Identifier
-
Mp00079:
Set partitions
—shape⟶
Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000185: Integer partitions ⟶ ℤ
Values
=>
Cc0009;cc-rep-0
Cc0002;cc-rep-1
Cc0002;cc-rep
{{1}}=>[1]=>[1]=>0
{{1,2}}=>[2]=>[1,1]=>1
{{1},{2}}=>[1,1]=>[2]=>0
{{1,2,3}}=>[3]=>[1,1,1]=>3
{{1,2},{3}}=>[2,1]=>[2,1]=>1
{{1,3},{2}}=>[2,1]=>[2,1]=>1
{{1},{2,3}}=>[2,1]=>[2,1]=>1
{{1},{2},{3}}=>[1,1,1]=>[3]=>0
{{1,2,3,4}}=>[4]=>[1,1,1,1]=>6
{{1,2,3},{4}}=>[3,1]=>[2,1,1]=>3
{{1,2,4},{3}}=>[3,1]=>[2,1,1]=>3
{{1,2},{3,4}}=>[2,2]=>[2,2]=>2
{{1,2},{3},{4}}=>[2,1,1]=>[3,1]=>1
{{1,3,4},{2}}=>[3,1]=>[2,1,1]=>3
{{1,3},{2,4}}=>[2,2]=>[2,2]=>2
{{1,3},{2},{4}}=>[2,1,1]=>[3,1]=>1
{{1,4},{2,3}}=>[2,2]=>[2,2]=>2
{{1},{2,3,4}}=>[3,1]=>[2,1,1]=>3
{{1},{2,3},{4}}=>[2,1,1]=>[3,1]=>1
{{1,4},{2},{3}}=>[2,1,1]=>[3,1]=>1
{{1},{2,4},{3}}=>[2,1,1]=>[3,1]=>1
{{1},{2},{3,4}}=>[2,1,1]=>[3,1]=>1
{{1},{2},{3},{4}}=>[1,1,1,1]=>[4]=>0
{{1,2,3,4,5}}=>[5]=>[1,1,1,1,1]=>10
{{1,2,3,4},{5}}=>[4,1]=>[2,1,1,1]=>6
{{1,2,3,5},{4}}=>[4,1]=>[2,1,1,1]=>6
{{1,2,3},{4,5}}=>[3,2]=>[2,2,1]=>4
{{1,2,3},{4},{5}}=>[3,1,1]=>[3,1,1]=>3
{{1,2,4,5},{3}}=>[4,1]=>[2,1,1,1]=>6
{{1,2,4},{3,5}}=>[3,2]=>[2,2,1]=>4
{{1,2,4},{3},{5}}=>[3,1,1]=>[3,1,1]=>3
{{1,2,5},{3,4}}=>[3,2]=>[2,2,1]=>4
{{1,2},{3,4,5}}=>[3,2]=>[2,2,1]=>4
{{1,2},{3,4},{5}}=>[2,2,1]=>[3,2]=>2
{{1,2,5},{3},{4}}=>[3,1,1]=>[3,1,1]=>3
{{1,2},{3,5},{4}}=>[2,2,1]=>[3,2]=>2
{{1,2},{3},{4,5}}=>[2,2,1]=>[3,2]=>2
{{1,2},{3},{4},{5}}=>[2,1,1,1]=>[4,1]=>1
{{1,3,4,5},{2}}=>[4,1]=>[2,1,1,1]=>6
{{1,3,4},{2,5}}=>[3,2]=>[2,2,1]=>4
{{1,3,4},{2},{5}}=>[3,1,1]=>[3,1,1]=>3
{{1,3,5},{2,4}}=>[3,2]=>[2,2,1]=>4
{{1,3},{2,4,5}}=>[3,2]=>[2,2,1]=>4
{{1,3},{2,4},{5}}=>[2,2,1]=>[3,2]=>2
{{1,3,5},{2},{4}}=>[3,1,1]=>[3,1,1]=>3
{{1,3},{2,5},{4}}=>[2,2,1]=>[3,2]=>2
{{1,3},{2},{4,5}}=>[2,2,1]=>[3,2]=>2
{{1,3},{2},{4},{5}}=>[2,1,1,1]=>[4,1]=>1
{{1,4,5},{2,3}}=>[3,2]=>[2,2,1]=>4
{{1,4},{2,3,5}}=>[3,2]=>[2,2,1]=>4
{{1,4},{2,3},{5}}=>[2,2,1]=>[3,2]=>2
{{1,5},{2,3,4}}=>[3,2]=>[2,2,1]=>4
{{1},{2,3,4,5}}=>[4,1]=>[2,1,1,1]=>6
{{1},{2,3,4},{5}}=>[3,1,1]=>[3,1,1]=>3
{{1,5},{2,3},{4}}=>[2,2,1]=>[3,2]=>2
{{1},{2,3,5},{4}}=>[3,1,1]=>[3,1,1]=>3
{{1},{2,3},{4,5}}=>[2,2,1]=>[3,2]=>2
{{1},{2,3},{4},{5}}=>[2,1,1,1]=>[4,1]=>1
{{1,4,5},{2},{3}}=>[3,1,1]=>[3,1,1]=>3
{{1,4},{2,5},{3}}=>[2,2,1]=>[3,2]=>2
{{1,4},{2},{3,5}}=>[2,2,1]=>[3,2]=>2
{{1,4},{2},{3},{5}}=>[2,1,1,1]=>[4,1]=>1
{{1,5},{2,4},{3}}=>[2,2,1]=>[3,2]=>2
{{1},{2,4,5},{3}}=>[3,1,1]=>[3,1,1]=>3
{{1},{2,4},{3,5}}=>[2,2,1]=>[3,2]=>2
{{1},{2,4},{3},{5}}=>[2,1,1,1]=>[4,1]=>1
{{1,5},{2},{3,4}}=>[2,2,1]=>[3,2]=>2
{{1},{2,5},{3,4}}=>[2,2,1]=>[3,2]=>2
{{1},{2},{3,4,5}}=>[3,1,1]=>[3,1,1]=>3
{{1},{2},{3,4},{5}}=>[2,1,1,1]=>[4,1]=>1
{{1,5},{2},{3},{4}}=>[2,1,1,1]=>[4,1]=>1
{{1},{2,5},{3},{4}}=>[2,1,1,1]=>[4,1]=>1
{{1},{2},{3,5},{4}}=>[2,1,1,1]=>[4,1]=>1
{{1},{2},{3},{4,5}}=>[2,1,1,1]=>[4,1]=>1
{{1},{2},{3},{4},{5}}=>[1,1,1,1,1]=>[5]=>0
{{1,2,3,4,5,6}}=>[6]=>[1,1,1,1,1,1]=>15
{{1,2,3,4,5},{6}}=>[5,1]=>[2,1,1,1,1]=>10
{{1,2,3,4,6},{5}}=>[5,1]=>[2,1,1,1,1]=>10
{{1,2,3,4},{5,6}}=>[4,2]=>[2,2,1,1]=>7
{{1,2,3,4},{5},{6}}=>[4,1,1]=>[3,1,1,1]=>6
{{1,2,3,5,6},{4}}=>[5,1]=>[2,1,1,1,1]=>10
{{1,2,3,5},{4,6}}=>[4,2]=>[2,2,1,1]=>7
{{1,2,3,5},{4},{6}}=>[4,1,1]=>[3,1,1,1]=>6
{{1,2,3,6},{4,5}}=>[4,2]=>[2,2,1,1]=>7
{{1,2,3},{4,5,6}}=>[3,3]=>[2,2,2]=>6
{{1,2,3},{4,5},{6}}=>[3,2,1]=>[3,2,1]=>4
{{1,2,3,6},{4},{5}}=>[4,1,1]=>[3,1,1,1]=>6
{{1,2,3},{4,6},{5}}=>[3,2,1]=>[3,2,1]=>4
{{1,2,3},{4},{5,6}}=>[3,2,1]=>[3,2,1]=>4
{{1,2,3},{4},{5},{6}}=>[3,1,1,1]=>[4,1,1]=>3
{{1,2,4,5,6},{3}}=>[5,1]=>[2,1,1,1,1]=>10
{{1,2,4,5},{3,6}}=>[4,2]=>[2,2,1,1]=>7
{{1,2,4,5},{3},{6}}=>[4,1,1]=>[3,1,1,1]=>6
{{1,2,4,6},{3,5}}=>[4,2]=>[2,2,1,1]=>7
{{1,2,4},{3,5,6}}=>[3,3]=>[2,2,2]=>6
{{1,2,4},{3,5},{6}}=>[3,2,1]=>[3,2,1]=>4
{{1,2,4,6},{3},{5}}=>[4,1,1]=>[3,1,1,1]=>6
{{1,2,4},{3,6},{5}}=>[3,2,1]=>[3,2,1]=>4
{{1,2,4},{3},{5,6}}=>[3,2,1]=>[3,2,1]=>4
{{1,2,4},{3},{5},{6}}=>[3,1,1,1]=>[4,1,1]=>3
{{1,2,5,6},{3,4}}=>[4,2]=>[2,2,1,1]=>7
{{1,2,5},{3,4,6}}=>[3,3]=>[2,2,2]=>6
{{1,2,5},{3,4},{6}}=>[3,2,1]=>[3,2,1]=>4
{{1,2,6},{3,4,5}}=>[3,3]=>[2,2,2]=>6
{{1,2},{3,4,5,6}}=>[4,2]=>[2,2,1,1]=>7
{{1,2},{3,4,5},{6}}=>[3,2,1]=>[3,2,1]=>4
{{1,2,6},{3,4},{5}}=>[3,2,1]=>[3,2,1]=>4
{{1,2},{3,4,6},{5}}=>[3,2,1]=>[3,2,1]=>4
{{1,2},{3,4},{5,6}}=>[2,2,2]=>[3,3]=>3
{{1,2},{3,4},{5},{6}}=>[2,2,1,1]=>[4,2]=>2
{{1,2,5,6},{3},{4}}=>[4,1,1]=>[3,1,1,1]=>6
{{1,2,5},{3,6},{4}}=>[3,2,1]=>[3,2,1]=>4
{{1,2,5},{3},{4,6}}=>[3,2,1]=>[3,2,1]=>4
{{1,2,5},{3},{4},{6}}=>[3,1,1,1]=>[4,1,1]=>3
{{1,2,6},{3,5},{4}}=>[3,2,1]=>[3,2,1]=>4
{{1,2},{3,5,6},{4}}=>[3,2,1]=>[3,2,1]=>4
{{1,2},{3,5},{4,6}}=>[2,2,2]=>[3,3]=>3
{{1,2},{3,5},{4},{6}}=>[2,2,1,1]=>[4,2]=>2
{{1,2,6},{3},{4,5}}=>[3,2,1]=>[3,2,1]=>4
{{1,2},{3,6},{4,5}}=>[2,2,2]=>[3,3]=>3
{{1,2},{3},{4,5,6}}=>[3,2,1]=>[3,2,1]=>4
{{1,2},{3},{4,5},{6}}=>[2,2,1,1]=>[4,2]=>2
{{1,2,6},{3},{4},{5}}=>[3,1,1,1]=>[4,1,1]=>3
{{1,2},{3,6},{4},{5}}=>[2,2,1,1]=>[4,2]=>2
{{1,2},{3},{4,6},{5}}=>[2,2,1,1]=>[4,2]=>2
{{1,2},{3},{4},{5,6}}=>[2,2,1,1]=>[4,2]=>2
{{1,2},{3},{4},{5},{6}}=>[2,1,1,1,1]=>[5,1]=>1
{{1,3,4,5,6},{2}}=>[5,1]=>[2,1,1,1,1]=>10
{{1,3,4,5},{2,6}}=>[4,2]=>[2,2,1,1]=>7
{{1,3,4,5},{2},{6}}=>[4,1,1]=>[3,1,1,1]=>6
{{1,3,4,6},{2,5}}=>[4,2]=>[2,2,1,1]=>7
{{1,3,4},{2,5,6}}=>[3,3]=>[2,2,2]=>6
{{1,3,4},{2,5},{6}}=>[3,2,1]=>[3,2,1]=>4
{{1,3,4,6},{2},{5}}=>[4,1,1]=>[3,1,1,1]=>6
{{1,3,4},{2,6},{5}}=>[3,2,1]=>[3,2,1]=>4
{{1,3,4},{2},{5,6}}=>[3,2,1]=>[3,2,1]=>4
{{1,3,4},{2},{5},{6}}=>[3,1,1,1]=>[4,1,1]=>3
{{1,3,5,6},{2,4}}=>[4,2]=>[2,2,1,1]=>7
{{1,3,5},{2,4,6}}=>[3,3]=>[2,2,2]=>6
{{1,3,5},{2,4},{6}}=>[3,2,1]=>[3,2,1]=>4
{{1,3,6},{2,4,5}}=>[3,3]=>[2,2,2]=>6
{{1,3},{2,4,5,6}}=>[4,2]=>[2,2,1,1]=>7
{{1,3},{2,4,5},{6}}=>[3,2,1]=>[3,2,1]=>4
{{1,3,6},{2,4},{5}}=>[3,2,1]=>[3,2,1]=>4
{{1,3},{2,4,6},{5}}=>[3,2,1]=>[3,2,1]=>4
{{1,3},{2,4},{5,6}}=>[2,2,2]=>[3,3]=>3
{{1,3},{2,4},{5},{6}}=>[2,2,1,1]=>[4,2]=>2
{{1,3,5,6},{2},{4}}=>[4,1,1]=>[3,1,1,1]=>6
{{1,3,5},{2,6},{4}}=>[3,2,1]=>[3,2,1]=>4
{{1,3,5},{2},{4,6}}=>[3,2,1]=>[3,2,1]=>4
{{1,3,5},{2},{4},{6}}=>[3,1,1,1]=>[4,1,1]=>3
{{1,3,6},{2,5},{4}}=>[3,2,1]=>[3,2,1]=>4
{{1,3},{2,5,6},{4}}=>[3,2,1]=>[3,2,1]=>4
{{1,3},{2,5},{4,6}}=>[2,2,2]=>[3,3]=>3
{{1,3},{2,5},{4},{6}}=>[2,2,1,1]=>[4,2]=>2
{{1,3,6},{2},{4,5}}=>[3,2,1]=>[3,2,1]=>4
{{1,3},{2,6},{4,5}}=>[2,2,2]=>[3,3]=>3
{{1,3},{2},{4,5,6}}=>[3,2,1]=>[3,2,1]=>4
{{1,3},{2},{4,5},{6}}=>[2,2,1,1]=>[4,2]=>2
{{1,3,6},{2},{4},{5}}=>[3,1,1,1]=>[4,1,1]=>3
{{1,3},{2,6},{4},{5}}=>[2,2,1,1]=>[4,2]=>2
{{1,3},{2},{4,6},{5}}=>[2,2,1,1]=>[4,2]=>2
{{1,3},{2},{4},{5,6}}=>[2,2,1,1]=>[4,2]=>2
{{1,3},{2},{4},{5},{6}}=>[2,1,1,1,1]=>[5,1]=>1
{{1,4,5,6},{2,3}}=>[4,2]=>[2,2,1,1]=>7
{{1,4,5},{2,3,6}}=>[3,3]=>[2,2,2]=>6
{{1,4,5},{2,3},{6}}=>[3,2,1]=>[3,2,1]=>4
{{1,4,6},{2,3,5}}=>[3,3]=>[2,2,2]=>6
{{1,4},{2,3,5,6}}=>[4,2]=>[2,2,1,1]=>7
{{1,4},{2,3,5},{6}}=>[3,2,1]=>[3,2,1]=>4
{{1,4,6},{2,3},{5}}=>[3,2,1]=>[3,2,1]=>4
{{1,4},{2,3,6},{5}}=>[3,2,1]=>[3,2,1]=>4
{{1,4},{2,3},{5,6}}=>[2,2,2]=>[3,3]=>3
{{1,4},{2,3},{5},{6}}=>[2,2,1,1]=>[4,2]=>2
{{1,5,6},{2,3,4}}=>[3,3]=>[2,2,2]=>6
{{1,5},{2,3,4,6}}=>[4,2]=>[2,2,1,1]=>7
{{1,5},{2,3,4},{6}}=>[3,2,1]=>[3,2,1]=>4
{{1,6},{2,3,4,5}}=>[4,2]=>[2,2,1,1]=>7
{{1},{2,3,4,5,6}}=>[5,1]=>[2,1,1,1,1]=>10
{{1},{2,3,4,5},{6}}=>[4,1,1]=>[3,1,1,1]=>6
{{1,6},{2,3,4},{5}}=>[3,2,1]=>[3,2,1]=>4
{{1},{2,3,4,6},{5}}=>[4,1,1]=>[3,1,1,1]=>6
{{1},{2,3,4},{5,6}}=>[3,2,1]=>[3,2,1]=>4
{{1},{2,3,4},{5},{6}}=>[3,1,1,1]=>[4,1,1]=>3
{{1,5,6},{2,3},{4}}=>[3,2,1]=>[3,2,1]=>4
{{1,5},{2,3,6},{4}}=>[3,2,1]=>[3,2,1]=>4
{{1,5},{2,3},{4,6}}=>[2,2,2]=>[3,3]=>3
{{1,5},{2,3},{4},{6}}=>[2,2,1,1]=>[4,2]=>2
{{1,6},{2,3,5},{4}}=>[3,2,1]=>[3,2,1]=>4
{{1},{2,3,5,6},{4}}=>[4,1,1]=>[3,1,1,1]=>6
{{1},{2,3,5},{4,6}}=>[3,2,1]=>[3,2,1]=>4
{{1},{2,3,5},{4},{6}}=>[3,1,1,1]=>[4,1,1]=>3
{{1,6},{2,3},{4,5}}=>[2,2,2]=>[3,3]=>3
{{1},{2,3,6},{4,5}}=>[3,2,1]=>[3,2,1]=>4
{{1},{2,3},{4,5,6}}=>[3,2,1]=>[3,2,1]=>4
{{1},{2,3},{4,5},{6}}=>[2,2,1,1]=>[4,2]=>2
{{1,6},{2,3},{4},{5}}=>[2,2,1,1]=>[4,2]=>2
{{1},{2,3,6},{4},{5}}=>[3,1,1,1]=>[4,1,1]=>3
{{1},{2,3},{4,6},{5}}=>[2,2,1,1]=>[4,2]=>2
{{1},{2,3},{4},{5,6}}=>[2,2,1,1]=>[4,2]=>2
{{1},{2,3},{4},{5},{6}}=>[2,1,1,1,1]=>[5,1]=>1
{{1,4,5,6},{2},{3}}=>[4,1,1]=>[3,1,1,1]=>6
{{1,4,5},{2,6},{3}}=>[3,2,1]=>[3,2,1]=>4
{{1,4,5},{2},{3,6}}=>[3,2,1]=>[3,2,1]=>4
{{1,4,5},{2},{3},{6}}=>[3,1,1,1]=>[4,1,1]=>3
{{1,4,6},{2,5},{3}}=>[3,2,1]=>[3,2,1]=>4
{{1,4},{2,5,6},{3}}=>[3,2,1]=>[3,2,1]=>4
{{1,4},{2,5},{3,6}}=>[2,2,2]=>[3,3]=>3
{{1,4},{2,5},{3},{6}}=>[2,2,1,1]=>[4,2]=>2
{{1,4,6},{2},{3,5}}=>[3,2,1]=>[3,2,1]=>4
{{1,4},{2,6},{3,5}}=>[2,2,2]=>[3,3]=>3
{{1,4},{2},{3,5,6}}=>[3,2,1]=>[3,2,1]=>4
{{1,4},{2},{3,5},{6}}=>[2,2,1,1]=>[4,2]=>2
{{1,4,6},{2},{3},{5}}=>[3,1,1,1]=>[4,1,1]=>3
{{1,4},{2,6},{3},{5}}=>[2,2,1,1]=>[4,2]=>2
{{1,4},{2},{3,6},{5}}=>[2,2,1,1]=>[4,2]=>2
{{1,4},{2},{3},{5,6}}=>[2,2,1,1]=>[4,2]=>2
{{1,4},{2},{3},{5},{6}}=>[2,1,1,1,1]=>[5,1]=>1
{{1,5,6},{2,4},{3}}=>[3,2,1]=>[3,2,1]=>4
{{1,5},{2,4,6},{3}}=>[3,2,1]=>[3,2,1]=>4
{{1,5},{2,4},{3,6}}=>[2,2,2]=>[3,3]=>3
{{1,5},{2,4},{3},{6}}=>[2,2,1,1]=>[4,2]=>2
{{1,6},{2,4,5},{3}}=>[3,2,1]=>[3,2,1]=>4
{{1},{2,4,5,6},{3}}=>[4,1,1]=>[3,1,1,1]=>6
{{1},{2,4,5},{3,6}}=>[3,2,1]=>[3,2,1]=>4
{{1},{2,4,5},{3},{6}}=>[3,1,1,1]=>[4,1,1]=>3
{{1,6},{2,4},{3,5}}=>[2,2,2]=>[3,3]=>3
{{1},{2,4,6},{3,5}}=>[3,2,1]=>[3,2,1]=>4
{{1},{2,4},{3,5,6}}=>[3,2,1]=>[3,2,1]=>4
{{1},{2,4},{3,5},{6}}=>[2,2,1,1]=>[4,2]=>2
{{1,6},{2,4},{3},{5}}=>[2,2,1,1]=>[4,2]=>2
{{1},{2,4,6},{3},{5}}=>[3,1,1,1]=>[4,1,1]=>3
{{1},{2,4},{3,6},{5}}=>[2,2,1,1]=>[4,2]=>2
{{1},{2,4},{3},{5,6}}=>[2,2,1,1]=>[4,2]=>2
{{1},{2,4},{3},{5},{6}}=>[2,1,1,1,1]=>[5,1]=>1
{{1,5,6},{2},{3,4}}=>[3,2,1]=>[3,2,1]=>4
{{1,5},{2,6},{3,4}}=>[2,2,2]=>[3,3]=>3
{{1,5},{2},{3,4,6}}=>[3,2,1]=>[3,2,1]=>4
{{1,5},{2},{3,4},{6}}=>[2,2,1,1]=>[4,2]=>2
{{1,6},{2,5},{3,4}}=>[2,2,2]=>[3,3]=>3
{{1},{2,5,6},{3,4}}=>[3,2,1]=>[3,2,1]=>4
{{1},{2,5},{3,4,6}}=>[3,2,1]=>[3,2,1]=>4
{{1},{2,5},{3,4},{6}}=>[2,2,1,1]=>[4,2]=>2
{{1,6},{2},{3,4,5}}=>[3,2,1]=>[3,2,1]=>4
{{1},{2,6},{3,4,5}}=>[3,2,1]=>[3,2,1]=>4
{{1},{2},{3,4,5,6}}=>[4,1,1]=>[3,1,1,1]=>6
{{1},{2},{3,4,5},{6}}=>[3,1,1,1]=>[4,1,1]=>3
{{1,6},{2},{3,4},{5}}=>[2,2,1,1]=>[4,2]=>2
{{1},{2,6},{3,4},{5}}=>[2,2,1,1]=>[4,2]=>2
{{1},{2},{3,4,6},{5}}=>[3,1,1,1]=>[4,1,1]=>3
{{1},{2},{3,4},{5,6}}=>[2,2,1,1]=>[4,2]=>2
{{1},{2},{3,4},{5},{6}}=>[2,1,1,1,1]=>[5,1]=>1
{{1,5,6},{2},{3},{4}}=>[3,1,1,1]=>[4,1,1]=>3
{{1,5},{2,6},{3},{4}}=>[2,2,1,1]=>[4,2]=>2
{{1,5},{2},{3,6},{4}}=>[2,2,1,1]=>[4,2]=>2
{{1,5},{2},{3},{4,6}}=>[2,2,1,1]=>[4,2]=>2
{{1,5},{2},{3},{4},{6}}=>[2,1,1,1,1]=>[5,1]=>1
{{1,6},{2,5},{3},{4}}=>[2,2,1,1]=>[4,2]=>2
{{1},{2,5,6},{3},{4}}=>[3,1,1,1]=>[4,1,1]=>3
{{1},{2,5},{3,6},{4}}=>[2,2,1,1]=>[4,2]=>2
{{1},{2,5},{3},{4,6}}=>[2,2,1,1]=>[4,2]=>2
{{1},{2,5},{3},{4},{6}}=>[2,1,1,1,1]=>[5,1]=>1
{{1,6},{2},{3,5},{4}}=>[2,2,1,1]=>[4,2]=>2
{{1},{2,6},{3,5},{4}}=>[2,2,1,1]=>[4,2]=>2
{{1},{2},{3,5,6},{4}}=>[3,1,1,1]=>[4,1,1]=>3
{{1},{2},{3,5},{4,6}}=>[2,2,1,1]=>[4,2]=>2
{{1},{2},{3,5},{4},{6}}=>[2,1,1,1,1]=>[5,1]=>1
{{1,6},{2},{3},{4,5}}=>[2,2,1,1]=>[4,2]=>2
{{1},{2,6},{3},{4,5}}=>[2,2,1,1]=>[4,2]=>2
{{1},{2},{3,6},{4,5}}=>[2,2,1,1]=>[4,2]=>2
{{1},{2},{3},{4,5,6}}=>[3,1,1,1]=>[4,1,1]=>3
{{1},{2},{3},{4,5},{6}}=>[2,1,1,1,1]=>[5,1]=>1
{{1,6},{2},{3},{4},{5}}=>[2,1,1,1,1]=>[5,1]=>1
{{1},{2,6},{3},{4},{5}}=>[2,1,1,1,1]=>[5,1]=>1
{{1},{2},{3,6},{4},{5}}=>[2,1,1,1,1]=>[5,1]=>1
{{1},{2},{3},{4,6},{5}}=>[2,1,1,1,1]=>[5,1]=>1
{{1},{2},{3},{4},{5,6}}=>[2,1,1,1,1]=>[5,1]=>1
{{1},{2},{3},{4},{5},{6}}=>[1,1,1,1,1,1]=>[6]=>0
{{1,2,3,4,5,6,7}}=>[7]=>[1,1,1,1,1,1,1]=>21
{{1,2,3,4,5,6},{7}}=>[6,1]=>[2,1,1,1,1,1]=>15
{{1,2,3,4,5,7},{6}}=>[6,1]=>[2,1,1,1,1,1]=>15
{{1,2,3,4,5},{6,7}}=>[5,2]=>[2,2,1,1,1]=>11
{{1,2,3,4,5},{6},{7}}=>[5,1,1]=>[3,1,1,1,1]=>10
{{1,2,3,4,6,7},{5}}=>[6,1]=>[2,1,1,1,1,1]=>15
{{1,2,3,4,6},{5,7}}=>[5,2]=>[2,2,1,1,1]=>11
{{1,2,3,4,6},{5},{7}}=>[5,1,1]=>[3,1,1,1,1]=>10
{{1,2,3,4,7},{5,6}}=>[5,2]=>[2,2,1,1,1]=>11
{{1,2,3,4},{5,6,7}}=>[4,3]=>[2,2,2,1]=>9
{{1,2,3,4},{5,6},{7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,3,4,7},{5},{6}}=>[5,1,1]=>[3,1,1,1,1]=>10
{{1,2,3,4},{5,7},{6}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,3,4},{5},{6,7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,3,4},{5},{6},{7}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1,2,3,5,6,7},{4}}=>[6,1]=>[2,1,1,1,1,1]=>15
{{1,2,3,5,6},{4,7}}=>[5,2]=>[2,2,1,1,1]=>11
{{1,2,3,5,6},{4},{7}}=>[5,1,1]=>[3,1,1,1,1]=>10
{{1,2,3,5,7},{4,6}}=>[5,2]=>[2,2,1,1,1]=>11
{{1,2,3,5},{4,6,7}}=>[4,3]=>[2,2,2,1]=>9
{{1,2,3,5},{4,6},{7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,3,5,7},{4},{6}}=>[5,1,1]=>[3,1,1,1,1]=>10
{{1,2,3,5},{4,7},{6}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,3,5},{4},{6,7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,3,5},{4},{6},{7}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1,2,3,6,7},{4,5}}=>[5,2]=>[2,2,1,1,1]=>11
{{1,2,3,6},{4,5,7}}=>[4,3]=>[2,2,2,1]=>9
{{1,2,3,6},{4,5},{7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,3,7},{4,5,6}}=>[4,3]=>[2,2,2,1]=>9
{{1,2,3},{4,5,6,7}}=>[4,3]=>[2,2,2,1]=>9
{{1,2,3},{4,5,6},{7}}=>[3,3,1]=>[3,2,2]=>6
{{1,2,3,7},{4,5},{6}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,3},{4,5,7},{6}}=>[3,3,1]=>[3,2,2]=>6
{{1,2,3},{4,5},{6,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,2,3},{4,5},{6},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2,3,6,7},{4},{5}}=>[5,1,1]=>[3,1,1,1,1]=>10
{{1,2,3,6},{4,7},{5}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,3,6},{4},{5,7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,3,6},{4},{5},{7}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1,2,3,7},{4,6},{5}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,3},{4,6,7},{5}}=>[3,3,1]=>[3,2,2]=>6
{{1,2,3},{4,6},{5,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,2,3},{4,6},{5},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2,3,7},{4},{5,6}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,3},{4,7},{5,6}}=>[3,2,2]=>[3,3,1]=>5
{{1,2,3},{4},{5,6,7}}=>[3,3,1]=>[3,2,2]=>6
{{1,2,3},{4},{5,6},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2,3,7},{4},{5},{6}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1,2,3},{4,7},{5},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2,3},{4},{5,7},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2,3},{4},{5},{6,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2,3},{4},{5},{6},{7}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1,2,4,5,6,7},{3}}=>[6,1]=>[2,1,1,1,1,1]=>15
{{1,2,4,5,6},{3,7}}=>[5,2]=>[2,2,1,1,1]=>11
{{1,2,4,5,6},{3},{7}}=>[5,1,1]=>[3,1,1,1,1]=>10
{{1,2,4,5,7},{3,6}}=>[5,2]=>[2,2,1,1,1]=>11
{{1,2,4,5},{3,6,7}}=>[4,3]=>[2,2,2,1]=>9
{{1,2,4,5},{3,6},{7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,4,5,7},{3},{6}}=>[5,1,1]=>[3,1,1,1,1]=>10
{{1,2,4,5},{3,7},{6}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,4,5},{3},{6,7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,4,5},{3},{6},{7}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1,2,4,6,7},{3,5}}=>[5,2]=>[2,2,1,1,1]=>11
{{1,2,4,6},{3,5,7}}=>[4,3]=>[2,2,2,1]=>9
{{1,2,4,6},{3,5},{7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,4,7},{3,5,6}}=>[4,3]=>[2,2,2,1]=>9
{{1,2,4},{3,5,6,7}}=>[4,3]=>[2,2,2,1]=>9
{{1,2,4},{3,5,6},{7}}=>[3,3,1]=>[3,2,2]=>6
{{1,2,4,7},{3,5},{6}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,4},{3,5,7},{6}}=>[3,3,1]=>[3,2,2]=>6
{{1,2,4},{3,5},{6,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,2,4},{3,5},{6},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2,4,6,7},{3},{5}}=>[5,1,1]=>[3,1,1,1,1]=>10
{{1,2,4,6},{3,7},{5}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,4,6},{3},{5,7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,4,6},{3},{5},{7}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1,2,4,7},{3,6},{5}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,4},{3,6,7},{5}}=>[3,3,1]=>[3,2,2]=>6
{{1,2,4},{3,6},{5,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,2,4},{3,6},{5},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2,4,7},{3},{5,6}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,4},{3,7},{5,6}}=>[3,2,2]=>[3,3,1]=>5
{{1,2,4},{3},{5,6,7}}=>[3,3,1]=>[3,2,2]=>6
{{1,2,4},{3},{5,6},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2,4,7},{3},{5},{6}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1,2,4},{3,7},{5},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2,4},{3},{5,7},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2,4},{3},{5},{6,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2,4},{3},{5},{6},{7}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1,2,5,6,7},{3,4}}=>[5,2]=>[2,2,1,1,1]=>11
{{1,2,5,6},{3,4,7}}=>[4,3]=>[2,2,2,1]=>9
{{1,2,5,6},{3,4},{7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,5,7},{3,4,6}}=>[4,3]=>[2,2,2,1]=>9
{{1,2,5},{3,4,6,7}}=>[4,3]=>[2,2,2,1]=>9
{{1,2,5},{3,4,6},{7}}=>[3,3,1]=>[3,2,2]=>6
{{1,2,5,7},{3,4},{6}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,5},{3,4,7},{6}}=>[3,3,1]=>[3,2,2]=>6
{{1,2,5},{3,4},{6,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,2,5},{3,4},{6},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2,6,7},{3,4,5}}=>[4,3]=>[2,2,2,1]=>9
{{1,2,6},{3,4,5,7}}=>[4,3]=>[2,2,2,1]=>9
{{1,2,6},{3,4,5},{7}}=>[3,3,1]=>[3,2,2]=>6
{{1,2,7},{3,4,5,6}}=>[4,3]=>[2,2,2,1]=>9
{{1,2},{3,4,5,6,7}}=>[5,2]=>[2,2,1,1,1]=>11
{{1,2},{3,4,5,6},{7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,7},{3,4,5},{6}}=>[3,3,1]=>[3,2,2]=>6
{{1,2},{3,4,5,7},{6}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2},{3,4,5},{6,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,2},{3,4,5},{6},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2,6,7},{3,4},{5}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,6},{3,4,7},{5}}=>[3,3,1]=>[3,2,2]=>6
{{1,2,6},{3,4},{5,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,2,6},{3,4},{5},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2,7},{3,4,6},{5}}=>[3,3,1]=>[3,2,2]=>6
{{1,2},{3,4,6,7},{5}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2},{3,4,6},{5,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,2},{3,4,6},{5},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2,7},{3,4},{5,6}}=>[3,2,2]=>[3,3,1]=>5
{{1,2},{3,4,7},{5,6}}=>[3,2,2]=>[3,3,1]=>5
{{1,2},{3,4},{5,6,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,2},{3,4},{5,6},{7}}=>[2,2,2,1]=>[4,3]=>3
{{1,2,7},{3,4},{5},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2},{3,4,7},{5},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2},{3,4},{5,7},{6}}=>[2,2,2,1]=>[4,3]=>3
{{1,2},{3,4},{5},{6,7}}=>[2,2,2,1]=>[4,3]=>3
{{1,2},{3,4},{5},{6},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,2,5,6,7},{3},{4}}=>[5,1,1]=>[3,1,1,1,1]=>10
{{1,2,5,6},{3,7},{4}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,5,6},{3},{4,7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,5,6},{3},{4},{7}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1,2,5,7},{3,6},{4}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,5},{3,6,7},{4}}=>[3,3,1]=>[3,2,2]=>6
{{1,2,5},{3,6},{4,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,2,5},{3,6},{4},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2,5,7},{3},{4,6}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,5},{3,7},{4,6}}=>[3,2,2]=>[3,3,1]=>5
{{1,2,5},{3},{4,6,7}}=>[3,3,1]=>[3,2,2]=>6
{{1,2,5},{3},{4,6},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2,5,7},{3},{4},{6}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1,2,5},{3,7},{4},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2,5},{3},{4,7},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2,5},{3},{4},{6,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2,5},{3},{4},{6},{7}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1,2,6,7},{3,5},{4}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,6},{3,5,7},{4}}=>[3,3,1]=>[3,2,2]=>6
{{1,2,6},{3,5},{4,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,2,6},{3,5},{4},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2,7},{3,5,6},{4}}=>[3,3,1]=>[3,2,2]=>6
{{1,2},{3,5,6,7},{4}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2},{3,5,6},{4,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,2},{3,5,6},{4},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2,7},{3,5},{4,6}}=>[3,2,2]=>[3,3,1]=>5
{{1,2},{3,5,7},{4,6}}=>[3,2,2]=>[3,3,1]=>5
{{1,2},{3,5},{4,6,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,2},{3,5},{4,6},{7}}=>[2,2,2,1]=>[4,3]=>3
{{1,2,7},{3,5},{4},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2},{3,5,7},{4},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2},{3,5},{4,7},{6}}=>[2,2,2,1]=>[4,3]=>3
{{1,2},{3,5},{4},{6,7}}=>[2,2,2,1]=>[4,3]=>3
{{1,2},{3,5},{4},{6},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,2,6,7},{3},{4,5}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2,6},{3,7},{4,5}}=>[3,2,2]=>[3,3,1]=>5
{{1,2,6},{3},{4,5,7}}=>[3,3,1]=>[3,2,2]=>6
{{1,2,6},{3},{4,5},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2,7},{3,6},{4,5}}=>[3,2,2]=>[3,3,1]=>5
{{1,2},{3,6,7},{4,5}}=>[3,2,2]=>[3,3,1]=>5
{{1,2},{3,6},{4,5,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,2},{3,6},{4,5},{7}}=>[2,2,2,1]=>[4,3]=>3
{{1,2,7},{3},{4,5,6}}=>[3,3,1]=>[3,2,2]=>6
{{1,2},{3,7},{4,5,6}}=>[3,2,2]=>[3,3,1]=>5
{{1,2},{3},{4,5,6,7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,2},{3},{4,5,6},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2,7},{3},{4,5},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2},{3,7},{4,5},{6}}=>[2,2,2,1]=>[4,3]=>3
{{1,2},{3},{4,5,7},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2},{3},{4,5},{6,7}}=>[2,2,2,1]=>[4,3]=>3
{{1,2},{3},{4,5},{6},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,2,6,7},{3},{4},{5}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1,2,6},{3,7},{4},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2,6},{3},{4,7},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2,6},{3},{4},{5,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2,6},{3},{4},{5},{7}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1,2,7},{3,6},{4},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2},{3,6,7},{4},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2},{3,6},{4,7},{5}}=>[2,2,2,1]=>[4,3]=>3
{{1,2},{3,6},{4},{5,7}}=>[2,2,2,1]=>[4,3]=>3
{{1,2},{3,6},{4},{5},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,2,7},{3},{4,6},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2},{3,7},{4,6},{5}}=>[2,2,2,1]=>[4,3]=>3
{{1,2},{3},{4,6,7},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2},{3},{4,6},{5,7}}=>[2,2,2,1]=>[4,3]=>3
{{1,2},{3},{4,6},{5},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,2,7},{3},{4},{5,6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2},{3,7},{4},{5,6}}=>[2,2,2,1]=>[4,3]=>3
{{1,2},{3},{4,7},{5,6}}=>[2,2,2,1]=>[4,3]=>3
{{1,2},{3},{4},{5,6,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,2},{3},{4},{5,6},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,2,7},{3},{4},{5},{6}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1,2},{3,7},{4},{5},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,2},{3},{4,7},{5},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,2},{3},{4},{5,7},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,2},{3},{4},{5},{6,7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,2},{3},{4},{5},{6},{7}}=>[2,1,1,1,1,1]=>[6,1]=>1
{{1,3,4,5,6,7},{2}}=>[6,1]=>[2,1,1,1,1,1]=>15
{{1,3,4,5,6},{2,7}}=>[5,2]=>[2,2,1,1,1]=>11
{{1,3,4,5,6},{2},{7}}=>[5,1,1]=>[3,1,1,1,1]=>10
{{1,3,4,5,7},{2,6}}=>[5,2]=>[2,2,1,1,1]=>11
{{1,3,4,5},{2,6,7}}=>[4,3]=>[2,2,2,1]=>9
{{1,3,4,5},{2,6},{7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,3,4,5,7},{2},{6}}=>[5,1,1]=>[3,1,1,1,1]=>10
{{1,3,4,5},{2,7},{6}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,3,4,5},{2},{6,7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,3,4,5},{2},{6},{7}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1,3,4,6,7},{2,5}}=>[5,2]=>[2,2,1,1,1]=>11
{{1,3,4,6},{2,5,7}}=>[4,3]=>[2,2,2,1]=>9
{{1,3,4,6},{2,5},{7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,3,4,7},{2,5,6}}=>[4,3]=>[2,2,2,1]=>9
{{1,3,4},{2,5,6,7}}=>[4,3]=>[2,2,2,1]=>9
{{1,3,4},{2,5,6},{7}}=>[3,3,1]=>[3,2,2]=>6
{{1,3,4,7},{2,5},{6}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,3,4},{2,5,7},{6}}=>[3,3,1]=>[3,2,2]=>6
{{1,3,4},{2,5},{6,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,3,4},{2,5},{6},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3,4,6,7},{2},{5}}=>[5,1,1]=>[3,1,1,1,1]=>10
{{1,3,4,6},{2,7},{5}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,3,4,6},{2},{5,7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,3,4,6},{2},{5},{7}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1,3,4,7},{2,6},{5}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,3,4},{2,6,7},{5}}=>[3,3,1]=>[3,2,2]=>6
{{1,3,4},{2,6},{5,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,3,4},{2,6},{5},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3,4,7},{2},{5,6}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,3,4},{2,7},{5,6}}=>[3,2,2]=>[3,3,1]=>5
{{1,3,4},{2},{5,6,7}}=>[3,3,1]=>[3,2,2]=>6
{{1,3,4},{2},{5,6},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3,4,7},{2},{5},{6}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1,3,4},{2,7},{5},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3,4},{2},{5,7},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3,4},{2},{5},{6,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3,4},{2},{5},{6},{7}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1,3,5,6,7},{2,4}}=>[5,2]=>[2,2,1,1,1]=>11
{{1,3,5,6},{2,4,7}}=>[4,3]=>[2,2,2,1]=>9
{{1,3,5,6},{2,4},{7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,3,5,7},{2,4,6}}=>[4,3]=>[2,2,2,1]=>9
{{1,3,5},{2,4,6,7}}=>[4,3]=>[2,2,2,1]=>9
{{1,3,5},{2,4,6},{7}}=>[3,3,1]=>[3,2,2]=>6
{{1,3,5,7},{2,4},{6}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,3,5},{2,4,7},{6}}=>[3,3,1]=>[3,2,2]=>6
{{1,3,5},{2,4},{6,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,3,5},{2,4},{6},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3,6,7},{2,4,5}}=>[4,3]=>[2,2,2,1]=>9
{{1,3,6},{2,4,5,7}}=>[4,3]=>[2,2,2,1]=>9
{{1,3,6},{2,4,5},{7}}=>[3,3,1]=>[3,2,2]=>6
{{1,3,7},{2,4,5,6}}=>[4,3]=>[2,2,2,1]=>9
{{1,3},{2,4,5,6,7}}=>[5,2]=>[2,2,1,1,1]=>11
{{1,3},{2,4,5,6},{7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,3,7},{2,4,5},{6}}=>[3,3,1]=>[3,2,2]=>6
{{1,3},{2,4,5,7},{6}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,3},{2,4,5},{6,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,3},{2,4,5},{6},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3,6,7},{2,4},{5}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,3,6},{2,4,7},{5}}=>[3,3,1]=>[3,2,2]=>6
{{1,3,6},{2,4},{5,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,3,6},{2,4},{5},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3,7},{2,4,6},{5}}=>[3,3,1]=>[3,2,2]=>6
{{1,3},{2,4,6,7},{5}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,3},{2,4,6},{5,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,3},{2,4,6},{5},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3,7},{2,4},{5,6}}=>[3,2,2]=>[3,3,1]=>5
{{1,3},{2,4,7},{5,6}}=>[3,2,2]=>[3,3,1]=>5
{{1,3},{2,4},{5,6,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,3},{2,4},{5,6},{7}}=>[2,2,2,1]=>[4,3]=>3
{{1,3,7},{2,4},{5},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3},{2,4,7},{5},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3},{2,4},{5,7},{6}}=>[2,2,2,1]=>[4,3]=>3
{{1,3},{2,4},{5},{6,7}}=>[2,2,2,1]=>[4,3]=>3
{{1,3},{2,4},{5},{6},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,3,5,6,7},{2},{4}}=>[5,1,1]=>[3,1,1,1,1]=>10
{{1,3,5,6},{2,7},{4}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,3,5,6},{2},{4,7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,3,5,6},{2},{4},{7}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1,3,5,7},{2,6},{4}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,3,5},{2,6,7},{4}}=>[3,3,1]=>[3,2,2]=>6
{{1,3,5},{2,6},{4,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,3,5},{2,6},{4},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3,5,7},{2},{4,6}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,3,5},{2,7},{4,6}}=>[3,2,2]=>[3,3,1]=>5
{{1,3,5},{2},{4,6,7}}=>[3,3,1]=>[3,2,2]=>6
{{1,3,5},{2},{4,6},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3,5,7},{2},{4},{6}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1,3,5},{2,7},{4},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3,5},{2},{4,7},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3,5},{2},{4},{6,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3,5},{2},{4},{6},{7}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1,3,6,7},{2,5},{4}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,3,6},{2,5,7},{4}}=>[3,3,1]=>[3,2,2]=>6
{{1,3,6},{2,5},{4,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,3,6},{2,5},{4},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3,7},{2,5,6},{4}}=>[3,3,1]=>[3,2,2]=>6
{{1,3},{2,5,6,7},{4}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,3},{2,5,6},{4,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,3},{2,5,6},{4},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3,7},{2,5},{4,6}}=>[3,2,2]=>[3,3,1]=>5
{{1,3},{2,5,7},{4,6}}=>[3,2,2]=>[3,3,1]=>5
{{1,3},{2,5},{4,6,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,3},{2,5},{4,6},{7}}=>[2,2,2,1]=>[4,3]=>3
{{1,3,7},{2,5},{4},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3},{2,5,7},{4},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3},{2,5},{4,7},{6}}=>[2,2,2,1]=>[4,3]=>3
{{1,3},{2,5},{4},{6,7}}=>[2,2,2,1]=>[4,3]=>3
{{1,3},{2,5},{4},{6},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,3,6,7},{2},{4,5}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,3,6},{2,7},{4,5}}=>[3,2,2]=>[3,3,1]=>5
{{1,3,6},{2},{4,5,7}}=>[3,3,1]=>[3,2,2]=>6
{{1,3,6},{2},{4,5},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3,7},{2,6},{4,5}}=>[3,2,2]=>[3,3,1]=>5
{{1,3},{2,6,7},{4,5}}=>[3,2,2]=>[3,3,1]=>5
{{1,3},{2,6},{4,5,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,3},{2,6},{4,5},{7}}=>[2,2,2,1]=>[4,3]=>3
{{1,3,7},{2},{4,5,6}}=>[3,3,1]=>[3,2,2]=>6
{{1,3},{2,7},{4,5,6}}=>[3,2,2]=>[3,3,1]=>5
{{1,3},{2},{4,5,6,7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,3},{2},{4,5,6},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3,7},{2},{4,5},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3},{2,7},{4,5},{6}}=>[2,2,2,1]=>[4,3]=>3
{{1,3},{2},{4,5,7},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3},{2},{4,5},{6,7}}=>[2,2,2,1]=>[4,3]=>3
{{1,3},{2},{4,5},{6},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,3,6,7},{2},{4},{5}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1,3,6},{2,7},{4},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3,6},{2},{4,7},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3,6},{2},{4},{5,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3,6},{2},{4},{5},{7}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1,3,7},{2,6},{4},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3},{2,6,7},{4},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3},{2,6},{4,7},{5}}=>[2,2,2,1]=>[4,3]=>3
{{1,3},{2,6},{4},{5,7}}=>[2,2,2,1]=>[4,3]=>3
{{1,3},{2,6},{4},{5},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,3,7},{2},{4,6},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3},{2,7},{4,6},{5}}=>[2,2,2,1]=>[4,3]=>3
