Identifier
-
Mp00118:
Dyck paths
—swap returns and last descent⟶
Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00308: Integer partitions —Bulgarian solitaire⟶ Integer partitions
St000477: Integer partitions ⟶ ℤ
Values
=>
Cc0005;cc-rep-0
Cc0005;cc-rep-1
Cc0002;cc-rep-2
Cc0002;cc-rep
[1,0,1,1,0,0]=>[1,0,1,1,0,0]=>[1,1]=>[2]=>2
[1,1,0,1,0,0]=>[1,1,0,0,1,0]=>[2]=>[1,1]=>-1
[1,1,1,0,0,0]=>[1,0,1,0,1,0]=>[2,1]=>[2,1]=>0
[1,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0]=>[1,1,1]=>[3]=>3
[1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,0]=>[2,1,1]=>[3,1]=>1
[1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0]=>[2,2,1]=>[3,1,1]=>-1
[1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,0]=>[1,1]=>[2]=>2
[1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0]=>[2,2]=>[2,1,1]=>0
[1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0]=>[2,1]=>[2,1]=>0
[1,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0]=>[3,1]=>[2,2]=>-2
[1,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0]=>[3,2]=>[2,2,1]=>0
[1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0]=>[2]=>[1,1]=>-1
[1,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,0]=>[3]=>[2,1]=>0
[1,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,0]=>[3,1,1]=>[3,2]=>0
[1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]=>[3,2,1]=>[3,2,1]=>0
[1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1]=>[4]=>4
[1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0]=>[2,1,1,1]=>[4,1]=>2
[1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>[2,2,2,1]=>[4,1,1,1]=>2
[1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1]=>[2]=>2
[1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,0]=>[2,2,1,1]=>[4,1,1]=>-2
[1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0]=>[2,1]=>[2,1]=>0
[1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]=>[4,2,1]=>0
[1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[3,3,1,1]=>[4,2,2]=>-2
[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0]=>[2]=>[1,1]=>-1
[1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0]=>[3,1,1,1]=>[4,2]=>2
[1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0]=>[3,2,2,1]=>[4,2,1,1]=>0
[1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0]=>[3,3,2,1]=>[4,2,2,1]=>0
[1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,1]=>[3]=>3
[1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[2,2,2]=>[3,1,1,1]=>1
[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0]=>[2,1,1]=>[3,1]=>1
[1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]=>[3,2,2]=>[3,2,1,1]=>0
[1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[3,3,2]=>[3,2,2,1]=>0
[1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,0]=>[2,2,1]=>[3,1,1]=>-1
[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]=>[3,3,1]=>[3,2,2]=>0
[1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0]=>[3,2,1]=>[3,2,1]=>0
[1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>[4,2,1]=>[3,3,1]=>-1
[1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>[4,3,1]=>[3,3,2]=>0
[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]=>[3,1,1]=>[3,2]=>0
[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[4,1,1]=>[3,3]=>-3
[1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[4,2,2]=>[3,3,1,1]=>1
[1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>[4,3,2]=>[3,3,2,1]=>0
[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>[2,2]=>[2,1,1]=>0
[1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[3,3]=>[2,2,2]=>2
[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]=>[3,2]=>[2,2,1]=>0
[1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>[4,2]=>[3,2,1]=>0
[1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>[4,3]=>[3,2,2]=>0
[1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]=>[3,1]=>[2,2]=>-2
[1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>[4,1]=>[3,2]=>0
[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>[4,2,1,1]=>[4,3,1]=>0
[1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>[4,3,1,1]=>[4,3,2]=>0
[1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0]=>[3]=>[2,1]=>0
[1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[4]=>[3,1]=>1
[1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>[4,1,1,1]=>[4,3]=>0
[1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>[4,2,2,1]=>[4,3,1,1]=>0
[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[4,3,2,1]=>0
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]=>[5]=>5
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,1,1,1]=>[5,1]=>3
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,2,2,2,1]=>[5,1,1,1,1]=>-3
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]=>[2]=>2
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,2,1,1,1]=>[5,1,1]=>-3
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1]=>[2,1]=>0
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[3,2,1,1,1]=>[5,2,1]=>0
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[3,3,2,2,1]=>[5,2,2,1,1]=>0
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[2]=>[1,1]=>-1
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,1,1,1]=>[5,2]=>4
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[3,2,2,2,1]=>[5,2,1,1,1]=>0
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[3,3,3,2,1]=>[5,2,2,2,1]=>0
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]=>[3]=>3
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,2,1,1]=>[5,1,1,1]=>3
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,1]=>[3,1]=>1
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1,1]=>[5,2,1,1]=>0
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,3,3,1,1]=>[5,2,2,2]=>4
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1]=>[3,1,1]=>-1
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[3,3,2,1,1]=>[5,2,2,1]=>0
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,1]=>[3,2,1]=>0
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,1]=>[5,3,2,1]=>0
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[4,4,2,1,1]=>[5,3,3,1]=>-1
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,1,1]=>[3,2]=>0
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[4,2,2,1,1]=>[5,3,1,1]=>-1
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[4,3,3,1,1]=>[5,3,2,2]=>0
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,2]=>[2,1,1]=>0
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,1,1,1]=>[5,2,2]=>-4
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[3,2]=>[2,2,1]=>0
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[4,3,1,1,1]=>[5,3,2]=>0
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[4,4,1,1,1]=>[5,3,3]=>-3
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[3,1]=>[2,2]=>-2
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[4,2,1,1,1]=>[5,3,1]=>1
