}}=>4
{{1,3,6},{2},{4,7},{5}}=>4
{{1,3,6},{2},{4},{5,7}}=>3
{{1,3,6},{2},{4},{5},{7}}=>4
{{1,3,7},{2,6},{4},{5}}=>5
{{1,3},{2,6,7},{4},{5}}=>4
{{1,3},{2,6},{4,7},{5}}=>2
{{1,3},{2,6},{4},{5,7}}=>1
{{1,3},{2,6},{4},{5},{7}}=>2
{{1,3,7},{2},{4,6},{5}}=>5
{{1,3},{2,7},{4,6},{5}}=>3
{{1,3},{2},{4,6,7},{5}}=>3
{{1,3},{2},{4,6},{5,7}}=>1
{{1,3},{2},{4,6},{5},{7}}=>2
{{1,3,7},{2},{4},{5,6}}=>4
{{1,3},{2,7},{4},{5,6}}=>2
{{1,3},{2},{4,7},{5,6}}=>2
{{1,3},{2},{4},{5,6,7}}=>1
{{1,3},{2},{4},{5,6},{7}}=>1
{{1,3,7},{2},{4},{5},{6}}=>5
{{1,3},{2,7},{4},{5},{6}}=>3
{{1,3},{2},{4,7},{5},{6}}=>3
{{1,3},{2},{4},{5,7},{6}}=>2
{{1,3},{2},{4},{5},{6,7}}=>1
{{1,3},{2},{4},{5},{6},{7}}=>1
{{1,4,5,6,7},{2,3}}=>4
{{1,4,5,6},{2,3,7}}=>0
{{1,4,5,6},{2,3},{7}}=>3
{{1,4,5,7},{2,3,6}}=>1
{{1,4,5},{2,3,6,7}}=>0
{{1,4,5},{2,3,6},{7}}=>0
{{1,4,5,7},{2,3},{6}}=>4
{{1,4,5},{2,3,7},{6}}=>1
{{1,4,5},{2,3},{6,7}}=>2
{{1,4,5},{2,3},{6},{7}}=>2
{{1,4,6,7},{2,3,5}}=>2
{{1,4,6},{2,3,5,7}}=>0
{{1,4,6},{2,3,5},{7}}=>1
{{1,4,7},{2,3,5,6}}=>1
{{1,4},{2,3,5,6,7}}=>0
{{1,4},{2,3,5,6},{7}}=>0
{{1,4,7},{2,3,5},{6}}=>2
{{1,4},{2,3,5,7},{6}}=>1
{{1,4},{2,3,5},{6,7}}=>0
{{1,4},{2,3,5},{6},{7}}=>0
{{1,4,6,7},{2,3},{5}}=>5
{{1,4,6},{2,3,7},{5}}=>2
{{1,4,6},{2,3},{5,7}}=>2
{{1,4,6},{2,3},{5},{7}}=>3
{{1,4,7},{2,3,6},{5}}=>3
{{1,4},{2,3,6,7},{5}}=>2
{{1,4},{2,3,6},{5,7}}=>0
{{1,4},{2,3,6},{5},{7}}=>1
{{1,4,7},{2,3},{5,6}}=>3
{{1,4},{2,3,7},{5,6}}=>1
{{1,4},{2,3},{5,6,7}}=>1
{{1,4},{2,3},{5,6},{7}}=>1
{{1,4,7},{2,3},{5},{6}}=>4
{{1,4},{2,3,7},{5},{6}}=>2
{{1,4},{2,3},{5,7},{6}}=>2
{{1,4},{2,3},{5},{6,7}}=>1
{{1,4},{2,3},{5},{6},{7}}=>1
{{1,5,6,7},{2,3,4}}=>3
{{1,5,6},{2,3,4,7}}=>0
{{1,5,6},{2,3,4},{7}}=>2
{{1,5,7},{2,3,4,6}}=>1
{{1,5},{2,3,4,6,7}}=>0
{{1,5},{2,3,4,6},{7}}=>0
{{1,5,7},{2,3,4},{6}}=>3
{{1,5},{2,3,4,7},{6}}=>1
{{1,5},{2,3,4},{6,7}}=>1
{{1,5},{2,3,4},{6},{7}}=>1
{{1,6,7},{2,3,4,5}}=>2
{{1,6},{2,3,4,5,7}}=>0
{{1,6},{2,3,4,5},{7}}=>1
{{1,7},{2,3,4,5,6}}=>1
{{1},{2,3,4,5,6,7}}=>0
{{1},{2,3,4,5,6},{7}}=>0
{{1,7},{2,3,4,5},{6}}=>2
{{1},{2,3,4,5,7},{6}}=>1
{{1},{2,3,4,5},{6,7}}=>0
{{1},{2,3,4,5},{6},{7}}=>0
{{1,6,7},{2,3,4},{5}}=>4
{{1,6},{2,3,4,7},{5}}=>2
{{1,6},{2,3,4},{5,7}}=>1
{{1,6},{2,3,4},{5},{7}}=>2
{{1,7},{2,3,4,6},{5}}=>3
{{1},{2,3,4,6,7},{5}}=>2
{{1},{2,3,4,6},{5,7}}=>0
{{1},{2,3,4,6},{5},{7}}=>1
{{1,7},{2,3,4},{5,6}}=>2
{{1},{2,3,4,7},{5,6}}=>1
{{1},{2,3,4},{5,6,7}}=>0
{{1},{2,3,4},{5,6},{7}}=>0
{{1,7},{2,3,4},{5},{6}}=>3
{{1},{2,3,4,7},{5},{6}}=>2
{{1},{2,3,4},{5,7},{6}}=>1
{{1},{2,3,4},{5},{6,7}}=>0
{{1},{2,3,4},{5},{6},{7}}=>0
{{1,5,6,7},{2,3},{4}}=>6
{{1,5,6},{2,3,7},{4}}=>3
{{1,5,6},{2,3},{4,7}}=>2
{{1,5,6},{2,3},{4},{7}}=>4
{{1,5,7},{2,3,6},{4}}=>4
{{1,5},{2,3,6,7},{4}}=>3
{{1,5},{2,3,6},{4,7}}=>0
{{1,5},{2,3,6},{4},{7}}=>2
{{1,5,7},{2,3},{4,6}}=>3
{{1,5},{2,3,7},{4,6}}=>1
{{1,5},{2,3},{4,6,7}}=>1
{{1,5},{2,3},{4,6},{7}}=>1
{{1,5,7},{2,3},{4},{6}}=>5
{{1,5},{2,3,7},{4},{6}}=>3
{{1,5},{2,3},{4,7},{6}}=>2
{{1,5},{2,3},{4},{6,7}}=>2
{{1,5},{2,3},{4},{6},{7}}=>2
{{1,6,7},{2,3,5},{4}}=>5
{{1,6},{2,3,5,7},{4}}=>3
{{1,6},{2,3,5},{4,7}}=>1
{{1,6},{2,3,5},{4},{7}}=>3
{{1,7},{2,3,5,6},{4}}=>4
{{1},{2,3,5,6,7},{4}}=>3
{{1},{2,3,5,6},{4,7}}=>0
{{1},{2,3,5,6},{4},{7}}=>2
{{1,7},{2,3,5},{4,6}}=>2
{{1},{2,3,5,7},{4,6}}=>1
{{1},{2,3,5},{4,6,7}}=>0
{{1},{2,3,5},{4,6},{7}}=>0
{{1,7},{2,3,5},{4},{6}}=>4
{{1},{2,3,5,7},{4},{6}}=>3
{{1},{2,3,5},{4,7},{6}}=>1
{{1},{2,3,5},{4},{6,7}}=>1
{{1},{2,3,5},{4},{6},{7}}=>1
{{1,6,7},{2,3},{4,5}}=>4
{{1,6},{2,3,7},{4,5}}=>2