{{1,3},{2},{4,6,7},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3},{2},{4,6},{5,7}}=>[2,2,2,1]=>[4,3]=>3
{{1,3},{2},{4,6},{5},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,3,7},{2},{4},{5,6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3},{2,7},{4},{5,6}}=>[2,2,2,1]=>[4,3]=>3
{{1,3},{2},{4,7},{5,6}}=>[2,2,2,1]=>[4,3]=>3
{{1,3},{2},{4},{5,6,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,3},{2},{4},{5,6},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,3,7},{2},{4},{5},{6}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1,3},{2,7},{4},{5},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,3},{2},{4,7},{5},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,3},{2},{4},{5,7},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,3},{2},{4},{5},{6,7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,3},{2},{4},{5},{6},{7}}=>[2,1,1,1,1,1]=>[6,1]=>1
{{1,4,5,6,7},{2,3}}=>[5,2]=>[2,2,1,1,1]=>11
{{1,4,5,6},{2,3,7}}=>[4,3]=>[2,2,2,1]=>9
{{1,4,5,6},{2,3},{7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,4,5,7},{2,3,6}}=>[4,3]=>[2,2,2,1]=>9
{{1,4,5},{2,3,6,7}}=>[4,3]=>[2,2,2,1]=>9
{{1,4,5},{2,3,6},{7}}=>[3,3,1]=>[3,2,2]=>6
{{1,4,5,7},{2,3},{6}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,4,5},{2,3,7},{6}}=>[3,3,1]=>[3,2,2]=>6
{{1,4,5},{2,3},{6,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,4,5},{2,3},{6},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,4,6,7},{2,3,5}}=>[4,3]=>[2,2,2,1]=>9
{{1,4,6},{2,3,5,7}}=>[4,3]=>[2,2,2,1]=>9
{{1,4,6},{2,3,5},{7}}=>[3,3,1]=>[3,2,2]=>6
{{1,4,7},{2,3,5,6}}=>[4,3]=>[2,2,2,1]=>9
{{1,4},{2,3,5,6,7}}=>[5,2]=>[2,2,1,1,1]=>11
{{1,4},{2,3,5,6},{7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,4,7},{2,3,5},{6}}=>[3,3,1]=>[3,2,2]=>6
{{1,4},{2,3,5,7},{6}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,4},{2,3,5},{6,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,4},{2,3,5},{6},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,4,6,7},{2,3},{5}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,4,6},{2,3,7},{5}}=>[3,3,1]=>[3,2,2]=>6
{{1,4,6},{2,3},{5,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,4,6},{2,3},{5},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,4,7},{2,3,6},{5}}=>[3,3,1]=>[3,2,2]=>6
{{1,4},{2,3,6,7},{5}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,4},{2,3,6},{5,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,4},{2,3,6},{5},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,4,7},{2,3},{5,6}}=>[3,2,2]=>[3,3,1]=>5
{{1,4},{2,3,7},{5,6}}=>[3,2,2]=>[3,3,1]=>5
{{1,4},{2,3},{5,6,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,4},{2,3},{5,6},{7}}=>[2,2,2,1]=>[4,3]=>3
{{1,4,7},{2,3},{5},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,4},{2,3,7},{5},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,4},{2,3},{5,7},{6}}=>[2,2,2,1]=>[4,3]=>3
{{1,4},{2,3},{5},{6,7}}=>[2,2,2,1]=>[4,3]=>3
{{1,4},{2,3},{5},{6},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,5,6,7},{2,3,4}}=>[4,3]=>[2,2,2,1]=>9
{{1,5,6},{2,3,4,7}}=>[4,3]=>[2,2,2,1]=>9
{{1,5,6},{2,3,4},{7}}=>[3,3,1]=>[3,2,2]=>6
{{1,5,7},{2,3,4,6}}=>[4,3]=>[2,2,2,1]=>9
{{1,5},{2,3,4,6,7}}=>[5,2]=>[2,2,1,1,1]=>11
{{1,5},{2,3,4,6},{7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,5,7},{2,3,4},{6}}=>[3,3,1]=>[3,2,2]=>6
{{1,5},{2,3,4,7},{6}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,5},{2,3,4},{6,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,5},{2,3,4},{6},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,6,7},{2,3,4,5}}=>[4,3]=>[2,2,2,1]=>9
{{1,6},{2,3,4,5,7}}=>[5,2]=>[2,2,1,1,1]=>11
{{1,6},{2,3,4,5},{7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,7},{2,3,4,5,6}}=>[5,2]=>[2,2,1,1,1]=>11
{{1},{2,3,4,5,6,7}}=>[6,1]=>[2,1,1,1,1,1]=>15
{{1},{2,3,4,5,6},{7}}=>[5,1,1]=>[3,1,1,1,1]=>10
{{1,7},{2,3,4,5},{6}}=>[4,2,1]=>[3,2,1,1]=>7
{{1},{2,3,4,5,7},{6}}=>[5,1,1]=>[3,1,1,1,1]=>10
{{1},{2,3,4,5},{6,7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1},{2,3,4,5},{6},{7}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1,6,7},{2,3,4},{5}}=>[3,3,1]=>[3,2,2]=>6
{{1,6},{2,3,4,7},{5}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,6},{2,3,4},{5,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,6},{2,3,4},{5},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,7},{2,3,4,6},{5}}=>[4,2,1]=>[3,2,1,1]=>7
{{1},{2,3,4,6,7},{5}}=>[5,1,1]=>[3,1,1,1,1]=>10
{{1},{2,3,4,6},{5,7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1},{2,3,4,6},{5},{7}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1,7},{2,3,4},{5,6}}=>[3,2,2]=>[3,3,1]=>5
{{1},{2,3,4,7},{5,6}}=>[4,2,1]=>[3,2,1,1]=>7
{{1},{2,3,4},{5,6,7}}=>[3,3,1]=>[3,2,2]=>6
{{1},{2,3,4},{5,6},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,7},{2,3,4},{5},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,3,4,7},{5},{6}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1},{2,3,4},{5,7},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,3,4},{5},{6,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,3,4},{5},{6},{7}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1,5,6,7},{2,3},{4}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,5,6},{2,3,7},{4}}=>[3,3,1]=>[3,2,2]=>6
{{1,5,6},{2,3},{4,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,5,6},{2,3},{4},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,5,7},{2,3,6},{4}}=>[3,3,1]=>[3,2,2]=>6
{{1,5},{2,3,6,7},{4}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,5},{2,3,6},{4,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,5},{2,3,6},{4},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,5,7},{2,3},{4,6}}=>[3,2,2]=>[3,3,1]=>5
{{1,5},{2,3,7},{4,6}}=>[3,2,2]=>[3,3,1]=>5
{{1,5},{2,3},{4,6,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,5},{2,3},{4,6},{7}}=>[2,2,2,1]=>[4,3]=>3
{{1,5,7},{2,3},{4},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,5},{2,3,7},{4},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,5},{2,3},{4,7},{6}}=>[2,2,2,1]=>[4,3]=>3
{{1,5},{2,3},{4},{6,7}}=>[2,2,2,1]=>[4,3]=>3
{{1,5},{2,3},{4},{6},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,6,7},{2,3,5},{4}}=>[3,3,1]=>[3,2,2]=>6
{{1,6},{2,3,5,7},{4}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,6},{2,3,5},{4,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,6},{2,3,5},{4},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,7},{2,3,5,6},{4}}=>[4,2,1]=>[3,2,1,1]=>7
{{1},{2,3,5,6,7},{4}}=>[5,1,1]=>[3,1,1,1,1]=>10
{{1},{2,3,5,6},{4,7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1},{2,3,5,6},{4},{7}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1,7},{2,3,5},{4,6}}=>[3,2,2]=>[3,3,1]=>5
{{1},{2,3,5,7},{4,6}}=>[4,2,1]=>[3,2,1,1]=>7
{{1},{2,3,5},{4,6,7}}=>[3,3,1]=>[3,2,2]=>6
{{1},{2,3,5},{4,6},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,7},{2,3,5},{4},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,3,5,7},{4},{6}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1},{2,3,5},{4,7},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,3,5},{4},{6,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,3,5},{4},{6},{7}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1,6,7},{2,3},{4,5}}=>[3,2,2]=>[3,3,1]=>5
{{1,6},{2,3,7},{4,5}}=>[3,2,2]=>[3,3,1]=>5
{{1,6},{2,3},{4,5,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,6},{2,3},{4,5},{7}}=>[2,2,2,1]=>[4,3]=>3
{{1,7},{2,3,6},{4,5}}=>[3,2,2]=>[3,3,1]=>5
{{1},{2,3,6,7},{4,5}}=>[4,2,1]=>[3,2,1,1]=>7
{{1},{2,3,6},{4,5,7}}=>[3,3,1]=>[3,2,2]=>6
{{1},{2,3,6},{4,5},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,7},{2,3},{4,5,6}}=>[3,2,2]=>[3,3,1]=>5
{{1},{2,3,7},{4,5,6}}=>[3,3,1]=>[3,2,2]=>6
{{1},{2,3},{4,5,6,7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1},{2,3},{4,5,6},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,7},{2,3},{4,5},{6}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2,3,7},{4,5},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,3},{4,5,7},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,3},{4,5},{6,7}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2,3},{4,5},{6},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,6,7},{2,3},{4},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,6},{2,3,7},{4},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,6},{2,3},{4,7},{5}}=>[2,2,2,1]=>[4,3]=>3
{{1,6},{2,3},{4},{5,7}}=>[2,2,2,1]=>[4,3]=>3
{{1,6},{2,3},{4},{5},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,7},{2,3,6},{4},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,3,6,7},{4},{5}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1},{2,3,6},{4,7},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,3,6},{4},{5,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,3,6},{4},{5},{7}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1,7},{2,3},{4,6},{5}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2,3,7},{4,6},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,3},{4,6,7},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,3},{4,6},{5,7}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2,3},{4,6},{5},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,7},{2,3},{4},{5,6}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2,3,7},{4},{5,6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,3},{4,7},{5,6}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2,3},{4},{5,6,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,3},{4},{5,6},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,7},{2,3},{4},{5},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2,3,7},{4},{5},{6}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1},{2,3},{4,7},{5},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2,3},{4},{5,7},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2,3},{4},{5},{6,7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2,3},{4},{5},{6},{7}}=>[2,1,1,1,1,1]=>[6,1]=>1
{{1,4,5,6,7},{2},{3}}=>[5,1,1]=>[3,1,1,1,1]=>10
{{1,4,5,6},{2,7},{3}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,4,5,6},{2},{3,7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,4,5,6},{2},{3},{7}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1,4,5,7},{2,6},{3}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,4,5},{2,6,7},{3}}=>[3,3,1]=>[3,2,2]=>6
{{1,4,5},{2,6},{3,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,4,5},{2,6},{3},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,4,5,7},{2},{3,6}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,4,5},{2,7},{3,6}}=>[3,2,2]=>[3,3,1]=>5
{{1,4,5},{2},{3,6,7}}=>[3,3,1]=>[3,2,2]=>6
{{1,4,5},{2},{3,6},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,4,5,7},{2},{3},{6}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1,4,5},{2,7},{3},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,4,5},{2},{3,7},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,4,5},{2},{3},{6,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,4,5},{2},{3},{6},{7}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1,4,6,7},{2,5},{3}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,4,6},{2,5,7},{3}}=>[3,3,1]=>[3,2,2]=>6
{{1,4,6},{2,5},{3,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,4,6},{2,5},{3},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,4,7},{2,5,6},{3}}=>[3,3,1]=>[3,2,2]=>6
{{1,4},{2,5,6,7},{3}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,4},{2,5,6},{3,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,4},{2,5,6},{3},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,4,7},{2,5},{3,6}}=>[3,2,2]=>[3,3,1]=>5
{{1,4},{2,5,7},{3,6}}=>[3,2,2]=>[3,3,1]=>5
{{1,4},{2,5},{3,6,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,4},{2,5},{3,6},{7}}=>[2,2,2,1]=>[4,3]=>3
{{1,4,7},{2,5},{3},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,4},{2,5,7},{3},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,4},{2,5},{3,7},{6}}=>[2,2,2,1]=>[4,3]=>3
{{1,4},{2,5},{3},{6,7}}=>[2,2,2,1]=>[4,3]=>3
{{1,4},{2,5},{3},{6},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,4,6,7},{2},{3,5}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,4,6},{2,7},{3,5}}=>[3,2,2]=>[3,3,1]=>5
{{1,4,6},{2},{3,5,7}}=>[3,3,1]=>[3,2,2]=>6
{{1,4,6},{2},{3,5},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,4,7},{2,6},{3,5}}=>[3,2,2]=>[3,3,1]=>5
{{1,4},{2,6,7},{3,5}}=>[3,2,2]=>[3,3,1]=>5
{{1,4},{2,6},{3,5,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,4},{2,6},{3,5},{7}}=>[2,2,2,1]=>[4,3]=>3
{{1,4,7},{2},{3,5,6}}=>[3,3,1]=>[3,2,2]=>6
{{1,4},{2,7},{3,5,6}}=>[3,2,2]=>[3,3,1]=>5
{{1,4},{2},{3,5,6,7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,4},{2},{3,5,6},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,4,7},{2},{3,5},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,4},{2,7},{3,5},{6}}=>[2,2,2,1]=>[4,3]=>3
{{1,4},{2},{3,5,7},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,4},{2},{3,5},{6,7}}=>[2,2,2,1]=>[4,3]=>3
{{1,4},{2},{3,5},{6},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,4,6,7},{2},{3},{5}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1,4,6},{2,7},{3},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,4,6},{2},{3,7},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,4,6},{2},{3},{5,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,4,6},{2},{3},{5},{7}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1,4,7},{2,6},{3},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,4},{2,6,7},{3},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,4},{2,6},{3,7},{5}}=>[2,2,2,1]=>[4,3]=>3
{{1,4},{2,6},{3},{5,7}}=>[2,2,2,1]=>[4,3]=>3
{{1,4},{2,6},{3},{5},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,4,7},{2},{3,6},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,4},{2,7},{3,6},{5}}=>[2,2,2,1]=>[4,3]=>3
{{1,4},{2},{3,6,7},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,4},{2},{3,6},{5,7}}=>[2,2,2,1]=>[4,3]=>3
{{1,4},{2},{3,6},{5},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,4,7},{2},{3},{5,6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,4},{2,7},{3},{5,6}}=>[2,2,2,1]=>[4,3]=>3
{{1,4},{2},{3,7},{5,6}}=>[2,2,2,1]=>[4,3]=>3
{{1,4},{2},{3},{5,6,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,4},{2},{3},{5,6},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,4,7},{2},{3},{5},{6}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1,4},{2,7},{3},{5},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,4},{2},{3,7},{5},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,4},{2},{3},{5,7},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,4},{2},{3},{5},{6,7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,4},{2},{3},{5},{6},{7}}=>[2,1,1,1,1,1]=>[6,1]=>1
{{1,5,6,7},{2,4},{3}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,5,6},{2,4,7},{3}}=>[3,3,1]=>[3,2,2]=>6
{{1,5,6},{2,4},{3,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,5,6},{2,4},{3},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,5,7},{2,4,6},{3}}=>[3,3,1]=>[3,2,2]=>6
{{1,5},{2,4,6,7},{3}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,5},{2,4,6},{3,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,5},{2,4,6},{3},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,5,7},{2,4},{3,6}}=>[3,2,2]=>[3,3,1]=>5
{{1,5},{2,4,7},{3,6}}=>[3,2,2]=>[3,3,1]=>5
{{1,5},{2,4},{3,6,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,5},{2,4},{3,6},{7}}=>[2,2,2,1]=>[4,3]=>3
{{1,5,7},{2,4},{3},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,5},{2,4,7},{3},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,5},{2,4},{3,7},{6}}=>[2,2,2,1]=>[4,3]=>3
{{1,5},{2,4},{3},{6,7}}=>[2,2,2,1]=>[4,3]=>3
{{1,5},{2,4},{3},{6},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,6,7},{2,4,5},{3}}=>[3,3,1]=>[3,2,2]=>6
{{1,6},{2,4,5,7},{3}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,6},{2,4,5},{3,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,6},{2,4,5},{3},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,7},{2,4,5,6},{3}}=>[4,2,1]=>[3,2,1,1]=>7
{{1},{2,4,5,6,7},{3}}=>[5,1,1]=>[3,1,1,1,1]=>10
{{1},{2,4,5,6},{3,7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1},{2,4,5,6},{3},{7}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1,7},{2,4,5},{3,6}}=>[3,2,2]=>[3,3,1]=>5
{{1},{2,4,5,7},{3,6}}=>[4,2,1]=>[3,2,1,1]=>7
{{1},{2,4,5},{3,6,7}}=>[3,3,1]=>[3,2,2]=>6
{{1},{2,4,5},{3,6},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,7},{2,4,5},{3},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,4,5,7},{3},{6}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1},{2,4,5},{3,7},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,4,5},{3},{6,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,4,5},{3},{6},{7}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1,6,7},{2,4},{3,5}}=>[3,2,2]=>[3,3,1]=>5
{{1,6},{2,4,7},{3,5}}=>[3,2,2]=>[3,3,1]=>5
{{1,6},{2,4},{3,5,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,6},{2,4},{3,5},{7}}=>[2,2,2,1]=>[4,3]=>3
{{1,7},{2,4,6},{3,5}}=>[3,2,2]=>[3,3,1]=>5
{{1},{2,4,6,7},{3,5}}=>[4,2,1]=>[3,2,1,1]=>7
{{1},{2,4,6},{3,5,7}}=>[3,3,1]=>[3,2,2]=>6
{{1},{2,4,6},{3,5},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,7},{2,4},{3,5,6}}=>[3,2,2]=>[3,3,1]=>5
{{1},{2,4,7},{3,5,6}}=>[3,3,1]=>[3,2,2]=>6
{{1},{2,4},{3,5,6,7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1},{2,4},{3,5,6},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,7},{2,4},{3,5},{6}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2,4,7},{3,5},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,4},{3,5,7},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,4},{3,5},{6,7}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2,4},{3,5},{6},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,6,7},{2,4},{3},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,6},{2,4,7},{3},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,6},{2,4},{3,7},{5}}=>[2,2,2,1]=>[4,3]=>3
{{1,6},{2,4},{3},{5,7}}=>[2,2,2,1]=>[4,3]=>3
{{1,6},{2,4},{3},{5},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,7},{2,4,6},{3},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,4,6,7},{3},{5}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1},{2,4,6},{3,7},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,4,6},{3},{5,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,4,6},{3},{5},{7}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1,7},{2,4},{3,6},{5}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2,4,7},{3,6},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,4},{3,6,7},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,4},{3,6},{5,7}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2,4},{3,6},{5},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,7},{2,4},{3},{5,6}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2,4,7},{3},{5,6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,4},{3,7},{5,6}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2,4},{3},{5,6,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,4},{3},{5,6},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,7},{2,4},{3},{5},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2,4,7},{3},{5},{6}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1},{2,4},{3,7},{5},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2,4},{3},{5,7},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2,4},{3},{5},{6,7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2,4},{3},{5},{6},{7}}=>[2,1,1,1,1,1]=>[6,1]=>1
{{1,5,6,7},{2},{3,4}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,5,6},{2,7},{3,4}}=>[3,2,2]=>[3,3,1]=>5
{{1,5,6},{2},{3,4,7}}=>[3,3,1]=>[3,2,2]=>6
{{1,5,6},{2},{3,4},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,5,7},{2,6},{3,4}}=>[3,2,2]=>[3,3,1]=>5
{{1,5},{2,6,7},{3,4}}=>[3,2,2]=>[3,3,1]=>5
{{1,5},{2,6},{3,4,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,5},{2,6},{3,4},{7}}=>[2,2,2,1]=>[4,3]=>3
{{1,5,7},{2},{3,4,6}}=>[3,3,1]=>[3,2,2]=>6
{{1,5},{2,7},{3,4,6}}=>[3,2,2]=>[3,3,1]=>5
{{1,5},{2},{3,4,6,7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,5},{2},{3,4,6},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,5,7},{2},{3,4},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,5},{2,7},{3,4},{6}}=>[2,2,2,1]=>[4,3]=>3
{{1,5},{2},{3,4,7},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,5},{2},{3,4},{6,7}}=>[2,2,2,1]=>[4,3]=>3
{{1,5},{2},{3,4},{6},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,6,7},{2,5},{3,4}}=>[3,2,2]=>[3,3,1]=>5
{{1,6},{2,5,7},{3,4}}=>[3,2,2]=>[3,3,1]=>5
{{1,6},{2,5},{3,4,7}}=>[3,2,2]=>[3,3,1]=>5
{{1,6},{2,5},{3,4},{7}}=>[2,2,2,1]=>[4,3]=>3
{{1,7},{2,5,6},{3,4}}=>[3,2,2]=>[3,3,1]=>5
{{1},{2,5,6,7},{3,4}}=>[4,2,1]=>[3,2,1,1]=>7
{{1},{2,5,6},{3,4,7}}=>[3,3,1]=>[3,2,2]=>6
{{1},{2,5,6},{3,4},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,7},{2,5},{3,4,6}}=>[3,2,2]=>[3,3,1]=>5
{{1},{2,5,7},{3,4,6}}=>[3,3,1]=>[3,2,2]=>6
{{1},{2,5},{3,4,6,7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1},{2,5},{3,4,6},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,7},{2,5},{3,4},{6}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2,5,7},{3,4},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,5},{3,4,7},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,5},{3,4},{6,7}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2,5},{3,4},{6},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,6,7},{2},{3,4,5}}=>[3,3,1]=>[3,2,2]=>6
{{1,6},{2,7},{3,4,5}}=>[3,2,2]=>[3,3,1]=>5
{{1,6},{2},{3,4,5,7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1,6},{2},{3,4,5},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,7},{2,6},{3,4,5}}=>[3,2,2]=>[3,3,1]=>5
{{1},{2,6,7},{3,4,5}}=>[3,3,1]=>[3,2,2]=>6
{{1},{2,6},{3,4,5,7}}=>[4,2,1]=>[3,2,1,1]=>7
{{1},{2,6},{3,4,5},{7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,7},{2},{3,4,5,6}}=>[4,2,1]=>[3,2,1,1]=>7
{{1},{2,7},{3,4,5,6}}=>[4,2,1]=>[3,2,1,1]=>7
{{1},{2},{3,4,5,6,7}}=>[5,1,1]=>[3,1,1,1,1]=>10
{{1},{2},{3,4,5,6},{7}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1,7},{2},{3,4,5},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,7},{3,4,5},{6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2},{3,4,5,7},{6}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1},{2},{3,4,5},{6,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2},{3,4,5},{6},{7}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1,6,7},{2},{3,4},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,6},{2,7},{3,4},{5}}=>[2,2,2,1]=>[4,3]=>3
{{1,6},{2},{3,4,7},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,6},{2},{3,4},{5,7}}=>[2,2,2,1]=>[4,3]=>3
{{1,6},{2},{3,4},{5},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,7},{2,6},{3,4},{5}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2,6,7},{3,4},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,6},{3,4,7},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,6},{3,4},{5,7}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2,6},{3,4},{5},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,7},{2},{3,4,6},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,7},{3,4,6},{5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2},{3,4,6,7},{5}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1},{2},{3,4,6},{5,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2},{3,4,6},{5},{7}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1,7},{2},{3,4},{5,6}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2,7},{3,4},{5,6}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2},{3,4,7},{5,6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2},{3,4},{5,6,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2},{3,4},{5,6},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,7},{2},{3,4},{5},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2,7},{3,4},{5},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2},{3,4,7},{5},{6}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1},{2},{3,4},{5,7},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2},{3,4},{5},{6,7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2},{3,4},{5},{6},{7}}=>[2,1,1,1,1,1]=>[6,1]=>1
{{1,5,6,7},{2},{3},{4}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1,5,6},{2,7},{3},{4}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,5,6},{2},{3,7},{4}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,5,6},{2},{3},{4,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,5,6},{2},{3},{4},{7}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1,5,7},{2,6},{3},{4}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,5},{2,6,7},{3},{4}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,5},{2,6},{3,7},{4}}=>[2,2,2,1]=>[4,3]=>3
{{1,5},{2,6},{3},{4,7}}=>[2,2,2,1]=>[4,3]=>3
{{1,5},{2,6},{3},{4},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,5,7},{2},{3,6},{4}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,5},{2,7},{3,6},{4}}=>[2,2,2,1]=>[4,3]=>3
{{1,5},{2},{3,6,7},{4}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,5},{2},{3,6},{4,7}}=>[2,2,2,1]=>[4,3]=>3
{{1,5},{2},{3,6},{4},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,5,7},{2},{3},{4,6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,5},{2,7},{3},{4,6}}=>[2,2,2,1]=>[4,3]=>3
{{1,5},{2},{3,7},{4,6}}=>[2,2,2,1]=>[4,3]=>3
{{1,5},{2},{3},{4,6,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,5},{2},{3},{4,6},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,5,7},{2},{3},{4},{6}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1,5},{2,7},{3},{4},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,5},{2},{3,7},{4},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,5},{2},{3},{4,7},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,5},{2},{3},{4},{6,7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,5},{2},{3},{4},{6},{7}}=>[2,1,1,1,1,1]=>[6,1]=>1
{{1,6,7},{2,5},{3},{4}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,6},{2,5,7},{3},{4}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,6},{2,5},{3,7},{4}}=>[2,2,2,1]=>[4,3]=>3
{{1,6},{2,5},{3},{4,7}}=>[2,2,2,1]=>[4,3]=>3
{{1,6},{2,5},{3},{4},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,7},{2,5,6},{3},{4}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,5,6,7},{3},{4}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1},{2,5,6},{3,7},{4}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,5,6},{3},{4,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,5,6},{3},{4},{7}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1,7},{2,5},{3,6},{4}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2,5,7},{3,6},{4}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,5},{3,6,7},{4}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,5},{3,6},{4,7}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2,5},{3,6},{4},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,7},{2,5},{3},{4,6}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2,5,7},{3},{4,6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,5},{3,7},{4,6}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2,5},{3},{4,6,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,5},{3},{4,6},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,7},{2,5},{3},{4},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2,5,7},{3},{4},{6}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1},{2,5},{3,7},{4},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2,5},{3},{4,7},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2,5},{3},{4},{6,7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2,5},{3},{4},{6},{7}}=>[2,1,1,1,1,1]=>[6,1]=>1
{{1,6,7},{2},{3,5},{4}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,6},{2,7},{3,5},{4}}=>[2,2,2,1]=>[4,3]=>3
{{1,6},{2},{3,5,7},{4}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,6},{2},{3,5},{4,7}}=>[2,2,2,1]=>[4,3]=>3
{{1,6},{2},{3,5},{4},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,7},{2,6},{3,5},{4}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2,6,7},{3,5},{4}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,6},{3,5,7},{4}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,6},{3,5},{4,7}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2,6},{3,5},{4},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,7},{2},{3,5,6},{4}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,7},{3,5,6},{4}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2},{3,5,6,7},{4}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1},{2},{3,5,6},{4,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2},{3,5,6},{4},{7}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1,7},{2},{3,5},{4,6}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2,7},{3,5},{4,6}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2},{3,5,7},{4,6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2},{3,5},{4,6,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2},{3,5},{4,6},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,7},{2},{3,5},{4},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2,7},{3,5},{4},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2},{3,5,7},{4},{6}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1},{2},{3,5},{4,7},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2},{3,5},{4},{6,7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2},{3,5},{4},{6},{7}}=>[2,1,1,1,1,1]=>[6,1]=>1
{{1,6,7},{2},{3},{4,5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,6},{2,7},{3},{4,5}}=>[2,2,2,1]=>[4,3]=>3
{{1,6},{2},{3,7},{4,5}}=>[2,2,2,1]=>[4,3]=>3
{{1,6},{2},{3},{4,5,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1,6},{2},{3},{4,5},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,7},{2,6},{3},{4,5}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2,6,7},{3},{4,5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,6},{3,7},{4,5}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2,6},{3},{4,5,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,6},{3},{4,5},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,7},{2},{3,6},{4,5}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2,7},{3,6},{4,5}}=>[2,2,2,1]=>[4,3]=>3
{{1},{2},{3,6,7},{4,5}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2},{3,6},{4,5,7}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2},{3,6},{4,5},{7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,7},{2},{3},{4,5,6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2,7},{3},{4,5,6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2},{3,7},{4,5,6}}=>[3,2,1,1]=>[4,2,1]=>4
{{1},{2},{3},{4,5,6,7}}=>[4,1,1,1]=>[4,1,1,1]=>6
{{1},{2},{3},{4,5,6},{7}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1,7},{2},{3},{4,5},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2,7},{3},{4,5},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2},{3,7},{4,5},{6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2},{3},{4,5,7},{6}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1},{2},{3},{4,5},{6,7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2},{3},{4,5},{6},{7}}=>[2,1,1,1,1,1]=>[6,1]=>1
{{1,6,7},{2},{3},{4},{5}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1,6},{2,7},{3},{4},{5}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,6},{2},{3,7},{4},{5}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,6},{2},{3},{4,7},{5}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,6},{2},{3},{4},{5,7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1,6},{2},{3},{4},{5},{7}}=>[2,1,1,1,1,1]=>[6,1]=>1
