Identifier
-
Mp00032:
Dyck paths
—inverse zeta map⟶
Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00323: Integer partitions —Loehr-Warrington inverse⟶ Integer partitions
St000010: Integer partitions ⟶ ℤ
Values
=>
Cc0005;cc-rep-0
Cc0005;cc-rep-1
Cc0002;cc-rep-2
Cc0002;cc-rep
[1,1,0,0]=>[1,0,1,0]=>[1]=>[1]=>1
[1,0,1,1,0,0]=>[1,0,1,1,0,0]=>[1,1]=>[2]=>1
[1,1,0,0,1,0]=>[1,1,0,1,0,0]=>[1]=>[1]=>1
[1,1,0,1,0,0]=>[1,1,0,0,1,0]=>[2]=>[1,1]=>2
[1,1,1,0,0,0]=>[1,0,1,0,1,0]=>[2,1]=>[1,1,1]=>3
[1,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0]=>[1,1,1]=>[3]=>1
[1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0]=>[1,1]=>[2]=>1
[1,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0]=>[3]=>[2,1]=>2
[1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0]=>[2,2,1]=>[2,2,1]=>3
[1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0]=>[1]=>[1]=>1
[1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0]=>[2,1,1]=>[3,1]=>2
[1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0]=>[2]=>[1,1]=>2
[1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0]=>[2,2]=>[2,1,1]=>3
[1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0]=>[3,1,1]=>[2,1,1,1]=>4
[1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,0]=>[2,1]=>[1,1,1]=>3
[1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,0]=>[3,1]=>[1,1,1,1]=>4
[1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,0]=>[3,2]=>[1,1,1,1,1]=>5
[1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]=>[3,2,1]=>[1,1,1,1,1,1]=>6
[1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1]=>[4]=>1
[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,1]=>[3]=>1
[1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[4]=>[2,2]=>2
[1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>[2,2,2,1]=>[3,2,2]=>3
[1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1]=>[2]=>1
[1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,0]=>[2,2,1,1]=>[4,2]=>2
[1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0]=>[3]=>[2,1]=>2
[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[2,2,2]=>[2,2,2]=>3
[1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>[4,1,1,1]=>[2,2,2,1]=>4
[1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0]=>[2,2,1]=>[2,2,1]=>3
[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[4,1,1]=>[2,2,1,1]=>4
[1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>[4,3]=>[2,2,1,1,1]=>5
[1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0]=>[3,3,2,1]=>[2,2,2,1,1,1]=>6
[1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,0]=>[1]=>[1]=>1
[1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,0]=>[2,1,1,1]=>[4,1]=>2
[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0]=>[2,1,1]=>[3,1]=>2
[1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>[4,1]=>[3,1,1]=>3
[1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,0]=>[2]=>[1,1]=>2
[1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,0]=>[3,1,1,1]=>[4,1,1]=>3
[1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>[2,2]=>[2,1,1]=>3
[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[3,3]=>[3,1,1,1]=>4
[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[3,3,1,1]=>[3,2,1,1,1]=>5
[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]=>[3,1,1]=>[2,1,1,1]=>4
[1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>[4,2]=>[2,1,1,1,1]=>5
[1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[3,3,2]=>[2,2,1,1,1,1]=>6
[1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>[4,2,2,1]=>[2,2,1,1,1,1,1]=>7
[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,0]=>[2,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]=>[4,1,1,1]=>4
[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]=>[3,1]=>[1,1,1,1]=>4
[1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]=>[3,2,2]=>[3,1,1,1,1]=>5
[1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>[4,2,1,1]=>[3,1,1,1,1,1]=>6
[1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]=>[3,2]=>[1,1,1,1,1]=>5
[1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]=>[3,3,1]=>[2,1,1,1,1,1]=>6
[1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[4,2,2]=>[2,1,1,1,1,1,1]=>7
[1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>[4,3,1,1]=>[2,1,1,1,1,1,1,1]=>8
[1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0]=>[3,2,1]=>[1,1,1,1,1,1]=>6
[1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>[4,2,1]=>[1,1,1,1,1,1,1]=>7
[1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>[4,3,1]=>[1,1,1,1,1,1,1,1]=>8
[1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>[4,3,2]=>[1,1,1,1,1,1,1,1,1]=>9
[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1]=>10
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]=>[5]=>1
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]=>[4]=>1
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5]=>[3,2]=>2
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,2,2,2,1]=>[3,3,3]=>3
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]=>[3]=>1
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,2,1,1]=>[5,3]=>2
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[4]=>[2,2]=>2
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,2,2]=>[3,3,2]=>3
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[5,1,1,1,1]=>[3,2,2,2]=>4
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,2,2,1]=>[3,2,2]=>3
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[5,1,1,1]=>[2,2,2,2]=>4
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[5,4]=>[2,2,2,2,1]=>5
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[3,3,3,2,1]=>[2,2,2,2,2,2]=>6
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]=>[2]=>1
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,2,1,1,1]=>[5,2]=>2
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,1,1]=>[4,2]=>2
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,1,1]=>[4,2,1]=>3
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[3,3,2,2,1]=>[4,3,2,2]=>4
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[3]=>[2,1]=>2
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[4,1,1,1,1]=>[5,2,1]=>3
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,2]=>[2,2,2]=>3
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,4]=>[4,2,1,1]=>4
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,3,3,1,1]=>[4,2,2,2,1]=>5
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,1,1,1]=>[2,2,2,1]=>4
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[5,3]=>[2,2,2,1,1]=>5
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[3,3,3,2]=>[2,2,2,2,2,1]=>6
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[5,2,2,2,1]=>[2,2,2,2,2,1,1]=>7
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1]=>[2,2,1]=>3
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[3,3,2,1,1]=>[5,2,2,1]=>4
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[4,1,1]=>[2,2,1,1]=>4
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[3,3,2,2]=>[4,2,2,1,1]=>5
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[5,2,2,1,1]=>[4,2,2,1,1,1]=>6
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3]=>[2,2,1,1,1]=>5
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,3,3,1]=>[2,2,2,2,1,1]=>6
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[5,2,2,2]=>[2,2,2,2,1,1,1]=>7
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[5,4,1,1,1]=>[2,2,2,2,1,1,1,1]=>8
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[3,3,2,1]=>[2,2,2,1,1,1]=>6
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[5,2,2,1]=>[2,2,2,1,1,1,1]=>7
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[5,4,1,1]=>[2,2,2,1,1,1,1,1]=>8
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[5,4,3]=>[2,2,2,1,1,1,1,1,1]=>9
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[4,4,3,2,1]=>[2,2,2,2,1,1,1,1,1,1]=>10
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1]=>[1]=>1
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,1,1,1]=>[5,1]=>2
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,1,1]=>[4,1]=>2
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1]=>[3,2,1]=>3
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[3,2,2,2,1]=>[3,3,3,1]=>4
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,1]=>[3,1]=>2
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1,1]=>[5,3,1]=>3
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1]=>[3,1,1]=>3
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[3,2,2,2]=>[3,3,2,1]=>4
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[5,2,1,1,1]=>[3,2,2,2,1]=>5
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[5,2,1,1]=>[3,3,1,1,1]=>5
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[5,4,1]=>[3,3,1,1,1,1]=>6
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[4,3,3,2,1]=>[3,2,2,2,2,1,1]=>7
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[2]=>[1,1]=>2
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,1,1,1]=>[5,1,1]=>3
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,1,1]=>[4,1,1]=>3
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,2]=>[3,2,1,1]=>4
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[4,2,2,2,1]=>[3,3,3,1,1]=>5
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,2]=>[2,1,1]=>3
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,1,1,1]=>[5,2,1,1]=>4
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[3,3]=>[3,1,1,1]=>4
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3,3]=>[3,2,2,1,1]=>5
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[4,4,1,1,1]=>[3,3,2,1,1,1]=>6
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[3,3,1,1]=>[3,2,1,1,1]=>5
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[5,2,2]=>[3,2,1,1,1,1]=>6
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[4,4,3]=>[3,3,1,1,1,1,1]=>7
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[4,4,2,2,1]=>[3,3,2,1,1,1,1,1]=>8
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,1,1]=>[2,1,1,1]=>4
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[4,2,2,1,1]=>[5,2,1,1,1]=>5
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,2]=>[2,1,1,1,1]=>5
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[4,2,2,2]=>[3,2,2,1,1,1]=>6
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[5,3,1,1,1]=>[3,2,2,1,1,1,1]=>7
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,3,2]=>[2,2,1,1,1,1]=>6
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[4,4,1,1]=>[3,2,1,1,1,1,1]=>7
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[5,3,3]=>[3,2,1,1,1,1,1,1]=>8
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[4,4,3,1,1]=>[3,2,2,1,1,1,1,1,1]=>9
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[4,2,2,1]=>[2,2,1,1,1,1,1]=>7
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[5,3,1,1]=>[2,2,1,1,1,1,1,1]=>8
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[5,4,2]=>[2,2,1,1,1,1,1,1,1]=>9
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[4,4,3,2]=>[2,2,2,1,1,1,1,1,1,1]=>10
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[5,3,3,2,1]=>[2,2,2,1,1,1,1,1,1,1,1]=>11
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[3,2,1,1,1]=>[5,1,1,1]=>4
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]=>[4,1,1,1]=>4
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[5,2,1]=>[4,1,1,1,1]=>5
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[4,3,2,2,1]=>[3,3,3,1,1,1]=>6
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[3,1]=>[1,1,1,1]=>4
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[4,2,1,1,1]=>[5,1,1,1,1]=>5
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,2]=>[3,1,1,1,1]=>5
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,4,1]=>[4,1,1,1,1,1]=>6
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[4,3,3,1,1]=>[4,2,2,1,1,1,1]=>7
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[4,2,1,1]=>[3,1,1,1,1,1]=>6
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[5,3,1]=>[3,1,1,1,1,1,1]=>7
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[4,3,3,2]=>[3,3,1,1,1,1,1,1]=>8
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[5,3,2,2,1]=>[3,3,1,1,1,1,1,1,1]=>9
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[3,2]=>[1,1,1,1,1]=>5
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[4,3,1,1,1]=>[5,1,1,1,1,1]=>6
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,3,1]=>[2,1,1,1,1,1]=>6
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[4,3,3]=>[4,1,1,1,1,1,1]=>7
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[4,4,2,1,1]=>[4,2,1,1,1,1,1,1]=>8
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[4,2,2]=>[2,1,1,1,1,1,1]=>7
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[4,4,2]=>[3,1,1,1,1,1,1,1]=>8
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[4,4,2,2]=>[3,2,1,1,1,1,1,1,1]=>9
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[5,3,3,1,1]=>[3,2,1,1,1,1,1,1,1,1]=>10
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[4,3,1,1]=>[2,1,1,1,1,1,1,1]=>8
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[5,3,2]=>[2,1,1,1,1,1,1,1,1]=>9
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[4,4,3,1]=>[2,2,1,1,1,1,1,1,1,1]=>10
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[5,3,3,2]=>[2,2,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[5,4,2,2,1]=>[2,2,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,1]=>[1,1,1,1,1,1]=>6
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,1]=>[5,1,1,1,1,1,1]=>7
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[4,2,1]=>[1,1,1,1,1,1,1]=>7
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[4,3,2,2]=>[4,1,1,1,1,1,1,1]=>8
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,1]=>[4,1,1,1,1,1,1,1,1]=>9
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[4,3,1]=>[1,1,1,1,1,1,1,1]=>8
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[4,3,3,1]=>[3,1,1,1,1,1,1,1,1]=>9
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[5,3,2,2]=>[3,1,1,1,1,1,1,1,1,1]=>10
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,1]=>[3,1,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[4,3,2]=>[1,1,1,1,1,1,1,1,1]=>9
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[4,4,2,1]=>[2,1,1,1,1,1,1,1,1,1]=>10
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[5,3,3,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[5,4,2,2]=>[2,1,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,1]=>[2,1,1,1,1,1,1,1,1,1,1,1,1]=>13
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1]=>10
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[5,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[5,4,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[5,4,3,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,1]=>13