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[4,3,2,2,1]=>[5,3,2,1,1]=>0
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[3]=>[2,1]=>0
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[4,1,1,1,1]=>[5,3]=>3
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[4,2,2,2,1]=>[5,3,1,1,1]=>1
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]=>[4]=>4
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,2,2]=>[4,1,1,1,1]=>-2
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,1,1]=>[4,1]=>2
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[3,2,2,2]=>[4,2,1,1,1]=>0
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[3,3,3,2]=>[4,2,2,2,1]=>0
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,1,1]=>[4,1,1]=>-2
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[3,3,2,2]=>[4,2,2,1,1]=>0
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]=>[4,2,1]=>0
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[4,3,2,2]=>[4,3,2,1,1]=>0
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[4,4,2,2]=>[4,3,3,1,1]=>0
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,1,1]=>[4,2]=>2
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[4,2,2,2]=>[4,3,1,1,1]=>0
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[4,3,3,2]=>[4,3,2,2,1]=>0
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,2,1]=>[4,1,1,1]=>2
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,3,3,1]=>[4,2,2,2]=>2
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]=>[4,2,1,1]=>0
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[4,3,3,1]=>[4,3,2,2]=>0
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[4,4,3,1]=>[4,3,3,2]=>0
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[3,3,2,1]=>[4,2,2,1]=>0
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[4,4,2,1]=>[4,3,3,1]=>0
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,1]=>[4,3,2,1]=>0
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[5,3,2,1]=>[4,4,2,1]=>0
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[5,4,2,1]=>[4,4,3,1]=>0
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[4,2,2,1]=>[4,3,1,1]=>0
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[5,2,2,1]=>[4,4,1,1]=>2
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[5,3,3,1]=>[4,4,2,2]=>2
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[3,3,1,1]=>[4,2,2]=>-2
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[4,4,1,1]=>[4,3,3]=>0
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[4,3,1,1]=>[4,3,2]=>0
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[5,3,1,1]=>[4,4,2]=>-2
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[5,4,1,1]=>[4,4,3]=>0
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[4,2,1,1]=>[4,3,1]=>0
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[5,2,1,1]=>[4,4,1]=>-2
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[5,3,2,2]=>[4,4,2,1,1]=>0
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,1,1,1]=>[4,3]=>0
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[5,1,1,1]=>[4,4]=>-4
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[5,2,2,2]=>[4,4,1,1,1]=>-2
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,2]=>[3,1,1,1]=>1
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3,3]=>[3,2,2,2]=>0
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,2]=>[3,2,1,1]=>0
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[4,3,3]=>[3,3,2,2]=>0
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[4,4,3]=>[3,3,3,2]=>0
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,3,2]=>[3,2,2,1]=>0
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[4,4,2]=>[3,3,3,1]=>1
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[4,3,2]=>[3,3,2,1]=>0
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[5,3,2]=>[4,3,2,1]=>0
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[5,4,2]=>[4,3,3,1]=>0
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[4,2,2]=>[3,3,1,1]=>1
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[5,2,2]=>[4,3,1,1]=>0
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[5,3,3]=>[4,3,2,2]=>0
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[5,4,3]=>[4,3,3,2]=>0
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,3,1]=>[3,2,2]=>0
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,4,1]=>[3,3,3]=>3
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[4,3,1]=>[3,3,2]=>0
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[5,3,1]=>[4,3,2]=>0
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[5,4,1]=>[4,3,3]=>0
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[4,2,1]=>[3,3,1]=>-1
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[5,2,1]=>[4,3,1]=>0
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,1]=>[5,4,2,1]=>0
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[4,1,1]=>[3,3]=>-3
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,1,1]=>[4,3]=>0
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[5,2,2,1,1]=>[5,4,1,1]=>0
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[3,3]=>[2,2,2]=>2
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,4]=>[3,3,2]=>0
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3]=>[3,2,2]=>0
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[5,3]=>[4,2,2]=>-2
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[5,4]=>[4,3,2]=>0
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,2]=>[3,2,1]=>0
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,2]=>[4,2,1]=>0
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[5,3,1,1,1]=>[5,4,2]=>0
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[5,4,1,1,1]=>[5,4,3]=>0
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1]=>[3,2]=>0
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1]=>[4,2]=>2
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[5,2,1,1,1]=>[5,4,1]=>0
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[4]=>[3,1]=>1
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5]=>[4,1]=>2
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[5,1,1,1,1]=>[5,4]=>0
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[5,2,2,2,1]=>[5,4,1,1,1]=>0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[6]=>6
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]=>[6,1]=>4
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]=>[6,1,1,1,1,1]=>4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[2]=>2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]=>[6,1,1]=>-4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]=>[2,1]=>0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1,1]=>[6,2,1]=>0
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2]=>[1,1]=>-1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]=>[6,2]=>6
