Identifier
-
Mp00100:
Dyck paths
—touch composition⟶
Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
St000228: Integer partitions ⟶ ℤ
Values
=>
Cc0005;cc-rep-0
Cc0002;cc-rep
[1,0]=>[1]=>[1]=>[1]=>1
[1,0,1,0]=>[1,1]=>[2]=>[2]=>2
[1,1,0,0]=>[2]=>[1]=>[1]=>1
[1,0,1,0,1,0]=>[1,1,1]=>[3]=>[3]=>3
[1,0,1,1,0,0]=>[1,2]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,0]=>[2,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,0]=>[3]=>[1]=>[1]=>1
[1,1,1,0,0,0]=>[3]=>[1]=>[1]=>1
[1,0,1,0,1,0,1,0]=>[1,1,1,1]=>[4]=>[4]=>4
[1,0,1,0,1,1,0,0]=>[1,1,2]=>[2,1]=>[2,1]=>3
[1,0,1,1,0,0,1,0]=>[1,2,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,0,0]=>[1,3]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,0,0]=>[1,3]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,0,1,0]=>[2,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,0,1,1,0,0]=>[2,2]=>[2]=>[2]=>2
[1,1,0,1,0,0,1,0]=>[3,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,0]=>[4]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,0]=>[4]=>[1]=>[1]=>1
[1,1,1,0,0,0,1,0]=>[3,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,0,0]=>[4]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,0]=>[4]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,0]=>[4]=>[1]=>[1]=>1
[1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1]=>[5]=>[5]=>5
[1,0,1,0,1,0,1,1,0,0]=>[1,1,1,2]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,1,0,0,1,0]=>[1,1,2,1]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,0,1,0,0]=>[1,1,3]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,0,0,0]=>[1,1,3]=>[2,1]=>[2,1]=>3
[1,0,1,1,0,0,1,0,1,0]=>[1,2,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,0,0,1,1,0,0]=>[1,2,2]=>[1,2]=>[2,1]=>3
[1,0,1,1,0,1,0,0,1,0]=>[1,3,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,0,1,0,0]=>[1,4]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,0,0,0]=>[1,4]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,0,0,1,0]=>[1,3,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,0,1,0,0]=>[1,4]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,0,0,0]=>[1,4]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,0,0,0]=>[1,4]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,0,1,0,1,0]=>[2,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,0,0,1,0,1,1,0,0]=>[2,1,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,0,0,1,0]=>[2,2,1]=>[2,1]=>[2,1]=>3
[1,1,0,0,1,1,0,1,0,0]=>[2,3]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,0,0,0]=>[2,3]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,0,1,0,1,0]=>[3,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,0,0,1,1,0,0]=>[3,2]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,0,1,0]=>[4,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,1,0,0]=>[5]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,0,0]=>[5]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,0,1,0]=>[4,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,0,1,0,0]=>[5]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,0,0]=>[5]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,0,0]=>[5]=>[1]=>[1]=>1
[1,1,1,0,0,0,1,0,1,0]=>[3,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,0,0,0,1,1,0,0]=>[3,2]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,0,0,1,0]=>[4,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,0,1,0,0]=>[5]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,0,0]=>[5]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,0,1,0]=>[4,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,0,1,0,0]=>[5]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,0,0]=>[5]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,0,0]=>[5]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,0,1,0]=>[4,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,0,1,0,0]=>[5]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,0,0]=>[5]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,0,0]=>[5]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,0,0]=>[5]=>[1]=>[1]=>1
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1]=>[6]=>[6]=>6
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,2]=>[4,1]=>[4,1]=>5
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,2,1]=>[3,1,1]=>[3,1,1]=>5
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,3]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,3]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,2,1,1]=>[2,1,2]=>[2,2,1]=>5
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,2,2]=>[2,2]=>[2,2]=>4
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,3,1]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,4]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,4]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,3,1]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,4]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,4]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,4]=>[2,1]=>[2,1]=>3
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1]=>[1,1,3]=>[3,1,1]=>5
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,1,2]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,1]=>[1,2,1]=>[2,1,1]=>4
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,3]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,2]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,4,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,5]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,5]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,4,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,5]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,5]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,5]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,5]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,5]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,5]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,5]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,5]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,4,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,5]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,1,1,1]=>[1,4]=>[4,1]=>5
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,1,2]=>[1,2,1]=>[2,1,1]=>4
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,2,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,1,1]=>[2,2]=>[2,2]=>4
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,2,2]=>[3]=>[3]=>3
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,4]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,4]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,4]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,0,1,0,0,1,0,1,1,0,0]=>[3,1,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,0,1,1,0,0,1,0]=>[3,2,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,0,1,1,0,1,0,0]=>[3,3]=>[2]=>[2]=>2
[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,3]=>[2]=>[2]=>2
[1,1,0,1,0,1,0,0,1,0,1,0]=>[4,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,0,1,0,0,1,1,0,0]=>[4,2]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,1,0,0,1,0]=>[5,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,0]=>[6]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,0,0,0]=>[6]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,0,0,1,0]=>[5,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,1,0,0,1,0,0]=>[6]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,1,0,0,0]=>[6]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,0,0,0,0]=>[6]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,0,1,0,1,0]=>[4,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,1,0,0,0,1,1,0,0]=>[4,2]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,0,1,0,0,1,0]=>[5,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,0,1,0,1,0,0]=>[6]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,0,0,0]=>[6]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,0,0,1,0]=>[5,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,1,0,0,1,0,0]=>[6]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,1,0,0,0]=>[6]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,0,0,0,0]=>[6]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,0,0,1,0]=>[5,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,1,0,0,0,1,0,0]=>[6]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,1,0,0,0]=>[6]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,0,0,0,0]=>[6]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,0,0,0,0]=>[6]=>[1]=>[1]=>1
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,3]=>[2]=>[2]=>2
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3]=>[2]=>[2]=>2
[1,1,1,0,0,1,0,0,1,0,1,0]=>[4,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,0,0,1,0,0,1,1,0,0]=>[4,2]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,0,1,0,0,1,0]=>[5,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,0,1,0,1,0,0]=>[6]=>[1]=>[1]=>1
[1,1,1,0,0,1,0,1,1,0,0,0]=>[6]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,0,0,1,0]=>[5,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,1,0,0,1,0,0]=>[6]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,1,0,0,0]=>[6]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,0,0,0,0]=>[6]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,2]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,0,1,0,0,1,0]=>[5,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,0,1,0,1,0,0]=>[6]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,1,1,0,0,0]=>[6]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,0,0,1,0]=>[5,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,1,0,0,1,0,0]=>[6]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,0,0,0]=>[6]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,1,0,0,0,0]=>[6]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,1,0,0,0,1,0,0]=>[6]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,1,0,0,0]=>[6]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,0,0,0,0]=>[6]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,0,0,0,0]=>[6]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,2]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,0,1,0,0,1,0]=>[5,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,0,1,0,1,0,0]=>[6]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,1,0,0,0]=>[6]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,1,0,0,1,0,0]=>[6]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,0,0,0]=>[6]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,0,0,0,0]=>[6]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,0,0,0,1,0,0]=>[6]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,1,0,0,0]=>[6]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,0,0,0]=>[6]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,0,0,0,0,0]=>[6]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,0,0,0,1,0,0]=>[6]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,1,0,0,0]=>[6]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,0,0,0,0]=>[6]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,0,0,0,0]=>[6]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6]=>[1]=>[1]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1]=>[7]=>[7]=>7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,2]=>[5,1]=>[5,1]=>6
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,2,1]=>[4,1,1]=>[4,1,1]=>6
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,3]=>[4,1]=>[4,1]=>5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,3]=>[4,1]=>[4,1]=>5
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,2,1,1]=>[3,1,2]=>[3,2,1]=>6
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,2,2]=>[3,2]=>[3,2]=>5
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,3,1]=>[3,1,1]=>[3,1,1]=>5
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,4]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,4]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,3,1]=>[3,1,1]=>[3,1,1]=>5
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,4]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,4]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,4]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,2,1,1,1]=>[2,1,3]=>[3,2,1]=>6
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,2,1,2]=>[2,1,1,1]=>[2,1,1,1]=>5
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,1]=>[2,2,1]=>[2,2,1]=>5
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,3]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,3]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,3,1,1]=>[2,1,2]=>[2,2,1]=>5
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,3,2]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,4,1]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,5]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,5]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,4,1]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,5]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,5]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,5]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,3,1,1]=>[2,1,2]=>[2,2,1]=>5
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,3,2]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,4,1]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,5]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,5]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,4,1]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,5]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,5]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,5]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,5]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,5]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,5]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,5]=>[2,1]=>[2,1]=>3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1]=>[1,1,4]=>[4,1,1]=>6
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,2]=>[1,1,2,1]=>[2,1,1,1]=>5
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,2,1]=>[1,1,1,1,1]=>[1,1,1,1,1]=>5
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,3]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,1,3]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,2,1,1]=>[1,2,2]=>[2,2,1]=>5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2]=>[1,3]=>[3,1]=>4
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,3,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,4]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,4]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,4]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,4]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,1,1,1]=>[1,1,3]=>[3,1,1]=>5
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,1,2]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,2,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,3]=>[1,2]=>[2,1]=>3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,3]=>[1,2]=>[2,1]=>3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,4,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,4,2]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,4,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,4,2]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,1,1,1]=>[1,1,3]=>[3,1,1]=>5
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,1,2]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,3]=>[1,2]=>[2,1]=>3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,3]=>[1,2]=>[2,1]=>3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,2]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,4,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,6]=>[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]=>[1,5]=>[5,1]=>6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,2]=>[1,3,1]=>[3,1,1]=>5
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]=>[1,2,1,1]=>[2,1,1,1]=>5
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,3]=>[1,2,1]=>[2,1,1]=>4
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,3]=>[1,2,1]=>[2,1,1]=>4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]=>[1,1,1,2]=>[2,1,1,1]=>5
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,2,2]=>[1,1,2]=>[2,1,1]=>4
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,4]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,4]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,4]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,4]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]=>[2,3]=>[3,2]=>5
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,1,2]=>[2,1,1]=>[2,1,1]=>4
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,1]=>[3,1]=>[3,1]=>4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,3]=>[2,1]=>[2,1]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,3]=>[2,1]=>[2,1]=>3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,3,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,4,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,5]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,5]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,4,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,5]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,5]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,5]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,4,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,5]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,5]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,4,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,5]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,5]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,5]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,5]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,5]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,5]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1]=>[1,4]=>[4,1]=>5
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,2]=>[1,2,1]=>[2,1,1]=>4
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,3]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]=>[1,2]=>[2,1]=>3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,3,1]=>[2,1]=>[2,1]=>3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,4]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,4]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]=>[2,1]=>[2,1]=>3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,4]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,4]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,4]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[4,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[4,1,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[4,2,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[4,3]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[4,3]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[5,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[5,2]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[5,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[5,2]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[4,1,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[4,2,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[4,3]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,3]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[5,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[5,2]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[5,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[5,2]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[5,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[5,2]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,1,1,1]=>[1,4]=>[4,1]=>5
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,1,2]=>[1,2,1]=>[2,1,1]=>4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,3]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,3]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,2]=>[1,2]=>[2,1]=>3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,3,1]=>[2,1]=>[2,1]=>3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,4]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,4]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]=>[2,1]=>[2,1]=>3