{{1,7},{2,6},{3},{4},{5}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2,6,7},{3},{4},{5}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1},{2,6},{3,7},{4},{5}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2,6},{3},{4,7},{5}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2,6},{3},{4},{5,7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2,6},{3},{4},{5},{7}}=>[2,1,1,1,1,1]=>[6,1]=>1
{{1,7},{2},{3,6},{4},{5}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2,7},{3,6},{4},{5}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2},{3,6,7},{4},{5}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1},{2},{3,6},{4,7},{5}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2},{3,6},{4},{5,7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2},{3,6},{4},{5},{7}}=>[2,1,1,1,1,1]=>[6,1]=>1
{{1,7},{2},{3},{4,6},{5}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2,7},{3},{4,6},{5}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2},{3,7},{4,6},{5}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2},{3},{4,6,7},{5}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1},{2},{3},{4,6},{5,7}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2},{3},{4,6},{5},{7}}=>[2,1,1,1,1,1]=>[6,1]=>1
{{1,7},{2},{3},{4},{5,6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2,7},{3},{4},{5,6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2},{3,7},{4},{5,6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2},{3},{4,7},{5,6}}=>[2,2,1,1,1]=>[5,2]=>2
{{1},{2},{3},{4},{5,6,7}}=>[3,1,1,1,1]=>[5,1,1]=>3
{{1},{2},{3},{4},{5,6},{7}}=>[2,1,1,1,1,1]=>[6,1]=>1
{{1,7},{2},{3},{4},{5},{6}}=>[2,1,1,1,1,1]=>[6,1]=>1
{{1},{2,7},{3},{4},{5},{6}}=>[2,1,1,1,1,1]=>[6,1]=>1
{{1},{2},{3,7},{4},{5},{6}}=>[2,1,1,1,1,1]=>[6,1]=>1
{{1},{2},{3},{4,7},{5},{6}}=>[2,1,1,1,1,1]=>[6,1]=>1
{{1},{2},{3},{4},{5,7},{6}}=>[2,1,1,1,1,1]=>[6,1]=>1
{{1},{2},{3},{4},{5},{6,7}}=>[2,1,1,1,1,1]=>[6,1]=>1
{{1},{2},{3},{4},{5},{6},{7}}=>[1,1,1,1,1,1,1]=>[7]=>0
{{1,2},{3,4},{5,6},{7,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,3},{2,4},{5,6},{7,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,4},{2,3},{5,6},{7,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,5},{2,3},{4,6},{7,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,6},{2,3},{4,5},{7,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,7},{2,3},{4,5},{6,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,8},{2,3},{4,5},{6,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,8},{2,4},{3,5},{6,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,7},{2,4},{3,5},{6,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,6},{2,4},{3,5},{7,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,5},{2,4},{3,6},{7,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,4},{2,5},{3,6},{7,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,3},{2,5},{4,6},{7,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,2},{3,5},{4,6},{7,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,2},{3,6},{4,5},{7,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,3},{2,6},{4,5},{7,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,4},{2,6},{3,5},{7,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,5},{2,6},{3,4},{7,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,6},{2,5},{3,4},{7,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,7},{2,5},{3,4},{6,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,8},{2,5},{3,4},{6,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,8},{2,6},{3,4},{5,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,7},{2,6},{3,4},{5,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,6},{2,7},{3,4},{5,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,5},{2,7},{3,4},{6,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,4},{2,7},{3,5},{6,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,3},{2,7},{4,5},{6,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,2},{3,7},{4,5},{6,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,2},{3,8},{4,5},{6,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,3},{2,8},{4,5},{6,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,4},{2,8},{3,5},{6,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,5},{2,8},{3,4},{6,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,6},{2,8},{3,4},{5,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,7},{2,8},{3,4},{5,6}}=>[2,2,2,2]=>[4,4]=>4
{{1,8},{2,7},{3,4},{5,6}}=>[2,2,2,2]=>[4,4]=>4
{{1,8},{2,7},{3,5},{4,6}}=>[2,2,2,2]=>[4,4]=>4
{{1,7},{2,8},{3,5},{4,6}}=>[2,2,2,2]=>[4,4]=>4
{{1,6},{2,8},{3,5},{4,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,5},{2,8},{3,6},{4,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,4},{2,8},{3,6},{5,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,3},{2,8},{4,6},{5,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,2},{3,8},{4,6},{5,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,2},{3,7},{4,6},{5,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,3},{2,7},{4,6},{5,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,4},{2,7},{3,6},{5,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,5},{2,7},{3,6},{4,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,6},{2,7},{3,5},{4,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,7},{2,6},{3,5},{4,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,8},{2,6},{3,5},{4,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,8},{2,5},{3,6},{4,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,7},{2,5},{3,6},{4,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,6},{2,5},{3,7},{4,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,5},{2,6},{3,7},{4,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,4},{2,6},{3,7},{5,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,3},{2,6},{4,7},{5,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,2},{3,6},{4,7},{5,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,2},{3,5},{4,7},{6,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,3},{2,5},{4,7},{6,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,4},{2,5},{3,7},{6,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,5},{2,4},{3,7},{6,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,6},{2,4},{3,7},{5,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,7},{2,4},{3,6},{5,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,8},{2,4},{3,6},{5,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,8},{2,3},{4,6},{5,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,7},{2,3},{4,6},{5,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,6},{2,3},{4,7},{5,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,5},{2,3},{4,7},{6,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,4},{2,3},{5,7},{6,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,3},{2,4},{5,7},{6,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,2},{3,4},{5,7},{6,8}}=>[2,2,2,2]=>[4,4]=>4
{{1,2},{3,4},{5,8},{6,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,3},{2,4},{5,8},{6,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,4},{2,3},{5,8},{6,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,5},{2,3},{4,8},{6,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,6},{2,3},{4,8},{5,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,7},{2,3},{4,8},{5,6}}=>[2,2,2,2]=>[4,4]=>4
{{1,8},{2,3},{4,7},{5,6}}=>[2,2,2,2]=>[4,4]=>4
{{1,8},{2,4},{3,7},{5,6}}=>[2,2,2,2]=>[4,4]=>4
{{1,7},{2,4},{3,8},{5,6}}=>[2,2,2,2]=>[4,4]=>4
{{1,6},{2,4},{3,8},{5,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,5},{2,4},{3,8},{6,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,4},{2,5},{3,8},{6,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,3},{2,5},{4,8},{6,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,2},{3,5},{4,8},{6,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,2},{3,6},{4,8},{5,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,3},{2,6},{4,8},{5,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,4},{2,6},{3,8},{5,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,5},{2,6},{3,8},{4,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,6},{2,5},{3,8},{4,7}}=>[2,2,2,2]=>[4,4]=>4
{{1,7},{2,5},{3,8},{4,6}}=>[2,2,2,2]=>[4,4]=>4
{{1,8},{2,5},{3,7},{4,6}}=>[2,2,2,2]=>[4,4]=>4
{{1,8},{2,6},{3,7},{4,5}}=>[2,2,2,2]=>[4,4]=>4
{{1,7},{2,6},{3,8},{4,5}}=>[2,2,2,2]=>[4,4]=>4
{{1,6},{2,7},{3,8},{4,5}}=>[2,2,2,2]=>[4,4]=>4
{{1,5},{2,7},{3,8},{4,6}}=>[2,2,2,2]=>[4,4]=>4
{{1,4},{2,7},{3,8},{5,6}}=>[2,2,2,2]=>[4,4]=>4
{{1,3},{2,7},{4,8},{5,6}}=>[2,2,2,2]=>[4,4]=>4
{{1,2},{3,7},{4,8},{5,6}}=>[2,2,2,2]=>[4,4]=>4
{{1,2},{3,8},{4,7},{5,6}}=>[2,2,2,2]=>[4,4]=>4
{{1,3},{2,8},{4,7},{5,6}}=>[2,2,2,2]=>[4,4]=>4
{{1,4},{2,8},{3,7},{5,6}}=>[2,2,2,2]=>[4,4]=>4
{{1,5},{2,8},{3,7},{4,6}}=>[2,2,2,2]=>[4,4]=>4
{{1,6},{2,8},{3,7},{4,5}}=>[2,2,2,2]=>[4,4]=>4
{{1,7},{2,8},{3,6},{4,5}}=>[2,2,2,2]=>[4,4]=>4
{{1,8},{2,7},{3,6},{4,5}}=>[2,2,2,2]=>[4,4]=>4
{{1,6},{2,7},{3,8},{4,9},{5,10}}=>[2,2,2,2,2]=>[5,5]=>5
{{1},{2},{3},{4},{5},{6},{7},{8}}=>[1,1,1,1,1,1,1,1]=>[8]=>0
{{1},{2},{3},{4},{5},{6},{7,8}}=>[2,1,1,1,1,1,1]=>[7,1]=>1
{{1},{2},{3},{4},{5},{6,8},{7}}=>[2,1,1,1,1,1,1]=>[7,1]=>1
{{1},{2},{3},{4},{5},{6,7,8}}=>[3,1,1,1,1,1]=>[6,1,1]=>3
{{1},{2},{3},{4},{5,6},{7},{8}}=>[2,1,1,1,1,1,1]=>[7,1]=>1
{{1},{2},{3},{4},{5,6},{7,8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1},{2},{3},{4},{5,7},{6},{8}}=>[2,1,1,1,1,1,1]=>[7,1]=>1
{{1},{2},{3},{4},{5,8},{6},{7}}=>[2,1,1,1,1,1,1]=>[7,1]=>1
{{1},{2},{3},{4},{5,7,8},{6}}=>[3,1,1,1,1,1]=>[6,1,1]=>3
{{1},{2},{3},{4},{5,6,7},{8}}=>[3,1,1,1,1,1]=>[6,1,1]=>3
{{1},{2},{3},{4},{5,8},{6,7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1},{2},{3},{4},{5,6,8},{7}}=>[3,1,1,1,1,1]=>[6,1,1]=>3
{{1},{2},{3},{4},{5,6,7,8}}=>[4,1,1,1,1]=>[5,1,1,1]=>6
{{1},{2},{3},{4,5},{6},{7,8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1},{2},{3},{4,8},{5},{6},{7}}=>[2,1,1,1,1,1,1]=>[7,1]=>1
{{1},{2},{3},{4,6,7,8},{5}}=>[4,1,1,1,1]=>[5,1,1,1]=>6
{{1},{2},{3},{4,8},{5,6},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1},{2},{3},{4,7,8},{5,6}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2},{3},{4,8},{5,7},{6}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1},{2},{3},{4,8},{5,6,7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2},{3},{4,5,6,7,8}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1},{2},{3,4},{5},{6},{7,8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1},{2},{3,4},{5},{6,8},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1},{2},{3,4},{5,6,7,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2},{3,5},{4},{6,7,8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2},{3,8},{4},{5},{6},{7}}=>[2,1,1,1,1,1,1]=>[7,1]=>1
{{1},{2},{3,7,8},{4},{5,6}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2},{3,5,7,8},{4},{6}}=>[4,1,1,1,1]=>[5,1,1,1]=>6
{{1},{2},{3,8},{4},{5,6,7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2},{3,5,8},{4},{6,7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2},{3,5,6,7,8},{4}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1},{2},{3,4,5},{6},{7},{8}}=>[3,1,1,1,1,1]=>[6,1,1]=>3
{{1},{2},{3,4,5},{6,7,8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2},{3,8},{4,5},{6},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1},{2},{3,6,7,8},{4,5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2},{3,8},{4,6},{5},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1},{2},{3,7,8},{4,6},{5}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2},{3,8},{4,7},{5},{6}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1},{2},{3,8},{4,6,7},{5}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2},{3,4,5,6},{7,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2},{3,8},{4,5,6},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2},{3,7,8},{4,5,6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2},{3,8},{4,7},{5,6}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2},{3,4,5,8},{6},{7}}=>[4,1,1,1,1]=>[5,1,1,1]=>6
{{1},{2},{3,4,5,6,7},{8}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1},{2},{3,8},{4,5,6,7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2},{3,4,8},{5,6,7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2},{3,4,5,8},{6,7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2},{3,4,5,6,8},{7}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1},{2},{3,4,5,6,7,8}}=>[6,1,1]=>[3,1,1,1,1,1]=>15
{{1},{2,3},{4},{5},{6},{7,8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1},{2,3},{4},{5},{6,8},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1},{2,3},{4},{5,6,7,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,3},{4,5},{6,7},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,3},{4,5},{6,8},{7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,3},{4,5},{6,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3},{4,6,7},{5},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,3},{4,6,8},{5},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,3},{4,6,7,8},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,3},{4,5,6},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3},{4,7},{5,6},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,3},{4,8},{5,6},{7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,3},{4,7,8},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3},{4,8},{5,7},{6}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,3},{4,5,8},{6},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,3},{4,8},{5,6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3},{4,5,8},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3},{4,5,6,8},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,3},{4,5,6,7,8}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1},{2,4},{3},{5},{6},{7,8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1},{2,4},{3},{5},{6,8},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1},{2,4},{3},{5},{6,7,8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,4},{3},{5,6},{7,8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,4},{3},{5,7,8},{6}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,4},{3},{5,8},{6,7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,4},{3},{5,6,7,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,5},{3},{4},{6,8},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1},{2,8},{3},{4},{5},{6},{7}}=>[2,1,1,1,1,1,1]=>[7,1]=>1
{{1},{2,5,8},{3},{4},{6},{7}}=>[3,1,1,1,1,1]=>[6,1,1]=>3
{{1},{2,8},{3},{4},{5,6,7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,5,6,8},{3},{4},{7}}=>[4,1,1,1,1]=>[5,1,1,1]=>6
{{1},{2,5,6,7,8},{3},{4}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1},{2,4,5},{3},{6,7},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,4,5},{3},{6,8},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,4,5},{3},{6,7,8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,6},{3},{4,5},{7,8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,6,8},{3},{4,5},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,6,7,8},{3},{4,5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,4,6},{3},{5},{7,8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,4,6,7},{3},{5},{8}}=>[4,1,1,1,1]=>[5,1,1,1]=>6
{{1},{2,8},{3},{4,6,7},{5}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,4,8},{3},{5},{6,7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,4,6,8},{3},{5},{7}}=>[4,1,1,1,1]=>[5,1,1,1]=>6
{{1},{2,4,6,7,8},{3},{5}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1},{2,7,8},{3},{4,5,6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,4,7},{3},{5,6},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,8},{3},{4,7},{5,6}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,4,8},{3},{5,6},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,4,7,8},{3},{5,6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,4,8},{3},{5,7},{6}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,4,5,7,8},{3},{6}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1},{2,4,8},{3},{5,6,7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,4,5,8},{3},{6,7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,4,5,6,8},{3},{7}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1},{2,4,5,6,7,8},{3}}=>[6,1,1]=>[3,1,1,1,1,1]=>15
{{1},{2,3,4},{5},{6},{7},{8}}=>[3,1,1,1,1,1]=>[6,1,1]=>3
{{1},{2,3,4},{5},{6,7,8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,3,4},{5,6},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3,4},{5,8},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3,4},{5,6,8},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,5},{3,4},{6,7},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,5},{3,4},{6,8},{7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,5},{3,4},{6,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,8},{3,4},{5},{6},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1},{2,6,7},{3,4},{5},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,6,8},{3,4},{5},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,7},{3,4},{5,6},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,8},{3,4},{5,6},{7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,7,8},{3,4},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,8},{3,4},{5,7},{6}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,8},{3,4},{5,6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,5,8},{3,4},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,5,6,7,8},{3,4}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1},{2,3,5},{4},{6},{7},{8}}=>[3,1,1,1,1,1]=>[6,1,1]=>3
{{1},{2,3,5},{4},{6,7,8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,6},{3,5},{4},{7,8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,7},{3,5},{4},{6},{8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1},{2,8},{3,5},{4},{6},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1},{2,6,7},{3,5},{4},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,8},{3,5},{4},{6,7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,6,8},{3,5},{4},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,6,7,8},{3,5},{4}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,3,6},{4},{5},{7},{8}}=>[3,1,1,1,1,1]=>[6,1,1]=>3
{{1},{2,3,7},{4},{5},{6},{8}}=>[3,1,1,1,1,1]=>[6,1,1]=>3
{{1},{2,8},{3,7},{4},{5},{6}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1},{2,3,8},{4},{5},{6},{7}}=>[3,1,1,1,1,1]=>[6,1,1]=>3
{{1},{2,3,7,8},{4},{5},{6}}=>[4,1,1,1,1]=>[5,1,1,1]=>6
{{1},{2,3,6,7},{4},{5},{8}}=>[4,1,1,1,1]=>[5,1,1,1]=>6
{{1},{2,3,6,8},{4},{5},{7}}=>[4,1,1,1,1]=>[5,1,1,1]=>6
{{1},{2,3,6,7,8},{4},{5}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1},{2,7},{3,5,6},{4},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,8},{3,5,6},{4},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,3,7},{4},{5,6},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,8},{3,7},{4},{5,6}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,3,5,7},{4},{6},{8}}=>[4,1,1,1,1]=>[5,1,1,1]=>6
{{1},{2,8},{3,5,7},{4},{6}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,3,5,8},{4},{6},{7}}=>[4,1,1,1,1]=>[5,1,1,1]=>6
{{1},{2,3,5,7,8},{4},{6}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1},{2,3,5,6,7},{4},{8}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1},{2,8},{3,5,6,7},{4}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,3,8},{4},{5,6,7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,3,5,8},{4},{6,7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,3,5,6,8},{4},{7}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1},{2,8},{3,4,5},{6},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,8},{3,4,5},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,6,8},{3,4,5},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,6,7,8},{3,4,5}}=>[4,3,1]=>[3,2,2,1]=>9
{{1},{2,3,6},{4,5},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,7},{3,6},{4,5},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,8},{3,6},{4,5},{7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,7,8},{3,6},{4,5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,8},{3,7},{4,5},{6}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,3,8},{4,5},{6},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,3,6,7},{4,5},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,8},{3,6,7},{4,5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3,8},{4,5},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3,6,8},{4,5},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,3,4,6},{5},{7,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,8},{3,4,6},{5},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,7,8},{3,4,6},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,8},{3,7},{4,6},{5}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,3,8},{4,6},{5},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,3,7,8},{4,6},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,3,4,8},{5},{6},{7}}=>[4,1,1,1,1]=>[5,1,1,1]=>6
{{1},{2,3,4,7,8},{5},{6}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1},{2,8},{3,4,6,7},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,3,8},{4,6,7},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,3,4,6,8},{5},{7}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1},{2,3,4,6,7,8},{5}}=>[6,1,1]=>[3,1,1,1,1,1]=>15
{{1},{2,3,4,5,6},{7},{8}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1},{2,3,4,5,6},{7,8}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1},{2,8},{3,4,5,6},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,8},{3,7},{4,5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3,8},{4,5,6},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,8},{3,4,7},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3,8},{4,7},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3,4,8},{5,6},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,3,4,5,7},{6},{8}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1},{2,8},{3,4,5,7},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,3,8},{4,5,7},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,3,4,8},{5,7},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,3,4,5,8},{6},{7}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1},{2,3,4,5,7,8},{6}}=>[6,1,1]=>[3,1,1,1,1,1]=>15
{{1},{2,3,4,8},{5,6,7}}=>[4,3,1]=>[3,2,2,1]=>9
{{1},{2,3,4,5,8},{6,7}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1},{2,3,4,5,6,8},{7}}=>[6,1,1]=>[3,1,1,1,1,1]=>15
{{1},{2,3,4,5,6,7,8}}=>[7,1]=>[2,1,1,1,1,1,1]=>21
{{1,2},{3},{4},{5},{6},{7},{8}}=>[2,1,1,1,1,1,1]=>[7,1]=>1
{{1,2},{3},{4},{5},{6},{7,8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,2},{3},{4},{5},{6,8},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,2},{3},{4},{5,6,7,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2},{3},{4,5},{6,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3},{4,6,7,8},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2},{3},{4,5,6},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3},{4,5,8},{6},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,2},{3},{4,5,8},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3},{4,5,6,8},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2},{3},{4,5,6,7,8}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2},{3,4},{5},{6,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,4},{5,7,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,4},{5,6,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,4},{5,6,7,8}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,2},{3,5},{4},{6,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,6,7,8},{4},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2},{3,5,6},{4},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,7,8},{4},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,5,7,8},{4},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2},{3,8},{4},{5,6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,5,8},{4},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,5,6,8},{4},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2},{3,5,6,7,8},{4}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2},{3,4,5},{6},{7},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,2},{3,8},{4,5},{6},{7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,2},{3,7,8},{4,5},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,6,8},{4,5},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,6,7,8},{4,5}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,2},{3,4,6},{5},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,7,8},{4,6},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,4,8},{5},{6},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,2},{3,4,7,8},{5},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2},{3,8},{4,6,7},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,4,8},{5},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,4,6,8},{5},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2},{3,4,6,7,8},{5}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2},{3,4,5,6},{7,8}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,2},{3,8},{4,5,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,4,8},{5,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,8},{4,5,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,4,8},{5,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,4,5,8},{6},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2},{3,4,5,7,8},{6}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2},{3,4,5,6,7},{8}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2},{3,8},{4,5,6,7}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,2},{3,4,8},{5,6,7}}=>[3,3,2]=>[3,3,2]=>7
{{1,2},{3,4,5,8},{6,7}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,2},{3,4,5,6,8},{7}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2},{3,4,5,6,7,8}}=>[6,2]=>[2,2,1,1,1,1]=>16
{{1,3},{2},{4},{5},{6},{7},{8}}=>[2,1,1,1,1,1,1]=>[7,1]=>1
{{1,3},{2},{4},{5},{6},{7,8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,3},{2},{4},{5},{6,8},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,3},{2},{4},{5},{6,7,8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,3},{2},{4},{5,7,8},{6}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,3},{2},{4},{5,8},{6,7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,3},{2},{4},{5,6,7,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3},{2},{4,5},{6,7},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,3},{2},{4,5},{6,8},{7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,3},{2},{4,5},{6,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2},{4,6},{5},{7,8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,3},{2},{4,6,7},{5},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,3},{2},{4,8},{5},{6,7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,3},{2},{4,6,8},{5},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,3},{2},{4,6,7,8},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3},{2},{4,5,6},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2},{4,7},{5,6},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,3},{2},{4,8},{5,6},{7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,3},{2},{4,7,8},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2},{4,8},{5,7},{6}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,3},{2},{4,5,7,8},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3},{2},{4,8},{5,6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2},{4,5,8},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2},{4,5,6,8},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3},{2},{4,5,6,7,8}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,4},{2},{3},{5},{6},{7},{8}}=>[2,1,1,1,1,1,1]=>[7,1]=>1
{{1,4},{2},{3},{5},{6,8},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,4},{2},{3},{5},{6,7,8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,4},{2},{3},{5,6},{7,8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,4},{2},{3},{5,8},{6},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,4},{2},{3},{5,6,7,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,5},{2},{3},{4},{6},{7},{8}}=>[2,1,1,1,1,1,1]=>[7,1]=>1
{{1,5},{2},{3},{4},{6,7,8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,6},{2},{3},{4},{5},{7},{8}}=>[2,1,1,1,1,1,1]=>[7,1]=>1
{{1,6},{2},{3},{4},{5},{7,8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,7},{2},{3},{4},{5},{6},{8}}=>[2,1,1,1,1,1,1]=>[7,1]=>1
{{1,8},{2},{3},{4},{5},{6},{7}}=>[2,1,1,1,1,1,1]=>[7,1]=>1
{{1,7,8},{2},{3},{4},{5},{6}}=>[3,1,1,1,1,1]=>[6,1,1]=>3
{{1,8},{2},{3},{4},{5},{6,7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,6,8},{2},{3},{4},{5},{7}}=>[3,1,1,1,1,1]=>[6,1,1]=>3
{{1,6,7,8},{2},{3},{4},{5}}=>[4,1,1,1,1]=>[5,1,1,1]=>6
{{1,7},{2},{3},{4},{5,6},{8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,5,7},{2},{3},{4},{6},{8}}=>[3,1,1,1,1,1]=>[6,1,1]=>3
{{1,8},{2},{3},{4},{5,7},{6}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,5,7,8},{2},{3},{4},{6}}=>[4,1,1,1,1]=>[5,1,1,1]=>6
{{1,8},{2},{3},{4},{5,6,7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,5,6,8},{2},{3},{4},{7}}=>[4,1,1,1,1]=>[5,1,1,1]=>6
{{1,5,6,7,8},{2},{3},{4}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1,4,5},{2},{3},{6},{7},{8}}=>[3,1,1,1,1,1]=>[6,1,1]=>3
{{1,4,5},{2},{3},{6,8},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,4,5},{2},{3},{6,7,8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,6},{2},{3},{4,5},{7},{8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,8},{2},{3},{4,5},{6},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,6,7},{2},{3},{4,5},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,6,7,8},{2},{3},{4,5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,7},{2},{3},{4,6},{5},{8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,4,6,8},{2},{3},{5},{7}}=>[4,1,1,1,1]=>[5,1,1,1]=>6
{{1,4,5,6},{2},{3},{7,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,7},{2},{3},{4,5,6},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,4,8},{2},{3},{5,6},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,4,7,8},{2},{3},{5,6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,5,8},{2},{3},{6},{7}}=>[4,1,1,1,1]=>[5,1,1,1]=>6
{{1,4,5,6,7},{2},{3},{8}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1,4,8},{2},{3},{5,6,7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4,5,8},{2},{3},{6,7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,5,6,8},{2},{3},{7}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1,3,4},{2},{5},{6},{7},{8}}=>[3,1,1,1,1,1]=>[6,1,1]=>3
{{1,3,4},{2},{5},{6},{7,8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,3,4},{2},{5},{6,8},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,3,4},{2},{5},{6,7,8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,4},{2},{5,6},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,4},{2},{5,7,8},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,4},{2},{5,8},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,4},{2},{5,6,8},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,4},{2},{5,6,7,8}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,5},{2},{3,4},{6},{7},{8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,5},{2},{3,4},{6},{7,8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,5},{2},{3,4},{6,8},{7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,8},{2},{3,4},{5},{6},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,6,7,8},{2},{3,4},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,5,6},{2},{3,4},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7,8},{2},{3,4},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,7},{2},{3,4},{6},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,5,7,8},{2},{3,4},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,5,6,7},{2},{3,4},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,8},{2},{3,4},{5,6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,8},{2},{3,4},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,6,8},{2},{3,4},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,5},{2},{4},{6},{7},{8}}=>[3,1,1,1,1,1]=>[6,1,1]=>3