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,2,1]=>[6,2,1,1,1,1]=>0
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[3]=>3
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]=>[6,1,1,1]=>4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]=>[3,1]=>1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1,1,1]=>[6,2,1,1]=>0
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]=>[3,1,1]=>-1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1,1,1]=>[6,2,2,1]=>0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1]=>[3,2,1]=>0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,1,1]=>[6,3,2,1]=>0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]=>[3,2]=>0
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1,1,1]=>[6,3,1,1]=>-2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2,1,1]=>0
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1,1]=>[6,2,2]=>-6
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]=>[2,2,1]=>0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1,1,1]=>[6,3,2]=>0
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]=>[2,2]=>-2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1,1,1]=>[6,3,1]=>2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[3]=>[2,1]=>0
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>[6,3]=>6
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[4]=>4
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]=>[6,1,1,1,1]=>-4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]=>[4,1]=>2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,1,1]=>[6,2,1,1,1]=>0
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]=>[4,1,1]=>-2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,1,1]=>[6,2,2,1,1]=>0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]=>[4,2,1]=>0
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]=>[4,2]=>2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,1,1]=>[6,3,1,1,1]=>2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]=>[4,1,1,1]=>2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]=>[4,2,1,1]=>0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1]=>[4,2,2,1]=>0
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1]=>[4,3,2,1]=>0
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1]=>[4,3,1,1]=>0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1]=>[4,2,2]=>-2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1]=>[4,3,2]=>0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1]=>[4,3,1]=>0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]=>[4,3]=>0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[3,1,1,1]=>1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1,1]=>[6,2,2,2]=>6
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2]=>[3,2,1,1]=>0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,3,2]=>[3,2,2,1]=>0
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,2]=>[3,3,2,1]=>0
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,2]=>[3,3,1,1]=>1
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,3,1]=>[3,2,2]=>0
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,3,1]=>[3,3,2]=>0
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,2,1]=>[3,3,1]=>-1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]=>[3,3]=>-3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1,1,1]=>[6,4,1,1]=>-2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[2,2,2]=>2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1,1]=>[6,3,3]=>-6
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]=>[3,2,2]=>0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]=>[3,2,1]=>0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1,1,1]=>[6,4,2]=>2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]=>[3,2]=>0
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1,1,1]=>[6,4,1]=>2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[4]=>[3,1]=>1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]=>[6,4]=>4
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[5]=>5
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]=>[5,1,1,1,1,1]=>3
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]=>[5,1]=>3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,2]=>[5,2,1,1,1,1]=>0
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]=>[5,1,1]=>-3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,2]=>[5,2,2,1,1,1]=>0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1]=>[5,2,1]=>0
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]=>[5,2]=>4
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,2]=>[5,3,1,1,1,1]=>-1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]=>[5,1,1,1]=>3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1,1]=>[5,2,1,1]=>0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1,1]=>[5,2,2,1]=>0
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,1]=>[5,3,2,1]=>0
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1,1]=>[5,3,1,1]=>-1
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1]=>[5,2,2]=>-4
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1,1]=>[5,3,2]=>0
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1,1]=>[5,3,1]=>1
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]=>[5,3]=>3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]=>[5,1,1,1,1]=>-3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,1]=>[5,2,1,1,1]=>0
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,1]=>[5,2,2,1,1]=>0
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,1]=>[5,3,2,1,1]=>0
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,1]=>[5,3,1,1,1]=>1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,1]=>[5,2,2,2,1]=>0
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,1]=>[5,4,1,1,1]=>0
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1]=>[5,2,2,2]=>4
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1,1]=>[5,3,2,2]=>0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1,1]=>[5,3,3,1]=>-1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,1]=>[5,4,2,1]=>0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1,1]=>[5,4,1,1]=>0
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1,1]=>[5,5,1,1]=>3
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1]=>[5,3,3]=>-3
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1,1]=>[5,4,3]=>0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1,1]=>[5,4,2]=>0
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1,1]=>[5,5,2]=>-4
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1,1]=>[5,4,1]=>0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1,1]=>[5,5,1]=>-3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]=>[5,4]=>0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]=>[5,5]=>-5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[4,1,1,1,1]=>-2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3]=>[4,2,2,2,2]=>-2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2]=>[4,2,1,1,1]=>0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2]=>[4,2,2,1,1]=>0