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,4]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[4,1,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,2,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,3]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,3]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[5,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[5,2]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[5,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[5,2]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,1,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,2,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,3]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,3]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[5,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[5,2]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[5,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[5,2]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[5,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,2]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,2,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[5,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,2]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,2]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,2]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,2]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[7]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7]=>[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]=>[8]=>[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]=>[6,1]=>[6,1]=>7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,2,1]=>[5,1,1]=>[5,1,1]=>7
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,3]=>[5,1]=>[5,1]=>6
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,3]=>[5,1]=>[5,1]=>6
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,2,1,1]=>[4,1,2]=>[4,2,1]=>7
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,2,2]=>[4,2]=>[4,2]=>6
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,3,1]=>[4,1,1]=>[4,1,1]=>6
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,4]=>[4,1]=>[4,1]=>5
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,4]=>[4,1]=>[4,1]=>5
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,3,1]=>[4,1,1]=>[4,1,1]=>6
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,4]=>[4,1]=>[4,1]=>5
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,4]=>[4,1]=>[4,1]=>5
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,4]=>[4,1]=>[4,1]=>5
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,2,1,1,1]=>[3,1,3]=>[3,3,1]=>7
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,2,1,2]=>[3,1,1,1]=>[3,1,1,1]=>6
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,2,2,1]=>[3,2,1]=>[3,2,1]=>6
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,2,3]=>[3,1,1]=>[3,1,1]=>5
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,2,3]=>[3,1,1]=>[3,1,1]=>5
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,3,1,1]=>[3,1,2]=>[3,2,1]=>6
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,3,2]=>[3,1,1]=>[3,1,1]=>5
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,4,1]=>[3,1,1]=>[3,1,1]=>5
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,5]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,5]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,4,1]=>[3,1,1]=>[3,1,1]=>5
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,5]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,5]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,5]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,3,1,1]=>[3,1,2]=>[3,2,1]=>6
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,3,2]=>[3,1,1]=>[3,1,1]=>5
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,4,1]=>[3,1,1]=>[3,1,1]=>5
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,5]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,5]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,4,1]=>[3,1,1]=>[3,1,1]=>5
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,5]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,5]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,5]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,4,1]=>[3,1,1]=>[3,1,1]=>5
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,5]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,5]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,5]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,5]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,2,1,1,1,1]=>[2,1,4]=>[4,2,1]=>7
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,2,1,1,2]=>[2,1,2,1]=>[2,2,1,1]=>6
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,2,1,2,1]=>[2,1,1,1,1]=>[2,1,1,1,1]=>6
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,2,1,3]=>[2,1,1,1]=>[2,1,1,1]=>5
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,2,1,3]=>[2,1,1,1]=>[2,1,1,1]=>5
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,2,2,1,1]=>[2,2,2]=>[2,2,2]=>6
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,2,2,2]=>[2,3]=>[3,2]=>5
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,2,3,1]=>[2,1,1,1]=>[2,1,1,1]=>5
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,2,4]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,2,4]=>[2,1,1]=>[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]=>[2,1,1,1]=>[2,1,1,1]=>5
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,2,4]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,2,4]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,2,4]=>[2,1,1]=>[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]=>[2,1,3]=>[3,2,1]=>6
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,3,1,2]=>[2,1,1,1]=>[2,1,1,1]=>5
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,3,2,1]=>[2,1,1,1]=>[2,1,1,1]=>5
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,3,3]=>[2,2]=>[2,2]=>4
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,3,3]=>[2,2]=>[2,2]=>4
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,4,1,1]=>[2,1,2]=>[2,2,1]=>5
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,4,2]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,5,1]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,5,1]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,4,1,1]=>[2,1,2]=>[2,2,1]=>5
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,4,2]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,5,1]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,5,1]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,5,1]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,3,1,1,1]=>[2,1,3]=>[3,2,1]=>6
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,3,1,2]=>[2,1,1,1]=>[2,1,1,1]=>5
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,3,2,1]=>[2,1,1,1]=>[2,1,1,1]=>5
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,3,3]=>[2,2]=>[2,2]=>4
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,3,3]=>[2,2]=>[2,2]=>4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,4,1,1]=>[2,1,2]=>[2,2,1]=>5
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,4,2]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,5,1]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,5,1]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,4,1,1]=>[2,1,2]=>[2,2,1]=>5
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,4,2]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,5,1]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,5,1]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,5,1]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,4,1,1]=>[2,1,2]=>[2,2,1]=>5
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,4,2]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,5,1]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,5,1]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,5,1]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,5,1]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,6]=>[2,1]=>[2,1]=>3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1,1]=>[1,1,5]=>[5,1,1]=>7
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,1,1,1,2]=>[1,1,3,1]=>[3,1,1,1]=>6
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,1,1,2,1]=>[1,1,2,1,1]=>[2,1,1,1,1]=>6
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,1,1,3]=>[1,1,2,1]=>[2,1,1,1]=>5
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,1,1,3]=>[1,1,2,1]=>[2,1,1,1]=>5
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,1,2,1,1]=>[1,1,1,1,2]=>[2,1,1,1,1]=>6
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,1,2,2]=>[1,1,1,2]=>[2,1,1,1]=>5
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,1,3,1]=>[1,1,1,1,1]=>[1,1,1,1,1]=>5
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,1,4]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,4]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,1,3,1]=>[1,1,1,1,1]=>[1,1,1,1,1]=>5
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,1,4]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,1,4]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,1,4]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,2,1,1,1]=>[1,2,3]=>[3,2,1]=>6
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,2,1,2]=>[1,2,1,1]=>[2,1,1,1]=>5
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,2,1]=>[1,3,1]=>[3,1,1]=>5
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,3]=>[1,2,1]=>[2,1,1]=>4
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,2,3]=>[1,2,1]=>[2,1,1]=>4
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,3,1,1]=>[1,1,1,2]=>[2,1,1,1]=>5
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,3,2]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,5]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,5]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,5]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,5]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,5]=>[1,1,1]=>[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]=>[1,1,1,2]=>[2,1,1,1]=>5
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,2]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,4,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,4,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,5]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,5]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,5]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,5]=>[1,1,1]=>[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]=>[1,1,4]=>[4,1,1]=>6
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,1,1,2]=>[1,1,2,1]=>[2,1,1,1]=>5
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,1,2,1]=>[1,1,1,1,1]=>[1,1,1,1,1]=>5
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,1,3]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,1,1]=>[1,1,1,2]=>[2,1,1,1]=>5
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,3,1]=>[1,2,1]=>[2,1,1]=>4
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,4]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,4]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,3,1]=>[1,2,1]=>[2,1,1]=>4
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,4]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,4]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,4,1,1,1]=>[1,1,3]=>[3,1,1]=>5
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,4,1,2]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,4,2,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,4,3]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,4,3]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,5,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,5,2]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,7]=>[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]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,5,2]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,7]=>[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]=>[1,1,3]=>[3,1,1]=>5
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,2,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,5,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,5,2]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,7]=>[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]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,5,2]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,7]=>[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]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,2]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,7]=>[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]=>[1,1,4]=>[4,1,1]=>6
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,3,1,1,2]=>[1,1,2,1]=>[2,1,1,1]=>5
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,3,1,2,1]=>[1,1,1,1,1]=>[1,1,1,1,1]=>5
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,3,1,3]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,3,1,3]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,1,1]=>[1,1,1,2]=>[2,1,1,1]=>5
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,2]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,3,3,1]=>[1,2,1]=>[2,1,1]=>4
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,3,4]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,3,4]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,3,3,1]=>[1,2,1]=>[2,1,1]=>4
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,3,4]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,3,4]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,3,4]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,4,1,1,1]=>[1,1,3]=>[3,1,1]=>5
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,4,1,2]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,2,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,4,3]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,4,3]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,5,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,5,2]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,7]=>[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]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,5,2]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,7]=>[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]=>[1,1,3]=>[3,1,1]=>5
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,4,2,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,4,3]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,4,3]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,5,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,5,2]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,7]=>[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]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,5,2]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,7]=>[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]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,5,2]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,7]=>[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]=>[1,1,3]=>[3,1,1]=>5
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,4,1,2]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,4,2,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,4,3]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,4,3]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,5,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,5,2]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,7]=>[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]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,5,2]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,7]=>[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]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,5,2]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,7]=>[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]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,5,2]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,7]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,7]=>[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]=>[1,6]=>[6,1]=>7
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,1,1,1,2]=>[1,4,1]=>[4,1,1]=>6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,1,2,1]=>[1,3,1,1]=>[3,1,1,1]=>6
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,1,3]=>[1,3,1]=>[3,1,1]=>5
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,1,1,3]=>[1,3,1]=>[3,1,1]=>5
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,1,2,1,1]=>[1,2,1,2]=>[2,2,1,1]=>6
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,1,2,2]=>[1,2,2]=>[2,2,1]=>5
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,1,3,1]=>[1,2,1,1]=>[2,1,1,1]=>5
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,4]=>[1,2,1]=>[2,1,1]=>4
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,1,4]=>[1,2,1]=>[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]=>[1,2,1,1]=>[2,1,1,1]=>5
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,4]=>[1,2,1]=>[2,1,1]=>4
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,1,4]=>[1,2,1]=>[2,1,1]=>4
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,4]=>[1,2,1]=>[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]=>[1,1,1,3]=>[3,1,1,1]=>6
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,2,1,2]=>[1,1,1,1,1]=>[1,1,1,1,1]=>5
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,2,2,1]=>[1,1,2,1]=>[2,1,1,1]=>5
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,2,3]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,2,3]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,3,1,1]=>[1,1,1,2]=>[2,1,1,1]=>5
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,3,2]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,5]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,5]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,5]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,5]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,5]=>[1,1,1]=>[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]=>[1,1,1,2]=>[2,1,1,1]=>5
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,2]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,4,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,5]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,5]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,5]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,5]=>[1,1,1]=>[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]=>[2,4]=>[4,2]=>6
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,2,1,1,2]=>[2,2,1]=>[2,2,1]=>5
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,2,1,2,1]=>[2,1,1,1]=>[2,1,1,1]=>5
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,2,1,3]=>[2,1,1]=>[2,1,1]=>4
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,2,1,3]=>[2,1,1]=>[2,1,1]=>4
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,2,1,1]=>[3,2]=>[3,2]=>5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[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]=>[2,1,1]=>[2,1,1]=>4
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,4]=>[2,1]=>[2,1]=>3
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,4]=>[2,1]=>[2,1]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,2,3,1]=>[2,1,1]=>[2,1,1]=>4
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,4]=>[2,1]=>[2,1]=>3
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,2,4]=>[2,1]=>[2,1]=>3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,4]=>[2,1]=>[2,1]=>3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,1,1]=>[1,1,3]=>[3,1,1]=>5
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,2]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,2,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,3]=>[1,2]=>[2,1]=>3
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,3]=>[1,2]=>[2,1]=>3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,4,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,4,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,6]=>[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]=>[1,1,2]=>[2,1,1]=>4