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[5,4,3,2]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>14
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>15
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[6]=>1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[5]=>1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6]=>[3,3]=>2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]=>[4,4,3]=>3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[4]=>1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]=>[6,4]=>2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[5]=>[3,2]=>2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]=>[4,3,3]=>3
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]=>[3,3,3,2]=>4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]=>[3,3,3]=>3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]=>[3,3,2,2]=>4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]=>[3,2,2,2,2]=>5
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,2,2]=>6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[3]=>1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]=>[6,3]=>2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]=>[5,3]=>2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>[5,2,2]=>3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,2,1]=>[5,3,3,3]=>4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[4]=>[2,2]=>2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]=>[6,2,2]=>3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[3,3,2]=>3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]=>[4,2,2,2]=>4
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,1,1]=>[5,3,2,2,2]=>5
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]=>[3,2,2,2]=>4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]=>[2,2,2,2,2]=>5
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,2]=>[3,3,2,2,2,2]=>6
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,2,1]=>[3,2,2,2,2,2,2]=>7
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]=>[3,2,2]=>3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,1,1]=>[6,3,2,2]=>4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[2,2,2,2]=>4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,2]=>[4,3,2,2,2]=>5
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,1,1]=>[4,2,2,2,2,2]=>6
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]=>[2,2,2,2,1]=>5
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,1]=>[3,2,2,2,2,2]=>6
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,2]=>[2,2,2,2,2,2,2]=>7
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1,1,1]=>[2,2,2,2,2,2,2,1]=>8
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,1]=>[2,2,2,2,2,2]=>6
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,1]=>[2,2,2,2,2,2,1]=>7
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1,1]=>[2,2,2,2,2,2,1,1]=>8
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[6,5,4]=>[2,2,2,2,2,2,1,1,1]=>9
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[2]=>1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]=>[6,2]=>2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]=>[5,2]=>2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]=>[4,2,2]=>3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,2,1]=>[4,4,3,2]=>4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]=>[4,2]=>2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,1,1]=>[6,4,2]=>3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]=>[4,2,1]=>3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,2]=>[4,3,3,2]=>4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1,1,1]=>[4,4,2,2,1]=>5
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,1]=>[4,3,2,2]=>4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1,1]=>[4,3,2,2,1]=>5
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1]=>[4,3,2,2,1,1]=>6
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[4,4,3,3,2,1]=>[4,4,2,2,2,2,1]=>7
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[3]=>[2,1]=>2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>[6,2,1]=>3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]=>[5,2,1]=>3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]=>[4,2,2,1]=>4
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,2,1]=>[4,4,3,2,1]=>5
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[2,2,2]=>3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1,1]=>[6,2,2,2]=>4
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[4,2,1,1]=>4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3]=>[4,2,2,2,2]=>5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1,1,1]=>[5,2,2,2,2,1]=>6
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1]=>[4,2,2,2,1]=>5
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2]=>[4,2,2,2,1,1]=>6
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,5,4]=>[4,3,2,2,1,1,1]=>7
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,4,4,2,2,1]=>[4,3,3,2,2,1,1,1]=>8
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]=>[2,2,2,1]=>4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,1,1]=>[6,2,2,2,1]=>5
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]=>[2,2,2,1,1]=>5
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,2]=>[4,2,2,2,2,1]=>6
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1,1,1]=>[4,2,2,2,2,1,1]=>7
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2]=>[2,2,2,2,2,1]=>6
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1,1]=>[4,2,2,2,1,1,1]=>7
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[6,4,4]=>[3,2,2,2,2,1,1,1]=>8
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[4,4,4,3,1,1]=>[4,2,2,2,2,2,1,1,1]=>9
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,1]=>[2,2,2,2,2,1,1]=>7
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1,1]=>[2,2,2,2,2,1,1,1]=>8
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[6,5,3]=>[2,2,2,2,2,1,1,1,1]=>9
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[4,4,4,3,2]=>[2,2,2,2,2,2,2,1,1,1]=>10
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]=>[2,2,1]=>3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1,1,1]=>[6,2,2,1]=>4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1,1]=>[5,2,2,1]=>4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1]=>[5,2,2,1,1]=>5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[4,4,3,2,2,1]=>[4,4,3,2,2,1]=>6
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]=>[2,2,1,1]=>4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1,1,1]=>[6,2,2,1,1]=>5
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2]=>[4,2,2,1,1]=>5
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1]=>[5,2,2,1,1,1]=>6
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[4,4,3,3,1,1]=>[5,2,2,2,2,2,1]=>7
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1,1]=>[4,2,2,1,1,1]=>6
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1]=>[3,2,2,2,1,1,1]=>7
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[4,4,3,3,2]=>[4,3,2,2,2,1,1,1]=>8
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,3,2,2,1]=>[4,3,2,2,2,1,1,1,1]=>9
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]=>[2,2,1,1,1]=>5
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1,1,1]=>[6,2,2,1,1,1]=>6
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1]=>[2,2,2,2,1,1]=>6
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,4,4]=>[5,2,2,1,1,1,1]=>7
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[4,4,4,2,1,1]=>[5,3,2,2,1,1,1,1]=>8
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2]=>[2,2,2,2,1,1,1]=>7
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,5,3]=>[3,2,2,2,1,1,1,1]=>8
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[4,4,4,2,2]=>[3,3,2,2,2,1,1,1,1]=>9
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,3,3,1,1]=>[3,2,2,2,2,2,1,1,1,1]=>10
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1,1]=>[2,2,2,2,1,1,1,1]=>8
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[6,4,3]=>[2,2,2,2,1,1,1,1,1]=>9
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[4,4,4,3,1]=>[2,2,2,2,2,2,1,1,1,1]=>10
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,3,3,2]=>[2,2,2,2,2,2,1,1,1,1,1]=>11
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1]=>[2,2,2,1,1,1]=>6
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[4,4,3,2,1,1]=>[6,2,2,2,1,1,1]=>7
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1]=>[2,2,2,1,1,1,1]=>7
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[4,4,3,2,2]=>[5,2,2,2,1,1,1,1]=>8
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,3,2,1,1]=>[5,2,2,2,1,1,1,1,1]=>9
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1]=>[2,2,2,1,1,1,1,1]=>8
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[4,4,3,3,1]=>[3,2,2,2,2,1,1,1,1]=>9
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,3,2,2]=>[3,2,2,2,2,1,1,1,1,1]=>10
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,2,1,1]=>[3,2,2,2,2,1,1,1,1,1,1]=>11
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[5,4,3]=>[2,2,2,1,1,1,1,1,1]=>9
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[4,4,4,2,1]=>[3,2,2,2,1,1,1,1,1,1]=>10
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,3,3,1]=>[2,2,2,2,2,1,1,1,1,1,1]=>11
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,2,2]=>[2,2,2,2,2,1,1,1,1,1,1,1]=>12
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[4,4,3,2,1]=>[2,2,2,2,1,1,1,1,1,1]=>10
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,3,2,1]=>[2,2,2,2,1,1,1,1,1,1,1]=>11
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,2,1]=>[2,2,2,2,1,1,1,1,1,1,1,1]=>12
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,1]=>[2,2,2,2,1,1,1,1,1,1,1,1,1]=>13
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1]=>[1]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]=>[6,1]=>2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]=>[5,1]=>2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[3,3,1]=>3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,2,1]=>[4,4,3,1]=>4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]=>[4,1]=>2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,1,1]=>[6,4,1]=>3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]=>[3,2,1]=>3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,2]=>[4,3,3,1]=>4
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1,1,1]=>[3,3,3,2,1]=>5
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,1]=>[3,3,3,1]=>4
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1,1]=>[3,3,2,2,1]=>5
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[6,5,1]=>[3,2,2,2,2,1]=>6
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,3,3,2,1]=>[3,3,3,2,2,2,1]=>7
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]=>[3,1]=>2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1,1,1]=>[6,3,1]=>3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1,1]=>[5,3,1]=>3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1]=>[5,3,1,1]=>4
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,3,2,2,1]=>[5,3,3,3,1]=>5
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]=>[3,1,1]=>3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1,1,1]=>[6,3,1,1]=>4
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2]=>[3,3,2,1]=>4
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,5,1]=>[5,3,1,1,1]=>5
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,3,3,1,1]=>[5,3,2,2,2,1]=>6
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1,1]=>[3,2,2,2,1]=>5
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[6,4,1]=>[3,2,2,2,1,1]=>6
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,3,3,2]=>[3,3,2,2,2,2,1]=>7
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,2,2,1]=>[3,2,2,2,2,2,2,1]=>8
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,3,2,1,1]=>[6,3,2,2,1]=>5
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1]=>[3,3,1,1,1]=>5
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,3,2,2]=>[4,3,2,2,2,1]=>6
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,2,1,1]=>[5,3,3,1,1,1,1]=>7
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,4,1]=>[3,3,1,1,1,1]=>6
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,3,3,1]=>[3,2,2,2,2,2,1]=>7
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,2,2]=>[3,2,2,2,2,2,1,1]=>8
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,1,1]=>[3,2,2,2,2,2,1,1,1]=>9
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,3,2,1]=>[3,2,2,2,2,1,1]=>7
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,2,1]=>[3,3,3,1,1,1,1,1]=>8
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,1]=>[3,3,3,1,1,1,1,1,1]=>9
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1]=>[3,3,3,1,1,1,1,1,1,1]=>10
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2]=>[1,1]=>2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]=>[6,1,1]=>3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]=>[5,1,1]=>3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]=>[3,3,1,1]=>4
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,2,1]=>[4,4,3,1,1]=>5
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]=>[4,1,1]=>3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,1,1]=>[6,4,1,1]=>4
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]=>[3,2,1,1]=>4
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,2]=>[4,3,3,1,1]=>5
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1,1,1]=>[3,3,3,2,1,1]=>6
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,1]=>[3,3,3,1,1]=>5
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1,1]=>[4,3,2,1,1,1]=>6
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[6,5,2]=>[3,3,2,2,1,1,1]=>7
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,2,1]=>[3,3,3,2,2,2,1,1]=>8
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2,1,1]=>3
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1,1]=>[6,2,1,1]=>4
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1]=>[5,2,1,1]=>4
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,2,2]=>[3,3,2,1,1]=>5
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,2,1]=>[4,4,3,2,1,1]=>6
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[3,1,1,1]=>4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1,1]=>[6,3,1,1,1]=>5
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,2,2,1,1]=>5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,4,4]=>[5,3,1,1,1,1]=>6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1,1,1]=>[4,4,2,2,1,1,1]=>7
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1]=>[3,3,2,1,1,1]=>6
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[6,3,3]=>[3,3,2,1,1,1,1]=>7
