Identifier
Mp00142:
Dyck paths
—promotion⟶
Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00027: Dyck paths —to partition⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1Cc0002;cc-rep-2Cc0002;cc-rep-3
[1,0]=>[1,0]=>[]=>[]
[1,0,1,0]=>[1,1,0,0]=>[]=>[]
[1,1,0,0]=>[1,0,1,0]=>[1]=>[1]
[1,0,1,0,1,0]=>[1,1,0,1,0,0]=>[1]=>[1]
[1,0,1,1,0,0]=>[1,1,0,0,1,0]=>[2]=>[1,1]
[1,1,0,0,1,0]=>[1,1,1,0,0,0]=>[]=>[]
[1,1,0,1,0,0]=>[1,0,1,0,1,0]=>[2,1]=>[2,1]
[1,1,1,0,0,0]=>[1,0,1,1,0,0]=>[1,1]=>[2]
[1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0]=>[2,1]=>[2,1]
[1,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,0]=>[3,1]=>[2,1,1]
[1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0]=>[1,1]=>[2]
[1,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0]=>[3,2]=>[2,2,1]
[1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0]=>[2,2]=>[2,2]
[1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0]=>[2]=>[1,1]
[1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0]=>[3]=>[1,1,1]
[1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,0]=>[1]=>[1]
[1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0]=>[3,2,1]=>[3,2,1]
[1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0]=>[2,2,1]=>[3,2]
[1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0]=>[]=>[]
[1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0]=>[3,1,1]=>[3,1,1]
[1,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0]=>[2,1,1]=>[3,1]
[1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0]=>[1,1,1]=>[3]
[1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0]=>[3,2,1]=>[3,2,1]
[1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>[4,2,1]=>[3,2,1,1]
[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0]=>[2,2,1]=>[3,2]
[1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>[4,3,1]=>[3,2,2,1]
[1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0]=>[3,3,1]=>[3,2,2]
[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,0]=>[3,1,1]=>[3,1,1]
[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[4,1,1]=>[3,1,1,1]
[1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0]=>[2,1,1]=>[3,1]
[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>[4,3,2]=>[3,3,2,1]
[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0]=>[3,3,2]=>[3,3,2]
[1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0]=>[1,1,1]=>[3]
[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[4,2,2]=>[3,3,1,1]
[1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0]=>[3,2,2]=>[3,3,1]
[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0]=>[2,2,2]=>[3,3]
[1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]=>[3,2]=>[2,2,1]
[1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>[4,2]=>[2,2,1,1]
[1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>[2,2]=>[2,2]
[1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>[4,3]=>[2,2,2,1]
[1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0]=>[3,3]=>[2,2,2]
[1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,0]=>[3,1]=>[2,1,1]
[1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>[4,1]=>[2,1,1,1]
[1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0]=>[2,1]=>[2,1]
[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[4,3,2,1]
[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0]=>[3,3,2,1]=>[4,3,2]
[1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0]=>[1,1]=>[2]
[1,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>[4,2,2,1]=>[4,3,1,1]
[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0]=>[3,2,2,1]=>[4,3,1]
[1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>[2,2,2,1]=>[4,3]
[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0]=>[3]=>[1,1,1]
[1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[4]=>[1,1,1,1]
[1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0]=>[2]=>[1,1]
[1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>[4,3,1,1]=>[4,2,2,1]
[1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[3,3,1,1]=>[4,2,2]
[1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0]=>[1]=>[1]
[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>[4,2,1,1]=>[4,2,1,1]
[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]=>[4,2,1]
[1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]=>[2,2,1,1]=>[4,2]
[1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0]=>[]=>[]
[1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>[4,1,1,1]=>[4,1,1,1]
[1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0]=>[3,1,1,1]=>[4,1,1]
[1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]=>[2,1,1,1]=>[4,1]
[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1]=>[4]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,1]=>[4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[5,3,2,1]=>[4,3,2,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[3,3,2,1]=>[4,3,2]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[5,4,2,1]=>[4,3,2,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[4,4,2,1]=>[4,3,2,2]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[4,2,2,1]=>[4,3,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[5,2,2,1]=>[4,3,1,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[3,2,2,1]=>[4,3,1]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[5,4,3,1]=>[4,3,3,2,1]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[4,4,3,1]=>[4,3,3,2]
[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]=>[4,3]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[5,3,3,1]=>[4,3,3,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[4,3,3,1]=>[4,3,3,1]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,3,3,1]=>[4,3,3]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[4,3,1,1]=>[4,2,2,1]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[5,3,1,1]=>[4,2,2,1,1]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[3,3,1,1]=>[4,2,2]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[5,4,1,1]=>[4,2,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[4,4,1,1]=>[4,2,2,2]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[4,2,1,1]=>[4,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[5,2,1,1]=>[4,2,1,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]=>[4,2,1]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[5,4,3,2]=>[4,4,3,2,1]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[4,4,3,2]=>[4,4,3,2]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,2,1,1]=>[4,2]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[5,3,3,2]=>[4,4,3,1,1]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[4,3,3,2]=>[4,4,3,1]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[3,3,3,2]=>[4,4,3]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[4,1,1,1]=>[4,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[5,1,1,1]=>[4,1,1,1,1]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,1,1]=>[4,1,1]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[5,4,2,2]=>[4,4,2,2,1]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[4,4,2,2]=>[4,4,2,2]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,1,1]=>[4,1]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[5,3,2,2]=>[4,4,2,1,1]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[4,3,2,2]=>[4,4,2,1]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[3,3,2,2]=>[4,4,2]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1]=>[4]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[5,2,2,2]=>[4,4,1,1,1]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[4,2,2,2]=>[4,4,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[3,2,2,2]=>[4,4,1]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,2,2,2]=>[4,4]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[4,3,2]=>[3,3,2,1]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[5,3,2]=>[3,3,2,1,1]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,3,2]=>[3,3,2]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[5,4,2]=>[3,3,2,2,1]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[4,4,2]=>[3,3,2,2]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[4,2,2]=>[3,3,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[5,2,2]=>[3,3,1,1,1]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,2]=>[3,3,1]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[5,4,3]=>[3,3,3,2,1]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[4,4,3]=>[3,3,3,2]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[2,2,2]=>[3,3]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[5,3,3]=>[3,3,3,1,1]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[4,3,3]=>[3,3,3,1]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,3,3]=>[3,3,3]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[4,3,1]=>[3,2,2,1]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[5,3,1]=>[3,2,2,1,1]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,3,1]=>[3,2,2]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[5,4,1]=>[3,2,2,2,1]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,4,1]=>[3,2,2,2]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[4,2,1]=>[3,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[5,2,1]=>[3,2,1,1,1]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,1]=>[3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[5,4,3,2,1]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[4,4,3,2,1]=>[5,4,3,2]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[2,2,1]=>[3,2]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[5,3,3,2,1]=>[5,4,3,1,1]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[4,3,3,2,1]=>[5,4,3,1]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[3,3,3,2,1]=>[5,4,3]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[4,1,1]=>[3,1,1,1]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[5,1,1]=>[3,1,1,1,1]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,1,1]=>[3,1,1]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[5,4,2,2,1]=>[5,4,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[4,4,2,2,1]=>[5,4,2,2]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,1]=>[3,1]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[5,3,2,2,1]=>[5,4,2,1,1]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[4,3,2,2,1]=>[5,4,2,1]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[3,3,2,2,1]=>[5,4,2]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1]=>[3]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[5,2,2,2,1]=>[5,4,1,1,1]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[4,2,2,2,1]=>[5,4,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[3,2,2,2,1]=>[5,4,1]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,2,2,2,1]=>[5,4]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3]=>[2,2,2,1]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[5,3]=>[2,2,2,1,1]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[3,3]=>[2,2,2]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[5,4]=>[2,2,2,2,1]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,4]=>[2,2,2,2]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,2]=>[2,2,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,2]=>[2,2,1,1,1]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[3,2]=>[2,2,1]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,1]=>[5,3,3,2,1]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[4,4,3,1,1]=>[5,3,3,2]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[2,2]=>[2,2]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[5,3,3,1,1]=>[5,3,3,1,1]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[4,3,3,1,1]=>[5,3,3,1]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[3,3,3,1,1]=>[5,3,3]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1]=>[2,1,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1]=>[2,1,1,1,1]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[3,1]=>[2,1,1]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,1]=>[5,3,2,2,1]