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6]=>[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]=>[1,1,3]=>[3,1,1]=>5
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,2]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,2,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,3]=>[1,2]=>[2,1]=>3
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,3]=>[1,2]=>[2,1]=>3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,6]=>[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]=>[1,1,2]=>[2,1,1]=>4
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,6]=>[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]=>[1,1,2]=>[2,1,1]=>4
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,6]=>[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]=>[1,5]=>[5,1]=>6
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>[1,3,1]=>[3,1,1]=>5
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>[1,2,1,1]=>[2,1,1,1]=>5
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,1,3]=>[1,2,1]=>[2,1,1]=>4
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]=>[1,2,1]=>[2,1,1]=>4
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]=>[1,1,1,2]=>[2,1,1,1]=>5
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]=>[1,1,2]=>[2,1,1]=>4
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,3,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,4]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,4]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,1,4]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,4]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,3]=>[3,1,1]=>5
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,2,1,2]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,2,1]=>[1,2,1]=>[2,1,1]=>4
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,3]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,3]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,3,1,1]=>[2,2]=>[2,2]=>4
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,3,2]=>[2,1]=>[2,1]=>3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,4,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,5]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,5]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,4,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,5]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,5]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,5]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,3,1,1]=>[2,2]=>[2,2]=>4
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,3,2]=>[2,1]=>[2,1]=>3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,4,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,5]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,5]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,4,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,5]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,5]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,5]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,4,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,5]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,5]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,5]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>[1,4]=>[4,1]=>5
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,2]=>[1,2,1]=>[2,1,1]=>4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[4,1,3]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[4,2,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]=>[1,2]=>[2,1]=>3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[4,3,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[4,4]=>[2]=>[2]=>2
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[4,4]=>[2]=>[2]=>2
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,4]=>[2]=>[2]=>2
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[4,4]=>[2]=>[2]=>2
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4]=>[2]=>[2]=>2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[5,1,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[5,2,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[5,3]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,3]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[5,1,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[5,3]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,3]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>[1,4]=>[4,1]=>5
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,2]=>[1,2,1]=>[2,1,1]=>4
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,3]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,2,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]=>[1,2]=>[2,1]=>3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,4]=>[2]=>[2]=>2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,4]=>[2]=>[2]=>2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,4]=>[2]=>[2]=>2
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,4]=>[2]=>[2]=>2
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]=>[2]=>[2]=>2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[5,1,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[5,2,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[5,3]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,3]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[5,1,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[5,3]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,3]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,1,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,3]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,3]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[8]=>[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]=>[1,5]=>[5,1]=>6
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,1,1,2]=>[1,3,1]=>[3,1,1]=>5
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,1,2,1]=>[1,2,1,1]=>[2,1,1,1]=>5
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,1,3]=>[1,2,1]=>[2,1,1]=>4
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,3]=>[1,2,1]=>[2,1,1]=>4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,2,1,1]=>[1,1,1,2]=>[2,1,1,1]=>5
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,2,2]=>[1,1,2]=>[2,1,1]=>4
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,3,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,4]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,4]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,3,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,1,4]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,4]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,2,1,1,1]=>[1,1,3]=>[3,1,1]=>5
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,2,1,2]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,2,1]=>[1,2,1]=>[2,1,1]=>4
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,2,3]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,3]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,3,1,1]=>[2,2]=>[2,2]=>4
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,3,2]=>[2,1]=>[2,1]=>3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,4,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,5]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,5]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,4,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,5]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,5]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,5]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,3,1,1]=>[2,2]=>[2,2]=>4
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,3,2]=>[2,1]=>[2,1]=>3
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,4,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,5]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,5]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,4,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,5]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,5]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,5]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,4,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,5]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,5]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,5]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>[1,4]=>[4,1]=>5
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,2]=>[1,2,1]=>[2,1,1]=>4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[4,1,3]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[4,2,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]=>[1,2]=>[2,1]=>3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[4,3,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[4,4]=>[2]=>[2]=>2
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[4,4]=>[2]=>[2]=>2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,4]=>[2]=>[2]=>2
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[4,4]=>[2]=>[2]=>2
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4]=>[2]=>[2]=>2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[5,1,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[5,2,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[5,3]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,3]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[5,1,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[5,3]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,3]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>[1,4]=>[4,1]=>5
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,2]=>[1,2,1]=>[2,1,1]=>4
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,3]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,2,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]=>[1,2]=>[2,1]=>3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,4]=>[2]=>[2]=>2
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,4]=>[2]=>[2]=>2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,4]=>[2]=>[2]=>2
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,4]=>[2]=>[2]=>2
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]=>[2]=>[2]=>2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[5,1,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[5,2,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[5,3]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,3]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[5,1,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[5,3]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,3]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,1,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,3]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,3]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,1,1,1]=>[1,4]=>[4,1]=>5
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,1,2]=>[1,2,1]=>[2,1,1]=>4
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,3]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,3]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,2,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,2,2]=>[1,2]=>[2,1]=>3
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,4]=>[2]=>[2]=>2
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,4]=>[2]=>[2]=>2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,4]=>[2]=>[2]=>2
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,4]=>[2]=>[2]=>2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4]=>[2]=>[2]=>2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[5,1,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[5,2,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[5,3]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[5,3]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[5,1,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[5,3]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,3]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[5,1,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[5,3]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,3]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,1,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,2,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,3]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,3]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,2]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,1]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,1]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,2]=>[2,1]=>3
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[8,1]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[2,1]=>[2,1]=>3
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,9]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,2]=>[2,1]=>3
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0,1,0]=>[8,1]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[2,1]=>[2,1]=>3
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,8]=>[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]=>[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]=>[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]=>[1,2]=>[2,1]=>3
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,8,1]=>[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]=>[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]=>[1,2]=>[2,1]=>3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0]=>[8,1]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[2,1]=>[2,1]=>3
[1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,8]=>[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]=>[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]=>[2,1]=>[2,1]=>3
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,8]=>[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]=>[2,1]=>[2,1]=>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]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[9]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[9]=>[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]=>[9]=>[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]=>[7,1]=>[7,1]=>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]=>[6,1]=>[6,1]=>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]=>[5,1]=>[5,1]=>6
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,5]=>[4,1]=>[4,1]=>5
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,6]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,7]=>[2,1]=>[2,1]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,8]=>[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]=>[10]=>[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]=>[8,1]=>[8,1]=>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]=>[6,1]=>[6,1]=>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]=>[7,1]=>[7,1]=>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]=>[5,1]=>[5,1]=>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]=>[6,1]=>[6,1]=>7
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,5]=>[4,1]=>[4,1]=>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]=>[5,1]=>6
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,6]=>[3,1]=>[3,1]=>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]=>[4,1]=>[4,1]=>5
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,7]=>[2,1]=>[2,1]=>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]=>[3,1]=>[3,1]=>4
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,8]=>[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]=>[2,1]=>[2,1]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,9]=>[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]=>[1]=>[1]=>1
[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]=>[9,1]=>[9,1]=>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]=>[7,1]=>[7,1]=>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]=>[8,1]=>[8,1]=>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]=>[5,1]=>[5,1]=>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]=>[6,1]=>[6,1]=>7
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,5]=>[4,1]=>[4,1]=>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]=>[5,1]=>[5,1]=>6
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,6]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,5]=>[4,1]=>[4,1]=>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]=>[5,1]=>[5,1]=>6
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,7]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,6]=>[3,1]=>[3,1]=>4
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,8]=>[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]=>[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]=>[2,1]=>[2,1]=>3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10]=>[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]=>[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]=>[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]=>[8,1]=>[8,1]=>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]=>[6,1]=>[6,1]=>7
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,5]=>[4,1]=>[4,1]=>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]=>[5,1]=>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]=>[6,1]=>[6,1]=>7
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,6]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,5]=>[4,1]=>[4,1]=>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]=>[4,1]=>[4,1]=>5
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,7]=>[2,1]=>[2,1]=>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]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,5]=>[4,1]=>[4,1]=>5
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,8]=>[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]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,8]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,6]=>[3,1]=>[3,1]=>4
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,9]=>[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]=>[2,1]=>[2,1]=>3
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,8]=>[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]=>[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]=>[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]=>[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]=>[5,1]=>6
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,6]=>[3,1]=>[3,1]=>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]=>[5,1]=>6
[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,6]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,5]=>[4,1]=>[4,1]=>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]=>[5,1]=>6
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,8]=>[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]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,7]=>[2,1]=>[2,1]=>3
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,7]=>[2,1]=>[2,1]=>3
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[11]=>[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]=>[4,1]=>[4,1]=>5
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,7]=>[2,1]=>[2,1]=>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]=>[4,1]=>[4,1]=>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]=>[5,1]=>6
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,8]=>[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]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,6]=>[3,1]=>[3,1]=>4
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,8]=>[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]=>[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]=>[2,1]=>[2,1]=>3
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,8]=>[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]=>[3,1]=>[3,1]=>4
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,8]=>[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]=>[3,1]=>[3,1]=>4
[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,8]=>[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]=>[3,1]=>[3,1]=>4