{{1,3,5},{2},{4},{6},{7,8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,3,5},{2},{4},{6,7},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,3,5},{2},{4},{6,8},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,3,5},{2},{4},{6,7,8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,6},{2},{3,5},{4},{7},{8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,6},{2},{3,5},{4},{7,8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,8},{2},{3,5},{4},{6},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,6,8},{2},{3,5},{4},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,6,7,8},{2},{3,5},{4}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,6},{2},{4},{5},{7},{8}}=>[3,1,1,1,1,1]=>[6,1,1]=>3
{{1,3,7},{2},{4},{5},{6},{8}}=>[3,1,1,1,1,1]=>[6,1,1]=>3
{{1,3,8},{2},{4},{5},{6},{7}}=>[3,1,1,1,1,1]=>[6,1,1]=>3
{{1,3,7,8},{2},{4},{5},{6}}=>[4,1,1,1,1]=>[5,1,1,1]=>6
{{1,3,5,6},{2},{4},{7,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,7},{2},{3,5,6},{4},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,7,8},{2},{3,5,6},{4}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,7},{2},{4},{5,6},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,3,5,7},{2},{4},{6},{8}}=>[4,1,1,1,1]=>[5,1,1,1]=>6
{{1,3,5,8},{2},{4},{6},{7}}=>[4,1,1,1,1]=>[5,1,1,1]=>6
{{1,3,5,7,8},{2},{4},{6}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1,3,8},{2},{4},{5,6,7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,5,8},{2},{4},{6,7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,5,6,8},{2},{4},{7}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1,3,4,5},{2},{6},{7,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,4,5},{2},{6,7},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,4,5},{2},{6,8},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,4,5},{2},{6,7,8}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,6},{2},{3,4,5},{7},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,6},{2},{3,4,5},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2},{3,4,5},{6},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,7,8},{2},{3,4,5},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,8},{2},{3,4,5},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,8},{2},{3,4,5},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,6},{2},{4,5},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2},{3,6},{4,5},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,7,8},{2},{3,6},{4,5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,7},{2},{4,5},{6},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,3,7,8},{2},{4,5},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,8},{2},{3,6,7},{4,5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,8},{2},{4,5},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,6,8},{2},{4,5},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,4,6},{2},{5},{7,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,7},{2},{4,6},{5},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,3,7,8},{2},{4,6},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,4,8},{2},{5},{6},{7}}=>[4,1,1,1,1]=>[5,1,1,1]=>6
{{1,3,4,7,8},{2},{5},{6}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1,8},{2},{3,4,6,7},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,8},{2},{4,6,7},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,4,6,8},{2},{5},{7}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1,3,4,5,6},{2},{7},{8}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1,3,4,5,6},{2},{7,8}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,8},{2},{3,4,5,6},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,7},{2},{4,5,6},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,8},{2},{4,5,6},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,8},{2},{3,4,7},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,8},{2},{4,7},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,4,8},{2},{5,6},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,8},{2},{3,4,5,7},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,8},{2},{4,5,7},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,4,8},{2},{5,7},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,4,5,8},{2},{6},{7}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1,3,4,5,6,7},{2},{8}}=>[6,1,1]=>[3,1,1,1,1,1]=>15
{{1,3,4,5,8},{2},{6,7}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,3,4,5,6,8},{2},{7}}=>[6,1,1]=>[3,1,1,1,1,1]=>15
{{1,3,4,5,6,7,8},{2}}=>[7,1]=>[2,1,1,1,1,1,1]=>21
{{1,2,3},{4},{5},{6},{7},{8}}=>[3,1,1,1,1,1]=>[6,1,1]=>3
{{1,2,3},{4},{5},{6},{7,8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,2,3},{4},{5},{6,8},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,2,3},{4,6,7},{5},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,3},{4,5,8},{6},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,3},{4,5,7,8},{6}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,2,3},{4,5,6,7},{8}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,2,3},{4,5,8},{6,7}}=>[3,3,2]=>[3,3,2]=>7
{{1,2,3},{4,5,6,7,8}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,4},{2,3},{5},{6},{7},{8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,4},{2,3},{5,7,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,3},{5,6,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,3},{5,6,7,8}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,5},{2,3},{4},{6},{7},{8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,5},{2,3},{4},{6,7},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,5},{2,3},{4},{6,8},{7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,6},{2,3},{4},{5},{7,8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,7},{2,3},{4},{5},{6},{8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,8},{2,3},{4},{5},{6},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,6,8},{2,3},{4},{5},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,5,6},{2,3},{4},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,3},{4},{5,6},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,7,8},{2,3},{4},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,7},{2,3},{4},{6},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,5,7,8},{2,3},{4},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,5,6,7},{2,3},{4},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,8},{2,3},{4},{5,6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,8},{2,3},{4},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,6,8},{2,3},{4},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,5},{2,3},{6,7},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,3},{4,5},{6},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,8},{2,3},{4,5},{6},{7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,7,8},{2,3},{4,5},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,7},{2,3},{4,5},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,8},{2,3},{4,5},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,7,8},{2,3},{4,5}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,4,6},{2,3},{5},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,3},{4,6},{5},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,7,8},{2,3},{4,6},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,8},{2,3},{5},{6},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,4,7,8},{2,3},{5},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,6,7},{2,3},{5},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,8},{2,3},{4,6,7},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,8},{2,3},{5},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,6,8},{2,3},{5},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,6,7,8},{2,3},{5}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,4,5,6},{2,3},{7,8}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,7},{2,3},{4,5,6},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,7},{2,3},{5,6},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,8},{2,3},{5,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,5,7},{2,3},{6},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,8},{2,3},{4,5,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,8},{2,3},{5,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,5,8},{2,3},{6},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,5,6,7},{2,3},{8}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,4,8},{2,3},{5,6,7}}=>[3,3,2]=>[3,3,2]=>7
{{1,4,5,8},{2,3},{6,7}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,4,5,6,8},{2,3},{7}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,4,5,6,7,8},{2,3}}=>[6,2]=>[2,2,1,1,1,1]=>16
{{1,2,4},{3},{5},{6},{7},{8}}=>[3,1,1,1,1,1]=>[6,1,1]=>3
{{1,2,4},{3},{5,6},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,4},{3},{5,8},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,4},{3},{5,6,8},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,4},{3},{5,6,7,8}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,5},{2,4},{3},{6},{7},{8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,5},{2,4},{3},{6},{7,8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,5},{2,4},{3},{6,7},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,5},{2,4},{3},{6,8},{7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,5},{2,4},{3},{6,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,4},{3},{5},{6},{8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,8},{2,4},{3},{5},{6},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,8},{2,4},{3},{5},{6,7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,6,7,8},{2,4},{3},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,5,6},{2,4},{3},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,4},{3},{5,6},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,7,8},{2,4},{3},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,7},{2,4},{3},{6},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,8},{2,4},{3},{5,7},{6}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,5,7,8},{2,4},{3},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,8},{2,4},{3},{5,6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,8},{2,4},{3},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,6,8},{2,4},{3},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,5},{3},{4},{6},{7},{8}}=>[3,1,1,1,1,1]=>[6,1,1]=>3
{{1,2,5},{3},{4},{6},{7,8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,6},{2,5},{3},{4},{7},{8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,6},{2,5},{3},{4},{7,8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,7},{2,5},{3},{4},{6},{8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,8},{2,5},{3},{4},{6},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,7,8},{2,5},{3},{4},{6}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,6,7,8},{2,5},{3},{4}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,6},{3},{4},{5},{7},{8}}=>[3,1,1,1,1,1]=>[6,1,1]=>3
{{1,2,6},{3},{4},{5},{7,8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,7,8},{2,6},{3},{4},{5}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,2,7},{3},{4},{5},{6},{8}}=>[3,1,1,1,1,1]=>[6,1,1]=>3
{{1,8},{2,7},{3},{4},{5},{6}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,2,8},{3},{4},{5},{6},{7}}=>[3,1,1,1,1,1]=>[6,1,1]=>3
{{1,2,7,8},{3},{4},{5},{6}}=>[4,1,1,1,1]=>[5,1,1,1]=>6
{{1,2,5,6},{3},{4},{7,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,7,8},{2,5,6},{3},{4}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,8},{2,5,7},{3},{4},{6}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,2,5,7,8},{3},{4},{6}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1,2,5,6,7},{3},{4},{8}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1,8},{2,5,6,7},{3},{4}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,5,6,8},{3},{4},{7}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1,6},{2,4,5},{3},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,4,5},{3},{6},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,7,8},{2,4,5},{3},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,6,7},{2,4,5},{3},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,8},{2,4,5},{3},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,8},{2,4,5},{3},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,6},{3},{4,5},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,6},{3},{4,5},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,7,8},{2,6},{3},{4,5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,7,8},{3},{4,5},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,8},{2,6,7},{3},{4,5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,8},{3},{4,5},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,6,8},{3},{4,5},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,4,6},{3},{5},{7,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,7},{2,4,6},{3},{5},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,7,8},{2,4,6},{3},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,7,8},{3},{4,6},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,8},{2,4,7},{3},{5},{6}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,2,4,8},{3},{5},{6},{7}}=>[4,1,1,1,1]=>[5,1,1,1]=>6
{{1,2,4,7,8},{3},{5},{6}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1,8},{2,4,6,7},{3},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,8},{3},{4,6,7},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,4,8},{3},{5},{6,7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,4,6,8},{3},{5},{7}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1,2,4,6,7,8},{3},{5}}=>[6,1,1]=>[3,1,1,1,1,1]=>15
{{1,2,4,5,6},{3},{7,8}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,7},{2,4,5,6},{3},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,8},{2,4,5,6},{3},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,8},{2,7},{3},{4,5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,8},{3},{4,5,6},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,4,7},{3},{5,6},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,8},{2,4,7},{3},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,8},{3},{4,7},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,4,8},{3},{5,6},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,8},{2,4,5,7},{3},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,8},{3},{4,5,7},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,4,8},{3},{5,7},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,4,5,7,8},{3},{6}}=>[6,1,1]=>[3,1,1,1,1,1]=>15
{{1,2,4,5,8},{3},{6,7}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2,4,5,6,8},{3},{7}}=>[6,1,1]=>[3,1,1,1,1,1]=>15
{{1,2,4,5,6,7,8},{3}}=>[7,1]=>[2,1,1,1,1,1,1]=>21
{{1,2,3,4},{5},{6},{7},{8}}=>[4,1,1,1,1]=>[5,1,1,1]=>6
{{1,2,3,4},{5},{6,7},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,3,4},{5,6},{7,8}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,2,3,4},{5,7,8},{6}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,2,3,4},{5,6,7},{8}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,2,3,4},{5,8},{6,7}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,2,3,4},{5,6,8},{7}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,2,3,4},{5,6,7,8}}=>[4,4]=>[2,2,2,2]=>12
{{1,5},{2,3,4},{6},{7},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,5},{2,3,4},{6,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,3,4},{5},{7},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,6},{2,3,4},{5},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,3,4},{5},{6},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,8},{2,3,4},{5},{6},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,8},{2,3,4},{5},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,8},{2,3,4},{5},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,5,6},{2,3,4},{7},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,7},{2,3,4},{5,6},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2,3,4},{5,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,7},{2,3,4},{6},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,8},{2,3,4},{5,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,8},{2,3,4},{6},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,5,6,7},{2,3,4},{8}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,5,8},{2,3,4},{6,7}}=>[3,3,2]=>[3,3,2]=>7
{{1,5,6,8},{2,3,4},{7}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,5,6,7,8},{2,3,4}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,2,5},{3,4},{6},{7},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,2,5},{3,4},{6,7},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,5},{3,4},{6,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,5},{3,4},{6,7,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,7},{2,5},{3,4},{6},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,7,8},{2,5},{3,4},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,7},{2,5},{3,4},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,8},{2,5},{3,4},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,7,8},{2,5},{3,4}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,2,6},{3,4},{5},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,6},{3,4},{5},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,8},{2,6},{3,4},{5},{7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,7,8},{2,6},{3,4},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2,7},{3,4},{5},{6}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,2,8},{3,4},{5},{6},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,2,7,8},{3,4},{5},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,8},{2,6,7},{3,4},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,8},{3,4},{5},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,6,8},{3,4},{5},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,5,6},{3,4},{7},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,8},{2,5,6},{3,4},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7,8},{2,5,6},{3,4}}=>[3,3,2]=>[3,3,2]=>7
{{1,2,7},{3,4},{5,6},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,8},{3,4},{5,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,5,7},{3,4},{6},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,8},{2,5,7},{3,4},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,8},{3,4},{5,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,5,8},{3,4},{6},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,5,6,8},{3,4},{7}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2,3,5},{4},{6},{7,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,3,5},{4},{6,7,8}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,6},{2,3,5},{4},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2,3,5},{4},{6},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,7,8},{2,3,5},{4},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,6,7},{2,3,5},{4},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,8},{2,3,5},{4},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,8},{2,3,5},{4},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,6},{3,5},{4},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,6},{3,5},{4},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,7,8},{2,6},{3,5},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,7,8},{3,5},{4},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,8},{2,6,7},{3,5},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,8},{3,5},{4},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,6,8},{3,5},{4},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,3,6},{4},{5},{7,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,8},{2,3,6},{4},{5},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,7,8},{2,3,6},{4},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,7,8},{3,6},{4},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,8},{2,3,7},{4},{5},{6}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,2,3,8},{4},{5},{6},{7}}=>[4,1,1,1,1]=>[5,1,1,1]=>6
{{1,2,3,7,8},{4},{5},{6}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1,8},{2,3,6,7},{4},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,8},{3,6,7},{4},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,3,8},{4},{5},{6,7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,3,6,8},{4},{5},{7}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1,2,3,6,7,8},{4},{5}}=>[6,1,1]=>[3,1,1,1,1,1]=>15
{{1,2,3,5,6},{4},{7},{8}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1,2,3,5,6},{4},{7,8}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,7},{2,3,5,6},{4},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,8},{2,3,5,6},{4},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,7},{3,5,6},{4},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,8},{2,7},{3,5,6},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,8},{3,5,6},{4},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,3,7},{4},{5,6},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,8},{2,3,7},{4},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,8},{3,7},{4},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,3,8},{4},{5,6},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,3,5,7},{4},{6},{8}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1,8},{2,3,5,7},{4},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,8},{3,5,7},{4},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,3,8},{4},{5,7},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,3,5,8},{4},{6},{7}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1,2,3,5,7,8},{4},{6}}=>[6,1,1]=>[3,1,1,1,1,1]=>15
{{1,2,3,5,6,7},{4},{8}}=>[6,1,1]=>[3,1,1,1,1,1]=>15
{{1,8},{2,3,5,6,7},{4}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2,3,5,6,7,8},{4}}=>[7,1]=>[2,1,1,1,1,1,1]=>21
{{1,2,3,4,5},{6},{7},{8}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1,2,3,4,5},{6,7},{8}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2,3,4,5},{6,8},{7}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2,3,4,5},{6,7,8}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,6},{2,3,4,5},{7},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,7},{2,3,4,5},{6},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,6,7,8},{2,3,4,5}}=>[4,4]=>[2,2,2,2]=>12
{{1,2,6},{3,4,5},{7},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,6},{3,4,5},{7,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,7},{2,6},{3,4,5},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2,6},{3,4,5},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7,8},{2,6},{3,4,5}}=>[3,3,2]=>[3,3,2]=>7
{{1,8},{2,7},{3,4,5},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,8},{3,4,5},{6,7}}=>[3,3,2]=>[3,3,2]=>7
{{1,2,6,7,8},{3,4,5}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,2,3,6},{4,5},{7},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,3,6},{4,5},{7,8}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,8},{2,3,6},{4,5},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,8},{3,6},{4,5},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,3,7},{4,5},{6},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,8},{2,3,7},{4,5},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,8},{3,7},{4,5},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,3,8},{4,5},{6},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,3,6,7},{4,5},{8}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,8},{2,3,6,7},{4,5}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,2,3,8},{4,5},{6,7}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,2,3,6,8},{4,5},{7}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2,3,6,7,8},{4,5}}=>[6,2]=>[2,2,1,1,1,1]=>16
{{1,2,3,4,6},{5},{7},{8}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1,2,3,4,6},{5},{7,8}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,8},{2,3,4,6},{5},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,8},{2,7},{3,4,6},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,8},{3,4,6},{5},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,7,8},{3,4,6},{5}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,2,3,7},{4,6},{5},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,8},{2,3,7},{4,6},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,8},{3,7},{4,6},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,3,8},{4,6},{5},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,3,7,8},{4,6},{5}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2,3,4,7},{5},{6},{8}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1,8},{2,3,4,7},{5},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,8},{3,4,7},{5},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,3,8},{4,7},{5},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,3,4,8},{5},{6},{7}}=>[5,1,1,1]=>[4,1,1,1,1]=>10
{{1,2,3,4,7,8},{5},{6}}=>[6,1,1]=>[3,1,1,1,1,1]=>15
{{1,2,3,4,6,7},{5},{8}}=>[6,1,1]=>[3,1,1,1,1,1]=>15
{{1,8},{2,3,4,6,7},{5}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2,3,4,6,8},{5},{7}}=>[6,1,1]=>[3,1,1,1,1,1]=>15
{{1,2,3,4,6,7,8},{5}}=>[7,1]=>[2,1,1,1,1,1,1]=>21
{{1,2,3,4,5,6},{7},{8}}=>[6,1,1]=>[3,1,1,1,1,1]=>15
{{1,2,3,4,5,6},{7,8}}=>[6,2]=>[2,2,1,1,1,1]=>16
{{1,7},{2,3,4,5,6},{8}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,8},{2,3,4,5,6},{7}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2,7},{3,4,5,6},{8}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,2,7,8},{3,4,5,6}}=>[4,4]=>[2,2,2,2]=>12
{{1,2,3,7},{4,5,6},{8}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,8},{2,3,7},{4,5,6}}=>[3,3,2]=>[3,3,2]=>7
{{1,2,8},{3,7},{4,5,6}}=>[3,3,2]=>[3,3,2]=>7
{{1,2,3,8},{4,5,6},{7}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,2,3,7,8},{4,5,6}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,2,3,4,7},{5,6},{8}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,8},{2,3,4,7},{5,6}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,2,8},{3,4,7},{5,6}}=>[3,3,2]=>[3,3,2]=>7
{{1,2,3,8},{4,7},{5,6}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,2,3,4,8},{5,6},{7}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2,3,4,5,7},{6},{8}}=>[6,1,1]=>[3,1,1,1,1,1]=>15
{{1,8},{2,3,4,5,7},{6}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2,8},{3,4,5,7},{6}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,2,3,8},{4,5,7},{6}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,2,3,4,8},{5,7},{6}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2,3,4,5,7,8},{6}}=>[7,1]=>[2,1,1,1,1,1,1]=>21
{{1,2,3,4,5,6,7},{8}}=>[7,1]=>[2,1,1,1,1,1,1]=>21
{{1,8},{2,3,4,5,6,7}}=>[6,2]=>[2,2,1,1,1,1]=>16
{{1,2,8},{3,4,5,6,7}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,2,3,8},{4,5,6,7}}=>[4,4]=>[2,2,2,2]=>12
{{1,2,3,4,8},{5,6,7}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,2,3,4,5,8},{6,7}}=>[6,2]=>[2,2,1,1,1,1]=>16
{{1,2,3,4,5,6,8},{7}}=>[7,1]=>[2,1,1,1,1,1,1]=>21
{{1,2,3,4,5,6,7,8}}=>[8]=>[1,1,1,1,1,1,1,1]=>28
{{1,3,5,6,7,8},{2,4}}=>[6,2]=>[2,2,1,1,1,1]=>16
{{1,3,4,6,7,8},{2,5}}=>[6,2]=>[2,2,1,1,1,1]=>16
{{1,2,4,6,7,8},{3,5}}=>[6,2]=>[2,2,1,1,1,1]=>16
{{1,2,4,5,7,8},{3,6}}=>[6,2]=>[2,2,1,1,1,1]=>16
{{1,2,3,5,7,8},{4,6}}=>[6,2]=>[2,2,1,1,1,1]=>16
{{1,2,4,5,6,8},{3,7}}=>[6,2]=>[2,2,1,1,1,1]=>16
{{1,2,3,5,6,8},{4,7}}=>[6,2]=>[2,2,1,1,1,1]=>16
{{1,2,3,4,6,8},{5,7}}=>[6,2]=>[2,2,1,1,1,1]=>16
{{1,2,4,5,6,7},{3,8}}=>[6,2]=>[2,2,1,1,1,1]=>16
{{1,3,5,7,8},{2,4,6}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,2,5,7,8},{3,4,6}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,3,4,7,8},{2,5,6}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,2,4,7,8},{3,5,6}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,2,5,6,8},{3,4,7}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,3,4,6,8},{2,5,7}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,2,4,6,8},{3,5,7}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,2,3,6,8},{4,5,7}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,2,3,5,8},{4,6,7}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,2,3,6,7},{4,5,8}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,3,4,5,7},{2,6,8}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,2,3,4,7},{5,6,8}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,2,4,5,6},{3,7,8}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,2,3,5,6},{4,7,8}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,2,3,4,6},{5,7,8}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,3,6,7,8},{2,4},{5}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,3,4,7,8},{2,6},{5}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2,4,7,8},{3,6},{5}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,3,4,5,8},{2,7},{6}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,3,4,6,7},{2,8},{5}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2,4,6,7},{3,8},{5}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,3,4,5,7},{2,8},{6}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2,3,5,7},{4,8},{6}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,3,4,5,6},{2,8},{7}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2,3,5,6},{4,8},{7}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2,3,4,6},{5,8},{7}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,3,5,6,7},{2,4},{8}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2,3,5,7},{4,6},{8}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2,3,5,6},{4,7},{8}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2,3,4,6},{5,7},{8}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,3,5,7},{2,4,6,8}}=>[4,4]=>[2,2,2,2]=>12
{{1,2,5,7},{3,4,6,8}}=>[4,4]=>[2,2,2,2]=>12
{{1,3,4,7},{2,5,6,8}}=>[4,4]=>[2,2,2,2]=>12
{{1,2,3,7},{4,5,6,8}}=>[4,4]=>[2,2,2,2]=>12
{{1,3,5,6},{2,4,7,8}}=>[4,4]=>[2,2,2,2]=>12
{{1,2,5,6},{3,4,7,8}}=>[4,4]=>[2,2,2,2]=>12
{{1,2,4,6},{3,5,7,8}}=>[4,4]=>[2,2,2,2]=>12
{{1,2,3,6},{4,5,7,8}}=>[4,4]=>[2,2,2,2]=>12