{{1,6},{2,3},{4,5,7}}=>1
{{1,6},{2,3},{4,5},{7}}=>2
{{1,7},{2,3,6},{4,5}}=>3
{{1},{2,3,6,7},{4,5}}=>2
{{1},{2,3,6},{4,5,7}}=>0
{{1},{2,3,6},{4,5},{7}}=>1
{{1,7},{2,3},{4,5,6}}=>2
{{1},{2,3,7},{4,5,6}}=>1
{{1},{2,3},{4,5,6,7}}=>0
{{1},{2,3},{4,5,6},{7}}=>0
{{1,7},{2,3},{4,5},{6}}=>3
{{1},{2,3,7},{4,5},{6}}=>2
{{1},{2,3},{4,5,7},{6}}=>1
{{1},{2,3},{4,5},{6,7}}=>0
{{1},{2,3},{4,5},{6},{7}}=>0
{{1,6,7},{2,3},{4},{5}}=>6
{{1,6},{2,3,7},{4},{5}}=>4
{{1,6},{2,3},{4,7},{5}}=>3
{{1,6},{2,3},{4},{5,7}}=>2
{{1,6},{2,3},{4},{5},{7}}=>3
{{1,7},{2,3,6},{4},{5}}=>5
{{1},{2,3,6,7},{4},{5}}=>4
{{1},{2,3,6},{4,7},{5}}=>2
{{1},{2,3,6},{4},{5,7}}=>1
{{1},{2,3,6},{4},{5},{7}}=>2
{{1,7},{2,3},{4,6},{5}}=>4
{{1},{2,3,7},{4,6},{5}}=>3
{{1},{2,3},{4,6,7},{5}}=>2
{{1},{2,3},{4,6},{5,7}}=>0
{{1},{2,3},{4,6},{5},{7}}=>1
{{1,7},{2,3},{4},{5,6}}=>3
{{1},{2,3,7},{4},{5,6}}=>2
{{1},{2,3},{4,7},{5,6}}=>1
{{1},{2,3},{4},{5,6,7}}=>0
{{1},{2,3},{4},{5,6},{7}}=>0
{{1,7},{2,3},{4},{5},{6}}=>4
{{1},{2,3,7},{4},{5},{6}}=>3
{{1},{2,3},{4,7},{5},{6}}=>2
{{1},{2,3},{4},{5,7},{6}}=>1
{{1},{2,3},{4},{5},{6,7}}=>0
{{1},{2,3},{4},{5},{6},{7}}=>0
{{1,4,5,6,7},{2},{3}}=>8
{{1,4,5,6},{2,7},{3}}=>4
{{1,4,5,6},{2},{3,7}}=>3
{{1,4,5,6},{2},{3},{7}}=>6
{{1,4,5,7},{2,6},{3}}=>5
{{1,4,5},{2,6,7},{3}}=>4
{{1,4,5},{2,6},{3,7}}=>0
{{1,4,5},{2,6},{3},{7}}=>3
{{1,4,5,7},{2},{3,6}}=>4
{{1,4,5},{2,7},{3,6}}=>1
{{1,4,5},{2},{3,6,7}}=>2
{{1,4,5},{2},{3,6},{7}}=>2
{{1,4,5,7},{2},{3},{6}}=>7
{{1,4,5},{2,7},{3},{6}}=>4
{{1,4,5},{2},{3,7},{6}}=>3
{{1,4,5},{2},{3},{6,7}}=>4
{{1,4,5},{2},{3},{6},{7}}=>4
{{1,4,6,7},{2,5},{3}}=>6
{{1,4,6},{2,5,7},{3}}=>4
{{1,4,6},{2,5},{3,7}}=>1
{{1,4,6},{2,5},{3},{7}}=>4
{{1,4,7},{2,5,6},{3}}=>5
{{1,4},{2,5,6,7},{3}}=>4
{{1,4},{2,5,6},{3,7}}=>0
{{1,4},{2,5,6},{3},{7}}=>3
{{1,4,7},{2,5},{3,6}}=>2
{{1,4},{2,5,7},{3,6}}=>1
{{1,4},{2,5},{3,6,7}}=>0
{{1,4},{2,5},{3,6},{7}}=>0
{{1,4,7},{2,5},{3},{6}}=>5
{{1,4},{2,5,7},{3},{6}}=>4
{{1,4},{2,5},{3,7},{6}}=>1
{{1,4},{2,5},{3},{6,7}}=>2
{{1,4},{2,5},{3},{6},{7}}=>2
{{1,4,6,7},{2},{3,5}}=>5
{{1,4,6},{2,7},{3,5}}=>2
{{1,4,6},{2},{3,5,7}}=>2
{{1,4,6},{2},{3,5},{7}}=>3
{{1,4,7},{2,6},{3,5}}=>3
{{1,4},{2,6,7},{3,5}}=>2
{{1,4},{2,6},{3,5,7}}=>0
{{1,4},{2,6},{3,5},{7}}=>1
{{1,4,7},{2},{3,5,6}}=>3
{{1,4},{2,7},{3,5,6}}=>1
{{1,4},{2},{3,5,6,7}}=>1
{{1,4},{2},{3,5,6},{7}}=>1
{{1,4,7},{2},{3,5},{6}}=>4
{{1,4},{2,7},{3,5},{6}}=>2
{{1,4},{2},{3,5,7},{6}}=>2
{{1,4},{2},{3,5},{6,7}}=>1
{{1,4},{2},{3,5},{6},{7}}=>1
{{1,4,6,7},{2},{3},{5}}=>8
{{1,4,6},{2,7},{3},{5}}=>5
{{1,4,6},{2},{3,7},{5}}=>4
{{1,4,6},{2},{3},{5,7}}=>4
{{1,4,6},{2},{3},{5},{7}}=>5
{{1,4,7},{2,6},{3},{5}}=>6
{{1,4},{2,6,7},{3},{5}}=>5
{{1,4},{2,6},{3,7},{5}}=>2
{{1,4},{2,6},{3},{5,7}}=>2
{{1,4},{2,6},{3},{5},{7}}=>3
{{1,4,7},{2},{3,6},{5}}=>5
{{1,4},{2,7},{3,6},{5}}=>3
{{1,4},{2},{3,6,7},{5}}=>3
{{1,4},{2},{3,6},{5,7}}=>1
{{1,4},{2},{3,6},{5},{7}}=>2
{{1,4,7},{2},{3},{5,6}}=>5
{{1,4},{2,7},{3},{5,6}}=>3
{{1,4},{2},{3,7},{5,6}}=>2
{{1,4},{2},{3},{5,6,7}}=>2
{{1,4},{2},{3},{5,6},{7}}=>2
{{1,4,7},{2},{3},{5},{6}}=>6
{{1,4},{2,7},{3},{5},{6}}=>4
{{1,4},{2},{3,7},{5},{6}}=>3
{{1,4},{2},{3},{5,7},{6}}=>3
{{1,4},{2},{3},{5},{6,7}}=>2
{{1,4},{2},{3},{5},{6},{7}}=>2
{{1,5,6,7},{2,4},{3}}=>7
{{1,5,6},{2,4,7},{3}}=>4
{{1,5,6},{2,4},{3,7}}=>2
{{1,5,6},{2,4},{3},{7}}=>5
{{1,5,7},{2,4,6},{3}}=>5
{{1,5},{2,4,6,7},{3}}=>4
{{1,5},{2,4,6},{3,7}}=>0
{{1,5},{2,4,6},{3},{7}}=>3
{{1,5,7},{2,4},{3,6}}=>3
{{1,5},{2,4,7},{3,6}}=>1
{{1,5},{2,4},{3,6,7}}=>1