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,7]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,6]=>[3,1]=>[3,1]=>4
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,8]=>[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]=>[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]=>[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]=>[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]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,8]=>[2,1]=>[2,1]=>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]=>[4,1]=>[4,1]=>5
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[10]=>[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]=>[4,1]=>[4,1]=>5
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[11]=>[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]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,7]=>[2,1]=>[2,1]=>3
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[10]=>[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]=>[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]=>[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]=>[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]=>[2,1]=>[2,1]=>3
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,9]=>[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]=>[6,1,1]=>[6,1,1]=>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]=>[5,1,2]=>[5,2,1]=>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]=>[5,2]=>[5,2]=>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]=>[5,1,1]=>[5,1,1]=>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]=>[4,1,3]=>[4,3,1]=>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]=>[4,1,1,1]=>[4,1,1,1]=>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]=>[4,2,1]=>[4,2,1]=>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]=>[4,1,1]=>[4,1,1]=>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]=>[4,1,2]=>[4,2,1]=>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]=>[4,1,1]=>[4,1,1]=>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]=>[4,1,1]=>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]=>[3,1,4]=>[4,3,1]=>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]=>[3,1,1,1,1]=>[3,1,1,1,1]=>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]=>[3,2,2]=>[3,2,2]=>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]=>[3,3]=>[3,3]=>6
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,2,4]=>[3,1,1]=>[3,1,1]=>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]=>[3,1,3]=>[3,3,1]=>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]=>[3,1,1,1]=>[3,1,1,1]=>6
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,3,3]=>[3,2]=>[3,2]=>5
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,5,1]=>[3,1,1]=>[3,1,1]=>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]=>[2,1,5]=>[5,2,1]=>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]=>[2,1,3,1]=>[3,2,1,1]=>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]=>[2,1,2,1,1]=>[2,2,1,1,1]=>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]=>[2,1,2,1]=>[2,2,1,1]=>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]=>[2,1,1,2]=>[2,2,1,1]=>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]=>[2,2,3]=>[3,2,2]=>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]=>[2,3,1]=>[3,2,1]=>6
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,2,2,3]=>[2,2,1]=>[2,2,1]=>5
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,2,3,2]=>[2,1,1,1]=>[2,1,1,1]=>5
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,2,4,1]=>[2,1,1,1]=>[2,1,1,1]=>5
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,2,5]=>[2,1,1]=>[2,1,1]=>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]=>[2,1,4]=>[4,2,1]=>7
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,3,2,2]=>[2,1,2]=>[2,2,1]=>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]=>[2,1,3]=>[3,2,1]=>6
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,4,3]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,5,1,1]=>[2,1,2]=>[2,2,1]=>5
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,5,2]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,6,1]=>[2,1,1]=>[2,1,1]=>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]=>[1,1,6]=>[6,1,1]=>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]=>[1,1,4,1]=>[4,1,1,1]=>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]=>[1,1,3,1,1]=>[3,1,1,1,1]=>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]=>[1,1,3,1]=>[3,1,1,1]=>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]=>[1,1,2,1,2]=>[2,2,1,1,1]=>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]=>[1,1,1,1,3]=>[3,1,1,1,1]=>7
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,1,5]=>[1,1,1,1]=>[1,1,1,1]=>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]=>[1,2,4]=>[4,2,1]=>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]=>[1,2,2,1]=>[2,2,1,1]=>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]=>[1,3,2]=>[3,2,1]=>6
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,2,2,2]=>[1,4]=>[4,1]=>5
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,2,3,1]=>[1,2,1,1]=>[2,1,1,1]=>5
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,2,4]=>[1,2,1]=>[2,1,1]=>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]=>[1,1,1,3]=>[3,1,1,1]=>6
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,3,3]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,5,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,6]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,1,1,1,1,1]=>[1,1,5]=>[5,1,1]=>7
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,2,1]=>[1,1,2,1]=>[2,1,1,1]=>5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,3,1,1]=>[1,2,2]=>[2,2,1]=>5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,3,2]=>[1,2,1]=>[2,1,1]=>4
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,5]=>[1,1,1]=>[1,1,1]=>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]=>[1,1,4]=>[4,1,1]=>6
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,4,1,3]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,4,2,1,1]=>[1,1,1,2]=>[2,1,1,1]=>5
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,4]=>[1,2]=>[2,1]=>3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,5,1,1,1]=>[1,1,3]=>[3,1,1]=>5
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,5,3]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,6,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,6,2]=>[1,1,1]=>[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]=>[1,7]=>[7,1]=>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]=>[1,5,1]=>[5,1,1]=>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]=>[1,4,1,1]=>[4,1,1,1]=>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]=>[1,4,1]=>[4,1,1]=>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]=>[1,3,1,2]=>[3,2,1,1]=>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]=>[1,3,2]=>[3,2,1]=>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]=>[1,3,1,1]=>[3,1,1,1]=>6
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,1,1,4]=>[1,3,1]=>[3,1,1]=>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]=>[1,2,1,3]=>[3,2,1,1]=>7
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,1,2,3]=>[1,2,1,1]=>[2,1,1,1]=>5
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,1,4,1]=>[1,2,1,1]=>[2,1,1,1]=>5
[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,1,5]=>[1,2,1]=>[2,1,1]=>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]=>[1,1,1,4]=>[4,1,1,1]=>7
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,2,2,2]=>[1,1,3]=>[3,1,1]=>5
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,3]=>[1,1,2]=>[2,1,1]=>4
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,5,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,6]=>[1,1,1]=>[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]=>[2,5]=>[5,2]=>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]=>[2,3,1]=>[3,2,1]=>6
[1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,2,1,4]=>[2,1,1]=>[2,1,1]=>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]=>[3,3]=>[3,3]=>6
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,2,2,1,2]=>[3,1,1]=>[3,1,1]=>5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,2,1]=>[4,1]=>[4,1]=>5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,2,2,3]=>[3,1]=>[3,1]=>4
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,2,3,1,1]=>[2,1,2]=>[2,2,1]=>5
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,2,3,2]=>[2,1,1]=>[2,1,1]=>4
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,5]=>[2,1]=>[2,1]=>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]=>[1,1,4]=>[4,1,1]=>6
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,3,3,1]=>[1,2,1]=>[2,1,1]=>4
[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,3,4]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,4,1,1,1]=>[1,1,3]=>[3,1,1]=>5
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,4,3]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,5,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,5,2]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,6]=>[6,1]=>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]=>[1,4,1]=>[4,1,1]=>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]=>[1,3,1,1]=>[3,1,1,1]=>6
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,1,1,3]=>[1,3,1]=>[3,1,1]=>5
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,2,1,2]=>[1,1,1,1,1]=>[1,1,1,1,1]=>5
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,2,2,1]=>[1,1,2,1]=>[2,1,1,1]=>5
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,5]=>[1,1,1]=>[1,1,1]=>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]=>[1,1,4]=>[4,1,1]=>6
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,2,2]=>[1,3]=>[3,1]=>4
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,3,1,1,1]=>[2,3]=>[3,2]=>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
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[3,4,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,6]=>[1,1]=>[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]=>[1,5]=>[5,1]=>6
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[4,1,1,1,2]=>[1,3,1]=>[3,1,1]=>5
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[4,1,1,3]=>[1,2,1]=>[2,1,1]=>4
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,3,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,4]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[4,2,1,1,1]=>[1,1,3]=>[3,1,1]=>5
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,2,2,1]=>[1,2,1]=>[2,1,1]=>4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[4,2,3]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[4,3,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[4,3,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[4,4,1]=>[2,1]=>[2,1]=>3
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>[1,4]=>[4,1]=>5
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0]=>[5,1,1,2]=>[1,2,1]=>[2,1,1]=>4
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[5,1,2,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[5,1,3]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>[5,2,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[5,3,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,4]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]=>[6,1,2]=>[1,1,1]=>[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]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[6,3]=>[1,1]=>[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]=>[7,1,1]=>[7,1,1]=>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]=>[6,1,2]=>[6,2,1]=>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]=>[6,2]=>[6,2]=>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]=>[6,1,1]=>[6,1,1]=>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]=>[5,1,3]=>[5,3,1]=>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]=>[5,2,1]=>[5,2,1]=>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]=>[5,1,1]=>[5,1,1]=>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]=>[4,1,4]=>[4,4,1]=>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]=>[4,3]=>[4,3]=>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]=>[4,1,3]=>[4,3,1]=>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]=>[4,1,1]=>[4,1,1]=>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]=>[3,1,5]=>[5,3,1]=>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]=>[3,1,3,1]=>[3,3,1,1]=>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]=>[3,2,3]=>[3,3,2]=>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]=>[3,3,1]=>[3,3,1]=>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]=>[3,1,4]=>[4,3,1]=>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]=>[3,1,1,1]=>[3,1,1,1]=>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]=>[3,1,1]=>[3,1,1]=>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]=>[3,1]=>[3,1]=>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]=>[2,1,6]=>[6,2,1]=>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]=>[2,2,4]=>[4,2,2]=>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]=>[2,4]=>[4,2]=>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]=>[2,1,5]=>[5,2,1]=>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]=>[2,2]=>[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]=>[2,1,3]=>[3,2,1]=>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]=>[2,1,1]=>[2,1,1]=>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]=>[2,1,1]=>[2,1,1]=>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]=>[1,1,7]=>[7,1,1]=>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]=>[1,1,5,1]=>[5,1,1,1]=>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]=>[1,1,4,1,1]=>[4,1,1,1,1]=>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]=>[1,1,4,1]=>[4,1,1,1]=>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]=>[1,1,1,1,1,1]=>[1,1,1,1,1,1]=>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]=>[1,2,5]=>[5,2,1]=>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]=>[1,3,3]=>[3,3,1]=>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]=>[1,4,1]=>[4,1,1]=>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]=>[1,3,1]=>[3,1,1]=>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]=>[1,1,1,2]=>[2,1,1,1]=>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]=>[1,1,1,1]=>[1,1,1,1]=>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]=>[1,1,1,3]=>[3,1,1,1]=>6
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,7]=>[1,1,1]=>[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]=>[1,1,6]=>[6,1,1]=>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]=>[1,1,3]=>[3,1,1]=>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]=>[1,3]=>[3,1]=>4
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,6]=>[1,1,1]=>[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]=>[1,1,5]=>[5,1,1]=>7
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,4,5]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,5,1,1,1,1]=>[1,1,4]=>[4,1,1]=>6
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,5,4]=>[1,1,1]=>[1,1,1]=>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]=>[1,1,3]=>[3,1,1]=>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]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,7,2]=>[1,1,1]=>[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]=>[1,8]=>[8,1]=>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]=>[1,6,1]=>[6,1,1]=>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]=>[1,5,1,1]=>[5,1,1,1]=>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]=>[1,5,1]=>[5,1,1]=>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]=>[1,4,1,2]=>[4,2,1,1]=>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]=>[1,4,1,1]=>[4,1,1,1]=>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]=>[1,4,1]=>[4,1,1]=>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]=>[1,3,1]=>[3,1,1]=>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]=>[1,1,1,5]=>[5,1,1,1]=>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]=>[1,1,1,1,1]=>[1,1,1,1,1]=>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]=>[1,1,1,1]=>[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]=>[1,1,1]=>[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]=>[2,6]=>[6,2]=>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]=>[2,2,2]=>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]=>[3,4]=>[4,3]=>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]=>[3,1,1,1]=>[3,1,1,1]=>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]=>[4,2]=>[4,2]=>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]=>[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]=>[3,1,1]=>[3,1,1]=>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]=>[3,1]=>[3,1]=>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]=>[2,1,3]=>[3,2,1]=>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]=>[2,2]=>[2,2]=>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]=>[1,1,5]=>[5,1,1]=>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]=>[1,2,1]=>[2,1,1]=>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]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,4,4]=>[1,2]=>[2,1]=>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]=>[1,1,2]=>[2,1,1]=>4
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,6,2]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,7]=>[7,1]=>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]=>[1,5,1]=>[5,1,1]=>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]=>[1,4,1,1]=>[4,1,1,1]=>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]=>[1,1,1,1]=>[1,1,1,1]=>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]=>[1,1,5]=>[5,1,1]=>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]=>[1,3,1]=>[3,1,1]=>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]=>[1,2,1]=>[2,1,1]=>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]=>[2,2]=>[2,2]=>4
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,3,4]=>[2,1]=>[2,1]=>3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,4,3]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,6,1]=>[1,1,1]=>[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]=>[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]=>[1,6]=>[6,1]=>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]=>[1,4,1]=>[4,1,1]=>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]=>[1,2,1]=>[2,1,1]=>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]=>[1,1,1,1]=>[1,1,1,1]=>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]=>[1,3]=>[3,1]=>4
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,2,4]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[4,3,3]=>[1,2]=>[2,1]=>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]=>[2,2]=>[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]=>[2,1]=>[2,1]=>3
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[4,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,6]=>[1,1]=>[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]=>[1,5]=>[5,1]=>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]=>[1,3,1]=>[3,1,1]=>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]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,1,4]=>[1,1,1]=>[1,1,1]=>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]=>[1,2,1]=>[2,1,1]=>4
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[5,4,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,5]=>[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]=>[1,4]=>[4,1]=>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]=>[1,2,1]=>[2,1,1]=>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]=>[1,1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,1]=>[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]=>[1,3]=>[3,1]=>4
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0]=>[7,1,2]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[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]=>[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]=>[1,6]=>[6,1]=>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]=>[1,5]=>[5,1]=>6
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>[1,4]=>[4,1]=>5