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,2]=>[4,3,2,1,1]=>0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2]=>[4,3,1,1,1]=>0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2]=>[4,2,2,2,1]=>0
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[4,3,3,2]=>[4,3,2,2,1]=>0
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2]=>[4,3,3,1,1]=>0
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,2]=>[4,4,2,1,1]=>0
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2]=>[4,4,1,1,1]=>-2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2]=>[5,4,1,1,1]=>0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1]=>[4,2,2,2]=>2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1]=>[4,3,2,2]=>0
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,4,3,1]=>[4,3,3,2]=>0
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[5,3,3,1]=>[4,4,2,2]=>2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1]=>[4,3,3,1]=>0
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1]=>[4,4,3,1]=>0
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1]=>[4,4,2,1]=>0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1]=>[5,4,2,1]=>0
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1]=>[4,4,1,1]=>2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1]=>[5,4,1,1]=>0
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1]=>[4,3,3]=>0
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1]=>[4,4,4]=>4
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1]=>[4,4,3]=>0
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1]=>[5,4,3]=>0
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1]=>[4,4,2]=>-2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1]=>[5,4,2]=>0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1]=>[4,4,1]=>-2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1]=>[5,4,1]=>0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[4,4]=>-4
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>[5,4]=>0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,2,2,2]=>0
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,4,4]=>[3,3,3,3]=>-3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,3]=>[3,3,2,2]=>0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,4,3]=>[3,3,3,2]=>0
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[5,4,3]=>[4,3,3,2]=>0
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[5,3,3]=>[4,3,2,2]=>0
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[6,3,3]=>[5,3,2,2]=>0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,4,2]=>[3,3,3,1]=>1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,5,2]=>[4,4,3,1]=>0
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[5,4,2]=>[4,3,3,1]=>0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[6,4,2]=>[5,3,3,1]=>-1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[5,3,2]=>[4,3,2,1]=>0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,3,2]=>[5,3,2,1]=>0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[5,2,2]=>[4,3,1,1]=>0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,2,2]=>[5,3,1,1]=>-1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,4,1]=>[3,3,3]=>3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,5,1]=>[4,4,3]=>0
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,4,1]=>[4,3,3]=>0
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[6,4,1]=>[5,3,3]=>-3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[6,5,1]=>[5,4,3]=>0
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[5,3,1]=>[4,3,2]=>0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,3,1]=>[5,3,2]=>0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[5,2,1]=>[4,3,1]=>0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,2,1]=>[5,3,1]=>1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]=>[4,3]=>0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]=>[5,3]=>3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[3,3,2]=>0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]=>[4,4,2]=>-2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]=>[4,3,2]=>0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]=>[5,3,2]=>0
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]=>[5,4,2]=>0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]=>[4,2,2]=>-2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]=>[5,2,2]=>-4
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]=>[4,2,1]=>0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]=>[5,2,1]=>0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]=>[4,2]=>2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[5,2]=>4
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1,1,1]=>[6,5,1]=>0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[5]=>[4,1]=>2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6]=>[5,1]=>3
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]=>[6,5]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[7]=>7
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[7,1]=>5
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[2]=>2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[7,1,1]=>-5
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[2,1]=>0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[7,2,1]=>0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2]=>[1,1]=>-1
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[7,2]=>8
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[3]=>3
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[7,1,1,1]=>5
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[3,1]=>1
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1,1]=>[7,2,1,1]=>0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[3,1,1]=>-1
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1,1]=>[7,2,2,1]=>0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]=>[3,2,1]=>0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[3,2]=>0
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1,1]=>[7,3,1,1]=>-3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2,1,1]=>0
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[7,2,2]=>-8
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2,2,1]=>0
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1,1]=>[7,3,2]=>0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[2,2]=>-2
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1,1]=>[7,3,1]=>3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[3]=>[2,1]=>0
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[7,3]=>9