{{1,5},{2,4},{3,6},{7}}=>1
{{1,5,7},{2,4},{3},{6}}=>6
{{1,5},{2,4,7},{3},{6}}=>4
{{1,5},{2,4},{3,7},{6}}=>2
{{1,5},{2,4},{3},{6,7}}=>3
{{1,5},{2,4},{3},{6},{7}}=>3
{{1,6,7},{2,4,5},{3}}=>6
{{1,6},{2,4,5,7},{3}}=>4
{{1,6},{2,4,5},{3,7}}=>1
{{1,6},{2,4,5},{3},{7}}=>4
{{1,7},{2,4,5,6},{3}}=>5
{{1},{2,4,5,6,7},{3}}=>4
{{1},{2,4,5,6},{3,7}}=>0
{{1},{2,4,5,6},{3},{7}}=>3
{{1,7},{2,4,5},{3,6}}=>2
{{1},{2,4,5,7},{3,6}}=>1
{{1},{2,4,5},{3,6,7}}=>0
{{1},{2,4,5},{3,6},{7}}=>0
{{1,7},{2,4,5},{3},{6}}=>5
{{1},{2,4,5,7},{3},{6}}=>4
{{1},{2,4,5},{3,7},{6}}=>1
{{1},{2,4,5},{3},{6,7}}=>2
{{1},{2,4,5},{3},{6},{7}}=>2
{{1,6,7},{2,4},{3,5}}=>4
{{1,6},{2,4,7},{3,5}}=>2
{{1,6},{2,4},{3,5,7}}=>1
{{1,6},{2,4},{3,5},{7}}=>2
{{1,7},{2,4,6},{3,5}}=>3
{{1},{2,4,6,7},{3,5}}=>2
{{1},{2,4,6},{3,5,7}}=>0
{{1},{2,4,6},{3,5},{7}}=>1
{{1,7},{2,4},{3,5,6}}=>2
{{1},{2,4,7},{3,5,6}}=>1
{{1},{2,4},{3,5,6,7}}=>0
{{1},{2,4},{3,5,6},{7}}=>0
{{1,7},{2,4},{3,5},{6}}=>3
{{1},{2,4,7},{3,5},{6}}=>2
{{1},{2,4},{3,5,7},{6}}=>1
{{1},{2,4},{3,5},{6,7}}=>0
{{1},{2,4},{3,5},{6},{7}}=>0
{{1,6,7},{2,4},{3},{5}}=>7
{{1,6},{2,4,7},{3},{5}}=>5
{{1,6},{2,4},{3,7},{5}}=>3
{{1,6},{2,4},{3},{5,7}}=>3
{{1,6},{2,4},{3},{5},{7}}=>4
{{1,7},{2,4,6},{3},{5}}=>6
{{1},{2,4,6,7},{3},{5}}=>5
{{1},{2,4,6},{3,7},{5}}=>2
{{1},{2,4,6},{3},{5,7}}=>2
{{1},{2,4,6},{3},{5},{7}}=>3
{{1,7},{2,4},{3,6},{5}}=>4
{{1},{2,4,7},{3,6},{5}}=>3
{{1},{2,4},{3,6,7},{5}}=>2
{{1},{2,4},{3,6},{5,7}}=>0
{{1},{2,4},{3,6},{5},{7}}=>1
{{1,7},{2,4},{3},{5,6}}=>4
{{1},{2,4,7},{3},{5,6}}=>3
{{1},{2,4},{3,7},{5,6}}=>1
{{1},{2,4},{3},{5,6,7}}=>1
{{1},{2,4},{3},{5,6},{7}}=>1
{{1,7},{2,4},{3},{5},{6}}=>5
{{1},{2,4,7},{3},{5},{6}}=>4
{{1},{2,4},{3,7},{5},{6}}=>2
{{1},{2,4},{3},{5,7},{6}}=>2
{{1},{2,4},{3},{5},{6,7}}=>1
{{1},{2,4},{3},{5},{6},{7}}=>1
{{1,5,6,7},{2},{3,4}}=>6
{{1,5,6},{2,7},{3,4}}=>3
{{1,5,6},{2},{3,4,7}}=>2
{{1,5,6},{2},{3,4},{7}}=>4
{{1,5,7},{2,6},{3,4}}=>4
{{1,5},{2,6,7},{3,4}}=>3
{{1,5},{2,6},{3,4,7}}=>0
{{1,5},{2,6},{3,4},{7}}=>2
{{1,5,7},{2},{3,4,6}}=>3
{{1,5},{2,7},{3,4,6}}=>1
{{1,5},{2},{3,4,6,7}}=>1
{{1,5},{2},{3,4,6},{7}}=>1
{{1,5,7},{2},{3,4},{6}}=>5
{{1,5},{2,7},{3,4},{6}}=>3
{{1,5},{2},{3,4,7},{6}}=>2
{{1,5},{2},{3,4},{6,7}}=>2
{{1,5},{2},{3,4},{6},{7}}=>2
{{1,6,7},{2,5},{3,4}}=>5
{{1,6},{2,5,7},{3,4}}=>3
{{1,6},{2,5},{3,4,7}}=>1
{{1,6},{2,5},{3,4},{7}}=>3
{{1,7},{2,5,6},{3,4}}=>4
{{1},{2,5,6,7},{3,4}}=>3
{{1},{2,5,6},{3,4,7}}=>0
{{1},{2,5,6},{3,4},{7}}=>2
{{1,7},{2,5},{3,4,6}}=>2
{{1},{2,5,7},{3,4,6}}=>1
{{1},{2,5},{3,4,6,7}}=>0
{{1},{2,5},{3,4,6},{7}}=>0
{{1,7},{2,5},{3,4},{6}}=>4
{{1},{2,5,7},{3,4},{6}}=>3
{{1},{2,5},{3,4,7},{6}}=>1
{{1},{2,5},{3,4},{6,7}}=>1
{{1},{2,5},{3,4},{6},{7}}=>1
{{1,6,7},{2},{3,4,5}}=>4
{{1,6},{2,7},{3,4,5}}=>2
{{1,6},{2},{3,4,5,7}}=>1
{{1,6},{2},{3,4,5},{7}}=>2
{{1,7},{2,6},{3,4,5}}=>3
{{1},{2,6,7},{3,4,5}}=>2
{{1},{2,6},{3,4,5,7}}=>0
{{1},{2,6},{3,4,5},{7}}=>1
{{1,7},{2},{3,4,5,6}}=>2
{{1},{2,7},{3,4,5,6}}=>1
{{1},{2},{3,4,5,6,7}}=>0
{{1},{2},{3,4,5,6},{7}}=>0
{{1,7},{2},{3,4,5},{6}}=>3
{{1},{2,7},{3,4,5},{6}}=>2
{{1},{2},{3,4,5,7},{6}}=>1
{{1},{2},{3,4,5},{6,7}}=>0
{{1},{2},{3,4,5},{6},{7}}=>0
{{1,6,7},{2},{3,4},{5}}=>6
{{1,6},{2,7},{3,4},{5}}=>4
{{1,6},{2},{3,4,7},{5}}=>3
{{1,6},{2},{3,4},{5,7}}=>2
{{1,6},{2},{3,4},{5},{7}}=>3
{{1,7},{2,6},{3,4},{5}}=>5
{{1},{2,6,7},{3,4},{5}}=>4
{{1},{2,6},{3,4,7},{5}}=>2
{{1},{2,6},{3,4},{5,7}}=>1
{{1},{2,6},{3,4},{5},{7}}=>2
{{1,7},{2},{3,4,6},{5}}=>4
{{1},{2,7},{3,4,6},{5}}=>3
{{1},{2},{3,4,6,7},{5}}=>2
{{1},{2},{3,4,6},{5,7}}=>0
