Identifier
-
Mp00100:
Dyck paths
—touch composition⟶
Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000147: Integer partitions ⟶ ℤ
Values
=>
Cc0005;cc-rep-0
Cc0002;cc-rep-2
Cc0002;cc-rep
[1,0]=>[1]=>[1]=>[1]=>1
[1,0,1,0]=>[1,1]=>[1,1]=>[2]=>2
[1,1,0,0]=>[2]=>[2]=>[1,1]=>1
[1,0,1,0,1,0]=>[1,1,1]=>[1,1,1]=>[3]=>3
[1,0,1,1,0,0]=>[1,2]=>[2,1]=>[2,1]=>2
[1,1,0,0,1,0]=>[2,1]=>[2,1]=>[2,1]=>2
[1,1,0,1,0,0]=>[3]=>[3]=>[1,1,1]=>1
[1,1,1,0,0,0]=>[3]=>[3]=>[1,1,1]=>1
[1,0,1,0,1,0,1,0]=>[1,1,1,1]=>[1,1,1,1]=>[4]=>4
[1,0,1,0,1,1,0,0]=>[1,1,2]=>[2,1,1]=>[3,1]=>3
[1,0,1,1,0,0,1,0]=>[1,2,1]=>[2,1,1]=>[3,1]=>3
[1,0,1,1,0,1,0,0]=>[1,3]=>[3,1]=>[2,1,1]=>2
[1,0,1,1,1,0,0,0]=>[1,3]=>[3,1]=>[2,1,1]=>2
[1,1,0,0,1,0,1,0]=>[2,1,1]=>[2,1,1]=>[3,1]=>3
[1,1,0,0,1,1,0,0]=>[2,2]=>[2,2]=>[2,2]=>2
[1,1,0,1,0,0,1,0]=>[3,1]=>[3,1]=>[2,1,1]=>2
[1,1,0,1,0,1,0,0]=>[4]=>[4]=>[1,1,1,1]=>1
[1,1,0,1,1,0,0,0]=>[4]=>[4]=>[1,1,1,1]=>1
[1,1,1,0,0,0,1,0]=>[3,1]=>[3,1]=>[2,1,1]=>2
[1,1,1,0,0,1,0,0]=>[4]=>[4]=>[1,1,1,1]=>1
[1,1,1,0,1,0,0,0]=>[4]=>[4]=>[1,1,1,1]=>1
[1,1,1,1,0,0,0,0]=>[4]=>[4]=>[1,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1]=>[1,1,1,1,1]=>[5]=>5
[1,0,1,0,1,0,1,1,0,0]=>[1,1,1,2]=>[2,1,1,1]=>[4,1]=>4
[1,0,1,0,1,1,0,0,1,0]=>[1,1,2,1]=>[2,1,1,1]=>[4,1]=>4
[1,0,1,0,1,1,0,1,0,0]=>[1,1,3]=>[3,1,1]=>[3,1,1]=>3
[1,0,1,0,1,1,1,0,0,0]=>[1,1,3]=>[3,1,1]=>[3,1,1]=>3
[1,0,1,1,0,0,1,0,1,0]=>[1,2,1,1]=>[2,1,1,1]=>[4,1]=>4
[1,0,1,1,0,0,1,1,0,0]=>[1,2,2]=>[2,2,1]=>[3,2]=>3
[1,0,1,1,0,1,0,0,1,0]=>[1,3,1]=>[3,1,1]=>[3,1,1]=>3
[1,0,1,1,0,1,0,1,0,0]=>[1,4]=>[4,1]=>[2,1,1,1]=>2
[1,0,1,1,0,1,1,0,0,0]=>[1,4]=>[4,1]=>[2,1,1,1]=>2
[1,0,1,1,1,0,0,0,1,0]=>[1,3,1]=>[3,1,1]=>[3,1,1]=>3
[1,0,1,1,1,0,0,1,0,0]=>[1,4]=>[4,1]=>[2,1,1,1]=>2
[1,0,1,1,1,0,1,0,0,0]=>[1,4]=>[4,1]=>[2,1,1,1]=>2
[1,0,1,1,1,1,0,0,0,0]=>[1,4]=>[4,1]=>[2,1,1,1]=>2
[1,1,0,0,1,0,1,0,1,0]=>[2,1,1,1]=>[2,1,1,1]=>[4,1]=>4
[1,1,0,0,1,0,1,1,0,0]=>[2,1,2]=>[2,2,1]=>[3,2]=>3
[1,1,0,0,1,1,0,0,1,0]=>[2,2,1]=>[2,2,1]=>[3,2]=>3
[1,1,0,0,1,1,0,1,0,0]=>[2,3]=>[3,2]=>[2,2,1]=>2
[1,1,0,0,1,1,1,0,0,0]=>[2,3]=>[3,2]=>[2,2,1]=>2
[1,1,0,1,0,0,1,0,1,0]=>[3,1,1]=>[3,1,1]=>[3,1,1]=>3
[1,1,0,1,0,0,1,1,0,0]=>[3,2]=>[3,2]=>[2,2,1]=>2
[1,1,0,1,0,1,0,0,1,0]=>[4,1]=>[4,1]=>[2,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,0]=>[5]=>[5]=>[1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,0,0]=>[5]=>[5]=>[1,1,1,1,1]=>1
[1,1,0,1,1,0,0,0,1,0]=>[4,1]=>[4,1]=>[2,1,1,1]=>2
[1,1,0,1,1,0,0,1,0,0]=>[5]=>[5]=>[1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,0,0]=>[5]=>[5]=>[1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,0,0]=>[5]=>[5]=>[1,1,1,1,1]=>1
[1,1,1,0,0,0,1,0,1,0]=>[3,1,1]=>[3,1,1]=>[3,1,1]=>3
[1,1,1,0,0,0,1,1,0,0]=>[3,2]=>[3,2]=>[2,2,1]=>2
[1,1,1,0,0,1,0,0,1,0]=>[4,1]=>[4,1]=>[2,1,1,1]=>2
[1,1,1,0,0,1,0,1,0,0]=>[5]=>[5]=>[1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,0,0]=>[5]=>[5]=>[1,1,1,1,1]=>1
[1,1,1,0,1,0,0,0,1,0]=>[4,1]=>[4,1]=>[2,1,1,1]=>2
[1,1,1,0,1,0,0,1,0,0]=>[5]=>[5]=>[1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,0]=>[5]=>[5]=>[1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,0,0]=>[5]=>[5]=>[1,1,1,1,1]=>1
[1,1,1,1,0,0,0,0,1,0]=>[4,1]=>[4,1]=>[2,1,1,1]=>2
[1,1,1,1,0,0,0,1,0,0]=>[5]=>[5]=>[1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,0]=>[5]=>[5]=>[1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,0,0]=>[5]=>[5]=>[1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,0]=>[5]=>[5]=>[1,1,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]=>[6]=>6
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,2]=>[2,1,1,1,1]=>[5,1]=>5
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,2,1]=>[2,1,1,1,1]=>[5,1]=>5
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,3]=>[3,1,1,1]=>[4,1,1]=>4
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,3]=>[3,1,1,1]=>[4,1,1]=>4
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,2,1,1]=>[2,1,1,1,1]=>[5,1]=>5
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,2,2]=>[2,2,1,1]=>[4,2]=>4
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,3,1]=>[3,1,1,1]=>[4,1,1]=>4
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,4]=>[4,1,1]=>[3,1,1,1]=>3
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,4]=>[4,1,1]=>[3,1,1,1]=>3
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,3,1]=>[3,1,1,1]=>[4,1,1]=>4
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,4]=>[4,1,1]=>[3,1,1,1]=>3
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,4]=>[4,1,1]=>[3,1,1,1]=>3
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,4]=>[4,1,1]=>[3,1,1,1]=>3
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1]=>[2,1,1,1,1]=>[5,1]=>5
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,1,2]=>[2,2,1,1]=>[4,2]=>4
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,1]=>[2,2,1,1]=>[4,2]=>4
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,3]=>[3,2,1]=>[3,2,1]=>3
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]=>[3,2,1]=>[3,2,1]=>3
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,1,1]=>[3,1,1,1]=>[4,1,1]=>4
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,2]=>[3,2,1]=>[3,2,1]=>3
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,4,1]=>[4,1,1]=>[3,1,1,1]=>3
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,5]=>[5,1]=>[2,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,5]=>[5,1]=>[2,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,4,1]=>[4,1,1]=>[3,1,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,5]=>[5,1]=>[2,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,5]=>[5,1]=>[2,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,5]=>[5,1]=>[2,1,1,1,1]=>2
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,1,1]=>[3,1,1,1]=>[4,1,1]=>4
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2]=>[3,2,1]=>[3,2,1]=>3
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,1]=>[4,1,1]=>[3,1,1,1]=>3
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,5]=>[5,1]=>[2,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,5]=>[5,1]=>[2,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,1]=>[4,1,1]=>[3,1,1,1]=>3
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,5]=>[5,1]=>[2,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,5]=>[5,1]=>[2,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,5]=>[5,1]=>[2,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,4,1]=>[4,1,1]=>[3,1,1,1]=>3
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5]=>[5,1]=>[2,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5]=>[5,1]=>[2,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5]=>[5,1]=>[2,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,5]=>[5,1]=>[2,1,1,1,1]=>2
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1]=>[2,1,1,1,1]=>[5,1]=>5
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,2]=>[2,2,1,1]=>[4,2]=>4
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,2,1]=>[2,2,1,1]=>[4,2]=>4
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3]=>[3,2,1]=>[3,2,1]=>3
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3]=>[3,2,1]=>[3,2,1]=>3
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,1,1]=>[2,2,1,1]=>[4,2]=>4
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2]=>[2,2,2]=>[3,3]=>3
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1]=>[3,2,1]=>[3,2,1]=>3
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,4]=>[4,2]=>[2,2,1,1]=>2
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,4]=>[4,2]=>[2,2,1,1]=>2
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1]=>[3,2,1]=>[3,2,1]=>3
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4]=>[4,2]=>[2,2,1,1]=>2
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,4]=>[4,2]=>[2,2,1,1]=>2
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4]=>[4,2]=>[2,2,1,1]=>2
[1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1]=>[3,1,1,1]=>[4,1,1]=>4
[1,1,0,1,0,0,1,0,1,1,0,0]=>[3,1,2]=>[3,2,1]=>[3,2,1]=>3
[1,1,0,1,0,0,1,1,0,0,1,0]=>[3,2,1]=>[3,2,1]=>[3,2,1]=>3
[1,1,0,1,0,0,1,1,0,1,0,0]=>[3,3]=>[3,3]=>[2,2,2]=>2
[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,3]=>[3,3]=>[2,2,2]=>2
[1,1,0,1,0,1,0,0,1,0,1,0]=>[4,1,1]=>[4,1,1]=>[3,1,1,1]=>3
[1,1,0,1,0,1,0,0,1,1,0,0]=>[4,2]=>[4,2]=>[2,2,1,1]=>2
[1,1,0,1,0,1,0,1,0,0,1,0]=>[5,1]=>[5,1]=>[2,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,0,0,1,0]=>[5,1]=>[5,1]=>[2,1,1,1,1]=>2
[1,1,0,1,0,1,1,0,0,1,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,0,1,0,1,0]=>[4,1,1]=>[4,1,1]=>[3,1,1,1]=>3
[1,1,0,1,1,0,0,0,1,1,0,0]=>[4,2]=>[4,2]=>[2,2,1,1]=>2
[1,1,0,1,1,0,0,1,0,0,1,0]=>[5,1]=>[5,1]=>[2,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,0,1,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,0,0,1,0]=>[5,1]=>[5,1]=>[2,1,1,1,1]=>2
[1,1,0,1,1,0,1,0,0,1,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,0,0,1,0]=>[5,1]=>[5,1]=>[2,1,1,1,1]=>2
[1,1,0,1,1,1,0,0,0,1,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,1,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1]=>[3,1,1,1]=>[4,1,1]=>4
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2]=>[3,2,1]=>[3,2,1]=>3
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1]=>[3,2,1]=>[3,2,1]=>3
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,3]=>[3,3]=>[2,2,2]=>2
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3]=>[3,3]=>[2,2,2]=>2
[1,1,1,0,0,1,0,0,1,0,1,0]=>[4,1,1]=>[4,1,1]=>[3,1,1,1]=>3
[1,1,1,0,0,1,0,0,1,1,0,0]=>[4,2]=>[4,2]=>[2,2,1,1]=>2
[1,1,1,0,0,1,0,1,0,0,1,0]=>[5,1]=>[5,1]=>[2,1,1,1,1]=>2
[1,1,1,0,0,1,0,1,0,1,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,1,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,0,0,1,0]=>[5,1]=>[5,1]=>[2,1,1,1,1]=>2
[1,1,1,0,0,1,1,0,0,1,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,0,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,1]=>[4,1,1]=>[3,1,1,1]=>3
[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,2]=>[4,2]=>[2,2,1,1]=>2
[1,1,1,0,1,0,0,1,0,0,1,0]=>[5,1]=>[5,1]=>[2,1,1,1,1]=>2
[1,1,1,0,1,0,0,1,0,1,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,0,1,0]=>[5,1]=>[5,1]=>[2,1,1,1,1]=>2
[1,1,1,0,1,0,1,0,0,1,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,1]=>[5,1]=>[2,1,1,1,1]=>2
[1,1,1,0,1,1,0,0,0,1,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,1]=>[4,1,1]=>[3,1,1,1]=>3
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,2]=>[4,2]=>[2,2,1,1]=>2
[1,1,1,1,0,0,0,1,0,0,1,0]=>[5,1]=>[5,1]=>[2,1,1,1,1]=>2
[1,1,1,1,0,0,0,1,0,1,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,1,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,1]=>[5,1]=>[2,1,1,1,1]=>2
[1,1,1,1,0,0,1,0,0,1,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1]=>[5,1]=>[2,1,1,1,1]=>2
[1,1,1,1,0,1,0,0,0,1,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,0,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>[5,1]=>[2,1,1,1,1]=>2
[1,1,1,1,1,0,0,0,0,1,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6]=>[6]=>[1,1,1,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>[7]=>7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,2]=>[2,1,1,1,1,1]=>[6,1]=>6
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,2,1]=>[2,1,1,1,1,1]=>[6,1]=>6
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,3]=>[3,1,1,1,1]=>[5,1,1]=>5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,3]=>[3,1,1,1,1]=>[5,1,1]=>5
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,2,1,1]=>[2,1,1,1,1,1]=>[6,1]=>6
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]=>[2,2,1,1,1]=>[5,2]=>5
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,3,1]=>[3,1,1,1,1]=>[5,1,1]=>5
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,4]=>[4,1,1,1]=>[4,1,1,1]=>4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,4]=>[4,1,1,1]=>[4,1,1,1]=>4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,3,1]=>[3,1,1,1,1]=>[5,1,1]=>5
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,4]=>[4,1,1,1]=>[4,1,1,1]=>4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,4]=>[4,1,1,1]=>[4,1,1,1]=>4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]=>[4,1,1,1]=>[4,1,1,1]=>4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,2,1,1,1]=>[2,1,1,1,1,1]=>[6,1]=>6
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]=>[2,2,1,1,1]=>[5,2]=>5
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,1]=>[2,2,1,1,1]=>[5,2]=>5
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,3]=>[3,2,1,1]=>[4,2,1]=>4
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]=>[3,2,1,1]=>[4,2,1]=>4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,3,1,1]=>[3,1,1,1,1]=>[5,1,1]=>5
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,3,2]=>[3,2,1,1]=>[4,2,1]=>4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,4,1]=>[4,1,1,1]=>[4,1,1,1]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,5]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,5]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,4,1]=>[4,1,1,1]=>[4,1,1,1]=>4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,5]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,5]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,5]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,3,1,1]=>[3,1,1,1,1]=>[5,1,1]=>5
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]=>[3,2,1,1]=>[4,2,1]=>4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,4,1]=>[4,1,1,1]=>[4,1,1,1]=>4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,5]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,5]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,4,1]=>[4,1,1,1]=>[4,1,1,1]=>4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,5]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,5]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,5]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]=>[4,1,1,1]=>[4,1,1,1]=>4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,5]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,5]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,5]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,5]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1]=>[2,1,1,1,1,1]=>[6,1]=>6
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,2]=>[2,2,1,1,1]=>[5,2]=>5
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,2,1]=>[2,2,1,1,1]=>[5,2]=>5
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,3]=>[3,2,1,1]=>[4,2,1]=>4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]=>[3,2,1,1]=>[4,2,1]=>4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,2,1,1]=>[2,2,1,1,1]=>[5,2]=>5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]=>[2,2,2,1]=>[4,3]=>4
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,3,1]=>[3,2,1,1]=>[4,2,1]=>4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,4]=>[4,2,1]=>[3,2,1,1]=>3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,4]=>[4,2,1]=>[3,2,1,1]=>3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]=>[3,2,1,1]=>[4,2,1]=>4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,4]=>[4,2,1]=>[3,2,1,1]=>3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,4]=>[4,2,1]=>[3,2,1,1]=>3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]=>[4,2,1]=>[3,2,1,1]=>3
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,1,1,1]=>[3,1,1,1,1]=>[5,1,1]=>5
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,1,2]=>[3,2,1,1]=>[4,2,1]=>4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,2,1]=>[3,2,1,1]=>[4,2,1]=>4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,3]=>[3,3,1]=>[3,2,2]=>3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,3]=>[3,3,1]=>[3,2,2]=>3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,4,1,1]=>[4,1,1,1]=>[4,1,1,1]=>4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,4,2]=>[4,2,1]=>[3,2,1,1]=>3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,5,1]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,5,1]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,4,1,1]=>[4,1,1,1]=>[4,1,1,1]=>4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,4,2]=>[4,2,1]=>[3,2,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,5,1]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,5,1]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,5,1]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,1,1,1]=>[3,1,1,1,1]=>[5,1,1]=>5
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]=>[3,2,1,1]=>[4,2,1]=>4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]=>[3,2,1,1]=>[4,2,1]=>4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,3]=>[3,3,1]=>[3,2,2]=>3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]=>[3,3,1]=>[3,2,2]=>3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,1,1]=>[4,1,1,1]=>[4,1,1,1]=>4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2]=>[4,2,1]=>[3,2,1,1]=>3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,5,1]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,5,1]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,1,1]=>[4,1,1,1]=>[4,1,1,1]=>4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,2]=>[4,2,1]=>[3,2,1,1]=>3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,5,1]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,5,1]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,5,1]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,4,1,1]=>[4,1,1,1]=>[4,1,1,1]=>4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]=>[4,2,1]=>[3,2,1,1]=>3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,1]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,1]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,1]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,6]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1]=>[2,1,1,1,1,1]=>[6,1]=>6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]=>[2,2,1,1,1]=>[5,2]=>5
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]=>[2,2,1,1,1]=>[5,2]=>5
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,3]=>[3,2,1,1]=>[4,2,1]=>4
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]=>[3,2,1,1]=>[4,2,1]=>4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]=>[2,2,1,1,1]=>[5,2]=>5
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]=>[2,2,2,1]=>[4,3]=>4
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,1]=>[3,2,1,1]=>[4,2,1]=>4
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,4]=>[4,2,1]=>[3,2,1,1]=>3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,4]=>[4,2,1]=>[3,2,1,1]=>3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]=>[3,2,1,1]=>[4,2,1]=>4
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,4]=>[4,2,1]=>[3,2,1,1]=>3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,4]=>[4,2,1]=>[3,2,1,1]=>3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]=>[4,2,1]=>[3,2,1,1]=>3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]=>[2,2,1,1,1]=>[5,2]=>5
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]=>[2,2,2,1]=>[4,3]=>4
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,1]=>[2,2,2,1]=>[4,3]=>4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,3]=>[3,2,2]=>[3,3,1]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]=>[3,2,2]=>[3,3,1]=>3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,1,1]=>[3,2,1,1]=>[4,2,1]=>4
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,3,2]=>[3,2,2]=>[3,3,1]=>3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,4,1]=>[4,2,1]=>[3,2,1,1]=>3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,5]=>[5,2]=>[2,2,1,1,1]=>2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,5]=>[5,2]=>[2,2,1,1,1]=>2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,4,1]=>[4,2,1]=>[3,2,1,1]=>3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,5]=>[5,2]=>[2,2,1,1,1]=>2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,5]=>[5,2]=>[2,2,1,1,1]=>2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,5]=>[5,2]=>[2,2,1,1,1]=>2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,1]=>[3,2,1,1]=>[4,2,1]=>4