[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]=>[5,3,2,2]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1]=>[2,1]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,1]=>[5,3,2,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,1]=>[5,3,2,1]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[3,3,2,1,1]=>[5,3,2]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1]=>[2]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[5,2,2,1,1]=>[5,3,1,1,1]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[4,2,2,1,1]=>[5,3,1,1]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,2,1,1]=>[5,3,1]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,2,2,1,1]=>[5,3]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[4]=>[1,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5]=>[1,1,1,1,1]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[3]=>[1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[5,4,1,1,1]=>[5,2,2,2,1]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[4,4,1,1,1]=>[5,2,2,2]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[2]=>[1,1]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[5,3,1,1,1]=>[5,2,2,1,1]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[4,3,1,1,1]=>[5,2,2,1]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[3,3,1,1,1]=>[5,2,2]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[1]=>[1]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[5,2,1,1,1]=>[5,2,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[4,2,1,1,1]=>[5,2,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[3,2,1,1,1]=>[5,2,1]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,2,1,1,1]=>[5,2]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[]=>[]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[5,1,1,1,1]=>[5,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[4,1,1,1,1]=>[5,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,1,1,1]=>[5,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,1,1,1]=>[5,1]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1]=>[5]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1]=>[5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1]=>[5,4,3,2,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[4,4,3,2,1]=>[5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1]=>[5,4,3,2,2,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[5,5,3,2,1]=>[5,4,3,2,2]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,1]=>[5,4,3,1,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,3,2,1]=>[5,4,3,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,3,2,1]=>[5,4,3,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[5,5,4,2,1]=>[5,4,3,3,2]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,1]=>[5,4,3]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,4,2,1]=>[5,4,3,3,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,4,2,1]=>[5,4,3,3,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[4,4,4,2,1]=>[5,4,3,3]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,1]=>[5,4,2,2,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,1]=>[5,4,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,1]=>[5,4,2,2]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,2,1]=>[5,4,2,2,2,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,1]=>[5,4,2,2,2]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,1]=>[5,4,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,2,1]=>[5,4,2,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,1]=>[5,4,2,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1]=>[5,4,4,3,2,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,1]=>[5,4,2]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,4,3,1]=>[5,4,4,3,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[4,4,4,3,1]=>[5,4,4,3]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,1]=>[5,4,1,1,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,1]=>[5,4,1,1,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,1]=>[5,4,1,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[5,5,3,3,1]=>[5,4,4,2,2]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,1]=>[5,4,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,3,1]=>[5,4,4,2,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,3,1]=>[5,4,4,2,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[4,4,3,3,1]=>[5,4,4,2]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1]=>[5,4]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,3,3,1]=>[5,4,4,1,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,1]=>[5,4,4,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,3,3,1]=>[5,4,4,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,1]=>[5,4,4]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,1]=>[5,3,3,2,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,1]=>[5,3,3,2,1,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[4,4,3,1,1]=>[5,3,3,2]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,1]=>[5,3,3,2,2,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[5,5,3,1,1]=>[5,3,3,2,2]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,3,1,1]=>[5,3,3,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1,1]=>[5,3,3,1,1,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1,1]=>[5,3,3,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,1]=>[5,3,3,3,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[5,5,4,1,1]=>[5,3,3,3,2]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1]=>[5,3,3]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,4,1,1]=>[5,3,3,3,1,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,4,1,1]=>[5,3,3,3,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1,1]=>[5,3,3,3]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,1]=>[5,3,2,2,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,1]=>[5,3,2,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1,1]=>[5,3,2,2]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,1]=>[5,3,2,2,2,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[5,5,2,1,1]=>[5,3,2,2,2]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,1]=>[5,3,2,1,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,1]=>[5,3,2,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,1]=>[5,3,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2]=>[5,5,4,3,2,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1,1]=>[5,3,2]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[4,4,4,3,2]=>[5,5,4,3]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1,1]=>[5,3,1,1,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1,1]=>[5,3,1,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1,1]=>[5,3,1,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1,1]=>[5,3,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,3,2]=>[5,5,4,2,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[4,4,3,3,2]=>[5,5,4,2]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1]=>[5,3]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,3,3,2]=>[5,5,4,1,1,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,2]=>[5,5,4,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,3,3,2]=>[5,5,4,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,2]=>[5,5,4]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1,1]=>[5,2,2,2,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1,1]=>[5,2,2,2,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1]=>[5,2,2,2]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1,1]=>[5,2,2,2,2,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1,1]=>[5,2,2,2,2]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1,1]=>[5,2,2,1,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1,1]=>[5,2,2,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1,1]=>[5,2,2,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1]=>[5,2,2]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,4,2,2]=>[5,5,3,3,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[4,4,4,2,2]=>[5,5,3,3]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1,1]=>[5,2,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1,1]=>[5,2,1,1,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1,1]=>[5,2,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[5,5,3,2,2]=>[5,5,3,2,2]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1]=>[5,2,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,2]=>[5,5,3,2,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,2]=>[5,5,3,2,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[4,4,3,2,2]=>[5,5,3,2]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1]=>[5,2]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,3,2,2]=>[5,5,3,1,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,2]=>[5,5,3,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,3,2,2]=>[5,5,3,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,2]=>[5,5,3]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1]=>[5,1,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1]=>[5,1,1,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1]=>[5,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,2,2]=>[5,5,2,2,2,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,2]=>[5,5,2,2,2]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1]=>[5,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,2]=>[5,5,2,2,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,2]=>[5,5,2,2,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,2]=>[5,5,2,2]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1]=>[5,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,2,2]=>[5,5,2,1,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,2]=>[5,5,2,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,2]=>[5,5,2,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,2]=>[5,5,2]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1]=>[5]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,2]=>[5,5,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,2]=>[5,5,1,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,2]=>[5,5,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,2]=>[5,5,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2]=>[5,5]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2]=>[4,4,3,2,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2]=>[4,4,3,2,1,1]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[4,4,3,2]=>[4,4,3,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2]=>[4,4,3,2,2,1]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[5,5,3,2]=>[4,4,3,2,2]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[5,3,3,2]=>[4,4,3,1,1]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[6,3,3,2]=>[4,4,3,1,1,1]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[4,3,3,2]=>[4,4,3,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2]=>[4,4,3,3,2,1]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[5,5,4,2]=>[4,4,3,3,2]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2]=>[4,4,3]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[6,4,4,2]=>[4,4,3,3,1,1]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[5,4,4,2]=>[4,4,3,3,1]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,4,4,2]=>[4,4,3,3]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,2]=>[4,4,2,2,1]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,2]=>[4,4,2,2,1,1]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2]=>[4,4,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,2]=>[4,4,2,2,2,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[5,5,2,2]=>[4,4,2,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,2]=>[4,4,2,1,1]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,2]=>[4,4,2,1,1,1]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,2]=>[4,4,2,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3]=>[4,4,4,3,2,1]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[5,5,4,3]=>[4,4,4,3,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2]=>[4,4,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[6,4,4,3]=>[4,4,4,3,1,1]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[5,4,4,3]=>[4,4,4,3,1]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,4,4,3]=>[4,4,4,3]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2]=>[4,4,1,1,1]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2]=>[4,4,1,1,1,1]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2]=>[4,4,1,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,3]=>[4,4,4,2,2,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[5,5,3,3]=>[4,4,4,2,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2]=>[4,4,1]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,3]=>[4,4,4,2,1,1]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,3]=>[4,4,4,2,1]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,4,3,3]=>[4,4,4,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2]=>[4,4]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[6,3,3,3]=>[4,4,4,1,1,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[5,3,3,3]=>[4,4,4,1,1]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,3,3]=>[4,4,4,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3]=>[4,4,4]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1]=>[4,3,3,2,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1]=>[4,3,3,2,1,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,4,3,1]=>[4,3,3,2]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1]=>[4,3,3,2,2,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[5,5,3,1]=>[4,3,3,2,2]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[5,3,3,1]=>[4,3,3,1,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1]=>[4,3,3,1,1,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1]=>[4,3,3,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1]=>[4,3,3,3,2,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[5,5,4,1]=>[4,3,3,3,2]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1]=>[4,3,3]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[6,4,4,1]=>[4,3,3,3,1,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[5,4,4,1]=>[4,3,3,3,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1]=>[4,3,3,3]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1]=>[4,3,2,2,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1]=>[4,3,2,2,1,