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,1]=>[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]=>[1,7]=>[7,1]=>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]=>[1,5]=>[5,1]=>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]=>[1,6]=>[6,1]=>7
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>[1,4]=>[4,1]=>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]=>[1,5]=>[5,1]=>6
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[1,3]=>[3,1]=>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]=>[1,4]=>[4,1]=>5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,1,1]=>[1,2]=>[2,1]=>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]=>[1,3]=>[3,1]=>4
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[8,1]=>[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]=>[1,2]=>[2,1]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,1]=>[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]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[10]=>[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]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[10]=>[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]=>[1,9]=>[9,1]=>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]=>[1,4,1]=>[4,1,1]=>6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[10]=>[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]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[10]=>[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]=>[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]=>[1,5,1]=>[5,1,1]=>7
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,1,1,3]=>[1,3,1]=>[3,1,1]=>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]=>[1,1,3,1]=>[3,1,1,1]=>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]=>[1,4,1]=>[4,1,1]=>6
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,1]=>[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]=>[1,2]=>[2,1]=>3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>[1,4]=>[4,1]=>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]=>[1,5]=>[5,1]=>6
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[10]=>[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]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[7,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>[1,4]=>[4,1]=>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]=>[1,5]=>[5,1]=>6
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,2]=>[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]=>[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]=>[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]=>[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]=>[1]=>[1]=>1
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,6]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,4]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,3]=>[1,1]=>[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]=>[1,1,4]=>[4,1,1]=>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]=>[2,1,4]=>[4,2,1]=>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]=>[5,1,2]=>[5,2,1]=>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]=>[5,1,1]=>[5,1,1]=>7
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[5,1,1,2]=>[1,2,1]=>[2,1,1]=>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]=>[1,1,4]=>[4,1,1]=>6
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[10]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,4]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,5]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,7]=>[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]=>[1]=>[1]=>1
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7]=>[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]=>[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]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,3]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,5]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[6,3]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,4]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,6]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[10]=>[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]=>[2,1,1,1]=>[2,1,1,1]=>5
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[7,2]=>[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]=>[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]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,6]=>[1,1]=>[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]=>[4,1,1]=>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]=>[4,1,2]=>[4,2,1]=>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]=>[2,1,5]=>[5,2,1]=>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]=>[1,1,5]=>[5,1,1]=>7
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,1,5]=>[1,2,1]=>[2,1,1]=>4
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[10]=>[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]=>[4,1,1]=>[4,1,1]=>6
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[10]=>[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]=>[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]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[6,2,1]=>[1,1,1]=>[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]=>[1,1,2]=>[2,1,1]=>4
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[4,2,1,1,1]=>[1,1,3]=>[3,1,1]=>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]=>[1,1,4]=>[4,1,1]=>6
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,2,2,1]=>[1,2,1]=>[2,1,1]=>4
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,1]=>[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]=>[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]=>[1,2]=>[2,1]=>3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,2,2]=>[1,3]=>[3,1]=>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]=>[1,3]=>[3,1]=>4
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>[1,1,1]=>[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]=>[1,2]=>[2,1]=>3
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[8,1]=>[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]=>[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]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[9,1]=>[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]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,2,1]=>[1,1,1]=>[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]=>[1,1,1]=>[1,1,1]=>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]=>[1,2,1]=>[2,1,1]=>4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,4,2,2]=>[1,1,2]=>[2,1,1]=>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]=>[1,3,1]=>[3,1,1]=>5
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[4,1,4]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[10]=>[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]=>[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]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[10]=>[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]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[10]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,1]=>[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]=>[1,1]=>[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]=>[1,1]=>[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]=>[1,1]=>[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]=>[1,1]=>[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]=>[1,1]=>[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]=>[1,1]=>[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]=>[1,1]=>[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]=>[1,1]=>[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]=>[1,1]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[10]=>[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]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[10]=>[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]=>[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]=>[1,5,1]=>[5,1,1]=>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]=>[1,3,1,1]=>[3,1,1,1]=>6
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,7]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,6]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,5]=>[4,1]=>[4,1]=>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]=>[5,1]=>[5,1]=>6
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[3,6]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[4,5]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[5,4]=>[1,1]=>[1,1]=>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]=>[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]=>[1,2]=>[2,1]=>3
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[4,1,2,1,1]=>[1,1,1,2]=>[2,1,1,1]=>5
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,6]=>[1,1]=>[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]=>[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]=>[1,1]=>[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]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[4,4,1]=>[2,1]=>[2,1]=>3
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,5]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[10]=>[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]=>[2,1]=>[2,1]=>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]=>[3,1]=>[3,1]=>4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>[1,4]=>[4,1]=>5
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,3]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,8]=>[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]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[10]=>[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]=>[1,3,1]=>[3,1,1]=>5
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[5,1,1,2]=>[1,2,1]=>[2,1,1]=>4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,1,2]=>[1,1,1]=>[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]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[10]=>[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]=>[4,1,1]=>6
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,8]=>[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]=>[2,1,2]=>[2,2,1]=>5
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,7]=>[2,1]=>[2,1]=>3
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[10]=>[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]=>[1,1,5]=>[5,1,1]=>7
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[11]=>[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]=>[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]=>[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]=>[10]=>[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]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,0,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,8]=>[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]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,6]=>[3,1]=>[3,1]=>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]=>[7,1,1]=>[7,1,1]=>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]=>[8,1,1]=>[8,1,1]=>10
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,5,1,1,1]=>[1,1,3]=>[3,1,1]=>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]=>[2,1,3]=>[3,2,1]=>6
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,4]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[10]=>[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]=>[5,1,1]=>[5,1,1]=>7
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,6]=>[3,1]=>[3,1]=>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]=>[6,1,1]=>[6,1,1]=>8
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,1,2]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[2,1]=>[2,1]=>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]=>[1,1,2]=>[2,1,1]=>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]=>[2,1,1]=>[2,1,1]=>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]=>[2,1,3,1]=>[3,2,1,1]=>7
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>[1,4]=>[4,1]=>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]=>[1,1,3,1]=>[3,1,1,1]=>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]=>[1,3,1]=>[3,1,1]=>5
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[10]=>[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]=>[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]=>[2,1]=>[2,1]=>3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,6,2]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,2]=>[2,1]=>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]=>[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]=>[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]=>[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]=>[1,1,3]=>[3,1,1]=>5
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,4,1]=>[2,1,1]=>[2,1,1]=>4
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[5,2,2]=>[1,2]=>[2,1]=>3
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,6]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,6,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,7]=>[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]=>[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]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,5,3]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,3]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[10]=>[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]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,7]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,6,1]=>[2,1,1]=>[2,1,1]=>4
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,1]=>[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]=>[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]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[8,1]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,6]=>[1,1,1]=>[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]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]=>[10]=>[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]=>[1,3,1,1]=>[3,1,1,1]=>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]=>[7,1,1]=>[7,1,1]=>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]=>[1,4,1,1]=>[4,1,1,1]=>7
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,1,3,1]=>[1,2,1,1]=>[2,1,1,1]=>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]=>[1,1,2,1,1]=>[2,1,1,1,1]=>6
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,5]=>[4,1]=>[4,1]=>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]=>[1,6]=>[6,1]=>7
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[8,2]=>[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]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,1,2]=>[1,1,1]=>[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]=>[1,2,1]=>[2,1,1]=>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]=>[1,4]=>[4,1]=>5
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0]=>[7,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[7,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0]=>[7,1,1]=>[1,2]=>[2,1]=>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]=>[1,3]=>[3,1]=>4
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[8,1]=>[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]=>[1,1,4]=>[4,1,1]=>6
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[4,1,1,2,1]=>[1,2,1,1]=>[2,1,1,1]=>5
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,5,1,1]=>[2,1,2]=>[2,2,1]=>5
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,6]=>[1,1,1]=>[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]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,1,1,4]=>[1,1,2,1]=>[2,1,1,1]=>5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,3]=>[3,1]=>[3,1]=>4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,2,3,1,1]=>[2,1,2]=>[2,2,1]=>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]=>[3,1,1]=>[3,1,1]=>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]=>[1,5]=>[5,1]=>6
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[5,2,2]=>[1,2]=>[2,1]=>3
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,2,2,1]=>[1,2,1]=>[2,1,1]=>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]=>[1,3]=>[3,1]=>4
[1,1,1,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,4]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[3,6]=>[1,1]=>[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]=>[4,1]=>[4,1]=>5
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,6]=>[3,1]=>[3,1]=>4
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,7]=>[2,1]=>[2,1]=>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]=>[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]=>[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]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[7,2]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,2]=>[2,1]=>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]=>[4,1,1]=>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]=>[3,1,3]=>[3,3,1]=>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]=>[4,1,3]=>[4,3,1]=>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]=>[3,1,4]=>[4,3,1]=>8
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,1,1,4]=>[1,3,1]=>[3,1,1]=>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]=>[1,1,6]=>[6,1,1]=>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]=>[1,1,4]=>[4,1,1]=>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]=>[2,1,3]=>[3,2,1]=>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]=>[3,1,2]=>[3,2,1]=>6
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,4]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0]=>[6,3]=>[1,1]=>[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]=>[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]=>[1,1,4]=>[4,1,1]=>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]=>[2,1,4]=>[4,2,1]=>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]=>[1,1,1,3]=>[3,1,1,1]=>6
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[11]=>[1]=>[1]=>1
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,6]=>[1,1,1]=>[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]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[4,1,4]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[4,5]=>[1,1]=>[1,1]=>2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,5]=>[4,1]=>[4,1]=>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]=>[6,1]=>[6,1]=>7
[1,0,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,7]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,6]=>[3,1]=>[3,1]=>4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,5,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,2,4,1]=>[2,1,1]=>[2,1,1]=>4
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>[1,4]=>[4,1]=>5
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>[1,4]=>[4,1]=>5
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,0,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,8]=>[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]=>[1,1,1,3]=>[3,1,1,1]=>6
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[3,3,1,1,1]=>[2,3]=>[3,2]=>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]=>[1,1,1,3]=>[3,1,1,1]=>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]=>[1,1,5]=>[5,1,1]=>7
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0]=>[8,1]=>[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]=>[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]=>[2,1,2]=>[2,2,1]=>5
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,6,1]=>[2,1,1]=>[2,1,1]=>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]=>[3,1,2]=>[3,2,1]=>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]=>[3,1,2]=>[3,2,1]=>6
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,5,1]=>[3,1,1]=>[3,1,1]=>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]=>[3,1,1]=>[3,1,1]=>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]=>[2,1,2]=>[2,2,1]=>5
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,6,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,4,1,1]=>[1,1,1,2]=>[2,1,1,1]=>5