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[4]=>4
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[7,1,1,1,1]=>-5
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[4,1]=>2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1,1]=>[7,2,1,1,1]=>0
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[4,1,1]=>-2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1]=>[4,2,1]=>0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[4,2]=>2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[4,1,1,1]=>2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]=>[4,2,1,1]=>0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1]=>[4,2,2,1]=>0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1]=>[4,3,2,1]=>0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1]=>[4,3,1,1]=>0
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[4,2,2]=>-2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]=>[4,3,2]=>0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[4,3,1]=>0
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[4,3]=>0
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[3,1,1,1]=>1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[3,2,1,1]=>0
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,2,2,1]=>0
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[4,3,2]=>[3,3,2,1]=>0
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[3,3,1,1]=>1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,2,2]=>0
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,3,1]=>[3,3,2]=>0
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[4,2,1]=>[3,3,1]=>-1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[3,3]=>-3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[2,2,2]=>2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[3,2,2]=>0
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[3,2,1]=>0
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[3,2]=>0
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1,1]=>[7,4,1]=>4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[4]=>[3,1]=>1
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[7,4]=>8
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[5]=>5
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[7,1,1,1,1,1]=>5
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[5,1]=>3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[5,1,1]=>-3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1]=>[5,2,1]=>0
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[5,2]=>4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[5,1,1,1]=>3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>[5,2,1,1]=>0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1]=>[5,2,2,1]=>0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1]=>[5,3,2,1]=>0
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1]=>[5,3,1,1]=>-1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[5,2,2]=>-4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1]=>[5,3,2]=>0
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1]=>[5,3,1]=>1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[5,3]=>3
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[5,1,1,1,1]=>-3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1]=>[5,2,1,1,1]=>0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1]=>[5,2,2,1,1]=>0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1]=>[5,3,2,1,1]=>0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1]=>[5,3,1,1,1]=>1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1]=>[5,2,2,2,1]=>0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1]=>[5,4,1,1,1]=>0
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[5,2,2,2]=>4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1]=>[5,3,2,2]=>0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1]=>[5,3,3,1]=>-1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,1]=>[5,4,2,1]=>0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1]=>[5,4,1,1]=>0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[5,3,3]=>-3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1]=>[5,4,3]=>0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1]=>[5,4,2]=>0
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1]=>[5,4,1]=>0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[5,4]=>0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[4,1,1,1,1]=>-2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[4,2,1,1,1]=>0
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[4,2,2,1,1]=>0
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2]=>[4,3,2,1,1]=>0
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[4,3,1,1,1]=>0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[4,2,2,2,1]=>0
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2]=>[4,3,2,2,1]=>0
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,3,3,1,1]=>0
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2]=>[4,4,2,1,1]=>0
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[4,4,1,1,1]=>-2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[4,2,2,2]=>2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1]=>[4,3,2,2]=>0
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1]=>[4,3,3,2]=>0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1]=>[4,4,2,2]=>2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1]=>[4,3,3,1]=>0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1]=>[4,4,3,1]=>0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1]=>[4,4,2,1]=>0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1]=>[4,4,1,1]=>2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,3,3]=>0
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1]=>[4,4,3]=>0
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1]=>[4,4,2]=>-2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1]=>[4,4,1]=>-2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[4,4]=>-4
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,2,2,2]=>0
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3,2,2]=>0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[3,3,3,2]=>0
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3]=>[4,3,3,2]=>0
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[4,3,2,2]=>0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[3,3,3,1]=>1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,4,2]=>[4,3,3,1]=>0