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1]=>[4,3,2,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1]=>[4,3,2,2,2,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[5,5,2,1]=>[4,3,2,2,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1]=>[4,3,2,1,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1]=>[4,3,2,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1]=>[4,3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[5,5,4,3,2,1]=>[6,5,4,3,2]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1]=>[4,3,2]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,4,3,2,1]=>[6,5,4,3,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[4,4,4,3,2,1]=>[6,5,4,3]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1]=>[4,3,1,1,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1]=>[4,3,1,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1]=>[4,3,1,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1]=>[4,3,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,3,2,1]=>[6,5,4,2,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[4,4,3,3,2,1]=>[6,5,4,2]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1]=>[4,3]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,2,1]=>[6,5,4,1,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,3,3,2,1]=>[6,5,4,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,2,1]=>[6,5,4]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1]=>[4,2,2,2,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1]=>[4,2,2,2,1,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1]=>[4,2,2,2]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1]=>[4,2,2,2,2,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1]=>[4,2,2,2,2]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1]=>[4,2,2,1,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1]=>[4,2,2,1,1,1]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1]=>[4,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1]=>[4,2,2]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[4,4,4,2,2,1]=>[6,5,3,3]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1]=>[4,2,1,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1]=>[4,2,1,1,1,1]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1]=>[4,2,1,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]=>[4,2,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,2,1]=>[6,5,3,2,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[4,4,3,2,2,1]=>[6,5,3,2]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1]=>[4,2]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,3,2,2,1]=>[6,5,3,1,1,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,2,1]=>[6,5,3,1,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,3,2,2,1]=>[6,5,3,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,2,1]=>[6,5,3]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1]=>[4,1,1,1,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1]=>[4,1,1,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1]=>[4,1,1,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,2,1]=>[6,5,2,2,2]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1]=>[4,1,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,2,1]=>[6,5,2,2,1,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,2,1]=>[6,5,2,2,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,2,1]=>[6,5,2,2]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1]=>[4,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,2,2,1]=>[6,5,2,1,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,2,1]=>[6,5,2,1,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,2,1]=>[6,5,2,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,2,1]=>[6,5,2]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1]=>[4]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,2,1]=>[6,5,1,1,1,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,2,1]=>[6,5,1,1,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,2,1]=>[6,5,1,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,2,1]=>[6,5,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,2,1]=>[6,5]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[5,4,3]=>[3,3,3,2,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[6,4,3]=>[3,3,3,2,1,1]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,4,3]=>[3,3,3,2]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[6,5,3]=>[3,3,3,2,2,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,5,3]=>[3,3,3,2,2]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[5,3,3]=>[3,3,3,1,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[6,3,3]=>[3,3,3,1,1,1]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,3]=>[3,3,3,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[6,5,4]=>[3,3,3,3,2,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,5,4]=>[3,3,3,3,2]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,3,3]=>[3,3,3]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[6,4,4]=>[3,3,3,3,1,1]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,4,4]=>[3,3,3,3,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,4,4]=>[3,3,3,3]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[5,4,2]=>[3,3,2,2,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[6,4,2]=>[3,3,2,2,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,4,2]=>[3,3,2,2]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[6,5,2]=>[3,3,2,2,2,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,5,2]=>[3,3,2,2,2]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[5,3,2]=>[3,3,2,1,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,3,2]=>[3,3,2,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,2]=>[3,3,2,1]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,3,2]=>[3,3,2]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[4,4,4,3,1,1]=>[6,4,4,3]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[5,2,2]=>[3,3,1,1,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,2,2]=>[3,3,1,1,1,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,2]=>[3,3,1,1]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,2,2]=>[3,3,1]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,3,1,1]=>[6,4,4,2,1]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[4,4,3,3,1,1]=>[6,4,4,2]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,2,2]=>[3,3]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,3,3,1,1]=>[6,4,4,1,1,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,3,3,1,1]=>[6,4,4,1,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,3,3,1,1]=>[6,4,4,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,3,3,3,1,1]=>[6,4,4]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,4,1]=>[3,2,2,2,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[6,4,1]=>[3,2,2,2,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,4,1]=>[3,2,2,2]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[6,5,1]=>[3,2,2,2,2,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,5,1]=>[3,2,2,2,2]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[5,3,1]=>[3,2,2,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[6,3,1]=>[3,2,2,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,3,1]=>[3,2,2,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,3,1]=>[3,2,2]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,4,2,1,1]=>[6,4,3,3,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[4,4,4,2,1,1]=>[6,4,3,3]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[5,2,1]=>[3,2,1,1,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[6,2,1]=>[3,2,1,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,2,1]=>[3,2,1,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[5,5,3,2,1,1]=>[6,4,3,2,2]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,2,1]=>[3,2,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,1]=>[6,4,3,2,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,1]=>[6,4,3,2,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[4,4,3,2,1,1]=>[6,4,3,2]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,2,1]=>[3,2]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,3,2,1,1]=>[6,4,3,1,1,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,3,2,1,1]=>[6,4,3,1,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,3,2,1,1]=>[6,4,3,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[3,3,3,2,1,1]=>[6,4,3]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,1]=>[3,1,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,1,1]=>[3,1,1,1,1,1]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,1,1]=>[3,1,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,2,1,1]=>[6,4,2,2,2,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[5,5,2,2,1,1]=>[6,4,2,2,2]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,1,1]=>[3,1,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,2,1,1]=>[6,4,2,2,1,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,2,1,1]=>[6,4,2,2,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[4,4,2,2,1,1]=>[6,4,2,2]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,1,1]=>[3,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,2,1,1]=>[6,4,2,1,1,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,2,1,1]=>[6,4,2,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,2,1,1]=>[6,4,2,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[3,3,2,2,1,1]=>[6,4,2]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1]=>[3]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,2,2,1,1]=>[6,4,1,1,1,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,2,2,1,1]=>[6,4,1,1,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,2,2,1,1]=>[6,4,1,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,2,2,1,1]=>[6,4,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,2,2,2,1,1]=>[6,4]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4]=>[2,2,2,2,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,4]=>[2,2,2,2,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,4]=>[2,2,2,2]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,5]=>[2,2,2,2,2,1]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,5]=>[2,2,2,2,2]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,3]=>[2,2,2,1,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,3]=>[2,2,2,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,3]=>[2,2,2,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[5,5,4,1,1,1]=>[6,3,3,3,2]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,3]=>[2,2,2]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,4,1,1,1]=>[6,3,3,3,1,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,4,1,1,1]=>[6,3,3,3,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[4,4,4,1,1,1]=>[6,3,3,3]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,2]=>[2,2,1,1,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,2]=>[2,2,1,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,2]=>[2,2,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,1,1]=>[6,3,3,2,2,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[5,5,3,1,1,1]=>[6,3,3,2,2]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,2]=>[2,2,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,1,1]=>[6,3,3,2,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,1,1]=>[6,3,3,2,1]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[4,4,3,1,1,1]=>[6,3,3,2]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,2]=>[2,2]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,3,1,1,1]=>[6,3,3,1,1,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,3,1,1,1]=>[6,3,3,1,1]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,3,1,1,1]=>[6,3,3,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[3,3,3,1,1,1]=>[6,3,3]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,1]=>[2,1,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1]=>[2,1,1,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[4,1]=>[2,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,1,1]=>[6,3,2,2,2,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[5,5,2,1,1,1]=>[6,3,2,2,2]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,1]=>[2,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,1,1]=>[6,3,2,2,1,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,1,1]=>[6,3,2,2,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[4,4,2,1,1,1]=>[6,3,2,2]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,1]=>[2,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,1,1]=>[6,3,2,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,1,1]=>[6,3,2,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,1,1]=>[6,3,2,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[3,3,2,1,1,1]=>[6,3,2]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1]=>[2]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,2,1,1,1]=>[6,3,1,1,1,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,2,1,1,1]=>[6,3,1,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,2,1,1,1]=>[6,3,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,2,1,1,1]=>[6,3,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,2,2,1,1,1]=>[6,3]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