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,7,1]=>[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]=>[1,1,1,1]=>[1,1,1,1]=>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]=>[2,1,1]=>[2,1,1]=>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]=>[3,1,1]=>[3,1,1]=>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]=>[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]=>[1,1]=>[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]=>[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]=>[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]=>[1,2]=>[2,1]=>3
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,8]=>[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]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,8]=>[2,1]=>[2,1]=>3
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[3,1,5]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,1,5]=>[1,2,1]=>[2,1,1]=>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]=>[4,1]=>[4,1]=>5
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[3,6]=>[1,1]=>[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]=>[1,1,1]=>[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]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[11]=>[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]=>[3,1,1,2]=>[3,2,1,1]=>7
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,1,0,0]=>[8,2]=>[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]=>[1,2,1]=>[2,1,1]=>4
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[6,2,1]=>[1,1,1]=>[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]=>[1,2]=>[2,1]=>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]=>[1,3]=>[3,1]=>4
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[6,2,1]=>[1,1,1]=>[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]=>[1,2]=>[2,1]=>3
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,1]=>[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]=>[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]=>[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]=>[1,1,2]=>[2,1,1]=>4
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[7,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[8,1]=>[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]=>[1,2]=>[2,1]=>3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,1]=>[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]=>[1,2]=>[2,1]=>3
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[8,1]=>[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]=>[1,2]=>[2,1]=>3
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[8,1]=>[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]=>[1,2]=>[2,1]=>3
[1,1,0,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,1,5]=>[1,2,1]=>[2,1,1]=>4
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,1]=>[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]=>[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]=>[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]=>[3,1,1]=>[3,1,1]=>5
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,7,1]=>[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]=>[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]=>[1,3,1]=>[3,1,1]=>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]=>[2,1,4]=>[4,2,1]=>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]=>[1,1,4]=>[4,1,1]=>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]=>[1,4]=>[4,1]=>5
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,9]=>[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]=>[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]=>[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]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[4,1,3,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,4,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,5,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,6,1]=>[2,1,1]=>[2,1,1]=>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]=>[1,1,1,1]=>[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]=>[1,2,1]=>[2,1,1]=>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]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,1,4]=>[1,2,1]=>[2,1,1]=>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]=>[1,1,1,1]=>[1,1,1,1]=>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]=>[1,1,1,1]=>[1,1,1,1]=>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]=>[1,1,1,1]=>[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]=>[1,2]=>[2,1]=>3
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]=>[8,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,5]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,1]=>[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]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,1,0]=>[8,1]=>[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]=>[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]=>[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]=>[4,1,1]=>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]=>[3,1,2]=>[3,2,1]=>6
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,5,1]=>[3,1,1]=>[3,1,1]=>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]=>[5,1,1]=>[5,1,1]=>7
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,8]=>[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]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[10]=>[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]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[10]=>[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]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,3]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[5,4]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,1,0,0]=>[5,4]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,8]=>[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]=>[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]=>[1]=>[1]=>1
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,8]=>[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]=>[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]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[8,1]=>[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
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,6]=>[1,1]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,1,1]=>[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]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[10]=>[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]=>[1,2,1]=>[2,1,1]=>4
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,6]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,8]=>[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]=>[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]=>[2,1]=>[2,1]=>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]=>[3,1]=>[3,1]=>4
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,6]=>[1,1,1]=>[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]=>[2,1]=>[2,1]=>3
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,8]=>[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]=>[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]=>[2,1]=>[2,1]=>3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,9]=>[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]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,7]=>[1,1,1]=>[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]=>[1,1,1]=>[1,1,1]=>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]=>[1,2,1]=>[2,1,1]=>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]=>[1,3,1]=>[3,1,1]=>5
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,5]=>[4,1]=>[4,1]=>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]=>[1,6]=>[6,1]=>7
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0]=>[5,1,3]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,1,1,3]=>[1,3,1]=>[3,1,1]=>5
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,8]=>[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]=>[2,1]=>[2,1]=>3
[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[11]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[10]=>[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]=>[1,3,1]=>[3,1,1]=>5
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[3,1,5]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[11]=>[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]=>[1,5]=>[5,1]=>6
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,6]=>[1,1,1]=>[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]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,4]=>[3,1,1]=>[3,1,1]=>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]=>[4,1,1]=>[4,1,1]=>6
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[11]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[10]=>[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]=>[3,1,1]=>[3,1,1]=>5
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,4,2,1]=>[2,1,1,1]=>[2,1,1,1]=>5
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,2,4,1,1]=>[1,1,1,2]=>[2,1,1,1]=>5
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,5,1,1,1]=>[1,1,3]=>[3,1,1]=>5
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[10]=>[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]=>[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]=>[1,1,1]=>[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]=>[1,6]=>[6,1]=>7
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,1,5]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,6,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,4]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[3,6]=>[1,1]=>[1,1]=>2
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,8]=>[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]=>[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]=>[1,1]=>[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]=>[1,1]=>[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]=>[1,3]=>[3,1]=>4
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[8,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[3,6]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,8]=>[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]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,8]=>[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]=>[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]=>[2,1,1,1]=>[2,1,1,1]=>5
[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,4]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,1]=>[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]=>[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]=>[4,1]=>[4,1]=>5
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[10]=>[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]=>[1,4]=>[4,1]=>5
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,1]=>[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]=>[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]=>[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]=>[1,1,1]=>[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]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[2,7]=>[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]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,6,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[7,2]=>[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]=>[1,1,1]=>[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]=>[1]=>[1]=>1
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,7]=>[2,1]=>[2,1]=>3
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,1,5]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,2,4,2]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,1,1]=>[1,2]=>[2,1]=>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]=>[1,3,1]=>[3,1,1]=>5
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,1,1,1]=>[1,4]=>[4,1]=>5
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[11]=>[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]=>[3,1,1]=>[3,1,1]=>5
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,4,2]=>[3,1,1]=>[3,1,1]=>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]=>[4,1,1]=>[4,1,1]=>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]=>[4,1,1]=>[4,1,1]=>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]=>[3,1,1,1]=>[3,1,1,1]=>6
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,5,2]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,5,2]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,5,2]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,5,2]=>[2,1,1]=>[2,1,1]=>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]=>[3,1,1,1]=>[3,1,1,1]=>6
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,7,1]=>[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]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,8,1]=>[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]=>[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]=>[2,1,1]=>[2,1,1]=>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]=>[1,5,1,1]=>[5,1,1,1]=>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]=>[1,3,1,1]=>[3,1,1,1]=>6
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,3,1,3,1]=>[1,1,1,1,1]=>[1,1,1,1,1]=>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]=>[2,1,1,1,1]=>[2,1,1,1,1]=>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]=>[1,1,2,1,1]=>[2,1,1,1,1]=>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]=>[1,6,1,1]=>[6,1,1,1]=>9
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[3,6]=>[1,1]=>[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
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,5,2]=>[1,1,1]=>[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]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,4,3]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,6,2]=>[1,1,1]=>[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]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,4]=>[1,2]=>[2,1]=>3
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[4,5]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,2,2]=>[1,2]=>[2,1]=>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]=>[1,1,2]=>[2,1,1]=>4
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[2,6,2]=>[1,1,1]=>[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]=>[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]=>[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]=>[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]=>[2,1,1]=>[2,1,1]=>4
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[4,4,2]=>[2,1]=>[2,1]=>3
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[8,2]=>[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]=>[1,1,1]=>[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]=>[2,1]=>[2,1]=>3
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[4,6]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[10]=>[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]=>[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]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[10]=>[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]=>[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]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[10]=>[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]=>[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]=>[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]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4]=>[1,1]=>[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]=>[1,2]=>[2,1]=>3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4]=>[1,1]=>[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]=>[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]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[10]=>[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]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[10]=>[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]=>[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]=>[1,4]=>[4,1]=>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]=>[1,3]=>[3,1]=>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]=>[1,1,3]=>[3,1,1]=>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]=>[1,3]=>[3,1]=>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]=>[1,1,2]=>[2,1,1]=>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]=>[2,1,2]=>[2,2,1]=>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]=>[2,2]=>[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]=>[1,1,2]=>[2,1,1]=>4
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[2,2,6,2]=>[2,1,1]=>[2,1,1]=>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]=>[1,1,1]=>[1,1,1]=>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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[3,1,1]=>[3,1,1]=>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]=>[1,1,1,1]=>[1,1,1,1]=>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]=>[1,1,1]=>[1,1,1]=>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]=>[1,2,1]=>[2,1,1]=>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]=>[1,1,1]=>[1,1,1]=>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]=>[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]=>[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]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,2,6,2]=>[2,1,1]=>[2,1,1]=>4
[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]=>[1,1,1]=>[1,1,1]=>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]=>[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]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,2,2,6]=>[3,1]=>[3,1]=>4
[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1]=>[1]=>1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,2,2,2,4]=>[4,1]=>[4,1]=>5
[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]=>[1,2,1]=>[2,1,1]=>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]=>[1,1,1]=>[1,1,1]=>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]=>[1,1,1,1]=>[1,1,1,1]=>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]=>[1,1,1]=>[1,1,1]=>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]=>[1,1,1]=>[1,1,1]=>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]=>[2,2]=>[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]=>[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]=>[1,1,1]=>[1,1,1]=>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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1]=>[1]=>1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,6]=>[3,1]=>[3,1]=>4
[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[4,4,1]=>[2,1]=>[2,1]=>3
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[3,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,2,1]=>[1,1,1]=>[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]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[6,3,1]=>[1,1,1]=>[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]=>[2,1]=>[2,1]=>3
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[5,4,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[3,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[4,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,6,1]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[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]=>[1,1,1]=>[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]=>[2,1]=>[2,1]=>3
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[5,4,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[3,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[4,4,1]=>[2,1]=>[2,1]=>3
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[4,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,6,1]=>[1,1,1]=>[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]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,6,1]=>[1,1,1]=>[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]=>[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]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[8,1]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1]=>[1]=>1