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,3,2]=>[4,3,2,1]=>0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[4,3,1,1]=>0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[3,3,3]=>3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,4,1]=>[4,3,3]=>0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]=>[4,3,2]=>0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,2,1]=>[4,3,1]=>0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[4,3]=>0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[3,3,2]=>0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[4,3,2]=>0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[4,2,2]=>-2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[4,2,1]=>0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[4,2]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[5]=>[4,1]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[7,5]=>5
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[6]=>6
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[6,1,1,1,1,1,1]=>-4
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[6,1]=>4
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[6,1,1]=>-4
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1]=>[6,2,1]=>0
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[6,2]=>6
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[6,1,1,1]=>4
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1]=>[6,2,1,1]=>0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1]=>[6,2,2,1]=>0
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1,1]=>[6,3,2,1]=>0
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1]=>[6,3,1,1]=>-2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[6,2,2]=>-6
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1]=>[6,3,2]=>0
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1]=>[6,3,1]=>2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[6,3]=>6
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[6,1,1,1,1]=>-4
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1]=>[6,2,1,1,1]=>0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]=>[6,2,2,1,1]=>0
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1]=>[6,3,1,1,1]=>2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[6,2,2,2]=>6
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1]=>[6,4,1,1]=>-2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[6,3,3]=>-6
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1]=>[6,4,2]=>2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]=>[6,4,1]=>2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[6,4]=>4
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[6,1,1,1,1,1]=>4
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1]=>[6,2,1,1,1,1]=>0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1]=>[6,5,1]=>0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[6,5]=>0
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[6,6]=>-6
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[5,1,1,1,1,1]=>3
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[5,2,1,1,1,1]=>0
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[5,2,2,1,1,1]=>0
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[5,3,1,1,1,1]=>-1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1]=>[5,5,1,1]=>3
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1]=>[5,5,2]=>-4
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1]=>[5,5,1]=>-3
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1]=>[6,5,1]=>0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[5,5]=>-5
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[6,5]=>0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[4,2,2,2,2]=>-2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[5,4,1,1,1]=>0
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1]=>[5,4,2,1]=>0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1]=>[5,4,1,1]=>0
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1]=>[6,4,1,1]=>-2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[4,4,4]=>4
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1]=>[5,4,3]=>0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1]=>[5,4,2]=>0
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1]=>[6,4,2]=>2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1]=>[5,4,1]=>0
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1]=>[6,4,1]=>2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[5,4]=>0
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[6,4]=>4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[3,3,3,3]=>-3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[5,3,2,2]=>0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[4,4,3,1]=>0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]=>[5,3,3,1]=>-1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[6,3,2]=>[5,3,2,1]=>0
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[7,3,2]=>[6,3,2,1]=>0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[5,3,1,1]=>-1
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[6,3,1,1]=>-2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[4,4,3]=>0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[6,5,1]=>[5,4,3]=>0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[6,4,1]=>[5,3,3]=>-3
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[7,4,1]=>[6,3,3]=>-6
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,3,1]=>[5,3,2]=>0
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[7,3,1]=>[6,3,2]=>0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,2,1]=>[5,3,1]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[7,2,1]=>[6,3,1]=>2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[5,3]=>3
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[6,3]=>6
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[4,4,2]=>-2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[5,5,2]=>-4
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[5,4,2]=>0
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[6,4,2]=>2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[5,3,2]=>0
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[6,3,2]=>0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[5,2,2]=>-4
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[6,2,2]=>-6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[5,2,1]=>0
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[6,2,1]=>0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[5,2]=>4
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[6,2]=>6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[6]=>[5,1]=>3
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7]=>[6,1]=>4
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[7]=>[6,1]=>4
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[8]=>[7,1]=>5
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[7,1]=>[6,2]=>6
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[9]=>[8,1]=>6
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[8,1]=>[7,2]=>8
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[7,2]=>[6,2,1]=>0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1]=>[6,3]=>6