[5]=>[1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6]=>[1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[4]=>[1,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,1,1,1]=>[6,2,2,2,2,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[5,5,1,1,1,1]=>[6,2,2,2,2]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[3]=>[1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,1,1,1]=>[6,2,2,2,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,1,1,1]=>[6,2,2,2,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[4,4,1,1,1,1]=>[6,2,2,2]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2]=>[1,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,1,1,1]=>[6,2,2,1,1,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,1,1,1]=>[6,2,2,1,1]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,1,1,1]=>[6,2,2,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,3,1,1,1,1]=>[6,2,2]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1]=>[1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,1,1,1]=>[6,2,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,1,1,1]=>[6,2,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,1,1,1]=>[6,2,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1,1,1]=>[6,2,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,2,1,1,1,1]=>[6,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[]=>[]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,1,1,1,1]=>[6,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,1,1,1,1]=>[6,1,1,1,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,1,1,1,1]=>[6,1,1,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,1,1,1,1]=>[6,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,1,1,1,1]=>[6,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[6]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3,2,1]=>[6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,2,1]=>[6,5,4,3,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2,1]=>[6,5,4,3]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,2,1]=>[6,5,4,2,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2,1]=>[6,5,4,2]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2,1]=>[6,5,4,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,1]=>[6,5,4,1]
[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]=>[6,5,4]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2,1]=>[6,5,4,4]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2,1]=>[6,5,3,3]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2,1]=>[6,5,3,2,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,1]=>[6,5,3,2]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2,1]=>[6,5,3,1,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,1]=>[6,5,3,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,1]=>[6,5,3,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,1]=>[6,5,3]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,3,1]=>[6,5,5,4]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2,1]=>[6,5,2,2,2]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2,1]=>[6,5,2,2,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,1]=>[6,5,2,2,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1]=>[6,5,2,2]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,1]=>[6,5,2,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2,1]=>[6,5,2,1,1,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,1]=>[6,5,2,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,1]=>[6,5,2,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,1]=>[6,5,2]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1]=>[6,5,1,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1]=>[6,5,1,1,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1]=>[6,5,1,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,1]=>[6,5,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,1]=>[6,5,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,1]=>[6,5]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3,1]=>[6,5,5,1]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1]=>[6,5,5]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,1,1]=>[6,4,4,3]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,1,1]=>[6,4,4,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1]=>[6,4,4,2]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,1,1]=>[6,4,4,1,1,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1,1]=>[6,4,4,1,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1]=>[6,4,4,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1]=>[6,4,4]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,1,1]=>[6,4,4,4]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,1,1]=>[6,4,3,3,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1,1]=>[6,4,3,3]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,1,1]=>[6,4,3,2,2]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,1]=>[6,4,3,2,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,1]=>[6,4,3,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2]=>[6,6,5,4,3,2,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1,1]=>[6,4,3,2]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1,1]=>[6,4,3,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,1,1]=>[6,4,3,1,1,1,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,1,1]=>[6,4,3,1,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,1,1]=>[6,4,3,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1]=>[6,4,3]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,3,2]=>[6,6,5,4]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,1,1]=>[6,4,2,2,2,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1]=>[6,4,2,2,2]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1,1]=>[6,4,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,1,1]=>[6,4,2,2,1,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,1,1]=>[6,4,2,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1]=>[6,4,2,2]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,1,1]=>[6,4,2,1,1,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,1,1]=>[6,4,2,1,1,1,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1,1]=>[6,4,2,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1,1]=>[6,4,2,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1,1]=>[6,4,2]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1]=>[6,4,1,1,1,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1]=>[6,4,1,1,1,1,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1]=>[6,4,1,1,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1,1]=>[6,4,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[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]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1,1]=>[6,4]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,2]=>[6,6,5]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1,1,1]=>[6,3,3,3,2]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1,1]=>[6,3,3,3,1,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1,1]=>[6,3,3,3,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1]=>[6,3,3,3]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,1,1]=>[6,3,3,2,2,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1,1]=>[6,3,3,2,2]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,1,1]=>[6,3,3,2,1,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,1,1]=>[6,3,3,2,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1,1]=>[6,3,3,2,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1]=>[6,3,3,2]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1]=>[6,3,3,1,1,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1]=>[6,3,3,1,1,1,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1]=>[6,3,3,1,1]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,2,2]=>[6,6,4,4,2,2]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1]=>[6,3,3,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1]=>[6,3,3]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,2,2]=>[6,6,4,4,1]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2,2]=>[6,6,4,4]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1,1]=>[6,3,2,2,2,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,1,1]=>[6,3,2,2,2,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1,1]=>[6,3,2,2,2]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1,1,1]=>[6,3,2,2,2,2]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,1,1]=>[6,3,2,2,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1,1]=>[6,3,2,2,1,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,1,1]=>[6,3,2,2,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1]=>[6,3,2,2]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,1,1]=>[6,3,2,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,1,1]=>[6,3,2,1,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,1,1]=>[6,3,2,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1,1]=>[6,3,2,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1]=>[6,3,2]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1]=>[6,3,1,1,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1]=>[6,3,1,1,1,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1]=>[6,3,1,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1]=>[6,3,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[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]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1,1]=>[6,3]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,2]=>[6,6,4,1]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2]=>[6,6,4]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1,1]=>[6,2,2,2,2,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1]=>[6,2,2,2,2,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1]=>[6,2,2,2,2]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1,1]=>[6,2,2,2,2,2,1]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1]=>[6,2,2,2,2,2]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1,1]=>[6,2,2,2,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1]=>[6,2,2,2,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1]=>[6,2,2,2,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1]=>[6,2,2,2]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1]=>[6,2,2,1,1,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1]=>[6,2,2,1,1,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1]=>[6,2,2,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1]=>[6,2,2,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1]=>[6,2,2]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1]=>[6,2,1,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1]=>[6,2,1,1,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1]=>[6,2,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2,2,2]=>[6,6,3,2,2,2]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1]=>[6,2,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1]=>[6,2,1]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,2]=>[6,6,3,2]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1,1]=>[6,2]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,2]=>[6,6,3,1,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,2]=>[6,6,3,1]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2]=>[6,6,3]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1]=>[6,1,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1]=>[6,1,1,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1]=>[6,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1]=>[6,1,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1,1]=>[6,1,1]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,2]=>[6,6,2,2,1]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2]=>[6,6,2,2]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1,1]=>[6,1]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,2]=>[6,6,2,1,1,1]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,2]=>[6,6,2,1,1]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,2]=>[6,6,2,1]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2]=>[6,6,2]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1]=>[6]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,2]=>[6,6,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2]=>[6,6,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2]=>[6,6,1,1,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2]=>[6,6,1,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2]=>[6,6,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[6,6]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2]=>[5,5,4,3,2,1]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,2]=>[5,5,4,3]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,2]=>[5,5,4,2,1]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,2]=>[5,5,4,2]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,2]=>[5,5,4,1,1,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,2]=>[5,5,4,1,1]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2]=>[5,5,4,1]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2]=>[5,5,4]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2]=>[5,5,4,4]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