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,4,4,3]=>[4,3,2,2,1,1,1,1]=>8
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,2,1]=>[3,3,2,2,2,2,1,1,1]=>9
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1]=>[3,2,1,1,1]=>5
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,1,1]=>[6,3,2,1,1,1]=>6
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[5,2,2]=>[3,2,1,1,1,1]=>6
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,2]=>[3,3,3,2,1,1,1]=>7
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1,1,1]=>[3,3,2,2,2,1,1,1]=>8
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,4,3]=>[3,3,1,1,1,1,1]=>7
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1,1]=>[4,2,2,2,1,1,1,1]=>8
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[6,3,3,3]=>[3,3,2,2,1,1,1,1,1]=>9
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[5,5,4,1,1,1]=>[4,2,2,2,2,1,1,1,1,1]=>10
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,1]=>[3,3,2,1,1,1,1,1]=>8
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1,1]=>[3,3,2,1,1,1,1,1,1]=>9
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,2]=>[3,3,2,1,1,1,1,1,1,1]=>10
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[5,5,4,3]=>[3,3,3,1,1,1,1,1,1,1,1]=>11
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]=>[2,1,1,1]=>4
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1,1,1]=>[6,2,1,1,1]=>5
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1,1]=>[5,2,1,1,1]=>5
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1]=>[5,2,1,1,1,1]=>6
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,2,1]=>[4,4,3,2,1,1,1]=>7
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]=>[2,1,1,1,1]=>5
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1,1,1]=>[6,2,1,1,1,1]=>6
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2]=>[3,2,2,1,1,1]=>6
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,5,2]=>[5,2,1,1,1,1,1]=>7
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,1,1]=>[4,3,3,2,1,1,1,1]=>8
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1,1]=>[3,2,2,1,1,1,1]=>7
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[6,4,2]=>[3,2,2,1,1,1,1,1]=>8
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,2]=>[4,2,2,2,2,1,1,1,1]=>9
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,2,1]=>[3,3,2,2,2,1,1,1,1,1]=>10
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,3,2]=>[2,2,1,1,1,1]=>6
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[4,4,3,1,1,1]=>[6,2,2,1,1,1,1]=>7
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1]=>[3,2,1,1,1,1,1]=>7
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,4,3,3]=>[5,2,2,1,1,1,1,1]=>8
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,1,1]=>[5,3,2,1,1,1,1,1,1]=>9
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[5,3,3]=>[3,2,1,1,1,1,1,1]=>8
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,4,4,2]=>[4,2,2,1,1,1,1,1,1]=>9
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,2]=>[3,3,2,2,1,1,1,1,1,1]=>10
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,4,1,1,1]=>[3,3,2,2,1,1,1,1,1,1,1]=>11
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[4,4,3,1,1]=>[3,2,2,1,1,1,1,1,1]=>9
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[6,3,3,2]=>[3,2,2,1,1,1,1,1,1,1]=>10
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[5,5,4,1,1]=>[3,3,2,1,1,1,1,1,1,1,1]=>11
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[6,4,4,3]=>[3,3,2,1,1,1,1,1,1,1,1,1]=>12
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1]=>[2,2,1,1,1,1,1]=>7
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,1,1]=>[6,2,2,1,1,1,1,1]=>8
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1]=>[2,2,1,1,1,1,1,1]=>8
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,2]=>[5,2,2,1,1,1,1,1,1]=>9
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,1,1]=>[4,2,2,2,1,1,1,1,1,1]=>10
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[5,4,2]=>[2,2,1,1,1,1,1,1,1]=>9
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,1]=>[2,2,2,2,2,1,1,1,1,1]=>10
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,2]=>[3,2,2,2,1,1,1,1,1,1,1]=>11
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,1,1]=>[3,2,2,2,1,1,1,1,1,1,1,1]=>12
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[4,4,3,2]=>[2,2,2,1,1,1,1,1,1,1]=>10
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,1]=>[3,2,2,1,1,1,1,1,1,1,1]=>11
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,4,1,1]=>[3,2,2,1,1,1,1,1,1,1,1,1]=>12
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,3]=>[3,2,2,1,1,1,1,1,1,1,1,1,1]=>13
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,1]=>[2,2,2,1,1,1,1,1,1,1,1]=>11
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,1]=>[2,2,2,1,1,1,1,1,1,1,1,1]=>12
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,1]=>[2,2,2,1,1,1,1,1,1,1,1,1,1]=>13
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2]=>[2,2,2,1,1,1,1,1,1,1,1,1,1,1]=>14
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1,1]=>[6,1,1,1]=>4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1]=>[5,1,1,1]=>4
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,2,1]=>[4,2,1,1,1]=>5
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,2,1]=>[4,4,3,1,1,1]=>6
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]=>[4,1,1,1]=>4
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,1,1]=>[6,4,1,1,1]=>5
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[5,2,1]=>[4,1,1,1,1]=>5
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,2]=>[4,3,3,1,1,1]=>6
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,1,1]=>[4,4,2,1,1,1,1]=>7
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,1]=>[3,3,3,1,1,1]=>6
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,1]=>[4,3,2,1,1,1,1]=>7
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1]=>[4,3,2,1,1,1,1,1]=>8
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]=>[1,1,1,1]=>4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1,1,1]=>[6,1,1,1,1]=>5
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1,1]=>[5,1,1,1,1]=>5
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,3,1]=>[4,2,1,1,1,1]=>6
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,2,1]=>[4,4,3,1,1,1,1]=>7
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2]=>[3,1,1,1,1]=>5
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1,1,1]=>[6,3,1,1,1,1]=>6
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,4,1]=>[4,1,1,1,1,1]=>6
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,3,3]=>[3,3,3,1,1,1,1]=>7
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[5,5,2,1,1,1]=>[4,3,3,1,1,1,1,1]=>8
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1,1]=>[4,2,2,1,1,1,1]=>7
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,2]=>[4,3,1,1,1,1,1,1]=>8
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[5,5,4,1]=>[4,4,1,1,1,1,1,1,1]=>9
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1]=>[3,1,1,1,1,1]=>6
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,1,1]=>[6,3,1,1,1,1,1]=>7
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[5,3,1]=>[3,1,1,1,1,1,1]=>7
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,2]=>[3,3,2,2,1,1,1,1]=>8
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,1,1]=>[4,2,2,2,1,1,1,1,1]=>9
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[4,3,3,2]=>[3,3,1,1,1,1,1,1]=>8
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[5,5,2,1,1]=>[4,3,1,1,1,1,1,1,1]=>9
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[6,4,4,1]=>[4,3,1,1,1,1,1,1,1,1]=>10
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,1]=>[3,3,1,1,1,1,1,1,1]=>9
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,1]=>[3,3,1,1,1,1,1,1,1,1]=>10
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1]=>[3,3,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]=>[1,1,1,1,1]=>5
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1,1,1]=>[6,1,1,1,1,1]=>6
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1,1]=>[5,1,1,1,1,1]=>6
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,3,2]=>[4,2,1,1,1,1,1]=>7
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,2,1]=>[4,4,3,1,1,1,1,1]=>8
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,3,1]=>[2,1,1,1,1,1]=>6
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1,1,1]=>[6,2,1,1,1,1,1]=>7
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,3]=>[4,1,1,1,1,1,1]=>7
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1]=>[5,2,1,1,1,1,1,1]=>8
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,4,1,1,1]=>[4,4,2,1,1,1,1,1,1]=>9
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1,1]=>[4,2,1,1,1,1,1,1]=>8
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1]=>[4,2,1,1,1,1,1,1,1]=>9
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[5,4,4,3]=>[4,4,1,1,1,1,1,1,1,1]=>10
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,2]=>[2,1,1,1,1,1,1]=>7
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,3,1,1,1]=>[6,2,1,1,1,1,1,1]=>8
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,4,2]=>[3,1,1,1,1,1,1,1]=>8
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[5,3,3,3]=>[3,2,2,2,1,1,1,1,1]=>9
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[5,5,3,1,1,1]=>[5,2,2,1,1,1,1,1,1,1]=>10
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2]=>[3,2,1,1,1,1,1,1,1]=>9
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[5,5,2,2]=>[4,2,1,1,1,1,1,1,1,1]=>10
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[5,5,3,3]=>[4,3,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,3,1,1]=>[3,2,1,1,1,1,1,1,1,1]=>10
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,2]=>[3,2,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[5,5,4,2]=>[3,3,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1]=>[2,1,1,1,1,1,1,1]=>8
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,1,1]=>[6,2,1,1,1,1,1,1,1]=>9
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[5,3,2]=>[2,1,1,1,1,1,1,1,1]=>9
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,2]=>[4,2,2,1,1,1,1,1,1,1]=>10
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,1,1]=>[4,2,2,1,1,1,1,1,1,1,1]=>11
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,4,3,1]=>[2,2,1,1,1,1,1,1,1,1]=>10
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,4,1,1]=>[4,2,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,3]=>[4,2,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[5,3,3,2]=>[2,2,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[5,5,3,1,1]=>[3,2,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[6,4,4,2]=>[3,2,1,1,1,1,1,1,1,1,1,1,1]=>13
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,1]=>[2,2,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,1]=>[2,2,1,1,1,1,1,1,1,1,1,1,1]=>13
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2]=>[2,2,1,1,1,1,1,1,1,1,1,1,1,1]=>14
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1]=>[1,1,1,1,1,1]=>6
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,1,1]=>[6,1,1,1,1,1,1]=>7
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,1]=>[5,1,1,1,1,1,1]=>7
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1]=>[5,1,1,1,1,1,1,1]=>8
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,2,1]=>[4,4,3,1,1,1,1,1,1]=>9
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,2,1]=>[1,1,1,1,1,1,1]=>7
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,1,1]=>[6,1,1,1,1,1,1,1]=>8
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,2]=>[4,1,1,1,1,1,1,1]=>8
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[5,5,2,1]=>[5,1,1,1,1,1,1,1,1]=>9
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,3,1,1]=>[4,3,3,1,1,1,1,1,1,1]=>10
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,1]=>[4,1,1,1,1,1,1,1,1]=>9
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1]=>[4,1,1,1,1,1,1,1,1,1]=>10
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,3,2]=>[4,4,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,3,1]=>[1,1,1,1,1,1,1,1]=>8
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,1,1]=>[6,1,1,1,1,1,1,1,1]=>9
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1]=>[3,1,1,1,1,1,1,1,1]=>9
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[5,4,4,1]=>[5,1,1,1,1,1,1,1,1,1]=>10
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,4,2,1,1]=>[5,3,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,2]=>[3,1,1,1,1,1,1,1,1,1]=>10
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[5,5,3,1]=>[4,1,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,4,2,2]=>[4,3,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,1]=>[3,1,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1]=>[3,1,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,4,3,1]=>[3,3,1,1,1,1,1,1,1,1,1,1,1]=>13
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,2]=>[1,1,1,1,1,1,1,1,1]=>9
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,1,1]=>[6,1,1,1,1,1,1,1,1,1]=>10
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1]=>[2,1,1,1,1,1,1,1,1,1]=>10
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,3]=>[5,1,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[5,5,3,2,1,1]=>[5,2,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[5,3,3,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[5,4,4,2]=>[4,1,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[5,5,3,2,2]=>[4,2,1,1,1,1,1,1,1,1,1,1,1]=>13
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,2]=>[2,1,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[5,5,3,2]=>[3,1,1,1,1,1,1,1,1,1,1,1,1]=>13
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[5,5,3,3,1]=>[3,2,1,1,1,1,1,1,1,1,1,1,1,1]=>14
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,1]=>[2,1,1,1,1,1,1,1,1,1,1,1,1]=>13
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2]=>[2,1,1,1,1,1,1,1,1,1,1,1,1,1]=>14
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[5,5,4,2,1]=>[2,2,1,1,1,1,1,1,1,1,1,1,1,1,1]=>15
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1]=>10
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,1]=>[6,1,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,2]=>[5,1,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,1]=>[5,1,1,1,1,1,1,1,1,1,1,1,1]=>13
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,3,1]=>[4,1,1,1,1,1,1,1,1,1,1,1,1]=>13
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,2]=>[4,1,1,1,1,1,1,1,1,1,1,1,1,1]=>14
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,1]=>13
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,4,2,1]=>[3,1,1,1,1,1,1,1,1,1,1,1,1,1]=>14
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,3,1]=>[3,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>15