{{1},{2},{3,4,6},{5},{7}}=>1
{{1,7},{2},{3,4},{5,6}}=>3
{{1},{2,7},{3,4},{5,6}}=>2
{{1},{2},{3,4,7},{5,6}}=>1
{{1},{2},{3,4},{5,6,7}}=>0
{{1},{2},{3,4},{5,6},{7}}=>0
{{1,7},{2},{3,4},{5},{6}}=>4
{{1},{2,7},{3,4},{5},{6}}=>3
{{1},{2},{3,4,7},{5},{6}}=>2
{{1},{2},{3,4},{5,7},{6}}=>1
{{1},{2},{3,4},{5},{6,7}}=>0
{{1},{2},{3,4},{5},{6},{7}}=>0
{{1,5,6,7},{2},{3},{4}}=>9
{{1,5,6},{2,7},{3},{4}}=>6
{{1,5,6},{2},{3,7},{4}}=>5
{{1,5,6},{2},{3},{4,7}}=>4
{{1,5,6},{2},{3},{4},{7}}=>6
{{1,5,7},{2,6},{3},{4}}=>7
{{1,5},{2,6,7},{3},{4}}=>6
{{1,5},{2,6},{3,7},{4}}=>3
{{1,5},{2,6},{3},{4,7}}=>2
{{1,5},{2,6},{3},{4},{7}}=>4
{{1,5,7},{2},{3,6},{4}}=>6
{{1,5},{2,7},{3,6},{4}}=>4
{{1,5},{2},{3,6,7},{4}}=>4
{{1,5},{2},{3,6},{4,7}}=>1
{{1,5},{2},{3,6},{4},{7}}=>3
{{1,5,7},{2},{3},{4,6}}=>5
{{1,5},{2,7},{3},{4,6}}=>3
{{1,5},{2},{3,7},{4,6}}=>2
{{1,5},{2},{3},{4,6,7}}=>2
{{1,5},{2},{3},{4,6},{7}}=>2
{{1,5,7},{2},{3},{4},{6}}=>7
{{1,5},{2,7},{3},{4},{6}}=>5
{{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}}=>3
{{1,6,7},{2,5},{3},{4}}=>8
{{1,6},{2,5,7},{3},{4}}=>6
{{1,6},{2,5},{3,7},{4}}=>4
{{1,6},{2,5},{3},{4,7}}=>3
{{1,6},{2,5},{3},{4},{7}}=>5
{{1,7},{2,5,6},{3},{4}}=>7
{{1},{2,5,6,7},{3},{4}}=>6
{{1},{2,5,6},{3,7},{4}}=>3
{{1},{2,5,6},{3},{4,7}}=>2
{{1},{2,5,6},{3},{4},{7}}=>4
{{1,7},{2,5},{3,6},{4}}=>5
{{1},{2,5,7},{3,6},{4}}=>4
{{1},{2,5},{3,6,7},{4}}=>3
{{1},{2,5},{3,6},{4,7}}=>0
{{1},{2,5},{3,6},{4},{7}}=>2
{{1,7},{2,5},{3},{4,6}}=>4
{{1},{2,5,7},{3},{4,6}}=>3
{{1},{2,5},{3,7},{4,6}}=>1
{{1},{2,5},{3},{4,6,7}}=>1
{{1},{2,5},{3},{4,6},{7}}=>1
{{1,7},{2,5},{3},{4},{6}}=>6
{{1},{2,5,7},{3},{4},{6}}=>5
{{1},{2,5},{3,7},{4},{6}}=>3
{{1},{2,5},{3},{4,7},{6}}=>2
{{1},{2,5},{3},{4},{6,7}}=>2
{{1},{2,5},{3},{4},{6},{7}}=>2
{{1,6,7},{2},{3,5},{4}}=>7
{{1,6},{2,7},{3,5},{4}}=>5
{{1,6},{2},{3,5,7},{4}}=>4
{{1,6},{2},{3,5},{4,7}}=>2
{{1,6},{2},{3,5},{4},{7}}=>4
{{1,7},{2,6},{3,5},{4}}=>6
{{1},{2,6,7},{3,5},{4}}=>5
{{1},{2,6},{3,5,7},{4}}=>3
{{1},{2,6},{3,5},{4,7}}=>1
{{1},{2,6},{3,5},{4},{7}}=>3
{{1,7},{2},{3,5,6},{4}}=>5
{{1},{2,7},{3,5,6},{4}}=>4
{{1},{2},{3,5,6,7},{4}}=>3
{{1},{2},{3,5,6},{4,7}}=>0
{{1},{2},{3,5,6},{4},{7}}=>2
{{1,7},{2},{3,5},{4,6}}=>3
{{1},{2,7},{3,5},{4,6}}=>2
{{1},{2},{3,5,7},{4,6}}=>1
{{1},{2},{3,5},{4,6,7}}=>0
{{1},{2},{3,5},{4,6},{7}}=>0
{{1,7},{2},{3,5},{4},{6}}=>5
{{1},{2,7},{3,5},{4},{6}}=>4
{{1},{2},{3,5,7},{4},{6}}=>3
{{1},{2},{3,5},{4,7},{6}}=>1
{{1},{2},{3,5},{4},{6,7}}=>1
{{1},{2},{3,5},{4},{6},{7}}=>1
{{1,6,7},{2},{3},{4,5}}=>6
{{1,6},{2,7},{3},{4,5}}=>4
{{1,6},{2},{3,7},{4,5}}=>3
{{1,6},{2},{3},{4,5,7}}=>2
{{1,6},{2},{3},{4,5},{7}}=>3
{{1,7},{2,6},{3},{4,5}}=>5
{{1},{2,6,7},{3},{4,5}}=>4
{{1},{2,6},{3,7},{4,5}}=>2
{{1},{2,6},{3},{4,5,7}}=>1
{{1},{2,6},{3},{4,5},{7}}=>2
{{1,7},{2},{3,6},{4,5}}=>4
{{1},{2,7},{3,6},{4,5}}=>3
{{1},{2},{3,6,7},{4,5}}=>2
{{1},{2},{3,6},{4,5,7}}=>0
{{1},{2},{3,6},{4,5},{7}}=>1
{{1,7},{2},{3},{4,5,6}}=>3
{{1},{2,7},{3},{4,5,6}}=>2
{{1},{2},{3,7},{4,5,6}}=>1
{{1},{2},{3},{4,5,6,7}}=>0
{{1},{2},{3},{4,5,6},{7}}=>0
{{1,7},{2},{3},{4,5},{6}}=>4
{{1},{2,7},{3},{4,5},{6}}=>3
{{1},{2},{3,7},{4,5},{6}}=>2
{{1},{2},{3},{4,5,7},{6}}=>1
{{1},{2},{3},{4,5},{6,7}}=>0
{{1},{2},{3},{4,5},{6},{7}}=>0
{{1,6,7},{2},{3},{4},{5}}=>8
{{1,6},{2,7},{3},{4},{5}}=>6
{{1,6},{2},{3,7},{4},{5}}=>5
{{1,6},{2},{3},{4,7},{5}}=>4
{{1,6},{2},{3},{4},{5,7}}=>3
{{1,6},{2},{3},{4},{5},{7}}=>4
{{1,7},{2,6},{3},{4},{5}}=>7
{{1},{2,6,7},{3},{4},{5}}=>6
{{1},{2,6},{3,7},{4},{5}}=>4
{{1},{2,6},{3},{4,7},{5}}=>3