,2]=>[5,5,3,3,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,2]=>[5,5,3,3]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,2]=>[5,5,3,2,2]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,2]=>[5,5,3,2,1,1]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,2]=>[5,5,3,2,1]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2]=>[5,5,3,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,2]=>[5,5,3,1,1,1]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,2]=>[5,5,3,1,1,1,1]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2]=>[5,5,3,1,1]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2]=>[5,5,3,1]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2]=>[5,5,3]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,3]=>[5,5,5,4]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2]=>[5,5,2,2,2,1]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,2]=>[5,5,2,2,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,2]=>[5,5,2,2,1,1]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,2]=>[5,5,2,2,1,1,1]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2]=>[5,5,2,2,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2]=>[5,5,2,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2]=>[5,5,2,1,1,1]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,2]=>[5,5,2,1,1,1,1]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2]=>[5,5,2,1,1]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2]=>[5,5,2,1]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2]=>[5,5,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2]=>[5,5,1,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2]=>[5,5,1,1,1,1,1]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2]=>[5,5,1,1,1]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2]=>[5,5,1,1]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2]=>[5,5,1]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,3]=>[5,5,5,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2]=>[5,5]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,3]=>[5,5,5,1,1]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,3]=>[5,5,5,1]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3]=>[5,5,5]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1]=>[5,4,4,3,2,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1]=>[5,4,4,3,2,1,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3,1]=>[5,4,4,3,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3,1]=>[5,4,4,3]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3,1]=>[5,4,4,2,2]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,1]=>[5,4,4,2,1,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3,1]=>[5,4,4,2,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1]=>[5,4,4,2]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,1]=>[5,4,4,1,1,1]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3,1]=>[5,4,4,1,1,1,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1]=>[5,4,4,1,1]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,6,4,4,1]=>[5,4,4,4,2,2]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1]=>[5,4,4,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1]=>[5,4,4]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,1]=>[5,4,4,4,1]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,1]=>[5,4,4,4]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2,1]=>[5,4,3,3,2]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2,1]=>[5,4,3,3,1,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2,1]=>[5,4,3,3,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1]=>[5,4,3,3]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1]=>[5,4,3,2,2,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2,1]=>[5,4,3,2,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1]=>[5,4,3,2,1,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1]=>[5,4,3,2,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1]=>[5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,6,5,4,3,2,1]=>[7,6,5,4,3,2]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1]=>[5,4,3,2]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,5,4,3,2,1]=>[7,6,5,4,3,1]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,5,5,4,3,2,1]=>[7,6,5,4,3]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1]=>[5,4,3,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2,1]=>[5,4,3,1,1,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,1]=>[5,4,3,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,1]=>[5,4,3,1]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,4,3,2,1]=>[7,6,5,4,2,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1]=>[5,4,3]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,4,4,3,2,1]=>[7,6,5,4,1,1]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,4,4,3,2,1]=>[7,6,5,4,1]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,3,2,1]=>[7,6,5,4]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,1]=>[5,4,2,2,2,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2,1]=>[5,4,2,2,2,1,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1]=>[5,4,2,2,2]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2,1]=>[5,4,2,2,2,2]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1]=>[5,4,2,2,1,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2,1]=>[5,4,2,2,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,1]=>[5,4,2,2,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1]=>[5,4,2,2]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,1]=>[5,4,2,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,1]=>[5,4,2,1,1,1,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1]=>[5,4,2,1,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1]=>[5,4,2,1]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,3,2,1]=>[7,6,5,3,2,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,1]=>[5,4,2]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1]=>[5,4,1,1,1,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1]=>[5,4,1,1,1,1,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1]=>[5,4,1,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,1]=>[5,4,1,1]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,3,3,2,1]=>[7,6,5,2,2,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,1]=>[5,4,1]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,3,3,2,1]=>[7,6,5,2,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,1]=>[5,4]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,3,3,3,2,1]=>[7,6,5,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,1]=>[5,3,3,3,2,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1,1]=>[5,3,3,3,2]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1,1]=>[5,3,3,3,1,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1,1]=>[5,3,3,3,1,1,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1]=>[5,3,3,3,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1]=>[5,3,3,3]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1,1]=>[5,3,3,3,3]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,1]=>[5,3,3,2,2,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,1]=>[5,3,3,2,2,1,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1]=>[5,3,3,2,2]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1,1]=>[5,3,3,2,2,2]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,1]=>[5,3,3,2,1,1]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,1]=>[5,3,3,2,1,1,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1]=>[5,3,3,2,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1]=>[5,3,3,2]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1]=>[5,3,3,1,1,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1]=>[5,3,3,1,1,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1]=>[5,3,3,1,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1]=>[5,3,3,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1]=>[5,3,3]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2,2,1]=>[7,6,4,4]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1]=>[5,3,2,2,2,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,1]=>[5,3,2,2,2,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1]=>[5,3,2,2,2]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,1]=>[5,3,2,2,2,2,1]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1,1]=>[5,3,2,2,2,2]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,1]=>[5,3,2,2,1,1]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1]=>[5,3,2,2,1,1,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,1]=>[5,3,2,2,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1]=>[5,3,2,2]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,1]=>[5,3,2,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,1]=>[5,3,2,1,1,1,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,1]=>[5,3,2,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1]=>[5,3,2,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,2,1]=>[7,6,4,3,2,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1]=>[5,3,2]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1]=>[5,3,1,1,1,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1]=>[5,3,1,1,1,1,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1]=>[5,3,1,1,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1]=>[5,3,1,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1,1]=>[5,3,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1,1]=>[5,3]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,2,1]=>[7,6,4]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1,1]=>[5,2,2,2,2,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1]=>[5,2,2,2,2,1,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1]=>[5,2,2,2,2]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1,1]=>[5,2,2,2,2,2,1]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1]=>[5,2,2,2,2,2]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1,1]=>[5,2,2,2,1,1]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1]=>[5,2,2,2,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1]=>[5,2,2,2,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1]=>[5,2,2,2]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1]=>[5,2,2,1,1,1]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1]=>[5,2,2,1,1,1,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1]=>[5,2,2,1,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1]=>[5,2,2,1]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,2,2,1]=>[7,6,3,3,2,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1]=>[5,2,2]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1]=>[5,2,1,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1]=>[5,2,1,1,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1]=>[5,2,1,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1]=>[5,2,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,2,2,1]=>[7,6,3,2,2,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1]=>[5,2,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1,1]=>[5,2]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,2,2,1]=>[7,6,3,1]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,2,2,1]=>[7,6,3]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1]=>[5,1,1,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1]=>[5,1,1,1,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1]=>[5,1,1,1,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1]=>[5,1,1,1]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2,2,2,1]=>[7,6,2,2,2,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1,1]=>[5,1,1]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,2,1]=>[7,6,2,2]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1,1]=>[5,1]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,2,1]=>[7,6,2,1,1]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,2,1]=>[7,6,2,1]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2,2,2,1]=>[7,6,2]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[5]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,2,1]=>[7,6,1,1,1,1]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,2,1]=>[7,6,1,1,1]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2,2,2,1]=>[7,6,1,1]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2,2,2,1]=>[7,6,1]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2,2,2,1]=>[7,6]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3]=>[4,4,4,3,2,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[5,5,4,3]=>[4,4,4,3,2]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,4,3]=>[4,4,4,3,1,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,4,3]=>[4,4,4,3,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[4,4,4,3]=>[4,4,4,3]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,3]=>[4,4,4,2,2,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[5,5,3,3]=>[4,4,4,2,2]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,3]=>[4,4,4,2,1,1]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,3]=>[4,4,4,2,1,1,1]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,3]=>[4,4,4,2,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3]=>[4,4,4,2]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