{{1,3,6,8},{2,5,7},{4}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,2,6,8},{3,5,7},{4}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,2,5,8},{3,6,7},{4}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,2,5,8},{3,4,6},{7}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,2,4,8},{3,5,6},{7}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,2,4,7},{3,6,8},{5}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,3,5,7},{2,4,8},{6}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,2,4,7},{3,5,8},{6}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,3,4,5},{2,7,8},{6}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,2,4,5},{3,7,8},{6}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,3,5,6},{2,4,8},{7}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,2,3,6},{4,5,8},{7}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,2,3,5},{4,6,7},{8}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,2,7,8},{3,5},{4,6}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,2,6,8},{3,5},{4,7}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,3,6,8},{2,4},{5,7}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,3,5,8},{2,6},{4,7}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,3,5,8},{2,4},{6,7}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,2,4,8},{3,5},{6,7}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,4,5,7},{2,6},{3,8}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,3,5,7},{2,6},{4,8}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,3,5,6},{2,4},{7,8}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,2,4,6},{3,5},{7,8}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,5,7,8},{2,6},{3},{4}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,7,8},{2,6},{3},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,7,8},{2,6},{4},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,7,8},{2,5},{4},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,7,8},{2,4},{5},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,5,6,8},{2,7},{3},{4}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,6,8},{2,7},{3},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,6,8},{2,7},{4},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,6,8},{3,7},{4},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,5,8},{2,7},{3},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,5,8},{2,7},{4},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,5,8},{3,7},{4},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,4,8},{2,7},{5},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,4,8},{3,7},{5},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,6,8},{2,5},{3},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,6,8},{2,5},{4},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,6,8},{2,4},{5},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,5,8},{2,6},{3},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,5,8},{2,6},{4},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,5,8},{3,6},{4},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,4,8},{2,6},{5},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,4,8},{3,6},{5},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,4,8},{2,5},{6},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,4,8},{3,5},{6},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,5,6,7},{2,8},{3},{4}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,6,7},{2,8},{3},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,6,7},{2,8},{4},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,6,7},{3,8},{4},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,5,7},{2,8},{3},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,5,7},{2,8},{4},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,5,7},{3,8},{4},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,4,7},{2,8},{5},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,4,7},{3,8},{5},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,5,6},{2,8},{3},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,5,6},{2,8},{4},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,5,6},{3,8},{4},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,4,6},{2,8},{5},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,4,6},{3,8},{5},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,3,6},{4,8},{5},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,4,5},{2,8},{6},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,4,5},{3,8},{6},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,3,5},{4,8},{6},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,6,7},{2,5},{3},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,6,7},{2,5},{4},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,5,7},{2,6},{3},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,5,7},{2,6},{4},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,5,7},{3,6},{4},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,4,7},{2,6},{5},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,4,7},{3,6},{5},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,5,7},{2,4},{6},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,4,7},{3,5},{6},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,5,6},{2,7},{3},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,4,6},{2,7},{5},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,4,6},{3,7},{5},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,3,6},{4,7},{5},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,4,5},{2,7},{6},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,4,5},{3,7},{6},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,3,5},{4,7},{6},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,4,6},{3,5},{7},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,4,5},{2,6},{7},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,4,5},{3,6},{7},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,3,5},{4,6},{7},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,7},{2,4,8},{5,6}}=>[3,3,2]=>[3,3,2]=>7
{{1,4,5},{2,6,8},{3,7}}=>[3,3,2]=>[3,3,2]=>7
{{1,3,4},{2,6,8},{5,7}}=>[3,3,2]=>[3,3,2]=>7
{{1,3,5},{2,4,8},{6,7}}=>[3,3,2]=>[3,3,2]=>7
{{1,2,5},{3,4,8},{6,7}}=>[3,3,2]=>[3,3,2]=>7
{{1,3,4},{2,5,8},{6,7}}=>[3,3,2]=>[3,3,2]=>7
{{1,2,4},{3,5,8},{6,7}}=>[3,3,2]=>[3,3,2]=>7
{{1,4,6},{2,5,7},{3,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,2,5},{3,4,6},{7,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,3,4},{2,5,6},{7,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,2,4},{3,5,6},{7,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,5,7},{2,6,8},{3},{4}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4,7},{2,6,8},{3},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,7},{2,6,8},{4},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,7},{3,6,8},{4},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4,7},{2,5,8},{3},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,7},{2,5,8},{4},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,7},{3,5,8},{4},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,7},{2,4,8},{5},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,7},{3,4,8},{5},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,5,6},{2,7,8},{3},{4}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4,6},{2,7,8},{3},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,6},{2,7,8},{4},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,6},{3,7,8},{4},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4,5},{2,7,8},{3},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,5},{2,7,8},{4},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,5},{3,7,8},{4},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,4},{2,7,8},{5},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,4},{3,7,8},{5},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4,6},{2,5,8},{3},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,6},{2,5,8},{4},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,6},{3,5,8},{4},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,6},{2,4,8},{5},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,6},{3,4,8},{5},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4,5},{2,6,8},{3},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,5},{2,6,8},{4},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,5},{3,6,8},{4},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,4},{2,6,8},{5},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,4},{3,6,8},{5},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,5},{3,4,8},{6},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,4},{3,5,8},{6},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4,6},{2,5,7},{3},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,6},{2,5,7},{4},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,6},{3,5,7},{4},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,6},{2,4,7},{5},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,5},{2,6,7},{4},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,5},{3,6,7},{4},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,4},{2,6,7},{5},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,5},{2,4,7},{6},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,5},{3,4,7},{6},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,4},{3,5,7},{6},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,5},{3,4,6},{7},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,5,8},{2,6},{3,7},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,8},{2,6},{3,7},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,8},{2,6},{4,7},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,8},{3,6},{4,7},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,8},{2,5},{3,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,8},{2,5},{4,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,8},{3,5},{4,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,8},{2,4},{5,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,8},{2,5},{3,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,8},{2,5},{4,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,8},{3,5},{4,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,8},{2,4},{5,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,7},{2,6},{3,8},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,7},{2,6},{3,8},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,7},{2,6},{4,8},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,7},{3,6},{4,8},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,7},{2,5},{3,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,7},{2,5},{4,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,7},{3,5},{4,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,7},{2,4},{5,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,7},{3,4},{5,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,6},{2,7},{3,8},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,6},{2,7},{3,8},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,6},{2,7},{4,8},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,6},{3,7},{4,8},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,5},{2,7},{3,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,5},{2,7},{4,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,5},{3,7},{4,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,4},{2,7},{5,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,4},{3,7},{5,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,6},{2,5},{3,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,6},{2,5},{4,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,6},{3,5},{4,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,6},{2,4},{5,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,6},{3,4},{5,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,5},{2,6},{3,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,5},{2,6},{4,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,5},{3,6},{4,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,4},{2,6},{5,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,4},{3,6},{5,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,3},{4,6},{5,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,5},{2,4},{6,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,4},{2,5},{6,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,7},{2,5},{3,6},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,7},{2,5},{4,6},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,7},{2,4},{5,6},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,6},{3,4},{5,7},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,5},{2,6},{3,7},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,4},{2,6},{5,7},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,4},{3,6},{5,7},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,3},{4,6},{5,7},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,4},{2,5},{6,7},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,8},{2,4},{5},{6},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,6,7},{2,8},{3},{4},{5}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,3,4},{2,8},{5},{6},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,4,7},{2,6},{3},{5},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,4,7},{2,5},{3},{6},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,3,7},{2,4},{5},{6},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,4,6},{2,7},{3},{5},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,3,5},{2,4},{6},{7},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,5},{2,6},{3,7},{4},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,3},{2,6},{4,7},{5},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,3},{2,5},{4,7},{6},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,4},{2,5},{3,6},{7},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,3},{2,5},{4,6},{7},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,7},{2,8},{3},{4},{5},{6}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,6},{2,8},{3},{4},{5},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,4},{2,8},{3},{5},{6},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,3},{2,8},{4},{5},{6},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,5},{2,6},{3},{4},{7},{8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,4},{2,5},{3},{6},{7},{8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,3},{2,4},{5},{6},{7},{8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,3,5,8},{2},{4,6},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,5,7},{2},{4},{6,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,5,7},{2,4},{3},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,4,8},{3},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,8},{2,4},{3,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,8},{2,4},{3,5},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3,5,8},{4,6},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,5,8},{2,6},{3,4},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,8},{2,6},{3,5},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,5,8},{3},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,7},{2,5},{3},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2},{3,6,7},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2},{3,6},{5,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2},{3,7},{5,6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2},{3,5,8},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2},{3,4,8},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,5},{3},{4,7,8},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,5,7},{3},{4,8},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,3,5,7},{4},{6,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,5,7},{2},{3,4},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,7},{2},{3,5},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2},{3,8},{5,6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,6},{2},{3,8},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,6},{2},{3,7},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,6},{3,4,7},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,3,7},{4},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,6,7},{4,8},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,6},{4,7,8},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,3},{4},{5,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,6},{3,4},{5,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,7},{3,4},{5,6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,3},{4},{5,6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,7},{4,6,8},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,5,8},{4,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,3,8},{4,5},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,5},{3,4,8},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4},{3,5,8},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4},{3,7},{5,6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4},{3,6},{5,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4},{3,6,7},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,6,7},{4},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,6},{4},{5,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,7},{4},{5,6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,7,8},{4,5},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,8},{2,4,7},{5},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4,8},{2,3,7},{5},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4,7},{2,3,8},{5},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,7},{2,8},{4,5},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,8},{4},{5,6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,6},{2,8},{4},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,6},{2,7},{4},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4,6},{3,7},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4,6},{3,8},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4},{3,8},{5,6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4,7},{3,5},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,5,7},{3,4},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,8},{3,4,6},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2,3,6},{4},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,6},{3,8},{4,7},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,3,6},{4},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,7},{3,4,6},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,6,8},{4,7},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,5,7},{4,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,7},{4,5,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,8},{2,7},{3},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,7},{2,8},{4},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,7},{2,8},{4,6},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,7},{2},{4,5,8},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,7},{2,3},{4,5,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,3,8},{4,6},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,3,8},{4},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7,8},{2,5},{3,6},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,4,6,8},{3},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,7},{2,4,5},{3,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,6},{2,5},{3},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,7,8},{2},{3,6},{4}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,5,8},{2,7},{3,6},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2,5,7},{3,6},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,8},{2,6,7},{3},{4}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4,5,7},{2},{3,8},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,5},{2,6},{4},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,6},{2,8},{4,7},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,6,8},{2},{3,7},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,8},{2,4,6},{3,7},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,8},{2,5},{3},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,5},{2,8},{4},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,3,8},{4},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2,6},{3,4,7},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,8},{2},{3,4,7},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,6,8},{2,4},{3,7},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,3,8},{4,7},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,3,7,8},{4},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,5},{2,3,7},{4,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,3,6},{4},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,7},{2,4},{3,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,7},{2,4,8},{3},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,6,8},{2,5,7},{3},{4}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,6,8},{2,7},{3,5},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,8},{2,7},{3},{4,5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,7},{2,8},{3,4},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,7},{2},{3,4,8},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,7},{2,5},{3,4,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,6,8},{3,4},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,8},{2,3,6},{5},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,5},{2,4,8},{3,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,4,7},{3,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,4,8},{3,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,4,8},{3,5},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,5},{3,4,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,3,5},{4,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,3,6},{4,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,6},{3,4,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,8},{2,7},{3,6},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,7},{2,8},{3,6},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,6},{2,8},{3,7},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,7},{2,8},{3,5},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,8},{3,4,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,3,8},{4,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,5},{3,8},{4,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,7},{3,4,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,8},{2,7},{3,5},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,6},{3,4,8},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,3,6},{4,8},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2,3,6},{4,7},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2,3,5},{4,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2,5},{3,4,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2,4,7},{3,5},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2,4,7},{3,6},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,4,8},{3,6},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,5},{2,8},{4,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,8},{2,7},{4,6},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,4,8},{3,7},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,4,7},{3,8},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,4,6},{3,8},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,4,8},{3,5},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,3,5},{4,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,7},{3,8},{4,6},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,8},{3,4,6},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,8},{3,4,7},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,3,7},{4,8},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,7},{3,4,8},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,5},{2},{4,6,8},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3},{2,4,6,8},{5},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,4,6,8},{3},{5,7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3},{2},{4,6,8},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,6},{2},{4,8},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,6},{2},{4,7},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,5},{2},{4,7},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,5,7},{2},{4,6},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,7},{2},{4,6,8},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,7},{2},{4,6},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,5,7},{2},{4,8},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3},{2,4,8},{5,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4,8},{3,5,7},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4},{2,8},{3,5,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,5,7},{3,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,5,7},{4,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,7},{4,6,8},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,7},{2,4,6},{5},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,7},{2,4,6},{3},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,7},{2,4,8},{3},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,8},{3,5,7},{4,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,4,6},{3,5},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,7},{2,6},{3,5},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,5,8},{3,7},{4,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,5,8},{3,6},{4,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4,8},{3,6},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4,6,8},{3,5},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4},{2,6,8},{3,5},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,5},{3,6,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,5},{4,6,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,4,6,8},{3},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,5},{2,4},{3,6,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,6,8},{3,5,7},{4}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,6},{2,8},{3,5,7},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,4,8},{3},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,4,7},{3},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,4,7},{3},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,7},{2,4,6},{3},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,5,7},{2,4},{3,6},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,6,8},{3,5},{4,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4,6,8},{3,7},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,6},{2,7},{3,5,8},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,5},{2,7},{4},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,6,8},{3,5},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,6},{3,5,8},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,4,6},{5,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,6},{4,5,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,5,6},{4,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,5,6},{3},{4,8},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,6},{3},{4,5,8},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,6},{2,3},{4,5,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,6},{2,3},{4,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,6},{2,3,8},{4},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,5,6},{2,8},{3,4},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,8},{3,4,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,3,8},{4,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,3,5,8},{4},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,5},{3,8},{4,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,4},{3,6},{5},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,4,6},{3},{5,8},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,4},{3,8},{5,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,4},{3,8},{5},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,3,8},{5},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,4},{2,8},{5},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,4},{2,8},{5,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,3,8},{5,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,6},{2,3},{5,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,3,6},{5},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,3,6,8},{5},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4},{2,3,6},{5,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2,4,5},{3,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,8},{2,6},{4,5},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,4},{2,6},{5},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,5,8},{3,4},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,4,5},{3,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,5},{2,8},{3,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,8},{2,5,6},{4},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,8},{2,5},{4},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,4},{3,7,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,6},{2,4},{3,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,8},{3,5,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,7,8},{3,5},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,7},{2,8},{3},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,7},{2,8},{3,4},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,7},{2,3,8},{4},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,5},{3,7},{4},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,3,7},{4},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,5},{2,7},{3},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,7},{3},{5,6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,6,7},{3},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,6},{3},{5,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,5,7,8},{3},{4}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,6,7},{2,5,8},{3},{4}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,7},{2,5,6,8},{3},{4}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,7},{2,6,8},{3},{4,5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,3,6,8},{4},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,8},{3,6},{4},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2,6},{3},{4,5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2,5,6},{3},{4,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2,5},{3},{4,6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7,8},{2,5},{3},{4,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2,4},{3,6,7},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7,8},{2,4},{3,6},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,3,7},{5,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,7},{4,5,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,6,7},{4,8},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,6},{4,7,8},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,4,7,8},{3},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,7},{2,4,8},{3},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,4,5,8},{3},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,7},{2,5,8},{3,4},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,3,5,8},{4},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,7},{3},{4,6},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2},{3,4,6},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2},{3,6},{4,5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2},{3,5,6},{4,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,7},{2},{3,5},{4,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2},{3,5},{4,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2},{3,7,8},{4,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2},{3,8},{4,6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,6},{2},{3,8},{4,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2},{3,8},{4,5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2},{3,4,8},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,6},{3},{4,8},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,6,8},{3},{4,7},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,6,8},{2,3},{4,7},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,8},{2},{3,7},{4,5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,6,8},{2},{3,7},{4}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,5,8},{2},{3,6,7},{4}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2},{3},{4},{5},{6},{7},{8},{9}}=>[1,1,1,1,1,1,1,1,1]=>[9]=>0
{{1},{2},{3},{4},{5},{6},{7},{8,9}}=>[2,1,1,1,1,1,1,1]=>[8,1]=>1