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]=>[3,2,2]=>[3,3,1]=>3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,4,1]=>[4,2,1]=>[3,2,1,1]=>3
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,5]=>[5,2]=>[2,2,1,1,1]=>2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,5]=>[5,2]=>[2,2,1,1,1]=>2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,4,1]=>[4,2,1]=>[3,2,1,1]=>3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,5]=>[5,2]=>[2,2,1,1,1]=>2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,5]=>[5,2]=>[2,2,1,1,1]=>2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,5]=>[5,2]=>[2,2,1,1,1]=>2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]=>[4,2,1]=>[3,2,1,1]=>3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,5]=>[5,2]=>[2,2,1,1,1]=>2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,5]=>[5,2]=>[2,2,1,1,1]=>2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,5]=>[5,2]=>[2,2,1,1,1]=>2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5]=>[5,2]=>[2,2,1,1,1]=>2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1]=>[3,1,1,1,1]=>[5,1,1]=>5
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,2]=>[3,2,1,1]=>[4,2,1]=>4
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,1]=>[3,2,1,1]=>[4,2,1]=>4
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,3]=>[3,3,1]=>[3,2,2]=>3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]=>[3,3,1]=>[3,2,2]=>3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,1]=>[3,2,1,1]=>[4,2,1]=>4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]=>[3,2,2]=>[3,3,1]=>3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,3,1]=>[3,3,1]=>[3,2,2]=>3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,4]=>[4,3]=>[2,2,2,1]=>2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,4]=>[4,3]=>[2,2,2,1]=>2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]=>[3,3,1]=>[3,2,2]=>3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,4]=>[4,3]=>[2,2,2,1]=>2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,4]=>[4,3]=>[2,2,2,1]=>2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,4]=>[4,3]=>[2,2,2,1]=>2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[4,1,1,1]=>[4,1,1,1]=>[4,1,1,1]=>4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[4,1,2]=>[4,2,1]=>[3,2,1,1]=>3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[4,2,1]=>[4,2,1]=>[3,2,1,1]=>3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[4,3]=>[4,3]=>[2,2,2,1]=>2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[4,3]=>[4,3]=>[2,2,2,1]=>2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[5,1,1]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[5,2]=>[5,2]=>[2,2,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[5,1,1]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[5,2]=>[5,2]=>[2,2,1,1,1]=>2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,1,1]=>[4,1,1,1]=>[4,1,1,1]=>4
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[4,1,2]=>[4,2,1]=>[3,2,1,1]=>3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[4,2,1]=>[4,2,1]=>[3,2,1,1]=>3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[4,3]=>[4,3]=>[2,2,2,1]=>2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,3]=>[4,3]=>[2,2,2,1]=>2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[5,1,1]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[5,2]=>[5,2]=>[2,2,1,1,1]=>2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[5,1,1]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[5,2]=>[5,2]=>[2,2,1,1,1]=>2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[5,1,1]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[5,2]=>[5,2]=>[2,2,1,1,1]=>2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1]=>[3,1,1,1,1]=>[5,1,1]=>5
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,2]=>[3,2,1,1]=>[4,2,1]=>4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,1]=>[3,2,1,1]=>[4,2,1]=>4
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,3]=>[3,3,1]=>[3,2,2]=>3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]=>[3,3,1]=>[3,2,2]=>3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,1]=>[3,2,1,1]=>[4,2,1]=>4
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]=>[3,2,2]=>[3,3,1]=>3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,3,1]=>[3,3,1]=>[3,2,2]=>3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,4]=>[4,3]=>[2,2,2,1]=>2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,4]=>[4,3]=>[2,2,2,1]=>2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]=>[3,3,1]=>[3,2,2]=>3
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,4]=>[4,3]=>[2,2,2,1]=>2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4]=>[4,3]=>[2,2,2,1]=>2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]=>[4,3]=>[2,2,2,1]=>2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,1,1]=>[4,1,1,1]=>[4,1,1,1]=>4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[4,1,2]=>[4,2,1]=>[3,2,1,1]=>3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,2,1]=>[4,2,1]=>[3,2,1,1]=>3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,3]=>[4,3]=>[2,2,2,1]=>2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,3]=>[4,3]=>[2,2,2,1]=>2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[5,1,1]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[5,2]=>[5,2]=>[2,2,1,1,1]=>2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[5,1,1]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[5,2]=>[5,2]=>[2,2,1,1,1]=>2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,1,1]=>[4,1,1,1]=>[4,1,1,1]=>4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,1,2]=>[4,2,1]=>[3,2,1,1]=>3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,2,1]=>[4,2,1]=>[3,2,1,1]=>3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,3]=>[4,3]=>[2,2,2,1]=>2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,3]=>[4,3]=>[2,2,2,1]=>2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[5,1,1]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[5,2]=>[5,2]=>[2,2,1,1,1]=>2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[5,1,1]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[5,2]=>[5,2]=>[2,2,1,1,1]=>2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[5,1,1]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,2]=>[5,2]=>[2,2,1,1,1]=>2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,1,1]=>[4,1,1,1]=>[4,1,1,1]=>4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2]=>[4,2,1]=>[3,2,1,1]=>3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,2,1]=>[4,2,1]=>[3,2,1,1]=>3
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3]=>[4,3]=>[2,2,2,1]=>2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3]=>[4,3]=>[2,2,2,1]=>2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[5,1,1]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,2]=>[5,2]=>[2,2,1,1,1]=>2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,1]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,2]=>[5,2]=>[2,2,1,1,1]=>2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,1]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,2]=>[5,2]=>[2,2,1,1,1]=>2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,1]=>[5,1,1]=>[3,1,1,1,1]=>3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,2]=>[5,2]=>[2,2,1,1,1]=>2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>[6,1]=>[2,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7]=>[7]=>[1,1,1,1,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1]=>[8]=>8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1]=>[7,1]=>7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1]=>[7,1]=>7
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]=>[6,1,1]=>6
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,3]=>[3,1,1,1,1,1]=>[6,1,1]=>6
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1]=>[7,1]=>7
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,2,2]=>[2,2,1,1,1,1]=>[6,2]=>6
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,3,1]=>[3,1,1,1,1,1]=>[6,1,1]=>6
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,4]=>[4,1,1,1,1]=>[5,1,1,1]=>5
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,4]=>[4,1,1,1,1]=>[5,1,1,1]=>5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,3,1]=>[3,1,1,1,1,1]=>[6,1,1]=>6
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,4]=>[4,1,1,1,1]=>[5,1,1,1]=>5
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,4]=>[4,1,1,1,1]=>[5,1,1,1]=>5
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]=>[4,1,1,1,1]=>[5,1,1,1]=>5
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1]=>[7,1]=>7
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,2,1,2]=>[2,2,1,1,1,1]=>[6,2]=>6
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,2,2,1]=>[2,2,1,1,1,1]=>[6,2]=>6
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,2,3]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,2,3]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,3,1,1]=>[3,1,1,1,1,1]=>[6,1,1]=>6
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,3,2]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,4,1]=>[4,1,1,1,1]=>[5,1,1,1]=>5
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,5]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,5]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,4,1]=>[4,1,1,1,1]=>[5,1,1,1]=>5
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,5]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,5]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,5]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,3,1,1]=>[3,1,1,1,1,1]=>[6,1,1]=>6
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,3,2]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,4,1]=>[4,1,1,1,1]=>[5,1,1,1]=>5
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,5]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,5]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,4,1]=>[4,1,1,1,1]=>[5,1,1,1]=>5
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,5]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,5]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,5]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,4,1]=>[4,1,1,1,1]=>[5,1,1,1]=>5
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,5]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,5]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,5]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,5]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1]=>[7,1]=>7
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]=>[2,2,1,1,1,1]=>[6,2]=>6
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]=>[2,2,1,1,1,1]=>[6,2]=>6
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,2,1,3]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,3]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,2,2,1,1]=>[2,2,1,1,1,1]=>[6,2]=>6
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2]=>[2,2,2,1,1]=>[5,3]=>5
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,2,3,1]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,4]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,4]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,2,3,1]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,2,4]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,2,4]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,3,1,1,1]=>[3,1,1,1,1,1]=>[6,1,1]=>6
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,3,1,2]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,3,2,1]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,3,3]=>[3,3,1,1]=>[4,2,2]=>4
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,3,3]=>[3,3,1,1]=>[4,2,2]=>4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,4,1,1]=>[4,1,1,1,1]=>[5,1,1,1]=>5
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,4,2]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,5,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,5,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,4,1,1]=>[4,1,1,1,1]=>[5,1,1,1]=>5
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,4,2]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,5,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,5,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,5,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,3,1,1,1]=>[3,1,1,1,1,1]=>[6,1,1]=>6
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,3,1,2]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,3,2,1]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,3,3]=>[3,3,1,1]=>[4,2,2]=>4
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]=>[3,3,1,1]=>[4,2,2]=>4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,4,1,1]=>[4,1,1,1,1]=>[5,1,1,1]=>5
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,4,2]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,5,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,5,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,4,1,1]=>[4,1,1,1,1]=>[5,1,1,1]=>5
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,4,2]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,5,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,5,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,5,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,4,1,1]=>[4,1,1,1,1]=>[5,1,1,1]=>5
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,4,2]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,5,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,5,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,5,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,5,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,6]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1]=>[7,1]=>7
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]=>[2,2,1,1,1,1]=>[6,2]=>6
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]=>[2,2,1,1,1,1]=>[6,2]=>6
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,3]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,1,2,1,1]=>[2,2,1,1,1,1]=>[6,2]=>6
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]=>[2,2,2,1,1]=>[5,3]=>5
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,1,3,1]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,1,4]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,4]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,1,4]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,1,4]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,2,1,1,1]=>[2,2,1,1,1,1]=>[6,2]=>6
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]=>[2,2,2,1,1]=>[5,3]=>5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]=>[2,2,2,1,1]=>[5,3]=>5
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,3]=>[3,2,2,1]=>[4,3,1]=>4
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]=>[3,2,2,1]=>[4,3,1]=>4
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,3,1,1]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,3,2]=>[3,2,2,1]=>[4,3,1]=>4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,5]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,5]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,5]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,5]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,5]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,3,1,1]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]=>[3,2,2,1]=>[4,3,1]=>4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,4,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,4,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,5]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,5]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,5]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,5]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]=>[3,1,1,1,1,1]=>[6,1,1]=>6
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,1,1,2]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,1,2,1]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,1,3]=>[3,3,1,1]=>[4,2,2]=>4
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]=>[3,3,1,1]=>[4,2,2]=>4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,1,1]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]=>[3,2,2,1]=>[4,3,1]=>4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,3,1]=>[3,3,1,1]=>[4,2,2]=>4
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,4]=>[4,3,1]=>[3,2,2,1]=>3
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,4]=>[4,3,1]=>[3,2,2,1]=>3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,3,1]=>[3,3,1,1]=>[4,2,2]=>4
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,4]=>[4,3,1]=>[3,2,2,1]=>3
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,4]=>[4,3,1]=>[3,2,2,1]=>3
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]=>[4,3,1]=>[3,2,2,1]=>3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,4,1,1,1]=>[4,1,1,1,1]=>[5,1,1,1]=>5
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,4,1,2]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,4,2,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,4,3]=>[4,3,1]=>[3,2,2,1]=>3
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,4,3]=>[4,3,1]=>[3,2,2,1]=>3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,5,1,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,5,2]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,5,1,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,5,2]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,1,1,1]=>[4,1,1,1,1]=>[5,1,1,1]=>5
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,2,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3]=>[4,3,1]=>[3,2,2,1]=>3
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3]=>[4,3,1]=>[3,2,2,1]=>3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,5,1,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,5,2]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,5,1,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,5,2]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,1,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,2]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1]=>[3,1,1,1,1,1]=>[6,1,1]=>6
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,3,1,1,2]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,3,1,2,1]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,3,1,3]=>[3,3,1,1]=>[4,2,2]=>4
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]=>[3,3,1,1]=>[4,2,2]=>4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,1,1]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]=>[3,2,2,1]=>[4,3,1]=>4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,3,3,1]=>[3,3,1,1]=>[4,2,2]=>4
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,3,4]=>[4,3,1]=>[3,2,2,1]=>3
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,3,4]=>[4,3,1]=>[3,2,2,1]=>3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,3,3,1]=>[3,3,1,1]=>[4,2,2]=>4
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,3,4]=>[4,3,1]=>[3,2,2,1]=>3
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,3,4]=>[4,3,1]=>[3,2,2,1]=>3
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]=>[4,3,1]=>[3,2,2,1]=>3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,4,1,1,1]=>[4,1,1,1,1]=>[5,1,1,1]=>5
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,4,1,2]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,2,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,4,3]=>[4,3,1]=>[3,2,2,1]=>3
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,4,3]=>[4,3,1]=>[3,2,2,1]=>3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,5,1,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,5,2]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,5,1,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,5,2]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,4,1,1,1]=>[4,1,1,1,1]=>[5,1,1,1]=>5
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,4,2,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,4,3]=>[4,3,1]=>[3,2,2,1]=>3