{{1},{2,6},{3},{4},{5,7}}=>2
{{1},{2,6},{3},{4},{5},{7}}=>3
{{1,7},{2},{3,6},{4},{5}}=>6
{{1},{2,7},{3,6},{4},{5}}=>5
{{1},{2},{3,6,7},{4},{5}}=>4
{{1},{2},{3,6},{4,7},{5}}=>2
{{1},{2},{3,6},{4},{5,7}}=>1
{{1},{2},{3,6},{4},{5},{7}}=>2
{{1,7},{2},{3},{4,6},{5}}=>5
{{1},{2,7},{3},{4,6},{5}}=>4
{{1},{2},{3,7},{4,6},{5}}=>3
{{1},{2},{3},{4,6,7},{5}}=>2
{{1},{2},{3},{4,6},{5,7}}=>0
{{1},{2},{3},{4,6},{5},{7}}=>1
{{1,7},{2},{3},{4},{5,6}}=>4
{{1},{2,7},{3},{4},{5,6}}=>3
{{1},{2},{3,7},{4},{5,6}}=>2
{{1},{2},{3},{4,7},{5,6}}=>1
{{1},{2},{3},{4},{5,6,7}}=>0
{{1},{2},{3},{4},{5,6},{7}}=>0
{{1,7},{2},{3},{4},{5},{6}}=>5
{{1},{2,7},{3},{4},{5},{6}}=>4
{{1},{2},{3,7},{4},{5},{6}}=>3
{{1},{2},{3},{4,7},{5},{6}}=>2
{{1},{2},{3},{4},{5,7},{6}}=>1
{{1},{2},{3},{4},{5},{6,7}}=>0
{{1},{2},{3},{4},{5},{6},{7}}=>0
{{1,2},{3,4},{5,6},{7,8}}=>0
{{1,3},{2,4},{5,6},{7,8}}=>0
{{1,4},{2,3},{5,6},{7,8}}=>1
{{1,5},{2,3},{4,6},{7,8}}=>1
{{1,6},{2,3},{4,5},{7,8}}=>2
{{1,7},{2,3},{4,5},{6,8}}=>2
{{1,8},{2,3},{4,5},{6,7}}=>3
{{1,8},{2,4},{3,5},{6,7}}=>3
{{1,7},{2,4},{3,5},{6,8}}=>2
{{1,6},{2,4},{3,5},{7,8}}=>2
{{1,5},{2,4},{3,6},{7,8}}=>1
{{1,4},{2,5},{3,6},{7,8}}=>0
{{1,3},{2,5},{4,6},{7,8}}=>0
{{1,2},{3,5},{4,6},{7,8}}=>0
{{1,2},{3,6},{4,5},{7,8}}=>1
{{1,3},{2,6},{4,5},{7,8}}=>1
{{1,4},{2,6},{3,5},{7,8}}=>1
{{1,5},{2,6},{3,4},{7,8}}=>2
{{1,6},{2,5},{3,4},{7,8}}=>3
{{1,7},{2,5},{3,4},{6,8}}=>3
{{1,8},{2,5},{3,4},{6,7}}=>4
{{1,8},{2,6},{3,4},{5,7}}=>4
{{1,7},{2,6},{3,4},{5,8}}=>3
{{1,6},{2,7},{3,4},{5,8}}=>2
{{1,5},{2,7},{3,4},{6,8}}=>2
{{1,4},{2,7},{3,5},{6,8}}=>1
{{1,3},{2,7},{4,5},{6,8}}=>1
{{1,2},{3,7},{4,5},{6,8}}=>1
{{1,2},{3,8},{4,5},{6,7}}=>2
{{1,3},{2,8},{4,5},{6,7}}=>2
{{1,4},{2,8},{3,5},{6,7}}=>2
{{1,5},{2,8},{3,4},{6,7}}=>3
{{1,6},{2,8},{3,4},{5,7}}=>3
{{1,7},{2,8},{3,4},{5,6}}=>4
{{1,8},{2,7},{3,4},{5,6}}=>5
{{1,8},{2,7},{3,5},{4,6}}=>5
{{1,7},{2,8},{3,5},{4,6}}=>4
{{1,6},{2,8},{3,5},{4,7}}=>3
{{1,5},{2,8},{3,6},{4,7}}=>2
{{1,4},{2,8},{3,6},{5,7}}=>2
{{1,3},{2,8},{4,6},{5,7}}=>2
{{1,2},{3,8},{4,6},{5,7}}=>2
{{1,2},{3,7},{4,6},{5,8}}=>1
{{1,3},{2,7},{4,6},{5,8}}=>1
{{1,4},{2,7},{3,6},{5,8}}=>1
{{1,5},{2,7},{3,6},{4,8}}=>1
{{1,6},{2,7},{3,5},{4,8}}=>2
{{1,7},{2,6},{3,5},{4,8}}=>3
{{1,8},{2,6},{3,5},{4,7}}=>4
{{1,8},{2,5},{3,6},{4,7}}=>3
{{1,7},{2,5},{3,6},{4,8}}=>2
{{1,6},{2,5},{3,7},{4,8}}=>1
{{1,5},{2,6},{3,7},{4,8}}=>0
{{1,4},{2,6},{3,7},{5,8}}=>0
{{1,3},{2,6},{4,7},{5,8}}=>0
{{1,2},{3,6},{4,7},{5,8}}=>0
{{1,2},{3,5},{4,7},{6,8}}=>0
{{1,3},{2,5},{4,7},{6,8}}=>0
{{1,4},{2,5},{3,7},{6,8}}=>0
{{1,5},{2,4},{3,7},{6,8}}=>1
{{1,6},{2,4},{3,7},{5,8}}=>1
{{1,7},{2,4},{3,6},{5,8}}=>2
{{1,8},{2,4},{3,6},{5,7}}=>3
{{1,8},{2,3},{4,6},{5,7}}=>3
{{1,7},{2,3},{4,6},{5,8}}=>2
{{1,6},{2,3},{4,7},{5,8}}=>1
{{1,5},{2,3},{4,7},{6,8}}=>1
{{1,4},{2,3},{5,7},{6,8}}=>1
{{1,3},{2,4},{5,7},{6,8}}=>0
{{1,2},{3,4},{5,7},{6,8}}=>0
{{1,2},{3,4},{5,8},{6,7}}=>1
{{1,3},{2,4},{5,8},{6,7}}=>1
{{1,4},{2,3},{5,8},{6,7}}=>2
{{1,5},{2,3},{4,8},{6,7}}=>2
{{1,6},{2,3},{4,8},{5,7}}=>2
{{1,7},{2,3},{4,8},{5,6}}=>3
{{1,8},{2,3},{4,7},{5,6}}=>4
{{1,8},{2,4},{3,7},{5,6}}=>4
{{1,7},{2,4},{3,8},{5,6}}=>3
{{1,6},{2,4},{3,8},{5,7}}=>2
{{1,5},{2,4},{3,8},{6,7}}=>2
{{1,4},{2,5},{3,8},{6,7}}=>1
{{1,3},{2,5},{4,8},{6,7}}=>1
{{1,2},{3,5},{4,8},{6,7}}=>1
{{1,2},{3,6},{4,8},{5,7}}=>1
{{1,3},{2,6},{4,8},{5,7}}=>1
{{1,4},{2,6},{3,8},{5,7}}=>1
{{1,5},{2,6},{3,8},{4,7}}=>1
{{1,6},{2,5},{3,8},{4,7}}=>2
{{1,7},{2,5},{3,8},{4,6}}=>3
{{1,8},{2,5},{3,7},{4,6}}=>4