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>14
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[5,5,3,2,1]=>[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>15
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,4,2,1]=>[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>16
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>15
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>16
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>17
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[7]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[6]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7]=>[4,3]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[5,4,4]=>3
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[5]=>1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[7,5]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[6]=>[3,3]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[4,4,4]=>3
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[4,3,3,3]=>4
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[4,4,3]=>3
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[3,3,3,3]=>4
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[3,3,3,2,2]=>5
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[4]=>1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1,1]=>[7,4]=>2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[6,4]=>2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[6,3,2]=>3
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2,1]=>[6,4,4,3]=>4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[5]=>[3,2]=>2
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[7,3,2]=>3
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[4,3,3]=>3
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[5,3,2,2]=>4
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1,1]=>[5,3,3,3,3]=>5
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[3,3,3,2]=>4
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[3,3,2,2,2]=>5
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2]=>[3,3,3,3,3,2]=>6
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[3,3,3]=>3
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1,1]=>[7,3,3,3]=>4
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[3,3,2,2]=>4
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2]=>[5,3,3,3,2]=>5
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1,1]=>[5,3,3,2,2,2]=>6
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[3,2,2,2,2]=>5
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1]=>[3,3,3,3,2,2]=>6
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,2]=>[3,3,3,2,2,2,2]=>7
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,2,2]=>6
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1]=>[3,3,2,2,2,2,2]=>7
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1]=>[3,2,2,2,2,2,2,2]=>8
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[3]=>1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1,1]=>[7,3]=>2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[6,3]=>2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[5,3,2]=>3
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2,1]=>[5,4,4,3]=>4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[5,3]=>2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1,1]=>[7,5,3]=>3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[5,2,2]=>3
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2]=>[5,4,3,3]=>4
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1,1]=>[5,4,3,2,2]=>5
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1]=>[5,3,3,3]=>4
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1]=>[4,4,3,2,2]=>5
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1]=>[4,4,2,2,2,2]=>6
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[4]=>[2,2]=>2
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[7,2,2]=>3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[6,2,2]=>3
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[5,2,2,2]=>4
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2,1]=>[5,4,4,2,2]=>5
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[3,3,2]=>3
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[7,3,3,2]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[4,2,2,2]=>4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[5,3,3,2,2]=>5
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1,1]=>[6,3,2,2,2,2]=>6
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[5,3,2,2,2]=>5
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[5,2,2,2,2,2]=>6
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,6,5]=>[5,2,2,2,2,2,2]=>7
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[3,2,2,2]=>4
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1,1]=>[7,3,2,2,2]=>5
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[2,2,2,2,2]=>5
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2]=>[5,3,2,2,2,2]=>6
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1,1]=>[4,3,2,2,2,2,2]=>7
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[3,3,2,2,2,2]=>6
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1]=>[4,2,2,2,2,2,2]=>7
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[7,5,5]=>[4,2,2,2,2,2,2,1]=>8
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1]=>[3,2,2,2,2,2,2]=>7
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1]=>[2,2,2,2,2,2,2,2]=>8
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[7,6,4]=>[2,2,2,2,2,2,2,2,1]=>9
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[3,2,2]=>3
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1,1]=>[7,3,2,2]=>4
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1]=>[6,3,2,2]=>4
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1]=>[6,2,2,2,2]=>5
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[2,2,2,2]=>4
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1,1]=>[7,2,2,2,2]=>5
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[4,3,2,2,2]=>5
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1]=>[6,2,2,2,2,1]=>6
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1]=>[4,2,2,2,2,2]=>6
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1]=>[4,2,2,2,2,2,1]=>7
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[2,2,2,2,1]=>5
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1,1]=>[7,2,2,2,2,1]=>6
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[3,2,2,2,2,2]=>6
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,5]=>[6,2,2,2,2,1,1]=>7
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[2,2,2,2,2,2,2]=>7
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,6,4]=>[4,2,2,2,2,2,1,1]=>8
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1]=>[2,2,2,2,2,2,2,1]=>8
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[7,5,4]=>[2,2,2,2,2,2,2,1,1]=>9
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1]=>[2,2,2,2,2,2]=>6
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1]=>[2,2,2,2,2,2,1]=>7
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1]=>[2,2,2,2,2,2,1,1]=>8
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4]=>[2,2,2,2,2,2,1,1,1]=>9
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[2]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[7,2]=>2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[6,2]=>2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[4,3,2]=>3
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2,1]=>[5,4,4,2]=>4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[5,2]=>2
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1,1]=>[7,5,2]=>3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[4,2,2]=>3
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2]=>[4,4,4,2]=>4
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1,1]=>[4,3,3,3,2]=>5
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1]=>[4,4,3,2]=>4
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1]=>[4,3,3,2,2]=>5
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1]=>[4,3,2,2,2,2]=>6
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[4,2]=>2
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1,1]=>[7,4,2]=>3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]=>[6,4,2]=>3
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1]=>[6,4,2,1]=>4
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[4,2,1]=>3
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1,1]=>[7,4,2,1]=>4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[4,3,3,2]=>4
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1]=>[6,4,2,1,1]=>5
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1]=>[4,4,2,2,1]=>5
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1]=>[4,4,2,2,1,1]=>6
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1]=>[4,3,2,2]=>4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1]=>[4,3,2,2,1]=>5
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1]=>[4,3,2,2,1,1]=>6
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2,1]=>[4,4,2,2,2,2,1]=>7
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[3]=>[2,1]=>2
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[7,2,1]=>3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[6,2,1]=>3
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[4,3,2,1]=>4
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2,1]=>[5,4,4,2,1]=>5
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[5,2,1]=>3
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1,1]=>[7,5,2,1]=>4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[4,2,2,1]=>4
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2]=>[4,4,4,2,1]=>5
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1,1]=>[4,3,3,3,2,1]=>6
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1]=>[4,4,3,2,1]=>5
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1]=>[4,3,3,2,2,1]=>6
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[7,6,3]=>[4,4,2,2,2,1,1]=>7
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[2,2,2]=>3
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[7,2,2,2]=>4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[6,2,2,2]=>4
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[4,3,3,2,1]=>5
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[4,2,1,1]=>4
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[7,4,2,1,1]=>5
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[4,2,2,2,2]=>5
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[6,3,2,2,1,1]=>6
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[5,2,2,2,2,1]=>6
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[4,3,2,2,2,1,1]=>7
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[4,2,2,2,1]=>5
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[4,2,2,2,1,1]=>6
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[4,3,2,2,1,1,1]=>7
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2,1]=>[4,3,3,2,2,1,1,1]=>8
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[2,2,2,1]=>4
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1,1]=>[7,2,2,2,1]=>5
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1]=>[6,2,2,2,1]=>5
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1]=>[6,2,2,2,1,1]=>6
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[2,2,2,1,1]=>5
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1,1]=>[7,2,2,2,1,1]=>6
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[4,2,2,2,2,1]=>6
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,6,3]=>[5,2,2,2,2,1,1]=>7
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1]=>[4,2,2,2,2,1,1]=>7
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[7,5,3]=>[4,2,2,2,2,1,1,1]=>8
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[2,2,2,2,2,1]=>6
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[4,2,2,2,1,1,1]=>7
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[3,2,2,2,2,1,1,1]=>8
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,1,1]=>[4,2,2,2,2,2,1,1,1]=>9
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1]=>[2,2,2,2,2,1,1]=>7
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1]=>[2,2,2,2,2,1,1,1]=>8
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[6,5,3]=>[2,2,2,2,2,1,1,1,1]=>9
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2]=>[2,2,2,2,2,2,2,1,1,1]=>10
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[2,2,1]=>3
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1,1]=>[7,2,2,1]=>4
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1]=>[6,2,2,1]=>4
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1]=>[5,2,2,2,1]=>5
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1]=>[5,2,2,1]=>4
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,1,1]=>[7,5,2,2,1]=>5
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1]=>[5,2,2,1,1]=>5
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,2]=>[4,4,4,2,2,1]=>6
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,1]=>[4,4,3,2,2,1]=>6
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,1,1]=>[4,4,3,2,2,1,1]=>7
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[2,2,1,1]=>4
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1,1]=>[7,2,2,1,1]=>5
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1]=>[6,2,2,1,1]=>5
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1]=>[5,2,2,2,1,1]=>6
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[4,2,2,1,1]=>5
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1,1]=>[7,4,2,2,1,1]=>6
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[5,2,2,1,1,1]=>6
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,3]=>[6,4,2,2,1,1,1]=>7
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1]=>[5,2,2,2,2,2,1]=>7
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,2]=>[5,3,2,2,2,1,1,1]=>8
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1]=>[4,2,2,1,1,1]=>6
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1]=>[3,2,2,2,1,1,1]=>7
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2]=>[4,3,2,2,2,1,1,1]=>8
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2,1]=>[4,3,2,2,2,1,1,1,1]=>9
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[2,2,1,1,1]=>5
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1,1]=>[7,2,2,1,1,1]=>6
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1]=>[6,2,2,1,1,1]=>6
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[7,4,3]=>[5,2,2,2,1,1,1]=>7
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[2,2,2,2,1,1]=>6
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1,1,1]=>[7,2,2,2,2,1,1]=>7
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[5,2,2,1,1,1,1]=>7