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,4,3]=>[4,3,1]=>[3,2,2,1]=>3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,5,1,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,5,2]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,5,1,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,5,2]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,5,1,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,5,2]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,4,1,1,1]=>[4,1,1,1,1]=>[5,1,1,1]=>5
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,4,2,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,4,3]=>[4,3,1]=>[3,2,2,1]=>3
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,4,3]=>[4,3,1]=>[3,2,2,1]=>3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,5,1,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,5,2]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,5,1,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,5,2]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,5,1,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,5,2]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,5,1,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,5,2]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,6,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,7]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1]=>[7,1]=>7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]=>[2,2,1,1,1,1]=>[6,2]=>6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]=>[2,2,1,1,1,1]=>[6,2]=>6
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,3]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]=>[2,2,1,1,1,1]=>[6,2]=>6
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]=>[2,2,2,1,1]=>[5,3]=>5
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,3,1]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,4]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,4]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,3,1]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,4]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,4]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,2,1,1,1]=>[2,2,1,1,1,1]=>[6,2]=>6
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]=>[2,2,2,1,1]=>[5,3]=>5
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]=>[2,2,2,1,1]=>[5,3]=>5
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,3]=>[3,2,2,1]=>[4,3,1]=>4
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]=>[3,2,2,1]=>[4,3,1]=>4
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,3,1,1]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,3,2]=>[3,2,2,1]=>[4,3,1]=>4
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,5]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,5]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,5]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,5]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,5]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,1,1]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]=>[3,2,2,1]=>[4,3,1]=>4
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,4,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,5]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,5]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,5]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1]=>[2,2,1,1,1,1]=>[6,2]=>6
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>[2,2,2,1,1]=>[5,3]=>5
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>[2,2,2,1,1]=>[5,3]=>5
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,3]=>[3,2,2,1]=>[4,3,1]=>4
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]=>[3,2,2,1]=>[4,3,1]=>4
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,2,1,1]=>[2,2,2,1,1]=>[5,3]=>5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2]=>[2,2,2,2]=>[4,4]=>4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,3,1]=>[3,2,2,1]=>[4,3,1]=>4
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,4]=>[4,2,2]=>[3,3,1,1]=>3
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,4]=>[4,2,2]=>[3,3,1,1]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]=>[3,2,2,1]=>[4,3,1]=>4
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,4]=>[4,2,2]=>[3,3,1,1]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,2,4]=>[4,2,2]=>[3,3,1,1]=>3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]=>[4,2,2]=>[3,3,1,1]=>3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,1,1]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,2]=>[3,2,2,1]=>[4,3,1]=>4
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,2,1]=>[3,2,2,1]=>[4,3,1]=>4
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,3]=>[3,3,2]=>[3,3,2]=>3
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,3]=>[3,3,2]=>[3,3,2]=>3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,4,1,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,4,2]=>[4,2,2]=>[3,3,1,1]=>3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,5,1]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,5,1]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,1,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,2]=>[4,2,2]=>[3,3,1,1]=>3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,5,1]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,5,1]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,1]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,1,1,1]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,2]=>[3,2,2,1]=>[4,3,1]=>4
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]=>[3,2,2,1]=>[4,3,1]=>4
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,3]=>[3,3,2]=>[3,3,2]=>3
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]=>[3,3,2]=>[3,3,2]=>3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,1,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,2]=>[4,2,2]=>[3,3,1,1]=>3
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,5,1]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,5,1]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,1,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,2]=>[4,2,2]=>[3,3,1,1]=>3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,5,1]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,5,1]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,5,1]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,4,1,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,2]=>[4,2,2]=>[3,3,1,1]=>3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,1]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,1]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,1]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,5,1]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,6]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>[3,1,1,1,1,1]=>[6,1,1]=>6
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,1,3]=>[3,3,1,1]=>[4,2,2]=>4
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]=>[3,3,1,1]=>[4,2,2]=>4
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]=>[3,2,2,1]=>[4,3,1]=>4
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,3,1]=>[3,3,1,1]=>[4,2,2]=>4
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,4]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,4]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]=>[3,3,1,1]=>[4,2,2]=>4
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,1,4]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,4]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,2,1,2]=>[3,2,2,1]=>[4,3,1]=>4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,2,1]=>[3,2,2,1]=>[4,3,1]=>4
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,3]=>[3,3,2]=>[3,3,2]=>3
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,3]=>[3,3,2]=>[3,3,2]=>3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,3,1,1]=>[3,3,1,1]=>[4,2,2]=>4
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,3,2]=>[3,3,2]=>[3,3,2]=>3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,4,1]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,5]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,5]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,4,1]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,5]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,5]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,5]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,3,1,1]=>[3,3,1,1]=>[4,2,2]=>4
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,3,2]=>[3,3,2]=>[3,3,2]=>3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,4,1]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,5]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,5]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,4,1]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,5]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,5]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,5]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,4,1]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,5]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,5]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,5]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>[4,1,1,1,1]=>[5,1,1,1]=>5
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,2]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[4,1,3]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[4,2,1,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]=>[4,2,2]=>[3,3,1,1]=>3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[4,3,1]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[4,4]=>[4,4]=>[2,2,2,2]=>2
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[4,4]=>[4,4]=>[2,2,2,2]=>2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,4]=>[4,4]=>[2,2,2,2]=>2
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[4,4]=>[4,4]=>[2,2,2,2]=>2
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4]=>[4,4]=>[2,2,2,2]=>2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[5,1,2]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[5,2,1]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[5,3]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,3]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[5,1,2]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[5,3]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,3]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>[4,1,1,1,1]=>[5,1,1,1]=>5
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,2]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,3]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,2,1,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]=>[4,2,2]=>[3,3,1,1]=>3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,1]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,4]=>[4,4]=>[2,2,2,2]=>2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,4]=>[4,4]=>[2,2,2,2]=>2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,4]=>[4,4]=>[2,2,2,2]=>2
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,4]=>[4,4]=>[2,2,2,2]=>2
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]=>[4,4]=>[2,2,2,2]=>2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[5,1,2]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[5,2,1]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[5,3]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,3]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[5,1,2]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[5,3]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,3]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,1,2]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,3]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,3]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1]=>[3,1,1,1,1,1]=>[6,1,1]=>6
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,1,3]=>[3,3,1,1]=>[4,2,2]=>4
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]=>[3,3,1,1]=>[4,2,2]=>4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]=>[3,2,2,1]=>[4,3,1]=>4
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,3,1]=>[3,3,1,1]=>[4,2,2]=>4
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,4]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,4]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]=>[3,3,1,1]=>[4,2,2]=>4
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,1,4]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,4]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]=>[3,2,1,1,1]=>[5,2,1]=>5
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,2,1,2]=>[3,2,2,1]=>[4,3,1]=>4
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,2,1]=>[3,2,2,1]=>[4,3,1]=>4
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,3]=>[3,3,2]=>[3,3,2]=>3
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,3]=>[3,3,2]=>[3,3,2]=>3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,3,1,1]=>[3,3,1,1]=>[4,2,2]=>4
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,3,2]=>[3,3,2]=>[3,3,2]=>3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,4,1]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,5]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,5]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,4,1]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,5]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,5]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,5]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,3,1,1]=>[3,3,1,1]=>[4,2,2]=>4
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,3,2]=>[3,3,2]=>[3,3,2]=>3
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,4,1]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,5]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,5]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,4,1]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,5]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,5]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,5]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,4,1]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,5]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,5]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,5]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>[4,1,1,1,1]=>[5,1,1,1]=>5
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,2]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[4,1,3]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[4,2,1,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]=>[4,2,2]=>[3,3,1,1]=>3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[4,3,1]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[4,4]=>[4,4]=>[2,2,2,2]=>2
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[4,4]=>[4,4]=>[2,2,2,2]=>2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,4]=>[4,4]=>[2,2,2,2]=>2
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[4,4]=>[4,4]=>[2,2,2,2]=>2
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4]=>[4,4]=>[2,2,2,2]=>2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[5,1,2]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[5,2,1]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[5,3]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,3]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[5,1,2]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[5,3]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,3]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>[4,1,1,1,1]=>[5,1,1,1]=>5
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,2]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,3]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,2,1,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]=>[4,2,2]=>[3,3,1,1]=>3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,1]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,4]=>[4,4]=>[2,2,2,2]=>2
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,4]=>[4,4]=>[2,2,2,2]=>2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,4]=>[4,4]=>[2,2,2,2]=>2
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,4]=>[4,4]=>[2,2,2,2]=>2
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]=>[4,4]=>[2,2,2,2]=>2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[5,1,2]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[5,2,1]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[5,3]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,3]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[5,1,2]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[5,3]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,3]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,1,2]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,3]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,3]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>[4,1,1,1,1]=>[5,1,1,1]=>5
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,2]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,3]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,2,1,1]=>[4,2,1,1]=>[4,2,1,1]=>4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]=>[4,2,2]=>[3,3,1,1]=>3
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,1]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,4]=>[4,4]=>[2,2,2,2]=>2
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,4]=>[4,4]=>[2,2,2,2]=>2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]=>[4,3,1]=>[3,2,2,1]=>3
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,4]=>[4,4]=>[2,2,2,2]=>2
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,4]=>[4,4]=>[2,2,2,2]=>2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]=>[4,4]=>[2,2,2,2]=>2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[5,1,2]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[5,2,1]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[5,3]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[5,3]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[5,1,2]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[5,3]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,3]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[5,1,2]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[5,3]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,3]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[5,1,1,1]=>[4,1,1,1,1]=>4
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,1,2]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>[5,2,1]=>[3,2,1,1,1]=>3