,3,3]=>[4,4,4,1,1,1]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,3,3]=>[4,4,4,1,1,1,1]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3]=>[4,4,4,1,1]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3]=>[4,4,4,1]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3]=>[4,4,4]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,4,4]=>[4,4,4,4,1]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4]=>[4,4,4,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2]=>[4,4,3,3,2,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[5,5,4,2]=>[4,4,3,3,2]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,4,2]=>[4,4,3,3,1,1]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,4,2]=>[4,4,3,3,1,1,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,4,2]=>[4,4,3,3,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2]=>[4,4,3,3]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,5,5,2]=>[4,4,3,3,3]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2]=>[4,4,3,2,2,1]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2]=>[4,4,3,2,2,1,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[5,5,3,2]=>[4,4,3,2,2]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[6,6,3,2]=>[4,4,3,2,2,2]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2]=>[4,4,3,2,1,1]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2]=>[4,4,3,2,1,1,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2]=>[4,4,3,2,1]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2]=>[4,4,3,2]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2]=>[4,4,3,1,1,1]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,3,2]=>[4,4,3,1,1,1,1]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2]=>[4,4,3,1,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2]=>[4,4,3,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2]=>[4,4,3]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,3,1,1]=>[7,5,5,4]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,2]=>[4,4,2,2,2,1]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,2]=>[4,4,2,2,2,1,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2]=>[4,4,2,2,2]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,2]=>[4,4,2,2,2,2,1]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[6,6,2,2]=>[4,4,2,2,2,2]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2]=>[4,4,2,2,1,1]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,2]=>[4,4,2,2,1,1,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2]=>[4,4,2,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2]=>[4,4,2,2]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2]=>[4,4,2,1,1,1]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2]=>[4,4,2,1,1,1,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2]=>[4,4,2,1,1]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2]=>[4,4,2,1]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[3,3,2,2]=>[4,4,2]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2]=>[4,4,1,1,1,1]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2]=>[4,4,1,1,1,1,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2]=>[4,4,1,1,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,2,2]=>[4,4,1,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,2,2]=>[4,4,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[2,2,2,2]=>[4,4]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,3,1,1]=>[7,5,5]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1]=>[4,3,3,3,2,1]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1]=>[4,3,3,3,2,1,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[5,5,4,1]=>[4,3,3,3,2]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[6,6,4,1]=>[4,3,3,3,2,2]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,4,1]=>[4,3,3,3,1,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,4,1]=>[4,3,3,3,1,1,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1]=>[4,3,3,3,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1]=>[4,3,3,3]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,5,1]=>[4,3,3,3,3,1]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,5,5,1]=>[4,3,3,3,3]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1]=>[4,3,3,2,2,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1]=>[4,3,3,2,2,1,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1]=>[4,3,3,2,2]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1]=>[4,3,3,2,2,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[6,6,3,1]=>[4,3,3,2,2,2]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1]=>[4,3,3,2,1,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1]=>[4,3,3,2,1,1,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1]=>[4,3,3,2,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1]=>[4,3,3,2]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1]=>[4,3,3,1,1,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1]=>[4,3,3,1,1,1,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1]=>[4,3,3,1,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1]=>[4,3,3,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1]=>[4,3,3]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,2,1,1]=>[7,5,4,4]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1]=>[4,3,2,2,2,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1]=>[4,3,2,2,2,1,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1]=>[4,3,2,2,2]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1]=>[4,3,2,2,2,2,1]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[6,6,2,1]=>[4,3,2,2,2,2]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1]=>[4,3,2,2,1,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1]=>[4,3,2,2,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1]=>[4,3,2,2,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1]=>[4,3,2,2]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1]=>[4,3,2,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1]=>[4,3,2,1,1,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1]=>[4,3,2,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1]=>[4,3,2,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,1]=>[7,5,4,3,2,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1]=>[4,3,2]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1]=>[4,3,1,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1]=>[4,3,1,1,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1]=>[4,3,1,1,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1]=>[4,3,1,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,2,1]=>[4,3,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[2,2,2,1]=>[4,3]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,2,1,1]=>[7,5,4,1]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,2,1,1]=>[7,5,4]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,1]=>[4,2,2,2,2,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1]=>[4,2,2,2,2,1,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1]=>[4,2,2,2,2]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,1]=>[4,2,2,2,2,2,1]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1]=>[4,2,2,2,2,2]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,1]=>[4,2,2,2,1,1]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1]=>[4,2,2,2,1,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1]=>[4,2,2,2,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1]=>[4,2,2,2]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1]=>[4,2,2,1,1,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1]=>[4,2,2,1,1,1,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1]=>[4,2,2,1,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1]=>[4,2,2,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1]=>[4,2,2]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1]=>[4,2,1,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1]=>[4,2,1,1,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1]=>[4,2,1,1,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1]=>[4,2,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1]=>[4,2,1]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,2,1,1]=>[7,5,3,2]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[2,2,1,1]=>[4,2]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,2,1,1]=>[7,5,3,1,1]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[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]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[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]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1]=>[4,1,1,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1]=>[4,1,1,1,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1]=>[4,1,1,1,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1]=>[4,1,1,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,1,1]=>[4,1,1]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,2,1,1]=>[7,5,2,2,1]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,2,1,1]=>[7,5,2,2]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,1,1]=>[4,1]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,2,1,1]=>[7,5,2,1,1,1]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,2,1,1]=>[7,5,2,1,1]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,2,1,1]=>[7,5,2,1]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[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]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1]=>[4]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,2,1,1]=>[7,5,1,1,1,1,1]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,2,1,1]=>[7,5,1,1,1,1]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,2,1,1]=>[7,5,1,1,1]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[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]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[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]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[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]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4]=>[3,3,3,3,2,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[7,5,4]=>[3,3,3,3,2,1,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,5,4]=>[3,3,3,3,2]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[7,6,4]=>[3,3,3,3,2,2,1]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,6,4]=>[3,3,3,3,2,2]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[6,4,4]=>[3,3,3,3,1,1]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[7,4,4]=>[3,3,3,3,1,1,1]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,4]=>[3,3,3,3,1]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,6,5]=>[3,3,3,3,3,2]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[4,4,4]=>[3,3,3,3]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[7,5,5]=>[3,3,3,3,3,1,1]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,5]=>[3,3,3,3,3,1]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,5,5]=>[3,3,3,3,3]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[6,5,3]=>[3,3,3,2,2,1]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[7,5,3]=>[3,3,3,2,2,1,1]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,5,3]=>[3,3,3,2,2]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[7,6,3]=>[3,3,3,2,2,2,1]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,6,3]=>[3,3,3,2,2,2]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[6,4,3]=>[3,3,3,2,1,1]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[7,4,3]=>[3,3,3,2,1,1,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3]=>[3,3,3,2,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[4,4,3]=>[3,3,3,2]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[6,3,3]=>[3,3,3,1,1,1]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[7,3,3]=>[3,3,3,1,1,1,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,3,3]=>[3,3,3,1,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[4,3,3]=>[3,3,3,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[3,3,3]=>[3,3,3]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,4,4,4,1,1,1]=>[7,4,4,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[6,5,2]=>[3,3,2,2,2,1]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[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]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,5,2]=>[3,3,2,2,2]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[7,6,2]=>[3,3,2,2,2,2,1]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,6,2]=>[3,3,2,2,2,2]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,4,2]=>[3,3,2,2,1,1]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[7,4,2]=>[3,3,2,2,1,1,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,4,2]=>[3,3,2,2,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[4,4,2]=>[3,3,2,2]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[6,3,2]=>[3,3,2,1,1,1]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[7,3,2]=>[3,3,2,1,1,1,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,3,2]=>[3,3,2,1,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[4,3,2]=>[3,3,2,1]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,1,1]=>[7