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,1]=>[8,2]=>10
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,1]=>[7,3]=>9
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[7,3]=>[6,2,2]=>-6
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[7,2,1]=>[6,3,1]=>2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1,1]=>[6,4]=>4
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]=>[8,2,1]=>[7,3,1]=>3
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,1,1]=>[7,4]=>8
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[7,2,2]=>[6,3,1,1]=>-2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1,1,1]=>[6,5]=>0
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[7,5]=>[6,4,2]=>2
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[7,2,1,1,1]=>[6,5,1]=>0
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1,1,1,1]=>[6,6]=>-6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[6,6]=>[5,5,2]=>-4
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[6]=>[5,1]=>3
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[6,1]=>[5,2]=>4
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[7]=>[6,1]=>4
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,1]=>[5,3]=>3
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,1,1,1]=>[7,5]=>5
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,1,1]=>[7,4]=>8
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[8,2,2]=>[7,3,1,1]=>-3
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[8,2,1]=>[7,3,1]=>3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,1]=>[7,3]=>9
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0]=>[8,4]=>[7,3,2]=>0
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[8,3]=>[7,2,2]=>-8
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[8,2]=>[7,2,1]=>0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[8,1]=>[7,2]=>8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8]=>[7,1]=>5
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[8]=>8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1]=>[8,1]=>6
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,1,1,1,1,1]=>[8,2,1]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[9]=>9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>7
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,1,1,1,1,1,1]=>[8,2]=>10
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,1,1,1,1,1,1]=>[9,2,1]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1]=>[10]=>10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1,1,1]=>[10,1]=>8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,1,1,1,1,1,1,1]=>[9,2]=>12
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[4,2,1,1,1,1,1,1]=>[8,3,1]=>4
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,1,1,1,1,1,1]=>[8,3]=>12
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1,1,1,1]=>[11,1]=>9
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[4,1,1,1,1,1,1,1,1]=>[9,3]=>15
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[2]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1,1,1,1,1,1]=>[8,1,1]=>-6
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[2]=>[1,1]=>-1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1]=>[3]=>3
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,1,1,1,1,1]=>[8,1,1,1]=>6
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1]=>[3,1]=>1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[2,2]=>[2,1,1]=>0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,3,1,1,1,1,1,1]=>[8,2,2]=>-10
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[3]=>[2,1]=>0
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[4]=>4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,1,1,1,1]=>[8,1,1,1,1]=>-6
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1]=>[4,1]=>2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1,1]=>[4,1,1]=>-2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2]=>[3,1,1,1]=>1
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[3,2,2]=>[3,2,1,1]=>0
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[3,3]=>[2,2,2]=>2
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[4]=>[3,1]=>1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[5]=>5
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1,1]=>[5,1]=>3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,1,1]=>[5,1,1,1]=>3
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[3,2,2,1,1]=>[5,2,1,1]=>0
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[3,3,3]=>[3,2,2,2]=>0
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[4,4]=>[3,3,2]=>0
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[5]=>[4,1]=>2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[6]=>6
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[6,1]=>4
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[6,1,1]=>-4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[6,1,1,1]=>4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[6,1,1,1,1]=>-4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[4,4,1,1,1,1]=>[6,3,3]=>-6
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,1,1,1,1]=>[6,4]=>4
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2]=>[5,1,1,1,1,1]=>3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[4,4,4]=>[3,3,3,3]=>-3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[5,5]=>[4,4,2]=>-2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[7]=>7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[7,1]=>5
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[7,1,1]=>-5
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[7,1,1,1]=>5
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[7,1,1,1,1,1]=>5
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,1,1,1,1,1]=>[7,5]=>5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[6,1,1,1,1,1,1]=>-4
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[2]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,2,1,1,1,1,1,1,1]=>[9,1,1]=>-7
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[2]=>[1,1]=>-1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[3]=>3
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,1]=>[3,1]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[2,2]=>[2,1,1]=>0
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[3]=>[2,1]=>0
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[4]=>4
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2]=>[3,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[4]=>[3,1]=>1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[5]=>5
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]=>[4,4]=>[3,3,2]=>0
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[5]=>[4,1]=>2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[6]=>6