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,3]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,3]=>[5,3]=>[2,2,2,1,1]=>2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,1,1]=>[6,1,1]=>[3,1,1,1,1,1]=>3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,2]=>[6,2]=>[2,2,1,1,1,1]=>2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,1]=>[7,1]=>[2,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8]=>[8]=>[1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[10,1]=>[10,1]=>[2,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,10]=>[10,1]=>[2,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1]=>[10,1]=>[2,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,10]=>[10,1]=>[2,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]=>[10,1]=>[10,1]=>[2,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1]=>[10,1]=>[2,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,10]=>[10,1]=>[2,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,10]=>[10,1]=>[2,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[10,1]=>[10,1]=>[2,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,10]=>[10,1]=>[2,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,10]=>[10,1]=>[2,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,10]=>[10,1]=>[2,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,2]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,7]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,10]=>[10,1]=>[2,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,7,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[7,2]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,7]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,10]=>[10,1]=>[2,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,2]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,7,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]=>[7,2]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,2]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,7]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,7]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,8]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,10]=>[10,1]=>[2,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[8,1,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]=>[8,2]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,7,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,7,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0]=>[7,2]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0]=>[7,2]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,2]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,7]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,7]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,8]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,8]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,10]=>[10,1]=>[2,1,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[9]=>[9]=>[1,1,1,1,1,1,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1]=>[9]=>9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1]=>[8,1]=>8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1]=>[7,1,1]=>7
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,4]=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,5]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,6]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1]=>[10]=>10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1]=>[7,1,1]=>7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1,1]=>[8,1,1]=>8
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,4]=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,4]=>[4,1,1,1,1,1,1]=>[7,1,1,1]=>7
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,5]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,5]=>[5,1,1,1,1,1]=>[6,1,1,1,1]=>6
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,6]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,6]=>[6,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,7]=>[7,1,1,1]=>[4,1,1,1,1,1,1]=>4
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,8]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1,1,1,1,1]=>[11]=>11
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,1,2]=>[2,1,1,1,1,1,1,1,1,1]=>[10,1]=>10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1,1]=>[8,1,1]=>8
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1,1,1]=>[9,1,1]=>9
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,4]=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,1,4]=>[4,1,1,1,1,1,1]=>[7,1,1,1]=>7
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,5]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,4]=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,6]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,5]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,6]=>[6,1,1,1,1,1]=>[6,1,1,1,1,1]=>6
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,6]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,9]=>[9,1,1]=>[3,1,1,1,1,1,1,1,1]=>3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,10]=>[10,1]=>[2,1,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,1,3]=>[3,1,1,1,1,1,1,1,1]=>[9,1,1]=>9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,4]=>[4,1,1,1,1,1,1]=>[7,1,1,1]=>7
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,5]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,5]=>[5,1,1,1,1,1]=>[6,1,1,1,1]=>6
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,4]=>[4,1,1,1,1,1,1]=>[7,1,1,1]=>7
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,6]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,5]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,6]=>[6,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,7]=>[7,1,1,1]=>[4,1,1,1,1,1,1]=>4
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,5]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,8]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,6]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,5]=>[5,1,1,1,1,1]=>[6,1,1,1,1]=>6
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,6]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,5]=>[5,1,1,1,1,1]=>[6,1,1,1,1]=>6
[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,6]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,5]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,5]=>[5,1,1,1,1,1]=>[6,1,1,1,1]=>6
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,6]=>[6,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,6]=>[6,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,5]=>[5,1,1,1,1,1]=>[6,1,1,1,1]=>6
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,6]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,7]=>[7,1,1,1]=>[4,1,1,1,1,1,1]=>4
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,7]=>[7,1,1,1]=>[4,1,1,1,1,1,1]=>4
[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,6]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,6]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,8]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,8]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,6]=>[6,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,6]=>[6,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,8]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1]=>[8,1]=>8
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1]=>[8,1]=>8
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1]=>[7,2]=>7
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,3,1]=>[3,1,1,1,1,1,1]=>[7,1,1]=>7
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1]=>[8,1]=>8
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,2,1,2]=>[2,2,1,1,1,1,1]=>[7,2]=>7
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,2,2,1]=>[2,2,1,1,1,1,1]=>[7,2]=>7
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,2,3]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,3,1,1]=>[3,1,1,1,1,1,1]=>[7,1,1]=>7
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,3,2]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,4,1]=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1]=>[8,1]=>8
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,2,1,2,1]=>[2,2,1,1,1,1,1]=>[7,2]=>7
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,2,2,1,1]=>[2,2,1,1,1,1,1]=>[7,2]=>7
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2,2]=>[2,2,2,1,1,1]=>[6,3]=>6
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,2,4]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,3,1,1,1]=>[3,1,1,1,1,1,1]=>[7,1,1]=>7
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,3,2,1]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,3,3]=>[3,3,1,1,1]=>[5,2,2]=>5
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,5,1]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]=>[8,1]=>8
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,1,2]=>[2,2,1,1,1,1,1]=>[7,2]=>7
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,2,1,1,2,1]=>[2,2,1,1,1,1,1]=>[7,2]=>7
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,1,3]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,2,1,2,2]=>[2,2,2,1,1,1]=>[6,3]=>6
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,2,2,1,1,1]=>[2,2,1,1,1,1,1]=>[7,2]=>7
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,2,1]=>[2,2,2,1,1,1]=>[6,3]=>6
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,2,3]=>[3,2,2,1,1]=>[5,3,1]=>5
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,2,3,2]=>[3,2,2,1,1]=>[5,3,1]=>5
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,2,4,1]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,2,5]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,3,1,1,1,1]=>[3,1,1,1,1,1,1]=>[7,1,1]=>7
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,3,2,2]=>[3,2,2,1,1]=>[5,3,1]=>5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,4,1,1,1]=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,4,3]=>[4,3,1,1]=>[4,2,2,1]=>4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,5,1,1]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,5,2]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,6,1]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]=>[8,1]=>8
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,1,2]=>[2,2,1,1,1,1,1]=>[7,2]=>7
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,1,2,1]=>[2,2,1,1,1,1,1]=>[7,2]=>7
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,1,3]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,1,1,2,1,1]=>[2,2,1,1,1,1,1]=>[7,2]=>7
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,1,2,1,1,1]=>[2,2,1,1,1,1,1]=>[7,2]=>7
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,1,5]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,2,1,1,1,1]=>[2,2,1,1,1,1,1]=>[7,2]=>7
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,2,1,1,2]=>[2,2,2,1,1,1]=>[6,3]=>6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,2,2,1,1]=>[2,2,2,1,1,1]=>[6,3]=>6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2,2]=>[2,2,2,2,1]=>[5,4]=>5
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,2,3,1]=>[3,2,2,1,1]=>[5,3,1]=>5
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,2,4]=>[4,2,2,1]=>[4,3,1,1]=>4
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,3,1,1,1]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,3,3]=>[3,3,2,1]=>[4,3,2]=>4
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,5,1]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,6]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1,1]=>[3,1,1,1,1,1,1]=>[7,1,1]=>7
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,2,1]=>[3,2,2,1,1]=>[5,3,1]=>5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,3,1,1]=>[3,3,1,1,1]=>[5,2,2]=>5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,3,2]=>[3,3,2,1]=>[4,3,2]=>4
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,5]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,1,1,1,1]=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,4,1,3]=>[4,3,1,1]=>[4,2,2,1]=>4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,4,2,1,1]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,4]=>[4,4,1]=>[3,2,2,2]=>3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,5,1,1,1]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,5,3]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,6,1,1]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,6,2]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1]=>[8,1]=>8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,2]=>[2,2,1,1,1,1,1]=>[7,2]=>7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,1,2,1]=>[2,2,1,1,1,1,1]=>[7,2]=>7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,1,3]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,1,2,1,1]=>[2,2,1,1,1,1,1]=>[7,2]=>7
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,1,2,2]=>[2,2,2,1,1,1]=>[6,3]=>6
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,1,3,1]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,1,4]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,1,2,1,1,1]=>[2,2,1,1,1,1,1]=>[7,2]=>7
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,1,2,3]=>[3,2,2,1,1]=>[5,3,1]=>5
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,1,4,1]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,1,5]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,2,1,1,1,1]=>[2,2,1,1,1,1,1]=>[7,2]=>7
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2,2]=>[2,2,2,2,1]=>[5,4]=>5
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,3]=>[3,3,2,1]=>[4,3,2]=>4
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,5,1]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,6]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1,1]=>[2,2,1,1,1,1,1]=>[7,2]=>7
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,1,2]=>[2,2,2,1,1,1]=>[6,3]=>6
[1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,2,1,4]=>[4,2,2,1]=>[4,3,1,1]=>4
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,2,2,1,1,1]=>[2,2,2,1,1,1]=>[6,3]=>6
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,2,1,2]=>[2,2,2,2,1]=>[5,4]=>5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,2,1]=>[2,2,2,2,1]=>[5,4]=>5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,2,3]=>[3,2,2,2]=>[4,4,1]=>4
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,2,3,1,1]=>[3,2,2,1,1]=>[5,3,1]=>5
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,2,3,2]=>[3,2,2,2]=>[4,4,1]=>4
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,5]=>[5,2,2]=>[3,3,1,1,1]=>3
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,1,1,1]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,3,1]=>[3,3,2,1]=>[4,3,2]=>4
[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4]=>[4,3,2]=>[3,3,2,1]=>3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,4,1,1,1]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,4,3]=>[4,3,2]=>[3,3,2,1]=>3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,5,1,1]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,5,2]=>[5,2,2]=>[3,3,1,1,1]=>3
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,6,1]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1]=>[3,1,1,1,1,1,1]=>[7,1,1]=>7
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,1,2]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,1,1,2,1]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,1,3]=>[3,3,1,1,1]=>[5,2,2]=>5
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,2,1,2]=>[3,2,2,1,1]=>[5,3,1]=>5
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,2,2,1]=>[3,2,2,1,1]=>[5,3,1]=>5
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,1]=>[4,3,1,1]=>[4,2,2,1]=>4
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,5]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,1,1,1]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,2,2]=>[3,2,2,2]=>[4,4,1]=>4
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,3,1,1,1]=>[3,3,1,1,1]=>[5,2,2]=>5
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3,3]=>[3,3,3]=>[3,3,3]=>3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[3,4,2]=>[4,3,2]=>[3,3,2,1]=>3
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,5,1]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,6]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1]=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[4,1,1,1,2]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[4,1,1,3]=>[4,3,1,1]=>[4,2,2,1]=>4
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,3,1]=>[4,3,1,1]=>[4,2,2,1]=>4
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,4]=>[4,4,1]=>[3,2,2,2]=>3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[4,2,1,1,1]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,2,2,1]=>[4,2,2,1]=>[4,3,1,1]=>4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[4,2,3]=>[4,3,2]=>[3,3,2,1]=>3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[4,3,1,1]=>[4,3,1,1]=>[4,2,2,1]=>4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[4,3,2]=>[4,3,2]=>[3,3,2,1]=>3
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[4,4,1]=>[4,4,1]=>[3,2,2,2]=>3
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0]=>[5,1,1,2]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[5,1,2,1]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[5,1,3]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>[5,2,1,1]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[5,3,1]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,4]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]=>[6,1,2]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[6,3]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,2,1,1]=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>9
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,2,2]=>[2,2,1,1,1,1,1,1]=>[8,2]=>8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,1,3,1]=>[3,1,1,1,1,1,1,1]=>[8,1,1]=>8
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,2,1,1,1]=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>9
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,2,2,1]=>[2,2,1,1,1,1,1,1]=>[8,2]=>8
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,4,1]=>[4,1,1,1,1,1,1]=>[7,1,1,1]=>7
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,2,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>9
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,2,2,2]=>[2,2,2,1,1,1,1]=>[7,3]=>7
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,3,1,1,1]=>[3,1,1,1,1,1,1,1]=>[8,1,1]=>8
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,5,1]=>[5,1,1,1,1,1]=>[6,1,1,1,1]=>6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>9
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,2,1,1,1,2]=>[2,2,1,1,1,1,1,1]=>[8,2]=>8
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,2,2,1,1,1]=>[2,2,1,1,1,1,1,1]=>[8,2]=>8
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,2,2,2,1]=>[2,2,2,1,1,1,1]=>[7,3]=>7
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,3,1,1,1,1]=>[3,1,1,1,1,1,1,1]=>[8,1,1]=>8
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,4,2,1]=>[4,2,1,1,1,1]=>[6,2,1,1]=>6
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,6,1]=>[6,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,7]=>[7,1,1,1]=>[4,1,1,1,1,1,1]=>4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>9
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,2,2,1,1,1,1]=>[2,2,1,1,1,1,1,1]=>[8,2]=>8
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2,2]=>[2,2,2,2,1,1]=>[6,4]=>6
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,3,1,1,1,1,1]=>[3,1,1,1,1,1,1,1]=>[8,1,1]=>8
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,4,4]=>[4,4,1,1]=>[4,2,2,2]=>4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,5,1,1,1]=>[5,1,1,1,1,1]=>[6,1,1,1,1]=>6
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,6,2]=>[6,2,1,1]=>[4,2,1,1,1,1]=>4
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,7,1]=>[7,1,1,1]=>[4,1,1,1,1,1,1]=>4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>9
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,1,1,2]=>[2,2,1,1,1,1,1,1]=>[8,2]=>8
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,1,1,2,1]=>[2,2,1,1,1,1,1,1]=>[8,2]=>8
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,1,1,3]=>[3,2,1,1,1,1,1]=>[7,2,1]=>7
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,1,3,1,2]=>[3,2,2,1,1,1]=>[6,3,1]=>6
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,2,1,1,1,1,1]=>[2,2,1,1,1,1,1,1]=>[8,2]=>8
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,2,2,1,1,1]=>[2,2,2,1,1,1,1]=>[7,3]=>7
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,2,2,1]=>[2,2,2,2,1,1]=>[6,4]=>6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,2,3]=>[3,2,2,2,1]=>[5,4,1]=>5
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,2,2]=>[3,2,2,2,1]=>[5,4,1]=>5
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[4,3,2,1]=>[4,3,2,1]=>4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,2,4,1,1,1]=>[4,2,1,1,1,1]=>[6,2,1,1]=>6
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,7]=>[7,2,1]=>[3,2,1,1,1,1,1]=>3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1,1,1]=>[3,1,1,1,1,1,1,1]=>[8,1,1]=>8
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2,2]=>[3,2,2,2,1]=>[5,4,1]=>5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3,3]=>[3,3,3,1]=>[4,3,3]=>4
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,6]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,4,1,1,1,1,1]=>[4,1,1,1,1,1,1]=>[7,1,1,1]=>7