{{1,8},{2,6},{3,7},{4,5}}=>5
{{1,7},{2,6},{3,8},{4,5}}=>4
{{1,6},{2,7},{3,8},{4,5}}=>3
{{1,5},{2,7},{3,8},{4,6}}=>2
{{1,4},{2,7},{3,8},{5,6}}=>2
{{1,3},{2,7},{4,8},{5,6}}=>2
{{1,2},{3,7},{4,8},{5,6}}=>2
{{1,2},{3,8},{4,7},{5,6}}=>3
{{1,3},{2,8},{4,7},{5,6}}=>3
{{1,4},{2,8},{3,7},{5,6}}=>3
{{1,5},{2,8},{3,7},{4,6}}=>3
{{1,6},{2,8},{3,7},{4,5}}=>4
{{1,7},{2,8},{3,6},{4,5}}=>5
{{1,8},{2,7},{3,6},{4,5}}=>6
{{1},{2},{3,4,5,6,7,8}}=>0
{{1},{2,4,5,6,7,8},{3}}=>5
{{1},{2,3,5,6,7,8},{4}}=>4
{{1},{2,3,4,6,7,8},{5}}=>3
{{1},{2,3,4,5,8},{6},{7}}=>2
{{1},{2,3,4,5,7,8},{6}}=>2
{{1},{2,3,4,5,6,7},{8}}=>0
{{1},{2,3,4,8},{5,6,7}}=>1
{{1},{2,3,4,5,8},{6,7}}=>1
{{1},{2,3,4,5,6,8},{7}}=>1
{{1},{2,3,4,5,6,7,8}}=>0
{{1,2},{3,4,5,6,7,8}}=>0
{{1,4,5,6,7,8},{2},{3}}=>10
{{1,3,5,6,7,8},{2},{4}}=>9
{{1,3,4,5,6,7,8},{2}}=>6
{{1,4,5,6,7,8},{2,3}}=>5
{{1,2,4,5,6,7,8},{3}}=>5
{{1,2,5,6,7,8},{3,4}}=>4
{{1,2,3,5,6,7},{4},{8}}=>3
{{1,2,3,5,6,7,8},{4}}=>4
{{1,2,3,6,7,8},{4,5}}=>3
{{1,2,3,4,7},{5},{6},{8}}=>2
{{1,2,3,4,6,7},{5},{8}}=>2
{{1,2,3,4,6,7,8},{5}}=>3
{{1,2,3,4,5,6},{7,8}}=>0
{{1,2,3,7},{4,5,6},{8}}=>1
{{1,2,3,4,7},{5,6},{8}}=>1
{{1,2,3,4,7,8},{5,6}}=>2
{{1,2,3,4,5,7},{6},{8}}=>1
{{1,2,3,4,5,7,8},{6}}=>2
{{1,2,3,4,5,6,7},{8}}=>0
{{1,8},{2,3,4,5,6,7}}=>1
{{1,2,3,4,5,8},{6,7}}=>1
{{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}}=>4
{{1,3,4,6,7,8},{2,5}}=>3
{{1,2,4,6,7,8},{3,5}}=>3
{{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}}=>1
{{1,2,4,5,6,8},{3,7}}=>1
{{1,2,3,5,6,8},{4,7}}=>1
{{1,2,3,4,6,8},{5,7}}=>1
{{1,3,4,5,6,7},{2,8}}=>0
{{1,2,4,5,6,7},{3,8}}=>0
{{1,2,3,5,6,7},{4,8}}=>0
{{1,2,3,4,6,7},{5,8}}=>0
{{1,2,3,4,5,7},{6,8}}=>0
{{1,3},{2,4,5,6,7,8}}=>0
{{1,4},{2,3,5,6,7,8}}=>0
{{1,5},{2,3,4,6,7,8}}=>0
{{1,6},{2,3,4,5,7,8}}=>0
{{1,7},{2,3,4,5,6,8}}=>0
{{1,2,3,4,5,6,7,8},{9}}=>0
{{1},{2,3,4,5,6,7,8,9}}=>0
{{1,2,3,4,5,6,8},{7},{9}}=>1
{{1},{2,3,4,5,6,7,9},{8}}=>1
{{1,2,3,4,5,8},{6,7},{9}}=>1
{{1,2,3,4,5,7,8},{6},{9}}=>2
{{1},{2,3,4,5,6,9},{7,8}}=>1
{{1},{2,3,4,5,6,8,9},{7}}=>2
{{1,2},{3,4},{5,6},{7,8},{9,10}}=>0
{{1,4},{2,3},{5,6},{7,8},{9,10}}=>1
{{1,6},{2,3},{4,5},{7,8},{9,10}}=>2
{{1,8},{2,3},{4,5},{6,7},{9,10}}=>3
{{1,10},{2,3},{4,5},{6,7},{8,9}}=>4
{{1,2},{3,6},{4,5},{7,8},{9,10}}=>1
{{1,6},{2,5},{3,4},{7,8},{9,10}}=>3
{{1,8},{2,5},{3,4},{6,7},{9,10}}=>4
{{1,10},{2,5},{3,4},{6,7},{8,9}}=>5
{{1,2},{3,8},{4,5},{6,7},{9,10}}=>2
{{1,8},{2,7},{3,4},{5,6},{9,10}}=>5
{{1,10},{2,7},{3,4},{5,6},{8,9}}=>6
{{1,2},{3,10},{4,5},{6,7},{8,9}}=>3
{{1,10},{2,9},{3,4},{5,6},{7,8}}=>7
{{1,2},{3,4},{5,8},{6,7},{9,10}}=>1
{{1,4},{2,3},{5,8},{6,7},{9,10}}=>2
{{1,8},{2,3},{4,7},{5,6},{9,10}}=>4
{{1,10},{2,3},{4,7},{5,6},{8,9}}=>5
{{1,2},{3,8},{4,7},{5,6},{9,10}}=>3
{{1,8},{2,7},{3,6},{4,5},{9,10}}=>6
{{1,10},{2,7},{3,6},{4,5},{8,9}}=>7
{{1,2},{3,10},{4,7},{5,6},{8,9}}=>4
{{1,10},{2,9},{3,6},{4,5},{7,8}}=>8
{{1,2},{3,4},{5,10},{6,7},{8,9}}=>2
{{1,4},{2,3},{5,10},{6,7},{8,9}}=>3
{{1,10},{2,3},{4,9},{5,6},{7,8}}=>6
{{1,2},{3,10},{4,9},{5,6},{7,8}}=>5
{{1,10},{2,9},{3,8},{4,5},{6,7}}=>9
{{1,2},{3,4},{5,6},{7,10},{8,9}}=>1
{{1,4},{2,3},{5,6},{7,10},{8,9}}=>2
{{1,6},{2,3},{4,5},{7,10},{8,9}}=>3
{{1,10},{2,3},{4,5},{6,9},{7,8}}=>5
{{1,2},{3,6},{4,5},{7,10},{8,9}}=>2
{{1,6},{2,5},{3,4},{7,10},{8,9}}=>4
{{1,10},{2,5},{3,4},{6,9},{7,8}}=>6
{{1,2},{3,10},{4,5},{6,9},{7,8}}=>4
{{1,10},{2,9},{3,4},{5,8},{6,7}}=>8
{{1,2},{3,4},{5,10},{6,9},{7,8}}=>3
{{1,4},{2,3},{5,10},{6,9},{7,8}}=>4
{{1,10},{2,3},{4,9},{5,8},{6,7}}=>7
{{1,2},{3,10},{4,9},{5,8},{6,7}}=>6