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,7]=>[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]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[10]=>[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]=>[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]=>[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]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,7,1]=>[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]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[4,5]=>[1,1]=>[1,1]=>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]=>[2,1]=>[2,1]=>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]=>[1,1,4]=>[4,1,1]=>6
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>[1,1,1]=>[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]=>[1,2]=>[2,1]=>3
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,2]=>[2,1]=>3
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,1]=>[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]=>[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]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[10]=>[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]=>[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]=>[1,1,3]=>[3,1,1]=>5
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[4,4,1]=>[2,1]=>[2,1]=>3
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[5,3,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,8,1]=>[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]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[2,1]=>[2,1]=>3
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[4,5,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[5,3,1]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,4,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[5,4,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>[1,1,1]=>[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]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[6,3,1]=>[1,1,1]=>[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]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[7,2,1]=>[1,1,1]=>[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]=>[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]=>[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]=>[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]=>[1,1]=>[1,1]=>2
[1,0,1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,8]=>[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]=>[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]=>[1,1,1,1]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,1,1,1]=>[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]=>[1,1,1,1,1]=>[1,1,1,1,1]=>5
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,9]=>[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]=>[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]=>[1,1,1,1]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,1,1,1]=>[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]=>[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]=>[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]=>[1,1,1,1]=>[1,1,1,1]=>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]=>[1,1,1,1,1]=>[1,1,1,1,1]=>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]=>[1,1,1,1]=>[1,1,1,1]=>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]=>[1,1,1,1,1]=>[1,1,1,1,1]=>5
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,9]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,1,1,1]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,1,1,1]=>[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]=>[1,1,1,1,1]=>[1,1,1,1,1]=>5
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,9]=>[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]=>[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]=>[1,1,1,1]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,1,1,1]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,1,1,1]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,1,1,1]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,1,1,1,1,1,1]=>[1,1,1,1,1,1,1]=>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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,1,1,1]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,1,1,1]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,1,1,1]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,1]=>[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]=>[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]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[3,1,5]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,7]=>[1,1]=>[1,1]=>2
[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]=>[1,1,6,1]=>[6,1,1,1]=>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]=>[1,1,4,1]=>[4,1,1,1]=>7
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,1,1,4]=>[1,1,2,1]=>[2,1,1,1]=>5
[1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,8]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,1,1]=>[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]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[8,1]=>[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]=>[1,1,2]=>[2,1,1]=>4
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[8,1]=>[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]=>[2,1,1]=>[2,1,1]=>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]=>[3,1]=>[3,1]=>4
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,6,1]=>[1,1,1]=>[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]=>[2,1,1]=>[2,1,1]=>4
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[4,4,1]=>[2,1]=>[2,1]=>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]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>[1,1,1]=>[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]=>[2,1]=>[2,1]=>3
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,1,1]=>[1,2]=>[2,1]=>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]=>[1,1,2]=>[2,1,1]=>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]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,8,1]=>[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]=>[2,1]=>[2,1]=>3
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,3]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,2]=>[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]=>[1,2]=>[2,1]=>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]=>[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]=>[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]=>[1,2]=>[2,1]=>3
[1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,2,6]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,8]=>[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]=>[2,1]=>[2,1]=>3
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,6]=>[2,1]=>[2,1]=>3
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,8]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1]=>[1]=>1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[1,3]=>[3,1]=>4
[1,0,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,8]=>[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]=>[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]=>[1,1]=>[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]=>[1,2,1]=>[2,1,1]=>4
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,9]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,1,1]=>[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]=>[1,2]=>[2,1]=>3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,6,2]=>[1,1,1]=>[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]=>[1,1,2,1]=>[2,1,1,1]=>5
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[7,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[8,1]=>[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]=>[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]=>[1,2]=>[2,1]=>3
[1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[10]=>[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]=>[1,2]=>[2,1]=>3
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,8,1]=>[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]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[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]=>[1,1,1]=>[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]=>[1,2]=>[2,1]=>3
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,8,1]=>[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]=>[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]=>[1,8,1]=>[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]=>[2,1]=>[2,1]=>3
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[6,3,1]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[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]=>[1,1,1]=>[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]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[10]=>[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]=>[1,1,1]=>[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]=>[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]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,2]=>[2,1]=>3
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,8,1]=>[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]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,8,1]=>[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]=>[2,1]=>[2,1]=>3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,6,3]=>[1,1,1]=>[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]=>[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]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[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]=>[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]=>[2,1]=>[2,1]=>3
[1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[10]=>[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]=>[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]=>[1,1,1]=>[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]=>[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]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,4,5]=>[1,1,1]=>[1,1,1]=>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]=>[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]=>[1,1,1]=>[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]=>[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]=>[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]=>[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]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,6,5]=>[1,1,1]=>[1,1,1]=>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]=>[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]=>[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]=>[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]=>[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]=>[1,1,1]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,1,1]=>[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]=>[1,1,1]=>[1,1,1]=>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]=>[1,1,1]=>[1,1,1]=>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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,1,1]=>[1,1,1]=>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]=>[1,1,1]=>[1,1,1]=>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]=>[1,1,1]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,1,1]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,1,1]=>[1,1,1]=>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]=>[1,1,1]=>[1,1,1]=>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]=>[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]=>[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]=>[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]=>[1,1,1]=>[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]=>[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]=>[1,1,1]=>[1,1,1]=>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]=>[1,1,1]=>[1,1,1]=>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]=>[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]=>[1,1,1]=>[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]=>[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]=>[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]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,1]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,9]=>[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]=>[1,1,2]=>[2,1,1]=>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]=>[1,1,1,2]=>[2,1,1,1]=>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]=>[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]=>[1,1,1]=>[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]=>[2,1]=>[2,1]=>3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,4,4]=>[1,2]=>[2,1]=>3
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,6,2]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[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]=>[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]=>[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]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[4,4,2]=>[2,1]=>[2,1]=>3
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[4,6]=>[1,1]=>[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]=>[1,2]=>[2,1]=>3
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[6,4]=>[1,1]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,2,2,2,4]=>[4,1]=>[4,1]=>5
[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]=>[3,1,1]=>[3,1,1]=>5
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,2,2,6]=>[3,1]=>[3,1]=>4
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,2,6]=>[3,1]=>[3,1]=>4
[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]=>[2,1,2]=>[2,2,1]=>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]=>[2,2]=>[2,2]=>4
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,2,6,2]=>[2,1,1]=>[2,1,1]=>4
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,2,6,2]=>[2,1,1]=>[2,1,1]=>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]=>[1,1,3]=>[3,1,1]=>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]=>[1,1,1,1]=>[1,1,1,1]=>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]=>[1,2,1]=>[2,1,1]=>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]=>[1,1,2]=>[2,1,1]=>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]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[2,6,2,2]=>[1,1,2]=>[2,1,1]=>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]=>[1,1,1]=>[1,1,1]=>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]=>[1,4]=>[4,1]=>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]=>[1,2,1]=>[2,1,1]=>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]=>[1,1,1,1]=>[1,1,1,1]=>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]=>[2,2]=>[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]=>[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]=>[1,1,1]=>[1,1,1]=>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]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,2,2,2]=>[1,3]=>[3,1]=>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]=>[1,1,1]=>[1,1,1]=>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]=>[1,1,1]=>[1,1,1]=>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]=>[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]=>[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]=>[1,3]=>[3,1]=>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]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,4,2]=>[1,1,1]=>[1,1,1]=>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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1]=>[1]=>1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,6,2]=>[1,1,1]=>[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]=>[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]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,2,1]=>[1,1,2,1]=>[2,1,1,1]=>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]=>[1,1,2,1]=>[2,1,1,1]=>5
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,6,2]=>[1,1,1]=>[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]=>[1,1,1,1]=>[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]=>[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]=>[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]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,7,2]=>[1,1,1]=>[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]=>[1,1,1,1]=>[1,1,1,1]=>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]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,4,2,1]=>[2,1,1,1]=>[2,1,1,1]=>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]=>[1,1,1,1]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[10]=>[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]=>[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]=>[1,2]=>[2,1]=>3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,5,1,1]=>[2,1,2]=>[2,2,1]=>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]=>[2,1,2,1]=>[2,2,1,1]=>6
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,4,3]=>[2,1]=>[2,1]=>3
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,1]=>[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]=>[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]=>[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]=>[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]=>[1,2]=>[2,1]=>3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0]=>[7,1,1]=>[1,2]=>[2,1]=>3
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[6,1,1,1]=>[1,3]=>[3,1]=>4
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,8]=>[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]=>[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]=>[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]=>[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]=>[1]=>[1]=>1
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[10]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[2,1,1]=>[2,1,1]=>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]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,8]=>[2,1]=>[2,1]=>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]=>[2,1,1]=>[2,1,1]=>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]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,5,4]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,8,1]=>[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]=>[1,1,1]=>[1,1,1]=>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]=>[1,1,2]=>[2,1,1]=>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]=>[1,1,2]=>[2,1,1]=>4
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[8,1,1]=>[1,2]=>[2,1]=>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]=>[1,1,2]=>[2,1,1]=>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]=>[1,1,2]=>[2,1,1]=>4
[1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,9]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[10]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,1,1]=>[1,1,1]=>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]=>[1,1,1]=>[1,1,1]=>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]=>[1,1,1]=>[1,1,1]=>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]=>[1,1,1]=>[1,1,1]=>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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,1]=>[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]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,2]=>[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]=>[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]=>[1,1,4]=>[4,1,1]=>6
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[11]=>[1]=>[1]=>1
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,7]=>[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]=>[1,1,1,4]=>[4,1,1,1]=>7
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[11]=>[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]=>[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]=>[1]=>[1]=>1
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,7]=>[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]=>[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]=>[1,5,1]=>[5,1,1]=>7