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,4,5]=>[5,4,1]=>[3,2,2,2,1]=>3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,5,1,1,1,1]=>[5,1,1,1,1,1]=>[6,1,1,1,1]=>6
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,5,4]=>[5,4,1]=>[3,2,2,2,1]=>3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,6,1,1,1]=>[6,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,7,1,1]=>[7,1,1,1]=>[4,1,1,1,1,1,1]=>4
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,7,2]=>[7,2,1]=>[3,2,1,1,1,1,1]=>3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>9
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,1,1,2]=>[2,2,1,1,1,1,1,1]=>[8,2]=>8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,1,1,2,1]=>[2,2,1,1,1,1,1,1]=>[8,2]=>8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,1,1,3]=>[3,2,1,1,1,1,1]=>[7,2,1]=>7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,1,1,2,1,1]=>[2,2,1,1,1,1,1,1]=>[8,2]=>8
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,1,1,1,3,1]=>[3,2,1,1,1,1,1]=>[7,2,1]=>7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,1,1,4]=>[4,2,1,1,1,1]=>[6,2,1,1]=>6
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,1,1,5]=>[5,2,1,1,1]=>[5,2,1,1,1]=>5
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,2,1,1,1,1,1]=>[2,2,1,1,1,1,1,1]=>[8,2]=>8
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,1,4,1,2]=>[4,2,2,1,1]=>[5,3,1,1]=>5
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,6,1]=>[6,2,1,1]=>[4,2,1,1,1,1]=>4
[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,7]=>[7,2,1]=>[3,2,1,1,1,1,1]=>3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,2,1,1,1,1,1,1]=>[2,2,1,1,1,1,1,1]=>[8,2]=>8
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,2,1,1,2,2]=>[2,2,2,2,1,1]=>[6,4]=>6
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,2,2,1,1,1,1]=>[2,2,2,1,1,1,1]=>[7,3]=>7
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,2,2,1,2,1]=>[2,2,2,2,1,1]=>[6,4]=>6
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,2,2,1,1]=>[2,2,2,2,1,1]=>[6,4]=>6
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2]=>[2,2,2,2,2]=>[5,5]=>5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,2,2,3,1]=>[3,2,2,2,1]=>[5,4,1]=>5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,2,4]=>[4,2,2,2]=>[4,4,1,1]=>4
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,2,3,1,1,1]=>[3,2,2,1,1,1]=>[6,3,1]=>6
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,2,3,3]=>[3,3,2,2]=>[4,4,2]=>4
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,1,1,1,1]=>[3,2,1,1,1,1,1]=>[7,2,1]=>7
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,3,2]=>[3,3,2,2]=>[4,4,2]=>4
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[2,4,3,1]=>[4,3,2,1]=>[4,3,2,1]=>4
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,4,4]=>[4,4,2]=>[3,3,2,2]=>3
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[2,6,1,1]=>[6,2,1,1]=>[4,2,1,1,1,1]=>4
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,6,2]=>[6,2,2]=>[3,3,1,1,1,1]=>3
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,7,1]=>[7,2,1]=>[3,2,1,1,1,1,1]=>3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1,1]=>[3,1,1,1,1,1,1,1]=>[8,1,1]=>8
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,1,1,2]=>[3,2,1,1,1,1,1]=>[7,2,1]=>7
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,1,1,1,2,1]=>[3,2,1,1,1,1,1]=>[7,2,1]=>7
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,5,1]=>[5,3,1,1]=>[4,2,2,1,1]=>4
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,1,1,1,1]=>[3,2,1,1,1,1,1]=>[7,2,1]=>7
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,2,2,1]=>[3,2,2,2,1]=>[5,4,1]=>5
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,2,3]=>[3,3,2,2]=>[4,4,2]=>4
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,3,2,2]=>[3,3,2,2]=>[4,4,2]=>4
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,3,4]=>[4,3,3]=>[3,3,3,1]=>3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,4,3]=>[4,3,3]=>[3,3,3,1]=>3
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,6,1]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,7]=>[7,3]=>[2,2,2,1,1,1,1]=>2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1,1]=>[4,1,1,1,1,1,1]=>[7,1,1,1]=>7
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[4,1,1,1,1,2]=>[4,2,1,1,1,1]=>[6,2,1,1]=>6
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,1,4]=>[4,4,1,1]=>[4,2,2,2]=>4
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[4,1,4,1]=>[4,4,1,1]=>[4,2,2,2]=>4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,2,2,2]=>[4,2,2,2]=>[4,4,1,1]=>4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,2,4]=>[4,4,2]=>[3,3,2,2]=>3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[4,3,3]=>[4,3,3]=>[3,3,3,1]=>3
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[4,4,1,1]=>[4,4,1,1]=>[4,2,2,2]=>4
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[4,4,2]=>[4,4,2]=>[3,3,2,2]=>3
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[4,5,1]=>[5,4,1]=>[3,2,2,2,1]=>3
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,6]=>[6,4]=>[2,2,2,2,1,1]=>2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1,1]=>[5,1,1,1,1,1]=>[6,1,1,1,1]=>6
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[5,1,1,1,2]=>[5,2,1,1,1]=>[5,2,1,1,1]=>5
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[5,1,3,1]=>[5,3,1,1]=>[4,2,2,1,1]=>4
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,1,4]=>[5,4,1]=>[3,2,2,2,1]=>3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[5,2,2,1]=>[5,2,2,1]=>[4,3,1,1,1]=>4
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[5,4,1]=>[5,4,1]=>[3,2,2,2,1]=>3
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,5]=>[5,5]=>[2,2,2,2,2]=>2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[6,1,1,1,1]=>[6,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0]=>[6,1,1,2]=>[6,2,1,1]=>[4,2,1,1,1,1]=>4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[6,1,2,1]=>[6,2,1,1]=>[4,2,1,1,1,1]=>4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[6,1,3]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[6,3,1]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,4]=>[6,4]=>[2,2,2,2,1,1]=>2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[7,1,1,1]=>[7,1,1,1]=>[4,1,1,1,1,1,1]=>4
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0]=>[7,1,2]=>[7,2,1]=>[3,2,1,1,1,1,1]=>3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[7,2,1]=>[7,2,1]=>[3,2,1,1,1,1,1]=>3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,3]=>[7,3]=>[2,2,2,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1]=>[3,1,1,1,1,1,1]=>[7,1,1]=>7
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1]=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1,1,1,1]=>[3,1,1,1,1,1,1,1]=>[8,1,1]=>8
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1]=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1,1]=>[4,1,1,1,1,1,1]=>[7,1,1,1]=>7
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1,1]=>[5,1,1,1,1,1]=>[6,1,1,1,1]=>6
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[6,1,1,1,1]=>[6,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,1,1,1]=>[7,1,1,1]=>[4,1,1,1,1,1,1]=>4
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,1,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1,1]=>[10,1]=>10
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,1,3]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,1,1,3]=>[3,2,1,1,1,1,1]=>[7,2,1]=>7
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,1,1,3]=>[3,3,1,1,1]=>[5,2,2]=>5
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,1,3]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,1,2]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1]=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1]=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,2]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,7]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,6]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,4]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,3]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,4,1,1,1,1]=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,3,1,1,1,1]=>[3,1,1,1,1,1,1]=>[7,1,1]=>7
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,3,1,1]=>[3,1,1,1,1,1,1,1]=>[8,1,1]=>8
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,4,1]=>[4,1,1,1,1,1,1]=>[7,1,1,1]=>7
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[5,1,1,2]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,1,1,1]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,2]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,7]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,3]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,4]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,5]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,6]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,7]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,2]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,3]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,5]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[6,3]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,4]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,6]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,2,1,4]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[7,2]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,7]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0]=>[6,3]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,6]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,4,1]=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,3,1,1]=>[3,1,1,1,1,1,1]=>[7,1,1]=>7
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,3,1,1,1,1,1]=>[3,1,1,1,1,1,1,1]=>[8,1,1]=>8
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,4,1,1,1,1,1]=>[4,1,1,1,1,1,1]=>[7,1,1,1]=>7
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,1,5]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,3,2]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[6,2,1]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[5,2,1,1]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[4,2,1,1,1]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,1,1,1]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,2,2,1]=>[4,2,2,1]=>[4,3,1,1]=>4
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,2]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[5,2,2]=>[5,2,2]=>[3,3,1,1,1]=>3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,2,2]=>[3,2,2,2]=>[4,4,1]=>4
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,2,2,2]=>[4,2,2,2]=>[4,4,1,1]=>4
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,2,2]=>[6,2,2]=>[3,3,1,1,1,1]=>3
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[8,2]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[5,4]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,2,1]=>[7,2,1]=>[3,2,1,1,1,1,1]=>3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[3,4,2]=>[4,3,2]=>[3,3,2,1]=>3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[5,2,2,1]=>[5,2,2,1]=>[4,3,1,1,1]=>4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,4,2,2]=>[4,2,2,1]=>[4,3,1,1]=>4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,2,2,1]=>[3,2,2,2,1]=>[5,4,1]=>5
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[4,1,4]=>[4,4,1]=>[3,2,2,2]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,7]=>[7,3]=>[2,2,2,1,1,1,1]=>2
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,7]=>[7,3]=>[2,2,2,1,1,1,1]=>2
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,7]=>[7,3]=>[2,2,2,1,1,1,1]=>2
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,7]=>[7,3]=>[2,2,2,1,1,1,1]=>2
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,7]=>[7,3]=>[2,2,2,1,1,1,1]=>2
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,5]=>[5,5]=>[2,2,2,2,2]=>2
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[5,5]=>[5,5]=>[2,2,2,2,2]=>2
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,5]=>[5,5]=>[2,2,2,2,2]=>2
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[5,5]=>[5,5]=>[2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[7,3]=>[7,3]=>[2,2,2,1,1,1,1]=>2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[7,3]=>[7,3]=>[2,2,2,1,1,1,1]=>2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[7,3]=>[7,3]=>[2,2,2,1,1,1,1]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[7,3]=>[7,3]=>[2,2,2,1,1,1,1]=>2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[7,3]=>[7,3]=>[2,2,2,1,1,1,1]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[7,5]=>[7,5]=>[2,2,2,2,2,1,1]=>2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,5]=>[7,5]=>[2,2,2,2,2,1,1]=>2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[7,5]=>[7,5]=>[2,2,2,2,2,1,1]=>2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,5]=>[7,5]=>[2,2,2,2,2,1,1]=>2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[7,5]=>[7,5]=>[2,2,2,2,2,1,1]=>2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,5]=>[7,5]=>[2,2,2,2,2,1,1]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[7,5]=>[7,5]=>[2,2,2,2,2,1,1]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,5]=>[7,5]=>[2,2,2,2,2,1,1]=>2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[7,5]=>[7,5]=>[2,2,2,2,2,1,1]=>2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,5]=>[7,5]=>[2,2,2,2,2,1,1]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,9]=>[9,2]=>[2,2,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,1,1,2]=>[3,2,1,1,1,1,1]=>[7,2,1]=>7
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,1,1,2,1]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,6]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,5]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,4]=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[3,6]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[4,5]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[5,4]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[9,2]=>[9,2]=>[2,2,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[4,1,2,1,1]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,6]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,7]=>[7,3]=>[2,2,2,1,1,1,1]=>2
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[3,6]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[4,6]=>[6,4]=>[2,2,2,2,1,1]=>2
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[4,4,1]=>[4,4,1]=>[3,2,2,2]=>3
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,5]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,8]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,7]=>[7,1,1,1]=>[4,1,1,1,1,1,1]=>4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,3]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[4,1,1,1,2]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[5,1,1,2]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,1,2]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,4,1]=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,5,1,1]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1,1]=>[3,1,1,1,1,1,1]=>[7,1,1]=>7
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,8]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[3,6]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,6]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,1,1,3,1]=>[3,1,1,1,1,1,1,1,1]=>[9,1,1]=>9
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1,1,1]=>[10,1]=>10
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,5,1,1,1]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,4,1,1,1]=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,4]=>[6,4]=>[2,2,2,2,1,1]=>2
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,3,1]=>[3,1,1,1,1,1,1]=>[7,1,1]=>7
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,6]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,3,1]=>[3,1,1,1,1,1,1,1]=>[8,1,1]=>8
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,1,2]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,6,2]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,7,1,1]=>[7,1,1,1]=>[4,1,1,1,1,1,1]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,7,1]=>[7,1,1,1]=>[4,1,1,1,1,1,1]=>4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,3,1,1,1,2]=>[3,2,1,1,1,1,1]=>[7,2,1]=>7
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,4,1,1,1,2]=>[4,2,1,1,1,1]=>[6,2,1,1]=>6
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[5,1,1,1,2]=>[5,2,1,1,1]=>[5,2,1,1,1]=>5
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1]=>[10,1]=>[2,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,6,2]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,6,1]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,10]=>[10,1]=>[2,1,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,1]=>[10,1]=>[2,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,1,1]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,4,1]=>[4,2,2,1]=>[4,3,1,1]=>4
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[5,2,2]=>[5,2,2]=>[3,3,1,1,1]=>3
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,6]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,6,1]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,7]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,7,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,3,4]=>[4,3,1,1]=>[4,2,2,1]=>4
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,5,3]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,3]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,3,4]=>[4,3,1,1]=>[4,2,2,1]=>4
[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,6,1]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[5,3,1]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,7,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,6]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,1,3,1]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,3,1]=>[3,1,1,1,1,1,1,1,1]=>[9,1,1]=>9
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,1,1,3,1]=>[3,2,1,1,1,1,1]=>[7,2,1]=>7
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,1,3,1]=>[3,3,1,1,1]=>[5,2,2]=>5
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,1,1,3,1]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,5]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1,1]=>[4,1,1,1,1,1,1]=>[7,1,1,1]=>7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[8,2]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,3]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,1,2]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[4,1,1,3]=>[4,3,1,1]=>[4,2,2,1]=>4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[6,1,1,1,1]=>[6,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[7,1,1,1]=>[7,1,1,1]=>[4,1,1,1,1,1,1]=>4
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,4,1,1,1,1]=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[4,1,1,2,1]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,5,1,1]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,6]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,1,5]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,1,1,4]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,3]=>[3,2,2,2]=>[4,4,1]=>4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,2,3,1,1]=>[3,2,2,1,1]=>[5,3,1]=>5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,2,3,1]=>[3,2,2,2,1]=>[5,4,1]=>5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2,2,2]=>[2,2,2,2,2,1]=>[6,5]=>6
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[5,2,2]=>[5,2,2]=>[3,3,1,1,1]=>3
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,2,2,1]=>[4,2,2,1]=>[4,3,1,1]=>4
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,2,2,2]=>[4,2,2,2]=>[4,4,1,1]=>4