{{1},{2},{3},{4},{5},{6},{7,9},{8}}=>[2,1,1,1,1,1,1,1]=>[8,1]=>1
{{1},{2},{3},{4},{5},{6,9},{7},{8}}=>[2,1,1,1,1,1,1,1]=>[8,1]=>1
{{1},{2},{3},{4},{5,9},{6},{7},{8}}=>[2,1,1,1,1,1,1,1]=>[8,1]=>1
{{1},{2},{3},{4,9},{5},{6},{7},{8}}=>[2,1,1,1,1,1,1,1]=>[8,1]=>1
{{1},{2},{3,9},{4},{5},{6},{7},{8}}=>[2,1,1,1,1,1,1,1]=>[8,1]=>1
{{1},{2,9},{3},{4},{5},{6},{7},{8}}=>[2,1,1,1,1,1,1,1]=>[8,1]=>1
{{1,9},{2},{3},{4},{5},{6},{7},{8}}=>[2,1,1,1,1,1,1,1]=>[8,1]=>1
{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}=>[1,1,1,1,1,1,1,1,1,1]=>[10]=>0
{{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>1
{{1},{2},{3},{4},{5},{6},{7,8,9}}=>[3,1,1,1,1,1,1]=>[7,1,1]=>3
{{1},{2},{3},{4},{5},{6},{7},{8,10},{9}}=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>1
{{1},{2},{3},{4},{5},{6,9},{7,8}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1},{2},{3},{4},{5},{6},{7,10},{8},{9}}=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>1
{{1},{2},{3},{4},{5,9},{6,7},{8}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1},{2},{3},{4},{5},{6,10},{7},{8},{9}}=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>1
{{1},{2},{3},{4,9},{5,6},{7},{8}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1},{2},{3},{4},{5,10},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>1
{{1},{2},{3,9},{4,5},{6},{7},{8}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1},{2},{3},{4,10},{5},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>1
{{1},{2,9},{3,4},{5},{6},{7},{8}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1},{2},{3,10},{4},{5},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>1
{{1,9},{2,3},{4},{5},{6},{7},{8}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1},{2,10},{3},{4},{5},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>1
{{1,10},{2},{3},{4},{5},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>1
{{1,2,3,4,5,6,7,8},{9}}=>[8,1]=>[2,1,1,1,1,1,1,1]=>28
{{1},{2,3,4,5,6,7,8,9}}=>[8,1]=>[2,1,1,1,1,1,1,1]=>28
{{1,2,3,4,5,6,7,8,9},{10}}=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>36
{{1,2,3,4,5,6,8},{7},{9}}=>[7,1,1]=>[3,1,1,1,1,1,1]=>21
{{1},{2,3,4,5,6,7,9},{8}}=>[7,1,1]=>[3,1,1,1,1,1,1]=>21
{{1},{2,3,4,5,6,7,8,9,10}}=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>36
{{1,2,3,4,5,6,7,9},{8},{10}}=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>28
{{1,2,3,4,5,8},{6,7},{9}}=>[6,2,1]=>[3,2,1,1,1,1]=>16
{{1,2,3,4,5,7,8},{6},{9}}=>[7,1,1]=>[3,1,1,1,1,1,1]=>21
{{1},{2,3,4,5,6,9},{7,8}}=>[6,2,1]=>[3,2,1,1,1,1]=>16
{{1},{2,3,4,5,6,8,9},{7}}=>[7,1,1]=>[3,1,1,1,1,1,1]=>21
{{1},{2,3,4,5,6,7,8,10},{9}}=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>28
{{1,4,6,8},{2},{3,5},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,5,7},{2,3},{4,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,8},{2},{3,6},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,8},{2},{4,6},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,7,8},{2},{3,6},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,6,7},{2},{3,5},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,8},{2},{3,7},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,8},{2},{3,7},{4,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,8},{2},{3,6},{4,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,7},{2,3},{5,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,5,8},{4,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,4,7,8},{3},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3},{2,4,8},{5,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,5,8},{4,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,4},{3,5,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,6},{3,5,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,5,6},{3,7},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,6,7},{3,8},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,5},{3,6},{4},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,4},{3,7},{5,6},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,4},{2,7},{5,6},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,7},{2,8},{3},{4,5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,6},{2,3},{4,7},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,6},{2,3},{5,7},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,3,6},{5,7},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,3,7},{5},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,4},{3,7},{5},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,4},{2,7},{5},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,6},{3},{4},{5,7,8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,7},{2,3,4},{5},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,4},{3,6,8},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,7},{3,6,8},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,6},{3,5,7},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,4},{3,5,7},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,7,8},{3},{4,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,4},{3,5,6},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,5},{3,7,8},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,6},{3,7,8},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,8},{3,6,7},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,4,5,6,7,8}}=>[6,2]=>[2,2,1,1,1,1]=>16
{{1,4},{2,3,5,6,7,8}}=>[6,2]=>[2,2,1,1,1,1]=>16
{{1,5},{2,3,4,6,7,8}}=>[6,2]=>[2,2,1,1,1,1]=>16
{{1,4},{2,6},{3,5,7,8}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,5},{2,6},{3,4,7,8}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,5},{2,4,6,8},{3,7}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,4,5,8},{2,3,6,7}}=>[4,4]=>[2,2,2,2]=>12
{{1,4},{2},{3,5,6},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,5},{2},{3,6},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2},{3,4,6},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2},{3,4,7,8},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,5},{2},{3,4,7,8},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,5},{2},{3,8},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,7},{2},{3,4,8},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,7},{2},{3,4,8},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,6,7},{2},{3,8},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,6},{2},{3,7,8},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,6},{2},{4},{5,7,8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2},{3,6},{4},{5,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2},{3,5,7,8},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,6},{2,4},{3},{5,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,7},{2,3},{4},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,4},{3},{5,6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,7},{2,4},{3},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,6,7},{4},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,6,7},{2},{4},{5,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,7},{2},{4},{5,6,8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2},{3,7},{4},{5,6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,7},{2},{3,8},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,4,5},{3},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2,4,5},{3,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2,4},{3,5,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,8},{2,3},{4,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2,5},{3,4,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,8},{2},{3,5,6},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4},{2},{3,6,8},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,7},{2,3},{4},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,6},{2},{3},{5,7,8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,5,6},{3,7},{4,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,5,6},{3},{4,7,8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,5},{3,7},{4,6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2},{3,6,7},{4,5,8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,3,6,7},{4},{5,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,3,6},{4,8},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2},{3,4,6,8},{5,7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2},{3,6},{4,5,7,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,5},{3},{4,6,7,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,5},{3,6},{4,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,5},{3,6,7},{4,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2},{3,5,6,7},{4,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2},{3,5,6},{4,7,8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2},{3,5},{4,6,7,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,4,8},{3,5},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4},{3,6,8},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4,7},{3,6},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,8},{4,5,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,4,7,8},{5},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,7},{2,3,4,8},{5},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,4,7},{3},{5,6,8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,7},{2},{3,4,5},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3,7},{4,8},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2},{3,7},{4,5,6,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2},{3,5,7},{4,6,8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,6},{3,5},{4,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,6},{3,5,7},{4,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2},{3,6,7},{4,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2},{3,6},{4,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2},{3},{4,6,7,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,6},{3},{4,5,7,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,6},{2},{3,4},{5,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,6},{3},{4,7,8},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,6},{2},{3,4,7},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,6},{3,7},{4,5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2},{3,7},{4,6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,6},{3},{4,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,6},{2,5},{4},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,4,6},{3},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,5},{2,6},{3},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,8},{2,7},{3,4},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,5},{2,8},{3},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,7},{2,8},{3,5},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,8},{3},{4,5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,5,8},{3},{4,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,4,5,8},{3},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,5},{2,7},{3},{4,6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,5},{3,6,8},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2,6},{3,5,7},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,8},{2,3},{4,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,3},{4,6,8},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,7},{2,3},{4,8},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2,5,6},{3,7},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,8},{2,6},{4},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,7},{2,5},{3,8},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,6,7},{3},{4,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,8},{2,7},{4,5},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,6},{2,4,8},{3},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,5,6},{2,8},{3},{4,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,7},{2},{3,6,8},{4}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,5},{2},{3,6,8},{4,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,8},{2,5},{3},{4,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,6,8},{3},{4,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,7},{2,6},{3},{4,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,5,7},{3},{4,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,7},{2},{3,6},{4,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,7},{2},{3,8},{4,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,6},{2},{3,7},{4,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,8},{2,6},{3},{4,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,5,8},{3,6},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,5,8},{3},{4,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,5,6},{3},{4,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,7},{2,5},{3},{4,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,5},{3},{4,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,6},{2,7},{3},{4,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,8},{2,7},{3},{4,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,5,8},{3,7},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,6},{2,8},{3,7},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,8},{3,6,7},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,7,8},{3,6},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2,5},{3,6,7},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2,5,7},{3},{4,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,7},{2,8},{3,6},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,7},{3,6,8},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,5},{3},{4,6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,8},{2,5},{3,7},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,6,8},{3,7},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,5,7},{3,8},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,7},{2,8},{3},{4,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,8},{3},{4,6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,7,8},{3,5},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,8},{3,5,6},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,5,6},{3,8},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,6,7},{3,8},{4}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,8},{2,4,6},{5},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,8},{2,3,5},{4,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2,4,6},{3,5},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,8},{3,4,5},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,7},{3,8},{4,5},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,5},{2},{4,6},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,6},{2},{4,7,8},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,6},{2},{3,7,8},{4,5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,7},{2},{3,8},{4,5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,6,7},{2},{4,8},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,8},{2},{3,6,7},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,5,6},{2},{3,4,8},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,6},{2},{3,5,7,8},{4}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,6,7},{2},{3,5,8},{4}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4},{2,6,8},{3},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2,4,6},{3},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2},{3,6,8},{4,5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,8},{2},{3,5,7},{4}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4},{2},{3,5,7},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,5,7},{4},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,8},{2},{3,4,7},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2},{3,4,7},{5},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,5},{3},{4,7},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,5,8},{3},{4,7},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2},{3,4,7},{5,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,5},{4,6,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,6},{3},{4,7},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,7},{2,6},{4},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,6},{3,7},{4},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,5},{3},{4,6,8},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,5},{3},{4,6},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,5,6},{4,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,8},{4,5,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,5},{2,8},{4,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,6},{3,8},{4,5},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,4,7},{3},{5,8},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,7},{2,5},{4},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,7},{3,4},{5},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,4,7},{3},{5},{6,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,4},{3},{5,7},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,4},{5,6,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,4,7},{5},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,5,8},{3,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,3,4},{5,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,4,7},{5,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,4,6},{5},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,4},{2,8},{5,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,3,4,8},{5},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4},{2,5,6},{3,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,6},{2,8},{3,5},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,8},{3,4,5},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,5,7},{3},{4},{6,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,5,8},{3},{4,6},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,6},{2,8},{4,5},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,6},{2},{3,5},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3,5,8},{4,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,5,7},{4},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,7},{3,5},{4},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,7},{2,4},{5},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3,4,7},{5},{6,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4},{2,5,7},{3},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,4,6},{5,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3,4},{5,7},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4,5},{3,7},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3,5},{4,7},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3,5},{4,6},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,5,8},{3,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4,5},{3,6},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,3,4,5},{6,7,8,9,10}}=>[5,5]=>[2,2,2,2,2]=>20
{{1,6},{2,4},{3,7,8},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,6},{2,3,4,7,8}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,5,7},{2,4,6,8},{3}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,5,6},{2,3,4,8},{7}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,5},{2,3},{4,7,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,4},{3,5,7,8}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,6},{2,5},{3,4,7,8}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,3,7},{2},{4,8},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,6},{2},{4,7},{5},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,3},{2},{4,7},{5,8},{6}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,4,7},{3},{5,8},{6}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,7},{3,4,5,8},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,6},{2,3,4,7},{5},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,8},{2,6,7},{3},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4,6},{2,8},{3},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,4},{3,5,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,8},{2,3,7},{4},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,5,8},{3,7},{4},{6}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,7},{3,5,8},{4,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,4,7},{3,5},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,5},{3,4,6},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,8},{3,6},{4,5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,3,7},{4,5},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,7},{3,4,8},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,6,8},{3,4},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,5,7},{3},{6},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,4},{2,5},{3},{6,8},{7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,5},{2,3,6,8},{4},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,5},{3,6,8},{4},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,5,6,7},{3,8},{4}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,8},{3,5},{4,6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,6,7},{3,4,8},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,5,6},{2,3,7},{4},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,6},{3,7},{4,8},{5}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,6},{3,7},{4},{5},{8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,6,7},{2,3,8},{4},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,4,6},{3,5,7},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4,6},{2},{3,5,8},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,6},{2},{3,8},{4},{5},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,5},{2},{3},{4,8},{6},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,7},{2},{3,4},{5,6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,8},{2},{3,4},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,7},{3},{4,5,8},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,6,7},{2},{3,4},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2},{3,4,6},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4,8},{3,7},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,8},{2,7},{4},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,7,8},{4},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4},{3,7,8},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,6,8},{4},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,6,8},{3,4},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,8},{2,3},{4},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,6,7},{3,4},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,6,8},{4,7},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,6,8},{2},{4,7},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,7},{2,6},{3},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,8},{2,4,7},{3},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4,5,7},{2},{3},{6,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,4},{2},{5,7},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,4},{5,7,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,5,6},{3},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,6,7,8},{3},{4}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,5},{2},{3,6,7,8},{4}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,5,8},{2},{3,7},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,5},{2,4,6},{3,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,5},{2},{3,7},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4,7},{3,8},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,3,8},{4},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,6},{3,4,8},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3},{4,5,7},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3},{4,6,8},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3,5,6},{4,7},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,3,5,7},{4,8},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,3,7},{4,6},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3,6},{4,7},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,5,8},{4,6,7}}=>[3,3,2]=>[3,3,2]=>7
{{1,5},{2},{3,4,6,7},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,5},{2,6,7},{3,4},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,5,7,8},{4,6}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,4,5,7},{2},{3,6},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4},{2},{3,5,6,8},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,8},{2},{3,5,7},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,8},{2,5,7},{4},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3},{2,5,6,8},{4},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,7},{2,6},{4,5},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,8},{2,4,7},{3},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,6,8},{2,4},{3},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,8},{2,6},{3},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2},{3,4,6,8},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,7},{3,4,5},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,6},{3,4,5,8},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,6},{2},{3,4,5,7},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,6},{2,7},{3,4,5},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,4},{3,5,6,8}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,4},{2,7},{3,5,6,8}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,4,8},{2,6},{3,5,7}}=>[3,3,2]=>[3,3,2]=>7
{{1,6,8},{2,4},{3,5,7}}=>[3,3,2]=>[3,3,2]=>7
{{1,3,8},{2,5,7},{4,6}}=>[3,3,2]=>[3,3,2]=>7
{{1,5},{2,7},{3,4,6},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4,8},{3,5,6},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,6},{2,4,5},{3,7},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,5,7},{3,8},{4},{6}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,7},{3,5,6},{4,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,5,8},{3,6,7},{4}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4,7},{2,5,6},{3},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,6,8},{3,4,7},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,5,7},{2,3,6},{4},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3},{2,6},{4,5,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,6},{2,3,8},{5},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4},{2,3,8},{5,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3,5},{4,8},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,5},{2},{4,8},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,6,7},{2},{3,4,8}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,2,5},{3},{4,8},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,5},{3},{4,8},{6,7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,5,8},{2,4},{3,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,7},{3,5,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,4,6},{3,7},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,3,5},{4,7},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,6},{2,7},{3},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,5},{3,8},{4,6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3,7},{4,8},{5},{6}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,4,7},{2,3},{5},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4},{3,7,8},{5},{6}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,5,7},{3,4,8},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,5,6},{2,4},{3,7},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4},{3,5},{6,7},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,4,8},{3,5},{6},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,4,6},{3,5},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,5},{3,6},{4},{7,8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,5,7},{3,6,8},{4}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,5,7},{3,8},{4,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2,4},{3,5,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,7},{2,4},{3,5},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,5},{3,6},{4,7},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,5},{3,6,8},{4,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3,6,7},{4,8},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,5,8},{2},{4,7},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,5,6},{2},{3,7,8},{4}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4,7},{2},{3,5,8},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4},{2,6,8},{3,7},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,3,7,8},{4},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,3,6,8},{4},{5,7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2},{3},{4,6},{5,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,5,6,8},{3},{4,7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2},{3,5,6,8},{4,7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,4,5,7},{3,8},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2},{3,4,6,7},{5,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,6},{3,7,8},{4,5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,6,7},{3,5},{4,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2},{3,6,8},{4,5,7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,3},{4,7},{5,6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7,8},{2,4},{3,5},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,6,8},{2},{3},{5,7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,4,6},{3,7,8},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3},{2},{4,6},{5,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4,6,7},{3},{5,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,5},{3,7,8},{4,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,7},{2},{3,6,8},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3},{2,4,5},{6,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,8},{4,6,7},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,4,5},{6,7},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,7,8},{3},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,3,7,8},{5},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,8},{2,4},{5},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,8},{2},{3},{4,5,7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,5},{2,3,7},{4,6},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,3,6,7},{5},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,6},{2,3,7},{5},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,6},{2,4,5,7},{3},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,7},{2,4,5},{3,6},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,6,7},{2},{3},{4,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,5,7},{2,6},{3,4},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,6,7},{3,5,8},{4}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3},{2},{4,6,7},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,5,8},{3,4,7}}=>[3,3,2]=>[3,3,2]=>7
{{1,3,6,7},{2,4,5,8}}=>[4,4]=>[2,2,2,2]=>12
{{1},{2,8},{3,5,6},{4,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,5,6,7},{3},{4,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,6},{2,7,8},{3,4},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,7},{3,4,6,8}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,7},{2},{3,8},{4,5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,4,5},{3,6,8}}=>[3,3,2]=>[3,3,2]=>7