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,1]=>[5,2,2,2,2,2,1,1]=>8
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1,1]=>[5,3,2,2,1,1,1,1]=>8
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,1]=>[5,2,2,2,2,1,1,1,1]=>9
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[2,2,2,2,1,1,1]=>7
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]=>[3,2,2,2,1,1,1,1]=>8
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2]=>[3,3,2,2,2,1,1,1,1]=>9
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,1,1]=>[3,2,2,2,2,2,1,1,1,1]=>10
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1]=>[2,2,2,2,1,1,1,1]=>8
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[6,4,3]=>[2,2,2,2,1,1,1,1,1]=>9
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,1]=>[2,2,2,2,2,2,1,1,1,1]=>10
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2]=>[2,2,2,2,2,2,1,1,1,1,1]=>11
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1]=>[2,2,2,1,1,1]=>6
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1,1,1]=>[7,2,2,2,1,1,1]=>7
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1,1]=>[6,2,2,2,1,1,1]=>7
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,1]=>[6,2,2,2,1,1,1,1]=>8
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1]=>[2,2,2,1,1,1,1]=>7
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1,1,1]=>[7,2,2,2,1,1,1,1]=>8
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2]=>[5,2,2,2,1,1,1,1]=>8
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,1]=>[6,2,2,2,1,1,1,1,1]=>9
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1,1]=>[5,2,2,2,1,1,1,1,1]=>9
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,1]=>[5,2,2,2,1,1,1,1,1,1]=>10
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1]=>[2,2,2,1,1,1,1,1]=>8
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1]=>[3,2,2,2,2,1,1,1,1]=>9
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2]=>[3,2,2,2,2,1,1,1,1,1]=>10
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,1,1]=>[3,2,2,2,2,1,1,1,1,1,1]=>11
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3]=>[2,2,2,1,1,1,1,1,1]=>9
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1]=>[3,2,2,2,1,1,1,1,1,1]=>10
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,1]=>[2,2,2,2,2,1,1,1,1,1,1]=>11
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2]=>[2,2,2,2,2,1,1,1,1,1,1,1]=>12
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1]=>[2,2,2,2,1,1,1,1,1,1]=>10
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1]=>[2,2,2,2,1,1,1,1,1,1,1]=>11
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,1]=>[2,2,2,2,1,1,1,1,1,1,1,1]=>12
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,1]=>[2,2,2,2,1,1,1,1,1,1,1,1,1]=>13
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1]=>[1]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[7,1]=>2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[6,1]=>2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[4,3,1]=>3
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2,1]=>[5,4,4,1]=>4
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[5,1]=>2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1,1]=>[7,5,1]=>3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[3,3,1]=>3
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2]=>[4,4,4,1]=>4
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1,1]=>[4,3,3,3,1]=>5
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1]=>[4,4,3,1]=>4
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1]=>[3,3,3,3,1]=>5
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[7,6,1]=>[3,3,3,2,2,1]=>6
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[4,1]=>2
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1,1]=>[7,4,1]=>3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1,1]=>[6,4,1]=>3
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1]=>[6,3,2,1]=>4
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[3,2,1]=>3
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1,1]=>[7,3,2,1]=>4
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[4,3,3,1]=>4
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,6,1]=>[5,3,2,2,1]=>5
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1]=>[3,3,3,2,1]=>5
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[7,5,1]=>[3,3,2,2,2,1]=>6
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1]=>[3,3,3,1]=>4
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,1,1]=>[7,3,3,3,1]=>5
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1]=>[3,3,2,2,1]=>5
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,2]=>[5,3,3,3,2,1]=>6
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[6,5,1]=>[3,2,2,2,2,1]=>6
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3,1]=>[3,3,3,3,2,2,1]=>7
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,1]=>[3,3,3,2,2,2,1]=>7
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2,1]=>[3,3,2,2,2,2,2,1]=>8
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[3,1]=>2
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1,1]=>[7,3,1]=>3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1,1]=>[6,3,1]=>3
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1]=>[5,3,2,1]=>4
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,2,1]=>[5,4,4,3,1]=>5
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>[5,3,1]=>3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,1,1]=>[7,5,3,1]=>4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1]=>[5,3,1,1]=>4
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,2]=>[5,4,3,3,1]=>5
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,1,1,1]=>[5,4,3,2,2,1]=>6
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,1]=>[5,3,3,3,1]=>5
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,1,1]=>[5,3,3,3,1,1]=>6
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,1]=>[5,3,3,3,1,1,1]=>7
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[3,1,1]=>3
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1,1]=>[7,3,1,1]=>4
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]=>[6,3,1,1]=>4
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[7,4,1]=>[5,3,2,1,1]=>5
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[3,3,2,1]=>4
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1,1]=>[7,3,3,2,1]=>5
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[5,3,1,1,1]=>5
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3]=>[5,3,3,2,2,1]=>6
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1]=>[5,3,2,2,2,1]=>6
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2]=>[5,3,2,2,2,1,1]=>7
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1]=>[3,2,2,2,1]=>5
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,1,1]=>[7,3,2,2,2,1]=>6
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[6,4,1]=>[3,2,2,2,1,1]=>6
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,2]=>[5,3,2,2,2,2,1]=>7
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2]=>[3,3,2,2,2,2,1]=>7
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1,1,1]=>[4,3,2,2,2,2,1,1]=>8
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,1]=>[3,2,2,2,2,2,2,1]=>8
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,1,1]=>[3,2,2,2,2,2,2,1,1]=>9
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,1,1,1]=>[7,3,2,2,1]=>5
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,1,1]=>[6,3,2,2,1]=>5
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,1]=>[6,3,3,1,1,1]=>6
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1]=>[3,3,1,1,1]=>5
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,1,1,1]=>[7,3,3,1,1,1]=>6
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2]=>[4,3,2,2,2,1]=>6
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1,1]=>[6,3,3,1,1,1,1]=>7
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,1,1]=>[5,3,3,1,1,1,1]=>7
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,1]=>[5,3,3,1,1,1,1,1]=>8
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,4,1]=>[3,3,1,1,1,1]=>6
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1,1,1]=>[7,3,3,1,1,1,1]=>7
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1]=>[3,2,2,2,2,2,1]=>7
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,5,1]=>[6,3,3,1,1,1,1,1]=>8
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2]=>[3,2,2,2,2,2,1,1]=>8
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[6,6,4,1]=>[5,3,3,1,1,1,1,1,1]=>9
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1,1]=>[3,2,2,2,2,2,1,1,1]=>9
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1]=>[3,3,3,2,1,1,1,1,1,1]=>10
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,1]=>[3,2,2,2,2,1,1]=>7
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,1]=>[3,3,3,1,1,1,1,1]=>8
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1]=>[3,3,3,1,1,1,1,1,1]=>9
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1]=>[3,3,3,1,1,1,1,1,1,1]=>10
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2]=>[1,1]=>2
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[7,1,1]=>3
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[6,1,1]=>3
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[4,3,1,1]=>4
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2,1]=>[5,4,4,1,1]=>5
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[5,1,1]=>3
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1,1]=>[7,5,1,1]=>4
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[3,3,1,1]=>4
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2]=>[4,4,4,1,1]=>5
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1,1]=>[4,3,3,3,1,1]=>6
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1]=>[4,4,3,1,1]=>5
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1]=>[3,3,3,3,1,1]=>6
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[7,6,2]=>[3,3,3,2,2,1,1]=>7
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[4,1,1]=>3
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1,1]=>[7,4,1,1]=>4
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1]=>[6,4,1,1]=>4
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1]=>[6,3,2,1,1]=>5
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[3,2,1,1]=>4
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1,1]=>[7,3,2,1,1]=>5
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[4,3,3,1,1]=>5
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,6,2]=>[4,3,3,2,1,1]=>6
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1]=>[3,3,3,2,1,1]=>6
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[7,5,2]=>[3,3,2,2,2,1,1]=>7
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1]=>[3,3,3,1,1]=>5
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1]=>[4,3,2,1,1,1]=>6
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[6,5,2]=>[3,3,2,2,1,1,1]=>7
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2,1]=>[3,3,3,2,2,2,1,1]=>8
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2,1,1]=>3
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[7,2,1,1]=>4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[6,2,1,1]=>4
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[4,3,2,1,1]=>5
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2,1]=>[5,4,4,2,1,1]=>6
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[5,2,1,1]=>4
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1,1]=>[7,5,2,1,1]=>5
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[3,3,2,1,1]=>5
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2]=>[4,4,4,2,1,1]=>6
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1,1]=>[4,3,3,3,2,1,1]=>7
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1]=>[4,4,3,2,1,1]=>6
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1]=>[5,3,3,2,1,1,1]=>7
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2]=>[5,3,3,2,1,1,1,1]=>8
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[3,1,1,1]=>4
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[7,3,1,1,1]=>5
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[6,3,1,1,1]=>5
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[5,3,2,1,1,1]=>6
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,2,2,1,1]=>5
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[7,3,2,2,1,1]=>6
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[5,3,1,1,1,1]=>6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,3,2,2,2,2,1]=>7
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1]=>[4,4,2,2,1,1,1]=>7
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3]=>[3,3,2,2,2,2,1,1]=>8
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[3,3,2,1,1,1]=>6
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3,2,1,1,1,1]=>7
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,3,2,2,1,1,1,1]=>8
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2,1]=>[3,3,2,2,2,2,1,1,1]=>9
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[3,2,1,1,1]=>5
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1,1]=>[7,3,2,1,1,1]=>6
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1]=>[6,3,2,1,1,1]=>6
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1]=>[6,3,2,1,1,1,1]=>7
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[3,2,1,1,1,1]=>6
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1,1]=>[7,3,2,1,1,1,1]=>7
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[3,3,3,2,1,1,1]=>7
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2]=>[6,3,2,1,1,1,1,1]=>8
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1]=>[3,3,2,2,2,1,1,1]=>8
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2]=>[3,3,3,2,1,1,1,1,1]=>9
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[3,3,1,1,1,1,1]=>7
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1]=>[4,2,2,2,1,1,1,1]=>8
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[3,3,2,2,1,1,1,1,1]=>9
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1,1,1]=>[4,2,2,2,2,1,1,1,1,1]=>10
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1]=>[3,3,2,1,1,1,1,1]=>8
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1]=>[3,3,2,1,1,1,1,1,1]=>9
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2]=>[3,3,2,1,1,1,1,1,1,1]=>10
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3]=>[3,3,3,1,1,1,1,1,1,1,1]=>11
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[2,1,1,1]=>4
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1,1]=>[7,2,1,1,1]=>5
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1]=>[6,2,1,1,1]=>5
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1]=>[3,3,2,2,1,1]=>6
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1]=>[5,2,1,1,1]=>5
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,1,1]=>[7,5,2,1,1,1]=>6