[1,1,1,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,4]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[3,6]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,5]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,6]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,10]=>[10,1]=>[2,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,3]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[7,2]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,4,1]=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,3,1,1,1]=>[3,1,1,1,1,1,1]=>[7,1,1]=>7
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,3,1,1,1]=>[3,1,1,1,1,1,1,1]=>[8,1,1]=>8
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,3,1,1,1,1]=>[3,1,1,1,1,1,1,1]=>[8,1,1]=>8
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,1,4]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1,1,1]=>[3,1,1,1,1,1,1,1]=>[8,1,1]=>8
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,1,1,1,1]=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,4,1,1,1]=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,4,1,1]=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,4]=>[6,4]=>[2,2,2,2,1,1]=>2
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0]=>[6,3]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,5,1,1,1,1]=>[5,1,1,1,1,1]=>[6,1,1,1,1]=>6
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,4,1,1,1,1]=>[4,1,1,1,1,1,1]=>[7,1,1,1]=>7
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,2,1,1,1]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,6]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[3,1,5]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[4,1,4]=>[4,4,1]=>[3,2,2,2]=>3
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[4,5]=>[5,4]=>[2,2,2,2,1]=>2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,5]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,4]=>[4,1,1,1,1,1,1]=>[7,1,1,1]=>7
[1,0,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,6]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,5,1,1]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,2,4,1]=>[4,2,2,1]=>[4,3,1,1]=>4
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,1,1,1]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[3,3,1,1,1]=>[3,3,1,1,1]=>[5,2,2]=>5
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,3,1,1,1]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,1,1,1,1]=>[3,2,1,1,1,1,1]=>[7,2,1]=>7
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,5,1,1]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,6,1]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,5,1,1]=>[5,1,1,1,1,1]=>[6,1,1,1,1]=>6
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,4,1,1]=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,5,1]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,6,1]=>[6,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,6,1,1]=>[6,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,6,1,1]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,4,1,1]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,7,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,1]=>[4,3,1,1]=>[4,2,2,1]=>4
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,7,1]=>[7,1,1,1]=>[4,1,1,1,1,1,1]=>4
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,7,1]=>[7,1,1,1,1]=>[5,1,1,1,1,1,1]=>5
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,9,1]=>[9,1,1]=>[3,1,1,1,1,1,1,1,1]=>3
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,3]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[7,3]=>[7,3]=>[2,2,2,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[5,2,2]=>[5,2,2]=>[3,3,1,1,1]=>3
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,8]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[3,1,5]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,1,0,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,1,5]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,6]=>[6,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[3,6]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,7,2]=>[7,2,1]=>[3,2,1,1,1,1,1]=>3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,5,1,2]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,2,3,1,1]=>[3,2,1,1,1,1,1]=>[7,2,1]=>7
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0]=>[8,2]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,2,2,1]=>[4,2,2,1]=>[4,3,1,1]=>4
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[6,2,1]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[5,2,2]=>[5,2,2]=>[3,3,1,1,1]=>3
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,2,2,2]=>[4,2,2,2]=>[4,4,1,1]=>4
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[6,2,1]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,2,2]=>[6,2,2]=>[3,3,1,1,1,1]=>3
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[8,2]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,4,2,2]=>[4,2,2,1]=>[4,3,1,1]=>4
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,0,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,1,5]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,5,1]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,7,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,7,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[4,1,1,1,2]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,4,1,1,1,1]=>[4,1,1,1,1,1,1]=>[7,1,1,1]=>7
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,5,1,1,1,1]=>[5,1,1,1,1,1]=>[6,1,1,1,1]=>6
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[6,1,1,1,1]=>[6,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[5,1,2,1]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[4,1,3,1]=>[4,3,1,1]=>[4,2,2,1]=>4
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,4,1]=>[4,3,1,1]=>[4,2,2,1]=>4
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,5,1]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,6,1]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[6,1,2,1]=>[6,2,1,1]=>[4,2,1,1,1,1]=>4
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[4,1,1,3]=>[4,3,1,1]=>[4,2,2,1]=>4
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[5,1,3,1]=>[5,3,1,1]=>[4,2,2,1,1]=>4
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,1,4]=>[4,3,1,1]=>[4,2,2,1]=>4
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[4,1,4,1]=>[4,4,1,1]=>[4,2,2,2]=>4
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,5,1]=>[5,3,1,1]=>[4,2,2,1,1]=>4
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,6,1]=>[6,2,1,1]=>[4,2,1,1,1,1]=>4
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]=>[8,1,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,5]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,4,1]=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,4,1,1]=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,5,1]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,4,1]=>[4,1,1,1,1,1,1]=>[7,1,1,1]=>7
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,8]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,3]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[5,4]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,1,0,0]=>[5,4]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,7]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,4]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[3,3,3]=>[3,3,3]=>[3,3,3]=>3
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,6]=>[6,4]=>[2,2,2,2,1,1]=>2
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,5]=>[5,5]=>[2,2,2,2,2]=>2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[5,5]=>[5,5]=>[2,2,2,2,2]=>2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,7]=>[7,3]=>[2,2,2,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,6,1]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,2,4]=>[4,2,2,1]=>[4,3,1,1]=>4
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,6]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,7]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,5]=>[5,2,2]=>[3,3,1,1,1]=>3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,2,4]=>[4,2,2,2]=>[4,4,1,1]=>4
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,6]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,6]=>[6,2,2]=>[3,3,1,1,1,1]=>3
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,8]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[4,5]=>[5,4]=>[2,2,2,2,1]=>2
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,7]=>[7,2,1]=>[3,2,1,1,1,1,1]=>3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3]=>[4,3,2]=>[3,3,2,1]=>3
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,5]=>[5,2,2,1]=>[4,3,1,1,1]=>4
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,3]=>[3,2,2,2,1]=>[5,4,1]=>5
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,5]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1,1]=>[4,1,1,1,1,1,1]=>[7,1,1,1]=>7
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0]=>[5,1,3]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,1,1,3]=>[3,3,1,1,1]=>[5,2,2]=>5
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,5]=>[5,2,2]=>[3,3,1,1,1]=>3
[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,1,4]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[3,1,5]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[6,1,1,1,1,1]=>[6,1,1,1,1,1]=>[6,1,1,1,1,1]=>6
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,6]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,2,5]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,4]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,2,3]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,5,1]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,4,2,1]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,2,4,1,1]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,5,1,1,1]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,7,1]=>[7,2,1]=>[3,2,1,1,1,1,1]=>3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1,1,1]=>[4,1,1,1,1,1,1]=>[7,1,1,1]=>7
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,1,5]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,6,1,1]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,4]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[3,6]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,8]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,6]=>[6,4]=>[2,2,2,2,1,1]=>2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,4]=>[6,4]=>[2,2,2,2,1,1]=>2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[8,1,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[3,6]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,4,1,2]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,4]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,5]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,6,2]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[2,7,1]=>[7,2,1]=>[3,2,1,1,1,1,1]=>3
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[2,7]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,6,1]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,6,1,1]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[7,2]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[1,7,2]=>[7,2,1]=>[3,2,1,1,1,1,1]=>3
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,1,5]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,2,4,2]=>[4,2,2,1]=>[4,3,1,1]=>4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,1,1,5]=>[5,2,1,1,1]=>[5,2,1,1,1]=>5
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,4,2]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,4,2]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,4,2]=>[4,2,1,1,1,1]=>[6,2,1,1]=>6
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,4,2]=>[4,2,1,1,1,1]=>[6,2,1,1]=>6
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,4,2,1]=>[4,2,1,1,1,1]=>[6,2,1,1]=>6
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,5,2]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,5,2]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,5,2]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,5,2]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,4,2,1]=>[4,2,1,1,1,1]=>[6,2,1,1]=>6
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,7,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,6,1]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,7,1]=>[7,1,1,1]=>[4,1,1,1,1,1,1]=>4
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,1,1,1,3,1]=>[3,2,1,1,1,1,1,1]=>[8,2,1]=>8
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,1,1,3,1]=>[3,3,1,1,1,1]=>[6,2,2]=>6
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,3,1,3,1]=>[3,3,1,1,1]=>[5,2,2]=>5
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,2,1,3,1]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,1,1,2,1]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,1,1,1,2,1]=>[2,2,1,1,1,1,1,1,1]=>[9,2]=>9
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[3,6]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[3,3,3]=>[3,3,3]=>[3,3,3]=>3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,5,2]=>[5,2,2]=>[3,3,1,1,1]=>3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,4,3]=>[4,3,2]=>[3,3,2,1]=>3
[1,1,0,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4]=>[4,3,2]=>[3,3,2,1]=>3
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,4,3]=>[4,3,1,1]=>[4,2,2,1]=>4
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,6,2]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,5,3]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,4]=>[4,4,1]=>[3,2,2,2]=>3
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[4,5]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,2,2]=>[6,2,2]=>[3,3,1,1,1,1]=>3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,2,2]=>[4,2,2,2]=>[4,4,1,1]=>4
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[2,6,2]=>[6,2,2]=>[3,3,1,1,1,1]=>3
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[8,2]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[8,2]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[8,2]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,4,2]=>[4,2,2,2]=>[4,4,1,1]=>4
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[4,4,2]=>[4,4,2]=>[3,3,2,2]=>3
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[8,2]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,6,2]=>[6,2,2]=>[3,3,1,1,1,1]=>3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,2,6]=>[6,2,2]=>[3,3,1,1,1,1]=>3
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[4,6]=>[6,4]=>[2,2,2,2,1,1]=>2
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,8]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[2,8]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,8]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[4,2,4]=>[4,4,2]=>[3,3,2,2]=>3
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4]=>[6,4]=>[2,2,2,2,1,1]=>2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,4]=>[4,4,2]=>[3,3,2,2]=>3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4]=>[6,4]=>[2,2,2,2,1,1]=>2
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[2,8]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[4,6]=>[6,4]=>[2,2,2,2,1,1]=>2
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2,2,2,2]=>[2,2,2,2,2,2]=>[6,6]=>6
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,2,2,2,2]=>[4,2,2,2,2]=>[5,5,1,1]=>5
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,2,2,2]=>[6,2,2,2]=>[4,4,1,1,1,1]=>4
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,2,2,2]=>[4,2,2,2,2]=>[5,5,1,1]=>5
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,2,2,2]=>[6,2,2,2]=>[4,4,1,1,1,1]=>4
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,6,2,2]=>[6,2,2,2]=>[4,4,1,1,1,1]=>4
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,4,2,2]=>[4,2,2,2,2]=>[5,5,1,1]=>5
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,4,2,2]=>[4,4,2,2]=>[4,4,2,2]=>4
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,6,2,2]=>[6,2,2,2]=>[4,4,1,1,1,1]=>4
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,6,2]=>[6,4,2]=>[3,3,2,2,1,1]=>3
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,2,4,2]=>[4,2,2,2,2]=>[5,5,1,1]=>5
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[4,2,4,2]=>[4,4,2,2]=>[4,4,2,2]=>4
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,4,2]=>[6,4,2]=>[3,3,2,2,1,1]=>3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,4,2]=>[4,4,2,2]=>[4,4,2,2]=>4
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,4,2]=>[6,4,2]=>[3,3,2,2,1,1]=>3
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[4,6,2]=>[6,4,2]=>[3,3,2,2,1,1]=>3
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,6]=>[6,6]=>[2,2,2,2,2,2]=>2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,6]=>[6,6]=>[2,2,2,2,2,2]=>2
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[4,2,2,4]=>[4,4,2,2]=>[4,4,2,2]=>4
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,2,4]=>[6,4,2]=>[3,3,2,2,1,1]=>3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,2,4]=>[4,4,2,2]=>[4,4,2,2]=>4
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,2,4]=>[6,4,2]=>[3,3,2,2,1,1]=>3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,6,4]=>[6,4,2]=>[3,3,2,2,1,1]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,4,4]=>[4,4,2,2]=>[4,4,2,2]=>4
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,4,4]=>[4,4,4]=>[3,3,3,3]=>3
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,6,4]=>[6,4,2]=>[3,3,2,2,1,1]=>3
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,6]=>[6,6]=>[2,2,2,2,2,2]=>2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,6]=>[6,6]=>[2,2,2,2,2,2]=>2
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[4,4,1]=>[4,4,1]=>[3,2,2,2]=>3
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[3,5,1]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,2,1]=>[7,2,1]=>[3,2,1,1,1,1,1]=>3
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[5,3,1]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[6,3,1]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[4,4,1]=>[4,4,1]=>[3,2,2,2]=>3
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[5,4,1]=>[5,4,1]=>[3,2,2,2,1]=>3
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[3,5,1]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[4,5,1]=>[5,4,1]=>[3,2,2,2,1]=>3
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,6,1]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,6,1]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,7,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,1]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[4,4,1]=>[4,4,1]=>[3,2,2,2]=>3
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[5,4,1]=>[5,4,1]=>[3,2,2,2,1]=>3
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[3,5,1]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[4,4,1]=>[4,4,1]=>[3,2,2,2]=>3
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[4,5,1]=>[5,4,1]=>[3,2,2,2,1]=>3
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,6,1]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[3,5,1]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,6,1]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,7,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,6,1]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,7,1]=>[7,2,1]=>[3,2,1,1,1,1,1]=>3
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,7,1]=>[7,3,1]=>[3,2,2,1,1,1,1]=>3
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,7,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,8,1]=>[8,2,1]=>[3,2,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,9,1]=>[9,1,1]=>[3,1,1,1,1,1,1,1,1]=>3
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[7,2]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,7]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[8,2]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,7,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[4,5]=>[5,4]=>[2,2,2,2,1]=>2
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,9]=>[9,1,1]=>[3,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,1,1,1,1]=>[4,1,1,1,1,1]=>[6,1,1,1]=>6