{{1,10},{2,9},{3,8},{4,7},{5,6}}=>10
{{1,2,3,4,5,6,7,8,9},{10}}=>0
{{1},{2,3,4,5,6,7,8,9,10}}=>0
{{1,2,3,4,5,6,7,9},{8},{10}}=>1
{{1},{2,3,4,5,6,7,8,10},{9}}=>1
{{1,2,3,4,5,6,7,8,9,10},{11}}=>0
{{1},{2,3,4,5,6,7,8,9,10,11}}=>0
{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}=>0
{{1,2},{3,4},{5,6},{7,8},{9,12},{10,11}}=>1
{{1,2},{3,4},{5,6},{7,10},{8,9},{11,12}}=>1
{{1,2},{3,4},{5,6},{7,12},{8,9},{10,11}}=>2
{{1,2},{3,4},{5,6},{7,12},{8,11},{9,10}}=>3
{{1,2},{3,4},{5,8},{6,7},{9,10},{11,12}}=>1
{{1,2},{3,4},{5,8},{6,7},{9,12},{10,11}}=>2
{{1,2},{3,4},{5,10},{6,7},{8,9},{11,12}}=>2
{{1,2},{3,4},{5,12},{6,7},{8,9},{10,11}}=>3
{{1,2},{3,4},{5,12},{6,7},{8,11},{9,10}}=>4
{{1,2},{3,4},{5,10},{6,9},{7,8},{11,12}}=>3
{{1,2},{3,4},{5,12},{6,9},{7,8},{10,11}}=>4
{{1,2},{3,4},{5,12},{6,11},{7,8},{9,10}}=>5
{{1,2},{3,4},{5,12},{6,11},{7,10},{8,9}}=>6
{{1,2},{3,6},{4,5},{7,8},{9,10},{11,12}}=>1
{{1,2},{3,6},{4,5},{7,8},{9,12},{10,11}}=>2
{{1,2},{3,6},{4,5},{7,10},{8,9},{11,12}}=>2
{{1,2},{3,6},{4,5},{7,12},{8,9},{10,11}}=>3
{{1,2},{3,6},{4,5},{7,12},{8,11},{9,10}}=>4
{{1,2},{3,8},{4,5},{6,7},{9,10},{11,12}}=>2
{{1,2},{3,8},{4,5},{6,7},{9,12},{10,11}}=>3
{{1,2},{3,10},{4,5},{6,7},{8,9},{11,12}}=>3
{{1,2},{3,12},{4,5},{6,7},{8,9},{10,11}}=>4
{{1,2},{3,12},{4,5},{6,7},{8,11},{9,10}}=>5
{{1,2},{3,10},{4,5},{6,9},{7,8},{11,12}}=>4
{{1,2},{3,12},{4,5},{6,9},{7,8},{10,11}}=>5
{{1,2},{3,12},{4,5},{6,11},{7,8},{9,10}}=>6
{{1,2},{3,12},{4,5},{6,11},{7,10},{8,9}}=>7
{{1,2},{3,8},{4,7},{5,6},{9,10},{11,12}}=>3
{{1,2},{3,8},{4,7},{5,6},{9,12},{10,11}}=>4
{{1,2},{3,10},{4,7},{5,6},{8,9},{11,12}}=>4
{{1,2},{3,12},{4,7},{5,6},{8,9},{10,11}}=>5
{{1,2},{3,12},{4,7},{5,6},{8,11},{9,10}}=>6
{{1,2},{3,10},{4,9},{5,6},{7,8},{11,12}}=>5
{{1,2},{3,12},{4,9},{5,6},{7,8},{10,11}}=>6
{{1,2},{3,12},{4,11},{5,6},{7,8},{9,10}}=>7
{{1,2},{3,12},{4,11},{5,6},{7,10},{8,9}}=>8
{{1,2},{3,10},{4,9},{5,8},{6,7},{11,12}}=>6
{{1,2},{3,12},{4,9},{5,8},{6,7},{10,11}}=>7
{{1,2},{3,12},{4,11},{5,8},{6,7},{9,10}}=>8
{{1,2},{3,12},{4,11},{5,10},{6,7},{8,9}}=>9
{{1,2},{3,12},{4,11},{5,10},{6,9},{7,8}}=>10
{{1,4},{2,3},{5,6},{7,8},{9,10},{11,12}}=>1
{{1,4},{2,3},{5,6},{7,8},{9,12},{10,11}}=>2
{{1,4},{2,3},{5,6},{7,10},{8,9},{11,12}}=>2
{{1,4},{2,3},{5,6},{7,12},{8,9},{10,11}}=>3
{{1,4},{2,3},{5,6},{7,12},{8,11},{9,10}}=>4
{{1,4},{2,3},{5,8},{6,7},{9,10},{11,12}}=>2
{{1,4},{2,3},{5,8},{6,7},{9,12},{10,11}}=>3
{{1,4},{2,3},{5,10},{6,7},{8,9},{11,12}}=>3
{{1,4},{2,3},{5,12},{6,7},{8,9},{10,11}}=>4
{{1,4},{2,3},{5,12},{6,7},{8,11},{9,10}}=>5
{{1,4},{2,3},{5,10},{6,9},{7,8},{11,12}}=>4
{{1,4},{2,3},{5,12},{6,9},{7,8},{10,11}}=>5
{{1,4},{2,3},{5,12},{6,11},{7,8},{9,10}}=>6
{{1,4},{2,3},{5,12},{6,11},{7,10},{8,9}}=>7
{{1,6},{2,3},{4,5},{7,8},{9,10},{11,12}}=>2
{{1,6},{2,3},{4,5},{7,8},{9,12},{10,11}}=>3
{{1,6},{2,3},{4,5},{7,10},{8,9},{11,12}}=>3
{{1,6},{2,3},{4,5},{7,12},{8,9},{10,11}}=>4
{{1,6},{2,3},{4,5},{7,12},{8,11},{9,10}}=>5
{{1,8},{2,3},{4,5},{6,7},{9,10},{11,12}}=>3
{{1,8},{2,3},{4,5},{6,7},{9,12},{10,11}}=>4
{{1,10},{2,3},{4,5},{6,7},{8,9},{11,12}}=>4
{{1,12},{2,3},{4,5},{6,7},{8,9},{10,11}}=>5
{{1,12},{2,3},{4,5},{6,7},{8,11},{9,10}}=>6
{{1,10},{2,3},{4,5},{6,9},{7,8},{11,12}}=>5
{{1,12},{2,3},{4,5},{6,9},{7,8},{10,11}}=>6
{{1,12},{2,3},{4,5},{6,11},{7,8},{9,10}}=>7
{{1,12},{2,3},{4,5},{6,11},{7,10},{8,9}}=>8
{{1,8},{2,3},{4,7},{5,6},{9,10},{11,12}}=>4
{{1,8},{2,3},{4,7},{5,6},{9,12},{10,11}}=>5
{{1,10},{2,3},{4,7},{5,6},{8,9},{11,12}}=>5