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1]=>[5,2,1,1,1,1]=>6
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,2]=>[4,4,4,2,1,1,1]=>7
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,1]=>[4,4,3,2,1,1,1]=>7
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,1,1]=>[4,4,3,2,1,1,1,1]=>8
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2,1,1,1,1]=>5
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1,1]=>[7,2,1,1,1,1]=>6
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1]=>[6,2,1,1,1,1]=>6
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[7,4,2]=>[5,3,1,1,1,1,1]=>7
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[3,2,2,1,1,1]=>6
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1,1,1]=>[7,3,2,2,1,1,1]=>7
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[5,2,1,1,1,1,1]=>7
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,3]=>[4,4,2,2,2,1,1,1]=>8
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1,1]=>[4,3,3,2,1,1,1,1]=>8
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,2]=>[3,3,3,3,1,1,1,1,1]=>9
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1]=>[3,2,2,1,1,1,1]=>7
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]=>[3,2,2,1,1,1,1,1]=>8
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2]=>[4,2,2,2,2,1,1,1,1]=>9
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2,1]=>[3,3,2,2,2,1,1,1,1,1]=>10
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[2,2,1,1,1,1]=>6
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1,1]=>[7,2,2,1,1,1,1]=>7
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1]=>[6,2,2,1,1,1,1]=>7
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2]=>[3,3,3,2,1,1,1,1]=>8
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[3,2,1,1,1,1,1]=>7
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1,1]=>[7,3,2,1,1,1,1,1]=>8
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[5,2,2,1,1,1,1,1]=>8
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1,1]=>[6,3,2,1,1,1,1,1,1]=>9
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1]=>[5,3,2,1,1,1,1,1,1]=>9
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1,1]=>[5,3,2,1,1,1,1,1,1,1]=>10
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,2,1,1,1,1,1,1]=>8
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,2,2,1,1,1,1,1,1]=>9
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2]=>[3,3,2,2,1,1,1,1,1,1]=>10
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1,1]=>[3,3,2,2,1,1,1,1,1,1,1]=>11
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1]=>[3,2,2,1,1,1,1,1,1]=>9
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2]=>[3,2,2,1,1,1,1,1,1,1]=>10
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1,1]=>[3,3,2,1,1,1,1,1,1,1,1]=>11
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3]=>[3,3,2,1,1,1,1,1,1,1,1,1]=>12
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1]=>[2,2,1,1,1,1,1]=>7
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,1,1,1]=>[7,2,2,1,1,1,1,1]=>8
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,1,1]=>[6,2,2,1,1,1,1,1]=>8
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,1]=>[6,2,2,1,1,1,1,1,1]=>9
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1]=>[2,2,1,1,1,1,1,1]=>8
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1,1,1]=>[7,2,2,1,1,1,1,1,1]=>9
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2]=>[5,2,2,1,1,1,1,1,1]=>9
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1,1]=>[6,2,2,1,1,1,1,1,1,1]=>10
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1,1]=>[4,2,2,2,1,1,1,1,1,1]=>10
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,1]=>[4,2,2,2,1,1,1,1,1,1,1]=>11
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,4,2]=>[2,2,1,1,1,1,1,1,1]=>9
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1]=>[2,2,2,2,2,1,1,1,1,1]=>10
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2]=>[3,2,2,2,1,1,1,1,1,1,1]=>11
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,1,1]=>[3,2,2,2,1,1,1,1,1,1,1,1]=>12
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2]=>[2,2,2,1,1,1,1,1,1,1]=>10
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1]=>[3,2,2,1,1,1,1,1,1,1,1]=>11
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1]=>[3,2,2,1,1,1,1,1,1,1,1,1]=>12
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3]=>[3,2,2,1,1,1,1,1,1,1,1,1,1]=>13
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,1]=>[2,2,2,1,1,1,1,1,1,1,1]=>11
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1]=>[2,2,2,1,1,1,1,1,1,1,1,1]=>12
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,1]=>[2,2,2,1,1,1,1,1,1,1,1,1,1]=>13
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2]=>[2,2,2,1,1,1,1,1,1,1,1,1,1,1]=>14
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[7,1,1,1]=>4
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1]=>[6,1,1,1]=>4
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[7,2,1]=>[4,3,1,1,1]=>5
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,2,1]=>[5,4,4,1,1,1]=>6
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1]=>[5,1,1,1]=>4
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,1,1]=>[7,5,1,1,1]=>5
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,2,1]=>[4,2,1,1,1]=>5
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,2]=>[4,4,4,1,1,1]=>6
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,1,1,1]=>[4,3,3,3,1,1,1]=>7
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,1]=>[4,4,3,1,1,1]=>6
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,1,1]=>[3,3,3,3,1,1,1]=>7
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1]=>[3,3,3,2,2,1,1,1]=>8
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1]=>[4,1,1,1]=>4
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1,1,1]=>[7,4,1,1,1]=>5
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1,1]=>[6,4,1,1,1]=>5
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,1]=>[6,4,1,1,1,1]=>6
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,2,1]=>[4,1,1,1,1]=>5
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,1,1,1]=>[7,4,1,1,1,1]=>6
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2]=>[4,3,3,1,1,1]=>6
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1]=>[6,4,1,1,1,1,1]=>7
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,1,1]=>[4,4,2,1,1,1,1]=>7
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1]=>[4,4,2,1,1,1,1,1]=>8
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1]=>[3,3,3,1,1,1]=>6
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,1]=>[4,3,2,1,1,1,1]=>7
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1]=>[4,3,2,1,1,1,1,1]=>8
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[1,1,1,1]=>4
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1,1]=>[7,1,1,1,1]=>5
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1]=>[6,1,1,1,1]=>5
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[7,3,1]=>[4,3,1,1,1,1]=>6
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,2,1]=>[5,4,4,1,1,1,1]=>7
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1]=>[5,1,1,1,1]=>5
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,1,1]=>[7,5,1,1,1,1]=>6
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,3,1]=>[4,2,1,1,1,1]=>6
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,2]=>[4,4,4,1,1,1,1]=>7
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1,1,1]=>[4,3,3,3,1,1,1,1]=>8
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,1]=>[4,4,3,1,1,1,1]=>7
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1,1]=>[3,3,3,3,1,1,1,1]=>8
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1]=>[4,4,2,2,1,1,1,1,1]=>9
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[3,1,1,1,1]=>5
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1,1]=>[7,3,1,1,1,1]=>6
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1]=>[6,3,1,1,1,1]=>6
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2]=>[4,3,3,1,1,1,1]=>7
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[4,1,1,1,1,1]=>6
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1,1,1]=>[7,4,1,1,1,1,1]=>7
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]=>[3,3,3,1,1,1,1]=>7
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1]=>[6,4,1,1,1,1,1,1]=>8
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1,1]=>[4,3,3,1,1,1,1,1]=>8
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1]=>[4,3,2,2,1,1,1,1,1]=>9
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1]=>[4,2,2,1,1,1,1]=>7
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2]=>[4,3,1,1,1,1,1,1]=>8
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1]=>[4,4,1,1,1,1,1,1,1]=>9
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[3,1,1,1,1,1]=>6
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1,1,1]=>[7,3,1,1,1,1,1]=>7
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1,1]=>[6,3,1,1,1,1,1]=>7
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1]=>[6,3,1,1,1,1,1,1]=>8
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]=>[3,1,1,1,1,1,1]=>7
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,1,1,1]=>[7,3,1,1,1,1,1,1]=>8
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2]=>[3,3,2,2,1,1,1,1]=>8
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1]=>[6,3,1,1,1,1,1,1,1]=>9
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,1,1]=>[4,2,2,2,1,1,1,1,1]=>9
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1]=>[4,3,2,1,1,1,1,1,1,1]=>10
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2]=>[3,3,1,1,1,1,1,1]=>8
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1]=>[4,3,1,1,1,1,1,1,1]=>9
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1]=>[4,3,1,1,1,1,1,1,1,1]=>10
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1]=>[3,3,1,1,1,1,1,1,1]=>9
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,1]=>[3,3,1,1,1,1,1,1,1,1]=>10
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1]=>[3,3,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[1,1,1,1,1]=>5
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1,1]=>[7,1,1,1,1,1]=>6
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1]=>[6,1,1,1,1,1]=>6
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[7,3,2]=>[4,3,1,1,1,1,1]=>7
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1]=>[5,1,1,1,1,1]=>6
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,1,1]=>[7,5,1,1,1,1,1]=>7
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[6,3,2]=>[4,2,1,1,1,1,1]=>7
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,2]=>[4,4,4,1,1,1,1,1]=>8
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,1]=>[4,4,3,1,1,1,1,1]=>8
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,1,1]=>[4,3,3,2,1,1,1,1,1]=>9
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[2,1,1,1,1,1]=>6
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1,1]=>[7,2,1,1,1,1,1]=>7
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1]=>[6,2,1,1,1,1,1]=>7
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1]=>[5,3,1,1,1,1,1,1]=>8
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[4,1,1,1,1,1,1]=>7
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1,1,1]=>[7,4,1,1,1,1,1,1]=>8
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[5,2,1,1,1,1,1,1]=>8
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4]=>[3,3,3,2,2,1,1,1,1]=>9
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1,1]=>[4,4,2,1,1,1,1,1,1]=>9
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3]=>[4,3,2,2,1,1,1,1,1,1]=>10
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1]=>[4,2,1,1,1,1,1,1]=>8
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1]=>[4,2,1,1,1,1,1,1,1]=>9
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3]=>[4,4,1,1,1,1,1,1,1,1]=>10
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[2,1,1,1,1,1,1]=>7
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1,1]=>[7,2,1,1,1,1,1,1]=>8
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1]=>[6,2,1,1,1,1,1,1]=>8
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2]=>[4,3,2,1,1,1,1,1,1]=>9
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[3,1,1,1,1,1,1,1]=>8
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1,1,1]=>[7,3,1,1,1,1,1,1,1]=>9
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3]=>[3,2,2,2,1,1,1,1,1]=>9
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2]=>[6,3,1,1,1,1,1,1,1,1]=>10
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1,1]=>[5,2,2,1,1,1,1,1,1,1]=>10
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2]=>[4,3,2,1,1,1,1,1,1,1,1]=>11
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[3,2,1,1,1,1,1,1,1]=>9
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[4,2,1,1,1,1,1,1,1,1]=>10
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3]=>[4,3,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1]=>[3,2,1,1,1,1,1,1,1,1]=>10
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2]=>[3,2,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2]=>[3,3,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]=>[2,1,1,1,1,1,1,1]=>8
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,1,1,1]=>[7,2,1,1,1,1,1,1,1]=>9
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,1,1]=>[6,2,1,1,1,1,1,1,1]=>9
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,1]=>[6,2,1,1,1,1,1,1,1,1]=>10
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,3,2]=>[2,1,1,1,1,1,1,1,1]=>9
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,1,1,1]=>[7,2,1,1,1,1,1,1,1,1]=>10
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2]=>[4,2,2,1,1,1,1,1,1,1]=>10
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2]=>[6,2,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,1,1]=>[4,2,2,1,1,1,1,1,1,1,1]=>11
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2]=>[4,2,2,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1]=>[2,2,1,1,1,1,1,1,1,1]=>10
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1]=>[4,2,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3]=>[4,2,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2]=>[2,2,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1]=>[3,2,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2]=>[3,2,1,1,1,1,1,1,1,1,1,1,1]=>13
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,1]=>[2,2,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,1]=>[2,2,1,1,1,1,1,1,1,1,1,1,1]=>13
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2]=>[2,2,1,1,1,1,1,1,1,1,1,1,1,1]=>14
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]=>[1,1,1,1,1,1]=>6
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1,1,1]=>[7,1,1,1,1,1,1]=>7
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1,1]=>[6,1,1,1,1,1,1]=>7