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[8,1]=>[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]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[10]=>[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]=>[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]=>[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]=>[1,1,1]=>[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]=>[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]=>[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]=>[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]=>[2,1]=>[2,1]=>3
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,4,4]=>[1,2]=>[2,1]=>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]=>[3,1]=>[3,1]=>4
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,1,4]=>[1,1,1,1]=>[1,1,1,1]=>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]=>[4,1]=>[4,1]=>5
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,1,1,4]=>[1,1,2,1]=>[2,1,1,1]=>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]=>[5,1]=>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]=>[5,1]=>[5,1]=>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]=>[2,1]=>[2,1]=>3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,9]=>[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]=>[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]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[4,5]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,7]=>[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]=>[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]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[5,4]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[7,2]=>[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]=>[1,1]=>[1,1]=>2
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,7]=>[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]=>[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]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,2]=>[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]=>[2,1]=>[2,1]=>3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[5,2,2]=>[1,2]=>[2,1]=>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]=>[3,1]=>[3,1]=>4
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[8,1]=>[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]=>[2,1]=>[2,1]=>3
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,8]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,2,1]=>[2,1,1]=>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]=>[1,2,1]=>[2,1,1]=>4
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,1,1,4]=>[1,3,1]=>[3,1,1]=>5
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,8]=>[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]=>[1,1,1]=>[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]=>[1,1,2]=>[2,1,1]=>4
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[7,2]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,1,1,1]=>[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]=>[1,2]=>[2,1]=>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]=>[1,1,2,1]=>[2,1,1,1]=>5
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,2,2,1]=>[1,1,2,1]=>[2,1,1,1]=>5
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[3,6]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,1,4]=>[1,2,1]=>[2,1,1]=>4
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[4,1,4]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,8,2]=>[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]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[10]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,1]=>[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]=>[2,1]=>[2,1]=>3
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,8]=>[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]=>[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]=>[1,4,1]=>[4,1,1]=>6
[1,1,0,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,8]=>[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]=>[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]=>[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]=>[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]=>[2,1]=>[2,1]=>3
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,1,1]=>[1,1,2]=>[2,1,1]=>4
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,3]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5]=>[1,1]=>[1,1]=>2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[7,2]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[2,2]=>[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]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[5,4,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,5,2]=>[1,1,1]=>[1,1,1]=>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]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[5,4,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,6]=>[1,1,1]=>[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]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[8,2]=>[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]=>[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]=>[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]=>[1,1]=>[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]=>[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]=>[1,1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[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]=>[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]=>[1,1,1]=>[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]=>[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]=>[1,1,1]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[10]=>[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]=>[1,1,1,1]=>[1,1,1,1]=>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]=>[1,2,1]=>[2,1,1]=>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]=>[1,1,1,1,1]=>[1,1,1,1,1]=>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]=>[1,1,1,1]=>[1,1,1,1]=>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]=>[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]=>[1,1,1]=>[1,1,1]=>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]=>[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]=>[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]=>[1,1,1]=>[1,1,1]=>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]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,5,4]=>[1,1,1]=>[1,1,1]=>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]=>[1,1,1]=>[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]=>[1,1]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,1]=>[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]=>[1,1]=>[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]=>[1,1,1]=>[1,1,1]=>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]=>[1,1,1]=>[1,1,1]=>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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1]=>[1]=>1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[10]=>[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]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0,0,0]=>[10]=>[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]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0]=>[10]=>[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]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[4,5]=>[1,1]=>[1,1]=>2
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[10]=>[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]=>[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]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]=>[10]=>[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]=>[3,1,1,1]=>[3,1,1,1]=>6
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0]=>[6,2,1]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[7,1,1]=>[1,2]=>[2,1]=>3
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,8]=>[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]=>[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]=>[2,1,1]=>[2,1,1]=>4
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[8,1]=>[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]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[5,2,2]=>[1,2]=>[2,1]=>3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[5,2,2]=>[1,2]=>[2,1]=>3
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,1,1]=>[1,2]=>[2,1]=>3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,6,1,1]=>[1,1,2]=>[2,1,1]=>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]=>[1,3]=>[3,1]=>4
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,5,1,1,1]=>[1,1,3]=>[3,1,1]=>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]=>[1,4]=>[4,1]=>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]=>[1,5]=>[5,1]=>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]=>[1,2]=>[2,1]=>3
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[8,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[5,3,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[2,7,1]=>[1,1,1]=>[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]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[7,1,1]=>[1,2]=>[2,1]=>3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,2,6]=>[2,1]=>[2,1]=>3
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,4]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,6,1]=>[1,1,1]=>[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]=>[1,2]=>[2,1]=>3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[4,3,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,5,2]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[3,4,4]=>[1,2]=>[2,1]=>3
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,4]=>[2,1]=>[2,1]=>3
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0]=>[10]=>[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]=>[1,3,1,1]=>[3,1,1,1]=>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]=>[1,1,3,1,1]=>[3,1,1,1,1]=>7
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,1,3,1]=>[1,2,1,1]=>[2,1,1,1]=>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]=>[1,4,1,1]=>[4,1,1,1]=>7
[1,0,1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,8]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,7]=>[2,1]=>[2,1]=>3
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,5,3]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,5,3]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,8]=>[2,1]=>[2,1]=>3
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,8]=>[2,1]=>[2,1]=>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]=>[2,1,1]=>[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]=>[1,1,1]=>[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]=>[2,1]=>[2,1]=>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]=>[3,1]=>[3,1]=>4
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6]=>[1,1,1]=>[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]=>[3,1]=>[3,1]=>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]=>[2,2,1]=>[2,2,1]=>5
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[3,1,6]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[5,1,4]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[5,1,4]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,8,1]=>[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]=>[2,1,1]=>[2,1,1]=>4
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,8,1]=>[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]=>[1,1,1,1]=>[1,1,1,1]=>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]=>[1,1,1,1,1]=>[1,1,1,1,1]=>5
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,6,1]=>[1,1,1]=>[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]=>[3,1]=>[3,1]=>4
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[5,4,1]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[5,4,1]=>[1,1,1]=>[1,1,1]=>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]=>[1,1,1,1]=>[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]=>[2,1,1,1]=>[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]=>[1,1,1,1]=>[1,1,1,1]=>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]=>[2,1,1,1]=>[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]=>[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]=>[2,3,1]=>[3,2,1]=>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]=>[1,1,1,1]=>[1,1,1,1]=>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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[2,1,1,1]=>[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]=>[1,1,1,1,1]=>[1,1,1,1,1]=>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]=>[1,1,2,1,1]=>[2,1,1,1,1]=>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]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,1,1,1]=>[1,1,1,1]=>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]=>[2,1,1,1]=>[2,1,1,1]=>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]=>[1,1,1]=>[1,1,1]=>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]=>[1,2,1]=>[2,1,1]=>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]=>[1,1,1]=>[1,1,1]=>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]=>[1,2,1]=>[2,1,1]=>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]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,1,1,1]=>[1,1,1,1]=>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]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,5,1]=>[3,1,1]=>[3,1,1]=>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]=>[5,1,1]=>[5,1,1]=>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]=>[4,1,1]=>[4,1,1]=>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]=>[3,1,1]=>[3,1,1]=>5
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5]=>[1,1]=>[1,1]=>2
[1,1,1,1,0,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,4]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,1,0,0,0]=>[6,3]=>[1,1]=>[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]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[5,2,3]=>[1,1,1]=>[1,1,1]=>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]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,1,1]=>[1,1,1]=>3
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[8,1]=>[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]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[8,1]=>[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]=>[1]=>[1]=>1
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,7,1]=>[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]=>[1,1,2]=>[2,1,1]=>4
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[9,1]=>[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]=>[1,1]=>[1,1]=>2
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,3]=>[1,1]=>[1,1]=>2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0]=>[7,2]=>[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]=>[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]=>[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]=>[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]=>[2,1,2,1]=>[2,2,1,1]=>6
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[5,4]=>[1,1]=>[1,1]=>2
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,2,2]=>[1,2]=>[2,1]=>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]=>[1,3]=>[3,1]=>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]=>[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]=>[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]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,5,4]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,4,1,3]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,8]=>[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]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,1,1,3]=>[1,1,2,1]=>[2,1,1,1]=>5
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,4,4]=>[1,2]=>[2,1]=>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]=>[1,1,2,1]=>[2,1,1,1]=>5
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,1,4]=>[1,1,1,1]=>[1,1,1,1]=>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]=>[1,1,3,1]=>[3,1,1,1]=>6
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[5,1,2,1]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,8]=>[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]=>[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]=>[1,2,1]=>[2,1,1]=>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]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,2,7]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,1,1,1]=>[1,1,1,1]=>4
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5]=>[1,1,1]=>[1,1,1]=>3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,6,3]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,2,1]=>[2,1,1]=>4
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,2,5]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,3]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,1,0,0]=>[10]=>[1]=>[1]=>1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[10]=>[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]=>[1,4,1]=>[4,1,1]=>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]=>[1,3,1]=>[3,1,1]=>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]=>[1,2,1,1]=>[2,1,1,1]=>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]=>[1,1,1,1,1]=>[1,1,1,1,1]=>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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1,1,2,1]=>[2,1,1,1]=>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]=>[1,2,1]=>[2,1,1]=>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]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,1,1]=>[1,1,1]=>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]=>[1,1,1]=>[1,1,1]=>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]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,3,1]=>[3,1,1]=>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]=>[1,1,1,1]=>[1,1,1,1]=>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]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,1,1,1]=>[1,1,1,1]=>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]=>[1,1,1]=>[1,1,1]=>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]=>[1,1,1]=>[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]=>[1,1,1]=>[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]=>[1,2,1]=>[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]=>[1,1,1]=>[1,1,1]=>3
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[5,4,3]=>[1,1,1]=>[1,1,1]=>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]=>[1,2,1]=>[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]=>[1,1,1]=>[1,1,1]=>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]=>[1,1,1]=>[1,1,1]=>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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[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]=>[1]=>[1]=>1
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,8]=>[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]=>[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]=>[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]=>[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]=>[1,1]=>[1,1]=>2
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Description
The size of a partition.
This statistic is the constant statistic of the level sets.
This statistic is the constant statistic of the level sets.
Map
touch composition
Description
Sends a Dyck path to its touch composition given by the composition of lengths of its touch points.
Map
delta morphism
Description
Apply the delta morphism to an integer composition.
The delta morphism of a composition $C$ is the compositions composed of the lengths of consecutive runs of the same integer in $C$.
The delta morphism of a composition $C$ is the compositions composed of the lengths of consecutive runs of the same integer in $C$.
Map
to partition
Description
Sends a composition to the partition obtained by sorting the entries.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!