{{1},{2,6,8},{3,7},{4,5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4,5,8},{3,7},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,4,5},{3,7,8},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,6},{3,8},{4,5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,5,6},{2},{3,8},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,5,6},{2},{4,8},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,4,6,7},{3,8},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,5},{2,7,8},{3,4},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,5},{2},{4,7,8},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3},{2,5},{4,7,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,6},{3},{4,5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,7,8},{4,6},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,5},{2,8},{3,7},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,6},{2,4},{5},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,6},{2},{4,5,8},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2},{3,5},{4,7,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3,4,7},{5,8},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,8},{2,5,7},{3},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,3,4,6},{5,8},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,4,5,8},{3,6},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,6},{2},{3,4,5,8},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,4},{3,6},{5,8},{7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,3},{2},{4,6},{5,8},{7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,3},{2,5},{4},{6,8},{7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,4,5,6},{3,8},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,6},{3,5},{4,8},{7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,5},{2,4},{3,7},{6},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,5},{2,4,6,7},{3},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,6},{3,5,7,8},{4}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,8},{3,5},{4,7},{6}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,7},{2,4},{3,6},{5},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,5,7,8},{3,6},{4}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,5,6},{2,4,7},{3},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3},{2,5,6,7},{4},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3},{2,6,7,8},{4},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,4},{3,6,7,8},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,4},{3,8},{5,7},{6}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,3},{2,7},{4,6},{5},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,4,7},{3,6,8},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4,7},{2,3,5},{6},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4,7},{2,3,6},{5},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,5},{2,3,6,7},{4},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4},{2,3,7},{5,6},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,5,8},{3,4,6},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,5,7},{3,4,6},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,3,6},{4,5,7},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,6},{2,3},{4,5,7},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3,6},{2},{4,5,7},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4},{2,3,5},{6,7},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,5,7},{3,4},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,3,5},{6,8},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3,6},{4,5,8},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,5,8},{3,4,7},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,3,7},{4,6,8},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,3,7},{4,5,8},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4,8},{2},{3,5},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,8},{2},{3,5},{4,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,3,5,8},{6},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,6,8},{3},{4},{5,7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2},{3,6,8},{4},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3},{4},{5},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1]=>[8,1]=>1
{{1,3},{2},{4},{5},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1]=>[8,1]=>1
{{1,4},{2},{3},{5},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1]=>[8,1]=>1
{{1,5},{2},{3},{4},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1]=>[8,1]=>1
{{1,6},{2},{3},{4},{5},{7},{8},{9}}=>[2,1,1,1,1,1,1,1]=>[8,1]=>1
{{1,7},{2},{3},{4},{5},{6},{8},{9}}=>[2,1,1,1,1,1,1,1]=>[8,1]=>1
{{1,8},{2},{3},{4},{5},{6},{7},{9}}=>[2,1,1,1,1,1,1,1]=>[8,1]=>1
{{1,2},{3},{4},{5},{6},{7},{8},{9},{10}}=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>1
{{1,2,3},{4},{5},{6},{7},{8},{9}}=>[3,1,1,1,1,1,1]=>[7,1,1]=>3
{{1,3},{2},{4},{5},{6},{7},{8},{9},{10}}=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>1
{{1,3,4},{2},{5},{6},{7},{8},{9}}=>[3,1,1,1,1,1,1]=>[7,1,1]=>3
{{1,4},{2},{3},{5},{6},{7},{8},{9},{10}}=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>1
{{1,5},{2},{3},{4},{6},{7},{8},{9},{10}}=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>1
{{1,6},{2},{3},{4},{5},{7},{8},{9},{10}}=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>1
{{1,7},{2},{3},{4},{5},{6},{8},{9},{10}}=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>1
{{1,8},{2},{3},{4},{5},{6},{7},{9},{10}}=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>1
{{1,8,9},{2},{3},{4},{5},{6},{7}}=>[3,1,1,1,1,1,1]=>[7,1,1]=>3
{{1,9},{2},{3},{4},{5},{6},{7},{8},{10}}=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>1
{{1,8},{2},{3,6},{4,5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2},{3,5,6},{4,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,8},{2},{3,4,6},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3},{2,4,8},{5},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,6},{3,4,7},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,4},{3,6,7},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,3,6},{4,7},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,3,4,6},{7},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,5,7},{2,3},{4,6},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,4},{3,8},{5,6},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,3,4,5,6,7,8,9}}=>[9]=>[1,1,1,1,1,1,1,1,1]=>36
{{1,2,3,4,5,6,7},{8,9}}=>[7,2]=>[2,2,1,1,1,1,1]=>22
{{1,2,3,4,5,6,7},{8},{9}}=>[7,1,1]=>[3,1,1,1,1,1,1]=>21
{{1,2,3,4,5,6},{7,8,9}}=>[6,3]=>[2,2,2,1,1,1]=>18
{{1,2,3,4,5,6},{7,8},{9}}=>[6,2,1]=>[3,2,1,1,1,1]=>16
{{1,2,3,4,5,6},{7},{8},{9}}=>[6,1,1,1]=>[4,1,1,1,1,1]=>15
{{1,2,3,4,5},{6,7,8,9}}=>[5,4]=>[2,2,2,2,1]=>16
{{1,2,3,4,5},{6,7,8},{9}}=>[5,3,1]=>[3,2,2,1,1]=>13
{{1,2,3,4,5},{6},{7},{8},{9}}=>[5,1,1,1,1]=>[5,1,1,1,1]=>10
{{1,2,3,4},{5},{6},{7},{8},{9}}=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
{{1,2,3,4,5,6,7,8,9,10}}=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>45
{{1,2,3,4,5,6,7,8},{9,10}}=>[8,2]=>[2,2,1,1,1,1,1,1]=>29
{{1,2,3,4,5,6,7,8},{9},{10}}=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>28
{{1,2,3,4,5,6,7},{8,9,10}}=>[7,3]=>[2,2,2,1,1,1,1]=>24
{{1,2,3,4,5,6,7},{8,9},{10}}=>[7,2,1]=>[3,2,1,1,1,1,1]=>22
{{1,2,3,4,5,6,7},{8},{9},{10}}=>[7,1,1,1]=>[4,1,1,1,1,1,1]=>21
{{1,2,3,4,5,6},{7,8,9,10}}=>[6,4]=>[2,2,2,2,1,1]=>21
{{1,2,3,4,5,6},{7},{8},{9},{10}}=>[6,1,1,1,1]=>[5,1,1,1,1,1]=>15
{{1,2,3,4,5},{6},{7},{8},{9},{10}}=>[5,1,1,1,1,1]=>[6,1,1,1,1]=>10
{{1,2,3,4},{5},{6},{7},{8},{9},{10}}=>[4,1,1,1,1,1,1]=>[7,1,1,1]=>6
{{1,2,3},{4},{5},{6},{7},{8},{9},{10}}=>[3,1,1,1,1,1,1,1]=>[8,1,1]=>3
{{1,4},{2,3},{5},{6},{7},{8},{9}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1,5},{2},{3,4},{6},{7},{8},{9}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1,6},{2},{3},{4,5},{7},{8},{9}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1,7},{2},{3},{4},{5,6},{8},{9}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1,8},{2},{3},{4},{5},{6,7},{9}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1,9},{2},{3},{4},{5},{6},{7,8}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1,2,3},{4,7},{5},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,5},{3},{4,6,7},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,7},{3},{4,8},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,5},{3,8},{4},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,5,7,8},{3},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,6},{3},{4,5,7},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,5,6},{3},{4,7},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,6},{3,4,7,8},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3},{2},{4,7},{5,6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2},{3,6,7,8},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,3,7},{4},{5,6,8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,3,6},{4},{5,7,8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,3},{4,6,7},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3},{4,6},{5,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,6},{3,7,8},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3,5,6},{4,8},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,3,5},{4,7,8},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,5},{3,4,7,8},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,7},{2},{3,6},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4,8},{3,6,7},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,3,6},{4,7,8},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4,5,7},{2,3,6,8}}=>[4,4]=>[2,2,2,2]=>12
{{1,5},{2,3,7},{4,6,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,5},{2,3,6,8},{4,7}}=>[4,2,2]=>[3,3,1,1]=>8
{{1},{2,5},{3,4,7},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,6,8},{3,4,7}}=>[3,3,2]=>[3,3,2]=>7
{{1,5,7},{2,6},{3,4,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,6},{2,5,7},{3,4,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,5,7},{2,3,6},{4,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,5,7},{2,3,8},{4,6}}=>[3,3,2]=>[3,3,2]=>7
{{1},{2,7},{3,6},{4,5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,4,5,8},{3,6}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,7},{2,5,8},{3,4,6}}=>[3,3,2]=>[3,3,2]=>7
{{1,6},{2,5},{3,4,7},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,4,5,8},{3,7}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,4,5},{2,7},{3,6},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4,5,7},{3,6},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,5,7},{2,8},{3,6}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,4,5},{2,7},{3,6,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,7},{2,5},{3,4,6,8}}=>[4,2,2]=>[3,3,1,1]=>8
{{1},{2,6},{3,4,5,7},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,7},{3,6,8},{4,5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,4,5,7},{3,8}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,5,7},{2,8},{3,4,6}}=>[3,3,2]=>[3,3,2]=>7
{{1,3,6},{2,7},{4,5},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,6,8},{3},{4,7},{5}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,3},{2},{4,7},{5},{6,8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,3,4,7},{2},{5},{6,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4},{2},{3,5},{6,8},{7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,5,7},{2},{3,6},{4},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,7},{3,5},{4},{6,8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,6},{2,4},{3},{5,7},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,7},{3,5,6,8},{4}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,8},{3,6},{4},{5,7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,7},{2,5},{3},{4,6},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,7},{3,4,6,8},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,6},{2,3,5,7},{4},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,5,8},{2},{3,6},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,4,6},{2},{5,8},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,6},{3},{4,8},{5,7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,5},{2},{3,7},{4,6},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,6},{3,5,8},{4,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,4,7},{3,6},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,5},{3,4,6,8},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4},{2,3,5,7},{6},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,5,6,8},{3,7},{4}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,7},{3,5},{4,6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5},{2,3,7},{4},{6},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,5},{2,3,8},{4},{6},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,5,8},{2,3,6},{4},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,6},{2,3,8},{4},{5},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,6},{2,4,8},{3},{5},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,6,8},{2,3,7},{4},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,6},{2,3},{4,7},{5},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,6},{2,3},{4,7,8},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,3},{4,8},{5},{6}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,7},{2,4},{3,8},{5},{6}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,5},{2},{3,4,7},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4},{3,5,7},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,5},{3},{4,8},{6}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,5,8},{2,4,6},{3},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4,8},{2,3,5},{6},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,4},{3,5,7},{6},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,4},{3,5,8},{6},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,4,7},{3,5,6},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,7},{2,3,5},{4},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4,5},{3,8},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3,8},{4,6},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4,5,7},{3},{6,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,7},{2},{4,5},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4,7},{3,5,8},{6}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2},{3,5,7,8},{4,6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2},{3,5,8},{4,6,7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,5,7},{3,6},{4,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,7,8},{2},{3},{4,6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,5,7,8},{3},{4,6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,4,5,6,7,8,9},{2}}=>[8,1]=>[2,1,1,1,1,1,1,1]=>28
{{1,7,8,9},{2},{3},{4},{5},{6}}=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
{{1,3,4,5,6,7,8,9,10},{2}}=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>36
{{1,8,9,10},{2},{3},{4},{5},{6},{7}}=>[4,1,1,1,1,1,1]=>[7,1,1,1]=>6
{{1,9,10},{2},{3},{4},{5},{6},{7},{8}}=>[3,1,1,1,1,1,1,1]=>[8,1,1]=>3
{{1,5,6,7},{2},{3,8},{4}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,7,8},{2},{3,5},{4,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,6,8},{2},{3},{4,7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,4,5,6,7,8,9},{3}}=>[7,1,1]=>[3,1,1,1,1,1,1]=>21
{{1,3,4,5,6,7,8},{2},{9}}=>[7,1,1]=>[3,1,1,1,1,1,1]=>21
{{1},{2,4,5,6,7,8,9,10},{3}}=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>28
{{1},{2,5,6,7,8,9},{3,4}}=>[6,2,1]=>[3,2,1,1,1,1]=>16
{{1,4,5,6,7,8},{2,3},{9}}=>[6,2,1]=>[3,2,1,1,1,1]=>16
{{1,3,4,5,6,7,8,9},{2},{10}}=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>28
{{1},{2,3,5},{4,6,7,8}}=>[4,3,1]=>[3,2,2,1]=>9
{{1},{2,3,5},{4,6,8},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2},{3,4,5,6,7,8,9,10}}=>[8,2]=>[2,2,1,1,1,1,1,1]=>29
{{1,2,3,4},{5,6,7,8,9,10}}=>[6,4]=>[2,2,2,2,1,1]=>21
{{1,3},{2,5,6},{4},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,5},{3,7,8},{6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2},{3,7},{4,5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2},{3,5},{4,6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,5,7,8},{4},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,7},{2},{3,5,6,8},{4}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,6},{2},{3,5,7},{4,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2},{3,5,7},{4,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,6},{2,3,5},{7},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,5,8},{2},{3},{4,6,7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,5,6},{2},{3,4,7},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,6},{2,4,5},{7},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2},{3},{4},{5},{6,7},{8,9}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1},{2,3,7},{4,5},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2},{4,5,7},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3},{4,5,7},{6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2},{3,4,6},{5,7,8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2},{3,4,7},{5,6,8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2},{3},{4,6,8},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3},{4,6,7},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,4},{5},{6,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,5},{3},{6,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,5},{4},{6,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,7},{2,8},{3},{4,5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,8},{3},{5,6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,6,7},{3},{4,5,8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4,8},{2,5,6},{3},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,6,8},{2,7},{3,4},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6,7},{2,4},{3,8},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2},{3,5},{6,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,4,8},{3,6},{5,10},{7},{9}}=>[4,2,2,1,1]=>[5,3,1,1]=>8
{{1,6},{2,7},{3},{4,5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3,4,6},{5,7},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,7,8},{3,5},{4,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,5,6},{2,7},{3,4},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2,7,8},{3},{4,5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,8},{2},{3,5},{4,6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,6},{2},{3,5,8},{4,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,3,8,9},{4},{5},{6},{7}}=>[5,1,1,1,1]=>[5,1,1,1,1]=>10
{{1,2,3,9},{4,5},{6},{7},{8}}=>[4,2,1,1,1]=>[5,2,1,1]=>7
{{1,2,3,4,9,10},{5},{6},{7},{8}}=>[6,1,1,1,1]=>[5,1,1,1,1,1]=>15
{{1,2,3,4,8,9},{5},{6},{7}}=>[6,1,1,1]=>[4,1,1,1,1,1]=>15
{{1,2,3,4,9},{5,6},{7},{8}}=>[5,2,1,1]=>[4,2,1,1,1]=>11
{{1,2,3,4,10},{5,6},{7},{8},{9}}=>[5,2,1,1,1]=>[5,2,1,1,1]=>11
{{1,2,3,9,10},{4},{5},{6},{7},{8}}=>[5,1,1,1,1,1]=>[6,1,1,1,1]=>10
{{1,2,8,9},{3,7},{4},{5},{6}}=>[4,2,1,1,1]=>[5,2,1,1]=>7
{{1,2,4,8,9},{3},{5},{6},{7}}=>[5,1,1,1,1]=>[5,1,1,1,1]=>10
{{1,2,9},{3,8},{4,5},{6},{7}}=>[3,2,2,1,1]=>[5,3,1]=>5
{{1,2,5,9},{3,4},{6},{7},{8}}=>[4,2,1,1,1]=>[5,2,1,1]=>7
{{1,2,3,10},{4,5},{6},{7},{8},{9}}=>[4,2,1,1,1,1]=>[6,2,1,1]=>7
{{1},{2,6,8},{3},{4,5,7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,6,7},{3,8},{4,5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,5,6},{3,8},{4,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,9},{2,3,4,5,6,7,8}}=>[7,2]=>[2,2,1,1,1,1,1]=>22
{{1,8},{2,3,4,5,6,7},{9}}=>[6,2,1]=>[3,2,1,1,1,1]=>16
{{1,7},{2,3,4,5,6},{8},{9}}=>[5,2,1,1]=>[4,2,1,1,1]=>11
{{1,6},{2,3,4,5},{7},{8},{9}}=>[4,2,1,1,1]=>[5,2,1,1]=>7
{{1,5},{2,3,4},{6},{7},{8},{9}}=>[3,2,1,1,1,1]=>[6,2,1]=>4
{{1,3,8},{2,6,7},{4},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,7},{3,6},{4},{5,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,8},{3},{4,6},{5,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,10},{2,3,4,5,6,7,8,9}}=>[8,2]=>[2,2,1,1,1,1,1,1]=>29
{{1,9},{2,3,4,5,6,8},{7}}=>[6,2,1]=>[3,2,1,1,1,1]=>16
{{1,10},{2,3,4,5,6,7,9},{8}}=>[7,2,1]=>[3,2,1,1,1,1,1]=>22
{{1,9},{2,3,4,5,8},{6,7}}=>[5,2,2]=>[3,3,1,1,1]=>12
{{1,9},{2,3,4,5,7,8},{6}}=>[6,2,1]=>[3,2,1,1,1,1]=>16
{{1,3},{2,5,6},{4,7},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,3},{2,7},{4,5,6},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,5,8},{3},{4,6,7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4},{2,6,7},{3,5},{8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,7,8},{3,6},{5}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,4,5},{3,6,7},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,4,5},{3,6,8},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,5,6},{3,7,8},{4}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,4},{3,5,6},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,6},{2,3,8},{5,7}}=>[3,3,2]=>[3,3,2]=>7
{{1,4},{2},{3,5,6,7},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,6},{2,7},{4,5,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,9},{2,8},{3,7},{4,6},{5},{10}}=>[2,2,2,2,1,1]=>[6,4]=>4
{{1},{2,10},{3,9},{4,8},{5,7},{6}}=>[2,2,2,2,1,1]=>[6,4]=>4
{{1,4,6},{2,3,5,7,8}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,2,4,6},{3},{5,7,8}}=>[4,3,1]=>[3,2,2,1]=>9
{{1},{2,4,6,7,8},{3,5}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2,6},{3,4,5,7,8}}=>[5,3]=>[2,2,2,1,1]=>13
{{1},{2,3,5,8},{4,7},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,3,4,5,6,7,9},{8}}=>[8,1]=>[2,1,1,1,1,1,1,1]=>28
{{1,2,3,4,5,6,7,8,10},{9}}=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>36
{{1,2},{3,4,5,6,7,8},{9}}=>[6,2,1]=>[3,2,1,1,1,1]=>16
{{1,3,4,5,6,7,9},{2},{8}}=>[7,1,1]=>[3,1,1,1,1,1,1]=>21
{{1,5,7,8},{2,3,4,6}}=>[4,4]=>[2,2,2,2]=>12
{{1,3,6,8},{2,4,5,7}}=>[4,4]=>[2,2,2,2]=>12
{{1,2,6,8},{3,4,5,7}}=>[4,4]=>[2,2,2,2]=>12
{{1,6},{2,3,4,5,7,8}}=>[6,2]=>[2,2,1,1,1,1]=>16
{{1,2,6},{3,4,5,8},{7}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,4,8},{2,3,5,6},{7}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,5},{2,3,4,8},{6,7}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,4,8},{2,3,5},{6,7}}=>[3,3,2]=>[3,3,2]=>7
{{1,2,4},{3,5,6,7,8}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,5,8},{2,3,4,6,7}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,3,4},{2,5,6,7,8}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,4,6,7},{2,3,8},{5}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,3,8},{2,4,6,7},{5}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,3,5},{2,8},{4,6,7}}=>[3,3,2]=>[3,3,2]=>7
{{1,4,7,8},{2,3,6},{5}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,6},{2,3,5},{4,7,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,2,6},{3,5},{4,7,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,2,5},{3,6},{4,7,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,5},{2,3,6},{4,7,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,4,7,8},{2,6},{3,5}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,7,8},{2,3,5},{4,6}}=>[3,3,2]=>[3,3,2]=>7
{{1,7,8},{2,5},{3,4,6}}=>[3,3,2]=>[3,3,2]=>7
{{1,7,8},{2,4,6},{3,5}}=>[3,3,2]=>[3,3,2]=>7
{{1,4,8},{2,3,5,7},{6}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,2,5},{3,4,6,7,8}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,7},{2,8},{3,9},{4,10},{5,11},{6,12}}=>[2,2,2,2,2,2]=>[6,6]=>6
{{1},{2},{3},{4},{5},{6,9},{7},{8},{10}}=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>1
{{1,8},{2,3},{4},{5},{6},{7},{9}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1,2},{3},{4},{5},{6},{7},{8,9}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1,3,4,5,6,7},{2,9},{8}}=>[6,2,1]=>[3,2,1,1,1,1]=>16
{{1,2,3,4,5,7},{6,8},{9}}=>[6,2,1]=>[3,2,1,1,1,1]=>16
{{1,3,4,5,6,8},{2,9},{7}}=>[6,2,1]=>[3,2,1,1,1,1]=>16
{{1,3,4,5,6,9},{2,8},{7}}=>[6,2,1]=>[3,2,1,1,1,1]=>16
{{1,3,4,5,6,7,8},{2,10},{9}}=>[7,2,1]=>[3,2,1,1,1,1,1]=>22
{{1,2},{3,4,5,6,7,8,9}}=>[7,2]=>[2,2,1,1,1,1,1]=>22
{{1,2,3},{4,5,6,7,8,9}}=>[6,3]=>[2,2,2,1,1,1]=>18
{{1,2,3,4},{5,6,7,8,9}}=>[5,4]=>[2,2,2,2,1]=>16
{{1},{2},{3,4,5,6,7,8,9}}=>[7,1,1]=>[3,1,1,1,1,1,1]=>21
{{1,2},{3,5,6,7,8,9},{4}}=>[6,2,1]=>[3,2,1,1,1,1]=>16
{{1,2,4,5,6,7},{3},{8,9}}=>[6,2,1]=>[3,2,1,1,1,1]=>16
{{1,2,3},{4,5,6,7,8,9,10}}=>[7,3]=>[2,2,2,1,1,1,1]=>24
{{1,2,3},{4,5,7,8,9},{6}}=>[5,3,1]=>[3,2,2,1,1]=>13
{{1,2,3,5,6},{4},{7,8,9}}=>[5,3,1]=>[3,2,2,1,1]=>13
{{1,2,3,4},{5,6,7,9},{8}}=>[4,4,1]=>[3,2,2,2]=>12
{{1},{2},{3},{4},{5,7},{6,8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1},{2},{3},{4,6},{5,8},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1},{2},{3,5},{4,8},{6},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1},{2,4},{3,8},{5},{6},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1},{2},{3},{4},{5},{6,8},{7,9}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1},{2},{3},{4,7},{5,8},{6}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1},{2},{3},{4},{5,7},{6,9},{8}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1},{2},{3,6},{4,8},{5},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1},{2},{3},{4,6,7},{5,8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2},{3},{4,6},{5,9},{7},{8}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1},{2,5},{3,8},{4},{6},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1},{2},{3,5,6},{4,8},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2},{3,5},{4,9},{6},{7},{8}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1},{2,4,5},{3,8},{6},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,4},{3,9},{5},{6},{7},{8}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1,3},{2,9},{4},{5},{6},{7},{8}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1,4,6,7,8},{2,3,5}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,3,6,7,8},{2,4,5}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,3,5},{2,6},{4,7,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,4,5,7,8},{2,3,6}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,3,7},{2,4,5,8},{6}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,5,8},{2,4,6},{3,7}}=>[3,3,2]=>[3,3,2]=>7
{{1,2,5,8},{3,4,6,7}}=>[4,4]=>[2,2,2,2]=>12
{{1},{2,3,5,7},{4,6},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,3,4,5,7},{6,8}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1},{2,3,5,8},{4,6,7}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,3},{2,6,8},{4,5},{7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4,6,7},{2},{3},{5,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,7,8},{2},{3,5},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,4,7,8},{3,5},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,4,7,8},{3,6},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4},{2},{3,7,8},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1},{2,3,4,6,8},{5,7}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1},{2,3,4,5,6,8},{7,9}}=>[6,2,1]=>[3,2,1,1,1,1]=>16
{{1,5,6},{2,3},{4,7,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,2,3,9},{4},{5},{6},{7},{8}}=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
{{1,2,9},{3},{4},{5},{6},{7},{8}}=>[3,1,1,1,1,1,1]=>[7,1,1]=>3
{{1,2,3,10},{4},{5},{6},{7},{8},{9}}=>[4,1,1,1,1,1,1]=>[7,1,1,1]=>6
{{1,3},{2,4,5,6,8},{7}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,6,7},{2,3,4,5,8}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,7},{2,3,4},{5,6,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,4,5},{2,3,7,8},{6}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,4,6,8},{2,3,5,7}}=>[4,4]=>[2,2,2,2]=>12
{{1,4,8},{2,3,6,7},{5}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,3,7},{2,6},{4,5,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,2,6},{3,7},{4,5,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,2},{3,4,6},{5,7,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,2,3},{4,7},{5,6,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,5},{2,6,7,8},{3,4}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,7},{2,6,8},{3,4,5}}=>[3,3,2]=>[3,3,2]=>7
{{1,2,6},{3,5,7,8},{4}}=>[4,3,1]=>[3,2,2,1]=>9
{{1},{2,3,6},{4,5,7,8}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,7,8},{2,4},{3,5,6}}=>[3,3,2]=>[3,3,2]=>7
{{1},{2,3,9},{4},{5},{6},{7},{8}}=>[3,1,1,1,1,1,1]=>[7,1,1]=>3
{{1,2,3,4,5,6,8,9},{7}}=>[8,1]=>[2,1,1,1,1,1,1,1]=>28
{{1,2,4,5,6,7,8,9},{3}}=>[8,1]=>[2,1,1,1,1,1,1,1]=>28
{{1,2,3,4,5,6,7,9,10},{8}}=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>36
{{1,2},{3,5},{4},{6},{7},{8},{9}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1,9},{2,4},{3},{5},{6},{7},{8}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1,9},{2},{3,4},{5},{6},{7},{8}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1,10},{2,3},{4},{5},{6},{7},{8},{9}}=>[2,2,1,1,1,1,1,1]=>[8,2]=>2
{{1,3},{2,5,8},{4},{6,7}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,9},{2,8},{3},{4},{5},{6},{7}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1,3,9},{2},{4},{5},{6},{7},{8}}=>[3,1,1,1,1,1,1]=>[7,1,1]=>3
{{1,10},{2,9},{3},{4},{5},{6},{7},{8}}=>[2,2,1,1,1,1,1,1]=>[8,2]=>2
{{1},{2,9},{3,8},{4},{5},{6},{7}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1,2,7},{3},{4},{5},{6},{8,9}}=>[3,2,1,1,1,1]=>[6,2,1]=>4
{{1,2},{3,4,9},{5},{6},{7},{8}}=>[3,2,1,1,1,1]=>[6,2,1]=>4
{{1,3,8},{2},{4},{5},{6},{7},{9}}=>[3,1,1,1,1,1,1]=>[7,1,1]=>3
{{1,3,10},{2},{4},{5},{6},{7},{8},{9}}=>[3,1,1,1,1,1,1,1]=>[8,1,1]=>3
{{1},{2,4},{3,5,6,7,8}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,5,6},{2},{3},{4,7,8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,3,5},{2},{4,6},{7},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,3,7},{2},{4},{5},{6,8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,3,6},{2},{4},{5,8},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2},{3,7},{4,8},{5},{6}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,7},{2},{3},{4},{5},{6,8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,6},{2},{3},{4},{5,8},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,4},{2,6},{3},{5,8},{7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,5},{2,6},{3},{4,8},{7}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,5,7},{2},{3},{4},{6,8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,5},{2},{3},{4,6},{7},{8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,4},{2},{3,6},{5},{7},{8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1},{2,5},{3,6},{4},{7},{8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,4,6},{2},{3,5,7},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,6},{2},{3},{4,7},{5},{8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,6},{2},{3},{4,7},{5,8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,5},{2},{3},{4,7},{6,8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,5,7},{2},{3},{4,6},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,4,7},{2},{3,6},{5},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,4},{2},{3,7},{5},{6,8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,5},{2},{3,7},{4,8},{6}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,5},{2},{3,7},{4},{6},{8}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,7},{2,5},{3,6},{4},{8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,6},{3},{4,8},{5},{7}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,5},{2,3,4,8},{6},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,5},{2,3,8},{6},{7}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,8},{2,3,4,6},{5,7}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,7},{2,3},{4,5,6,8}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,7},{2,3,5,6},{4,8}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,4,7,8},{2,3,5,6}}=>[4,4]=>[2,2,2,2]=>12