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,2,2]=>[6,2,2]=>[3,3,1,1,1,1]=>3
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[6,2,1]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[6,2,1]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2,2]=>[3,2,2,2,1]=>[5,4,1]=>5
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,5,1]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[4,4,1]=>[4,4,1]=>[3,2,2,2]=>3
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[5,3,1]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,8,1]=>[8,2,1]=>[3,2,1,1,1,1,1,1]=>3
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,6,1]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,7,1]=>[7,3,1]=>[3,2,2,1,1,1,1]=>3
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[4,4,1]=>[4,4,1]=>[3,2,2,2]=>3
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[4,5,1]=>[5,4,1]=>[3,2,2,2,1]=>3
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[5,3,1]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,4,1]=>[4,3,1,1]=>[4,2,2,1]=>4
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[5,4,1]=>[5,4,1]=>[3,2,2,2,1]=>3
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,1]=>[4,3,1,1]=>[4,2,2,1]=>4
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[6,3,1]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,5,2,1]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[7,2,1]=>[7,2,1]=>[3,2,1,1,1,1,1]=>3
[1,1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[9,2]=>[9,2]=>[2,2,1,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[8,2]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[5,4]=>[5,4]=>[2,2,2,2,1]=>2
[1,0,1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,1,6]=>[6,2,1,1]=>[4,2,1,1,1,1]=>4
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,6,1,2]=>[6,2,1,1]=>[4,2,1,1,1,1]=>4
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,5,1,2,1]=>[5,2,1,1,1]=>[5,2,1,1,1]=>5
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,2,1,6]=>[6,2,1,1]=>[4,2,1,1,1,1]=>4
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,2,1,6]=>[6,2,1,1]=>[4,2,1,1,1,1]=>4
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,4,1,4]=>[4,4,1,1]=>[4,2,2,2]=>4
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,1,4,1]=>[4,3,1,1,1]=>[5,2,2,1]=>5
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,5,1,3]=>[5,3,1,1]=>[4,2,2,1,1]=>4
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,4,1,3,1]=>[4,3,1,1,1]=>[5,2,2,1]=>5
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,1,6]=>[6,2,1,1]=>[4,2,1,1,1,1]=>4
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,6,1,2]=>[6,2,1,1]=>[4,2,1,1,1,1]=>4
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,5,1,2,1]=>[5,2,1,1,1]=>[5,2,1,1,1]=>5
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,2,1,6]=>[6,2,1,1]=>[4,2,1,1,1,1]=>4
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,8,1,2]=>[8,2,1,1]=>[4,2,1,1,1,1,1,1]=>4
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,8,1,2]=>[8,2,1,1]=>[4,2,1,1,1,1,1,1]=>4
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,8,1,2]=>[8,2,1,1]=>[4,2,1,1,1,1,1,1]=>4
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,1,2,1,3,1]=>[3,3,2,1,1,1,1]=>[7,3,2]=>7
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,8,1,2]=>[8,2,1,1]=>[4,2,1,1,1,1,1,1]=>4
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,8,1,2]=>[8,2,1,1]=>[4,2,1,1,1,1,1,1]=>4
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,8,1,2]=>[8,2,1,1]=>[4,2,1,1,1,1,1,1]=>4
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0]=>[7,3]=>[7,3]=>[2,2,2,1,1,1,1]=>2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[6,4]=>[6,4]=>[2,2,2,2,1,1]=>2
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[5,5]=>[5,5]=>[2,2,2,2,2]=>2
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[4,6]=>[6,4]=>[2,2,2,2,1,1]=>2
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[3,1,5]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,7]=>[7,3]=>[2,2,2,1,1,1,1]=>2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>[11,1]=>11
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,1,1,1,2]=>[2,2,1,1,1,1,1,1,1]=>[9,2]=>9
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,1,1,3]=>[3,2,1,1,1,1,1]=>[7,2,1]=>7
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,1,1,4]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,10]=>[10,1]=>[2,1,1,1,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,5,2]=>[5,2,2]=>[3,3,1,1,1]=>3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,2,1]=>[4,2,2,1]=>[4,3,1,1]=>4
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,4,2,2]=>[4,2,2,2]=>[4,4,1,1]=>4
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,4,2]=>[4,2,2,2]=>[4,4,1,1]=>4
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,4]=>[4,2,2,2]=>[4,4,1,1]=>4
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,6,1]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,2,5,1]=>[5,2,2,1]=>[4,3,1,1,1]=>4
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[4,4,1]=>[4,4,1]=>[3,2,2,2]=>3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,5,2,1]=>[5,2,2,1]=>[4,3,1,1,1]=>4
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[1,7,1,1]=>[7,1,1,1]=>[4,1,1,1,1,1,1]=>4
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,7,1]=>[7,1,1,1]=>[4,1,1,1,1,1,1]=>4
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,8]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,3]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,2]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,2,2]=>[6,2,2]=>[3,3,1,1,1,1]=>3
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,6]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,2,5]=>[5,2,2]=>[3,3,1,1,1]=>3
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,6]=>[6,2,2]=>[3,3,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,8]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,8]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[8,2]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,0,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[3,6]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,1,1,2]=>[6,2,1,1]=>[4,2,1,1,1,1]=>4
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,10]=>[10,1]=>[2,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,10]=>[10,1]=>[2,1,1,1,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,6,1]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[5,2,2]=>[5,2,2]=>[3,3,1,1,1]=>3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2]=>[4,3,2]=>[3,3,2,1]=>3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,6,2]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,4,2,2,1]=>[4,2,2,1,1]=>[5,3,1,1]=>5
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[8,1,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[8,1,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[6,3,1]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,1,3]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,6,1]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[8,1,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,4,3]=>[4,3,3]=>[3,3,3,1]=>3
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,8]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[6,3,1]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[6,1,3]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,6,3]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,6,1]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[3,1,6]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,0,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,6]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[8,1,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,4,3]=>[4,3,3]=>[3,3,3,1]=>3
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,8]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,6,3]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,6]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,6]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,8]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,8,3]=>[8,3,1]=>[3,2,2,1,1,1,1,1]=>3
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,4,5]=>[5,4,3]=>[3,3,3,2,1]=>3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,4,5]=>[5,4,3]=>[3,3,3,2,1]=>3
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,8,3]=>[8,3,1]=>[3,2,2,1,1,1,1,1]=>3
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,6,5]=>[6,5,1]=>[3,2,2,2,2,1]=>3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,6,5]=>[6,5,1]=>[3,2,2,2,2,1]=>3
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,8,3]=>[8,3,1]=>[3,2,2,1,1,1,1,1]=>3
[1,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[3,8,1]=>[8,3,1]=>[3,2,2,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,6,5]=>[6,5,1]=>[3,2,2,2,2,1]=>3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,6,5]=>[6,5,1]=>[3,2,2,2,2,1]=>3
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,6,1]=>[6,5,1]=>[3,2,2,2,2,1]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,6,1]=>[6,5,1]=>[3,2,2,2,2,1]=>3
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,8,3]=>[8,3,1]=>[3,2,2,1,1,1,1,1]=>3
[1,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[3,8,1]=>[8,3,1]=>[3,2,2,1,1,1,1,1]=>3
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[5,6,1]=>[6,5,1]=>[3,2,2,2,2,1]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[5,6,1]=>[6,5,1]=>[3,2,2,2,2,1]=>3
[1,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[3,8,1]=>[8,3,1]=>[3,2,2,1,1,1,1,1]=>3
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[5,4,3]=>[5,4,3]=>[3,3,3,2,1]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[5,4,3]=>[5,4,3]=>[3,3,3,2,1]=>3
[1,1,0,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[3,8,1]=>[8,3,1]=>[3,2,2,1,1,1,1,1]=>3
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,1,5]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[5,1,2,2]=>[5,2,2,1]=>[4,3,1,1,1]=>4
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,1,2,2]=>[3,2,2,2,1]=>[5,4,1]=>5
[1,0,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,10]=>[10,1]=>[2,1,1,1,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[2,6,1]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,6]=>[6,2,2]=>[3,3,1,1,1,1]=>3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,4,4]=>[4,4,2]=>[3,3,2,2]=>3
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,6,2]=>[6,2,2]=>[3,3,1,1,1,1]=>3
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,6,2]=>[6,2,2]=>[3,3,1,1,1,1]=>3
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,8]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,8]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,8]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[4,2,4]=>[4,4,2]=>[3,3,2,2]=>3
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[4,4,2]=>[4,4,2]=>[3,3,2,2]=>3
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[4,6]=>[6,4]=>[2,2,2,2,1,1]=>2
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[6,2,2]=>[6,2,2]=>[3,3,1,1,1,1]=>3
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[6,4]=>[6,4]=>[2,2,2,2,1,1]=>2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[8,2]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[8,2]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[8,2]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[8,2]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,2,2,4,2]=>[4,2,2,2,2]=>[5,5,1,1]=>5
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,2,4,2,2]=>[4,2,2,2,2]=>[5,5,1,1]=>5
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,2,4,4]=>[4,4,2,2]=>[4,4,2,2]=>4
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,2,2,2]=>[4,2,2,2,2]=>[5,5,1,1]=>5
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,4,2,4]=>[4,4,2,2]=>[4,4,2,2]=>4
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,4,2]=>[4,4,2,2]=>[4,4,2,2]=>4
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,6,2,2]=>[6,2,2,2]=>[4,4,1,1,1,1]=>4
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,6,4]=>[6,4,2]=>[3,3,2,2,1,1]=>3
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[2,6,2,2]=>[6,2,2,2]=>[4,4,1,1,1,1]=>4
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[2,6,4]=>[6,4,2]=>[3,3,2,2,1,1]=>3
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,2,2,2,2]=>[4,2,2,2,2]=>[5,5,1,1]=>5
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[4,2,2,4]=>[4,4,2,2]=>[4,4,2,2]=>4
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[4,2,4,2]=>[4,4,2,2]=>[4,4,2,2]=>4
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,4,2,2]=>[4,4,2,2]=>[4,4,2,2]=>4
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,4,4]=>[4,4,4]=>[3,3,3,3]=>3
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[4,6,2]=>[6,4,2]=>[3,3,2,2,1,1]=>3
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,6,2]=>[6,4,2]=>[3,3,2,2,1,1]=>3
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,2,2,2]=>[6,2,2,2]=>[4,4,1,1,1,1]=>4
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[6,2,4]=>[6,4,2]=>[3,3,2,2,1,1]=>3
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,4,2]=>[6,4,2]=>[3,3,2,2,1,1]=>3
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[6,6]=>[6,6]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[6,6]=>[6,6]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,2,2,2]=>[6,2,2,2]=>[4,4,1,1,1,1]=>4
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[6,2,4]=>[6,4,2]=>[3,3,2,2,1,1]=>3
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,4,2]=>[6,4,2]=>[3,3,2,2,1,1]=>3
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[6,6]=>[6,6]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[6,6]=>[6,6]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,6,2]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,7,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,5,2,1]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,2,1]=>[3,2,2,1,1]=>[5,3,1]=>5
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,4,2,2,1]=>[4,2,2,1,1]=>[5,3,1,1]=>5
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,6,2]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,6,2,1]=>[6,2,1,1]=>[4,2,1,1,1,1]=>4
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,5,3]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,7,2]=>[7,2,1]=>[3,2,1,1,1,1,1]=>3
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,4,1]=>[4,3,1,1]=>[4,2,2,1]=>4
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,5,2,2]=>[5,2,2,1]=>[4,3,1,1,1]=>4
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,4,2,1]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,6,2,1]=>[6,2,1,1]=>[4,2,1,1,1,1]=>4
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[10,1]=>[10,1]=>[2,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[10,1]=>[10,1]=>[2,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,2,4,2]=>[4,2,2,1]=>[4,3,1,1]=>4
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,3]=>[7,3]=>[2,2,2,1,1,1,1]=>2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,1,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,5,1,1]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,3,1,1,2]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,8]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,8]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,8]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[2,8]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,2,6]=>[6,2,1,1]=>[4,2,1,1,1,1]=>4
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,2,6]=>[6,2,1,1]=>[4,2,1,1,1,1]=>4
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,8]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,7,1]=>[7,1,1,1]=>[4,1,1,1,1,1,1]=>4
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,7,1]=>[7,1,1,1]=>[4,1,1,1,1,1,1]=>4
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,5,4]=>[5,4,1]=>[3,2,2,2,1]=>3
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[4,2,4]=>[4,4,2]=>[3,3,2,2]=>3
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,7,1,1]=>[7,1,1,1]=>[4,1,1,1,1,1,1]=>4
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,7,1,1]=>[7,1,1,1]=>[4,1,1,1,1,1,1]=>4
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[8,1,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[6,2,1,1]=>[6,2,1,1]=>[4,2,1,1,1,1]=>4
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[6,2,1,1]=>[6,2,1,1]=>[4,2,1,1,1,1]=>4
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[8,2]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[8,2]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[8,2]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[8,2]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,2,4]=>[6,4,2]=>[3,3,2,2,1,1]=>3
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[6,5,1]=>[6,5,1]=>[3,2,2,2,2,1]=>3
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,2,4]=>[6,4,2]=>[3,3,2,2,1,1]=>3
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[6,5,1]=>[6,5,1]=>[3,2,2,2,2,1]=>3
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,11]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,2]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,4,1,1,1,1]=>[4,2,1,1,1,1]=>[6,2,1,1]=>6
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,7]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,1,1,1,1]=>[3,2,1,1,1,1,1]=>[7,2,1]=>7
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,7]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,2,2,2,1]=>[2,2,2,2,2,1,1]=>[7,5]=>7
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0]=>[8,2]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,6,2]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,8]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,4,4]=>[4,4,1]=>[3,2,2,2]=>3
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,7]=>[7,1,1,1]=>[4,1,1,1,1,1,1]=>4
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,1,4]=>[4,3,1,1]=>[4,2,2,1]=>4
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,6]=>[6,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,1,4]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,5]=>[5,1,1,1,1,1]=>[6,1,1,1,1]=>6
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,6]=>[6,1,1,1,1,1]=>[6,1,1,1,1,1]=>6
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,9]=>[9,1,1]=>[3,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,3]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[4,5]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,7]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,6]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[5,4]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[7,2]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[4,5]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,7]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,6]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,2]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,2,6]=>[6,2,2]=>[3,3,1,1,1,1]=>3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[5,2,2]=>[5,2,2]=>[3,3,1,1,1]=>3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,2,4]=>[4,2,2,2]=>[4,4,1,1]=>4
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[4,4,1]=>[4,4,1]=>[3,2,2,2]=>3
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,8]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,2,2,1]=>[4,2,2,1]=>[4,3,1,1]=>4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[5,2,2,1]=>[5,2,2,1]=>[4,3,1,1,1]=>4
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,1,4]=>[4,2,1,1,1]=>[5,2,1,1]=>5
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,6,2]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,4,2,2]=>[4,2,2,1]=>[4,3,1,1]=>4
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[7,2]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[7,2]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,6,2,1]=>[6,2,1,1]=>[4,2,1,1,1,1]=>4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[5,2,2]=>[5,2,2]=>[3,3,1,1,1]=>3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,4,2,2,1]=>[4,2,2,1,1]=>[5,3,1,1]=>5