{{1,12},{2,3},{4,7},{5,6},{8,9},{10,11}}=>6
{{1,12},{2,3},{4,7},{5,6},{8,11},{9,10}}=>7
{{1,10},{2,3},{4,9},{5,6},{7,8},{11,12}}=>6
{{1,12},{2,3},{4,9},{5,6},{7,8},{10,11}}=>7
{{1,12},{2,3},{4,11},{5,6},{7,8},{9,10}}=>8
{{1,12},{2,3},{4,11},{5,6},{7,10},{8,9}}=>9
{{1,10},{2,3},{4,9},{5,8},{6,7},{11,12}}=>7
{{1,12},{2,3},{4,9},{5,8},{6,7},{10,11}}=>8
{{1,12},{2,3},{4,11},{5,8},{6,7},{9,10}}=>9
{{1,12},{2,3},{4,11},{5,10},{6,7},{8,9}}=>10
{{1,12},{2,3},{4,11},{5,10},{6,9},{7,8}}=>11
{{1,6},{2,5},{3,4},{7,8},{9,10},{11,12}}=>3
{{1,6},{2,5},{3,4},{7,8},{9,12},{10,11}}=>4
{{1,6},{2,5},{3,4},{7,10},{8,9},{11,12}}=>4
{{1,6},{2,5},{3,4},{7,12},{8,9},{10,11}}=>5
{{1,6},{2,5},{3,4},{7,12},{8,11},{9,10}}=>6
{{1,8},{2,5},{3,4},{6,7},{9,10},{11,12}}=>4
{{1,8},{2,5},{3,4},{6,7},{9,12},{10,11}}=>5
{{1,10},{2,5},{3,4},{6,7},{8,9},{11,12}}=>5
{{1,12},{2,5},{3,4},{6,7},{8,9},{10,11}}=>6
{{1,12},{2,5},{3,4},{6,7},{8,11},{9,10}}=>7
{{1,10},{2,5},{3,4},{6,9},{7,8},{11,12}}=>6
{{1,12},{2,5},{3,4},{6,9},{7,8},{10,11}}=>7
{{1,12},{2,5},{3,4},{6,11},{7,8},{9,10}}=>8
{{1,12},{2,5},{3,4},{6,11},{7,10},{8,9}}=>9
{{1,8},{2,7},{3,4},{5,6},{9,10},{11,12}}=>5
{{1,8},{2,7},{3,4},{5,6},{9,12},{10,11}}=>6
{{1,10},{2,7},{3,4},{5,6},{8,9},{11,12}}=>6
{{1,12},{2,7},{3,4},{5,6},{8,9},{10,11}}=>7
{{1,12},{2,7},{3,4},{5,6},{8,11},{9,10}}=>8
{{1,10},{2,9},{3,4},{5,6},{7,8},{11,12}}=>7
{{1,12},{2,9},{3,4},{5,6},{7,8},{10,11}}=>8
{{1,12},{2,11},{3,4},{5,6},{7,8},{9,10}}=>9
{{1,12},{2,11},{3,4},{5,6},{7,10},{8,9}}=>10
{{1,10},{2,9},{3,4},{5,8},{6,7},{11,12}}=>8
{{1,12},{2,9},{3,4},{5,8},{6,7},{10,11}}=>9
{{1,12},{2,11},{3,4},{5,8},{6,7},{9,10}}=>10
{{1,12},{2,11},{3,4},{5,10},{6,7},{8,9}}=>11
{{1,12},{2,11},{3,4},{5,10},{6,9},{7,8}}=>12
{{1,8},{2,7},{3,6},{4,5},{9,10},{11,12}}=>6
{{1,8},{2,7},{3,6},{4,5},{9,12},{10,11}}=>7
{{1,10},{2,7},{3,6},{4,5},{8,9},{11,12}}=>7
{{1,12},{2,7},{3,6},{4,5},{8,9},{10,11}}=>8
{{1,12},{2,7},{3,6},{4,5},{8,11},{9,10}}=>9
{{1,10},{2,9},{3,6},{4,5},{7,8},{11,12}}=>8
{{1,12},{2,9},{3,6},{4,5},{7,8},{10,11}}=>9
{{1,12},{2,11},{3,6},{4,5},{7,8},{9,10}}=>10
{{1,12},{2,11},{3,6},{4,5},{7,10},{8,9}}=>11
{{1,10},{2,9},{3,8},{4,5},{6,7},{11,12}}=>9
{{1,12},{2,9},{3,8},{4,5},{6,7},{10,11}}=>10
{{1,12},{2,11},{3,8},{4,5},{6,7},{9,10}}=>11
{{1,12},{2,11},{3,10},{4,5},{6,7},{8,9}}=>12
{{1,12},{2,11},{3,10},{4,5},{6,9},{7,8}}=>13
{{1,10},{2,9},{3,8},{4,7},{5,6},{11,12}}=>10
{{1,12},{2,9},{3,8},{4,7},{5,6},{10,11}}=>11
{{1,12},{2,11},{3,8},{4,7},{5,6},{9,10}}=>12
{{1,12},{2,11},{3,10},{4,7},{5,6},{8,9}}=>13
{{1,12},{2,11},{3,10},{4,9},{5,6},{7,8}}=>14
{{1,12},{2,11},{3,10},{4,9},{5,8},{6,7}}=>15
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Description
The rcs 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 rcs (right-closer-smaller) of $S$ is given by a pair $i > j$ such that $j = \operatorname{max} B_b$ and $i \in B_a$ for $a < b$.
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 rcs (right-closer-smaller) of $S$ is given by a pair $i > j$ such that $j = \operatorname{max} B_b$ and $i \in B_a$ for $a < b$.
References
[1] Steingrimsson, E. Statistics on ordered partitions of sets arXiv:math/0605670
Code
def statistic(S): S = sorted( sorted(B) for B in S ) n = sum( len(B) for B in S ) rcs = 0 for k in range(len(S)): j = S[k][-1] for l in range(k): for i in S[l]: if i > j: rcs += 1 return rcs
Created
May 18, 2016 at 12:26 by Christian Stump
Updated
Dec 28, 2017 at 20:39 by Martin Rubey
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