,4,4,3,2,1]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[3,3,2]=>[3,3,2]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[6,2,2]=>[3,3,1,1,1,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,2,2]=>[3,3,1,1,1,1,1]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,2,2]=>[3,3,1,1,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[4,2,2]=>[3,3,1,1]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[3,2,2]=>[3,3,1]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,4,3,3,1,1,1]=>[7,4,4,2]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[2,2,2]=>[3,3]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,3,3,1,1,1]=>[7,4,4,1,1]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,3,3,1,1,1]=>[7,4,4,1]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,3,3,3,1,1,1]=>[7,4,4]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[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]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[7,5,1]=>[3,2,2,2,2,1,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,5,1]=>[3,2,2,2,2]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[7,6,1]=>[3,2,2,2,2,2,1]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,6,1]=>[3,2,2,2,2,2]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[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]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[7,4,1]=>[3,2,2,2,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,4,1]=>[3,2,2,2,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[4,4,1]=>[3,2,2,2]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[6,3,1]=>[3,2,2,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[7,3,1]=>[3,2,2,1,1,1,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,3,1]=>[3,2,2,1,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[4,3,1]=>[3,2,2,1]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,1,1]=>[7,4,3,3,2,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[3,3,1]=>[3,2,2]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,4,4,2,1,1,1]=>[7,4,3,3]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,2,1]=>[3,2,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[7,2,1]=>[3,2,1,1,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,2,1]=>[3,2,1,1,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[4,2,1]=>[3,2,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,2,1]=>[3,2,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,1,1]=>[7,4,3,2,1]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,4,3,2,1,1,1]=>[7,4,3,2]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[2,2,1]=>[3,2]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,3,2,1,1,1]=>[7,4,3,1,1,1]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,3,2,1,1,1]=>[7,4,3,1,1]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,3,2,1,1,1]=>[7,4,3,1]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,3,3,2,1,1,1]=>[7,4,3]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[6,1,1]=>[3,1,1,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,1]=>[3,1,1,1,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,1,1]=>[3,1,1,1,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[4,1,1]=>[3,1,1,1]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,5,2,2,1,1,1]=>[7,4,2,2,2]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[3,1,1]=>[3,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,2,1,1,1]=>[7,4,2,2,1,1]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,2,1,1,1]=>[7,4,2,2,1]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,4,2,2,1,1,1]=>[7,4,2,2]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,1,1]=>[3,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,2,1,1,1]=>[7,4,2,1,1,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,2,1,1,1]=>[7,4,2,1,1,1]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,2,1,1,1]=>[7,4,2,1,1]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,2,1,1,1]=>[7,4,2,1]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[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]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1]=>[3]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,2,2,1,1,1]=>[7,4,1,1,1,1,1]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,2,2,1,1,1]=>[7,4,1,1,1,1]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,2,2,1,1,1]=>[7,4,1,1,1]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[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]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[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]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[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]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5]=>[2,2,2,2,2,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,5]=>[2,2,2,2,2,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[5,5]=>[2,2,2,2,2]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,6]=>[2,2,2,2,2,2,1]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,6]=>[2,2,2,2,2,2]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,4]=>[2,2,2,2,1,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,4]=>[2,2,2,2,1,1,1]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[5,4]=>[2,2,2,2,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[4,4]=>[2,2,2,2]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,3]=>[2,2,2,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,3]=>[2,2,2,1,1,1,1]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[5,3]=>[2,2,2,1,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[4,3]=>[2,2,2,1]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,1,1,1]=>[7,3,3,3,2,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[3,3]=>[2,2,2]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,4,1,1,1,1]=>[7,3,3,3,1]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,4,4,1,1,1,1]=>[7,3,3,3]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,2]=>[2,2,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,2]=>[2,2,1,1,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[5,2]=>[2,2,1,1,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[4,2]=>[2,2,1,1]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,5,3,1,1,1,1]=>[7,3,3,2,2]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[3,2]=>[2,2,1]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,1,1,1]=>[7,3,3,2,1,1]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,1,1,1]=>[7,3,3,2,1]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,4,3,1,1,1,1]=>[7,3,3,2]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,2]=>[2,2]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,3,1,1,1,1]=>[7,3,3,1,1,1,1]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,3,1,1,1,1]=>[7,3,3,1,1,1]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,3,1,1,1,1]=>[7,3,3,1,1]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,3,1,1,1,1]=>[7,3,3,1]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,3,3,1,1,1,1]=>[7,3,3]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,1]=>[2,1,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[5,1]=>[2,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[4,1]=>[2,1,1,1]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,1,1,1]=>[7,3,2,2,2,1]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,5,2,1,1,1,1]=>[7,3,2,2,2]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[3,1]=>[2,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,1,1,1]=>[7,3,2,2,1,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,1,1,1]=>[7,3,2,2,1,1]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,1,1,1]=>[7,3,2,2,1]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,4,2,1,1,1,1]=>[7,3,2,2]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,1]=>[2,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,1,1,1]=>[7,3,2,1,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,1,1,1]=>[7,3,2,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,1,1,1]=>[7,3,2,1,1]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,1,1,1]=>[7,3,2,1]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,3,2,1,1,1,1]=>[7,3,2]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1]=>[2]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,2,1,1,1,1]=>[7,3,1,1,1,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,2,1,1,1,1]=>[7,3,1,1,1,1]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,2,1,1,1,1]=>[7,3,1,1,1]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,2,1,1,1,1]=>[7,3,1,1]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[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]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[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]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[6]=>[1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7]=>[1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[5]=>[1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,6,1,1,1,1,1]=>[7,2,2,2,2,2]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[4]=>[1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,1,1,1,1]=>[7,2,2,2,2,1,1]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[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]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,5,1,1,1,1,1]=>[7,2,2,2,2]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[3]=>[1,1,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,1,1,1,1]=>[7,2,2,2,1,1,1]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[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]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,1,1,1,1]=>[7,2,2,2,1]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,4,1,1,1,1,1]=>[7,2,2,2]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2]=>[1,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,1,1,1,1]=>[7,2,2,1,1,1,1]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,1,1,1,1]=>[7,2,2,1,1,1]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,1,1,1,1]=>[7,2,2,1,1]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,1,1,1,1]=>[7,2,2,1]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,3,1,1,1,1,1]=>[7,2,2]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1]=>[1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,1,1,1,1]=>[7,2,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,1,1,1,1]=>[7,2,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,1,1,1,1]=>[7,2,1,1,1]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,1,1,1,1]=>[7,2,1,1]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,1,1,1,1]=>[7,2,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[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]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[]=>[]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,1,1,1,1,1]=>[7,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,1,1,1,1,1]=>[7,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,1,1,1,1,1]=>[7,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,1,1,1,1,1]=>[7,1,1,1]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[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]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[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]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1]=>[7]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[]=>[]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[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]=>[7,7]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[]=>[]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1]=>[1]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[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]=>[7,7,1]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[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]=>[8,8]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[]=>[]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1]=>[1]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[2]=>[1,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1]=>[2]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[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]=>[7,7,1,1]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[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]=>[7,7,2]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,2,2,2,2,2,2]=>[8,8,1]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2,2]=>[9,9]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1]=>[1]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[2]=>[1,1]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1]=>[2]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[3]=>[1,1,1]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,1]=>[2,1]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1]=>[3]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,2,2,2,2]=>[7,7,2,1]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[3]=>[1,1,1]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[2,1]=>[2,1]