{{1,5,7,8},{2,3},{4,6}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,5,6,8},{2,3},{4,7}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,5},{2},{3,4,6,8},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,6},{2},{3},{4,5,7,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4},{2,6,7,8},{3},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,5},{3,6,7,8},{4}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,4,7},{2},{5,8},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,4,9},{3,6},{5,10},{7},{8}}=>[4,2,2,1,1]=>[5,3,1,1]=>8
{{1,2,4,8},{3,7},{5,10},{6},{9}}=>[4,2,2,1,1]=>[5,3,1,1]=>8
{{1,2,4,9},{3,7},{5,10},{6},{8}}=>[4,2,2,1,1]=>[5,3,1,1]=>8
{{1,2,4,9},{3,8},{5,10},{6},{7}}=>[4,2,2,1,1]=>[5,3,1,1]=>8
{{1,2,5,10},{3,6},{4,8},{7},{9}}=>[4,2,2,1,1]=>[5,3,1,1]=>8
{{1,2,5,10},{3,6},{4,9},{7},{8}}=>[4,2,2,1,1]=>[5,3,1,1]=>8
{{1,2,5,10},{3,7},{4,8},{6},{9}}=>[4,2,2,1,1]=>[5,3,1,1]=>8
{{1,2,5,10},{3,7},{4,9},{6},{8}}=>[4,2,2,1,1]=>[5,3,1,1]=>8
{{1,2,5,10},{3,8},{4,9},{6},{7}}=>[4,2,2,1,1]=>[5,3,1,1]=>8
{{1,2,6},{3,7},{4,8},{5,10},{9}}=>[3,2,2,2,1]=>[5,4,1]=>6
{{1,2,6},{3,7},{4,9},{5,10},{8}}=>[3,2,2,2,1]=>[5,4,1]=>6
{{1,2,6},{3,8},{4,9},{5,10},{7}}=>[3,2,2,2,1]=>[5,4,1]=>6
{{1,2,7},{3,8},{4,9},{5,10},{6}}=>[3,2,2,2,1]=>[5,4,1]=>6
{{1,3,6},{2,4,8},{5,10},{7},{9}}=>[3,3,2,1,1]=>[5,3,2]=>7
{{1,3,6},{2,4,9},{5,10},{7},{8}}=>[3,3,2,1,1]=>[5,3,2]=>7
{{1,3,7},{2,4,8},{5,10},{6},{9}}=>[3,3,2,1,1]=>[5,3,2]=>7
{{1,3,7},{2,4,9},{5,10},{6},{8}}=>[3,3,2,1,1]=>[5,3,2]=>7
{{1,3,8},{2,4,9},{5,10},{6},{7}}=>[3,3,2,1,1]=>[5,3,2]=>7
{{1,3,6},{2,5,10},{4,8},{7},{9}}=>[3,3,2,1,1]=>[5,3,2]=>7
{{1,3,6},{2,5,10},{4,9},{7},{8}}=>[3,3,2,1,1]=>[5,3,2]=>7
{{1,3,7},{2,5,10},{4,8},{6},{9}}=>[3,3,2,1,1]=>[5,3,2]=>7
{{1,3,7},{2,5,10},{4,9},{6},{8}}=>[3,3,2,1,1]=>[5,3,2]=>7
{{1,3,8},{2,5,10},{4,9},{6},{7}}=>[3,3,2,1,1]=>[5,3,2]=>7
{{1,3,7},{2,6},{4,8},{5,10},{9}}=>[3,2,2,2,1]=>[5,4,1]=>6
{{1,3,7},{2,6},{4,9},{5,10},{8}}=>[3,2,2,2,1]=>[5,4,1]=>6
{{1,3,8},{2,6},{4,9},{5,10},{7}}=>[3,2,2,2,1]=>[5,4,1]=>6
{{1,3,8},{2,7},{4,9},{5,10},{6}}=>[3,2,2,2,1]=>[5,4,1]=>6
{{1,4,8},{2,5,10},{3,6},{7},{9}}=>[3,3,2,1,1]=>[5,3,2]=>7
{{1,4,9},{2,5,10},{3,6},{7},{8}}=>[3,3,2,1,1]=>[5,3,2]=>7
{{1,4,8},{2,5,10},{3,7},{6},{9}}=>[3,3,2,1,1]=>[5,3,2]=>7
{{1,4,9},{2,5,10},{3,7},{6},{8}}=>[3,3,2,1,1]=>[5,3,2]=>7
{{1,4,9},{2,5,10},{3,8},{6},{7}}=>[3,3,2,1,1]=>[5,3,2]=>7
{{1,4,8},{2,6},{3,7},{5,10},{9}}=>[3,2,2,2,1]=>[5,4,1]=>6
{{1,4,9},{2,6},{3,7},{5,10},{8}}=>[3,2,2,2,1]=>[5,4,1]=>6
{{1,4,9},{2,6},{3,8},{5,10},{7}}=>[3,2,2,2,1]=>[5,4,1]=>6
{{1,4,9},{2,7},{3,8},{5,10},{6}}=>[3,2,2,2,1]=>[5,4,1]=>6
{{1,5,10},{2,6},{3,7},{4,8},{9}}=>[3,2,2,2,1]=>[5,4,1]=>6
{{1,5,10},{2,6},{3,7},{4,9},{8}}=>[3,2,2,2,1]=>[5,4,1]=>6
{{1,5,10},{2,6},{3,8},{4,9},{7}}=>[3,2,2,2,1]=>[5,4,1]=>6
{{1,5,10},{2,7},{3,8},{4,9},{6}}=>[3,2,2,2,1]=>[5,4,1]=>6
{{1,3,7},{2,4,8},{5,10},{6,12},{9},{11}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,3,7},{2,4,8},{5,11},{6,12},{9},{10}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,3,7},{2,4,9},{5,10},{6,12},{8},{11}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,3,7},{2,4,9},{5,11},{6,12},{8},{10}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,3,7},{2,4,10},{5,11},{6,12},{8},{9}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,3,8},{2,4,9},{5,10},{6,12},{7},{11}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,3,8},{2,4,9},{5,11},{6,12},{7},{10}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,3,8},{2,4,10},{5,11},{6,12},{7},{9}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,3,9},{2,4,10},{5,11},{6,12},{7},{8}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,3,7},{2,5,10},{4,8},{6,12},{9},{11}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,3,7},{2,5,11},{4,8},{6,12},{9},{10}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,3,7},{2,5,10},{4,9},{6,12},{8},{11}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,3,7},{2,5,11},{4,9},{6,12},{8},{10}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,3,7},{2,5,11},{4,10},{6,12},{8},{9}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,3,8},{2,5,10},{4,9},{6,12},{7},{11}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,3,8},{2,5,11},{4,9},{6,12},{7},{10}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,3,8},{2,5,11},{4,10},{6,12},{7},{9}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,3,9},{2,5,11},{4,10},{6,12},{7},{8}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,3,7},{2,6,12},{4,8},{5,10},{9},{11}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,3,7},{2,6,12},{4,8},{5,11},{9},{10}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,3,7},{2,6,12},{4,9},{5,10},{8},{11}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,3,7},{2,6,12},{4,9},{5,11},{8},{10}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,3,7},{2,6,12},{4,10},{5,11},{8},{9}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,3,8},{2,6,12},{4,9},{5,10},{7},{11}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,3,8},{2,6,12},{4,9},{5,11},{7},{10}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,3,8},{2,6,12},{4,10},{5,11},{7},{9}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,3,9},{2,6,12},{4,10},{5,11},{7},{8}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,4,8},{2,5,10},{3,7},{6,12},{9},{11}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,4,8},{2,5,11},{3,7},{6,12},{9},{10}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,4,9},{2,5,10},{3,7},{6,12},{8},{11}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,4,9},{2,5,11},{3,7},{6,12},{8},{10}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,4,10},{2,5,11},{3,7},{6,12},{8},{9}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,4,9},{2,5,10},{3,8},{6,12},{7},{11}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,4,9},{2,5,11},{3,8},{6,12},{7},{10}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,4,10},{2,5,11},{3,8},{6,12},{7},{9}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,4,10},{2,5,11},{3,9},{6,12},{7},{8}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,4,8},{2,6,12},{3,7},{5,10},{9},{11}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,4,8},{2,6,12},{3,7},{5,11},{9},{10}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,4,9},{2,6,12},{3,7},{5,10},{8},{11}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,4,9},{2,6,12},{3,7},{5,11},{8},{10}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,4,10},{2,6,12},{3,7},{5,11},{8},{9}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,4,9},{2,6,12},{3,8},{5,10},{7},{11}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,4,9},{2,6,12},{3,8},{5,11},{7},{10}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,4,10},{2,6,12},{3,8},{5,11},{7},{9}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,4,10},{2,6,12},{3,9},{5,11},{7},{8}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,5,10},{2,6,12},{3,7},{4,8},{9},{11}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,5,11},{2,6,12},{3,7},{4,8},{9},{10}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,5,10},{2,6,12},{3,7},{4,9},{8},{11}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,5,11},{2,6,12},{3,7},{4,9},{8},{10}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,5,11},{2,6,12},{3,7},{4,10},{8},{9}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,5,10},{2,6,12},{3,8},{4,9},{7},{11}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,5,11},{2,6,12},{3,8},{4,9},{7},{10}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,5,11},{2,6,12},{3,8},{4,10},{7},{9}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,5,11},{2,6,12},{3,9},{4,10},{7},{8}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,4,6},{2,3,5},{7,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,2},{3,6,8},{4,5,7}}=>[3,3,2]=>[3,3,2]=>7
{{1},{2,3,4},{5},{6},{7},{8},{9}}=>[3,1,1,1,1,1,1]=>[7,1,1]=>3
{{1,6,9},{2},{3},{4},{5},{7},{8}}=>[3,1,1,1,1,1,1]=>[7,1,1]=>3
{{1,5,9},{2},{3},{4},{6},{7},{8}}=>[3,1,1,1,1,1,1]=>[7,1,1]=>3
{{1,6,7,9},{2},{3},{4},{5},{8}}=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
{{1,3},{2,4,5,6,7},{8}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1},{2,4},{3,5,6,7,8,9}}=>[6,2,1]=>[3,2,1,1,1,1]=>16
{{1},{2,5},{3,4,6,7,8}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,4},{2,3,5,6,7},{8}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2,4},{3,5,6,7},{8}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,3},{2,4,5,6,7,8},{9}}=>[6,2,1]=>[3,2,1,1,1,1]=>16
{{1},{2,4},{3,5,6,7,8,9,10}}=>[7,2,1]=>[3,2,1,1,1,1,1]=>22
{{1},{2,5},{3,4,6,7,8,9}}=>[6,2,1]=>[3,2,1,1,1,1]=>16
{{1},{2,3,5},{4,6,7,8,9}}=>[5,3,1]=>[3,2,2,1,1]=>13
{{1},{2,6},{3,4,5,7,8}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1},{2,3,4,6},{5,7,8}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,5},{2,3,4,6,7},{8}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,4},{2,3,5,6,7,8},{9}}=>[6,2,1]=>[3,2,1,1,1,1]=>16
{{1,2,4},{3,5,6,7,8},{9}}=>[5,3,1]=>[3,2,2,1,1]=>13
{{1,3},{2,4,5,6,7,8,9},{10}}=>[7,2,1]=>[3,2,1,1,1,1,1]=>22
{{1,2,7},{3},{4,6,8},{5}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,2,4,6,8,10},{3},{5},{7},{9}}=>[6,1,1,1,1]=>[5,1,1,1,1,1]=>15
{{1,2,4,6,9},{3,10},{5},{7},{8}}=>[5,2,1,1,1]=>[5,2,1,1,1]=>11
{{1,2,4,7,10},{3,8},{5},{6},{9}}=>[5,2,1,1,1]=>[5,2,1,1,1]=>11
{{1,2,4,7,9},{3},{5,10},{6},{8}}=>[5,2,1,1,1]=>[5,2,1,1,1]=>11
{{1,2,4,8},{3,9},{5,10},{6},{7}}=>[4,2,2,1,1]=>[5,3,1,1]=>8
{{1,2,5,8,10},{3,6},{4},{7},{9}}=>[5,2,1,1,1]=>[5,2,1,1,1]=>11
{{1,2,5,9},{3,6,10},{4},{7},{8}}=>[4,3,1,1,1]=>[5,2,2,1]=>9
{{1,2,5,7,10},{3},{4,8},{6},{9}}=>[5,2,1,1,1]=>[5,2,1,1,1]=>11
{{1,2,5,7,9},{3},{4},{6,10},{8}}=>[5,2,1,1,1]=>[5,2,1,1,1]=>11
{{1,2,5,8},{3,9},{4},{6,10},{7}}=>[4,2,2,1,1]=>[5,3,1,1]=>8
{{1,2,6,10},{3,7},{4,8},{5},{9}}=>[4,2,2,1,1]=>[5,3,1,1]=>8
{{1,2,6,9},{3,7},{4},{5,10},{8}}=>[4,2,2,1,1]=>[5,3,1,1]=>8
{{1,2,6,8},{3},{4,9},{5,10},{7}}=>[4,2,2,1,1]=>[5,3,1,1]=>8
{{1,3,6,8,10},{2,4},{5},{7},{9}}=>[5,2,1,1,1]=>[5,2,1,1,1]=>11
{{1,3,6,9},{2,4,10},{5},{7},{8}}=>[4,3,1,1,1]=>[5,2,2,1]=>9
{{1,3,7,10},{2,4,8},{5},{6},{9}}=>[4,3,1,1,1]=>[5,2,2,1]=>9
{{1,3,7,9},{2,4},{5,10},{6},{8}}=>[4,2,2,1,1]=>[5,3,1,1]=>8
{{1,3,5,8,10},{2},{4,6},{7},{9}}=>[5,2,1,1,1]=>[5,2,1,1,1]=>11
{{1,3,5,9},{2},{4,6,10},{7},{8}}=>[4,3,1,1,1]=>[5,2,2,1]=>9
{{1,3,5,7,10},{2},{4},{6,8},{9}}=>[5,2,1,1,1]=>[5,2,1,1,1]=>11
{{1,3,5,7,9},{2},{4},{6},{8,10}}=>[5,2,1,1,1]=>[5,2,1,1,1]=>11
{{1,3,5,8},{2,9},{4},{6},{7,10}}=>[4,2,2,1,1]=>[5,3,1,1]=>8
{{1,3,6,10},{2,7},{4},{5,8},{9}}=>[4,2,2,1,1]=>[5,3,1,1]=>8
{{1,3,6,9},{2,7},{4},{5},{8,10}}=>[4,2,2,1,1]=>[5,3,1,1]=>8
{{1,3,6,8},{2},{4,9},{5},{7,10}}=>[4,2,2,1,1]=>[5,3,1,1]=>8
{{1,3,7},{2,8},{4,9},{5},{6,10}}=>[3,2,2,2,1]=>[5,4,1]=>6
{{1,4,8,10},{2,5},{3,6},{7},{9}}=>[4,2,2,1,1]=>[5,3,1,1]=>8
{{1,4,7,10},{2,5},{3},{6,8},{9}}=>[4,2,2,1,1]=>[5,3,1,1]=>8
{{1,4,7,9},{2,5},{3},{6},{8,10}}=>[4,2,2,1,1]=>[5,3,1,1]=>8
{{1,4,8},{2,5,9},{3},{6},{7,10}}=>[3,3,2,1,1]=>[5,3,2]=>7
{{1,4,6,10},{2},{3,7},{5,8},{9}}=>[4,2,2,1,1]=>[5,3,1,1]=>8
{{1,4,6,9},{2},{3,7},{5},{8,10}}=>[4,2,2,1,1]=>[5,3,1,1]=>8
{{1,4,6,8},{2},{3},{5,9},{7,10}}=>[4,2,2,1,1]=>[5,3,1,1]=>8
{{1,4,7},{2,8},{3},{5,9},{6,10}}=>[3,2,2,2,1]=>[5,4,1]=>6
{{1,5,9},{2,6},{3,7},{4},{8,10}}=>[3,2,2,2,1]=>[5,4,1]=>6
{{1,5,8},{2,6},{3},{4,9},{7,10}}=>[3,2,2,2,1]=>[5,4,1]=>6
{{1,5,7},{2},{3,8},{4,9},{6,10}}=>[3,2,2,2,1]=>[5,4,1]=>6
{{1,4,9},{2,5,10},{3,11},{6},{7},{8,12}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,5,10},{2,6,11},{3,7},{4},{8},{9,12}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1,5,9},{2,6,10},{3},{4},{7,11},{8,12}}=>[3,3,2,2,1,1]=>[6,4,2]=>8
{{1},{2,4,6},{3},{5,7,8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,5,7},{3},{4,6,8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,8},{2,9},{3},{4},{5},{6},{7}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1},{2,7},{3,8},{4},{5},{6}}=>[2,2,1,1,1,1]=>[6,2]=>2
{{1,7},{2},{3,9},{4},{5},{6},{8}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1,6},{2},{3},{4,9},{5},{7},{8}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1,5,6},{2},{3,8},{4},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,5},{2},{3},{4},{6,9},{7},{8}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1,4},{2},{3},{5},{6},{7,9},{8}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1,3},{2},{4},{5},{6},{7},{8,9}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1,2,3,4,5,6,9},{7,8}}=>[7,2]=>[2,2,1,1,1,1,1]=>22
{{1,2,3,4,5,6,7,10},{8,9}}=>[8,2]=>[2,2,1,1,1,1,1,1]=>29
{{1},{2,3,4,5,6,7,10},{8,9}}=>[7,2,1]=>[3,2,1,1,1,1,1]=>22
{{1,3,4,5,6,9},{2},{7,8}}=>[6,2,1]=>[3,2,1,1,1,1]=>16
{{1},{2},{3},{4,6,8},{5,7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2},{3,5,8},{4,6},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,2,8},{3},{4},{5},{6},{7},{9}}=>[3,1,1,1,1,1,1]=>[7,1,1]=>3
{{1,2,7},{3},{4},{5},{6},{8},{9}}=>[3,1,1,1,1,1,1]=>[7,1,1]=>3
{{1,2,9},{3,4,5,6,7,8}}=>[6,3]=>[2,2,2,1,1,1]=>18
{{1},{2,3,4,5,6,7},{8,9}}=>[6,2,1]=>[3,2,1,1,1,1]=>16
{{1},{2,3,4,5,6,9},{7},{8}}=>[6,1,1,1]=>[4,1,1,1,1,1]=>15
{{1},{2,3,4,5,9},{6},{7},{8}}=>[5,1,1,1,1]=>[5,1,1,1,1]=>10
{{1},{2,3,4,9},{5},{6},{7},{8}}=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
{{1},{2,3,4,5,6,7,10},{8},{9}}=>[7,1,1,1]=>[4,1,1,1,1,1,1]=>21
{{1},{2,3,4,5,9},{6,7},{8}}=>[5,2,1,1]=>[4,2,1,1,1]=>11
{{1},{2,3,4,5,6,10},{7},{8},{9}}=>[6,1,1,1,1]=>[5,1,1,1,1,1]=>15
{{1},{2,3,4,9},{5,6},{7},{8}}=>[4,2,1,1,1]=>[5,2,1,1]=>7
{{1},{2,3,4,5,10},{6},{7},{8},{9}}=>[5,1,1,1,1,1]=>[6,1,1,1,1]=>10
{{1},{2,3,9},{4,5},{6},{7},{8}}=>[3,2,1,1,1,1]=>[6,2,1]=>4
{{1},{2,3,4,10},{5},{6},{7},{8},{9}}=>[4,1,1,1,1,1,1]=>[7,1,1,1]=>6
{{1},{2,3,10},{4},{5},{6},{7},{8},{9}}=>[3,1,1,1,1,1,1,1]=>[8,1,1]=>3
{{1},{2,3},{4},{5},{6},{7,9},{8}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1,2,7},{3,8},{4},{5,6}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2,6,7},{3},{4,8},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,4},{3,6},{5,7,8}}=>[3,3,2]=>[3,3,2]=>7
{{1},{2,5},{3},{4,7},{6,8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1,4,8},{2,3,7},{5,6}}=>[3,3,2]=>[3,3,2]=>7
{{1,2},{3,4,7},{5,6,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,4,7},{2,3},{5,6,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,3,7},{2,4},{5,6,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,3,7},{2,6,8},{4,5}}=>[3,3,2]=>[3,3,2]=>7
{{1,7},{2,3,5,8},{4,6}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,2,6},{3,8},{4,5,7}}=>[3,3,2]=>[3,3,2]=>7
{{1,2,8},{3,4,6},{5,7}}=>[3,3,2]=>[3,3,2]=>7
{{1,2},{3,5,7,8},{4,6}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,5,7,8},{2,6},{3,4}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,5,8},{2,7},{3,4,6}}=>[3,3,2]=>[3,3,2]=>7
{{1,6,8},{2,3},{4,5,7}}=>[3,3,2]=>[3,3,2]=>7
{{1,6,8},{2,5,7},{3,4}}=>[3,3,2]=>[3,3,2]=>7
{{1,6,8},{2,4,7},{3,5}}=>[3,3,2]=>[3,3,2]=>7
{{1},{2,4},{3,5},{6,7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,5,6,8},{3},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,5,6,9},{2},{3},{4},{7},{8}}=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
{{1,4,5,9},{2},{3},{6},{7},{8}}=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
{{1,3,4,9},{2},{5},{6},{7},{8}}=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
{{1,6},{2},{3},{4},{5},{7,8,9}}=>[3,2,1,1,1,1]=>[6,2,1]=>4
{{1,5},{2},{3},{4},{6,7,8,9}}=>[4,2,1,1,1]=>[5,2,1,1]=>7
{{1,7,8,10},{2},{3},{4},{5},{6},{9}}=>[4,1,1,1,1,1,1]=>[7,1,1,1]=>6
{{1,4},{2},{3},{5,6,7,9},{8}}=>[4,2,1,1,1]=>[5,2,1,1]=>7
{{1,6,7,10},{2},{3},{4},{5},{8},{9}}=>[4,1,1,1,1,1,1]=>[7,1,1,1]=>6
{{1,3},{2},{4,5,6,9},{7},{8}}=>[4,2,1,1,1]=>[5,2,1,1]=>7
{{1,5,6,10},{2},{3},{4},{7},{8},{9}}=>[4,1,1,1,1,1,1]=>[7,1,1,1]=>6
{{1,2},{3,4,5,9},{6},{7},{8}}=>[4,2,1,1,1]=>[5,2,1,1]=>7
{{1,4,5,10},{2},{3},{6},{7},{8},{9}}=>[4,1,1,1,1,1,1]=>[7,1,1,1]=>6
{{1,3,4,10},{2},{5},{6},{7},{8},{9}}=>[4,1,1,1,1,1,1]=>[7,1,1,1]=>6
{{1,5},{2,3,4,6},{7,8}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,3,4},{2,8},{5,6,7}}=>[3,3,2]=>[3,3,2]=>7
{{1,3,6,7},{2,8},{4,5}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,8},{2,3,6},{4,5,7}}=>[3,3,2]=>[3,3,2]=>7
{{1,2,7},{3,4,5,6,8}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,2},{3,5,6},{4,7,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,5,6},{2,7,8},{3,4}}=>[3,3,2]=>[3,3,2]=>7
{{1,4,5},{2,7,8},{3,6}}=>[3,3,2]=>[3,3,2]=>7
{{1,7},{2,6},{3,4,5,8}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,2},{3,7},{4,5,6,8}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,7},{2,5,6,8},{3,4}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,2,3,7},{4},{5,8},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,4,5,6,7},{2},{8,9}}=>[6,2,1]=>[3,2,1,1,1,1]=>16
{{1,3,4},{2,6},{5,7,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,3,4,5,6},{2,8,9},{7}}=>[5,3,1]=>[3,2,2,1,1]=>13
{{1,3,4,5,6},{2},{7,8,9}}=>[5,3,1]=>[3,2,2,1,1]=>13
{{1,3,4,5,6,7,8},{2},{9,10}}=>[7,2,1]=>[3,2,1,1,1,1,1]=>22
{{1,7},{2},{3,4,5,8},{6}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4},{2,3,5,6},{7},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,5},{2,4},{6},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2,5,6,7},{3},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2,6},{3},{4},{5},{7},{8},{9}}=>[3,1,1,1,1,1,1]=>[7,1,1]=>3
{{1,2,5},{3},{4},{6},{7},{8},{9}}=>[3,1,1,1,1,1,1]=>[7,1,1]=>3
{{1,2,4},{3},{5},{6},{7},{8},{9}}=>[3,1,1,1,1,1,1]=>[7,1,1]=>3
{{1},{2},{3,4,5,7},{6,8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,4,7},{2},{3},{5,6,8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1,4,5},{2},{3,6,7},{8}}=>[3,3,1,1]=>[4,2,2]=>6
{{1},{2,5},{3,4,6,7},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,4,5,6},{3,7},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,2},{3},{4},{5},{6},{7,9},{8}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1,2},{3},{4},{5},{6},{7},{8,10},{9}}=>[2,2,1,1,1,1,1,1]=>[8,2]=>2
{{1,3},{2},{4},{5},{6},{7,9},{8}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1},{2,3},{4},{5},{6},{7},{8,9}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1,2},{3},{4},{5},{6},{7},{8},{9,10}}=>[2,2,1,1,1,1,1,1]=>[8,2]=>2
{{1},{2,3,6},{4},{5,8},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,3,7},{4},{5,8},{6}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,4},{3,7},{5},{6,8}}=>[2,2,2,1,1]=>[5,3]=>3
{{1},{2,5},{3},{4,6,8},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,5},{3},{4,6,7},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,2},{3,4,6,8},{5,7}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,2,3,4,5,8,9},{6},{7}}=>[7,1,1]=>[3,1,1,1,1,1,1]=>21
{{1,2,3,4,5,9},{6,7},{8}}=>[6,2,1]=>[3,2,1,1,1,1]=>16
{{1,2,3,4,5,6,9,10},{7},{8}}=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>28
{{1,2,3,4,8,9},{5,7},{6}}=>[6,2,1]=>[3,2,1,1,1,1]=>16
{{1,2,3,4,6,8,9},{5},{7}}=>[7,1,1]=>[3,1,1,1,1,1,1]=>21
{{1,2,3,4,9},{5,8},{6,7}}=>[5,2,2]=>[3,3,1,1,1]=>12
{{1,2,3,4,7,9},{5,6},{8}}=>[6,2,1]=>[3,2,1,1,1,1]=>16
{{1,2,3,4,5,6,10},{7,8},{9}}=>[7,2,1]=>[3,2,1,1,1,1,1]=>22
{{1,4,6,7,8},{2},{3,5}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,4,5},{2,3,6,7,8}}=>[5,3]=>[2,2,2,1,1]=>13
{{1,4,5},{2,3,6},{7,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,4,5},{2,3,8},{6,7}}=>[3,3,2]=>[3,3,2]=>7
{{1,4,7},{2,3,8},{5,6}}=>[3,3,2]=>[3,3,2]=>7
{{1,3,4},{2,7},{5,6,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,3,6,8},{2,7},{4,5}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,2},{3,6,7},{4,5,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,6,7},{2,3},{4,5,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,6,7},{2,5,8},{3,4}}=>[3,3,2]=>[3,3,2]=>7
{{1,5,6},{2,8},{3,4,7}}=>[3,3,2]=>[3,3,2]=>7
{{1,6,7},{2,4,5},{3,8}}=>[3,3,2]=>[3,3,2]=>7
{{1},{2,4,6,8,10},{3},{5},{7},{9}}=>[5,1,1,1,1,1]=>[6,1,1,1,1]=>10
{{1},{2,4,6,10},{3},{5},{7,9},{8}}=>[4,2,1,1,1,1]=>[6,2,1,1]=>7
{{1},{2,4,8,10},{3},{5,7},{6},{9}}=>[4,2,1,1,1,1]=>[6,2,1,1]=>7
{{1},{2,4,10},{3},{5,7,9},{6},{8}}=>[3,3,1,1,1,1]=>[6,2,2]=>6
{{1},{2,4,10},{3},{5,9},{6,8},{7}}=>[3,2,2,1,1,1]=>[6,3,1]=>5
{{1},{2,6,8,10},{3,5},{4},{7},{9}}=>[4,2,1,1,1,1]=>[6,2,1,1]=>7
{{1},{2,6,10},{3,5},{4},{7,9},{8}}=>[3,2,2,1,1,1]=>[6,3,1]=>5
{{1},{2,8,10},{3,5,7},{4},{6},{9}}=>[3,3,1,1,1,1]=>[6,2,2]=>6
{{1},{2,8,10},{3,7},{4,6},{5},{9}}=>[3,2,2,1,1,1]=>[6,3,1]=>5
{{1},{2,10},{3,5,7,9},{4},{6},{8}}=>[4,2,1,1,1,1]=>[6,2,1,1]=>7
{{1},{2,10},{3,5,9},{4},{6,8},{7}}=>[3,2,2,1,1,1]=>[6,3,1]=>5
{{1},{2,10},{3,7,9},{4,6},{5},{8}}=>[3,2,2,1,1,1]=>[6,3,1]=>5
{{1},{2,10},{3,9},{4,6,8},{5},{7}}=>[3,2,2,1,1,1]=>[6,3,1]=>5
{{1,3},{2},{4,6,8,10},{5},{7},{9}}=>[4,2,1,1,1,1]=>[6,2,1,1]=>7
{{1,3},{2},{4,6,10},{5},{7,9},{8}}=>[3,2,2,1,1,1]=>[6,3,1]=>5
{{1,3},{2},{4,8,10},{5,7},{6},{9}}=>[3,2,2,1,1,1]=>[6,3,1]=>5
{{1,3},{2},{4,10},{5,7,9},{6},{8}}=>[3,2,2,1,1,1]=>[6,3,1]=>5
{{1,3},{2},{4,10},{5,9},{6,8},{7}}=>[2,2,2,2,1,1]=>[6,4]=>4
{{1,3,5},{2},{4},{6,8,10},{7},{9}}=>[3,3,1,1,1,1]=>[6,2,2]=>6
{{1,3,5},{2},{4},{6,10},{7,9},{8}}=>[3,2,2,1,1,1]=>[6,3,1]=>5
{{1,5},{2,4},{3},{6,8,10},{7},{9}}=>[3,2,2,1,1,1]=>[6,3,1]=>5
{{1,5},{2,4},{3},{6,10},{7,9},{8}}=>[2,2,2,2,1,1]=>[6,4]=>4
{{1,3,5,7},{2},{4},{6},{8,10},{9}}=>[4,2,1,1,1,1]=>[6,2,1,1]=>7
{{1,3,7},{2},{4,6},{5},{8,10},{9}}=>[3,2,2,1,1,1]=>[6,3,1]=>5
{{1,5,7},{2,4},{3},{6},{8,10},{9}}=>[3,2,2,1,1,1]=>[6,3,1]=>5
{{1,7},{2,4,6},{3},{5},{8,10},{9}}=>[3,2,2,1,1,1]=>[6,3,1]=>5
{{1,7},{2,6},{3,5},{4},{8,10},{9}}=>[2,2,2,2,1,1]=>[6,4]=>4
{{1,3,5,7,9},{2},{4},{6},{8},{10}}=>[5,1,1,1,1,1]=>[6,1,1,1,1]=>10
{{1,3,5,9},{2},{4},{6,8},{7},{10}}=>[4,2,1,1,1,1]=>[6,2,1,1]=>7
{{1,3,7,9},{2},{4,6},{5},{8},{10}}=>[4,2,1,1,1,1]=>[6,2,1,1]=>7
{{1,3,9},{2},{4,6,8},{5},{7},{10}}=>[3,3,1,1,1,1]=>[6,2,2]=>6
{{1,3,9},{2},{4,8},{5,7},{6},{10}}=>[3,2,2,1,1,1]=>[6,3,1]=>5
{{1,5,7,9},{2,4},{3},{6},{8},{10}}=>[4,2,1,1,1,1]=>[6,2,1,1]=>7
{{1,5,9},{2,4},{3},{6,8},{7},{10}}=>[3,2,2,1,1,1]=>[6,3,1]=>5
{{1,7,9},{2,4,6},{3},{5},{8},{10}}=>[3,3,1,1,1,1]=>[6,2,2]=>6
{{1,7,9},{2,6},{3,5},{4},{8},{10}}=>[3,2,2,1,1,1]=>[6,3,1]=>5
{{1,9},{2,4,6,8},{3},{5},{7},{10}}=>[4,2,1,1,1,1]=>[6,2,1,1]=>7
{{1,9},{2,4,8},{3},{5,7},{6},{10}}=>[3,2,2,1,1,1]=>[6,3,1]=>5
{{1,9},{2,6,8},{3,5},{4},{7},{10}}=>[3,2,2,1,1,1]=>[6,3,1]=>5
{{1,9},{2,8},{3,5,7},{4},{6},{10}}=>[3,2,2,1,1,1]=>[6,3,1]=>5
{{1},{2,4,12},{3},{5,11},{6,10},{7,9},{8}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1},{2,6,12},{3,5},{4},{7,11},{8,10},{9}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1},{2,8,12},{3,7},{4,6},{5},{9,11},{10}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1},{2,10,12},{3,9},{4,8},{5,7},{6},{11}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1},{2,12},{3,5,11},{4},{6,10},{7,9},{8}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1},{2,12},{3,7,11},{4,6},{5},{8,10},{9}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1},{2,12},{3,9,11},{4,8},{5,7},{6},{10}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1},{2,12},{3,11},{4,6,10},{5},{7,9},{8}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1},{2,12},{3,11},{4,8,10},{5,7},{6},{9}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1},{2,12},{3,11},{4,10},{5,7,9},{6},{8}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1},{2,12},{3,11},{4,10},{5,9},{6,8},{7}}=>[2,2,2,2,2,1,1]=>[7,5]=>5
{{1,3},{2},{4,6,12},{5},{7,11},{8,10},{9}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,3},{2},{4,8,12},{5,7},{6},{9,11},{10}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,3},{2},{4,10,12},{5,9},{6,8},{7},{11}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,3},{2},{4,12},{5,7,11},{6},{8,10},{9}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,3},{2},{4,12},{5,9,11},{6,8},{7},{10}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,3},{2},{4,12},{5,11},{6,8,10},{7},{9}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,3},{2},{4,12},{5,11},{6,10},{7,9},{8}}=>[2,2,2,2,2,1,1]=>[7,5]=>5
{{1,3,5},{2},{4},{6,12},{7,11},{8,10},{9}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,5},{2,4},{3},{6,8,12},{7},{9,11},{10}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,5},{2,4},{3},{6,10,12},{7,9},{8},{11}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,5},{2,4},{3},{6,12},{7,9,11},{8},{10}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,5},{2,4},{3},{6,12},{7,11},{8,10},{9}}=>[2,2,2,2,2,1,1]=>[7,5]=>5
{{1,3,7},{2},{4,6},{5},{8,12},{9,11},{10}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,5,7},{2,4},{3},{6},{8,12},{9,11},{10}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,7},{2,4,6},{3},{5},{8,12},{9,11},{10}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,7},{2,6},{3,5},{4},{8,10,12},{9},{11}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,7},{2,6},{3,5},{4},{8,12},{9,11},{10}}=>[2,2,2,2,2,1,1]=>[7,5]=>5
{{1,3,9},{2},{4,8},{5,7},{6},{10,12},{11}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,5,9},{2,4},{3},{6,8},{7},{10,12},{11}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,7,9},{2,6},{3,5},{4},{8},{10,12},{11}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,9},{2,4,8},{3},{5,7},{6},{10,12},{11}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,9},{2,6,8},{3,5},{4},{7},{10,12},{11}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,9},{2,8},{3,5,7},{4},{6},{10,12},{11}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,9},{2,8},{3,7},{4,6},{5},{10,12},{11}}=>[2,2,2,2,2,1,1]=>[7,5]=>5
{{1,3,11},{2},{4,10},{5,9},{6,8},{7},{12}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,5,11},{2,4},{3},{6,10},{7,9},{8},{12}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,7,11},{2,6},{3,5},{4},{8,10},{9},{12}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,9,11},{2,8},{3,7},{4,6},{5},{10},{12}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,11},{2,4,10},{3},{5,9},{6,8},{7},{12}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,11},{2,6,10},{3,5},{4},{7,9},{8},{12}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,11},{2,8,10},{3,7},{4,6},{5},{9},{12}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,11},{2,10},{3,5,9},{4},{6,8},{7},{12}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,11},{2,10},{3,7,9},{4,6},{5},{8},{12}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,11},{2,10},{3,9},{4,6,8},{5},{7},{12}}=>[3,2,2,2,1,1,1]=>[7,4,1]=>6
{{1,11},{2,10},{3,9},{4,8},{5,7},{6},{12}}=>[2,2,2,2,2,1,1]=>[7,5]=>5
{{1,9},{2},{3},{4},{5},{6,7},{8}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1,9},{2},{3},{4},{5},{6,8},{7}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1},{2,5},{3},{4},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1]=>[8,1]=>1
{{1},{2},{3,5},{4},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1]=>[8,1]=>1
{{1},{2},{3},{4,5},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1]=>[8,1]=>1
{{1},{2},{3},{4},{5},{6,7},{8},{9},{10}}=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>1
{{1,9},{2},{3},{4},{5},{6,7,8}}=>[3,2,1,1,1,1]=>[6,2,1]=>4
{{1},{2},{3},{4},{5},{6,8},{7},{9},{10}}=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>1
{{1,6,8,9},{2},{3},{4},{5},{7}}=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
{{1,5},{2},{3},{4},{6},{7},{8,9}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1,2,9},{3,6},{4},{5},{7},{8}}=>[3,2,1,1,1,1]=>[6,2,1]=>4
{{1,10},{2,6},{3},{4},{5},{7},{8},{9}}=>[2,2,1,1,1,1,1,1]=>[8,2]=>2
{{1,10},{2},{3,6},{4},{5},{7},{8},{9}}=>[2,2,1,1,1,1,1,1]=>[8,2]=>2
{{1},{2,3},{4,5},{6},{7},{8},{9}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1,10},{2},{3},{4,6},{5},{7},{8},{9}}=>[2,2,1,1,1,1,1,1]=>[8,2]=>2
{{1},{2},{3,4},{5},{6},{7},{8},{9}}=>[2,1,1,1,1,1,1,1]=>[8,1]=>1
{{1,10},{2},{3},{4},{5,6},{7},{8},{9}}=>[2,2,1,1,1,1,1,1]=>[8,2]=>2
{{1,2,4},{3,6,7,8},{5}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,2,4},{3,5,6,8},{7}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,2,3,6},{4},{5,8},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,4},{3,5,6,8},{7}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1},{2,5},{3,4,6},{7,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,2},{3},{4,7},{5,6,8}}=>[3,2,2,1]=>[4,3,1]=>5
{{1,4},{2},{3},{5},{6,9},{7},{8}}=>[2,2,1,1,1,1,1]=>[7,2]=>2
{{1},{2,4,6},{3},{5,7},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1,4,6},{2,3,5,8},{7}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,6},{2,3,5,8},{4,7}}=>[4,2,2]=>[3,3,1,1]=>8
{{1,3,5},{2,7,8},{4,6}}=>[3,3,2]=>[3,3,2]=>7
{{1,3,4},{2,5,7,8},{6}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,4,5,6},{2},{3,7,8}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,2,5,7,8},{3},{4,6}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1},{2,3,6,8},{4,7},{5}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3,6},{2,4},{5,7,8}}=>[3,3,2]=>[3,3,2]=>7
{{1,4,8},{2,5,7},{3,6}}=>[3,3,2]=>[3,3,2]=>7
{{1,2,6,8},{3},{4,5,7}}=>[4,3,1]=>[3,2,2,1]=>9
{{1,4,6,8},{2,3,5},{7}}=>[4,3,1]=>[3,2,2,1]=>9
{{1},{2,3,4,6,7},{5,8}}=>[5,2,1]=>[3,2,1,1,1]=>11
{{1,2,3,4,5,7},{6},{8,9}}=>[6,2,1]=>[3,2,1,1,1,1]=>16
{{1},{2,3,6},{4,7},{5},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,4,7},{3,8},{5},{6}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,5,7},{3},{4,8},{6}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,4,7},{3,5},{6},{8}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,5,8},{3,6},{4},{7}}=>[3,2,1,1,1]=>[5,2,1]=>4
{{1},{2,4,6,7},{3,5},{8}}=>[4,2,1,1]=>[4,2,1,1]=>7
{{1,3},{2},{4,5,6,7,8,9}}=>[6,2,1]=>[3,2,1,1,1,1]=>16
{{1,2,4},{3},{5,6,7,8,9}}=>[5,3,1]=>[3,2,2,1,1]=>13
{{1,2,3,5},{4},{6,7,8,9}}=>[4,4,1]=>[3,2,2,2]=>12
{{1,2,3,4,6},{5},{7,8,9}}=>[5,3,1]=>[3,2,2,1,1]=>13
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Description
The weighted size of a partition.
Let λ=(λ0≥λ1≥⋯≥λm) be an integer partition. Then the weighted size of λ is
m∑i=0i⋅λi.
This is also the sum of the leg lengths of the cells in λ, or
\sum_i \binom{\lambda^{\prime}_i}{2}
where \lambda^{\prime} is the conjugate partition of \lambda.
This is the minimal number of inversions a permutation with the given shape can have, see [1, cor.2.2].
This is also the smallest possible sum of the entries of a semistandard tableau (allowing 0 as a part) of shape \lambda=(\lambda_0,\lambda_1,\ldots,\lambda_m), obtained uniquely by placing i-1 in all the cells of the ith row of \lambda, see [2, eq.7.103].
Let λ=(λ0≥λ1≥⋯≥λm) be an integer partition. Then the weighted size of λ is
m∑i=0i⋅λi.
This is also the sum of the leg lengths of the cells in λ, or
\sum_i \binom{\lambda^{\prime}_i}{2}
where \lambda^{\prime} is the conjugate partition of \lambda.
This is the minimal number of inversions a permutation with the given shape can have, see [1, cor.2.2].
This is also the smallest possible sum of the entries of a semistandard tableau (allowing 0 as a part) of shape \lambda=(\lambda_0,\lambda_1,\ldots,\lambda_m), obtained uniquely by placing i-1 in all the cells of the ith row of \lambda, see [2, eq.7.103].
Map
shape
Description
Sends a set partition to the integer partition obtained by the sizes of the blocks.
Map
conjugate
Description
Return the conjugate partition of the partition.
The conjugate partition of the partition \lambda of n is the partition \lambda^* whose Ferrers diagram is obtained from the diagram of \lambda by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
The conjugate partition of the partition \lambda of n is the partition \lambda^* whose Ferrers diagram is obtained from the diagram of \lambda by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
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