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,2,2,1]=>[3,2,2,1,1]=>[5,3,1]=>5
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[3,6]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,1,4]=>[4,3,1,1]=>[4,2,2,1]=>4
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[4,1,4]=>[4,4,1]=>[3,2,2,2]=>3
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,8,2]=>[8,2,1]=>[3,2,1,1,1,1,1,1]=>3
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2,8]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[7,2]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,3]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,1,8]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,1,1,4]=>[4,2,1,1,1,1]=>[6,2,1,1]=>6
[1,1,0,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,8]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,7]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,8]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,7]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,0,1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,1,1]=>[4,3,1,1]=>[4,2,2,1]=>4
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,3]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[7,2]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[7,2]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,7]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,7]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,7]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,7]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,0,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,7]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[4,4,1,1]=>[4,4,1,1]=>[4,2,2,2]=>4
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,5,2]=>[5,2,2,1]=>[4,3,1,1,1]=>4
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[5,4,1]=>[5,4,1]=>[3,2,2,2,1]=>3
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,5,2]=>[5,3,2]=>[3,3,2,1,1]=>3
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[4,1,4,1]=>[4,4,1,1]=>[4,2,2,2]=>4
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[5,4,1]=>[5,4,1]=>[3,2,2,2,1]=>3
[1,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,6]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[4,1,5]=>[5,4,1]=>[3,2,2,2,1]=>3
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[8,2]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[5,5]=>[5,5]=>[2,2,2,2,2]=>2
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[8,2]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[4,6]=>[6,4]=>[2,2,2,2,1,1]=>2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,3]=>[7,3]=>[2,2,2,1,1,1,1]=>2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[6,1,2,1]=>[6,2,1,1]=>[4,2,1,1,1,1]=>4
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0]=>[7,2,1]=>[7,2,1]=>[3,2,1,1,1,1,1]=>3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[6,1,3]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0]=>[8,2]=>[8,2]=>[2,2,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[7,3]=>[7,3]=>[2,2,2,1,1,1,1]=>2
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,1,7]=>[7,2,1]=>[3,2,1,1,1,1,1]=>3
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,7]=>[7,3]=>[2,2,2,1,1,1,1]=>2
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,1,7]=>[7,2,1]=>[3,2,1,1,1,1,1]=>3
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,7]=>[7,3]=>[2,2,2,1,1,1,1]=>2
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,2,1,4]=>[5,4,2,1]=>[4,3,2,2,1]=>4
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,4,4,1]=>[4,4,3,1]=>[4,3,3,2]=>4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[3,1,2,1,5]=>[5,3,2,1,1]=>[5,3,2,1,1]=>5
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,1,3,5]=>[5,3,3,1]=>[4,3,3,1,1]=>4
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[9,2,1]=>[9,2,1]=>[3,2,1,1,1,1,1,1,1]=>3
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,3,4]=>[5,4,3]=>[3,3,3,2,1]=>3
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[9,2,1]=>[9,2,1]=>[3,2,1,1,1,1,1,1,1]=>3
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4]=>[4,4,4]=>[3,3,3,3]=>3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,3,5]=>[5,4,3]=>[3,3,3,2,1]=>3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,1]=>[7,4,1]=>[3,2,2,2,1,1,1]=>3
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,5,4]=>[5,4,3]=>[3,3,3,2,1]=>3
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,1]=>[7,4,1]=>[3,2,2,2,1,1,1]=>3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[7,5]=>[7,5]=>[2,2,2,2,2,1,1]=>2
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[6,6]=>[6,6]=>[2,2,2,2,2,2]=>2
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[6,6]=>[6,6]=>[2,2,2,2,2,2]=>2
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[7,5]=>[7,5]=>[2,2,2,2,2,1,1]=>2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[7,5]=>[7,5]=>[2,2,2,2,2,1,1]=>2
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,6,1]=>[6,5,1]=>[3,2,2,2,2,1]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,6,1]=>[6,5,1]=>[3,2,2,2,2,1]=>3
[1,1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[9,2,1]=>[9,2,1]=>[3,2,1,1,1,1,1,1,1]=>3
[1,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[9,2,1]=>[9,2,1]=>[3,2,1,1,1,1,1,1,1]=>3
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[10,2]=>[10,2]=>[2,2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[4,5]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0]=>[11]=>[11]=>[1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,2,1,3]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[6,2,1]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,6,1]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1,1,1,1,1,1,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>[11,1]=>11
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[5,2,2]=>[5,2,2]=>[3,3,1,1,1]=>3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[5,2,2]=>[5,2,2]=>[3,3,1,1,1]=>3
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,1,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,6,1,1]=>[6,1,1,1]=>[4,1,1,1,1,1]=>4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,1,1,1]=>[7,1,1,1]=>[4,1,1,1,1,1,1]=>4
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,5,1,1,1]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[6,1,1,1,1]=>[6,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1,1]=>[5,1,1,1,1,1]=>[6,1,1,1,1]=>6
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,5,5]=>[5,5,1]=>[3,2,2,2,2]=>3
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[8,1,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[5,3,1]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[2,7,1]=>[7,2,1]=>[3,2,1,1,1,1,1]=>3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3]=>[4,3,2]=>[3,3,2,1]=>3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[7,1,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,2,6]=>[6,2,2]=>[3,3,1,1,1,1]=>3
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,4]=>[4,3,2]=>[3,3,2,1]=>3
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,6,1]=>[6,2,1]=>[3,2,1,1,1,1]=>3
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[6,2,2]=>[6,2,2]=>[3,3,1,1,1,1]=>3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[4,3,2]=>[4,3,2]=>[3,3,2,1]=>3
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,5,2]=>[5,3,2]=>[3,3,2,1,1]=>3
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,4]=>[4,3,3]=>[3,3,3,1]=>3
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,1,1,3,1]=>[3,3,1,1,1,1]=>[6,2,2]=>6
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,1,1,1,3,1]=>[3,2,1,1,1,1,1]=>[7,2,1]=>7
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,1,3,1]=>[3,3,1,1,1]=>[5,2,2]=>5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,1,1,1,2,1]=>[3,2,1,1,1,1,1]=>[7,2,1]=>7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,2,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>[11,1]=>11
[1,0,1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,8]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,7]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,5,3]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,5,3]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,8]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,8]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,3,5]=>[5,3,1,1]=>[4,2,2,1,1]=>4
[1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,6]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,0,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,8]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,7]=>[7,1,1,1]=>[4,1,1,1,1,1,1]=>4
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,7]=>[7,1,1,1]=>[4,1,1,1,1,1,1]=>4
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,2,2,4]=>[4,2,2,1,1]=>[5,3,1,1]=>5
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[3,1,6]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,6]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,2,4]=>[4,3,2,1]=>[4,3,2,1]=>4
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[5,1,4]=>[5,4,1]=>[3,2,2,2,1]=>3
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[5,1,4]=>[5,4,1]=>[3,2,2,2,1]=>3
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,7,1]=>[7,1,1,1]=>[4,1,1,1,1,1,1]=>4
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,8,1]=>[8,1,1]=>[3,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,5,3,1]=>[5,3,1,1]=>[4,2,2,1,1]=>4
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,3,1]=>[3,3,2,1,1]=>[5,3,2]=>5
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,6,1]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,3,3,1]=>[3,3,3,1]=>[4,3,3]=>4
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[5,4,1]=>[5,4,1]=>[3,2,2,2,1]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[5,4,1]=>[5,4,1]=>[3,2,2,2,1]=>3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,6,2,1]=>[6,2,1,1]=>[4,2,1,1,1,1]=>4
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,5,2,1]=>[5,2,1,1,1]=>[5,2,1,1,1]=>5
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,2,1]=>[4,3,2,1]=>[4,3,2,1]=>4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,5,2,1]=>[5,2,1,1,1]=>[5,2,1,1,1]=>5
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,5,5]=>[5,5,1,1]=>[4,2,2,2,2]=>4
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,2,2,2,4]=>[4,2,2,2,1,1]=>[6,4,1,1]=>6
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,3,5]=>[5,3,3,1]=>[4,3,3,1,1]=>4
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,10,1]=>[10,1,1]=>[3,1,1,1,1,1,1,1,1,1]=>3
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,6,3,1]=>[6,3,1,1,1]=>[5,2,2,1,1,1]=>5
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,5,2,3,1]=>[5,3,2,1,1]=>[5,3,2,1,1]=>5
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,2,3,1]=>[3,3,2,2,1,1]=>[6,4,2]=>6
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,8,1]=>[8,3,1]=>[3,2,2,1,1,1,1,1]=>3
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,8,1]=>[8,3,1]=>[3,2,2,1,1,1,1,1]=>3
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,5,3,1]=>[5,3,3,1]=>[4,3,3,1,1]=>4
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[3,3,2,3,1]=>[3,3,3,2,1]=>[5,4,3]=>5
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[5,6,1]=>[6,5,1]=>[3,2,2,2,2,1]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[5,3,3,1]=>[5,3,3,1]=>[4,3,3,1,1]=>4
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[5,6,1]=>[6,5,1]=>[3,2,2,2,2,1]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[5,3,3,1]=>[5,3,3,1]=>[4,3,3,1,1]=>4
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,1]=>[7,4,1]=>[3,2,2,2,1,1,1]=>3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,1]=>[7,4,1]=>[3,2,2,2,1,1,1]=>3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,1]=>[7,4,1]=>[3,2,2,2,1,1,1]=>3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,1]=>[7,4,1]=>[3,2,2,2,1,1,1]=>3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,1]=>[7,4,1]=>[3,2,2,2,1,1,1]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[5,4,2,1]=>[5,4,2,1]=>[4,3,2,2,1]=>4
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[5,4,2,1]=>[5,4,2,1]=>[4,3,2,2,1]=>4
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,5,1]=>[5,1,1,1,1]=>[5,1,1,1,1]=>5
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,4,1]=>[4,1,1,1,1,1,1]=>[7,1,1,1]=>7
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,5,1]=>[5,1,1,1,1,1]=>[6,1,1,1,1]=>6
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,6,1]=>[6,1,1,1,1]=>[5,1,1,1,1,1]=>5
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,4]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0]=>[6,3]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[5,2,3]=>[5,3,2]=>[3,3,2,1,1]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[5,2,3]=>[5,3,2]=>[3,3,2,1,1]=>3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[7,2,3]=>[7,3,2]=>[3,3,2,1,1,1,1]=>3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[7,2,3]=>[7,3,2]=>[3,3,2,1,1,1,1]=>3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[7,2,3]=>[7,3,2]=>[3,3,2,1,1,1,1]=>3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[7,2,3]=>[7,3,2]=>[3,3,2,1,1,1,1]=>3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[7,2,3]=>[7,3,2]=>[3,3,2,1,1,1,1]=>3
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[8,1]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,7,1]=>[7,1,1]=>[3,1,1,1,1,1,1]=>3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[5,2,1,1]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[9,1]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,0,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,3]=>[6,3]=>[2,2,2,1,1,1]=>2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0]=>[7,2]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,7]=>[7,2]=>[2,2,1,1,1,1,1]=>2
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,2,1,1,3]=>[3,2,1,1,1,1]=>[6,2,1]=>6
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[5,4]=>[5,4]=>[2,2,2,2,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,2,2]=>[6,2,2]=>[3,3,1,1,1,1]=>3
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,2,2,2]=>[4,2,2,2]=>[4,4,1,1]=>4
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[11,1]=>[11,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,5,3]=>[5,3,1]=>[3,2,2,1,1]=>3
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,5,4]=>[5,4,1]=>[3,2,2,2,1]=>3
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,4,1,3]=>[4,3,1,1]=>[4,2,2,1]=>4
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,4,1,4]=>[4,4,1,1]=>[4,2,2,2]=>4
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,1,1,3]=>[3,3,1,1,1]=>[5,2,2]=>5
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,4,4]=>[4,4,1]=>[3,2,2,2]=>3
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,1,1,4]=>[4,3,1,1,1]=>[5,2,2,1]=>5
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,1,4]=>[4,3,1,1]=>[4,2,2,1]=>4
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,1,1,4]=>[4,2,1,1,1,1]=>[6,2,1,1]=>6
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[5,1,2,1]=>[5,2,1,1]=>[4,2,1,1,1]=>4
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,2,5]=>[5,2,2,1]=>[4,3,1,1,1]=>4
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,2,4,3]=>[4,3,2,1]=>[4,3,2,1]=>4
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,2,7]=>[7,2,1]=>[3,2,1,1,1,1,1]=>3
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,2,7]=>[7,2,1]=>[3,2,1,1,1,1,1]=>3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,4,2,3]=>[4,3,2,1]=>[4,3,2,1]=>4
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5]=>[5,4,1]=>[3,2,2,2,1]=>3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,6,3]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,6,3]=>[6,3,1]=>[3,2,2,1,1,1]=>3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,2,3]=>[3,3,2,2]=>[4,4,2]=>4
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,2,5]=>[5,3,2]=>[3,3,2,1,1]=>3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,3]=>[4,3,3]=>[3,3,3,1]=>3
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[10]=>[10]=>[1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,2,2,3]=>[3,2,2,2,2,1]=>[6,5,1]=>6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,2,2,5]=>[5,2,2,2,1]=>[5,4,1,1,1]=>5
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,2,2,4,3]=>[4,3,2,2,1]=>[5,4,2,1]=>5
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,2,3]=>[4,3,2,2,1]=>[5,4,2,1]=>5
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,2,9]=>[9,2,1]=>[3,2,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,2,9]=>[9,2,1]=>[3,2,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,2,9]=>[9,2,1]=>[3,2,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,2,9]=>[9,2,1]=>[3,2,1,1,1,1,1,1,1]=>3
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,2,9]=>[9,2,1]=>[3,2,1,1,1,1,1,1,1]=>3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,4,2,2,3]=>[4,3,2,2,1]=>[5,4,2,1]=>5
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,4,4,3]=>[4,4,3,1]=>[4,3,3,2]=>4
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,7]=>[7,4,1]=>[3,2,2,2,1,1,1]=>3
[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,4,7]=>[7,4,1]=>[3,2,2,2,1,1,1]=>3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,6,5]=>[6,5,1]=>[3,2,2,2,2,1]=>3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,6,5]=>[6,5,1]=>[3,2,2,2,2,1]=>3
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,8,3]=>[8,3,1]=>[3,2,2,1,1,1,1,1]=>3
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,8,3]=>[8,3,1]=>[3,2,2,1,1,1,1,1]=>3
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,8,3]=>[8,3,1]=>[3,2,2,1,1,1,1,1]=>3
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,8,3]=>[8,3,1]=>[3,2,2,1,1,1,1,1]=>3
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,8,3]=>[8,3,1]=>[3,2,2,1,1,1,1,1]=>3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,2,2,3]=>[3,3,2,2,2]=>[5,5,2]=>5
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,2,4,3]=>[4,3,3,2]=>[4,4,3,1]=>4
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,2,7]=>[7,3,2]=>[3,3,2,1,1,1,1]=>3
[1,1,0,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,2,7]=>[7,3,2]=>[3,3,2,1,1,1,1]=>3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,4,2,3]=>[4,3,3,2]=>[4,4,3,1]=>4
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,4,5]=>[5,4,3]=>[3,3,3,2,1]=>3
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[3,6,3]=>[6,3,3]=>[3,3,3,1,1,1]=>3
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[3,6,3]=>[6,3,3]=>[3,3,3,1,1,1]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[5,2,2,3]=>[5,3,2,2]=>[4,4,2,1,1]=>4
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[5,2,5]=>[5,5,2]=>[3,3,2,2,2]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[5,4,3]=>[5,4,3]=>[3,3,3,2,1]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[5,2,2,3]=>[5,3,2,2]=>[4,4,2,1,1]=>4
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[5,2,5]=>[5,5,2]=>[3,3,2,2,2]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[5,4,3]=>[5,4,3]=>[3,3,3,2,1]=>3
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[12]=>[12]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,9]=>[9,1]=>[2,1,1,1,1,1,1,1,1]=>2
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,8]=>[8,1]=>[2,1,1,1,1,1,1,1]=>2
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Description
The largest part of an integer partition.
Map
touch composition
Description
Sends a Dyck path to its touch composition given by the composition of lengths of its touch points.
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.
Map
to partition
Description
Sends a composition to the partition obtained by sorting the entries.
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