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1]=>[4,2,2,1,1,1,1,1]=>8
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1]=>[5,1,1,1,1,1,1]=>7
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1]=>[5,1,1,1,1,1,1,1]=>8
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2,1]=>[4,4,3,1,1,1,1,1,1]=>9
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[4,2,1]=>[1,1,1,1,1,1,1]=>7
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,1,1,1]=>[7,1,1,1,1,1,1,1]=>8
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,1,1]=>[6,1,1,1,1,1,1,1]=>8
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1]=>[5,2,1,1,1,1,1,1,1]=>9
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2]=>[4,1,1,1,1,1,1,1]=>8
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1]=>[5,1,1,1,1,1,1,1,1]=>9
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,1,1]=>[4,3,3,1,1,1,1,1,1,1]=>10
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,1]=>[4,1,1,1,1,1,1,1,1]=>9
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1]=>[4,1,1,1,1,1,1,1,1,1]=>10
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,2]=>[4,4,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,3,1]=>[1,1,1,1,1,1,1,1]=>8
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,1,1,1]=>[7,1,1,1,1,1,1,1,1]=>9
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,1,1]=>[6,1,1,1,1,1,1,1,1]=>9
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1]=>[5,2,1,1,1,1,1,1,1,1]=>10
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1]=>[3,1,1,1,1,1,1,1,1]=>9
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1]=>[5,1,1,1,1,1,1,1,1,1]=>10
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,1,1]=>[5,3,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2]=>[3,1,1,1,1,1,1,1,1,1]=>10
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1]=>[4,1,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,2]=>[4,3,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,1]=>[3,1,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1]=>[3,1,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,1]=>[3,3,1,1,1,1,1,1,1,1,1,1,1]=>13
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[4,3,2]=>[1,1,1,1,1,1,1,1,1]=>9
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1,1,1]=>[7,1,1,1,1,1,1,1,1,1]=>10
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1,1]=>[6,1,1,1,1,1,1,1,1,1]=>10
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2]=>[5,2,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1]=>[2,1,1,1,1,1,1,1,1,1]=>10
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3]=>[5,1,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,1,1]=>[5,2,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1]=>[2,1,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2]=>[4,1,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,2]=>[4,2,1,1,1,1,1,1,1,1,1,1,1]=>13
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2]=>[2,1,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2]=>[3,1,1,1,1,1,1,1,1,1,1,1,1]=>13
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,1]=>[3,2,1,1,1,1,1,1,1,1,1,1,1,1]=>14
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1]=>[2,1,1,1,1,1,1,1,1,1,1,1,1]=>13
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2]=>[2,1,1,1,1,1,1,1,1,1,1,1,1,1]=>14
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,1]=>[2,2,1,1,1,1,1,1,1,1,1,1,1,1,1]=>15
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1]=>10
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,1,1]=>[7,1,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,1]=>[6,1,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1]=>[6,1,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2]=>[5,1,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,1]=>[5,1,1,1,1,1,1,1,1,1,1,1,1]=>13
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,1]=>[4,1,1,1,1,1,1,1,1,1,1,1,1]=>13
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,2]=>[4,1,1,1,1,1,1,1,1,1,1,1,1,1]=>14
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,1]=>13
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,1]=>[3,1,1,1,1,1,1,1,1,1,1,1,1,1]=>14
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,1]=>[3,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>15
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>14
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,1]=>[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>15
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,1]=>[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>16
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>15
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>16
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>17
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[8]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8]=>[4,4]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2]=>[5,5,4]=>3
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,7]=>[6,3,3,2]=>4
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[9]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,1]=>[5,5,5]=>3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9]=>[5,4]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,1,1,1,1,1]=>[4,4,3,3]=>4
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2]=>[6,5,5]=>3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,8]=>[6,4,3,3]=>4
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1]=>[10]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2,1]=>[6,6,5]=>3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[10]=>[5,5]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[8,7]=>[3,3,3,3,3]=>5
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,1,1,1,1,1,1]=>[4,4,4,4]=>4
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]=>[11]=>[6,5]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[9,8]=>[4,4,3,3,3]=>5
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[7]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[6]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1,1]=>[8,6]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[5,4,4]=>3
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[5]=>1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,1,1,1]=>[8,5]=>2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,1,1]=>[7,5]=>2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[4,4,3]=>3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[4]=>1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,1,1,1,1]=>[8,4]=>2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[6,4]=>2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,1]=>[3,3,3]=>3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,2,1,1,1]=>[8,3,3,3]=>4
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,2,1,1]=>[7,3,3,3]=>4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,2,2]=>6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1]=>[3]=>1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,1,1,1,1,1]=>[8,3]=>2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,1,1]=>[5,3]=>2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,1]=>[3,2,2]=>3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[3,3,3,2,1,1,1,1]=>[8,3,2,2]=>4
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[3,3,3,2,1]=>[2,2,2,2,2,2]=>6
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[2]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1,1,1,1,1,1]=>[8,2]=>2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1,1,1,1,1]=>[7,2]=>2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,3,2,2,2,2,2,1]=>[5,5,5,2]=>4
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[6,2]=>2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1,1,1]=>[5,2]=>2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1,1]=>[4,2]=>2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[3,3,2,2,1,1,1,1]=>[8,4,2]=>3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1]=>[2,2,1]=>3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[3,3,2,1,1,1,1,1]=>[8,2,2,1]=>4
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[3,3,2,1]=>[2,2,2,1,1,1]=>6
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,4,3,2,1,1]=>[6,2,2,2,1,1,1]=>7
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,4,3,2,1]=>[2,2,2,2,1,1,1,1,1,1]=>10
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1]=>[1]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1]=>[8,1]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[7,1]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,2,2,2,2,2,1]=>[5,5,5,1]=>4
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[6,1]=>2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,2,2,2,2,1,1]=>[8,6,1]=>3
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,2,2,2,2,1]=>[5,4,4,1]=>4
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1,1]=>[5,1]=>2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1]=>[4,1]=>2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1]=>[3,1]=>2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[3,2,2,1,1,1,1,1]=>[8,3,1]=>3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[3,2,2,1,1]=>[5,3,1]=>3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,3,2,2,1,1]=>[7,5,3,1]=>4
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,3,2,1]=>[3,2,2,2,2,1,1]=>7
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,1,1,1,1,1]=>[8,1,1,1]=>4
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[7,1,1,1]=>4
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,1,1,1]=>[6,1,1,1]=>4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,2,2,1,1,1]=>[8,5,1,1,1]=>5
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,2,2,1]=>[4,4,3,1,1,1]=>6
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,1]=>[4,1,1,1]=>4
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,2,1,1,1,1]=>[8,4,1,1,1]=>5
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,2,1]=>[3,3,3,1,1,1]=>6
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1]=>[1,1,1,1,1,1]=>6
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1,1,1,1,1]=>[8,1,1,1,1,1,1]=>7
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1,1]=>[5,1,1,1,1,1,1]=>7
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,2,1]=>[4,4,3,1,1,1,1,1,1]=>9
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1]=>10
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,1,1]=>[7,1,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,1]=>[6,1,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>15
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[8]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[7]=>1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,1,1]=>[9,7]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,1]=>[5,5,5]=>3
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[6]=>1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[5,4,4]=>3
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[5]=>1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[4,4,3]=>3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[4]=>1
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,1,1,1,1,1]=>[9,4]=>2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[3,3,3,3,2,1]=>[3,3,3,2,2,2]=>6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[3]=>1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,1]=>[3,2,2]=>3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[3,3,3,2,1,1,1,1,1]=>[9,3,2,2]=>4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[2]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,2,1,1,1,1,1,1,1]=>[9,2]=>2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,2,1,1,1,1,1,1]=>[8,2]=>2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,2,1,1]=>[4,2]=>2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,2,1]=>[2,2,1]=>3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[3,3,2,1,1,1,1,1,1]=>[9,2,2,1]=>4
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[4,4,3,2,1]=>[2,2,2,2,1,1,1,1,1,1]=>10
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1]=>[1]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1]=>[8,1]=>2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1]=>[7,1]=>2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[6,1]=>2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,1,1]=>[4,1]=>2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,1]=>[3,1]=>2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[4,3,3,2,2,1,1]=>[7,5,3,1]=>4
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,2,1]=>[3,2,2,1]=>4
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[1,1,1]=>3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,1,1,1,1,1,1]=>[9,1,1,1]=>4
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,1]=>[4,1,1,1]=>4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1]=>[1,1,1,1,1,1]=>6
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1,1,1,1,1,1]=>[9,1,1,1,1,1,1]=>7
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1]=>10
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>15
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[2]=>[1,1]=>2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[2,2]=>[2,1,1]=>3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[3,3]=>[3,1,1,1]=>4
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[3,3,3]=>[3,2,2,1,1]=>5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[4,4,4]=>[5,3,1,1,1,1]=>6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4,4,4]=>[4,3,2,2,2,2,1]=>7
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[2]=>[1,1]=>2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,1]=>[2,1,1,1]=>4
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[2,2]=>[2,1,1]=>3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,3,1,1]=>[3,2,1,1,1]=>5
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[3,3]=>[3,1,1,1]=>4
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[4,4,1,1,1]=>[3,3,2,1,1,1]=>6
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[3,3,3]=>[3,2,2,1,1]=>5
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[4,4,4,1,1,1]=>[4,4,2,2,1,1,1]=>7
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[4,4,4]=>[5,3,1,1,1,1]=>6
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,4,4,4]=>[4,3,2,2,2,2,1]=>7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1]=>[1]=>1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[8,1]=>[4,4,1]=>3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[9,1]=>[5,4,1]=>3
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[8,2]=>[4,4,1,1]=>4