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[4,4,4]=>[3,3,3,3]=>-3
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[6]=>[5,1]=>3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[7]=>7
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[7,1]=>5
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[6,1,1,1,1,1,1]=>-4
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]=>[6,6]=>[5,5,2]=>-4
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[8]=>8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1]=>[8,1]=>6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[9]=>9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9]=>[8,1]=>6
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[10]=>[9,1]=>7
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[9,1]=>[8,2]=>10
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,1]=>[5,1,1,1,1]=>-3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,2,1]=>[3,1,1]=>-1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[3,2,1]=>0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1]=>[3,2,1]=>0
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1]=>[3,1,1]=>-1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[6,1,1,1,1,1]=>4
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1]=>[9,2]=>12
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[9,2,1]=>[8,3,1]=>4
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]=>[11]=>[10,1]=>8
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[9,2]=>[8,2,1]=>0
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,1]=>[8,3]=>12
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[3,1]=>[2,2]=>-2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[4,4,2,1]=>[4,3,3,1]=>0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[6,1,1,1,1,1]=>4
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0]=>[3,3,3,1]=>[4,2,2,2]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[2,1]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[2,1]=>0
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,1,1,1]=>[5,4]=>0
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,1,1]=>[8,4]=>12
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[6,3,2,1]=>[5,4,2,1]=>0
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[7,2,1]=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,1]=>[2,1]=>0
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,1,1,1,1,1]=>[8,2,1]=>0
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,1,1,1]=>[6,2,1]=>0
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,1]=>[3,2]=>0
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,1]=>[4,1,1,1]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,1]=>[4,1,1,1]=>2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,3,1,1]=>[4,2,2]=>-2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[3,3,2,1]=>[4,2,2,1]=>0
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2]=>[3,3,2,1]=>0
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,1,1,1,1]=>[6,5]=>0
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[3,2]=>[2,2,1]=>0
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[3,3,1]=>[3,2,2]=>0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[3,2]=>[2,2,1]=>0
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[3,2,2,1,1,1,1,1]=>[8,2,1,1]=>0
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>[4,2,2]=>[3,3,1,1]=>1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[5,1]=>[4,2]=>2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0]=>[3,3,2]=>[3,2,2,1]=>0
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,1]=>[4,4,2,1]=>0
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,1,1]=>[5,2,1]=>0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>7
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0]=>[4,2,2,1]=>[4,3,1,1]=>0
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,1]=>[4,2,1]=>0
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0]=>[3,3,2]=>[3,2,2,1]=>0
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2]=>[3,3,2,1]=>0
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[3,3,3,2,1]=>[5,2,2,2,1]=>0
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0]=>[6,1]=>[5,2]=>4
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[7,1]=>[6,2]=>6
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0]=>[8,1]=>[7,2]=>8
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0]=>[6,2,1]=>[5,3,1]=>1
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,1,1]=>[5,4]=>0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1]=>[4,3,2,1]=>0
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1,1]=>[9,3]=>15
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[3]=>3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0]=>[4,4,1]=>[3,3,3]=>3
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0]=>[7,2,1]=>[6,3,1]=>2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1]=>[4,3,2,1]=>0
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[4,1]=>[3,2]=>0
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[4,3,1]=>[3,3,2]=>0
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[4,3]=>[3,2,2]=>0
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,3]=>[4,3,3,2]=>0
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]=>[5,4,2]=>[4,3,3,1]=>0
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[7,2,1]=>0
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[4,2,1]=>[3,3,1]=>-1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[3,1]=>[2,2]=>-2
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[5,3,2,1]=>[4,4,2,1]=>0
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searching the database for the individual values of this statistic
Description
The weight of a partition according to Alladi.
Map
swap returns and last descent
Description
Return a Dyck path with number of returns and length of the last descent interchanged.
This is the specialisation of the map $\Phi$ in [1] to Dyck paths. It is characterised by the fact that the number of up steps before a down step that is neither a return nor part of the last descent is preserved.
This is the specialisation of the map $\Phi$ in [1] to Dyck paths. It is characterised by the fact that the number of up steps before a down step that is neither a return nor part of the last descent is preserved.
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
Map
Bulgarian solitaire
Description
A move in Bulgarian solitaire.
Remove the first column of the Ferrers diagram and insert it as a new row.
If the partition is empty, return the empty partition.
Remove the first column of the Ferrers diagram and insert it as a new row.
If the partition is empty, return the empty partition.
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