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1]=>[3]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[3,1]=>[2,1,1]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[2,2]=>[2,2]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1]=>[3,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1]=>[4]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[4]=>[1,1,1,1]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[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]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[4,1]=>[2,1,1,1]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1]=>[5]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[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]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[6]=>[1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[3,3]=>[2,2,2]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[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]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8]=>[1,1,1,1,1,1,1,1]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,3,3]=>[6,6,6]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[3,3]=>[2,2,2]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[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]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[7]=>[1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[6,1]=>[2,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[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]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[8,1]=>[2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[7]=>[1,1,1,1,1,1,1]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[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]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9]=>[1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[7,1]=>[2,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[8,2]=>[2,2,1,1,1,1,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,1]=>[3,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[8]=>[1,1,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[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]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[9,1]=>[2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[3,3,3]=>[3,3,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,6,5,4,3,2,1]=>[8,7,6,5,4,3,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,6,6,5,4,3,2,1]=>[8,7,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,5,4,3,2,1]=>[8,7,6,5,4,2,1]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,5,5,4,3,2,1]=>[8,7,6,5,4,1,1]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,4,3,2,1]=>[8,7,6,5,3,2,1]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,4,4,3,2,1]=>[8,7,6,5,2,2,1]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,3,2,1]=>[8,7,6,4,3,2,1]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,3,3,2,1]=>[8,7,6,3,3,2,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,2,1]=>[8,7,5,4,3,2,1]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,2,2,1]=>[8,7,4,4,3,2,1]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[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]=>[8,7,1,1]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[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]=>[8,7,1]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[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]=>[8,7]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,1,1]=>[8,6,5,4,3,2,1]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[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]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,1,1,1]=>[8,5,5,4,3,2,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,2,2,2,1,1,1]=>[8,5,1,1,1,1]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[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]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,4,3,2,1,1,1,1]=>[8,4,3,2]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[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]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,2,2,1,1,1,1]=>[8,4,1,1,1]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[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]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[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]=>[8,3,3,2,1]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[4,3,3,1,1,1,1,1]=>[8,3,3,1]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[4,4,2,1,1,1,1,1]=>[8,3,2,2]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[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]=>[8,3,2]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[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]=>[8,3,1,1,1,1,1,1]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[4,2,2,1,1,1,1,1]=>[8,3,1,1]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,1,1,1,1,1]=>[8,3]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[8,3,1,1,1,1,1,1]=>[8,2,2,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[5,3,1,1,1,1,1,1]=>[8,2,2,1,1]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[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]=>[8,2,2,1]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,3,1,1,1,1,1,1]=>[8,2,2]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[8,2,1,1,1,1,1,1]=>[8,2,1,1,1,1,1,1]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,1,1,1,1,1]=>[8,2,1]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,2,1,1,1,1,1,1]=>[8,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[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]=>[8,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[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]=>[8,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[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]=>[8,1,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[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]=>[8,1,1,1,1]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[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]=>[8,1,1,1]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[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]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1]=>[8,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1]=>[8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,6,5,4,3,2,1]=>[7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,5,5,4,3,2,1]=>[7,6,5,4,3]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,4,4,4,3,2,1]=>[7,6,5,4]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[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]=>[7,6]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[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]=>[7,1,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2]=>[6,6,5,4,3,2,1]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,2,2,2,2,2]=>[6,6]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,4,4,4]=>[4,4,4,4]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[7,6]=>[2,2,2,2,2,2,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[8,6]=>[2,2,2,2,2,2,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,7]=>[2,2,2,2,2,2,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[7,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[6,6,6,5,4,3,2,1]=>[8,7,6,5,4,3]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[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]=>[8,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[8,7]=>[2,2,2,2,2,2,2,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,8]=>[2,2,2,2,2,2,2,2]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1]=>[9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[5,5,4,3,2,1]=>[6,5,4,3,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,2,1,1,1,1,1,1,1]=>[9,2]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[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]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[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]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[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]=>[9,3,2]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[4,3,1,1,1,1,1,1,1]=>[9,2,2,1]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[3,1,1,1,1,1,1,1,1,1]=>[10,1,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1]=>[5,4,3,2,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,1]=>[5,4,3,2,1,1,1]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,2,2,1]=>[9,8]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[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]=>[9,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[7,5]=>[2,2,2,2,2,1,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,0]=>[7,6,4]=>[3,3,3,3,2,2,1]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1,1]=>[9,1]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,1,1,1,1,1,1]=>[9,3]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[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]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,1,1,1,1]=>[9,5]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,2,2,2,2,2,1,1,1]=>[9,6]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[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]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,1]=>[6,4,3,2,1]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,2,1]=>[9,8,6,5,4,3,2,1]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,1,1,1,1,1,1,1,1,1]=>[10,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[7,7,1]=>[3,2,2,2,2,2,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[7,6,5,5,4,3,2,1]=>[8,7,6,5,4,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2]=>[5,5,4,3,2,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,1,1,1]=>[5,1,1,1,1,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,7,1,1]=>[4,2,2,2,2,2,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[8,7]=>[2,2,2,2,2,2,2,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[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]=>[9,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[7,1,1,1,1,1,1,1,1]=>[9,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[6,1,1,1,1,1,1,1,1]=>[9,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[5,1,1,1,1,1,1,1,1]=>[9,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[4,1,1,1,1,1,1,1,1]=>[9,1,1,1]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,5,4,3,2,1]=>[9,8,7,6,5,3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,7,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,1]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[8,7,6,6,5,4,3,2,1]=>[9,8,7,6,5,4,2,1]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,4,3,2,1]=>[9,8,7,6,4,3,2,1]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,3,2,1]=>[9,8,7,5,4,3,2,1]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,1,1]=>[9,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[3,3,1,1,1,1,1,1,1]=>[9,2,2]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,1,1,1,1,1,1,1,1]=>[10]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1]=>[4,3,2,1]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1]=>[4,3,2,1]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1]=>[5,4,3,2,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[10]=>[1,1,1,1,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,5,4,3,2,1]=>[7,6,5,4,3,1]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,2,2,2,2]=>[6,6,1]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,3,3,3,2,2,1]=>[7,6,4]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[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]=>[5,4,3,2,1]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,1]=>[4,3,2,1,1]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1,1]=>[5,3,2,1]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[4,4,4]=>[3,3,3,3]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[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]
Map
promotion
Description
The promotion of the two-row standard Young tableau of a Dyck path.
Dyck paths of semilength $n$ are in bijection with standard Young tableaux of shape $(n^2)$, see Mp00033to two-row standard tableau.
This map is the bijection on such standard Young tableaux given by Schützenberger's promotion. For definitions and details, see [1] and the references therein.
Dyck paths of semilength $n$ are in bijection with standard Young tableaux of shape $(n^2)$, see Mp00033to two-row standard tableau.
This map is the bijection on such standard Young tableaux given by Schützenberger's promotion. For definitions and details, see [1] and the references therein.
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
Map
conjugate
Description
Return the conjugate partition of the partition.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
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