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,1]=>[4,4,2]=>3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,1,1,1,1,1,1]=>[8,1,1]=>3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0]=>[5,5,3,3]=>[4,3,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,4,2,2]=>[3,2,1,1,1,1,1,1,1]=>9
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>[4,2,2]=>[2,1,1,1,1,1,1]=>7
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[3,2]=>[1,1,1,1,1]=>5
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>16
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[4,2,1]=>[1,1,1,1,1,1,1]=>7
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[3,1]=>[1,1,1,1]=>4
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2]=>[2,2,2]=>3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[4]=>[2,2]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[7]=>[4,3]=>2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2]=>[5,5,4]=>3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[4,4,1,1,1,1,1,1]=>[8,3,1,1,1]=>5
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[4,1]=>[3,1,1]=>3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,5,5,1]=>[6,4,1,1,1,1,1,1]=>8
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,3,3,2,2,2,2]=>[5,5,4,3]=>4
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[4,4,4]=>3
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[6]=>[3,3]=>2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[4]=>[2,2]=>2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2]=>[2,2,2]=>3
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[7,7,1]=>[6,3,3,2,1]=>5
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1,1,1,1,1,1]=>[8,3,3]=>3
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[4,4,4,1,1,1,1]=>[7,3,2,2,1,1]=>6
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[4,4,1,1,1,1]=>[6,3,1,1,1]=>5
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,3,1,1,1]=>[5,2,1,1]=>4
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,1,1]=>[4,1,1]=>3
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,3,2,2,1,1]=>[7,5,2,1,1,1]=>6
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[6,4,2]=>[3,2,2,1,1,1,1,1]=>8
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[2]=>[1,1]=>2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,1,1,1,1,1,1,1]=>[9,1,1]=>3
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,1,1,1,1,1]=>[7,1,1]=>3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,1,1,1,1,1,1]=>[4,4,4,3]=>4
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>14
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2]=>[1,1,1,1,1,1,1,1,1]=>9
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[4,3,1,1,1,1,1,1]=>[8,1,1,1,1,1]=>6
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,1,1,1,1,1]=>[8,1,1,1,1,1,1,1,1,1]=>10
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[7,6]=>[3,3,3,2,2]=>5
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,2,2,2]=>[2,2,2,2,2,2,2]=>7
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[3]=>[2,1]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[9]=>1
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,2,2]=>[2,2,2,2,1,1,1]=>7
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[7]=>[4,3]=>2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[8]=>[4,4]=>2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[4,4,4,1,1,1,1,1]=>[8,3,2,2,1,1]=>6
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[5,1,1,1,1,1,1,1,1]=>[9,2,2]=>3
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[3,3,1]=>[2,1,1,1,1,1]=>6
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[4,4,1,1,1,1,1,1,1]=>[9,3,1,1,1]=>5
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[5,2,1,1,1]=>[3,2,2,2,1]=>5
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[5,5,5]=>[6,3,2,2,1,1]=>6
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[2]=>1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[7,1]=>[4,3,1]=>3
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[8,1]=>[4,4,1]=>3
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[3,2]=>[1,1,1,1,1]=>5
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,3,3]=>[5,3,3,2,2,1,1]=>7
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,1]=>[4,4,1,1,1,1,1,1]=>8
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>14
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[5,5,3,2,1]=>[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>15
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2]=>[2,1,1,1,1,1,1,1,1,1,1,1,1,1]=>14
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,2]=>[5,1,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,0]=>[4,4,2,1]=>[2,1,1,1,1,1,1,1,1,1]=>10
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,1]=>[2,2,1,1]=>4
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[7,2,1,1]=>4
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0]=>[8,7,1,1]=>[4,3,3,3,2,2]=>6
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[8,6]=>[3,3,3,3,2]=>5
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1,1,1,1,1]=>[4,3,3,3]=>4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[5]=>[3,2]=>2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[6]=>[3,3]=>2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[5]=>[3,2]=>2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,2,2,2,2,2]=>[5,5,4,1]=>4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[3]=>[2,1]=>2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,1,1]=>[2,2,2,1]=>4
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,1,1,1]=>[3,2,2,2]=>4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,1,1,1,1]=>[3,3,3,2]=>4
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0]=>[4,4]=>[4,2,1,1]=>4
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0]=>[4,4,1]=>[4,1,1,1,1,1]=>6
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,1,1,1,1,1,1,1]=>[5,4,4,4]=>4
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,1,1]=>[3,1,1,1,1,1,1,1,1,1,1]=>11
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[4,2]=>[2,1,1,1,1]=>5
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[5,1]=>[3,2,1]=>3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[4,1]=>[3,1,1]=>3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[5,5]=>[4,2,2,2]=>4
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]=>[6,6]=>[5,3,2,2]=>4
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2]=>[4,3,3]=>3
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[7,1,1,1,1]=>[6,3,2]=>3
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,1]=>[4,3,2,1,1,1,1,1,1,1]=>10
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,1,1,1]=>[4,2,2,2,1,1,1,1,1]=>9
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,4,3,2]=>[2,2,2,1,1,1,1,1,1,1]=>10
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0]=>[4,4,4,3]=>[4,3,2,2,1,1,1,1]=>8
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,3,1,1,1,1,1,1]=>[8,2,1,1]=>4
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[4,4,1,1,1,1,1]=>[7,3,1,1,1]=>5
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0]=>[7,2,2]=>[4,3,2,1,1]=>5
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>[6,6,1]=>[5,3,2,2,1]=>5
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3]=>[5,3,3,2,2]=>5
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[8,2,2]=>[4,4,2,1,1]=>5
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,2,2,2,2,2]=>[5,5,4,1,1]=>5
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0]=>[4,4,2]=>[3,1,1,1,1,1,1,1]=>8
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1,1,1,1]=>[3,3,3,3]=>4
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,1,1,1,1,1]=>[4,4,3,3]=>4
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,3,3,3]=>[5,3,3,2,2,1]=>6
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,1]=>[2,1,1,1]=>4
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[8,2,1]=>[4,4,1,1,1]=>5
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[8,7,1]=>[3,3,3,3,3,1]=>6
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[4,3,1,1,1,1,1]=>[7,1,1,1,1,1]=>6
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]=>[7,7,2]=>[6,3,3,2,1,1]=>6
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>15
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,7,1,1,1]=>[7,4,2,2,2]=>5
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,1,1,1,1]=>[7,3,3]=>3
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[3,1]=>[1,1,1,1]=>4
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,7,1,1]=>[6,4,2,2,2]=>5
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0]=>[7,7,3]=>[4,4,3,2,2,2]=>6
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,2]=>[5,2,2,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]=>[4,3,1]=>[1,1,1,1,1,1,1,1]=>8
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0]=>[3,3,2]=>[2,2,1,1,1,1]=>6
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,2,2,1,1]=>[6,4,2,2]=>4
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,1,1,1]=>[3,3,2,2]=>4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,1,1]=>[2,2,2,2]=>4
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,3,3]=>[3,3,3,1,1,1,1]=>7
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[7,1]=>[4,3,1]=>3
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,2,2,2,2,2]=>[5,5,4,1]=>4
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]=>[8,8,1]=>[6,4,3,3,1]=>5
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0]=>[4,3,1,1]=>[2,1,1,1,1,1,1,1]=>8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1,1]=>[9,1]=>2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,1]=>[1,1,1]=>3
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4,4,4,1]=>[5,2,2,2,2,2,1,1]=>8
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2]=>[1,1,1,1,1,1,1,1,1]=>9
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0]=>[5,3,2]=>[2,1,1,1,1,1,1,1,1]=>9
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[4,3]=>[2,2,1,1,1]=>5
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0]=>[4,2,1,1]=>[3,1,1,1,1,1]=>6
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,1,1,1]=>[6,3,2]=>3
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[8,5]=>[5,3,3,2]=>4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,1,1,1,1,1,1]=>[8,3,2]=>3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,1,1,1,1,1,1,1]=>[9,4,3]=>3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,3,2,1]=>[2,2,2,1,1,1,1,1,1,1,1]=>11
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1,1,1]=>[10,1]=>2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[4,3,1]=>[1,1,1,1,1,1,1,1]=>8
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0]=>[7,7,2,1]=>[6,3,3,2,1,1,1]=>7
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[4,4]=>[4,2,1,1]=>4
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[4,4,4]=>3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0]=>[5,5]=>[4,2,2,2]=>4
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1]=>[2]=>1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[2,2,1,1,1,1,1,1,1,1]=>[10,2]=>2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,1]=>[5,4,2]=>3
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,3,2,2,2,2,2]=>[5,5,4,2]=>4
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,2,1]=>[3,3,1,1,1,1,1,1,1]=>9
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0]=>[8,4,2]=>[5,3,2,1,1,1,1]=>7
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,1,1,1,1]=>[6,1,1]=>3
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[7,7]=>[6,3,3,2]=>4
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0]=>[6,3,3]=>[3,3,2,1,1,1,1]=>7
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,1,1,1,1]=>[7,1,1,1,1,1,1,1,1,1]=>10
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0]=>[8,3,3]=>[5,3,3,1,1,1]=>6
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,1,1,1,1,1,1]=>[8,2,1]=>3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[7,5,3]=>[4,2,2,2,2,1,1,1]=>8
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,4,1,1,1,1,1]=>[7,2,2,2,1,1]=>6
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[5,5,3,2,1,1]=>[5,2,1,1,1,1,1,1,1,1,1,1]=>12
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,1,1,1,1,1,1]=>[8,2,2]=>3
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>17
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,2,2,1,1,1,1,1]=>[4,4,4,3,2]=>5
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[6,3,2,2,2,1]=>[3,2,2,2,2,2,2,1]=>8
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[6,6]=>[5,3,2,2]=>4
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,1,1,1,1]=>[6,2,1]=>3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,1,1,1]=>[6,1,1,1,1,1,1,1]=>8
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,1]=>13
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,2,2,2]=>[4,3,3,1,1]=>5
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,1,1,1]=>[6,3,3]=>3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[5,1,1,1,1,1]=>[6,2,2]=>3
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0]=>[6,3,2,1]=>[5,1,1,1,1,1,1,1]=>8
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,2,2,2,1]=>[3,2,2,2,2,2,2]=>7
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[5,4,1,1,1]=>[2,2,2,2,1,1,1,1]=>8
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,1]=>[3,2,2,2,2,2]=>6
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[5,4,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1]=>12
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0,0,0]=>[6,5,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]=>17
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1]=>[10]=>1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,2,2,2,2]=>[3,3,3,2,2,2,2]=>7
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[8,7]=>[3,3,3,3,3]=>5
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[3]=>1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,2,2,2,2,2,1]=>[5,5,5,1,1]=>5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[5,5,1,1,1,1]=>[5,2,2,2,2,1]=>6
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0,0]=>[5,5,4,3]=>[3,3,3,1,1,1,1,1,1,1,1]=>11
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,1,1,1,1,1]=>[8,1,1,1,1,1,1,1]=>8
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Description
The length of the partition.
Map
inverse zeta map
Description
The inverse zeta map on Dyck paths.
See its inverse, the zeta map Mp00030zeta map, for the definition and details.
See its inverse, the zeta map Mp00030zeta map, for the definition and details.
Map
Loehr-Warrington inverse
Description
Return a partition whose length is the diagonal inversion number of the preimage.
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
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